Finite Group Databasebeta

← #13320713

Subgroups — #13320713

Order 1792.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742908C211yesmaximal, characteristic
2C7×#2925C211yesmaximal, characteristic, complemented
3#11739962C211yesmaximal, characteristic, complemented
4#11728557C211yesmaximal, characteristic, complemented
5#11728554C211yesmaximal, characteristic, complemented
6#11728553C211yesmaximal, characteristic, complemented
7#11728552C211yesmaximal, characteristic, complemented
8#11728523C211yesmaximal, characteristic, complemented
9#11728513C211yesmaximal, characteristic, complemented
10#11728510C211yesmaximal, characteristic, complemented
11#11728508C211yesmaximal, characteristic, complemented
12#11728253C211yesmaximal, characteristic, complemented
13#11728251C211yesmaximal, characteristic, complemented
14#11728181C211yesmaximal, characteristic, complemented
15#11728179C211yesmaximal, characteristic, complemented
16C4×C7×#41C2211yescharacteristic
17#90519—21no—
18#90275C411yescharacteristic
19#90272—21no—
20#90270C411yescharacteristic
21#90254C411yescharacteristic
22#90249—21no—
23#90247—21no—
24#90247—21no—
25#90242C411yescharacteristic
26#90241C411yescharacteristic
27#90241C411yescharacteristic
28#90232C411yescharacteristic
29#90232C411yescharacteristic
30#90219—21no—
31#90219—21no—
32D7×#117—21no—
33#90170C2211yescharacteristic
34#90170C2211yescharacteristic
35C4×#1157C2211yescharacteristic
36C4×#1157C2211yescharacteristic
37C2×C4×D28C2211yescharacteristic
38#90161C2211yescharacteristic
39C7×#433—21no—
40C7×#433—21no—
41C7×#432C2211yescharacteristic
42C7×#432C2211yescharacteristic, complemented
43C7×#431C2211yescharacteristic
44C7×#431C2211yescharacteristic, complemented
45C7×#423C2211yescharacteristic, complemented
46C2×C7×C4⋊C8C2211yescharacteristic, complemented
47C7×#408—21no—
48C7×#405—21no—
49#89796—21no—
50#89784—21no—
51#89783—21no—
52#89783—21no—
53#89697C2211yescharacteristic
54#89697C2211yescharacteristic, complemented
55#89697C2211yescharacteristic, complemented
56C4×#1136C2211yescharacteristic
57C4×#1136C2211yescharacteristic, complemented
58C2×C4×C7⋊C8C2211yescharacteristic, complemented
59#89279C2211yescharacteristic, complemented
60#89279C2211yescharacteristic, complemented
61#89279C2211yescharacteristic, complemented
62#89279C2211yescharacteristic, complemented
63#89279C2211yescharacteristic, complemented
64#89279C2211yescharacteristic, complemented
65#89279C2211yescharacteristic, complemented
66#89279C2211yescharacteristic, complemented
67#89278C2211yescharacteristic
68#89278C2211yescharacteristic
69#89278C2211yescharacteristic
70#89278C2211yescharacteristic
71#89278C2211yescharacteristic
72#89278C2211yescharacteristic
73#89278C2211yescharacteristic
74#89278C2211yescharacteristic
75#17513—71nomaximal, Sylow
76C2×C7×#41D411yescharacteristic
77C2×#1157C2×C411yescharacteristic
78C2×#1157C2×C411yescharacteristic
79C22×D28C2×C411yescharacteristic
80C22×C4×D7—21no—
81C2×C7×M16—21no—
82C22×C7×C8—21no—
83C4×C7×Q8C2×C411yescharacteristic
84C4×C7×Q8D411yescharacteristic
85C4×C7×D4C2×C411yescharacteristic
86C4×C7×D4C2×C411yescharacteristic
87C4×C7×D4C2×C411yescharacteristic
88C4×C7×D4D411yescharacteristic
89C4×C7×D4D411yescharacteristic
90C4×C7×D4D411yescharacteristic
91C7×#117D411yescharacteristic
92C7×#117D411yescharacteristic
93C7×#117D411yescharacteristic
94C2×C42×C7C2311yescharacteristic
95C2×C42×C7C2311yescharacteristic
96C2×C42×C7C2311yescharacteristic
97#6509—21no—
98#6509—21no—
99#6501—21no—
100#6501—21no—
101#6500—21no—
102#6500—21no—
103#6498—21no—
104#6498—21no—
105#6493C2×C411yescharacteristic
106#6493C2×C411yescharacteristic
107#6492—21no—
108#6492—21no—
109C4×C22⋊D7—21no—
110C4×C22⋊D7—21no—
111C4×C22⋊D7—21no—
112C4×C22⋊D7—21no—
113C4×C22⋊D7—21no—
114C4×C22⋊D7—21no—
115C2×(C2×D7)⋊C4—21no—
116#6489—21no—
117#6489C2×C411yescharacteristic
118#6489C2×C411yescharacteristic
119C2×C4⋊Dic7C2×C411yescharacteristic
120#6487—21no—
121#6487C2×C411yescharacteristic
122#6487C2×C411yescharacteristic
123#6487C2×C411yescharacteristic
124#6487C2×C411yescharacteristic
125C2×#1136—21no—
126C2×#1136—21no—
127C22×C7⋊C8—21no—
128#6461—21no—
129#6461—21no—
130#6459—21no—
131#6459—21no—
132#6457—21no—
133#6457—21no—
134#6455—21no—
135#6455—21no—
136D7×C4⋊C4—21no—
137D7×C4⋊C4—21no—
138#6452—21no—
139#6452—21no—
140#6448—21no—
141#6448—21no—
142#6447—21no—
143#6447—21no—
144#6446—21no—
145#6446—21no—
146D7×C22⋊C4—21no—
147D7×C22⋊C4—21no—
148#6442—21no—
149#6442—21no—
150#6440—21no—
151#6440—21no—
152#6439—21no—
153#6439—21no—
154#6438C2×C411yescharacteristic
155#6438C2×C411yescharacteristic
156C4×D28—21no—
157C4×D28—21no—
158C4×D28C2×C411yescharacteristic
159C4×D28C2×C411yescharacteristic
160C4×D28C2×C411yescharacteristic
161C4×D28C2×C411yescharacteristic
162C4×D28C2311yescharacteristic
163C4×D28C2311yescharacteristic
164#6435—21no—
165#6435—21no—
166#6435—21no—
167#6435—21no—
168C42×D7—21no—
169C42×D7—21no—
170#6433—21no—
171#6433C2×C411yescharacteristic
172#6433C2×C411yescharacteristic
173#6432C2×C411yescharacteristic
174#6432C2×C411yescharacteristic
175C4×Dic14—21no—
176C4×Dic14C2×C411yescharacteristic
177C4×Dic14C2×C411yescharacteristic
178C4×Dic14C2311yescharacteristic
179C4×Dic14C2311yescharacteristic
180C7×C4⋊C8—21no—
181C7×C4⋊C8—21no—
182C7×C4⋊C8C2311yescharacteristic
183C7×C4⋊C8C2311yescharacteristic
184C7×C4⋊C8C2311yescharacteristic
185C7×C4⋊C8C2311yescharacteristic
186C7×C22⋊C8—21no—
187C7×C22⋊C8—21no—
188C7×C22⋊C8—21no—
189C7×C22⋊C8—21no—
190C7×#97—21no—
191C7×#97—21no—
192C4×C7×C8—21no—
193C4×C7×C8—21no—
194C22⋊(C7⋊C8)—21no—
195C22⋊(C7⋊C8)—21no—
196C22⋊(C7⋊C8)—21no—
197C4⋊(C7⋊C8)—21no—
198C4⋊(C7⋊C8)—21no—
199C4⋊(C7⋊C8)—21no—
200#6377—21no—
201#6377—21no—
202C4×C7⋊C8—21no—
203C4×C7⋊C8C2311yescharacteristic
204C4×C7⋊C8C2311yescharacteristic
205C4×C7⋊C8C2311yescharacteristic
206C4×C7⋊C8C2311yescharacteristic
207#3475—71no—
208#2965—71no—
209#2925D711yescharacteristic, complemented
210#1497—71no—
211#1495—71no—
212#1494—71no—
213#1490—71no—
214#1489—71no—
215#1488—71no—
216#1485—71no—
217#1483—71no—
218#1482—71no—
219#1478—71no—
220#1477—71no—
221#1476—71no—
222C23×D7—21no—
223C7×#41—41no—
224C7×#41—41no—
225C2×C7×Q8C22⋊C411yescharacteristic
226C2×C7×D4C22⋊C411yescharacteristic
227C2×C7×D4C22⋊C411yescharacteristic
228C2×C7×D4C22⋊C411yescharacteristic
229C22×C4×C7C22×C411yescharacteristic
230C22×C4×C7C22×C411yescharacteristic
231C22×C4×C7C22×C411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C2×C22⋊D7—21no—
239C2×C22⋊D7—21no—
240C2×C22⋊D7—21no—
241C2×C22⋊D7—21no—
242C22×Dic7—21no—
243#1157—22no—
244#1157—22no—
245#1157—41no—
246#1157—41no—
247C2×D28—22no—
248C2×D28—21no—
249C2×D28—41no—
250C2×D28C22×C411yescharacteristic
251C2×D28C22×C411yescharacteristic
252C2×C4×D7—21no—
253C2×C4×D7—21no—
254C2×C4×D7—21no—
255C2×C4×D7—21no—
256C2×C4×D7—21no—
257C2×C4×D7—21no—
258C2×C4×D7—21no—
259C2×C4×D7—21no—
260C2×C4×D7—42no—
261C2×C4×D7—42no—
262C2×Dic14—21no—
263C2×Dic14C22×C411yescharacteristic
264C2×Dic14C22×C411yescharacteristic
265C7×M16—42no—
266C2×C7×C8—21no—
267C2×C7×C8—21no—
268C2×C7×C8—21no—
269C2×C7×C8—21no—
270C2×C7×C8—42no—
271C7×C4⋊C4C22⋊C411yescharacteristic
272C7×C4⋊C4C22⋊C411yescharacteristic
273C7×C4⋊C4C22⋊C411yescharacteristic
274C7×C4⋊C4C22⋊C411yescharacteristic
275C7×C4⋊C4C22⋊C411yescharacteristic
276C7×C4⋊C4C22⋊C411yescharacteristic
277C7×C22⋊C4C22⋊C411yescharacteristic
278C7×C22⋊C4C22⋊C411yescharacteristic
279C7×C22⋊C4C22⋊C411yescharacteristic
280C7×C22⋊C4C22⋊C411yescharacteristic
281C7×C22⋊C4C22⋊C411yescharacteristic
282C7×C22⋊C4C22⋊C411yescharacteristic
283C42×C7C22×C411yescharacteristic
284C42×C7C22×C411yescharacteristic
285C42×C7C22×C411yescharacteristic
286C42×C7C2×D411yescharacteristic
287C42×C7C2×D411yescharacteristic
288C42×C7C2×D411yescharacteristic
289C42×C7C2×D411yescharacteristic
290C42×C7C2×D411yescharacteristic
291C42×C7C2×D411yescharacteristic
292C42×C7C2411yescharacteristic
293C22⋊Dic7—21no—
294C22⋊Dic7—21no—
295C22⋊Dic7—21no—
296C22⋊Dic7—21no—
297C22⋊Dic7—21no—
298C22⋊Dic7—21no—
299(C2×D7)⋊C4—21no—
300(C2×D7)⋊C4—21no—
301(C2×D7)⋊C4—21no—
302(C2×D7)⋊C4—21no—
303(C2×D7)⋊C4—21no—
304(C2×D7)⋊C4—21no—
305(C2×D7)⋊C4—21no—
306(C2×D7)⋊C4—21no—
307(C2×D7)⋊C4—21no—
308(C2×D7)⋊C4—21no—
309(C2×D7)⋊C4—21no—
310(C2×D7)⋊C4—21no—
311C4⋊Dic7—21no—
312C4⋊Dic7—21no—
313C4⋊Dic7—21no—
314C4⋊Dic7—21no—
315C4⋊Dic7C22×C411yescharacteristic
316C4⋊Dic7C22×C411yescharacteristic
317C4⋊Dic7C22×C411yescharacteristic
318C4⋊Dic7C22×C411yescharacteristic
319Dic7⋊C4—21no—
320Dic7⋊C4—21no—
321Dic7⋊C4—21no—
322Dic7⋊C4—21no—
323Dic7⋊C4—21no—
324Dic7⋊C4—21no—
325Dic7⋊C4—21no—
326Dic7⋊C4—21no—
327Dic7⋊C4—21no—
328Dic7⋊C4—21no—
329Dic7⋊C4—21no—
330Dic7⋊C4—21no—
331C4×Dic7—21no—
332C4×Dic7—21no—
333C4×Dic7—21no—
334C4×Dic7—21no—
335C4×Dic7—21no—
336C4×Dic7—21no—
337#1136—42no—
338#1136—42no—
339C2×C7⋊C8—21no—
340C2×C7⋊C8—21no—
341C2×C7⋊C8—21no—
342C2×C7⋊C8—21no—
343C2×C7⋊C8—42no—
344#556—71no—
345#555—71no—
346#554—71no—
347#553—141no—
348#552—71no—
349#552—71no—
350#552—141no—
351#551—141no—
352#551—141no—
353#547—71no—
354#546—71no—
355#546—71no—
356#533—71no—
357#529—71no—
358#529—71no—
359#529—141no—
360#529—141no—
361#525—141no—
362C4×#41—71no—
363C4×#41—71no—
364C4×#41C2×D711yescharacteristic
365C2×C4×D4—71no—
366C2×#117—141no—
367#446—141no—
368#436—141no—
369#435—141no—
370#435—141no—
371#433—21no—
372#433—21no—
373#432C2×D711yescharacteristic
374#432C2×D711yescharacteristic, complemented
375#431—71no—
376#431—71no—
377#431—71no—
378#431C2×D711yescharacteristic
379#431C2×D711yescharacteristic, complemented
380#423C2×D711yescharacteristic, complemented
381C2×C4⋊C8C2×D711yescharacteristic, complemented
382#408—21no—
383#405—21no—
384C4×M16—71no—
385C4×M16—71no—
386C2×C4×C8—71no—
387Q8⋊C8—71no—
388Q8⋊C8—71no—
389Q8⋊C8—71no—
390Q8⋊C8—71no—
391Q8⋊C8—71no—
392Q8⋊C8—71no—
393Q8⋊C8—71no—
394Q8⋊C8—71no—
395D4⋊C8—71no—
396D4⋊C8—71no—
397D4⋊C8—71no—
398D4⋊C8—71no—
399D4⋊C8—71no—
400D4⋊C8—71no—
401D4⋊C8—71no—
402D4⋊C8—71no—
403C23×C7C2×C22⋊C411yescharacteristic
404C23×C7C2×C22⋊C411yescharacteristic
405C23×C7C2×C22⋊C411yescharacteristic
406C22×D7—21no—
407C22×D7—21no—
408C22×D7—42no—
409C22×D7—42no—
410C22×D7—81no—
411C7×Q8—41no—
412C7×D4—41no—
413C7×D4—41no—
414C7×D4—41no—
415C2×C4×C7—21no—
416C2×C4×C7—21no—
417C2×C4×C7—21no—
418C2×C4×C7—21no—
419C2×C4×C7—21no—
420C2×C4×C7—21no—
421C2×C4×C7—21no—
422C2×C4×C7—21no—
423C2×C4×C7—21no—
424C2×C4×C7—21no—
425C2×C4×C7—21no—
426C2×C4×C7—21no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7C2×C22⋊C411yescharacteristic
431C2×C4×C7C2×C22⋊C411yescharacteristic
432C2×C4×C7C2×C22⋊C411yescharacteristic
433C2×C4×C7C2×C22⋊C411yescharacteristic
434C2×C4×C7C2×C22⋊C411yescharacteristic
435C2×C4×C7C2×C22⋊C411yescharacteristic
436C2×C4×C7C2×C22⋊C411yescharacteristic
437C2×C4×C7C2×C22⋊C411yescharacteristic
438C2×C4×C7C2×C22⋊C411yescharacteristic
439C2×C4×C7C23×C411yescharacteristic
440C2×C4×C7C22×D411yescharacteristic
441C2×C4×C7C22×D411yescharacteristic
442C22⋊D7—42no—
443C22⋊D7—42no—
444C22⋊D7—81no—
445C22⋊D7—81no—
446C2×Dic7—21no—
447C2×Dic7—21no—
448C2×Dic7—21no—
449C2×Dic7—21no—
450C2×Dic7—21no—
451C2×Dic7—21no—
452C2×Dic7—42no—
453D28—21no—
454D28—21no—
455D28—21no—
456D28—42no—
457D28#13112yes—
458C4×D7—42no—
459C4×D7—42no—
460C4×D7—42no—
461C4×D7—42no—
462C4×D7—41no—
463C4×D7—41no—
464C4×D7—41no—
465C4×D7—41no—
466C4×D7—81no—
467C4×D7—81no—
468Dic14—21no—
469Dic14—21no—
470Dic14—21no—
471Dic14—21no—
472Dic14—81no—
473C7×C8—41no—
474C7×C8—41no—
475C7×C8—41no—
476C7×C8—41no—
477C7⋊C8—22no—
478C7⋊C8—41no—
479C7⋊C8—41no—
480C7⋊C8—41no—
481C2×#41—71no—
482C2×#41—71no—
483C2×#41C22⋊D711yescharacteristic
484C22×D4—71no—
485C23×C4—141no—
486C2×M16—21no—
487C2×M16—141no—
488C2×M16—141no—
489C22×C8—21no—
490C22×C8—141no—
491C4⋊Q8—71no—
492C4⋊Q8—71no—
493#126—141no—
494#126—141no—
495#126—141no—
496#126—141no—
497#126—141no—
498#126—141no—
499#125—71no—
500#125—71no—
501#125—141no—
502#125—141no—
503#125—141no—
504#124—71no—
505#124—71no—
506#124—141no—
507#124—141no—
508#123—141no—
509#123—141no—
510#123—141no—
511#123—141no—
512#123—141no—
513#123—141no—
514#123—141no—
515#123—141no—
516C22⋊Q8—71no—
517C22⋊Q8—71no—
518C22⋊Q8—71no—
519C22⋊Q8—71no—
520C22⋊Q8—141no—
521C22⋊Q8—141no—
522C22⋊Q8—141no—
523C22⋊Q8—141no—
524C22⋊Q8—141no—
525#121—71no—
526#121—71no—
527#121—141no—
528#121—141no—
529#121—141no—
530#121—141no—
531#120—141no—
532#120—141no—
533C4×Q8—71no—
534C4×Q8—71no—
535C4×Q8—71no—
536C4×Q8—71no—
537C4×Q8—141no—
538C4×Q8C4×D711yescharacteristic
539C4×Q8D2811yescharacteristic
540C4×D4—71no—
541C4×D4—71no—
542C4×D4—71no—
543C4×D4—71no—
544C4×D4—71no—
545C4×D4—71no—
546C4×D4—141no—
547C4×D4—141no—
548C4×D4—141no—
549C4×D4—141no—
550C4×D4—141no—
551C4×D4—141no—
552C4×D4—141no—
553C4×D4—141no—
554C4×D4C4×D711yescharacteristic
555C4×D4C4×D711yescharacteristic
556C4×D4C4×D711yescharacteristic
557C4×D4D2811yescharacteristic
558C4×D4D2811yescharacteristic
559C4×D4D2811yescharacteristic
560#117—71no—
561#117—71no—
562#117—141no—
563#117—141no—
564#117—141no—
565#117—141no—
566#117—141no—
567#117—141no—
568#117—141no—
569#117—141no—
570#117—141no—
571#117C22⋊D711yescharacteristic
572#117C22⋊D711yescharacteristic
573#117C22⋊D711yescharacteristic
574C2×C4⋊C4—71no—
575C2×C4⋊C4—141no—
576C2×C4⋊C4—141no—
577C2×C22⋊C4—141no—
578C2×C22⋊C4—141no—
579C2×C22⋊C4—141no—
580C2×C42—141no—
581C2×C42—141no—
582C2×C42C22×D711yescharacteristic
583C2×C42C22×D711yescharacteristic
584C2×C42C22×D711yescharacteristic
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—141no—
588C4⋊C8—141no—
589C4⋊C8—141no—
590C4⋊C8C22×D711yescharacteristic
591C4⋊C8C22×D711yescharacteristic
592C4⋊C8C22×D711yescharacteristic
593C4⋊C8C22×D711yescharacteristic
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8—21no—
598C22⋊C8—141no—
599C22⋊C8—141no—
600C22⋊C8—141no—
601#97—21no—
602#97—21no—
603#97—141no—
604#97—141no—
605C4×C8—21no—
606C4×C8—21no—
607C4×C8—71no—
608C4×C8—71no—
609C4×C8—71no—
610C4×C8—71no—
611C4×C8—141no—
612C22×C7—21no—
613C22×C7—21no—
614C22×C7—21no—
615C22×C7—21no—
616C22×C7—21no—
617C22×C7—21no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—21no—
621C22×C7C22×C22⋊C411yescharacteristic
622C2×D7—22no—
623C2×D7—41no—
624C2×D7—41no—
625C2×D7—41no—
626C2×D7—41no—
627C2×D7—41no—
628C2×D7—84no—
629C4×C7—21no—
630C4×C7—21no—
631C4×C7—21no—
632C4×C7—21no—
633C4×C7—21no—
634C4×C7—21no—
635C4×C7—21no—
636C4×C7—21no—
637C4×C7—21no—
638C4×C7—21no—
639C4×C7C2×#13111yescharacteristic
640C4×C7#56811yescharacteristic
641C4×C7#57511yescharacteristic
642C4×C7#57511yescharacteristic
643Dic7—41no—
644Dic7—41no—
645Dic7—41no—
646Dic7—41no—
647Dic7—41no—
648Dic7—41no—
649C24—141no—
650#41—41no—
651#41—41no—
652#41—142no—
653#41—142no—
654#41—281no—
655#41—281no—
656C2×Q8—71no—
657C2×Q8—71no—
658C2×Q8—141no—
659C2×Q8(C2×D7)⋊C411yescharacteristic
660C2×D4—71no—
661C2×D4—71no—
662C2×D4—142no—
663C2×D4—141no—
664C2×D4—141no—
665C2×D4—141no—
666C2×D4—141no—
667C2×D4—141no—
668C2×D4—281no—
669C2×D4(C2×D7)⋊C411yescharacteristic
670C2×D4(C2×D7)⋊C411yescharacteristic
671C2×D4(C2×D7)⋊C411yescharacteristic
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—282no—
682C22×C4—282no—
683C22×C4C2×C4×D711yescharacteristic
684C22×C4C2×C4×D711yescharacteristic
685C22×C4C2×C4×D711yescharacteristic
686C22×C4C2×D2811yescharacteristic
687C22×C4C2×D2811yescharacteristic
688C22×C4C2×D2811yescharacteristic
689C22×C4C2×C22⋊D711yescharacteristic
690C22×C4C2×C22⋊D711yescharacteristic
691C22×C4C2×C22⋊D711yescharacteristic
692M16—42no—
693M16—282no—
694M16—282no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—141no—
701C2×C8—141no—
702C2×C8—141no—
703C2×C8—141no—
704C2×C8—282no—
705C4⋊C4—71no—
706C4⋊C4—71no—
707C4⋊C4—71no—
708C4⋊C4—71no—
709C4⋊C4—141no—
710C4⋊C4—141no—
711C4⋊C4—141no—
712C4⋊C4—141no—
713C4⋊C4—141no—
714C4⋊C4—141no—
715C4⋊C4—141no—
716C4⋊C4—141no—
717C4⋊C4—141no—
718C4⋊C4—141no—
719C4⋊C4—141no—
720C4⋊C4—141no—
721C4⋊C4—141no—
722C4⋊C4—141no—
723C4⋊C4—141no—
724C4⋊C4—141no—
725C4⋊C4(C2×D7)⋊C411yescharacteristic
726C4⋊C4(C2×D7)⋊C411yescharacteristic
727C4⋊C4(C2×D7)⋊C411yescharacteristic
728C4⋊C4(C2×D7)⋊C411yescharacteristic
729C4⋊C4(C2×D7)⋊C411yescharacteristic
730C4⋊C4(C2×D7)⋊C411yescharacteristic
731C22⋊C4—141no—
732C22⋊C4—141no—
733C22⋊C4—141no—
734C22⋊C4—141no—
735C22⋊C4—141no—
736C22⋊C4—141no—
737C22⋊C4—141no—
738C22⋊C4—141no—
739C22⋊C4—141no—
740C22⋊C4—141no—
741C22⋊C4—141no—
742C22⋊C4—141no—
743C22⋊C4—141no—
744C22⋊C4—141no—
745C22⋊C4—141no—
746C22⋊C4—141no—
747C22⋊C4—141no—
748C22⋊C4—141no—
749C22⋊C4(C2×D7)⋊C411yescharacteristic
750C22⋊C4(C2×D7)⋊C411yescharacteristic
751C22⋊C4(C2×D7)⋊C411yescharacteristic
752C22⋊C4(C2×D7)⋊C411yescharacteristic
753C22⋊C4(C2×D7)⋊C411yescharacteristic
754C22⋊C4(C2×D7)⋊C411yescharacteristic
755C42—141no—
756C42—141no—
757C42—141no—
758C42—141no—
759C42—141no—
760C42—141no—
761C42C2×C4×D711yescharacteristic
762C42C2×C4×D711yescharacteristic
763C42C2×C4×D711yescharacteristic
764C42C2×D2811yescharacteristic
765C42C2×D2811yescharacteristic
766C42C2×D2811yescharacteristic
767C42C2×C22⋊D711yescharacteristic
768C42C2×C22⋊D711yescharacteristic
769C42C2×C22⋊D711yescharacteristic
770C42C23×D711yescharacteristic
771C2×C7—41no—
772C2×C7—41no—
773C2×C7—41no—
774C2×C7#288011yescharacteristic
775C2×C7#289611yescharacteristic
776C2×C7#290111yescharacteristic
777D7—42no—
778D7—81no—
779C23—141no—
780C23—141no—
781C23—282no—
782C23—282no—
783C23—561no—
784C23C2×(C2×D7)⋊C411yescharacteristic
785C23C2×(C2×D7)⋊C411yescharacteristic
786C23C2×(C2×D7)⋊C411yescharacteristic
787Q8—41no—
788Q8—141no—
789Q8—141no—
790Q8—141no—
791Q8—141no—
792Q8—561no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—72no—
797D4—141no—
798D4—141no—
799D4—141no—
800D4—282no—
801D4—282no—
802D4—282no—
803D4—561no—
804D4—561no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—141no—
821C2×C4—141no—
822C2×C4—141no—
823C2×C4—141no—
824C2×C4—141no—
825C2×C4—141no—
826C2×C4—282no—
827C2×C4—282no—
828C2×C4—282no—
829C2×C4—282no—
830C2×C4—282no—
831C2×C4—281no—
832C2×C4—281no—
833C2×C4—281no—
834C2×C4—281no—
835C2×C4—561no—
836C2×C4—561no—
837C2×C4C2×(C2×D7)⋊C411yescharacteristic
838C2×C4C2×(C2×D7)⋊C411yescharacteristic
839C2×C4C2×(C2×D7)⋊C411yescharacteristic
840C2×C4C2×(C2×D7)⋊C411yescharacteristic
841C2×C4C2×(C2×D7)⋊C411yescharacteristic
842C2×C4C2×(C2×D7)⋊C411yescharacteristic
843C2×C4C2×(C2×D7)⋊C411yescharacteristic
844C2×C4C2×(C2×D7)⋊C411yescharacteristic
845C2×C4C2×(C2×D7)⋊C411yescharacteristic
846C2×C4C22×C4×D711yescharacteristic
847C2×C4C22×D2811yescharacteristic
848C2×C4C22×C22⋊D711yescharacteristic
849C8—41no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—142no—
854C8—281no—
855C8—281no—
856C8—281no—
857C7#1751311yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—142no—
868C22—281no—
869C22—281no—
870C22—281no—
871C22—281no—
872C22—281no—
873C22—564no—
874C22C22×(C2×D7)⋊C411yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—281no—
886C4—281no—
887C4—281no—
888C4—281no—
889C4—281no—
890C4—281no—
891C4D7×#13111yescharacteristic
892C4#9044111yescharacteristic
893C4#9051311yescharacteristic
894C4#9051311yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—282no—
899C2—561no—
900C2#1173965811yescharacteristic
901C2#1174123811yescharacteristic
902C2#1174126211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#2925C2
socleC22×C7C22×C22⋊C4
prime radical#11742908C2
cosocleC42×C7C24
hypercenter#2925D7
hypocenterC7#17513
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. C7×#2925C2semidirect
3. #11739962C2semidirect
4. #11728557C2semidirect
5. #11728554C2semidirect
6. #11728553C2semidirect
7. #11728552C2semidirect
8. #11728523C2semidirect
9. #11728513C2semidirect
10. #11728510C2semidirect
11. #11728508C2semidirect
12. #11728253C2semidirect
13. #11728251C2semidirect
14. #11728181C2semidirect
15. #11728179C2semidirect
42. C7×#432C22semidirect
44. C7×#431C22semidirect
45. C7×#423C22semidirect
46. C2×C7×C4⋊C8C22semidirect
54. #89697C22semidirect
55. #89697C22semidirect
57. C4×#1136C22semidirect
58. C2×C4×C7⋊C8C22semidirect
59. #89279C22semidirect
60. #89279C22semidirect
61. #89279C22semidirect
62. #89279C22semidirect
63. #89279C22semidirect
64. #89279C22semidirect
65. #89279C22semidirect
66. #89279C22semidirect
209. #2925D7semidirect
374. #432C2×D7semidirect
379. #431C2×D7semidirect
380. #423C2×D7semidirect
381. C2×C4⋊C8C2×D7semidirect
857. C7#17513semidirect

Maximal subgroups

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

subgroupindex
#117429082
C7×#29252
#117399622
#117285572
#117285542
#117285532
#117285522
#117285232
#117285132
#117285102
#117285082
#117282532
#117282512
#117281812
#117281792
#175137