Finite Group Databasebeta

← #14224718

Subgroups — #14224718

Order 1792.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3449C211yesmaximal, characteristic, complemented
2#11744332C211yesmaximal, characteristic, complemented
3C2×#90011C211yesmaximal, characteristic, complemented
4#11741526C211yesmaximal, characteristic, complemented
5#11741520C211yesmaximal, characteristic, complemented
6#11740874C212yesmaximal, complemented
7#11740873C212yesmaximal, complemented
8#11740873C212yesmaximal, complemented
9#11740871C212yesmaximal, complemented
10#11740856C211yesmaximal, characteristic, complemented
11#11740845C211yesmaximal, characteristic, complemented
12#11740844C211yesmaximal, characteristic, complemented
13#11740842C211yesmaximal, characteristic, complemented
14#11740835C211yesmaximal, characteristic, complemented
15#11740824C211yesmaximal, characteristic, complemented
16#11740822C211yesmaximal, characteristic, complemented
17#11740821C211yesmaximal, characteristic, complemented
18#11740380C212yesmaximal, complemented
19#11740379C212yesmaximal, complemented
20#11740377C212yesmaximal, complemented
21#11740375C212yesmaximal, complemented
22#11739665C211yesmaximal, characteristic, complemented
23#11739660C211yesmaximal, characteristic, complemented
24C22×C7×#41C2211yescharacteristic
25C22×C7×#41C2211yescharacteristic
26C2×#6554C2211yescharacteristic
27C7×#537C2212yes—
28C7×#537C2212yes—
29C7×#536—21no—
30C7×#536C2211yescharacteristic
31C7×#536C2211yescharacteristic
32C7×#535—21no—
33C7×#535C2211yescharacteristic
34C7×#535C2211yescharacteristic
35C7×#534—22no—
36C7×#532—21no—
37C7×#532—21no—
38C7×#525—22no—
39C7×#525C2212yes—
40C7×#525C2212yes—
41C2×C7×#117C2211yescharacteristic
42#90524C2211yescharacteristic
43#90524C2212yescomplemented
44#90522—21no—
45#90518C2211yescharacteristic
46#90516C2211yescharacteristic
47#90516C2212yescomplemented
48#90515—22no—
49#90515—21no—
50C2×#6511C2211yescharacteristic
51C2×#6511C2211yescharacteristic
52Q8×C22⋊D7—21no—
53C22×#1144C2211yescharacteristic, complemented
54C2×#6505C2211yescharacteristic, complemented
55#90497—21no—
56#90497—22no—
57C22×#1142C2211yescharacteristic, complemented
58C2×#6495C2211yescharacteristic, complemented
59#90482C2211yescharacteristic
60#90482C2212yescomplemented
61C2×#6487C2211yescharacteristic
62C2×#6487C2212yescomplemented
63#90011C2212yes—
64#90011C2212yes—
65#90011C2212yes—
66#90011C2212yescomplemented
67#90011C2212yescomplemented
68#90011C2212yescomplemented
69#90010C2212yes—
70#90010C2212yescomplemented
71#90006C2211yescharacteristic
72#90006C2211yescharacteristic
73#90006C2212yescomplemented
74#90006C2212yescomplemented
75#89997C2211yescharacteristic, complemented
76C2×#6409C2211yescharacteristic, complemented
77#89987C2211yescharacteristic, complemented
78C2×#6406C2211yescharacteristic, complemented
79#89979C2211yescharacteristic
80#89979C2212yescomplemented
81C2×C22⋊(C7⋊C8)C2211yescharacteristic
82C2×C22⋊(C7⋊C8)C2212yescomplemented
83#89824C2212yescomplemented
84#89824C2212yescomplemented
85#89824C2212yescomplemented
86#89823C2212yescomplemented
87#89823C2212yescomplemented
88#89823C2212yescomplemented
89#89822C2212yescomplemented
90#89822C2212yescomplemented
91#89821C2212yescomplemented
92#89820C2212yescomplemented
93#89819C2212yescomplemented
94#89819C2212yescomplemented
95#89817C2212yescomplemented
96#89817C2212yescomplemented
97#89816C2212yescomplemented
98#89815C2212yescomplemented
99#89814C2212yescomplemented
100#89814C2212yescomplemented
101#89814C2212yescomplemented
102#89813C2212yescomplemented
103#89813C2212yescomplemented
104#89813C2212yescomplemented
105#89812C2212yescomplemented
106#89812C2212yescomplemented
107#89811C2212yescomplemented
108#89810C2212yescomplemented
109#89809C2212yescomplemented
110#89809C2212yescomplemented
111#89807C2212yescomplemented
112#89807C2212yescomplemented
113#89806C2212yescomplemented
114#89805C2212yescomplemented
115#89776C2211yescharacteristic, complemented
116#89776C2211yescharacteristic, complemented
117#89775C2211yescharacteristic, complemented
118#89775C2211yescharacteristic, complemented
119#89774C2211yescharacteristic, complemented
120#89774C2211yescharacteristic, complemented
121#89770C2211yescharacteristic, complemented
122#89770C2211yescharacteristic, complemented
123#89768C2211yescharacteristic, complemented
124#89768C2211yescharacteristic, complemented
125#89768C2212yescomplemented
126#89768C2212yescomplemented
127#89767C2211yescharacteristic, complemented
128#89767C2211yescharacteristic, complemented
129#89743C2211yescharacteristic, complemented
130#89743C2212yescomplemented
131#89742C2211yescharacteristic, complemented
132#89742C2212yescomplemented
133#89740C2211yescharacteristic, complemented
134#89739C2211yescharacteristic, complemented
135#60761—71nomaximal, Sylow
136C2×C7×#41—21no—
137C2×C7×#41—21no—
138C2×C7×#41—42no—
139C2×C7×#41—42no—
140C2×C7×#41—42no—
141C2×C7×#41—42no—
142C2×C7×#41D412yes—
143C2×C7×#41D411yescharacteristic
144C2×C7×#41D411yescharacteristic
145C2×C7×#41C2312yes—
146C2×C7×#41C2312yes—
147C2×C7×#41C2311yescharacteristic
148C2×C7×#41C2311yescharacteristic
149C2×C7×#41C2312yes—
150C22×C7×Q8D411yescharacteristic
151C22×C7×Q8C2311yescharacteristic
152C22×C7×D4—21no—
153C22×C7×D4D412yes—
154C22×C7×D4D411yescharacteristic
155C22×C7×D4C2311yescharacteristic
156C23×C4×C7—21no—
157C23×C4×C7C2311yescharacteristic
158C23×C4×C7C2312yes—
159#6554—42no—
160#6554—42no—
161C2×Q8×D7—21no—
162C2×#1159—22no—
163C2×#1159—21no—
164C2×#1157C2311yescharacteristic
165C2×#1157C2312yes—
166C22×Dic14C2311yescharacteristic
167C22×Dic14C2312yes—
168C7×C4⋊Q8—21no—
169C7×C4⋊Q8—21no—
170C7×#127—21no—
171C7×#127—21no—
172C7×#124—21no—
173C7×#124—21no—
174C7×#124—21no—
175C7×#124—21no—
176C7×#123—22no—
177C7×#123—22no—
178C7×#123—22no—
179C7×#123—22no—
180C7×C22⋊Q8—22no—
181C7×C22⋊Q8—22no—
182C7×C22⋊Q8C2312yes—
183C7×C22⋊Q8C2312yes—
184C7×C22⋊Q8C2312yes—
185C7×C22⋊Q8C2312yes—
186C7×#121—22no—
187C7×#121—22no—
188C7×#121—22no—
189C7×#121—22no—
190C7×#121—22no—
191C7×#121—22no—
192C7×#121C2312yes—
193C7×#121C2312yes—
194C7×#121C2312yes—
195C7×#121C2312yes—
196C7×#120—22no—
197C7×#120—22no—
198C7×#120—22no—
199C7×#120—22no—
200C4×C7×D4—22no—
201C4×C7×D4—22no—
202C4×C7×D4—22no—
203C4×C7×D4—22no—
204C7×#117—21no—
205C7×#117—21no—
206C7×#117C2311yescharacteristic
207C7×#117C2311yescharacteristic
208C7×#117C2311yescharacteristic
209C7×#117C2311yescharacteristic
210C2×C7×C4⋊C4C2311yescharacteristic
211C2×C7×C4⋊C4C2311yescharacteristic
212C2×C7×C22⋊C4—21no—
213C2×C42×C7—21no—
214#6516—21no—
215#6516—22no—
216C2×C22⋊Dic7—21no—
217C2×C22⋊Dic7—22no—
218#6511—42no—
219#6511—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—
229#6505—42no—
230C2×#1143C2312yes—
231#6502—22no—
232#6502—22no—
233#6502—22no—
234#6501—21no—
235#6501—22no—
236#6499—21no—
237#6499—22no—
238#6498—22no—
239#6498—22no—
240#6498—22no—
241D4×Dic7—22no—
242D4×Dic7—21no—
243C2×#1142—42no—
244C2×#1142C2312yes—
245C2×#1142C2312yes—
246C2×#1142C2312yes—
247#6495—42no—
248C2×#1141C2312yes—
249#6493C2311yescharacteristic
250#6493C2311yescharacteristic
251#6493C2312yes—
252#6492—21no—
253#6492—22no—
254C4×C22⋊D7—21no—
255C4×C22⋊D7—21no—
256C4×C22⋊D7—22no—
257C4×C22⋊D7—22no—
258#6489C2311yescharacteristic
259#6489C2312yes—
260C2×C4⋊Dic7C2311yescharacteristic
261C2×C4⋊Dic7C2312yes—
262#6487—21no—
263#6487—21no—
264#6487—22no—
265#6487—22no—
266#6487C2312yes—
267#6487C2312yes—
268#6487C2311yescharacteristic
269#6487C2312yes—
270#6487C2312yes—
271#6487C2311yescharacteristic
272#6487C2312yes—
273C2×Dic7⋊C4—21no—
274C2×Dic7⋊C4—22no—
275C2×#1136C2311yescharacteristic
276C2×#1136C2311yescharacteristic
277C2×#1136C2312yes—
278C2×#1136C2312yes—
279C22×C7⋊C8C2311yescharacteristic
280C22×C7⋊C8C2311yescharacteristic
281C22×C7⋊C8C2312yes—
282C22×C7⋊C8C2312yes—
283#6409C2312yes—
284#6409C2312yes—
285#6409C2312yes—
286#6409C2312yes—
287#6406C2312yes—
288#6406C2312yes—
289#6406C2312yes—
290#6406C2312yes—
291C22⋊(C7⋊C8)C2311yescharacteristic
292C22⋊(C7⋊C8)C2311yescharacteristic
293C22⋊(C7⋊C8)C2311yescharacteristic
294C22⋊(C7⋊C8)C2311yescharacteristic
295C22⋊(C7⋊C8)C2312yes—
296C22⋊(C7⋊C8)C2312yes—
297C22⋊(C7⋊C8)C2312yes—
298C22⋊(C7⋊C8)C2312yes—
299C22⋊(C7⋊C8)C2312yes—
300C22⋊(C7⋊C8)C2312yes—
301#6384C2311yescharacteristic
302#6384C2311yescharacteristic
303#6384C2312yes—
304#6384C2312yes—
305#6384C2311yescharacteristic
306#6384C2311yescharacteristic
307#6384C2312yes—
308#6384C2312yes—
309#6383C2311yescharacteristic
310#6383C2311yescharacteristic
311#6383C2311yescharacteristic
312#6383C2311yescharacteristic
313#6382C2311yescharacteristic
314#6382C2311yescharacteristic
315#6382C2312yes—
316#6382C2312yes—
317#6382C2311yescharacteristic
318#6382C2311yescharacteristic
319#6381C2311yescharacteristic
320#6381C2311yescharacteristic
321#6381C2312yes—
322#6381C2312yes—
323#6381C2311yescharacteristic
324#6381C2311yescharacteristic
325#3489—71no—
326#3449D711yescharacteristic, complemented
327#3204—72no—
328#3203—72no—
329#3201—72no—
330#3201—72no—
331#3197—72no—
332#3196—72no—
333#3191—72no—
334#3190—72no—
335#3097—71no—
336#3096—71no—
337#3095—71no—
338#3091—71no—
339#3063—71no—
340#3062—71no—
341#3059—71no—
342#3057—71no—
343#3011—71no—
344#3010—71no—
345#3005—71no—
346C2×#452—71no—
347#2880—71no—
348C24×C7—21no—
349C24×C7C2×D411yescharacteristic
350C24×C7C2×D412yes—
351C7×#41—22no—
352C7×#41—22no—
353C7×#41—22no—
354C7×#41—22no—
355C7×#41—42no—
356C7×#41—42no—
357C7×#41—44no—
358C7×#41—42no—
359C7×#41—42no—
360C7×#41—42no—
361C7×#41—42no—
362C7×#41—42no—
363C7×#41—42no—
364C7×#41—44no—
365C7×#41—44no—
366C2×C7×Q8—21no—
367C2×C7×Q8—22no—
368C2×C7×Q8—22no—
369C2×C7×Q8—42no—
370C2×C7×Q8C2×D411yescharacteristic
371C2×C7×Q8C2×D411yescharacteristic
372C2×C7×Q8C2×D412yes—
373C2×C7×Q8C2412yes—
374C2×C7×D4—22no—
375C2×C7×D4—22no—
376C2×C7×D4—22no—
377C2×C7×D4—22no—
378C2×C7×D4—22no—
379C2×C7×D4—22no—
380C2×C7×D4—21no—
381C2×C7×D4—22no—
382C2×C7×D4—22no—
383C2×C7×D4—42no—
384C2×C7×D4—44no—
385C2×C7×D4—44no—
386C2×C7×D4C2×D412yes—
387C2×C7×D4C2×D411yescharacteristic
388C2×C7×D4C2×D412yes—
389C2×C7×D4C2×D411yescharacteristic
390C2×C7×D4C2×D412yes—
391C2×C7×D4C2×D412yes—
392C2×C7×D4C2×D412yes—
393C2×C7×D4C2412yes—
394C22×C4×C7—22no—
395C22×C4×C7—22no—
396C22×C4×C7—21no—
397C22×C4×C7—21no—
398C22×C4×C7—21no—
399C22×C4×C7—22no—
400C22×C4×C7—22no—
401C22×C4×C7—42no—
402C22×C4×C7—42no—
403C22×C4×C7—44no—
404C22×C4×C7C2×D411yescharacteristic
405C22×C4×C7C2×D411yescharacteristic
406C22×C4×C7C2×D411yescharacteristic
407C22×C4×C7C2×D412yes—
408C22×C4×C7C2×D412yes—
409C22×C4×C7C2×D412yes—
410C22×C4×C7C2411yescharacteristic
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2412yes—
413C22×C4×C7C2412yes—
414C22×C4×C7C2411yescharacteristic
415C2×C22⋊D7—21no—
416C2×C22⋊D7—22no—
417C2×C22⋊D7—21no—
418C2×C22⋊D7—22no—
419C2×C22⋊D7—21no—
420C22×Dic7—22no—
421C22×Dic7—21no—
422C22×Dic7—22no—
423C22×Dic7—21no—
424Q8×D7—44no—
425#1159—48no—
426#1159—44no—
427#1157—22no—
428#1157—22no—
429#1157—42no—
430#1157—42no—
431C2×D28C2411yescharacteristic
432C2×C4×D7—22no—
433C2×C4×D7—21no—
434C2×Dic14—22no—
435C2×Dic14—22no—
436C2×Dic14—22no—
437C2×Dic14—21no—
438C2×Dic14—42no—
439C2×Dic14—42no—
440C2×Dic14C2412yes—
441C2×Dic14C2411yescharacteristic
442C7×C4⋊C4—21no—
443C7×C4⋊C4—21no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—22no—
447C7×C4⋊C4—22no—
448C7×C4⋊C4C2411yescharacteristic
449C7×C4⋊C4C2411yescharacteristic
450C7×C4⋊C4C2411yescharacteristic
451C7×C4⋊C4C2411yescharacteristic
452C7×C22⋊C4—21no—
453C7×C22⋊C4—21no—
454C7×C22⋊C4—21no—
455C7×C22⋊C4—21no—
456C7×C22⋊C4—22no—
457C7×C22⋊C4—22no—
458C7×C22⋊C4—22no—
459C7×C22⋊C4—22no—
460C7×C22⋊C4—22no—
461C7×C22⋊C4—22no—
462C7×C22⋊C4—22no—
463C7×C22⋊C4—22no—
464C42×C7—21no—
465C42×C7—21no—
466C42×C7—21no—
467C42×C7—21no—
468C22⋊Dic7—22no—
469C22⋊Dic7—21no—
470C22⋊Dic7—22no—
471C22⋊Dic7—22no—
472C22⋊Dic7—22no—
473C22⋊Dic7—22no—
474C22⋊Dic7—21no—
475C22⋊Dic7—22no—
476C22⋊Dic7—21no—
477#1144—42no—
478#1144—42no—
479#1144—42no—
480#1143—42no—
481#1142—42no—
482#1142—42no—
483#1142—42no—
484#1141—42no—
485(C2×D7)⋊C4—21no—
486(C2×D7)⋊C4—22no—
487(C2×D7)⋊C4—21no—
488C4⋊Dic7—22no—
489C4⋊Dic7—21no—
490C4⋊Dic7C2412yes—
491C4⋊Dic7C2411yescharacteristic
492C4⋊Dic7C2411yescharacteristic
493Dic7⋊C4—22no—
494Dic7⋊C4—21no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—22no—
499Dic7⋊C4—21no—
500C4×Dic7—22no—
501C4×Dic7—21no—
502#1136—22no—
503#1136—22no—
504#1136—42no—
505#1136—42no—
506C2×C7⋊C8—22no—
507C2×C7⋊C8—22no—
508C2×C7⋊C8—42no—
509C2×C7⋊C8—42no—
510C2×C7⋊C8C2411yescharacteristic
511C2×C7⋊C8C2412yes—
512C2×C7⋊C8C2411yescharacteristic
513C2×C7⋊C8C2411yescharacteristic
514C2×C7⋊C8C2412yes—
515C2×C7⋊C8C2411yescharacteristic
516C2×2−1+4—71no—
517C22×#41C2×D711yescharacteristic
518C22×#41C2×D711yescharacteristic
519C2×#137—71no—
520C2×AGL(1,ℤ/8)—71no—
521C22×Q16—71no—
522C22×SD16—71no—
523C2×#131—71no—
524C2×#131—71no—
525D4×Q8—141no—
526#548—141no—
527#547—142no—
528#547—141no—
529#546—142no—
530#546—141no—
531#537—72no—
532#537—71no—
533#537C2×D712yes—
534#537C2×D712yes—
535#536—21no—
536#536—72no—
537#536—71no—
538#536C2×D711yescharacteristic
539#536C2×D711yescharacteristic
540#535—21no—
541#535C2×D711yescharacteristic
542#535C2×D711yescharacteristic
543#534—22no—
544#532—21no—
545#532—21no—
546#525—22no—
547#525—71no—
548#525—72no—
549#525C2×D712yes—
550#525C2×D712yes—
551C2×C22⋊Q8—71no—
552C2×C22⋊Q8—72no—
553#520—71no—
554C2×#117C2×D711yescharacteristic
555#485—72no—
556#485—72no—
557#485—71no—
558#485—71no—
559#485—72no—
560#485—72no—
561#484—72no—
562#484—71no—
563#484—72no—
564#483—72no—
565#483—71no—
566#483—72no—
567#482—72no—
568#482—72no—
569#482—71no—
570#482—71no—
571#481—72no—
572#481—71no—
573#480—72no—
574#480—71no—
575#470—72no—
576#470—72no—
577#470—72no—
578#469—72no—
579#468—72no—
580#468—72no—
581#468—72no—
582#468—72no—
583#467—72no—
584#467—72no—
585#467—72no—
586#466—72no—
587#465—72no—
588#465—72no—
589#465—72no—
590#465—72no—
591#452—72no—
592#452—72no—
593#452—72no—
594#452—72no—
595#452—72no—
596#452—72no—
597#452—72no—
598#452—72no—
599#451—72no—
600#451—72no—
601#449—72no—
602#449—72no—
603#449—72no—
604#449—72no—
605#448—72no—
606#448—72no—
607#428—71no—
608#428—71no—
609#427—71no—
610#427—71no—
611#419—71no—
612#419—71no—
613#419—71no—
614#418—71no—
615#416—71no—
616#416—71no—
617C2×#103—71no—
618C2×#102—71no—
619#408—71no—
620#408—71no—
621#408—72no—
622#408—72no—
623#407—71no—
624#407—72no—
625C2×C22⋊C8—71no—
626C2×C22⋊C8—72no—
627C23×C7—22no—
628C23×C7—22no—
629C23×C7—42no—
630C23×C7—41no—
631C23×C7—41no—
632C23×C7—42no—
633C23×C7—42no—
634C23×C7—42no—
635C23×C7—81no—
636C23×C7—81no—
637C23×C7C22×D411yescharacteristic
638C23×C7C22×D412yes—
639C23×C7C22×D411yescharacteristic
640C23×C7C22×D412yes—
641C23×C7C22×D411yescharacteristic
642C22×D7—21no—
643C7×Q8—22no—
644C7×Q8—22no—
645C7×Q8—22no—
646C7×Q8—22no—
647C7×Q8—42no—
648C7×Q8—42no—
649C7×D4—24no—
650C7×D4—24no—
651C7×D4—22no—
652C7×D4—22no—
653C7×D4—22no—
654C7×D4—22no—
655C7×D4—42no—
656C7×D4—42no—
657C7×D4—42no—
658C7×D4—44no—
659C7×D4—44no—
660C7×D4—42no—
661C7×D4—82no—
662C7×D4—82no—
663C7×D4—82no—
664C7×D4—82no—
665C2×C4×C7—22no—
666C2×C4×C7—22no—
667C2×C4×C7—22no—
668C2×C4×C7—22no—
669C2×C4×C7—22no—
670C2×C4×C7—22no—
671C2×C4×C7—22no—
672C2×C4×C7—21no—
673C2×C4×C7—21no—
674C2×C4×C7—21no—
675C2×C4×C7—21no—
676C2×C4×C7—21no—
677C2×C4×C7—21no—
678C2×C4×C7—21no—
679C2×C4×C7—21no—
680C2×C4×C7—22no—
681C2×C4×C7—42no—
682C2×C4×C7—42no—
683C2×C4×C7—42no—
684C2×C4×C7—44no—
685C2×C4×C7—44no—
686C2×C4×C7—42no—
687C2×C4×C7—81no—
688C2×C4×C7—81no—
689C2×C4×C7C22×D412yes—
690C2×C4×C7C22×D411yescharacteristic
691C2×C4×C7C22×D412yes—
692C2×C4×C7C22×D411yescharacteristic
693C2×C4×C7C22×D411yescharacteristic
694C2×C4×C7H(5,𝔽2)12yes—
695C2×C4×C7H(5,𝔽2)12yes—
696C2×C4×C7C2511yescharacteristic
697C22⋊D7—44no—
698C22⋊D7—42no—
699C22⋊D7—42no—
700C22⋊D7—81no—
701C22⋊D7—82no—
702C2×Dic7—21no—
703C2×Dic7—22no—
704C2×Dic7—21no—
705C2×Dic7—22no—
706C2×Dic7—21no—
707C2×Dic7—44no—
708C2×Dic7—42no—
709C2×Dic7—81no—
710C2×Dic7—82no—
711D28—21no—
712D28—21no—
713C4×D7—44no—
714C4×D7—42no—
715Dic14—22no—
716Dic14—21no—
717Dic14—22no—
718Dic14—21no—
719Dic14—44no—
720Dic14—42no—
721C7⋊C8—21no—
722C7⋊C8—21no—
723C7⋊C8—21no—
724C7⋊C8—21no—
725C7⋊C8—22no—
726C7⋊C8—22no—
7272−1+4—282no—
7282−1+4—282no—
729C2×#41—21no—
730C2×#41—21no—
731C2×#41—42no—
732C2×#41—42no—
733C2×#41—42no—
734C2×#41—42no—
735C2×#41—71no—
736C2×#41—72no—
737C2×#41—142no—
738C2×#41—141no—
739C2×#41C22⋊D712yes—
740C2×#41C22⋊D711yescharacteristic
741C2×#41C22⋊D711yescharacteristic
742C2×#41C22×D712yes—
743C2×#41C22×D712yes—
744C2×#41C22×D711yescharacteristic
745C2×#41C22×D711yescharacteristic
746C2×#41C22×D712yes—
747C22×Q8—71no—
748C22×Q8—72no—
749C22×Q8—141no—
750C22×Q8C22⋊D711yescharacteristic
751C22×Q8C22×D711yescharacteristic
752C22×D4—21no—
753C22×D4C22⋊D712yes—
754C22×D4C22⋊D711yescharacteristic
755C22×D4C22×D711yescharacteristic
756C23×C4—21no—
757C23×C4C22×D711yescharacteristic
758C23×C4C22×D712yes—
759#137—282no—
760AGL(1,ℤ/8)—282no—
761C2×Q16—72no—
762C2×Q16—72no—
763C2×Q16—72no—
764C2×Q16—282no—
765C2×SD16—72no—
766C2×SD16—72no—
767C2×SD16—72no—
768C2×SD16—72no—
769C2×SD16—282no—
770C2×D8—72no—
771#131—282no—
772#131—282no—
773C2×M16—71no—
774C2×M16—71no—
775C2×M16—72no—
776C2×M16—72no—
777C22×C8—71no—
778C22×C8—71no—
779C22×C8—72no—
780C22×C8—72no—
781C4⋊Q8—21no—
782C4⋊Q8—21no—
783C4⋊Q8—141no—
784C4⋊Q8—142no—
785#127—21no—
786#127—21no—
787#124—21no—
788#124—21no—
789#124—21no—
790#124—21no—
791#124—141no—
792#124—142no—
793#123—22no—
794#123—22no—
795#123—22no—
796#123—22no—
797#123—142no—
798#123—142no—
799#123—142no—
800#123—141no—
801#123—142no—
802C22⋊Q8—22no—
803C22⋊Q8—22no—
804C22⋊Q8—72no—
805C22⋊Q8—71no—
806C22⋊Q8—72no—
807C22⋊Q8—72no—
808C22⋊Q8—72no—
809C22⋊Q8—71no—
810C22⋊Q8—72no—
811C22⋊Q8—141no—
812C22⋊Q8—142no—
813C22⋊Q8—141no—
814C22⋊Q8—142no—
815C22⋊Q8—141no—
816C22⋊Q8—142no—
817C22⋊Q8C22×D712yes—
818C22⋊Q8C22×D712yes—
819C22⋊Q8C22×D712yes—
820C22⋊Q8C22×D712yes—
821#121—22no—
822#121—22no—
823#121—22no—
824#121—22no—
825#121—22no—
826#121—22no—
827#121—71no—
828#121—71no—
829#121—72no—
830#121—142no—
831#121—142no—
832#121—142no—
833#121—141no—
834#121—142no—
835#121C22×D712yes—
836#121C22×D712yes—
837#121C22×D712yes—
838#121C22×D712yes—
839#120—22no—
840#120—22no—
841#120—22no—
842#120—22no—
843#120—141no—
844#120—142no—
845C4×Q8—141no—
846C4×D4—22no—
847C4×D4—22no—
848C4×D4—22no—
849C4×D4—22no—
850C4×D4—142no—
851C4×D4—141no—
852C4×D4—141no—
853C4×D4—142no—
854C4×D4—141no—
855C4×D4—142no—
856#117—21no—
857#117—21no—
858#117—71no—
859#117—72no—
860#117C22×D711yescharacteristic
861#117C22×D711yescharacteristic
862#117C22×D711yescharacteristic
863#117C22×D711yescharacteristic
864C2×C4⋊C4—71no—
865C2×C4⋊C4—72no—
866C2×C4⋊C4—141no—
867C2×C4⋊C4—142no—
868C2×C4⋊C4C22×D711yescharacteristic
869C2×C4⋊C4C22×D711yescharacteristic
870C2×C22⋊C4—21no—
871C2×C22⋊C4—141no—
872C2×C22⋊C4—142no—
873C2×C42—21no—
874#107—71no—
875#107—71no—
876#107—71no—
877#107—71no—
878#107—72no—
879#107—72no—
880#106—71no—
881#106—71no—
882#106—71no—
883#106—71no—
884#106—72no—
885#106—72no—
886#103—72no—
887#103—72no—
888#103—72no—
889#103—72no—
890#103—71no—
891#103—71no—
892#103—71no—
893#103—71no—
894#103—72no—
895#103—72no—
896#103—72no—
897#103—72no—
898#102—72no—
899#102—72no—
900#102—72no—
901#102—72no—
902#102—71no—
903#102—71no—
904#102—71no—
905#102—71no—
906C22⋊C8—71no—
907C22⋊C8—72no—
908C22⋊C8—71no—
909C22⋊C8—72no—
910C22⋊C8—72no—
911C22⋊C8—71no—
912C22⋊C8—71no—
913C22⋊C8—72no—
914C22⋊C8—72no—
915C22⋊C8—72no—
916C22×C7—21no—
917C22×C7—21no—
918C22×C7—22no—
919C22×C7—21no—
920C22×C7—22no—
921C22×C7—21no—
922C22×C7—21no—
923C22×C7—21no—
924C22×C7—22no—
925C22×C7—22no—
926C22×C7—22no—
927C22×C7—21no—
928C22×C7—21no—
929C22×C7—22no—
930C22×C7—42no—
931C22×C7—42no—
932C22×C7—42no—
933C22×C7—82no—
934C22×C7—84no—
935C22×C7—84no—
936C22×C7#53412yes—
937C22×C7C23×D411yescharacteristic
938C2×D7—41no—
939C2×D7—41no—
940C2×D7—41no—
941C4×C7—22no—
942C4×C7—21no—
943C4×C7—21no—
944C4×C7—22no—
945C4×C7—41no—
946C4×C7—41no—
947C4×C7—41no—
948C4×C7—41no—
949C4×C7—42no—
950C4×C7#53412yes—
951C4×C7C2×H(5,𝔽2)11yescharacteristic
952C4×C7C2×H(5,𝔽2)11yescharacteristic
953Dic7—42no—
954Dic7—41no—
955Dic7—41no—
956Dic7—42no—
957Dic7—41no—
958C24—21no—
959C24C2×C22⋊D711yescharacteristic
960C24C2×C22⋊D712yes—
961#41—22no—
962#41—22no—
963#41—22no—
964#41—22no—
965#41—42no—
966#41—42no—
967#41—44no—
968#41—42no—
969#41—42no—
970#41—42no—
971#41—42no—
972#41—42no—
973#41—42no—
974#41—44no—
975#41—44no—
976#41—142no—
977#41—142no—
978#41—282no—
979#41—282no—
980#41—288no—
981#41—284no—
982C2×Q8—21no—
983C2×Q8—22no—
984C2×Q8—22no—
985C2×Q8—42no—
986C2×Q8—72no—
987C2×Q8—71no—
988C2×Q8—142no—
989C2×Q8—141no—
990C2×Q8—142no—
991C2×Q8—142no—
992C2×Q8—282no—
993C2×Q8—282no—
994C2×Q8—284no—
995C2×Q8C2×C22⋊D711yescharacteristic
996C2×Q8C2×C22⋊D711yescharacteristic
997C2×Q8C2×C22⋊D712yes—
998C2×Q8C23×D712yes—
999C2×D4—22no—
1000C2×D4—22no—
1001C2×D4—22no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—21no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—71no—
1012C2×D4—141no—
1013C2×D4—142no—
1014C2×D4—141no—
1015C2×D4—142no—
1016C2×D4—141no—
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×D712yes—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—21no—
1028C22×C4—21no—
1029C22×C4—21no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
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×D711yescharacteristic
1049C22×C4C23×D711yescharacteristic
1050C22×C4C23×D712yes—
1051C22×C4C23×D711yescharacteristic
1052Q16—282no—
1053Q16—282no—
1054Q16—282no—
1055SD16—282no—
1056SD16—282no—
1057SD16—282no—
1058SD16—282no—
1059D8—282no—
1060M16—142no—
1061M16—142no—
1062M16—282no—
1063M16—282no—
1064C2×C8—71no—
1065C2×C8—71no—
1066C2×C8—72no—
1067C2×C8—71no—
1068C2×C8—71no—
1069C2×C8—72no—
1070C2×C8—142no—
1071C2×C8—142no—
1072C2×C8—282no—
1073C2×C8—282no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—72no—
1081C4⋊C4—71no—
1082C4⋊C4—71no—
1083C4⋊C4—142no—
1084C4⋊C4—141no—
1085C4⋊C4—142no—
1086C4⋊C4—142no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—141no—
1090C4⋊C4—142no—
1091C4⋊C4—141no—
1092C4⋊C4C23×D711yescharacteristic
1093C4⋊C4C23×D711yescharacteristic
1094C4⋊C4C23×D711yescharacteristic
1095C4⋊C4C23×D711yescharacteristic
1096C22⋊C4—21no—
1097C22⋊C4—21no—
1098C22⋊C4—21no—
1099C22⋊C4—21no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—22no—
1108C22⋊C4—142no—
1109C22⋊C4—141no—
1110C22⋊C4—142no—
1111C22⋊C4—142no—
1112C22⋊C4—142no—
1113C22⋊C4—142no—
1114C22⋊C4—141no—
1115C22⋊C4—142no—
1116C22⋊C4—141no—
1117C22⋊C4—141no—
1118C22⋊C4—142no—
1119C22⋊C4—141no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—142no—
1125C42—141no—
1126C2×C7—22no—
1127C2×C7—42no—
1128C2×C7—41no—
1129C2×C7—42no—
1130C2×C7—41no—
1131C2×C7—82no—
1132C2×C7C2×#53411yescharacteristic
1133C2×C7#358411yescharacteristic
1134C2×C7#358611yescharacteristic
1135D7—81no—
1136C23—22no—
1137C23—22no—
1138C23—42no—
1139C23—41no—
1140C23—41no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—81no—
1145C23—81no—
1146C23—141no—
1147C23C22×C22⋊D711yescharacteristic
1148C23C22×C22⋊D712yes—
1149C23C22×C22⋊D712yes—
1150C23C22×C22⋊D711yescharacteristic
1151C23C22×C22⋊D711yescharacteristic
1152Q8—22no—
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—42no—
1157Q8—42no—
1158Q8—142no—
1159Q8—141no—
1160Q8—142no—
1161Q8—141no—
1162Q8—284no—
1163Q8—282no—
1164D4—24no—
1165D4—24no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—42no—
1171D4—42no—
1172D4—42no—
1173D4—44no—
1174D4—44no—
1175D4—42no—
1176D4—82no—
1177D4—82no—
1178D4—82no—
1179D4—82no—
1180D4—141no—
1181D4—141no—
1182D4—282no—
1183D4—284no—
1184D4—282no—
1185D4—561no—
1186D4—562no—
1187C2×C4—22no—
1188C2×C4—22no—
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—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—42no—
1209C2×C4—81no—
1210C2×C4—81no—
1211C2×C4—141no—
1212C2×C4—142no—
1213C2×C4—141no—
1214C2×C4—142no—
1215C2×C4—141no—
1216C2×C4—284no—
1217C2×C4—284no—
1218C2×C4—282no—
1219C2×C4—282no—
1220C2×C4—561no—
1221C2×C4—562no—
1222C2×C4#654812yes—
1223C2×C4#654812yes—
1224C2×C4C22×C22⋊D711yescharacteristic
1225C2×C4C22×C22⋊D712yes—
1226C2×C4C22×C22⋊D712yes—
1227C2×C4C22×C22⋊D711yescharacteristic
1228C2×C4C22×C22⋊D711yescharacteristic
1229C2×C4C24×D711yescharacteristic
1230C8—141no—
1231C8—141no—
1232C8—141no—
1233C8—141no—
1234C8—142no—
1235C8—142no—
1236C7#6076111yescharacteristic, complemented, Sylow
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—22no—
1242C22—22no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—21no—
1247C22—21no—
1248C22—22no—
1249C22—22no—
1250C22—21no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—82no—
1255C22—84no—
1256C22—84no—
1257C22—281no—
1258C22—281no—
1259C22—281no—
1260C22#9049512yes—
1261C22C23×C22⋊D711yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—22no—
1266C4—42no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—282no—
1272C4—281no—
1273C4—282no—
1274C4—281no—
1275C4—281no—
1276C4#9049512yes—
1277C4C2×#654811yescharacteristic
1278C4C2×#654811yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—42no—
1283C2—42no—
1284C2—82no—
1285C2—561no—
1286C2C2×#9049511yescharacteristic
1287C2#1174436511yescharacteristic
1288C2#1174436711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC7×#3449C2
socleC22×C7C23×D4
hypercenter#3449D7
hypocenterC7#60761
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C7×#3449C2semidirect
2. #11744332C2semidirect
3. C2×#90011C2semidirect
4. #11741526C2semidirect
5. #11741520C2semidirect
6. #11740874C2semidirect
7. #11740873C2semidirect
8. #11740873C2semidirect
9. #11740871C2semidirect
10. #11740856C2semidirect
11. #11740845C2semidirect
12. #11740844C2semidirect
13. #11740842C2semidirect
14. #11740835C2semidirect
15. #11740824C2semidirect
16. #11740822C2semidirect
17. #11740821C2semidirect
18. #11740380C2semidirect
19. #11740379C2semidirect
20. #11740377C2semidirect
21. #11740375C2semidirect
22. #11739665C2semidirect
23. #11739660C2semidirect
43. #90524C22semidirect
47. #90516C22semidirect
53. C22×#1144C22semidirect
54. C2×#6505C22semidirect
57. C22×#1142C22semidirect
58. C2×#6495C22semidirect
60. #90482C22semidirect
62. C2×#6487C22semidirect
66. #90011C22semidirect
67. #90011C22semidirect
68. #90011C22semidirect
70. #90010C22semidirect
73. #90006C22semidirect
74. #90006C22semidirect
75. #89997C22semidirect
76. C2×#6409C22semidirect
77. #89987C22semidirect
78. C2×#6406C22semidirect
80. #89979C22semidirect
82. C2×C22⋊(C7⋊C8)C22semidirect
83. #89824C22semidirect
84. #89824C22semidirect
85. #89824C22semidirect
86. #89823C22semidirect
87. #89823C22semidirect
88. #89823C22semidirect
89. #89822C22semidirect
90. #89822C22semidirect
91. #89821C22semidirect
92. #89820C22semidirect
93. #89819C22semidirect
94. #89819C22semidirect
95. #89817C22semidirect
96. #89817C22semidirect
97. #89816C22semidirect
98. #89815C22semidirect
99. #89814C22semidirect
100. #89814C22semidirect
101. #89814C22semidirect
102. #89813C22semidirect
103. #89813C22semidirect
104. #89813C22semidirect
105. #89812C22semidirect
106. #89812C22semidirect
107. #89811C22semidirect
108. #89810C22semidirect
109. #89809C22semidirect
110. #89809C22semidirect
111. #89807C22semidirect
112. #89807C22semidirect
113. #89806C22semidirect
114. #89805C22semidirect
115. #89776C22semidirect
116. #89776C22semidirect
117. #89775C22semidirect
118. #89775C22semidirect
119. #89774C22semidirect
120. #89774C22semidirect
121. #89770C22semidirect
122. #89770C22semidirect
123. #89768C22semidirect
124. #89768C22semidirect
125. #89768C22semidirect
126. #89768C22semidirect
127. #89767C22semidirect
128. #89767C22semidirect
129. #89743C22semidirect
130. #89743C22semidirect
131. #89742C22semidirect
132. #89742C22semidirect
133. #89740C22semidirect
134. #89739C22semidirect
326. #3449D7semidirect
1236. C7#60761semidirect

Maximal subgroups

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

subgroupindex
C7×#34492
#117443322
C2×#900112
#117415262
#117415202
#117408742
#117408732
#117408712
#117408562
#117408452
#117408442
#117408422
#117408352
#117408242
#117408222
#117408212
#117403802
#117403792
#117403772
#117403752
#117396652
#117396602
#607617