Finite Group Databasebeta

← #14224934

Subgroups — #14224934

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3489C211yesmaximal, characteristic, complemented
2#11744332C211yesmaximal, characteristic, complemented
3#11741562C211yesmaximal, characteristic, complemented
4#11741559C211yesmaximal, characteristic, complemented
5#11741519C211yesmaximal, characteristic, complemented
6#11740874C212yesmaximal, complemented
7#11740873C212yesmaximal, complemented
8#11740872C211yesmaximal, characteristic, complemented
9#11740864C211yesmaximal, characteristic, complemented
10#11740858C212yesmaximal, complemented
11#11740856C211yesmaximal, characteristic, complemented
12#11740853C212yesmaximal, complemented
13#11740842C211yesmaximal, characteristic, complemented
14#11740380C212yesmaximal, complemented
15#11740377C212yesmaximal, complemented
16#11740370C211yesmaximal, characteristic, complemented
17#11740368C211yesmaximal, characteristic, complemented
18#11740187C212yesmaximal, complemented
19#11740184C212yesmaximal, complemented
20#11740177C211yesmaximal, characteristic, complemented
21C2×#89824C211yesmaximal, characteristic, complemented
22#11740019C211yesmaximal, characteristic, complemented
23#11740018C211yesmaximal, characteristic, complemented
24C2×C7×2−1+4C2211yescharacteristic
25C22×C7×#41C2211yescharacteristic
26C2×#6554C2211yescharacteristic
27C7×D4×Q8—21no—
28C7×#548—21no—
29C7×#547—22no—
30C7×#547—21no—
31C7×#546—22no—
32C7×#546—21no—
33C7×#537C2211yescharacteristic
34C7×#537C2212yes—
35C7×#536C2211yescharacteristic
36C7×#536C2212yes—
37C7×#525C2211yescharacteristic
38C7×#525C2212yes—
39C2×C7×C22⋊Q8C2211yescharacteristic
40C2×C7×C22⋊Q8C2212yes—
41C7×#520C2211yescharacteristic
42#90524C2211yescharacteristic
43#90524C2212yes—
44#90522—21no—
45#90518C2211yescharacteristic
46#90516C2211yescharacteristic
47#90516C2212yes—
48#90515—22no—
49#90515—21no—
50C2×#6514C2211yescharacteristic, complemented
51C2×#6513C2211yescharacteristic, complemented
52Q8×C22⋊D7—21no—
53C22×#1144C2211yescharacteristic, complemented
54C2×#6505C2211yescharacteristic, complemented
55#90497—21no—
56#90497—22no—
57#90482C2211yescharacteristic
58#90482C2212yes—
59C2×#6487C2211yescharacteristic
60C2×#6487C2212yes—
61C22×#1136C2211yescharacteristic
62C22×#1136C2211yescharacteristic
63#90011C2212yescomplemented
64#90011C2212yescomplemented
65#90011C2212yescomplemented
66#90010C2212yescomplemented
67#90006C2211yescharacteristic
68#90006C2211yescharacteristic
69#90006C2211yescharacteristic
70#90006C2212yes—
71#90006C2211yescharacteristic
72#90006C2212yes—
73#90005C2211yescharacteristic, complemented
74#90004C2211yescharacteristic, complemented
75#90000C2212yescomplemented
76#90000C2212yescomplemented
77#90000C2212yescomplemented
78#89999C2212yescomplemented
79#89997C2211yescharacteristic, complemented
80C2×#6409C2211yescharacteristic, complemented
81#89979C2212yes—
82#89979C2212yes—
83#89824C2212yes—
84#89824C2212yes—
85#89824C2212yes—
86#89824C2212yes—
87#89824C2211yescharacteristic
88#89824C2212yescomplemented
89#89824C2212yescomplemented
90#89824C2211yescharacteristic, complemented
91#89823C2212yescomplemented
92#89823C2212yescomplemented
93#89822C2212yescomplemented
94#89822C2212yescomplemented
95#89822C2212yescomplemented
96#89821C2212yes—
97#89821C2211yescharacteristic
98#89821C2211yescharacteristic, complemented
99#89820C2212yescomplemented
100#89819C2212yescomplemented
101#89819C2212yescomplemented
102#89819C2212yescomplemented
103#89817C2212yescomplemented
104#89817C2212yescomplemented
105#89817C2212yescomplemented
106#89816C2212yescomplemented
107#89815C2212yescomplemented
108#89815C2212yescomplemented
109#89814C2211yescharacteristic
110#89814C2212yes—
111#89814C2211yescharacteristic, complemented
112#89813C2212yescomplemented
113#89812C2212yescomplemented
114#89811C2211yescharacteristic
115#89811C2211yescharacteristic, complemented
116#89809C2212yescomplemented
117#89807C2212yescomplemented
118#89806C2212yescomplemented
119#89776C2211yescharacteristic, complemented
120#89775C2212yescomplemented
121#89774C2211yescharacteristic, complemented
122#89770C2211yescharacteristic, complemented
123#89768C2212yescomplemented
124#89768C2212yescomplemented
125#89768C2212yescomplemented
126#89767C2211yescharacteristic, complemented
127#89743C2212yescomplemented
128#89743C2212yescomplemented
129#89742C2212yescomplemented
130C2×#6384C2211yescharacteristic, complemented
131#89740C2212yescomplemented
132#89738C2211yescharacteristic, complemented
133#89736C2211yescharacteristic, complemented
134C2×#6382C2211yescharacteristic, complemented
135#60773—71nomaximal, Sylow
136C7×2−1+4—42no—
137C7×2−1+4—42no—
138C2×C7×#41—22no—
139C2×C7×#41—21no—
140C2×C7×#41—42no—
141C2×C7×#41—42no—
142C2×C7×#41D412yes—
143C2×C7×#41D411yescharacteristic
144C2×C7×#41D411yescharacteristic
145C2×C7×#41C2311yescharacteristic
146C2×C7×#41C2312yes—
147C2×C7×#41C2311yescharacteristic
148C2×C7×#41C2311yescharacteristic
149C2×C7×#41C2312yes—
150C22×C7×Q8—21no—
151C22×C7×Q8D411yescharacteristic
152C22×C7×Q8C2311yescharacteristic
153C22×C7×Q8C2312yes—
154C22×C7×D4D411yescharacteristic
155C22×C7×D4D412yes—
156C23×C4×C7C2311yescharacteristic
157C23×C4×C7C2312yes—
158#6554—42no—
159#6554—42no—
160C2×Q8×D7—21no—
161C2×#1159—22no—
162C2×#1159—21no—
163C2×#1157C2311yescharacteristic
164C2×#1157C2312yes—
165C22×Dic14C2311yescharacteristic
166C22×Dic14C2312yes—
167C7×C4⋊Q8—21no—
168C7×C4⋊Q8—22no—
169C7×#124—21no—
170C7×#124—22no—
171C7×#123—22no—
172C7×#123—22no—
173C7×#123—22no—
174C7×#123—21no—
175C7×#123—22no—
176C7×C22⋊Q8—21no—
177C7×C22⋊Q8—22no—
178C7×C22⋊Q8—21no—
179C7×C22⋊Q8—22no—
180C7×C22⋊Q8—21no—
181C7×C22⋊Q8—22no—
182C7×C22⋊Q8C2312yes—
183C7×C22⋊Q8C2311yescharacteristic
184C7×C22⋊Q8C2312yes—
185C7×C22⋊Q8C2312yes—
186C7×C22⋊Q8C2312yes—
187C7×C22⋊Q8C2312yes—
188C7×C22⋊Q8C2311yescharacteristic
189C7×#121—22no—
190C7×#121—22no—
191C7×#121—22no—
192C7×#121—21no—
193C7×#121—22no—
194C7×#121C2311yescharacteristic
195C7×#121C2312yes—
196C7×#121C2311yescharacteristic
197C7×#120—21no—
198C7×#120—22no—
199C4×C7×Q8—21no—
200C4×C7×D4—22no—
201C4×C7×D4—21no—
202C4×C7×D4—21no—
203C4×C7×D4—22no—
204C4×C7×D4—21no—
205C4×C7×D4—22no—
206C7×#117C2311yescharacteristic
207C7×#117C2312yes—
208C2×C7×C4⋊C4—21no—
209C2×C7×C4⋊C4—22no—
210C2×C7×C4⋊C4C2311yescharacteristic
211C2×C7×C4⋊C4C2312yes—
212C2×C7×C22⋊C4—21no—
213C2×C7×C22⋊C4—22no—
214#6516—21no—
215#6516—22no—
216C2×C22⋊Dic7—21no—
217C2×C22⋊Dic7—22no—
218#6514—42no—
219#6513—42no—
220#6509—21no—
221#6509—22no—
222Q8×Dic7—21no—
223#6507—21no—
224#6507—22no—
225C2×#1144—42no—
226C2×#1144C2312yes—
227C2×#1144C2312yes—
228C2×#1144C2312yes—
229C2×#1144C2311yescharacteristic
230C2×#1144C2312yes—
231#6505—42no—
232C2×#1143C2312yes—
233C2×#1143C2311yescharacteristic
234#6502—22no—
235#6502—22no—
236#6502—22no—
237#6501—21no—
238#6501—22no—
239#6499—21no—
240#6499—22no—
241#6498—22no—
242#6498—22no—
243#6498—22no—
244D4×Dic7—22no—
245D4×Dic7—21no—
246C2×#1142C2311yescharacteristic
247C2×#1142C2312yes—
248C2×#1141C2311yescharacteristic
249#6493C2311yescharacteristic
250#6493C2312yes—
251#6493C2311yescharacteristic
252#6492—21no—
253#6492—22no—
254C4×C22⋊D7—21no—
255C4×C22⋊D7—22no—
256C4×C22⋊D7—21no—
257C4×C22⋊D7—22no—
258#6489C2311yescharacteristic
259#6489C2312yes—
260C2×C4⋊Dic7C2311yescharacteristic
261C2×C4⋊Dic7C2312yes—
262#6487—21no—
263#6487—22no—
264#6487—21no—
265#6487—22no—
266#6487C2312yes—
267#6487C2311yescharacteristic
268#6487C2312yes—
269#6487C2312yes—
270#6487C2312yes—
271#6487C2312yes—
272#6487C2311yescharacteristic
273C2×Dic7⋊C4—21no—
274C2×Dic7⋊C4—22no—
275C2×#1136—42no—
276C2×#1136—42no—
277C2×#1136C2311yescharacteristic
278C2×#1136C2311yescharacteristic
279C2×#1136C2311yescharacteristic
280C2×#1136C2312yes—
281C2×#1136C2311yescharacteristic
282C2×#1136C2311yescharacteristic
283C2×#1136C2311yescharacteristic
284C22×C7⋊C8C2311yescharacteristic
285C22×C7⋊C8C2311yescharacteristic
286C22×C7⋊C8C2312yes—
287#6409C2312yes—
288#6409C2312yes—
289#6409C2312yes—
290#6409C2312yes—
291#6409C2312yes—
292#6409C2311yescharacteristic
293#6409C2311yescharacteristic
294#6406C2312yes—
295#6406C2311yescharacteristic
296#6406C2311yescharacteristic
297C22⋊(C7⋊C8)C2312yes—
298C22⋊(C7⋊C8)C2312yes—
299C22⋊(C7⋊C8)C2312yes—
300C22⋊(C7⋊C8)C2312yes—
301C22⋊(C7⋊C8)C2312yes—
302C22⋊(C7⋊C8)C2312yes—
303C22⋊(C7⋊C8)C2312yes—
304C22⋊(C7⋊C8)C2312yes—
305#6384C2312yes—
306#6384C2312yes—
307#6384C2312yes—
308#6384C2312yes—
309#6384C2311yescharacteristic
310#6384C2311yescharacteristic
311#6384C2312yes—
312#6383C2312yes—
313#6383C2311yescharacteristic
314#6383C2311yescharacteristic
315#6382C2312yes—
316#6382C2312yes—
317#6382C2312yes—
318#6382C2312yes—
319#6382C2311yescharacteristic
320#6382C2311yescharacteristic
321#6381C2312yes—
322#6381C2311yescharacteristic
323#6381C2312yes—
324#6381C2311yescharacteristic
325#3489—71no—
326#3489D711yescharacteristic, complemented
327#3204—72no—
328#3202—72no—
329#3201—72no—
330#3201—72no—
331#3197—72no—
332#3196—72no—
333#3196—72no—
334#3195—72no—
335#3099—71no—
336#3099—71no—
337#3097—71no—
338#3097—71no—
339#3056—71no—
340#3056—71no—
341#3054—71no—
342C2×#470—71no—
343#3013—71no—
344#3013—71no—
345#3011—71no—
346#3011—71no—
347#2879—71no—
348C24×C7C2×D411yescharacteristic
349C24×C7C2×D412yes—
350C7×#41—22no—
351C7×#41—22no—
352C7×#41—22no—
353C7×#41—22no—
354C7×#41—22no—
355C7×#41—22no—
356C7×#41—42no—
357C7×#41—42no—
358C7×#41—44no—
359C7×#41—42no—
360C7×#41—42no—
361C7×#41—42no—
362C7×#41—42no—
363C7×#41—48no—
364C7×#41—44no—
365C2×C7×Q8—22no—
366C2×C7×Q8—21no—
367C2×C7×Q8—22no—
368C2×C7×Q8—22no—
369C2×C7×Q8—42no—
370C2×C7×Q8—42no—
371C2×C7×Q8—42no—
372C2×C7×Q8—44no—
373C2×C7×Q8C2×D411yescharacteristic
374C2×C7×Q8C2×D411yescharacteristic
375C2×C7×Q8C2×D412yes—
376C2×C7×Q8C2412yes—
377C2×C7×Q8C2411yescharacteristic
378C2×C7×D4—21no—
379C2×C7×D4—22no—
380C2×C7×D4—21no—
381C2×C7×D4—21no—
382C2×C7×D4—22no—
383C2×C7×D4—42no—
384C2×C7×D4—44no—
385C2×C7×D4C2×D412yes—
386C2×C7×D4C2×D411yescharacteristic
387C2×C7×D4C2×D412yes—
388C2×C7×D4C2×D411yescharacteristic
389C2×C7×D4C2×D412yes—
390C2×C7×D4C2×D412yes—
391C2×C7×D4C2×D412yes—
392C2×C7×D4C2411yescharacteristic
393C22×C4×C7—22no—
394C22×C4×C7—22no—
395C22×C4×C7—22no—
396C22×C4×C7—21no—
397C22×C4×C7—22no—
398C22×C4×C7—21no—
399C22×C4×C7—22no—
400C22×C4×C7—21no—
401C22×C4×C7—42no—
402C22×C4×C7—42no—
403C22×C4×C7C2×D411yescharacteristic
404C22×C4×C7C2×D411yescharacteristic
405C22×C4×C7C2×D411yescharacteristic
406C22×C4×C7C2×D412yes—
407C22×C4×C7C2×D412yes—
408C22×C4×C7C2×D412yes—
409C22×C4×C7C2412yes—
410C22×C4×C7C2412yes—
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2411yescharacteristic
413C22×C4×C7C2411yescharacteristic
414C2×C22⋊D7—21no—
415C2×C22⋊D7—22no—
416C2×C22⋊D7—21no—
417C2×C22⋊D7—21no—
418C2×C22⋊D7—22no—
419C22×Dic7—22no—
420C22×Dic7—21no—
421C22×Dic7—22no—
422C22×Dic7—21no—
423Q8×D7—44no—
424#1159—48no—
425#1159—44no—
426#1157—22no—
427#1157—22no—
428#1157—42no—
429#1157—42no—
430C2×D28C2411yescharacteristic
431C2×C4×D7—22no—
432C2×C4×D7—21no—
433C2×Dic14—22no—
434C2×Dic14—22no—
435C2×Dic14—22no—
436C2×Dic14—21no—
437C2×Dic14—42no—
438C2×Dic14—42no—
439C2×Dic14C2412yes—
440C2×Dic14C2411yescharacteristic
441C7×C4⋊C4—22no—
442C7×C4⋊C4—21no—
443C7×C4⋊C4—22no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—22no—
447C7×C4⋊C4—21no—
448C7×C4⋊C4—22no—
449C7×C4⋊C4—21no—
450C7×C4⋊C4C2412yes—
451C7×C4⋊C4C2411yescharacteristic
452C7×C4⋊C4C2411yescharacteristic
453C7×C22⋊C4—22no—
454C7×C22⋊C4—21no—
455C7×C22⋊C4—22no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—22no—
458C7×C22⋊C4—22no—
459C7×C22⋊C4—21no—
460C7×C22⋊C4—21no—
461C7×C22⋊C4—22no—
462C7×C22⋊C4—21no—
463C7×C22⋊C4—22no—
464C7×C22⋊C4—21no—
465C42×C7—22no—
466C42×C7—21no—
467C22⋊Dic7—22no—
468C22⋊Dic7—21no—
469C22⋊Dic7—22no—
470C22⋊Dic7—22no—
471C22⋊Dic7—22no—
472C22⋊Dic7—21no—
473C22⋊Dic7—22no—
474C22⋊Dic7—22no—
475C22⋊Dic7—21no—
476#1144—42no—
477#1144—42no—
478#1144—42no—
479#1144—41no—
480#1144—42no—
481#1143—42no—
482#1143—41no—
483#1142—41no—
484#1142—42no—
485#1141—41no—
486(C2×D7)⋊C4—21no—
487(C2×D7)⋊C4—22no—
488(C2×D7)⋊C4—21no—
489C4⋊Dic7—22no—
490C4⋊Dic7—21no—
491C4⋊Dic7C2412yes—
492C4⋊Dic7C2411yescharacteristic
493C4⋊Dic7C2411yescharacteristic
494Dic7⋊C4—22no—
495Dic7⋊C4—21no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—22no—
500Dic7⋊C4—21no—
501C4×Dic7—22no—
502C4×Dic7—21no—
503#1136—22no—
504#1136—22no—
505#1136—41no—
506#1136—41no—
507#1136—41no—
508#1136—41no—
509#1136—42no—
510C2×C7⋊C8—22no—
511C2×C7⋊C8—22no—
512C2×C7⋊C8—42no—
513C2×C7⋊C8C2412yes—
514C2×C7⋊C8C2411yescharacteristic
515C2×C7⋊C8C2411yescharacteristic
516C2×C7⋊C8C2411yescharacteristic
517C2×C7⋊C8C2411yescharacteristic
518C2×C7⋊C8C2412yes—
519C2×2−1+4—71no—
520C2×2−1+4C2×D711yescharacteristic
521C22×#41C2×D711yescharacteristic
522C2×#137—71no—
523C2×#137—71no—
524C2×#135—71no—
525C22×Q16—71no—
526C22×M16—71no—
527C22×M16—71no—
528D4×Q8—21no—
529D4×Q8—141no—
530#548—21no—
531#548—141no—
532#547—22no—
533#547—21no—
534#547—142no—
535#547—141no—
536#546—22no—
537#546—21no—
538#546—142no—
539#546—141no—
540#537—71no—
541#537—72no—
542#537C2×D711yescharacteristic
543#537C2×D712yes—
544#536—71no—
545#536—72no—
546#536C2×D711yescharacteristic
547#536C2×D712yes—
548#525—72no—
549#525—71no—
550#525C2×D712yes—
551#525C2×D711yescharacteristic
552C2×C22⋊Q8—72no—
553C2×C22⋊Q8—71no—
554C2×C22⋊Q8C2×D712yes—
555C2×C22⋊Q8C2×D711yescharacteristic
556#520—71no—
557#520C2×D711yescharacteristic
558#485—72no—
559#485—72no—
560#485—72no—
561#485—72no—
562#485—72no—
563#485—72no—
564#484—72no—
565#484—72no—
566#483—72no—
567#483—72no—
568#483—72no—
569#483—72no—
570#482—72no—
571#482—72no—
572#481—72no—
573#481—72no—
574#470—71no—
575#470—72no—
576#470—72no—
577#470—72no—
578#470—72no—
579#470—72no—
580#470—71no—
581#470—72no—
582#469—71no—
583#469—71no—
584#468—71no—
585#468—72no—
586#468—71no—
587#468—71no—
588#468—72no—
589#468—71no—
590#467—72no—
591#467—72no—
592#465—72no—
593#465—72no—
594#452—72no—
595#452—72no—
596#452—72no—
597#452—72no—
598#452—72no—
599#452—72no—
600#451—72no—
601#451—72no—
602#451—72no—
603#451—72no—
604#451—72no—
605#451—72no—
606#449—72no—
607#449—72no—
608#448—72no—
609#448—72no—
610#428—71no—
611#428—71no—
612#427—71no—
613C2×#106—71no—
614#419—71no—
615#419—71no—
616#417—71no—
617#417—71no—
618#416—71no—
619#416—71no—
620C2×#103—71no—
621C2×#103—71no—
622#408—71no—
623#408—71no—
624#408—71no—
625#408—71no—
626#408—72no—
627#408—72no—
628#407—72no—
629#407—72no—
630C23×C7—22no—
631C23×C7—21no—
632C23×C7—42no—
633C23×C7—41no—
634C23×C7—41no—
635C23×C7—42no—
636C23×C7—42no—
637C23×C7C22×D411yescharacteristic
638C23×C7C22×D411yescharacteristic
639C23×C7C22×D412yes—
640C23×C7C22×D412yes—
641C23×C7C22×D411yescharacteristic
642C22×D7—21no—
643C7×Q8—22no—
644C7×Q8—22no—
645C7×Q8—22no—
646C7×Q8—21no—
647C7×Q8—22no—
648C7×Q8—21no—
649C7×Q8—42no—
650C7×Q8—44no—
651C7×Q8—42no—
652C7×D4—24no—
653C7×D4—24no—
654C7×D4—22no—
655C7×D4—22no—
656C7×D4—21no—
657C7×D4—21no—
658C7×D4—42no—
659C7×D4—42no—
660C7×D4—42no—
661C7×D4—42no—
662C7×D4—44no—
663C7×D4—42no—
664C7×D4—81no—
665C7×D4—82no—
666C2×C4×C7—22no—
667C2×C4×C7—22no—
668C2×C4×C7—22no—
669C2×C4×C7—21no—
670C2×C4×C7—21no—
671C2×C4×C7—21no—
672C2×C4×C7—21no—
673C2×C4×C7—22no—
674C2×C4×C7—22no—
675C2×C4×C7—22no—
676C2×C4×C7—22no—
677C2×C4×C7—21no—
678C2×C4×C7—22no—
679C2×C4×C7—21no—
680C2×C4×C7—22no—
681C2×C4×C7—21no—
682C2×C4×C7—42no—
683C2×C4×C7—42no—
684C2×C4×C7—42no—
685C2×C4×C7—44no—
686C2×C4×C7—44no—
687C2×C4×C7—42no—
688C2×C4×C7—42no—
689C2×C4×C7—81no—
690C2×C4×C7—82no—
691C2×C4×C7C22×D412yes—
692C2×C4×C7C22×D412yes—
693C2×C4×C7C22×D411yescharacteristic
694C2×C4×C7C22×D411yescharacteristic
695C2×C4×C7C22×D411yescharacteristic
696C2×C4×C7H(5,𝔽2)12yes—
697C2×C4×C7H(5,𝔽2)12yes—
698C2×C4×C7C2511yescharacteristic
699C22⋊D7—44no—
700C22⋊D7—42no—
701C22⋊D7—42no—
702C22⋊D7—81no—
703C22⋊D7—82no—
704C2×Dic7—21no—
705C2×Dic7—22no—
706C2×Dic7—21no—
707C2×Dic7—22no—
708C2×Dic7—21no—
709C2×Dic7—44no—
710C2×Dic7—42no—
711C2×Dic7—81no—
712C2×Dic7—82no—
713D28—21no—
714D28—21no—
715C4×D7—44no—
716C4×D7—42no—
717Dic14—22no—
718Dic14—21no—
719Dic14—22no—
720Dic14—21no—
721Dic14—44no—
722Dic14—42no—
723C7⋊C8—21no—
724C7⋊C8—21no—
725C7⋊C8—21no—
726C7⋊C8—21no—
727C7⋊C8—22no—
728C7⋊C8—22no—
7292−1+4—42no—
7302−1+4—42no—
7312−1+4—282no—
7322−1+4—282no—
733C2×#41—22no—
734C2×#41—21no—
735C2×#41—42no—
736C2×#41—42no—
737C2×#41—71no—
738C2×#41—72no—
739C2×#41—142no—
740C2×#41—141no—
741C2×#41C22⋊D712yes—
742C2×#41C22⋊D711yescharacteristic
743C2×#41C22⋊D711yescharacteristic
744C2×#41C22×D711yescharacteristic
745C2×#41C22×D712yes—
746C2×#41C22×D711yescharacteristic
747C2×#41C22×D711yescharacteristic
748C2×#41C22×D712yes—
749C22×Q8—21no—
750C22×Q8—71no—
751C22×Q8—72no—
752C22×Q8—141no—
753C22×Q8C22⋊D711yescharacteristic
754C22×Q8C22×D711yescharacteristic
755C22×Q8C22×D712yes—
756C22×D4C22⋊D711yescharacteristic
757C22×D4C22⋊D712yes—
758C23×C4C22×D711yescharacteristic
759C23×C4C22×D712yes—
760#137—282no—
761#137—282no—
762#135—282no—
763C2×Q16—72no—
764C2×Q16—72no—
765C2×Q16—71no—
766C2×Q16—72no—
767C2×Q16—72no—
768C2×Q16—282no—
769C2×SD16—71no—
770C2×SD16—72no—
771C2×SD16—71no—
772C2×SD16—72no—
773C2×D8—71no—
774C2×M16—71no—
775C2×M16—71no—
776C2×M16—71no—
777C2×M16—72no—
778C2×M16—71no—
779C2×M16—71no—
780C2×M16—71no—
781C2×M16—282no—
782C2×M16—282no—
783C22×C8—71no—
784C22×C8—71no—
785C22×C8—72no—
786C4⋊Q8—21no—
787C4⋊Q8—22no—
788C4⋊Q8—141no—
789C4⋊Q8—142no—
790#124—21no—
791#124—22no—
792#124—141no—
793#124—142no—
794#123—22no—
795#123—22no—
796#123—22no—
797#123—21no—
798#123—22no—
799#123—142no—
800#123—142no—
801#123—142no—
802#123—141no—
803#123—142no—
804C22⋊Q8—21no—
805C22⋊Q8—22no—
806C22⋊Q8—21no—
807C22⋊Q8—22no—
808C22⋊Q8—21no—
809C22⋊Q8—22no—
810C22⋊Q8—71no—
811C22⋊Q8—72no—
812C22⋊Q8—72no—
813C22⋊Q8—72no—
814C22⋊Q8—72no—
815C22⋊Q8—72no—
816C22⋊Q8—71no—
817C22⋊Q8—141no—
818C22⋊Q8—142no—
819C22⋊Q8—141no—
820C22⋊Q8—142no—
821C22⋊Q8—141no—
822C22⋊Q8—142no—
823C22⋊Q8C22×D711yescharacteristic
824C22⋊Q8C22×D712yes—
825C22⋊Q8C22×D712yes—
826C22⋊Q8C22×D712yes—
827C22⋊Q8C22×D712yes—
828C22⋊Q8C22×D712yes—
829C22⋊Q8C22×D711yescharacteristic
830#121—22no—
831#121—22no—
832#121—22no—
833#121—21no—
834#121—22no—
835#121—71no—
836#121—72no—
837#121—71no—
838#121—142no—
839#121—142no—
840#121—142no—
841#121—141no—
842#121—142no—
843#121C22×D711yescharacteristic
844#121C22×D712yes—
845#121C22×D711yescharacteristic
846#120—21no—
847#120—22no—
848#120—141no—
849#120—142no—
850C4×Q8—21no—
851C4×Q8—141no—
852C4×D4—22no—
853C4×D4—21no—
854C4×D4—21no—
855C4×D4—22no—
856C4×D4—21no—
857C4×D4—22no—
858C4×D4—142no—
859C4×D4—141no—
860C4×D4—141no—
861C4×D4—142no—
862C4×D4—141no—
863C4×D4—142no—
864#117—71no—
865#117—72no—
866#117C22×D711yescharacteristic
867#117C22×D712yes—
868C2×C4⋊C4—21no—
869C2×C4⋊C4—22no—
870C2×C4⋊C4—71no—
871C2×C4⋊C4—72no—
872C2×C4⋊C4—141no—
873C2×C4⋊C4—142no—
874C2×C4⋊C4C22×D711yescharacteristic
875C2×C4⋊C4C22×D712yes—
876C2×C22⋊C4—21no—
877C2×C22⋊C4—22no—
878C2×C22⋊C4—141no—
879C2×C22⋊C4—142no—
880#107—71no—
881#107—71no—
882#107—72no—
883#107—72no—
884#106—72no—
885#106—72no—
886#106—71no—
887#106—71no—
888#106—72no—
889#106—72no—
890#103—72no—
891#103—72no—
892#103—71no—
893#103—71no—
894#103—72no—
895#103—72no—
896#103—72no—
897#103—72no—
898#103—72no—
899#103—71no—
900#103—71no—
901#103—72no—
902#103—72no—
903#103—72no—
904#102—71no—
905#102—71no—
906#102—72no—
907#102—71no—
908#102—71no—
909#102—72no—
910C22⋊C8—72no—
911C22⋊C8—72no—
912C22⋊C8—72no—
913C22⋊C8—72no—
914C22⋊C8—72no—
915C22⋊C8—72no—
916C22⋊C8—72no—
917C22⋊C8—72no—
918C22×C7—21no—
919C22×C7—21no—
920C22×C7—22no—
921C22×C7—21no—
922C22×C7—21no—
923C22×C7—22no—
924C22×C7—22no—
925C22×C7—21no—
926C22×C7—21no—
927C22×C7—22no—
928C22×C7—22no—
929C22×C7—21no—
930C22×C7—21no—
931C22×C7—22no—
932C22×C7—41no—
933C22×C7—41no—
934C22×C7—41no—
935C22×C7—82no—
936C22×C7—84no—
937C22×C7#53412yes—
938C22×C7C23×D411yescharacteristic
939C2×D7—41no—
940C2×D7—41no—
941C2×D7—41no—
942C4×C7—22no—
943C4×C7—21no—
944C4×C7—21no—
945C4×C7—22no—
946C4×C7—42no—
947C4×C7—41no—
948C4×C7—41no—
949C4×C7—42no—
950C4×C7—41no—
951C4×C7#53412yes—
952C4×C7C2×H(5,𝔽2)11yescharacteristic
953C4×C7C2×H(5,𝔽2)11yescharacteristic
954Dic7—42no—
955Dic7—41no—
956Dic7—41no—
957Dic7—42no—
958Dic7—41no—
959C24C2×C22⋊D711yescharacteristic
960C24C2×C22⋊D712yes—
961#41—22no—
962#41—22no—
963#41—22no—
964#41—22no—
965#41—22no—
966#41—22no—
967#41—42no—
968#41—42no—
969#41—44no—
970#41—42no—
971#41—42no—
972#41—42no—
973#41—42no—
974#41—48no—
975#41—44no—
976#41—142no—
977#41—142no—
978#41—282no—
979#41—282no—
980#41—288no—
981#41—284no—
982C2×Q8—22no—
983C2×Q8—21no—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—44no—
990C2×Q8—72no—
991C2×Q8—71no—
992C2×Q8—142no—
993C2×Q8—141no—
994C2×Q8—142no—
995C2×Q8—142no—
996C2×Q8—282no—
997C2×Q8—282no—
998C2×Q8—284no—
999C2×Q8C2×C22⋊D711yescharacteristic
1000C2×Q8C2×C22⋊D711yescharacteristic
1001C2×Q8C2×C22⋊D712yes—
1002C2×Q8C23×D712yes—
1003C2×Q8C23×D711yescharacteristic
1004C2×D4—21no—
1005C2×D4—22no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—22no—
1009C2×D4—42no—
1010C2×D4—44no—
1011C2×D4—71no—
1012C2×D4—141no—
1013C2×D4—142no—
1014C2×D4—141no—
1015C2×D4—141no—
1016C2×D4—142no—
1017C2×D4C2×C22⋊D712yes—
1018C2×D4C2×C22⋊D711yescharacteristic
1019C2×D4C2×C22⋊D712yes—
1020C2×D4C2×C22⋊D711yescharacteristic
1021C2×D4C2×C22⋊D712yes—
1022C2×D4C2×C22⋊D712yes—
1023C2×D4C2×C22⋊D712yes—
1024C2×D4C23×D711yescharacteristic
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—21no—
1029C22×C4—22no—
1030C22×C4—21no—
1031C22×C4—22no—
1032C22×C4—21no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—142no—
1036C22×C4—141no—
1037C22×C4—142no—
1038C22×C4—141no—
1039C22×C4—142no—
1040C22×C4—141no—
1041C22×C4C2×C22⋊D711yescharacteristic
1042C22×C4C2×C22⋊D711yescharacteristic
1043C22×C4C2×C22⋊D711yescharacteristic
1044C22×C4C2×C22⋊D712yes—
1045C22×C4C2×C22⋊D712yes—
1046C22×C4C2×C22⋊D712yes—
1047C22×C4C23×D712yes—
1048C22×C4C23×D712yes—
1049C22×C4C23×D711yescharacteristic
1050C22×C4C23×D711yescharacteristic
1051C22×C4C23×D711yescharacteristic
1052Q16—282no—
1053Q16—282no—
1054Q16—281no—
1055Q16—282no—
1056Q16—282no—
1057SD16—281no—
1058SD16—282no—
1059SD16—281no—
1060SD16—282no—
1061D8—281no—
1062M16—142no—
1063M16—142no—
1064M16—281no—
1065M16—281no—
1066M16—281no—
1067M16—281no—
1068M16—282no—
1069C2×C8—71no—
1070C2×C8—71no—
1071C2×C8—72no—
1072C2×C8—72no—
1073C2×C8—71no—
1074C2×C8—71no—
1075C2×C8—142no—
1076C2×C8—142no—
1077C2×C8—282no—
1078C4⋊C4—22no—
1079C4⋊C4—21no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—21no—
1085C4⋊C4—22no—
1086C4⋊C4—21no—
1087C4⋊C4—71no—
1088C4⋊C4—72no—
1089C4⋊C4—71no—
1090C4⋊C4—142no—
1091C4⋊C4—141no—
1092C4⋊C4—142no—
1093C4⋊C4—142no—
1094C4⋊C4—142no—
1095C4⋊C4—142no—
1096C4⋊C4—141no—
1097C4⋊C4—142no—
1098C4⋊C4—141no—
1099C4⋊C4C23×D711yescharacteristic
1100C4⋊C4C23×D712yes—
1101C4⋊C4C23×D711yescharacteristic
1102C22⋊C4—22no—
1103C22⋊C4—21no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—22no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—22no—
1111C22⋊C4—21no—
1112C22⋊C4—22no—
1113C22⋊C4—21no—
1114C22⋊C4—142no—
1115C22⋊C4—141no—
1116C22⋊C4—142no—
1117C22⋊C4—142no—
1118C22⋊C4—142no—
1119C22⋊C4—142no—
1120C22⋊C4—141no—
1121C22⋊C4—141no—
1122C22⋊C4—142no—
1123C22⋊C4—141no—
1124C22⋊C4—142no—
1125C22⋊C4—141no—
1126C42—22no—
1127C42—21no—
1128C42—142no—
1129C42—141no—
1130C2×C7—22no—
1131C2×C7—42no—
1132C2×C7—42no—
1133C2×C7—41no—
1134C2×C7—41no—
1135C2×C7—81no—
1136C2×C7C2×#53411yescharacteristic
1137C2×C7#358611yescharacteristic
1138C2×C7#358611yescharacteristic
1139D7—81no—
1140C23—22no—
1141C23—21no—
1142C23—42no—
1143C23—41no—
1144C23—41no—
1145C23—42no—
1146C23—42no—
1147C23—141no—
1148C23C22×C22⋊D711yescharacteristic
1149C23C22×C22⋊D711yescharacteristic
1150C23C22×C22⋊D712yes—
1151C23C22×C22⋊D712yes—
1152C23C22×C22⋊D711yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—21no—
1157Q8—22no—
1158Q8—21no—
1159Q8—42no—
1160Q8—44no—
1161Q8—42no—
1162Q8—142no—
1163Q8—141no—
1164Q8—142no—
1165Q8—141no—
1166Q8—284no—
1167Q8—282no—
1168D4—24no—
1169D4—24no—
1170D4—22no—
1171D4—22no—
1172D4—21no—
1173D4—21no—
1174D4—42no—
1175D4—42no—
1176D4—42no—
1177D4—42no—
1178D4—44no—
1179D4—42no—
1180D4—81no—
1181D4—82no—
1182D4—141no—
1183D4—141no—
1184D4—282no—
1185D4—284no—
1186D4—282no—
1187D4—561no—
1188D4—562no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—81no—
1213C2×C4—82no—
1214C2×C4—141no—
1215C2×C4—142no—
1216C2×C4—141no—
1217C2×C4—142no—
1218C2×C4—141no—
1219C2×C4—284no—
1220C2×C4—284no—
1221C2×C4—282no—
1222C2×C4—282no—
1223C2×C4—561no—
1224C2×C4—562no—
1225C2×C4#654812yes—
1226C2×C4#654812yes—
1227C2×C4C22×C22⋊D712yes—
1228C2×C4C22×C22⋊D712yes—
1229C2×C4C22×C22⋊D711yescharacteristic
1230C2×C4C22×C22⋊D711yescharacteristic
1231C2×C4C22×C22⋊D711yescharacteristic
1232C2×C4C24×D711yescharacteristic
1233C8—141no—
1234C8—141no—
1235C8—141no—
1236C8—141no—
1237C8—142no—
1238C8—142no—
1239C7#6077311yescharacteristic, complemented, Sylow
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—21no—
1248C22—21no—
1249C22—22no—
1250C22—22no—
1251C22—21no—
1252C22—22no—
1253C22—21no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—82no—
1258C22—84no—
1259C22—281no—
1260C22—281no—
1261C22—281no—
1262C22#9049512yes—
1263C22C23×C22⋊D711yescharacteristic
1264C4—21no—
1265C4—21no—
1266C4—22no—
1267C4—22no—
1268C4—42no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—282no—
1274C4—281no—
1275C4—282no—
1276C4—281no—
1277C4—281no—
1278C4#9049512yes—
1279C4C2×#654811yescharacteristic
1280C4C2×#654811yescharacteristic
1281C2—22no—
1282C2—41no—
1283C2—41no—
1284C2—42no—
1285C2—42no—
1286C2—81no—
1287C2—561no—
1288C2C2×#9049511yescharacteristic
1289C2#1174435511yescharacteristic
1290C2#1174436711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC7×#3489C2
socleC22×C7C23×D4
hypercenter#3489D7
hypocenterC7#60773
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C7×#3489C2semidirect
2. #11744332C2semidirect
3. #11741562C2semidirect
4. #11741559C2semidirect
5. #11741519C2semidirect
6. #11740874C2semidirect
7. #11740873C2semidirect
8. #11740872C2semidirect
9. #11740864C2semidirect
10. #11740858C2semidirect
11. #11740856C2semidirect
12. #11740853C2semidirect
13. #11740842C2semidirect
14. #11740380C2semidirect
15. #11740377C2semidirect
16. #11740370C2semidirect
17. #11740368C2semidirect
18. #11740187C2semidirect
19. #11740184C2semidirect
20. #11740177C2semidirect
21. C2×#89824C2semidirect
22. #11740019C2semidirect
23. #11740018C2semidirect
50. C2×#6514C22semidirect
51. C2×#6513C22semidirect
53. C22×#1144C22semidirect
54. C2×#6505C22semidirect
63. #90011C22semidirect
64. #90011C22semidirect
65. #90011C22semidirect
66. #90010C22semidirect
73. #90005C22semidirect
74. #90004C22semidirect
75. #90000C22semidirect
76. #90000C22semidirect
77. #90000C22semidirect
78. #89999C22semidirect
79. #89997C22semidirect
80. C2×#6409C22semidirect
88. #89824C22semidirect
89. #89824C22semidirect
90. #89824C22semidirect
91. #89823C22semidirect
92. #89823C22semidirect
93. #89822C22semidirect
94. #89822C22semidirect
95. #89822C22semidirect
98. #89821C22semidirect
99. #89820C22semidirect
100. #89819C22semidirect
101. #89819C22semidirect
102. #89819C22semidirect
103. #89817C22semidirect
104. #89817C22semidirect
105. #89817C22semidirect
106. #89816C22semidirect
107. #89815C22semidirect
108. #89815C22semidirect
111. #89814C22semidirect
112. #89813C22semidirect
113. #89812C22semidirect
115. #89811C22semidirect
116. #89809C22semidirect
117. #89807C22semidirect
118. #89806C22semidirect
119. #89776C22semidirect
120. #89775C22semidirect
121. #89774C22semidirect
122. #89770C22semidirect
123. #89768C22semidirect
124. #89768C22semidirect
125. #89768C22semidirect
126. #89767C22semidirect
127. #89743C22semidirect
128. #89743C22semidirect
129. #89742C22semidirect
130. C2×#6384C22semidirect
131. #89740C22semidirect
132. #89738C22semidirect
133. #89736C22semidirect
134. C2×#6382C22semidirect
326. #3489D7semidirect
1239. C7#60773semidirect

Maximal subgroups

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

subgroupindex
C7×#34892
#117443322
#117415622
#117415592
#117415192
#117408742
#117408732
#117408722
#117408642
#117408582
#117408562
#117408532
#117408422
#117403802
#117403772
#117403702
#117403682
#117401872
#117401842
#117401772
C2×#898242
#117400192
#117400182
#607737