Finite Group Databasebeta

← #14262334

Subgroups — #14262334

Order 1792.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90616C211yesmaximal, characteristic, complemented
2C22×D7×#41C211yesmaximal, characteristic, complemented
3C7×#3449C211yesmaximal, characteristic, complemented
4#11744336C211yesmaximal, characteristic, complemented
5C2×#90519C211yesmaximal, characteristic, complemented
6#11743448C214yesmaximal, complemented
7#11743447C214yesmaximal, complemented
8#11743424C214yesmaximal, complemented
9#11743423C212yesmaximal, complemented
10#11743422C212yesmaximal, complemented
11#11743399C214yesmaximal, complemented
12#11743398C212yesmaximal, complemented
13#11743383C212yesmaximal, complemented
14#11743376C214yesmaximal, complemented
15#11743364C214yesmaximal, complemented
16#11743306C218yesmaximal, complemented
17#11743105C218yesmaximal, complemented
18#11743103C214yesmaximal, complemented
19D7×#525C214yesmaximal, complemented
20C2×#90215C211yesmaximal, characteristic, complemented
21#11742799C211yesmaximal, characteristic, complemented
22C22×C7×#41C2211yescharacteristic, complemented
23C22×C7×#41C2211yescharacteristic, complemented
24#90616—216no—
25C2×#6554C2212yescomplemented
26C2×#6554C2212yescomplemented
27C2×#6553C2212yescomplemented
28C2×#6553C2212yescomplemented
29C2×D7×#41—216no—
30C2×D7×#41C2214yescomplemented
31C2×D7×#41C2214yescomplemented
32C2×D7×#41C2214yescomplemented
33C2×D7×#41C2214yescomplemented
34C2×D7×#41C2214yescomplemented
35C2×D7×#41C2214yescomplemented
36C2×#6551C2212yescomplemented
37C22×#1161C2211yescharacteristic, complemented
38C22×Q8×D7C2211yescharacteristic, complemented
39C2×#6548C2212yescomplemented
40C2×#6548C2214yescomplemented
41C22×#1159C2212yescomplemented
42C22×#1159C2211yescharacteristic, complemented
43C22×D4×D7C2212yescomplemented
44C22×D4×D7C2211yescharacteristic, complemented
45C22×#1157C2211yescharacteristic
46C22×#1157C2212yescomplemented
47C22×#1157C2211yescharacteristic, complemented
48C22×#1157C2214yescomplemented
49C23×C4×D7C2211yescharacteristic, complemented
50C23×C4×D7C2212yescomplemented
51C7×#537C2214yescomplemented
52C7×#536C2212yescomplemented
53C7×#536C2212yescomplemented
54C7×#535C2212yescomplemented
55C7×#535C2212yescomplemented
56C7×#534C2214yescomplemented
57C7×#532C2214yescomplemented
58C7×#525C2214yescomplemented
59C7×#525C2214yescomplemented
60C2×C7×#117C2211yescharacteristic, complemented
61#90524C2214yescomplemented
62#90523C2214yescomplemented
63#90521C2212yescomplemented
64#90519C2212yescomplemented
65#90519C2212yescomplemented
66#90519C2212yescomplemented
67#90519C2212yescomplemented
68#90519C2214yescomplemented
69#90519C2214yescomplemented
70#90519C2214yescomplemented
71#90516C2212yescomplemented
72#90507C2212yescomplemented
73C2×#6509C2212yescomplemented
74#90496C2212yescomplemented
75#90495C2214yescomplemented
76C2×#6501C2212yescomplemented
77C2×#6500C2212yescomplemented
78C2×#6498C2212yescomplemented
79#90482C2214yescomplemented
80C2×C4×C22⋊D7C2214yescomplemented
81C2×#6489C2211yescharacteristic, complemented
82#90418C2218yescomplemented
83#90417C2218yescomplemented
84#90409C2218yescomplemented
85#90408C2218yescomplemented
86#90368C2218yescomplemented
87#90368C2218yescomplemented
88#90367C2218yescomplemented
89#90367C2218yescomplemented
90#90347C2218yescomplemented
91#90346C22116yescomplemented
92#90345C22116yescomplemented
93#90344C2218yescomplemented
94D7×#123C2218yescomplemented
95#90339C2218yescomplemented
96#90324C2218yescomplemented
97#90323C2218yescomplemented
98#90322C2218yescomplemented
99#90321C2218yescomplemented
100#90320C2218yescomplemented
101#90319C2218yescomplemented
102#90318C2218yescomplemented
103D7×C22⋊Q8C2218yescomplemented
104#90303C2218yescomplemented
105#90302C22116yescomplemented
106#90301C22116yescomplemented
107#90301C22116yescomplemented
108#90300C2218yescomplemented
109#90300C22116yescomplemented
110#90299C2218yescomplemented
111#90298C2218yescomplemented
112#90297C2218yescomplemented
113D7×#121C2218yescomplemented
114#90290C2218yescomplemented
115#90289C2218yescomplemented
116#90283C2218yescomplemented
117#90282C22116yescomplemented
118#90281C22116yescomplemented
119#90280C2218yescomplemented
120D7×#120C2218yescomplemented
121#90277C2218yescomplemented
122#90239C22116yescomplemented
123#90238C22116yescomplemented
124#90238C22116yescomplemented
125C4×D4×D7C22116yescomplemented
126#90215C2212yescomplemented
127#90215C2212yescomplemented
128#90215C2214yescomplemented
129#90215C2214yescomplemented
130#90215C2212yescomplemented
131#90215C2212yescomplemented
132#90214C2214yescomplemented
133#90213C2214yescomplemented
134#90212C2212yescomplemented
135D7×#117C2214yescomplemented
136#90207C2212yescomplemented
137C2×#6460C2212yescomplemented
138C2×#6458C2212yescomplemented
139#90195C2214yescomplemented
140C2×#6449C2212yescomplemented
141C2×#6445C2212yescomplemented
142#90177C2214yescomplemented
143C4×#1157C2214yescomplemented
144C2×C4×D28C2214yescomplemented
145#62811—71nomaximal, Sylow
146C24×D7C2311yescharacteristic
147C24×D7C2312yes—
148C2×C7×#41—28no—
149C2×C7×#41—28no—
150C2×C7×#41C2312yes—
151C2×C7×#41C2312yes—
152C2×C7×#41C2312yes—
153C2×C7×#41C2312yes—
154C2×C7×#41C2312yes—
155C2×C7×#41C2312yes—
156C2×C7×#41C2312yescomplemented
157C2×C7×#41C2312yescomplemented
158C22×C7×Q8C2311yescharacteristic
159C22×C7×Q8C2311yescharacteristic, complemented
160C22×C7×D4C2312yes—
161C22×C7×D4C2312yes—
162C22×C7×D4C2311yescharacteristic
163C22×C7×D4C2311yescharacteristic, complemented
164C23×C4×C7C2312yes—
165C23×C4×C7C2311yescharacteristic
166C23×C4×C7C2312yescomplemented
167C22×C22⋊D7C2312yes—
168C22×C22⋊D7C2312yes—
169C22×C22⋊D7C2312yes—
170C22×C22⋊D7C2314yes—
171C22×C22⋊D7C2312yes—
172C22×C22⋊D7C2318yescomplemented
173C23×Dic7C2311yescharacteristic
174C23×Dic7C2312yes—
175#6554—216no—
176#6554—216no—
177#6553—216no—
178#6553—216no—
179D7×#41—232no—
180D7×#41—232no—
181D7×#41—232no—
182D7×#41—232no—
183D7×#41—232no—
184D7×#41—232no—
185#6551—216no—
186C2×#1161—28no—
187C2×#1161C2314yes—
188C2×#1161C2314yes—
189C2×#1161C2314yescomplemented
190C2×#1161C2314yescomplemented
191C2×Q8×D7—28no—
192C2×Q8×D7C2314yes—
193C2×Q8×D7C2314yes—
194C2×Q8×D7C2314yescomplemented
195C2×Q8×D7C2314yescomplemented
196#6548—232no—
197#6548—216no—
198C2×#1159—216no—
199C2×#1159—28no—
200C2×#1159C2314yes—
201C2×#1159C2318yes—
202C2×#1159C2318yes—
203C2×#1159C2314yes—
204C2×#1159C2318yes—
205C2×#1159C2314yescomplemented
206C2×#1159C2314yescomplemented
207C2×#1159C2318yescomplemented
208C2×D4×D7—216no—
209C2×D4×D7—28no—
210C2×D4×D7C2314yes—
211C2×D4×D7C2318yes—
212C2×D4×D7C2318yes—
213C2×D4×D7C2318yes—
214C2×D4×D7C2314yes—
215C2×D4×D7C23116yes—
216C2×D4×D7C2314yescomplemented
217C2×D4×D7C2314yescomplemented
218C2×D4×D7C2318yescomplemented
219C2×#1157—28no—
220C2×#1157—232no—
221C2×#1157—216no—
222C2×#1157D4116yescomplemented
223C2×#1157C2312yes—
224C2×#1157C2312yes—
225C2×#1157C2318yes—
226C2×#1157C2318yes—
227C2×#1157C2312yes—
228C2×#1157C2312yes—
229C2×#1157C2312yes—
230C2×#1157C2312yes—
231C2×#1157C2312yescomplemented
232C2×#1157C2312yescomplemented
233C2×#1157C2318yescomplemented
234C2×#1157C2314yescomplemented
235C2×#1157C2314yescomplemented
236C2×#1157C2318yescomplemented
237C22×D28C2312yes—
238C22×D28C2314yes—
239C22×D28C2311yescharacteristic
240C22×D28C2311yescharacteristic, complemented
241C22×D28C2314yescomplemented
242C22×C4×D7—28no—
243C22×C4×D7—216no—
244C22×C4×D7C2312yes—
245C22×C4×D7C2312yes—
246C22×C4×D7C2312yes—
247C22×C4×D7C2312yes—
248C22×C4×D7C2311yescharacteristic
249C22×C4×D7C2311yescharacteristic
250C22×C4×D7C2311yescharacteristic
251C22×C4×D7C2311yescharacteristic
252C22×C4×D7C2318yes—
253C22×C4×D7C2318yes—
254C22×C4×D7C2312yes—
255C22×C4×D7C2312yes—
256C22×C4×D7C2312yes—
257C22×C4×D7C2312yescomplemented
258C22×C4×D7C2318yescomplemented
259C22×Dic14C2312yes—
260C22×Dic14C2311yescharacteristic
261C22×Dic14C2311yescharacteristic, complemented
262C22×Dic14C2314yescomplemented
263C7×C4⋊Q8C2314yescomplemented
264C7×#127C2314yescomplemented
265C7×#124C2314yescomplemented
266C7×#124C2314yescomplemented
267C7×#123C2318yes—
268C7×#123C2318yescomplemented
269C7×C22⋊Q8C2318yescomplemented
270C7×C22⋊Q8C2318yescomplemented
271C7×#121C2318yescomplemented
272C7×#121C2318yescomplemented
273C7×#121C23116yescomplemented
274C7×#120C2318yes—
275C7×#120C2318yescomplemented
276C4×C7×D4C23116yescomplemented
277C7×#117C2312yes—
278C7×#117C2312yes—
279C7×#117C2312yescomplemented
280C7×#117C2312yescomplemented
281C2×C7×C4⋊C4C2312yescomplemented
282C2×C7×C22⋊C4C2312yes—
283C2×C42×C7C2312yescomplemented
284#6516C2318yes—
285C2×C22⋊Dic7C2312yes—
286C2×C22⋊Dic7C2314yescomplemented
287#6510C2314yescomplemented
288#6509C2314yes—
289#6509C2314yes—
290#6509C2314yescomplemented
291#6509C2318yescomplemented
292#6509C2314yescomplemented
293#6507C2314yescomplemented
294#6503C23116yescomplemented
295#6503C2314yescomplemented
296#6502C23116yescomplemented
297#6502C23116yescomplemented
298#6502C23116yescomplemented
299#6501C2314yes—
300#6501C2314yes—
301#6501C2318yescomplemented
302#6501C23116yescomplemented
303#6501C2314yescomplemented
304#6501C2314yescomplemented
305#6500C23116yes—
306#6500C2314yes—
307#6500C2314yes—
308#6500C2318yes—
309#6500C23116yescomplemented
310#6500C2318yescomplemented
311#6499C2314yescomplemented
312#6498C2314yes—
313#6498C2314yes—
314#6498C2318yescomplemented
315#6498C2318yescomplemented
316D4×Dic7C23116yescomplemented
317#6493C2318yescomplemented
318#6492C2318yes—
319C4×C22⋊D7C2318yes—
320C4×C22⋊D7C2318yes—
321C4×C22⋊D7C23116yescomplemented
322C4×C22⋊D7C2318yescomplemented
323C4×C22⋊D7C2318yescomplemented
324C4×C22⋊D7C23116yescomplemented
325C2×(C2×D7)⋊C4C2314yes—
326C2×(C2×D7)⋊C4C2314yes—
327C2×(C2×D7)⋊C4C2314yescomplemented
328#6489C2312yes—
329#6489C2312yes—
330#6489C2312yescomplemented
331#6489C2312yescomplemented
332C2×C4⋊Dic7C2314yescomplemented
333C2×C4⋊Dic7C2312yescomplemented
334#6487C2318yescomplemented
335C2×Dic7⋊C4C2314yescomplemented
336C2×C4×Dic7C2312yescomplemented
337#6460C2314yes—
338#6460C2314yes—
339#6460C2314yescomplemented
340#6460C2314yescomplemented
341#6459C23116yes—
342#6459C23116yescomplemented
343#6458C2314yes—
344#6458C2314yes—
345#6458C23116yescomplemented
346#6458C2314yescomplemented
347#6458C2314yescomplemented
348#6457C23116yescomplemented
349#6457C23116yescomplemented
350#6456C23116yes—
351#6456C2318yescomplemented
352#6455C2318yescomplemented
353D7×C4⋊C4C23116yescomplemented
354D7×C4⋊C4C2318yescomplemented
355#6451C23116yescomplemented
356#6450C2318yescomplemented
357#6449C2314yes—
358#6449C2314yes—
359#6449C2318yescomplemented
360#6448C23116yescomplemented
361#6448C23116yescomplemented
362#6447C23116yes—
363#6447C23116yescomplemented
364#6447C23116yescomplemented
365#6447C23116yescomplemented
366#6446C23116yescomplemented
367#6446C23116yescomplemented
368#6445C2314yes—
369#6445C2318yes—
370#6445C2314yes—
371#6445C23116yes—
372#6445C23116yescomplemented
373(C22⋊D7)⋊C4C23116yes—
374(C22⋊D7)⋊C4C23116yescomplemented
375(C22⋊D7)⋊C4C23116yescomplemented
376D7×C22⋊C4C2318yes—
377D7×C22⋊C4C23116yes—
378D7×C22⋊C4C23116yescomplemented
379#6441C23116yescomplemented
380#6441C23116yescomplemented
381#6440C2318yes—
382C4×D28C2318yes—
383C4×D28C2318yes—
384C4×D28C2318yescomplemented
385C4×D28C2318yescomplemented
386C4×D28C2318yescomplemented
387#6435C2318yescomplemented
388C42×D7C2318yescomplemented
389C4×Dic14C2318yescomplemented
390C2×#585—71no—
391C23×#41—71no—
392#3489—74no—
393#3489—74no—
394#3488—74no—
395#3488—74no—
396#3487—72no—
397#3486—72no—
398#3485—72no—
399#3485—74no—
400#3484—72no—
401#3484—74no—
402D4×#41—78no—
403D4×#41—78no—
404#3449—71no—
405#3449—74no—
406#3449D711yescharacteristic, complemented
407C2×#525—71no—
408C2×#525—74no—
409C2×#525—71no—
410#3428—71no—
411C24×C7C2412yes—
412C24×C7C2412yes—
413C24×C7C2411yescharacteristic
414C23×D7—24no—
415C23×D7—28no—
416C23×D7—44no—
417C23×D7—48no—
418C23×D7C2411yescharacteristic
419C23×D7C2418yes—
420C23×D7C2412yes—
421C23×D7C2412yes—
422C23×D7C2418yes—
423C23×D7C2411yescharacteristic
424C23×D7C2412yes—
425C23×D7C2412yes—
426C7×#41—28no—
427C7×#41—28no—
428C7×#41—28no—
429C7×#41—28no—
430C7×#41—28no—
431C7×#41—28no—
432C7×#41—28no—
433C7×#41—28no—
434C2×C7×Q8—24no—
435C2×C7×Q8—24no—
436C2×C7×Q8C2412yes—
437C2×C7×Q8C2412yes—
438C2×C7×Q8C2412yes—
439C2×C7×Q8C2412yes—
440C2×C7×D4—28no—
441C2×C7×D4—28no—
442C2×C7×D4—24no—
443C2×C7×D4—24no—
444C2×C7×D4C2414yes—
445C2×C7×D4C2414yes—
446C2×C7×D4C2414yes—
447C2×C7×D4C2412yes—
448C2×C7×D4C2412yes—
449C2×C7×D4C2412yes—
450C2×C7×D4C2412yes—
451C2×C7×D4C2414yes—
452C2×C7×D4C24116yes—
453C22×C4×C7—28no—
454C22×C4×C7—28no—
455C22×C4×C7C2×D418yescomplemented
456C22×C4×C7C2412yes—
457C22×C4×C7C2414yes—
458C22×C4×C7C2414yes—
459C22×C4×C7C2414yes—
460C22×C4×C7C2414yes—
461C22×C4×C7C2412yes—
462C22×C4×C7C2414yes—
463C22×C4×C7C2411yescharacteristic
464C22×C4×C7C2411yescharacteristic
465C22×C4×C7C2411yescharacteristic
466C22×C4×C7C2411yescharacteristic
467C22×C4×C7C2411yescharacteristic
468C22×C4×C7C2411yescharacteristic
469C2×C22⋊D7—28no—
470C2×C22⋊D7—28no—
471C2×C22⋊D7—232no—
472C2×C22⋊D7—28no—
473C2×C22⋊D7—48no—
474C2×C22⋊D7C2×D4116yescomplemented
475C2×C22⋊D7C2418yes—
476C2×C22⋊D7C2414yes—
477C2×C22⋊D7C2414yes—
478C2×C22⋊D7C2418yes—
479C2×C22⋊D7C2418yes—
480C2×C22⋊D7C2418yes—
481C2×C22⋊D7C2418yes—
482C2×C22⋊D7C24116yes—
483C2×C22⋊D7C2418yes—
484C2×C22⋊D7C2414yes—
485C2×C22⋊D7C2414yes—
486C22×Dic7—24no—
487C22×Dic7—28no—
488C22×Dic7C2418yes—
489C22×Dic7C2418yes—
490C22×Dic7C2411yescharacteristic
491C22×Dic7C2411yescharacteristic
492C22×Dic7C2412yes—
493C22×Dic7C2412yes—
494C22×Dic7C2412yes—
495C22×Dic7C2414yes—
496C22×Dic7C2412yes—
497#1161—216no—
498#1161—216no—
499#1161—216no—
500#1161—216no—
501Q8×D7—216no—
502Q8×D7—216no—
503Q8×D7—216no—
504Q8×D7—216no—
505#1159—232no—
506#1159—232no—
507#1159—232no—
508#1159—232no—
509#1159—216no—
510#1159—216no—
511#1159—216no—
512#1159—216no—
513D4×D7—232no—
514D4×D7—232no—
515D4×D7—232no—
516D4×D7—232no—
517D4×D7—216no—
518D4×D7—216no—
519D4×D7—216no—
520D4×D7—216no—
521D4×D7—432no—
522#1157—28no—
523#1157—28no—
524#1157—28no—
525#1157—28no—
526#1157—232no—
527#1157—216no—
528#1157—232no—
529#1157—232no—
530#1157—232no—
531#1157—216no—
532#1157C2×D4116yescomplemented
533#1157C2×D4116yescomplemented
534#1157C2×D4116yescomplemented
535#1157C2×D4116yescomplemented
536C2×D28—28no—
537C2×D28—24no—
538C2×D28—216no—
539C2×D28—48no—
540C2×D28C2×D418yescomplemented
541C2×D28C2418yes—
542C2×D28C2418yes—
543C2×D28C2418yes—
544C2×D28C2412yes—
545C2×D28C2412yes—
546C2×D28C2418yes—
547C2×D28C2412yes—
548C2×D28C2412yes—
549C2×C4×D7—28no—
550C2×C4×D7—24no—
551C2×C4×D7—24no—
552C2×C4×D7—24no—
553C2×C4×D7—24no—
554C2×C4×D7—28no—
555C2×C4×D7—28no—
556C2×C4×D7—28no—
557C2×C4×D7—28no—
558C2×C4×D7—28no—
559C2×C4×D7—28no—
560C2×C4×D7—232no—
561C2×C4×D7—232no—
562C2×C4×D7—232no—
563C2×C4×D7C2×D4116yescomplemented
564C2×C4×D7C2412yes—
565C2×C4×D7C2412yes—
566C2×C4×D7C2414yes—
567C2×C4×D7C2414yes—
568C2×C4×D7C2412yes—
569C2×C4×D7C2412yes—
570C2×C4×D7C2418yes—
571C2×C4×D7C2418yes—
572C2×C4×D7C2418yes—
573C2×C4×D7C2418yes—
574C2×C4×D7C2412yes—
575C2×C4×D7C2412yes—
576C2×C4×D7C2412yes—
577C2×C4×D7C2412yes—
578C2×C4×D7C24116yes—
579C2×C4×D7C2414yes—
580C2×C4×D7C2414yes—
581C2×Dic14—24no—
582C2×Dic14—28no—
583C2×Dic14—216no—
584C2×Dic14C2×D418yescomplemented
585C2×Dic14C2418yes—
586C2×Dic14C2418yes—
587C2×Dic14C2412yes—
588C2×Dic14C2412yes—
589C2×Dic14C2412yes—
590C2×Dic14C2412yes—
591C7×C4⋊C4C2414yes—
592C7×C4⋊C4C24116yes—
593C7×C4⋊C4C2414yes—
594C7×C22⋊C4C2414yes—
595C7×C22⋊C4C24116yes—
596C7×C22⋊C4C24116yes—
597C7×C22⋊C4C2414yes—
598C42×C7C2414yes—
599C42×C7C2414yes—
600C22⋊Dic7C2414yes—
601C22⋊Dic7C2418yes—
602C22⋊Dic7C24116yes—
603C22⋊Dic7C2418yes—
604C22⋊Dic7C2414yes—
605(C2×D7)⋊C4C24116yes—
606(C2×D7)⋊C4C2418yes—
607(C2×D7)⋊C4C2418yes—
608(C2×D7)⋊C4C2418yes—
609(C2×D7)⋊C4C2418yes—
610(C2×D7)⋊C4C2418yes—
611(C2×D7)⋊C4C24116yes—
612(C2×D7)⋊C4C2418yes—
613C4⋊Dic7C2414yes—
614C4⋊Dic7C2418yes—
615C4⋊Dic7C2418yes—
616C4⋊Dic7C2414yes—
617Dic7⋊C4C24116yes—
618Dic7⋊C4C2418yes—
619Dic7⋊C4C24116yes—
620Dic7⋊C4C2418yes—
621C4×Dic7C24116yes—
622C4×Dic7C2414yes—
623C4×Dic7C2414yes—
624#585—1416no—
625C2×2−1+4—72no—
626C2×2−1+4—72no—
627C2×2−1+4—72no—
628C2×H(5,𝔽2)—72no—
629C2×H(5,𝔽2)—72no—
630C2×H(5,𝔽2)—74no—
631C2×H(5,𝔽2)—72no—
632C22×#41—74no—
633C22×#41—74no—
634C22×#41—74no—
635C22×#41—74no—
636C22×#41—74no—
637C22×#41—74no—
638C22×#41—71no—
639C22×#41—72no—
640C22×#41—71no—
641C22×#41—71no—
642C22×#41—72no—
643C22×#41—71no—
644C22×#41—74no—
645C22×#41—1416no—
646C22×#41C2×D711yescharacteristic, complemented
647C22×#41C2×D711yescharacteristic, complemented
648C23×Q8—71no—
649C23×D4—72no—
650C23×D4—71no—
651C24×C4—72no—
652C24×C4—71no—
653#550—78no—
654#550—78no—
655D4×Q8—78no—
656D4×Q8—78no—
657#548—78no—
658#548—78no—
659#548—78no—
660#548—78no—
661#547—78no—
662#547—716no—
663#547—78no—
664#547—716no—
665#546—78no—
666#546—78no—
667#546—716no—
668#546—78no—
669#546—716no—
670#546—78no—
671#546—716no—
672#546—716no—
673D42—78no—
674D42—78no—
675D42—716no—
676D42—716no—
677#537—74no—
678#537—78no—
679#537—78no—
680#537C2×D714yescomplemented
681#536—72no—
682#536—72no—
683#536—78no—
684#536—78no—
685#536C2×D712yescomplemented
686#536C2×D712yescomplemented
687#535—72no—
688#535—72no—
689#535—78no—
690#535—78no—
691#535C2×D712yescomplemented
692#535C2×D712yescomplemented
693#534—74no—
694#534—78no—
695#534—78no—
696#534C2×D714yescomplemented
697#532—74no—
698#532—716no—
699#532C2×D714yescomplemented
700#525—72no—
701#525—72no—
702#525—72no—
703#525—72no—
704#525—74no—
705#525—74no—
706#525—74no—
707#525—74no—
708#525—78no—
709#525—78no—
710#525—78no—
711#525—78no—
712#525—716no—
713#525—716no—
714#525—72no—
715#525—72no—
716#525—72no—
717#525—72no—
718#525—74no—
719#525—74no—
720#525C2×D714yescomplemented
721#525C2×D714yescomplemented
722C2×#123—72no—
723C2×#123—78no—
724C2×#123—72no—
725C2×C22⋊Q8—72no—
726C2×C22⋊Q8—78no—
727C2×C22⋊Q8—72no—
728C2×#121—72no—
729C2×#121—78no—
730C2×#121—72no—
731C2×#120—72no—
732C2×#120—78no—
733C2×#120—72no—
734#520—74no—
735#520—74no—
736#519—72no—
737#518—72no—
738#518—74no—
739C4×#41—74no—
740C4×#41—74no—
741C2×C4×D4—74no—
742C2×C4×D4—716no—
743C2×C4×D4—74no—
744C2×#117—71no—
745C2×#117—74no—
746C2×#117C2×D711yescharacteristic, complemented
747C23×C7—24no—
748C23×C7—24no—
749C23×C7—42no—
750C23×C7—44no—
751C23×C7—44no—
752C23×C7C22×D414yes—
753C23×C7C2514yes—
754C23×C7C2514yes—
755C23×C7C2511yescharacteristic
756C23×C7C2511yescharacteristic
757C23×C7C2511yescharacteristic
758C22×D7—22no—
759C22×D7—24no—
760C22×D7—22no—
761C22×D7—24no—
762C22×D7—24no—
763C22×D7—24no—
764C22×D7—216no—
765C22×D7—24no—
766C22×D7—216no—
767C22×D7—24no—
768C22×D7—216no—
769C22×D7—44no—
770C22×D7—48no—
771C22×D7—42no—
772C22×D7—42no—
773C22×D7—42no—
774C22×D7—44no—
775C22×D7—416no—
776C22×D7—432no—
777C22×D7—416no—
778C22×D7C22×D418yes—
779C22×D7C2514yes—
780C22×D7C2512yes—
781C22×D7C2514yes—
782C22×D7C2512yes—
783C7×Q8—24no—
784C7×Q8—24no—
785C7×Q8—24no—
786C7×Q8—24no—
787C7×D4—28no—
788C7×D4—28no—
789C7×D4—28no—
790C7×D4—28no—
791C7×D4—24no—
792C7×D4—24no—
793C7×D4—24no—
794C7×D4—24no—
795C7×D4—416no—
796C2×C4×C7—24no—
797C2×C4×C7—24no—
798C2×C4×C7—28no—
799C2×C4×C7—28no—
800C2×C4×C7—28no—
801C2×C4×C7—28no—
802C2×C4×C7—44no—
803C2×C4×C7C22×D414yes—
804C2×C4×C7C22×D414yes—
805C2×C4×C7C22×D414yes—
806C2×C4×C7C22×D414yes—
807C2×C4×C7C22×D414yes—
808C2×C4×C7C22×D414yes—
809C2×C4×C7C2518yes—
810C2×C4×C7C2514yes—
811C2×C4×C7C2514yes—
812C2×C4×C7C2511yescharacteristic
813C2×C4×C7C2511yescharacteristic
814C2×C4×C7C2511yescharacteristic
815C2×C4×C7C2511yescharacteristic
816C22⋊D7—28no—
817C22⋊D7—28no—
818C22⋊D7—216no—
819C22⋊D7—216no—
820C22⋊D7—216no—
821C22⋊D7—216no—
822C22⋊D7—216no—
823C22⋊D7—416no—
824C22⋊D7—48no—
825C22⋊D7C22×D4116yes—
826C22⋊D7C22×D4116yes—
827C2×Dic7—22no—
828C2×Dic7—24no—
829C2×Dic7—22no—
830C2×Dic7—24no—
831C2×Dic7—24no—
832C2×Dic7—216no—
833C2×Dic7—216no—
834C2×Dic7—44no—
835C2×Dic7C22×D418yes—
836C2×Dic7C2518yes—
837C2×Dic7C2514yes—
838C2×Dic7C2512yes—
839C2×Dic7C2512yes—
840C2×Dic7C2514yes—
841D28—216no—
842D28—216no—
843D28—216no—
844D28—24no—
845D28—24no—
846D28—48no—
847D28C22×D418yes—
848D28C22×D418yes—
849C4×D7—216no—
850C4×D7—216no—
851C4×D7—24no—
852C4×D7—24no—
853C4×D7—24no—
854C4×D7—24no—
855C4×D7—28no—
856C4×D7—24no—
857C4×D7—24no—
858C4×D7—24no—
859C4×D7—24no—
860C4×D7—28no—
861C4×D7—216no—
862C4×D7—216no—
863C4×D7—416no—
864C4×D7C22×D4116yes—
865C4×D7C22×D4116yes—
866Dic14—24no—
867Dic14—24no—
868Dic14—216no—
869Dic14—216no—
870Dic14C22×D418yes—
871Dic14C22×D418yes—
872C25—72no—
873C25—71no—
8742−1+4—1416no—
8752−1+4—1416no—
8762−1+4—1416no—
877H(5,𝔽2)—1432no—
878H(5,𝔽2)—1416no—
879H(5,𝔽2)—1416no—
880H(5,𝔽2)—1416no—
881C2×#41—28no—
882C2×#41—28no—
883C2×#41—74no—
884C2×#41—74no—
885C2×#41—74no—
886C2×#41—74no—
887C2×#41—78no—
888C2×#41—74no—
889C2×#41—78no—
890C2×#41—78no—
891C2×#41—78no—
892C2×#41—74no—
893C2×#41—74no—
894C2×#41—74no—
895C2×#41—716no—
896C2×#41—72no—
897C2×#41—72no—
898C2×#41—72no—
899C2×#41—72no—
900C2×#41—72no—
901C2×#41—78no—
902C2×#41—78no—
903C2×#41—72no—
904C2×#41—72no—
905C2×#41—72no—
906C2×#41—78no—
907C2×#41—74no—
908C2×#41—78no—
909C2×#41—74no—
910C2×#41—1416no—
911C2×#41—1432no—
912C2×#41—1432no—
913C2×#41—1416no—
914C2×#41—148no—
915C2×#41—148no—
916C2×#41—1432no—
917C2×#41—1432no—
918C2×#41—1432no—
919C2×#41—1432no—
920C2×#41—1432no—
921C2×#41—148no—
922C2×#41C22×D712yes—
923C2×#41C22×D712yes—
924C2×#41C22×D712yes—
925C2×#41C22×D712yes—
926C2×#41C22×D712yes—
927C2×#41C22×D712yes—
928C2×#41C22×D712yescomplemented
929C2×#41C22×D712yescomplemented
930C22×Q8—74no—
931C22×Q8—74no—
932C22×Q8—74no—
933C22×Q8—74no—
934C22×Q8—71no—
935C22×Q8—71no—
936C22×Q8—72no—
937C22×Q8—74no—
938C22×Q8—148no—
939C22×Q8C22×D711yescharacteristic
940C22×Q8C22×D711yescharacteristic, complemented
941C22×D4—72no—
942C22×D4—72no—
943C22×D4—72no—
944C22×D4—72no—
945C22×D4—78no—
946C22×D4—74no—
947C22×D4—78no—
948C22×D4—74no—
949C22×D4—78no—
950C22×D4—78no—
951C22×D4—74no—
952C22×D4—74no—
953C22×D4—78no—
954C22×D4—74no—
955C22×D4—716no—
956C22×D4—71no—
957C22×D4—71no—
958C22×D4—72no—
959C22×D4—74no—
960C22×D4—74no—
961C22×D4—1416no—
962C22×D4—148no—
963C22×D4C22×D712yes—
964C22×D4C22×D712yes—
965C22×D4C22×D711yescharacteristic
966C22×D4C22×D711yescharacteristic, complemented
967C23×C4—72no—
968C23×C4—71no—
969C23×C4—72no—
970C23×C4—78no—
971C23×C4—72no—
972C23×C4—72no—
973C23×C4—78no—
974C23×C4—72no—
975C23×C4—78no—
976C23×C4—72no—
977C23×C4—72no—
978C23×C4—72no—
979C23×C4—71no—
980C23×C4—72no—
981C23×C4—71no—
982C23×C4—71no—
983C23×C4—71no—
984C23×C4—1416no—
985C23×C4—148no—
986C23×C4C22×D712yes—
987C23×C4C22×D711yescharacteristic
988C23×C4C22×D712yescomplemented
989C4⋊Q8—74no—
990C4⋊Q8—716no—
991C4⋊Q8C22×D714yescomplemented
992#127—716no—
993#127—74no—
994#127C22×D714yescomplemented
995#124—74no—
996#124—74no—
997#124—716no—
998#124—716no—
999#124C22×D714yescomplemented
1000#124C22×D714yescomplemented
1001#123—74no—
1002#123—74no—
1003#123—78no—
1004#123—78no—
1005#123—78no—
1006#123—716no—
1007#123—716no—
1008#123—74no—
1009#123—74no—
1010#123—716no—
1011#123—78no—
1012#123—716no—
1013#123C22×D718yes—
1014#123C22×D718yescomplemented
1015C22⋊Q8—74no—
1016C22⋊Q8—74no—
1017C22⋊Q8—74no—
1018C22⋊Q8—74no—
1019C22⋊Q8—78no—
1020C22⋊Q8—78no—
1021C22⋊Q8—74no—
1022C22⋊Q8—74no—
1023C22⋊Q8—716no—
1024C22⋊Q8—74no—
1025C22⋊Q8—74no—
1026C22⋊Q8—716no—
1027C22⋊Q8—716no—
1028C22⋊Q8—716no—
1029C22⋊Q8C22×D718yescomplemented
1030C22⋊Q8C22×D718yescomplemented
1031#121—74no—
1032#121—74no—
1033#121—74no—
1034#121—74no—
1035#121—716no—
1036#121—78no—
1037#121—716no—
1038#121—716no—
1039#121—716no—
1040#121—78no—
1041#121—74no—
1042#121—74no—
1043#121—74no—
1044#121—74no—
1045#121—716no—
1046#121—716no—
1047#121—716no—
1048#121—716no—
1049#121—716no—
1050#121C22×D718yescomplemented
1051#121C22×D718yescomplemented
1052#121C22×D7116yescomplemented
1053#120—78no—
1054#120—74no—
1055#120—74no—
1056#120—78no—
1057#120—716no—
1058#120—78no—
1059#120—716no—
1060#120—74no—
1061#120—74no—
1062#120—716no—
1063#120—78no—
1064#120—716no—
1065#120C22×D718yes—
1066#120C22×D718yescomplemented
1067C4×Q8—78no—
1068C4×Q8—78no—
1069C4×D4—716no—
1070C4×D4—78no—
1071C4×D4—716no—
1072C4×D4—78no—
1073C4×D4—78no—
1074C4×D4—78no—
1075C4×D4—716no—
1076C4×D4—716no—
1077C4×D4—78no—
1078C4×D4—716no—
1079C4×D4—716no—
1080C4×D4—716no—
1081C4×D4—78no—
1082C4×D4—78no—
1083C4×D4—78no—
1084C4×D4—78no—
1085C4×D4—78no—
1086C4×D4C22×D7116yescomplemented
1087#117—72no—
1088#117—72no—
1089#117—72no—
1090#117—72no—
1091#117—78no—
1092#117—78no—
1093#117—78no—
1094#117C22×D712yes—
1095#117C22×D712yes—
1096#117C22×D712yescomplemented
1097#117C22×D712yescomplemented
1098C2×C4⋊C4—72no—
1099C2×C4⋊C4—74no—
1100C2×C4⋊C4—74no—
1101C2×C4⋊C4—78no—
1102C2×C4⋊C4—716no—
1103C2×C4⋊C4C22×D712yescomplemented
1104C2×C22⋊C4—72no—
1105C2×C22⋊C4—74no—
1106C2×C22⋊C4—74no—
1107C2×C22⋊C4—74no—
1108C2×C22⋊C4—74no—
1109C2×C22⋊C4—78no—
1110C2×C22⋊C4—716no—
1111C2×C22⋊C4—716no—
1112C2×C22⋊C4C22×D712yes—
1113C2×C42—72no—
1114C2×C42—78no—
1115C2×C42C22×D712yescomplemented
1116C22×C7—22no—
1117C22×C7—22no—
1118C22×C7—22no—
1119C22×C7—24no—
1120C22×C7—24no—
1121C22×C7—28no—
1122C22×C7—28no—
1123C22×C7—44no—
1124C22×C7—48no—
1125C22×C7—84no—
1126C22×C7C23×D412yes—
1127C22×C7C23×D412yes—
1128C22×C7C23×D412yes—
1129C22×C7C2611yescharacteristic
1130C2×D7—28no—
1131C2×D7—22no—
1132C2×D7—28no—
1133C2×D7—22no—
1134C2×D7—22no—
1135C2×D7—24no—
1136C2×D7—28no—
1137C2×D7—22no—
1138C2×D7—22no—
1139C2×D7—48no—
1140C2×D7—432no—
1141C2×D7—48no—
1142C2×D7—48no—
1143C2×D7—44no—
1144C2×D7—816no—
1145C2×D7—84no—
1146C2×D7C23×D418yes—
1147C2×D7#58514yescomplemented
1148C4×C7—24no—
1149C4×C7—24no—
1150C4×C7—28no—
1151C4×C7C23×D412yes—
1152C4×C7C23×D412yes—
1153C4×C7C23×D412yes—
1154C4×C7C23×D412yes—
1155Dic7—24no—
1156Dic7—22no—
1157Dic7—22no—
1158Dic7—28no—
1159Dic7C23×D418yes—
1160C24—72no—
1161C24—71no—
1162C24—78no—
1163C24—72no—
1164C24—72no—
1165C24—78no—
1166C24—72no—
1167C24—71no—
1168C24—148no—
1169C24—144no—
1170C24—284no—
1171C24—288no—
1172C24C23×D712yes—
1173C24C23×D712yes—
1174C24C23×D711yescharacteristic
1175#41—28no—
1176#41—28no—
1177#41—28no—
1178#41—28no—
1179#41—28no—
1180#41—28no—
1181#41—28no—
1182#41—28no—
1183#41—716no—
1184#41—716no—
1185#41—716no—
1186#41—716no—
1187#41—1432no—
1188#41—1432no—
1189#41—1432no—
1190#41—1432no—
1191#41—1416no—
1192#41—1416no—
1193#41—1432no—
1194#41—1416no—
1195#41—1416no—
1196#41—1432no—
1197#41—1432no—
1198#41—1432no—
1199#41—1416no—
1200#41—1416no—
1201#41—1416no—
1202#41—1416no—
1203#41—1416no—
1204#41—1416no—
1205#41—148no—
1206#41—148no—
1207#41—148no—
1208#41—148no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—78no—
1212C2×Q8—72no—
1213C2×Q8—72no—
1214C2×Q8—72no—
1215C2×Q8—78no—
1216C2×Q8—78no—
1217C2×Q8—72no—
1218C2×Q8—148no—
1219C2×Q8—1416no—
1220C2×Q8—1416no—
1221C2×Q8—1416no—
1222C2×Q8—1416no—
1223C2×Q8—1416no—
1224C2×Q8—144no—
1225C2×Q8C23×D712yes—
1226C2×Q8C23×D712yes—
1227C2×Q8C23×D712yes—
1228C2×Q8C23×D712yes—
1229C2×D4—28no—
1230C2×D4—28no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—716no—
1234C2×D4—74no—
1235C2×D4—74no—
1236C2×D4—78no—
1237C2×D4—74no—
1238C2×D4—78no—
1239C2×D4—78no—
1240C2×D4—74no—
1241C2×D4—78no—
1242C2×D4—78no—
1243C2×D4—78no—
1244C2×D4—716no—
1245C2×D4—78no—
1246C2×D4—72no—
1247C2×D4—72no—
1248C2×D4—78no—
1249C2×D4—78no—
1250C2×D4—78no—
1251C2×D4—72no—
1252C2×D4—72no—
1253C2×D4—78no—
1254C2×D4—1416no—
1255C2×D4—148no—
1256C2×D4—1416no—
1257C2×D4—148no—
1258C2×D4—1432no—
1259C2×D4—1432no—
1260C2×D4—1416no—
1261C2×D4—1416no—
1262C2×D4—1432no—
1263C2×D4—1416no—
1264C2×D4—1432no—
1265C2×D4—1432no—
1266C2×D4—148no—
1267C2×D4—148no—
1268C2×D4—144no—
1269C2×D4—288no—
1270C2×D4—2832no—
1271C2×D4—288no—
1272C2×D4C23×D714yes—
1273C2×D4C23×D714yes—
1274C2×D4C23×D714yes—
1275C2×D4C23×D714yes—
1276C2×D4C23×D712yes—
1277C2×D4C23×D712yes—
1278C2×D4C23×D712yes—
1279C2×D4C23×D712yes—
1280C2×D4C23×D7116yes—
1281C22×C4—28no—
1282C22×C4—28no—
1283C22×C4—72no—
1284C22×C4—716no—
1285C22×C4—74no—
1286C22×C4—74no—
1287C22×C4—72no—
1288C22×C4—72no—
1289C22×C4—72no—
1290C22×C4—78no—
1291C22×C4—78no—
1292C22×C4—71no—
1293C22×C4—71no—
1294C22×C4—74no—
1295C22×C4—78no—
1296C22×C4—78no—
1297C22×C4—78no—
1298C22×C4—72no—
1299C22×C4—72no—
1300C22×C4—72no—
1301C22×C4—72no—
1302C22×C4—78no—
1303C22×C4—74no—
1304C22×C4—72no—
1305C22×C4—72no—
1306C22×C4—72no—
1307C22×C4—74no—
1308C22×C4—72no—
1309C22×C4—716no—
1310C22×C4—148no—
1311C22×C4—1432no—
1312C22×C4—1432no—
1313C22×C4—1432no—
1314C22×C4—148no—
1315C22×C4—148no—
1316C22×C4—144no—
1317C22×C4—144no—
1318C22×C4—144no—
1319C22×C4—144no—
1320C22×C4—144no—
1321C22×C4—148no—
1322C22×C4—148no—
1323C22×C4—148no—
1324C22×C4—148no—
1325C22×C4—148no—
1326C22×C4D4×D718yescomplemented
1327C22×C4C23×D712yes—
1328C22×C4C23×D714yes—
1329C22×C4C23×D714yes—
1330C22×C4C23×D712yes—
1331C22×C4C23×D714yes—
1332C22×C4C23×D714yes—
1333C22×C4C23×D714yes—
1334C22×C4C23×D711yescharacteristic
1335C22×C4C23×D711yescharacteristic
1336C22×C4C23×D711yescharacteristic
1337C22×C4C23×D711yescharacteristic
1338C22×C4C23×D711yescharacteristic
1339C22×C4C23×D711yescharacteristic
1340C4⋊C4—78no—
1341C4⋊C4—716no—
1342C4⋊C4—716no—
1343C4⋊C4—78no—
1344C4⋊C4—74no—
1345C4⋊C4—78no—
1346C4⋊C4—74no—
1347C4⋊C4—78no—
1348C4⋊C4C23×D714yes—
1349C4⋊C4C23×D7116yes—
1350C4⋊C4C23×D714yes—
1351C22⋊C4—74no—
1352C22⋊C4—78no—
1353C22⋊C4—74no—
1354C22⋊C4—78no—
1355C22⋊C4—716no—
1356C22⋊C4—78no—
1357C22⋊C4—78no—
1358C22⋊C4—78no—
1359C22⋊C4—716no—
1360C22⋊C4—78no—
1361C22⋊C4—716no—
1362C22⋊C4—78no—
1363C22⋊C4—78no—
1364C22⋊C4C23×D714yes—
1365C22⋊C4C23×D7116yes—
1366C22⋊C4C23×D7116yes—
1367C22⋊C4C23×D714yes—
1368C42—716no—
1369C42—74no—
1370C42—74no—
1371C42C23×D714yes—
1372C42C23×D714yes—
1373C2×C7—22no—
1374C2×C7—22no—
1375C2×C7—22no—
1376C2×C7—44no—
1377C2×C7—44no—
1378C2×C7C24×D411yescharacteristic
1379C2×C7C2×#58512yes—
1380D7—24no—
1381D7—28no—
1382D7—42no—
1383D7—44no—
1384C23—24no—
1385C23—24no—
1386C23—42no—
1387C23—44no—
1388C23—44no—
1389C23—72no—
1390C23—74no—
1391C23—78no—
1392C23—74no—
1393C23—72no—
1394C23—144no—
1395C23—1416no—
1396C23—144no—
1397C23—144no—
1398C23—1416no—
1399C23—1416no—
1400C23—142no—
1401C23—144no—
1402C23—144no—
1403C23—142no—
1404C23—144no—
1405C23—282no—
1406C23—282no—
1407C23—284no—
1408C23—282no—
1409C23—288no—
1410C23—284no—
1411C23—2816no—
1412C23—2816no—
1413C23—2832no—
1414C23C2×D4×D714yes—
1415C23C24×D714yes—
1416C23C24×D714yes—
1417C23C24×D711yescharacteristic
1418C23C24×D711yescharacteristic
1419C23C24×D711yescharacteristic
1420Q8—24no—
1421Q8—24no—
1422Q8—24no—
1423Q8—24no—
1424Q8—78no—
1425Q8—78no—
1426Q8—1416no—
1427Q8—1416no—
1428Q8—144no—
1429Q8—144no—
1430D4—28no—
1431D4—28no—
1432D4—28no—
1433D4—28no—
1434D4—24no—
1435D4—24no—
1436D4—24no—
1437D4—24no—
1438D4—416no—
1439D4—716no—
1440D4—716no—
1441D4—78no—
1442D4—78no—
1443D4—1416no—
1444D4—1416no—
1445D4—1416no—
1446D4—1416no—
1447D4—1416no—
1448D4—1416no—
1449D4—1416no—
1450D4—1416no—
1451D4—148no—
1452D4—148no—
1453D4—144no—
1454D4—144no—
1455D4—288no—
1456D4—288no—
1457D4—2816no—
1458C2×C4—24no—
1459C2×C4—24no—
1460C2×C4—28no—
1461C2×C4—28no—
1462C2×C4—28no—
1463C2×C4—28no—
1464C2×C4—44no—
1465C2×C4—74no—
1466C2×C4—78no—
1467C2×C4—716no—
1468C2×C4—716no—
1469C2×C4—78no—
1470C2×C4—72no—
1471C2×C4—74no—
1472C2×C4—72no—
1473C2×C4—1416no—
1474C2×C4—1416no—
1475C2×C4—1416no—
1476C2×C4—1416no—
1477C2×C4—1416no—
1478C2×C4—1416no—
1479C2×C4—142no—
1480C2×C4—142no—
1481C2×C4—144no—
1482C2×C4—144no—
1483C2×C4—144no—
1484C2×C4—144no—
1485C2×C4—144no—
1486C2×C4—144no—
1487C2×C4—144no—
1488C2×C4—144no—
1489C2×C4—144no—
1490C2×C4—148no—
1491C2×C4—144no—
1492C2×C4—144no—
1493C2×C4—148no—
1494C2×C4—2816no—
1495C2×C4—284no—
1496C2×C4C2×D4×D714yes—
1497C2×C4C2×D4×D714yes—
1498C2×C4C2×D4×D714yes—
1499C2×C4C2×D4×D714yes—
1500C2×C4C2×D4×D714yes—
1501C2×C4C2×D4×D714yes—
1502C2×C4C24×D718yes—
1503C2×C4C24×D714yes—
1504C2×C4C24×D714yes—
1505C2×C4C24×D711yescharacteristic
1506C2×C4C24×D711yescharacteristic
1507C2×C4C24×D711yescharacteristic
1508C2×C4C24×D711yescharacteristic
1509C7#6281111yescharacteristic, complemented, Sylow
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—24no—
1514C22—24no—
1515C22—28no—
1516C22—28no—
1517C22—44no—
1518C22—48no—
1519C22—78no—
1520C22—74no—
1521C22—84no—
1522C22—148no—
1523C22—142no—
1524C22—148no—
1525C22—142no—
1526C22—142no—
1527C22—144no—
1528C22—148no—
1529C22—142no—
1530C22—142no—
1531C22—288no—
1532C22—288no—
1533C22—288no—
1534C22—284no—
1535C22—2832no—
1536C22—564no—
1537C22—5616no—
1538C22C22×D4×D712yes—
1539C22C22×D4×D712yes—
1540C22C22×D4×D712yes—
1541C22C25×D711yescharacteristic
1542C4—24no—
1543C4—24no—
1544C4—28no—
1545C4—78no—
1546C4—142no—
1547C4—144no—
1548C4—142no—
1549C4—148no—
1550C4C22×D4×D712yes—
1551C4C22×D4×D712yes—
1552C4C22×D4×D712yes—
1553C4C22×D4×D712yes—
1554C2—22no—
1555C2—22no—
1556C2—22no—
1557C2—44no—
1558C2—44no—
1559C2—144no—
1560C2—148no—
1561C2—282no—
1562C2—284no—
1563C2C23×D4×D711yescharacteristic
1564C2D7×#58512yes—
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC7×#3449C2
hypercenter#3449D7
hypocenterC7#62811
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #3449

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#90616C2semidirect
2. C22×D7×#41C2semidirect
3. C7×#3449C2semidirect
4. #11744336C2semidirect
5. C2×#90519C2semidirect
6. #11743448C2semidirect
7. #11743447C2semidirect
8. #11743424C2semidirect
9. #11743423C2semidirect
10. #11743422C2semidirect
11. #11743399C2semidirect
12. #11743398C2semidirect
13. #11743383C2semidirect
14. #11743376C2semidirect
15. #11743364C2semidirect
16. #11743306C2semidirect
17. #11743105C2semidirect
18. #11743103C2semidirect
19. D7×#525C2semidirect
20. C2×#90215C2semidirect
21. #11742799C2semidirect
22. C22×C7×#41C22semidirect
23. C22×C7×#41C22semidirect
25. C2×#6554C22semidirect
26. C2×#6554C22semidirect
27. C2×#6553C22semidirect
28. C2×#6553C22semidirect
30. C2×D7×#41C22semidirect
31. C2×D7×#41C22semidirect
32. C2×D7×#41C22semidirect
33. C2×D7×#41C22semidirect
34. C2×D7×#41C22semidirect
35. C2×D7×#41C22semidirect
36. C2×#6551C22semidirect
37. C22×#1161C22semidirect
38. C22×Q8×D7C22semidirect
39. C2×#6548C22semidirect
40. C2×#6548C22semidirect
41. C22×#1159C22semidirect
42. C22×#1159C22semidirect
43. C22×D4×D7C22semidirect
44. C22×D4×D7C22semidirect
46. C22×#1157C22semidirect
47. C22×#1157C22semidirect
48. C22×#1157C22semidirect
49. C23×C4×D7C22semidirect
50. C23×C4×D7C22semidirect
51. C7×#537C22semidirect
52. C7×#536C22semidirect
53. C7×#536C22semidirect
54. C7×#535C22semidirect
55. C7×#535C22semidirect
56. C7×#534C22semidirect
57. C7×#532C22semidirect
58. C7×#525C22semidirect
59. C7×#525C22semidirect
60. C2×C7×#117C22semidirect
61. #90524C22semidirect
62. #90523C22semidirect
63. #90521C22semidirect
64. #90519C22semidirect
65. #90519C22semidirect
66. #90519C22semidirect
67. #90519C22semidirect
68. #90519C22semidirect
69. #90519C22semidirect
70. #90519C22semidirect
71. #90516C22semidirect
72. #90507C22semidirect
73. C2×#6509C22semidirect
74. #90496C22semidirect
75. #90495C22semidirect
76. C2×#6501C22semidirect
77. C2×#6500C22semidirect
78. C2×#6498C22semidirect
79. #90482C22semidirect
80. C2×C4×C22⋊D7C22semidirect
81. C2×#6489C22semidirect
82. #90418C22semidirect
83. #90417C22semidirect
84. #90409C22semidirect
85. #90408C22semidirect
86. #90368C22semidirect
87. #90368C22semidirect
88. #90367C22semidirect
89. #90367C22semidirect
90. #90347C22semidirect
91. #90346C22semidirect
92. #90345C22semidirect
93. #90344C22semidirect
94. D7×#123C22semidirect
95. #90339C22semidirect
96. #90324C22semidirect
97. #90323C22semidirect
98. #90322C22semidirect
99. #90321C22semidirect
100. #90320C22semidirect
101. #90319C22semidirect
102. #90318C22semidirect
103. D7×C22⋊Q8C22semidirect
104. #90303C22semidirect
105. #90302C22semidirect
106. #90301C22semidirect
107. #90301C22semidirect
108. #90300C22semidirect
109. #90300C22semidirect
110. #90299C22semidirect
111. #90298C22semidirect
112. #90297C22semidirect
113. D7×#121C22semidirect
114. #90290C22semidirect
115. #90289C22semidirect
116. #90283C22semidirect
117. #90282C22semidirect
118. #90281C22semidirect
119. #90280C22semidirect
120. D7×#120C22semidirect
121. #90277C22semidirect
122. #90239C22semidirect
123. #90238C22semidirect
124. #90238C22semidirect
125. C4×D4×D7C22semidirect
126. #90215C22semidirect
127. #90215C22semidirect
128. #90215C22semidirect
129. #90215C22semidirect
130. #90215C22semidirect
131. #90215C22semidirect
132. #90214C22semidirect
133. #90213C22semidirect
134. #90212C22semidirect
135. D7×#117C22semidirect
136. #90207C22semidirect
137. C2×#6460C22semidirect
138. C2×#6458C22semidirect
139. #90195C22semidirect
140. C2×#6449C22semidirect
141. C2×#6445C22semidirect
142. #90177C22semidirect
143. C4×#1157C22semidirect
144. C2×C4×D28C22semidirect
156. C2×C7×#41C23semidirect
157. C2×C7×#41C23semidirect
159. C22×C7×Q8C23semidirect
163. C22×C7×D4C23semidirect
166. C23×C4×C7C23semidirect
172. C22×C22⋊D7C23semidirect
189. C2×#1161C23semidirect
190. C2×#1161C23semidirect
194. C2×Q8×D7C23semidirect
195. C2×Q8×D7C23semidirect
205. C2×#1159C23semidirect
206. C2×#1159C23semidirect
207. C2×#1159C23semidirect
216. C2×D4×D7C23semidirect
217. C2×D4×D7C23semidirect
218. C2×D4×D7C23semidirect
222. C2×#1157D4semidirect
231. C2×#1157C23semidirect
232. C2×#1157C23semidirect
233. C2×#1157C23semidirect
234. C2×#1157C23semidirect
235. C2×#1157C23semidirect
236. C2×#1157C23semidirect
240. C22×D28C23semidirect
241. C22×D28C23semidirect
257. C22×C4×D7C23semidirect
258. C22×C4×D7C23semidirect
261. C22×Dic14C23semidirect
262. C22×Dic14C23semidirect
263. C7×C4⋊Q8C23semidirect
264. C7×#127C23semidirect
265. C7×#124C23semidirect
266. C7×#124C23semidirect
268. C7×#123C23semidirect
269. C7×C22⋊Q8C23semidirect
270. C7×C22⋊Q8C23semidirect
271. C7×#121C23semidirect
272. C7×#121C23semidirect
273. C7×#121C23semidirect
275. C7×#120C23semidirect
276. C4×C7×D4C23semidirect
279. C7×#117C23semidirect
280. C7×#117C23semidirect
281. C2×C7×C4⋊C4C23semidirect
283. C2×C42×C7C23semidirect
286. C2×C22⋊Dic7C23semidirect
287. #6510C23semidirect
290. #6509C23semidirect
291. #6509C23semidirect
292. #6509C23semidirect
293. #6507C23semidirect
294. #6503C23semidirect
295. #6503C23semidirect
296. #6502C23semidirect
297. #6502C23semidirect
298. #6502C23semidirect
301. #6501C23semidirect
302. #6501C23semidirect
303. #6501C23semidirect
304. #6501C23semidirect
309. #6500C23semidirect
310. #6500C23semidirect
311. #6499C23semidirect
314. #6498C23semidirect
315. #6498C23semidirect
316. D4×Dic7C23semidirect
317. #6493C23semidirect
321. C4×C22⋊D7C23semidirect
322. C4×C22⋊D7C23semidirect
323. C4×C22⋊D7C23semidirect
324. C4×C22⋊D7C23semidirect
327. C2×(C2×D7)⋊C4C23semidirect
330. #6489C23semidirect
331. #6489C23semidirect
332. C2×C4⋊Dic7C23semidirect
333. C2×C4⋊Dic7C23semidirect
334. #6487C23semidirect
335. C2×Dic7⋊C4C23semidirect
336. C2×C4×Dic7C23semidirect
339. #6460C23semidirect
340. #6460C23semidirect
342. #6459C23semidirect
345. #6458C23semidirect
346. #6458C23semidirect
347. #6458C23semidirect
348. #6457C23semidirect
349. #6457C23semidirect
351. #6456C23semidirect
352. #6455C23semidirect
353. D7×C4⋊C4C23semidirect
354. D7×C4⋊C4C23semidirect
355. #6451C23semidirect
356. #6450C23semidirect
359. #6449C23semidirect
360. #6448C23semidirect
361. #6448C23semidirect
363. #6447C23semidirect
364. #6447C23semidirect
365. #6447C23semidirect
366. #6446C23semidirect
367. #6446C23semidirect
372. #6445C23semidirect
374. (C22⋊D7)⋊C4C23semidirect
375. (C22⋊D7)⋊C4C23semidirect
378. D7×C22⋊C4C23semidirect
379. #6441C23semidirect
380. #6441C23semidirect
384. C4×D28C23semidirect
385. C4×D28C23semidirect
386. C4×D28C23semidirect
387. #6435C23semidirect
388. C42×D7C23semidirect
389. C4×Dic14C23semidirect
406. #3449D7semidirect
455. C22×C4×C7C2×D4semidirect
474. C2×C22⋊D7C2×D4semidirect
532. #1157C2×D4semidirect
533. #1157C2×D4semidirect
534. #1157C2×D4semidirect
535. #1157C2×D4semidirect
540. C2×D28C2×D4semidirect
563. C2×C4×D7C2×D4semidirect
584. C2×Dic14C2×D4semidirect
646. C22×#41C2×D7semidirect
647. C22×#41C2×D7semidirect
680. #537C2×D7semidirect
685. #536C2×D7semidirect
686. #536C2×D7semidirect
691. #535C2×D7semidirect
692. #535C2×D7semidirect
696. #534C2×D7semidirect
699. #532C2×D7semidirect
720. #525C2×D7semidirect
721. #525C2×D7semidirect
746. C2×#117C2×D7semidirect
928. C2×#41C22×D7semidirect
929. C2×#41C22×D7semidirect
940. C22×Q8C22×D7semidirect
966. C22×D4C22×D7semidirect
988. C23×C4C22×D7semidirect
991. C4⋊Q8C22×D7semidirect
994. #127C22×D7semidirect
999. #124C22×D7semidirect
1000. #124C22×D7semidirect
1014. #123C22×D7semidirect
1029. C22⋊Q8C22×D7semidirect
1030. C22⋊Q8C22×D7semidirect
1050. #121C22×D7semidirect
1051. #121C22×D7semidirect
1052. #121C22×D7semidirect
1066. #120C22×D7semidirect
1086. C4×D4C22×D7semidirect
1096. #117C22×D7semidirect
1097. #117C22×D7semidirect
1103. C2×C4⋊C4C22×D7semidirect
1115. C2×C42C22×D7semidirect
1147. C2×D7#585semidirect
1326. C22×C4D4×D7semidirect
1509. C7#62811semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#906162
C22×D7×#412
C7×#34492
#117443362
C2×#905192
#117434482
#117434472
#117434242
#117434232
#117434222
#117433992
#117433982
#117433832
#117433762
#117433642
#117433062
#117431052
#117431032
D7×#5252
C2×#902152
#117427992
#628117