Finite Group Databasebeta

← #13370291

Subgroups — #13370291

Order 1792.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742832C211yesmaximal, characteristic
2C7×#2290C211yesmaximal, characteristic, complemented
3D4×#1136C211yesmaximal, characteristic, complemented
4#11729345C211yesmaximal, characteristic, complemented
5#11729332C211yesmaximal, characteristic, complemented
6#11729286C211yesmaximal, characteristic, complemented
7C2×#89318C211yesmaximal, characteristic, complemented
8#11727248C211yesmaximal, characteristic, complemented
9#11727247C211yesmaximal, characteristic, complemented
10#11727207C211yesmaximal, characteristic, complemented
11#11727207C211yesmaximal, characteristic, complemented
12#11727196C211yesmaximal, characteristic, complemented
13#11727196C211yesmaximal, characteristic, complemented
14#11727195C211yesmaximal, characteristic, complemented
15#11727184C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19#90497—21no—
20#90482C2211yescharacteristic
21#90482C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C2×#6489C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26#90256C411yescharacteristic, complemented
27#90256C411yescharacteristic, complemented
28#90254C411yescharacteristic, complemented
29#90248—21no—
30#90246C411yescharacteristic, complemented
31#90234C411yescharacteristic, complemented
32#90233C411yescharacteristic, complemented
33#90232C411yescharacteristic, complemented
34#90232C411yescharacteristic, complemented
35#90229—21no—
36#90229—21no—
37C4×#1159—21no—
38#90204—21no—
39#90186—21no—
40#90186—21no—
41C4×#1157C2211yescharacteristic
42#90161C2211yescharacteristic
43C7×#388—21no—
44C7×#387—21no—
45C7×#386—21no—
46C7×#385—21no—
47C4×C7×C4⋊C4C2211yescharacteristic
48C4×C7×C22⋊C4C2211yescharacteristic
49C4×C7×C22⋊C4C2211yescharacteristic
50C7×#376C2211yescharacteristic
51#89979C2211yescharacteristic
52#89979C2211yescharacteristic
53#89784—21no—
54#89783—21no—
55#89783—21no—
56D4×C7⋊C8—21no—
57C2×#6379C2211yescharacteristic
58C2×#6379C2211yescharacteristic
59C2×#6379C2211yescharacteristic
60C2×#6379C2211yescharacteristic
61#89696C2211yescharacteristic
62C4×#1136C2211yescharacteristic
63#89318C2211yescharacteristic
64#89318C2211yescharacteristic
65#89318C2211yescharacteristic
66#89318C2211yescharacteristic
67#89318C2211yescharacteristic
68#89318C2211yescharacteristic
69#89318C2211yescharacteristic
70#89318C2211yescharacteristic
71#89318C2211yescharacteristic
72#89318C2211yescharacteristic
73#89318C2211yescharacteristic
74#89318C2211yescharacteristic
75#22506—71nomaximal, Sylow
76C22×C7×D4D411yescharacteristic
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C2×#1159—21no—
81C2×#1157C2311yescharacteristic
82C4×C7×D4C2×C411yescharacteristic
83C4×C7×D4C2×C411yescharacteristic
84C4×C7×D4C2×C411yescharacteristic
85C4×C7×D4C2×C411yescharacteristic
86C4×C7×D4D411yescharacteristic
87C4×C7×D4D411yescharacteristic
88C4×C7×D4D411yescharacteristic
89C4×C7×D4D411yescharacteristic
90C7×#117—22no—
91C7×#117—41no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4D411yescharacteristic
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4D411yescharacteristic
99C2×C7×C22⋊C4D411yescharacteristic
100C2×C42×C7—22no—
101C2×C42×C7—21no—
102C2×C42×C7—41no—
103C2×C42×C7C2311yescharacteristic
104C2×C42×C7C2311yescharacteristic
105C2×C42×C7C2311yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108#6516—21no—
109#6516—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112#6502—21no—
113#6502—21no—
114#6501—21no—
115#6499—21no—
116#6498—21no—
117#6498—21no—
118D4×Dic7—21no—
119#6493C2×C411yescharacteristic
120#6493C2×C411yescharacteristic
121#6493C2×C411yescharacteristic, complemented
122#6493C2×C411yescharacteristic, complemented
123#6492—21no—
124#6492—21no—
125C4×C22⋊D7—21no—
126C4×C22⋊D7—21no—
127C4×C22⋊D7—21no—
128C4×C22⋊D7—21no—
129C4×C22⋊D7—21no—
130C4×C22⋊D7—21no—
131#6489—21no—
132#6489—21no—
133#6489—21no—
134#6489—21no—
135#6489C2×C411yescharacteristic
136#6489C2×C411yescharacteristic
137#6489C2×C411yescharacteristic, complemented
138#6489C2×C411yescharacteristic, complemented
139#6489C2311yescharacteristic
140#6489C2311yescharacteristic
141#6489C2311yescharacteristic
142C2×C4⋊Dic7C2×C411yescharacteristic
143C2×C4⋊Dic7C2×C411yescharacteristic
144C2×C4⋊Dic7C2×C411yescharacteristic, complemented
145C2×C4⋊Dic7C2×C411yescharacteristic, complemented
146#6487—21no—
147#6487—21no—
148#6487C2×C411yescharacteristic
149#6487C2×C411yescharacteristic
150#6487C2×C411yescharacteristic, complemented
151#6487C2×C411yescharacteristic, complemented
152C2×C4×Dic7—21no—
153C2×C4×Dic7—21no—
154C2×#1136—21no—
155C2×#1136—21no—
156C2×#1136—22no—
157C2×#1136—22no—
158C2×#1136—41no—
159C2×#1136—41no—
160C2×#1136C2311yescharacteristic
161C2×#1136C2311yescharacteristic
162C2×#1136C2311yescharacteristic
163C2×#1136C2311yescharacteristic
164C22×C7⋊C8—21no—
165C22×C7⋊C8—21no—
166#6461—21no—
167#6461—21no—
168#6460—21no—
169#6455—21no—
170#6453—21no—
171#6452—21no—
172#6452—21no—
173#6450—21no—
174#6449—21no—
175#6449—21no—
176#6448—21no—
177#6448—21no—
178#6446—21no—
179#6446—21no—
180(C22⋊D7)⋊C4—21no—
181(C22⋊D7)⋊C4—21no—
182#6442—21no—
183#6442—21no—
184#6442—21no—
185#6442—21no—
186#6441—21no—
187#6441—21no—
188#6440—21no—
189#6440—21no—
190C4×D28C2×C411yescharacteristic, complemented
191C4×D28C2×C411yescharacteristic, complemented
192#6435—21no—
193C42×D7—21no—
194#6433C2×C411yescharacteristic, complemented
195#6433C2×C411yescharacteristic, complemented
196#6432C2×C411yescharacteristic, complemented
197#6432C2×C411yescharacteristic, complemented
198C4×Dic14—21no—
199C4×Dic14—21no—
200C4×Dic14C2×C411yescharacteristic, complemented
201C4×Dic14C2×C411yescharacteristic, complemented
202C7×#95—21no—
203C7×#95—21no—
204C7×#95—21no—
205C7×#95—21no—
206C7×#95—21no—
207C22⋊(C7⋊C8)—21no—
208C22⋊(C7⋊C8)—21no—
209C22⋊(C7⋊C8)—21no—
210C22⋊(C7⋊C8)—21no—
211#6379—22no—
212#6379—22no—
213#6379—41no—
214#6379—41no—
215C4⋊(C7⋊C8)—21no—
216C4⋊(C7⋊C8)—21no—
217#6377—21no—
218C4×C7⋊C8—21no—
219#3475—71no—
220D4×M16—71no—
221#2290D711yescharacteristic, complemented
222#1995—71no—
223#1986—71no—
224#1897—71no—
225#1896—71no—
226#1871—71no—
227#1871—71no—
228#1826—71no—
229#1826—71no—
230#1806—71no—
231#1759—71no—
232#1733—71no—
233C2×#339—71no—
234C24×C7C2×D411yescharacteristic
235C24×C7C2×D411yescharacteristic
236C2×C7×D4—42no—
237C2×C7×D4C22⋊C411yescharacteristic
238C2×C7×D4C22⋊C411yescharacteristic
239C2×C7×D4C22⋊C411yescharacteristic
240C2×C7×D4C22⋊C411yescharacteristic
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—42no—
254C22×C4×C7—42no—
255C22×C4×C7—42no—
256C22×C4×C7C22×C411yescharacteristic
257C22×C4×C7C22×C411yescharacteristic
258C22×C4×C7C22×C411yescharacteristic
259C22×C4×C7C22×C411yescharacteristic
260C22×C4×C7C2×D411yescharacteristic
261C22×C4×C7C2×D411yescharacteristic
262C22×C4×C7C2×D411yescharacteristic
263C22×C4×C7C2×D411yescharacteristic
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2×D411yescharacteristic
266C22×C4×C7C2×D411yescharacteristic
267C22×C4×C7C2×D411yescharacteristic
268C22×C4×C7C2411yescharacteristic
269C2×C22⋊D7—21no—
270C2×C22⋊D7—21no—
271C2×C22⋊D7—21no—
272C2×C22⋊D7—21no—
273C2×C22⋊D7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—21no—
277C22×Dic7—21no—
278#1159—44no—
279#1157—21no—
280#1157—21no—
281#1157—21no—
282#1157—21no—
283C2×D28C22×C411yescharacteristic
284C2×C4×D7—21no—
285C2×C4×D7—21no—
286C2×C4×D7—21no—
287C2×Dic14—21no—
288C2×Dic14—21no—
289C2×Dic14C22×C411yescharacteristic
290C7×C4⋊C4—42no—
291C7×C4⋊C4—42no—
292C7×C4⋊C4C22⋊C411yescharacteristic
293C7×C4⋊C4C22⋊C411yescharacteristic
294C7×C4⋊C4C22⋊C411yescharacteristic
295C7×C4⋊C4C22⋊C411yescharacteristic
296C7×C22⋊C4—42no—
297C7×C22⋊C4—42no—
298C7×C22⋊C4—42no—
299C7×C22⋊C4C22⋊C411yescharacteristic
300C7×C22⋊C4C22⋊C411yescharacteristic
301C7×C22⋊C4C22⋊C411yescharacteristic
302C7×C22⋊C4C22⋊C411yescharacteristic
303C7×C22⋊C4C22⋊C411yescharacteristic
304C7×C22⋊C4C22⋊C411yescharacteristic
305C7×C22⋊C4C22⋊C411yescharacteristic
306C7×C22⋊C4C22⋊C411yescharacteristic
307C42×C7—21no—
308C42×C7—21no—
309C42×C7—21no—
310C42×C7—21no—
311C42×C7—21no—
312C42×C7—21no—
313C42×C7—21no—
314C42×C7—42no—
315C42×C7C22×C411yescharacteristic
316C42×C7C22×C411yescharacteristic
317C42×C7C2×D411yescharacteristic
318C42×C7C2×D411yescharacteristic
319C42×C7#4112yescomplemented
320C22⋊Dic7—21no—
321C22⋊Dic7—21no—
322C22⋊Dic7—21no—
323C22⋊Dic7—21no—
324C22⋊Dic7—21no—
325C22⋊Dic7—21no—
326C22⋊Dic7—21no—
327C22⋊Dic7—21no—
328C22⋊Dic7—21no—
329C22⋊Dic7—21no—
330C22⋊Dic7—21no—
331(C2×D7)⋊C4—21no—
332(C2×D7)⋊C4—21no—
333(C2×D7)⋊C4—21no—
334(C2×D7)⋊C4—21no—
335(C2×D7)⋊C4—21no—
336(C2×D7)⋊C4—21no—
337C4⋊Dic7—21no—
338C4⋊Dic7—21no—
339C4⋊Dic7—21no—
340C4⋊Dic7—21no—
341C4⋊Dic7—21no—
342C4⋊Dic7—21no—
343C4⋊Dic7C22×C411yescharacteristic
344C4⋊Dic7C22×C411yescharacteristic
345C4⋊Dic7C22×C411yescharacteristic
346C4⋊Dic7C22×C411yescharacteristic
347C4⋊Dic7C22×C411yescharacteristic
348C4⋊Dic7C22×C411yescharacteristic
349Dic7⋊C4—21no—
350Dic7⋊C4—21no—
351Dic7⋊C4—21no—
352Dic7⋊C4—21no—
353Dic7⋊C4—21no—
354Dic7⋊C4—21no—
355Dic7⋊C4—21no—
356Dic7⋊C4—21no—
357Dic7⋊C4—21no—
358Dic7⋊C4—21no—
359C4×Dic7—21no—
360C4×Dic7—21no—
361C4×Dic7—21no—
362C4×Dic7—21no—
363C4×Dic7—21no—
364C4×Dic7—21no—
365C4×Dic7—21no—
366C4×Dic7—21no—
367C4×Dic7—21no—
368#1136—21no—
369#1136—21no—
370#1136—21no—
371#1136—21no—
372#1136—21no—
373#1136—21no—
374#1136—21no—
375#1136—42no—
376#1136—42no—
377#1136#4112yescomplemented
378C2×C7⋊C8—21no—
379C2×C7⋊C8—21no—
380C2×C7⋊C8—21no—
381C2×C7⋊C8—21no—
382C2×C7⋊C8—42no—
383C2×C7⋊C8—42no—
384C22×M16—71no—
385C22×M16—71no—
386#556—71no—
387#555—71no—
388#554—71no—
389#553—71no—
390#553—71no—
391#552—71no—
392#552—71no—
393#552—141no—
394#551—141no—
395#551—141no—
396#547—71no—
397#546—141no—
398#533—71no—
399#529—141no—
400#529—141no—
401#529—141no—
402#525—71no—
403#525—71no—
404C4×#41—71no—
405C4×#41—141no—
406C2×C4×D4C2×D711yescharacteristic
407C2×#117—71no—
408C2×#117—71no—
409C2×#117C2×D711yescharacteristic
410C22×C42C2×D711yescharacteristic
411#436—141no—
412#435—141no—
413#435—141no—
414C8×D4—141no—
415#423—71no—
416C2×#104—71no—
417C2×#104—71no—
418C2×#104—71no—
419C2×#104—71no—
420#407—71no—
421#407—71no—
422C4×M16—71no—
423#388—21no—
424#387—21no—
425#386—21no—
426#385—21no—
427C4×C4⋊C4C2×D711yescharacteristic
428C4×C22⋊C4C2×D711yescharacteristic
429C4×C22⋊C4C2×D711yescharacteristic
430#376C2×D711yescharacteristic
431#339—71no—
432#339—71no—
433#339—71no—
434#339—71no—
435#339—71no—
436#339—71no—
437#339—71no—
438#339—71no—
439#339—71no—
440#339—71no—
441#339—71no—
442#339—71no—
443C23×C7—21no—
444C23×C7—21no—
445C23×C7—22no—
446C23×C7—21no—
447C23×C7—21no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7C2×C22⋊C411yescharacteristic
452C23×C7C2×C22⋊C411yescharacteristic
453C23×C7C2×C22⋊C411yescharacteristic
454C23×C7C2×C22⋊C411yescharacteristic
455C23×C7C22×D411yescharacteristic
456C22×D7—21no—
457C7×D4—22no—
458C7×D4—22no—
459C7×D4—41no—
460C7×D4—41no—
461C2×C4×C7—21no—
462C2×C4×C7—21no—
463C2×C4×C7—21no—
464C2×C4×C7—21no—
465C2×C4×C7—21no—
466C2×C4×C7—21no—
467C2×C4×C7—21no—
468C2×C4×C7—21no—
469C2×C4×C7—21no—
470C2×C4×C7—21no—
471C2×C4×C7—21no—
472C2×C4×C7—21no—
473C2×C4×C7—21no—
474C2×C4×C7—21no—
475C2×C4×C7—21no—
476C2×C4×C7—21no—
477C2×C4×C7—21no—
478C2×C4×C7—21no—
479C2×C4×C7—21no—
480C2×C4×C7—21no—
481C2×C4×C7—22no—
482C2×C4×C7—22no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—48no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—41no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7C2×C22⋊C411yescharacteristic
497C2×C4×C7C2×C22⋊C411yescharacteristic
498C2×C4×C7C2×C22⋊C411yescharacteristic
499C2×C4×C7C2×C22⋊C411yescharacteristic
500C2×C4×C7C2×C22⋊C411yescharacteristic
501C2×C4×C7C2×C22⋊C411yescharacteristic
502C2×C4×C7C2×C22⋊C411yescharacteristic
503C2×C4×C7C2×C22⋊C411yescharacteristic
504C2×C4×C7C23×C411yescharacteristic
505C2×C4×C7C22×D411yescharacteristic
506C2×C4×C7C2×#4111yescharacteristic
507C2×C4×C7C2×#4111yescharacteristic
508C2×C4×C7H(5,𝔽2)11yescharacteristic
509C2×C4×C72−1+411yescharacteristic
510C22⋊D7—42no—
511C22⋊D7—41no—
512C22⋊D7—41no—
513C22⋊D7—42no—
514C22⋊D7—81no—
515C22⋊D7—81no—
516C2×Dic7—21no—
517C2×Dic7—21no—
518C2×Dic7—21no—
519C2×Dic7—21no—
520C2×Dic7—21no—
521C2×Dic7—21no—
522C2×Dic7—21no—
523C2×Dic7—42no—
524C2×Dic7—42no—
525C2×Dic7—81no—
526C2×Dic7—81no—
527D28—21no—
528D28—21no—
529C4×D7—42no—
530C4×D7—41no—
531C4×D7—41no—
532C4×D7—81no—
533Dic14—21no—
534Dic14—21no—
535Dic14—42no—
536Dic14—81no—
537C7⋊C8—22no—
538C7⋊C8—41no—
539C7⋊C8—41no—
540C7⋊C8—41no—
541C2×#41—71no—
542C2×#41—141no—
543C22×D4C22⋊D711yescharacteristic
544C23×C4—21no—
545C23×C4C22×D711yescharacteristic
546C23×C4C22×D711yescharacteristic
547C2×M16—71no—
548C2×M16—71no—
549C2×M16—71no—
550C2×M16—71no—
551C2×M16—141no—
552C2×M16—141no—
553C2×M16—142no—
554C2×M16—142no—
555C2×M16—281no—
556C2×M16—281no—
557C22×C8—141no—
558C22×C8—141no—
559C4⋊Q8—71no—
560C4⋊Q8—71no—
561#126—141no—
562#126—141no—
563#126—141no—
564#126—141no—
565#126—141no—
566#126—141no—
567#125—71no—
568#125—71no—
569#125—141no—
570#125—141no—
571#125—141no—
572#124—141no—
573#124—141no—
574#124—141no—
575#123—141no—
576#123—141no—
577#123—141no—
578#123—141no—
579#123—141no—
580#123—141no—
581#123—141no—
582#123—141no—
583C22⋊Q8—71no—
584C22⋊Q8—71no—
585C22⋊Q8—71no—
586C22⋊Q8—71no—
587C22⋊Q8—141no—
588C22⋊Q8—141no—
589C22⋊Q8—141no—
590C22⋊Q8—141no—
591C22⋊Q8—141no—
592#121—71no—
593#121—71no—
594#121—71no—
595#121—71no—
596#121—141no—
597#121—141no—
598#121—141no—
599#120—141no—
600#120—141no—
601C4×Q8—71no—
602C4×Q8—71no—
603C4×Q8—141no—
604C4×Q8—141no—
605C4×Q8—141no—
606C4×D4—71no—
607C4×D4—71no—
608C4×D4—141no—
609C4×D4—141no—
610C4×D4—141no—
611C4×D4—141no—
612C4×D4—141no—
613C4×D4—141no—
614C4×D4—141no—
615C4×D4—141no—
616C4×D4—141no—
617C4×D4C4×D711yescharacteristic
618C4×D4C4×D711yescharacteristic
619C4×D4C4×D711yescharacteristic
620C4×D4C4×D711yescharacteristic
621C4×D4D2811yescharacteristic
622C4×D4D2811yescharacteristic
623C4×D4D2811yescharacteristic
624C4×D4D2811yescharacteristic
625#117—22no—
626#117—41no—
627#117—71no—
628#117—71no—
629#117—71no—
630#117—71no—
631#117—71no—
632#117—71no—
633#117—71no—
634#117—141no—
635#117—141no—
636#117—141no—
637#117—141no—
638#117—141no—
639#117—141no—
640#117—141no—
641#117—141no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—71no—
645C2×C4⋊C4—71no—
646C2×C4⋊C4—71no—
647C2×C4⋊C4—71no—
648C2×C4⋊C4C22⋊D711yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—141no—
653C2×C22⋊C4—141no—
654C2×C22⋊C4C22⋊D711yescharacteristic
655C2×C22⋊C4C22⋊D711yescharacteristic
656C2×C42—22no—
657C2×C42—21no—
658C2×C42—41no—
659C2×C42—141no—
660C2×C42—141no—
661C2×C42—141no—
662C2×C42C22×D711yescharacteristic
663C2×C42C22×D711yescharacteristic
664C2×C42C22×D711yescharacteristic
665C2×C42C22×D711yescharacteristic
666C2×C42C22×D711yescharacteristic
667C4⋊C8—141no—
668C4⋊C8—141no—
669#104—142no—
670#104—142no—
671#104—281no—
672#104—281no—
673C22⋊C8—141no—
674C22⋊C8—141no—
675C22⋊C8—141no—
676C22⋊C8—141no—
677#97—141no—
678C4×C8—141no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684C22×C7—21no—
685C22×C7—21no—
686C22×C7—21no—
687C22×C7—21no—
688C22×C7—21no—
689C22×C7—21no—
690C22×C7—21no—
691C22×C7—21no—
692C22×C7—21no—
693C22×C7—21no—
694C22×C7—21no—
695C22×C7—21no—
696C22×C7—21no—
697C22×C7—42no—
698C22×C7—42no—
699C22×C7—81no—
700C22×C7—81no—
701C22×C7#42112yes—
702C22×C7C22×C22⋊C411yescharacteristic
703C22×C7#54611yescharacteristic
704C22×C7#54711yescharacteristic
705C2×D7—41no—
706C2×D7—41no—
707C2×D7—41no—
708C4×C7—21no—
709C4×C7—21no—
710C4×C7—21no—
711C4×C7—21no—
712C4×C7—21no—
713C4×C7—21no—
714C4×C7—21no—
715C4×C7—21no—
716C4×C7—42no—
717C4×C7—42no—
718C4×C7—81no—
719C4×C7—81no—
720C4×C7C4×#4111yescharacteristic
721C4×C7#52011yescharacteristic
722C4×C7#54611yescharacteristic
723C4×C7#54711yescharacteristic
724Dic7—41no—
725Dic7—41no—
726Dic7—41no—
727Dic7—41no—
728Dic7—41no—
729Dic7—41no—
730Dic7—41no—
731C24C2×C22⋊D711yescharacteristic
732C24C2×C22⋊D711yescharacteristic
733#41—141no—
734#41—141no—
735#41—141no—
736#41—141no—
737#41—284no—
738C2×Q8—71no—
739C2×Q8—141no—
740C2×Q8—141no—
741C2×D4—42no—
742C2×D4—71no—
743C2×D4—141no—
744C2×D4—141no—
745C2×D4—141no—
746C2×D4—141no—
747C2×D4—141no—
748C2×D4(C2×D7)⋊C411yescharacteristic
749C2×D4(C2×D7)⋊C411yescharacteristic
750C2×D4(C2×D7)⋊C411yescharacteristic
751C2×D4(C2×D7)⋊C411yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4C2×C4×D711yescharacteristic
775C22×C4C2×C4×D711yescharacteristic
776C22×C4C2×C4×D711yescharacteristic
777C22×C4C2×C4×D711yescharacteristic
778C22×C4C2×D2811yescharacteristic
779C22×C4C2×D2811yescharacteristic
780C22×C4C2×D2811yescharacteristic
781C22×C4C2×D2811yescharacteristic
782C22×C4C2×C22⋊D711yescharacteristic
783C22×C4C2×C22⋊D711yescharacteristic
784C22×C4C2×C22⋊D711yescharacteristic
785C22×C4C2×C22⋊D711yescharacteristic
786C22×C4C23×D711yescharacteristic
787M16—72no—
788M16—141no—
789M16—141no—
790M16—141no—
791M16—141no—
792M16—141no—
793M16—141no—
794M16—141no—
795M16—282no—
796M16—282no—
797C2×C8—141no—
798C2×C8—141no—
799C2×C8—141no—
800C2×C8—141no—
801C2×C8—282no—
802C2×C8—282no—
803C4⋊C4—42no—
804C4⋊C4—42no—
805C4⋊C4—71no—
806C4⋊C4—71no—
807C4⋊C4—71no—
808C4⋊C4—71no—
809C4⋊C4—71no—
810C4⋊C4—71no—
811C4⋊C4—141no—
812C4⋊C4—141no—
813C4⋊C4—141no—
814C4⋊C4—141no—
815C4⋊C4—141no—
816C4⋊C4—141no—
817C4⋊C4—141no—
818C4⋊C4—141no—
819C4⋊C4—141no—
820C4⋊C4—141no—
821C4⋊C4—141no—
822C4⋊C4—141no—
823C4⋊C4—141no—
824C4⋊C4—141no—
825C4⋊C4—141no—
826C4⋊C4—141no—
827C4⋊C4(C2×D7)⋊C411yescharacteristic
828C4⋊C4(C2×D7)⋊C411yescharacteristic
829C4⋊C4(C2×D7)⋊C411yescharacteristic
830C4⋊C4(C2×D7)⋊C411yescharacteristic
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—141no—
835C22⋊C4—141no—
836C22⋊C4—141no—
837C22⋊C4—141no—
838C22⋊C4—141no—
839C22⋊C4—141no—
840C22⋊C4—141no—
841C22⋊C4—141no—
842C22⋊C4—141no—
843C22⋊C4—141no—
844C22⋊C4—141no—
845C22⋊C4—141no—
846C22⋊C4—141no—
847C22⋊C4—141no—
848C22⋊C4—141no—
849C22⋊C4—141no—
850C22⋊C4—141no—
851C22⋊C4(C2×D7)⋊C411yescharacteristic
852C22⋊C4(C2×D7)⋊C411yescharacteristic
853C22⋊C4(C2×D7)⋊C411yescharacteristic
854C22⋊C4(C2×D7)⋊C411yescharacteristic
855C22⋊C4(C2×D7)⋊C411yescharacteristic
856C22⋊C4(C2×D7)⋊C411yescharacteristic
857C22⋊C4(C2×D7)⋊C411yescharacteristic
858C22⋊C4(C2×D7)⋊C411yescharacteristic
859C42—21no—
860C42—21no—
861C42—21no—
862C42—21no—
863C42—21no—
864C42—21no—
865C42—21no—
866C42—42no—
867C42—141no—
868C42—141no—
869C42—141no—
870C42—141no—
871C42—141no—
872C42—141no—
873C42—141no—
874C42—141no—
875C42—141no—
876C42C2×C4×D711yescharacteristic
877C42C2×C4×D711yescharacteristic
878C42C2×D2811yescharacteristic
879C42C2×D2811yescharacteristic
880C42#115912yescomplemented
881C2×C7—21no—
882C2×C7—21no—
883C2×C7—22no—
884C2×C7—41no—
885C2×C7—41no—
886C2×C7—41no—
887C2×C7#233911yescharacteristic
888C2×C7C2×#42111yescharacteristic
889C2×C7#290111yescharacteristic
890D7—81no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—141no—
900C23C2×(C2×D7)⋊C411yescharacteristic
901C23C2×(C2×D7)⋊C411yescharacteristic
902C23C2×(C2×D7)⋊C411yescharacteristic
903C23C2×(C2×D7)⋊C411yescharacteristic
904C23C22×C22⋊D711yescharacteristic
905Q8—141no—
906Q8—141no—
907Q8—282no—
908Q8—561no—
909D4—22no—
910D4—22no—
911D4—41no—
912D4—41no—
913D4—141no—
914D4—141no—
915D4—282no—
916D4—281no—
917D4—281no—
918D4—282no—
919D4—561no—
920D4—561no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—48no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—141no—
957C2×C4—141no—
958C2×C4—141no—
959C2×C4—141no—
960C2×C4—141no—
961C2×C4—141no—
962C2×C4—141no—
963C2×C4—282no—
964C2×C4—282no—
965C2×C4—282no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—561no—
969C2×C4—561no—
970C2×C4—561no—
971C2×C4C2×(C2×D7)⋊C411yescharacteristic
972C2×C4C2×(C2×D7)⋊C411yescharacteristic
973C2×C4C2×(C2×D7)⋊C411yescharacteristic
974C2×C4C2×(C2×D7)⋊C411yescharacteristic
975C2×C4C2×(C2×D7)⋊C411yescharacteristic
976C2×C4C2×(C2×D7)⋊C411yescharacteristic
977C2×C4C2×(C2×D7)⋊C411yescharacteristic
978C2×C4C2×(C2×D7)⋊C411yescharacteristic
979C2×C4C22×C4×D711yescharacteristic
980C2×C4C22×D2811yescharacteristic
981C2×C4C2×#115911yescharacteristic
982C2×C4#654811yescharacteristic
983C2×C4D7×#4111yescharacteristic
984C2×C4#655411yescharacteristic
985C8—142no—
986C8—281no—
987C8—281no—
988C8—281no—
989C7#2250611yescharacteristic, complemented, Sylow
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—281no—
1008C22—281no—
1009C22—281no—
1010C22#8977712yes—
1011C22C22×(C2×D7)⋊C411yescharacteristic
1012C22#9049711yescharacteristic
1013C22#9051511yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—281no—
1027C4—281no—
1028C4—281no—
1029C4—281no—
1030C4—281no—
1031C4—281no—
1032C4—281no—
1033C4C4×#115911yescharacteristic
1034C4#9023711yescharacteristic
1035C4#9024511yescharacteristic
1036C4#9024611yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—561no—
1044C2C2×#8977711yescharacteristic
1045C2#1173977511yescharacteristic
1046C2#1173998111yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2290C2
socleC22×C7C22×C22⋊C4
prime radical#11742832C2
cosocleC22×C4×C7C24
hypercenter#2290D7
hypocenterC7#22506
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C7×#2290C2semidirect
3. D4×#1136C2semidirect
4. #11729345C2semidirect
5. #11729332C2semidirect
6. #11729286C2semidirect
7. C2×#89318C2semidirect
8. #11727248C2semidirect
9. #11727247C2semidirect
10. #11727207C2semidirect
11. #11727207C2semidirect
12. #11727196C2semidirect
13. #11727196C2semidirect
14. #11727195C2semidirect
15. #11727184C2semidirect
26. #90256C4semidirect
27. #90256C4semidirect
28. #90254C4semidirect
30. #90246C4semidirect
31. #90234C4semidirect
32. #90233C4semidirect
33. #90232C4semidirect
34. #90232C4semidirect
121. #6493C2×C4semidirect
122. #6493C2×C4semidirect
137. #6489C2×C4semidirect
138. #6489C2×C4semidirect
144. C2×C4⋊Dic7C2×C4semidirect
145. C2×C4⋊Dic7C2×C4semidirect
150. #6487C2×C4semidirect
151. #6487C2×C4semidirect
190. C4×D28C2×C4semidirect
191. C4×D28C2×C4semidirect
194. #6433C2×C4semidirect
195. #6433C2×C4semidirect
196. #6432C2×C4semidirect
197. #6432C2×C4semidirect
200. C4×Dic14C2×C4semidirect
201. C4×Dic14C2×C4semidirect
221. #2290D7semidirect
319. C42×C7#41semidirect
377. #1136#41semidirect
880. C42#1159semidirect
989. C7#22506semidirect

Maximal subgroups

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

subgroupindex
#117428322
C7×#22902
D4×#11362
#117293452
#117293322
#117292862
C2×#893182
#117272482
#117272472
#117272072
#117271962
#117271952
#117271842
#225067