Finite Group Databasebeta

← #13369481

Subgroups — #13369481

Order 1792.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×#41C211yesmaximal, characteristic
2C2×#90008C211yesmaximal, characteristic, complemented
3C22×#6411C211yesmaximal, characteristic, complemented
4#11739763C211yesmaximal, characteristic, complemented
5D4×#1136C211yesmaximal, characteristic, complemented
6#11729892C211yesmaximal, characteristic, complemented
7#11729892C211yesmaximal, characteristic, complemented
8#11729572C211yesmaximal, characteristic, complemented
9#11729570C211yesmaximal, characteristic, complemented
10#11729467C211yesmaximal, characteristic, complemented
11#11729467C211yesmaximal, characteristic, complemented
12#11729466C211yesmaximal, characteristic, complemented
13#11729465C211yesmaximal, characteristic, complemented
14#11729400C211yesmaximal, characteristic, complemented
15#11729397C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C7×#550C411yescharacteristic, complemented
19C7×D4×Q8C411yescharacteristic, complemented
20C7×#548C411yescharacteristic, complemented
21C7×#548C411yescharacteristic, complemented
22C7×#547—21no—
23C7×#547C411yescharacteristic, complemented
24C7×#546—21no—
25C7×#546—21no—
26C7×#546C411yescharacteristic, complemented
27C7×#546C411yescharacteristic, complemented
28C7×D42—21no—
29C7×D42C411yescharacteristic, complemented
30C7×#532—21no—
31C7×#532C2211yescharacteristic
32C7×#525—21no—
33C7×#525—21no—
34C7×#525C2211yescharacteristic
35C7×#525C2211yescharacteristic
36C4×C7×#41C2211yescharacteristic
37C2×C4×C7×D4—21no—
38C2×C4×C7×D4C2211yescharacteristic
39C2×#6489C2211yescharacteristic, complemented
40C22×C4×Dic7C2211yescharacteristic, complemented
41C22×#1136C2211yescharacteristic, complemented
42C22×#1136C2211yescharacteristic, complemented
43#90008—24no—
44C2×#6411—24no—
45C2×#6411C2211yescharacteristic
46C2×#6411C2211yescharacteristic
47C2×#6411C2211yescharacteristic
48C2×#6411C2211yescharacteristic
49C2×#6411C2211yescharacteristic, complemented
50C2×#6411C2211yescharacteristic, complemented
51C2×#6411C2211yescharacteristic, complemented
52C2×#6411C2211yescharacteristic, complemented
53C2×#6411C2211yescharacteristic, complemented
54C2×#6411C2211yescharacteristic, complemented
55C2×#6411C2211yescharacteristic, complemented
56C2×#6411C2211yescharacteristic, complemented
57#89992—21no—
58C4×C22⋊Dic7C2211yescharacteristic, complemented
59C4×C22⋊Dic7C2211yescharacteristic, complemented
60#89979C2211yescharacteristic, complemented
61#89979C2211yescharacteristic, complemented
62#89784—21no—
63#89783—21no—
64#89783—21no—
65D4×C7⋊C8—21no—
66#89753—21no—
67#89723—21no—
68#89722—21no—
69C4×C4⋊Dic7C2211yescharacteristic, complemented
70#89704C2211yescharacteristic, complemented
71#89696C2211yescharacteristic, complemented
72C4×#1136C2211yescharacteristic, complemented
73#89327C2211yescharacteristic, complemented
74#89327C2211yescharacteristic, complemented
75#89327C2211yescharacteristic, complemented
76#89327C2211yescharacteristic, complemented
77#22434—71nomaximal, Sylow
78C2×C7×#41—21no—
79C2×C7×#41—21no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—22no—
83C2×C7×#41—22no—
84C2×C7×#41—22no—
85C2×C7×#41—22no—
86C2×C7×#41—41no—
87C2×C7×#41—41no—
88C2×C7×#41—41no—
89C2×C7×#41—41no—
90C2×C7×#41C2×C411yescharacteristic
91C2×C7×#41C2×C411yescharacteristic
92C2×C7×#41C2×C411yescharacteristic, complemented
93C2×C7×#41C2×C411yescharacteristic, complemented
94C2×C7×#41C2311yescharacteristic
95C2×C7×#41C2311yescharacteristic
96C2×C7×#41C2311yescharacteristic
97C22×C7×Q8C2×C411yescharacteristic
98C22×C7×Q8C2×C411yescharacteristic, complemented
99C22×C7×D4—21no—
100C22×C7×D4—21no—
101C22×C7×D4—21no—
102C22×C7×D4C2×C411yescharacteristic
103C22×C7×D4C2×C411yescharacteristic, complemented
104C22×C7×D4D411yescharacteristic
105C23×C4×C7—21no—
106C23×C4×C7—21no—
107C23×C4×C7C2311yescharacteristic
108C23×C4×C7C2311yescharacteristic
109C23×Dic7—21no—
110C7×C4⋊Q8—21no—
111C7×C4⋊Q8C2×C411yescharacteristic, complemented
112C7×#127—21no—
113C7×#127C2×C411yescharacteristic, complemented
114C7×#124—21no—
115C7×#124—21no—
116C7×#124C2×C411yescharacteristic, complemented
117C7×#124C2×C411yescharacteristic, complemented
118C7×#123—21no—
119C7×#123—21no—
120C7×#123—21no—
121C7×#123—21no—
122C7×#123—21no—
123C7×#123—21no—
124C7×C22⋊Q8—21no—
125C7×C22⋊Q8—21no—
126C7×C22⋊Q8—21no—
127C7×C22⋊Q8—21no—
128C7×C22⋊Q8C2×C411yescharacteristic
129C7×C22⋊Q8C2×C411yescharacteristic
130C7×C22⋊Q8C2×C411yescharacteristic, complemented
131C7×C22⋊Q8C2×C411yescharacteristic, complemented
132C7×#121—21no—
133C7×#121—21no—
134C7×#121—21no—
135C7×#121—21no—
136C7×#121—21no—
137C7×#121—21no—
138C7×#121—21no—
139C7×#121—21no—
140C7×#121—21no—
141C7×#121—21no—
142C7×#121C2×C411yescharacteristic
143C7×#121C2×C411yescharacteristic
144C7×#121C2×C411yescharacteristic, complemented
145C7×#121C2×C411yescharacteristic, complemented
146C7×#120—21no—
147C7×#120—21no—
148C7×#120—21no—
149C7×#120—21no—
150C7×#120—21no—
151C7×#120—21no—
152C4×C7×Q8C2×C411yescharacteristic, complemented
153C4×C7×Q8C2×C411yescharacteristic, complemented
154C4×C7×D4—21no—
155C4×C7×D4—21no—
156C4×C7×D4—21no—
157C4×C7×D4—21no—
158C4×C7×D4—21no—
159C4×C7×D4—21no—
160C4×C7×D4—21no—
161C4×C7×D4—21no—
162C4×C7×D4—21no—
163C4×C7×D4—21no—
164C4×C7×D4—21no—
165C4×C7×D4—21no—
166C4×C7×D4C2×C411yescharacteristic
167C4×C7×D4C2×C411yescharacteristic
168C4×C7×D4C2×C411yescharacteristic
169C4×C7×D4C2×C411yescharacteristic
170C4×C7×D4C2×C411yescharacteristic, complemented
171C4×C7×D4C2×C411yescharacteristic, complemented
172C4×C7×D4D411yescharacteristic
173C4×C7×D4D411yescharacteristic
174C4×C7×D4D411yescharacteristic
175C4×C7×D4D411yescharacteristic
176C7×#117—21no—
177C7×#117C2311yescharacteristic
178C2×C7×C4⋊C4—21no—
179C2×C7×C4⋊C4D411yescharacteristic
180C2×C7×C22⋊C4—21no—
181C2×C7×C22⋊C4—21no—
182C2×C7×C22⋊C4D411yescharacteristic
183C2×C7×C22⋊C4D411yescharacteristic
184C2×C42×C7—21no—
185C2×C42×C7C2311yescharacteristic
186C2×C22⋊Dic7—21no—
187C2×C22⋊Dic7—21no—
188C2×C22⋊Dic7—21no—
189#6489—22no—
190#6489—41no—
191C2×C4⋊Dic7—21no—
192C2×C4⋊Dic7—21no—
193C2×C4×Dic7—22no—
194C2×C4×Dic7—21no—
195C2×C4×Dic7—41no—
196C2×C4×Dic7C2311yescharacteristic
197C2×C4×Dic7C2311yescharacteristic
198C2×C4×Dic7C2311yescharacteristic
199C2×C4×Dic7C2311yescharacteristic
200C2×#1136—21no—
201C2×#1136—21no—
202C2×#1136—22no—
203C2×#1136—22no—
204C2×#1136—41no—
205C2×#1136—41no—
206C2×#1136C2311yescharacteristic
207C2×#1136C2311yescharacteristic
208C2×#1136C2311yescharacteristic
209C2×#1136C2311yescharacteristic
210C22×C7⋊C8—21no—
211C22×C7⋊C8—21no—
212#6411—22no—
213#6411—22no—
214#6411—22no—
215#6411—22no—
216#6411—22no—
217#6411—22no—
218#6411—22no—
219#6411—41no—
220#6411—41no—
221#6411—41no—
222#6411—41no—
223#6411D414yescomplemented
224C7⋊#95—21no—
225C7⋊#95—21no—
226C7⋊#95—21no—
227C7⋊#95—21no—
228C7⋊#95—21no—
229C22⋊(C7⋊C8)—21no—
230C22⋊(C7⋊C8)—21no—
231C22⋊(C7⋊C8)—21no—
232C22⋊(C7⋊C8)—21no—
233C4⋊(C7⋊C8)—21no—
234C4⋊(C7⋊C8)—21no—
235#6377—21no—
236C4×C7⋊C8—21no—
237D4×#41D711yescharacteristic
238D4×M16—71no—
239C2×#421—71no—
240C22×#104—71no—
241#2290—71no—
242#1980—71no—
243#1963—71no—
244#1897—71no—
245#1896—71no—
246#1871—71no—
247#1871—71no—
248#1806—71no—
249#1789—71no—
250#1789—71no—
251#1759—71no—
252C24×C7—21no—
253C24×C7—21no—
254C24×C7C2×D411yescharacteristic
255C24×C7C2×D411yescharacteristic
256C7×#41—21no—
257C7×#41—21no—
258C7×#41—22no—
259C7×#41—22no—
260C7×#41—22no—
261C7×#41—22no—
262C7×#41—21no—
263C7×#41—21no—
264C7×#41—21no—
265C7×#41—21no—
266C7×#41—21no—
267C7×#41—21no—
268C7×#41—21no—
269C7×#41—21no—
270C7×#41—42no—
271C7×#41—42no—
272C7×#41—42no—
273C7×#41—42no—
274C7×#41—41no—
275C7×#41—41no—
276C7×#41—41no—
277C7×#41—41no—
278C7×#41—42no—
279C7×#41—42no—
280C7×#41—42no—
281C7×#41—42no—
282C7×#41C2×D412yes—
283C7×#41#4112yes—
284C2×C7×Q8—21no—
285C2×C7×Q8—21no—
286C2×C7×Q8—22no—
287C2×C7×Q8—22no—
288C2×C7×Q8—41no—
289C2×C7×Q8—41no—
290C2×C7×Q8C22×C411yescharacteristic
291C2×C7×Q8C22×C411yescharacteristic
292C2×C7×Q8C22×C411yescharacteristic
293C2×C7×D4—21no—
294C2×C7×D4—22no—
295C2×C7×D4—22no—
296C2×C7×D4—21no—
297C2×C7×D4—21no—
298C2×C7×D4—21no—
299C2×C7×D4—21no—
300C2×C7×D4—21no—
301C2×C7×D4—21no—
302C2×C7×D4—21no—
303C2×C7×D4—21no—
304C2×C7×D4—21no—
305C2×C7×D4—21no—
306C2×C7×D4—21no—
307C2×C7×D4—21no—
308C2×C7×D4—21no—
309C2×C7×D4—21no—
310C2×C7×D4—41no—
311C2×C7×D4—41no—
312C2×C7×D4—42no—
313C2×C7×D4—42no—
314C2×C7×D4—42no—
315C2×C7×D4—42no—
316C2×C7×D4—42no—
317C2×C7×D4—44no—
318C2×C7×D4C22⋊C411yescharacteristic
319C2×C7×D4C22⋊C411yescharacteristic
320C2×C7×D4C22⋊C411yescharacteristic
321C2×C7×D4C22⋊C411yescharacteristic
322C2×C7×D4C22×C411yescharacteristic
323C2×C7×D4C22×C411yescharacteristic
324C2×C7×D4C22×C411yescharacteristic
325C22×C4×C7—21no—
326C22×C4×C7—21no—
327C22×C4×C7—21no—
328C22×C4×C7—21no—
329C22×C4×C7—21no—
330C22×C4×C7—21no—
331C22×C4×C7—21no—
332C22×C4×C7—21no—
333C22×C4×C7—21no—
334C22×C4×C7—21no—
335C22×C4×C7—21no—
336C22×C4×C7—21no—
337C22×C4×C7—21no—
338C22×C4×C7—21no—
339C22×C4×C7—21no—
340C22×C4×C7—21no—
341C22×C4×C7—21no—
342C22×C4×C7—21no—
343C22×C4×C7—21no—
344C22×C4×C7—42no—
345C22×C4×C7—42no—
346C22×C4×C7—42no—
347C22×C4×C7—42no—
348C22×C4×C7C22×C411yescharacteristic
349C22×C4×C7C22×C411yescharacteristic
350C22×C4×C7C22×C411yescharacteristic
351C22×C4×C7C22×C411yescharacteristic
352C22×C4×C7C2×D411yescharacteristic
353C22×C4×C7C2×D411yescharacteristic
354C22×C4×C7C2×D411yescharacteristic
355C22×C4×C7C2×D411yescharacteristic
356C22×C4×C7C2×D411yescharacteristic
357C22×C4×C7C2×D411yescharacteristic
358C22×C4×C7C2×D411yescharacteristic
359C22×C4×C7C2×D411yescharacteristic
360C22×C4×C7C2411yescharacteristic
361C22×Dic7—21no—
362C22×Dic7—21no—
363C22×Dic7—21no—
364C22×Dic7—21no—
365C22×Dic7—42no—
366C22×Dic7—42no—
367C22×Dic7—42no—
368C7×C4⋊C4—21no—
369C7×C4⋊C4—21no—
370C7×C4⋊C4—21no—
371C7×C4⋊C4—21no—
372C7×C4⋊C4—21no—
373C7×C4⋊C4—21no—
374C7×C4⋊C4—21no—
375C7×C4⋊C4—21no—
376C7×C4⋊C4C22⋊C411yescharacteristic
377C7×C4⋊C4C22⋊C411yescharacteristic
378C7×C4⋊C4C22⋊C411yescharacteristic
379C7×C4⋊C4C22⋊C411yescharacteristic
380C7×C4⋊C4C22×C411yescharacteristic
381C7×C4⋊C4C22×C411yescharacteristic
382C7×C22⋊C4—21no—
383C7×C22⋊C4—21no—
384C7×C22⋊C4—21no—
385C7×C22⋊C4—21no—
386C7×C22⋊C4—21no—
387C7×C22⋊C4—21no—
388C7×C22⋊C4—21no—
389C7×C22⋊C4—21no—
390C7×C22⋊C4—21no—
391C7×C22⋊C4—21no—
392C7×C22⋊C4—21no—
393C7×C22⋊C4—21no—
394C7×C22⋊C4—21no—
395C7×C22⋊C4—21no—
396C7×C22⋊C4—21no—
397C7×C22⋊C4C22⋊C411yescharacteristic
398C7×C22⋊C4C22⋊C411yescharacteristic
399C7×C22⋊C4C22⋊C411yescharacteristic
400C7×C22⋊C4C22⋊C411yescharacteristic
401C7×C22⋊C4C22⋊C411yescharacteristic
402C7×C22⋊C4C22⋊C411yescharacteristic
403C7×C22⋊C4C22⋊C411yescharacteristic
404C7×C22⋊C4C22⋊C411yescharacteristic
405C42×C7—21no—
406C42×C7—21no—
407C42×C7—21no—
408C42×C7C22×C411yescharacteristic
409C42×C7C22×C411yescharacteristic
410C42×C7C2×D411yescharacteristic
411C42×C7C2×D411yescharacteristic
412C22⋊Dic7—42no—
413C22⋊Dic7—42no—
414C22⋊Dic7—42no—
415C4⋊Dic7—42no—
416C4⋊Dic7—42no—
417C4×Dic7—21no—
418C4×Dic7—21no—
419C4×Dic7—21no—
420C4×Dic7—21no—
421C4×Dic7—21no—
422C4×Dic7—21no—
423C4×Dic7—21no—
424C4×Dic7—42no—
425C4×Dic7C2×D412yescomplemented
426#1136—21no—
427#1136—21no—
428#1136—21no—
429#1136—21no—
430#1136—21no—
431#1136—21no—
432#1136—21no—
433#1136—42no—
434#1136—42no—
435#1136C2×D412yescomplemented
436C2×C7⋊C8—21no—
437C2×C7⋊C8—21no—
438C2×C7⋊C8—21no—
439C2×C7⋊C8—21no—
440C2×C7⋊C8—42no—
441C2×C7⋊C8—42no—
442C22×#41C2×D711yescharacteristic
443C22×#41C2×D711yescharacteristic
444C22×M16—71no—
445C22×M16—71no—
446#550Dic711yescharacteristic, complemented
447D4×Q8Dic711yescharacteristic, complemented
448#548Dic711yescharacteristic, complemented
449#548Dic711yescharacteristic, complemented
450#547—21no—
451#547Dic711yescharacteristic, complemented
452#546—21no—
453#546—21no—
454#546Dic711yescharacteristic, complemented
455#546Dic711yescharacteristic, complemented
456D42—21no—
457D42Dic711yescharacteristic, complemented
458#532—21no—
459#532C2×D711yescharacteristic
460#525—21no—
461#525—21no—
462#525C2×D711yescharacteristic
463#525C2×D711yescharacteristic
464C4×#41C2×D711yescharacteristic
465C2×C4×D4—21no—
466C2×C4×D4C2×D711yescharacteristic
467C2×#117—71no—
468C22×C42—71no—
469#436—141no—
470#435—141no—
471#435—141no—
472C8×D4—141no—
473#423—71no—
474#421—144no—
475C2×#104—71no—
476C2×#104—71no—
477C2×#104—71no—
478C2×#104—71no—
479C2×#104—71no—
480C2×#104—71no—
481C2×#104—71no—
482C2×#104—71no—
483C2×#104—71no—
484C2×#104—71no—
485C2×#104—71no—
486C2×#104—71no—
487C2×#104—144no—
488#407—71no—
489#407—71no—
490C4×M16—71no—
491#388—141no—
492#387—141no—
493#386—141no—
494#385—141no—
495C4×C4⋊C4—71no—
496C4×C22⋊C4—71no—
497C4×C22⋊C4—71no—
498#376—71no—
499#339—71no—
500#339—71no—
501#339—71no—
502#339—71no—
503C23×C7—21no—
504C23×C7—21no—
505C23×C7—21no—
506C23×C7—22no—
507C23×C7—21no—
508C23×C7—21no—
509C23×C7—21no—
510C23×C7—21no—
511C23×C7—41no—
512C23×C7—41no—
513C23×C7—41no—
514C23×C7—42no—
515C23×C7—42no—
516C23×C7—42no—
517C23×C7—42no—
518C23×C7—81no—
519C23×C7—81no—
520C23×C7C2×C22⋊C411yescharacteristic
521C23×C7C2×C22⋊C411yescharacteristic
522C23×C7C2×C22⋊C411yescharacteristic
523C23×C7C2×C22⋊C411yescharacteristic
524C23×C7C22×D411yescharacteristic
525C7×Q8—21no—
526C7×Q8—21no—
527C7×Q8—21no—
528C7×Q8—21no—
529C7×Q8—21no—
530C7×Q8—42no—
531C7×Q8—42no—
532C7×Q8C4×D412yes—
533C7×D4—22no—
534C7×D4—22no—
535C7×D4—22no—
536C7×D4—22no—
537C7×D4—21no—
538C7×D4—21no—
539C7×D4—21no—
540C7×D4—21no—
541C7×D4—21no—
542C7×D4—41no—
543C7×D4—41no—
544C7×D4—42no—
545C7×D4—42no—
546C7×D4—42no—
547C7×D4—42no—
548C7×D4—42no—
549C7×D4—42no—
550C7×D4—42no—
551C7×D4—42no—
552C7×D4—41no—
553C7×D4—41no—
554C7×D4—41no—
555C7×D4—41no—
556C7×D4—42no—
557C7×D4—81no—
558C7×D4—81no—
559C7×D4—81no—
560C7×D4C4×D412yes—
561C2×C4×C7—21no—
562C2×C4×C7—21no—
563C2×C4×C7—21no—
564C2×C4×C7—21no—
565C2×C4×C7—21no—
566C2×C4×C7—21no—
567C2×C4×C7—21no—
568C2×C4×C7—21no—
569C2×C4×C7—21no—
570C2×C4×C7—21no—
571C2×C4×C7—21no—
572C2×C4×C7—21no—
573C2×C4×C7—21no—
574C2×C4×C7—21no—
575C2×C4×C7—21no—
576C2×C4×C7—21no—
577C2×C4×C7—21no—
578C2×C4×C7—22no—
579C2×C4×C7—21no—
580C2×C4×C7—21no—
581C2×C4×C7—21no—
582C2×C4×C7—21no—
583C2×C4×C7—22no—
584C2×C4×C7—21no—
585C2×C4×C7—21no—
586C2×C4×C7—21no—
587C2×C4×C7—21no—
588C2×C4×C7—41no—
589C2×C4×C7—41no—
590C2×C4×C7—42no—
591C2×C4×C7—42no—
592C2×C4×C7—42no—
593C2×C4×C7—42no—
594C2×C4×C7—42no—
595C2×C4×C7—42no—
596C2×C4×C7—42no—
597C2×C4×C7—41no—
598C2×C4×C7—41no—
599C2×C4×C7—41no—
600C2×C4×C7—41no—
601C2×C4×C7—81no—
602C2×C4×C7C2×C22⋊C411yescharacteristic
603C2×C4×C7C2×C22⋊C411yescharacteristic
604C2×C4×C7C2×C22⋊C411yescharacteristic
605C2×C4×C7C2×C22⋊C411yescharacteristic
606C2×C4×C7C2×C22⋊C411yescharacteristic
607C2×C4×C7C2×C22⋊C411yescharacteristic
608C2×C4×C7C2×C22⋊C411yescharacteristic
609C2×C4×C7C2×C22⋊C411yescharacteristic
610C2×C4×C7C23×C411yescharacteristic
611C2×C4×C7C22×D411yescharacteristic
612C2×C4×C7C22×D411yescharacteristic
613C2×C4×C7C2×#4111yescharacteristic
614C2×C4×C7H(5,𝔽2)11yescharacteristic
615C2×C4×C7H(5,𝔽2)11yescharacteristic
616C2×Dic7—22no—
617C2×Dic7—22no—
618C2×Dic7—41no—
619C2×Dic7—41no—
620C2×Dic7—41no—
621C2×Dic7—48no—
622C2×Dic7—41no—
623C2×Dic7—41no—
624C2×Dic7—41no—
625C2×Dic7—41no—
626C2×Dic7—41no—
627C2×Dic7—41no—
628C2×Dic7—41no—
629C7⋊C8—22no—
630C7⋊C8—41no—
631C7⋊C8—41no—
632C7⋊C8—41no—
633C2×#41—21no—
634C2×#41—21no—
635C2×#41—21no—
636C2×#41—21no—
637C2×#41—22no—
638C2×#41—22no—
639C2×#41—22no—
640C2×#41—22no—
641C2×#41—41no—
642C2×#41—41no—
643C2×#41—41no—
644C2×#41—41no—
645C2×#41C2×Dic711yescharacteristic
646C2×#41C2×Dic711yescharacteristic
647C2×#41C2×Dic711yescharacteristic, complemented
648C2×#41C2×Dic711yescharacteristic, complemented
649C2×#41C22×D711yescharacteristic
650C2×#41C22×D711yescharacteristic
651C2×#41C22×D711yescharacteristic
652C22×Q8C2×Dic711yescharacteristic
653C22×Q8C2×Dic711yescharacteristic, complemented
654C22×D4—21no—
655C22×D4—21no—
656C22×D4—21no—
657C22×D4C2×Dic711yescharacteristic
658C22×D4C2×Dic711yescharacteristic, complemented
659C22×D4C22⋊D711yescharacteristic
660C23×C4—21no—
661C23×C4—21no—
662C23×C4—141no—
663C23×C4C22×D711yescharacteristic
664C23×C4C22×D711yescharacteristic
665C2×M16—71no—
666C2×M16—71no—
667C2×M16—71no—
668C2×M16—71no—
669C2×M16—141no—
670C2×M16—141no—
671C2×M16—142no—
672C2×M16—142no—
673C2×M16—281no—
674C2×M16—281no—
675C22×C8—141no—
676C22×C8—141no—
677C4⋊Q8—21no—
678C4⋊Q8C2×Dic711yescharacteristic, complemented
679#127—21no—
680#127C2×Dic711yescharacteristic, complemented
681#124—21no—
682#124—21no—
683#124C2×Dic711yescharacteristic, complemented
684#124C2×Dic711yescharacteristic, complemented
685#123—21no—
686#123—21no—
687#123—21no—
688#123—21no—
689#123—21no—
690#123—21no—
691C22⋊Q8—21no—
692C22⋊Q8—21no—
693C22⋊Q8—21no—
694C22⋊Q8—21no—
695C22⋊Q8C2×Dic711yescharacteristic
696C22⋊Q8C2×Dic711yescharacteristic
697C22⋊Q8C2×Dic711yescharacteristic, complemented
698C22⋊Q8C2×Dic711yescharacteristic, complemented
699#121—21no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—21no—
707#121—21no—
708#121—21no—
709#121C2×Dic711yescharacteristic
710#121C2×Dic711yescharacteristic
711#121C2×Dic711yescharacteristic, complemented
712#121C2×Dic711yescharacteristic, complemented
713#120—21no—
714#120—21no—
715#120—21no—
716#120—21no—
717#120—21no—
718#120—21no—
719C4×Q8C2×Dic711yescharacteristic, complemented
720C4×Q8C2×Dic711yescharacteristic, complemented
721C4×D4—21no—
722C4×D4—21no—
723C4×D4—21no—
724C4×D4—21no—
725C4×D4—21no—
726C4×D4—21no—
727C4×D4—21no—
728C4×D4—21no—
729C4×D4—21no—
730C4×D4—21no—
731C4×D4—21no—
732C4×D4—21no—
733C4×D4C2×Dic711yescharacteristic
734C4×D4C2×Dic711yescharacteristic
735C4×D4C2×Dic711yescharacteristic
736C4×D4C2×Dic711yescharacteristic
737C4×D4C2×Dic711yescharacteristic, complemented
738C4×D4C2×Dic711yescharacteristic, complemented
739C4×D4C22⋊D711yescharacteristic
740C4×D4C22⋊D711yescharacteristic
741C4×D4C22⋊D711yescharacteristic
742C4×D4C22⋊D711yescharacteristic
743#117—21no—
744#117—142no—
745#117—281no—
746#117C22×D711yescharacteristic
747C2×C4⋊C4—21no—
748C2×C4⋊C4—141no—
749C2×C4⋊C4—141no—
750C2×C4⋊C4C22⋊D711yescharacteristic
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—141no—
754C2×C22⋊C4—141no—
755C2×C22⋊C4—141no—
756C2×C22⋊C4C22⋊D711yescharacteristic
757C2×C22⋊C4C22⋊D711yescharacteristic
758C2×C42—21no—
759C2×C42—71no—
760C2×C42—71no—
761C2×C42—71no—
762C2×C42—71no—
763C2×C42—142no—
764C2×C42—141no—
765C2×C42—281no—
766C2×C42C22×D711yescharacteristic
767C4⋊C8—141no—
768C4⋊C8—141no—
769#104—74no—
770#104—142no—
771#104—142no—
772#104—142no—
773#104—142no—
774#104—142no—
775#104—142no—
776#104—142no—
777#104—281no—
778#104—281no—
779#104—281no—
780#104—281no—
781C22⋊C8—141no—
782C22⋊C8—141no—
783C22⋊C8—141no—
784C22⋊C8—141no—
785#97—141no—
786C4×C8—141no—
787#95—141no—
788#95—141no—
789#95—141no—
790#95—141no—
791#95—141no—
792C22×C7—21no—
793C22×C7—21no—
794C22×C7—21no—
795C22×C7—21no—
796C22×C7—21no—
797C22×C7—21no—
798C22×C7—21no—
799C22×C7—22no—
800C22×C7—21no—
801C22×C7—21no—
802C22×C7—21no—
803C22×C7—21no—
804C22×C7—21no—
805C22×C7—21no—
806C22×C7—42no—
807C22×C7—42no—
808C22×C7—41no—
809C22×C7—41no—
810C22×C7—41no—
811C22×C7—41no—
812C22×C7—41no—
813C22×C7—41no—
814C22×C7—41no—
815C22×C7—41no—
816C22×C7—81no—
817C22×C7—81no—
818C22×C7—84no—
819C22×C7—84no—
820C22×C7#42112yescomplemented
821C22×C7C22×C22⋊C411yescharacteristic
822C22×C7D4211yescharacteristic
823C22×C7#54611yescharacteristic
824C4×C7—21no—
825C4×C7—21no—
826C4×C7—21no—
827C4×C7—21no—
828C4×C7—22no—
829C4×C7—21no—
830C4×C7—21no—
831C4×C7—21no—
832C4×C7—21no—
833C4×C7—41no—
834C4×C7—41no—
835C4×C7—41no—
836C4×C7—41no—
837C4×C7C2×C4×D411yescharacteristic
838C4×C7#51811yescharacteristic
839C4×C7D4211yescharacteristic
840C4×C7#54611yescharacteristic
841Dic7—42no—
842Dic7—42no—
843Dic7—81no—
844Dic7—81no—
845C24—21no—
846C24—21no—
847C24C2×C22⋊D711yescharacteristic
848C24C2×C22⋊D711yescharacteristic
849#41—21no—
850#41—21no—
851#41—22no—
852#41—22no—
853#41—22no—
854#41—22no—
855#41—21no—
856#41—21no—
857#41—21no—
858#41—21no—
859#41—21no—
860#41—21no—
861#41—21no—
862#41—21no—
863#41—42no—
864#41—42no—
865#41—42no—
866#41—42no—
867#41—41no—
868#41—41no—
869#41—41no—
870#41—41no—
871#41—42no—
872#41—42no—
873#41—42no—
874#41—42no—
875#41D4×D712yes—
876#41#115912yes—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—41no—
882C2×Q8—41no—
883C2×Q8C22×Dic711yescharacteristic
884C2×Q8C22×Dic711yescharacteristic
885C2×Q8C22×Dic711yescharacteristic
886C2×D4—21no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—44no—
911C2×D4C22⋊Dic711yescharacteristic
912C2×D4C22⋊Dic711yescharacteristic
913C2×D4C22⋊Dic711yescharacteristic
914C2×D4C22⋊Dic711yescharacteristic
915C2×D4C22×Dic711yescharacteristic
916C2×D4C22×Dic711yescharacteristic
917C2×D4C22×Dic711yescharacteristic
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—141no—
942C22×C4—141no—
943C22×C4—141no—
944C22×C4—141no—
945C22×C4—282no—
946C22×C4—282no—
947C22×C4—282no—
948C22×C4C22×Dic711yescharacteristic
949C22×C4C22×Dic711yescharacteristic
950C22×C4C22×Dic711yescharacteristic
951C22×C4C22×Dic711yescharacteristic
952C22×C4C2×C22⋊D711yescharacteristic
953C22×C4C2×C22⋊D711yescharacteristic
954C22×C4C2×C22⋊D711yescharacteristic
955C22×C4C2×C22⋊D711yescharacteristic
956C22×C4C2×C22⋊D711yescharacteristic
957C22×C4C2×C22⋊D711yescharacteristic
958C22×C4C2×C22⋊D711yescharacteristic
959C22×C4C2×C22⋊D711yescharacteristic
960C22×C4C23×D711yescharacteristic
961M16—72no—
962M16—141no—
963M16—141no—
964M16—141no—
965M16—141no—
966M16—141no—
967M16—141no—
968M16—141no—
969M16—282no—
970M16—282no—
971C2×C8—141no—
972C2×C8—141no—
973C2×C8—141no—
974C2×C8—141no—
975C2×C8—282no—
976C2×C8—282no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—282no—
986C4⋊C4—282no—
987C4⋊C4C22⋊Dic711yescharacteristic
988C4⋊C4C22⋊Dic711yescharacteristic
989C4⋊C4C22⋊Dic711yescharacteristic
990C4⋊C4C22⋊Dic711yescharacteristic
991C4⋊C4C22×Dic711yescharacteristic
992C4⋊C4C22×Dic711yescharacteristic
993C22⋊C4—21no—
994C22⋊C4—21no—
995C22⋊C4—21no—
996C22⋊C4—21no—
997C22⋊C4—21no—
998C22⋊C4—21no—
999C22⋊C4—21no—
1000C22⋊C4—21no—
1001C22⋊C4—21no—
1002C22⋊C4—21no—
1003C22⋊C4—21no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—282no—
1009C22⋊C4—282no—
1010C22⋊C4—282no—
1011C22⋊C4C22⋊Dic711yescharacteristic
1012C22⋊C4C22⋊Dic711yescharacteristic
1013C22⋊C4C22⋊Dic711yescharacteristic
1014C22⋊C4C22⋊Dic711yescharacteristic
1015C22⋊C4C22⋊Dic711yescharacteristic
1016C22⋊C4C22⋊Dic711yescharacteristic
1017C22⋊C4C22⋊Dic711yescharacteristic
1018C22⋊C4C22⋊Dic711yescharacteristic
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—72no—
1023C42—141no—
1024C42—141no—
1025C42—141no—
1026C42—141no—
1027C42—141no—
1028C42—141no—
1029C42—141no—
1030C42—282no—
1031C42C22×Dic711yescharacteristic
1032C42C22×Dic711yescharacteristic
1033C42C2×C22⋊D711yescharacteristic
1034C42C2×C22⋊D711yescharacteristic
1035C2×C7—21no—
1036C2×C7—21no—
1037C2×C7—22no—
1038C2×C7—41no—
1039C2×C7—41no—
1040C2×C7—41no—
1041C2×C7—42no—
1042C2×C7—81no—
1043C2×C7—81no—
1044C2×C7D4×C22⋊C411yescharacteristic
1045C2×C7C2×#42111yescharacteristic
1046C2×C7#290111yescharacteristic
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—81no—
1063C23—81no—
1064C23C2×C22⋊Dic711yescharacteristic
1065C23C2×C22⋊Dic711yescharacteristic
1066C23C2×C22⋊Dic711yescharacteristic
1067C23C2×C22⋊Dic711yescharacteristic
1068C23C22×C22⋊D711yescharacteristic
1069Q8—21no—
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—42no—
1075Q8—42no—
1076Q8D4×Dic712yes—
1077D4—22no—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—21no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—41no—
1087D4—41no—
1088D4—42no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—42no—
1101D4—81no—
1102D4—81no—
1103D4—81no—
1104D4D4×Dic712yes—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—81no—
1146C2×C4—142no—
1147C2×C4—142no—
1148C2×C4—281no—
1149C2×C4—281no—
1150C2×C4—281no—
1151C2×C4—288no—
1152C2×C4—281no—
1153C2×C4—281no—
1154C2×C4—281no—
1155C2×C4—281no—
1156C2×C4—281no—
1157C2×C4—281no—
1158C2×C4—281no—
1159C2×C4C2×C22⋊Dic711yescharacteristic
1160C2×C4C2×C22⋊Dic711yescharacteristic
1161C2×C4C2×C22⋊Dic711yescharacteristic
1162C2×C4C2×C22⋊Dic711yescharacteristic
1163C2×C4C2×C22⋊Dic711yescharacteristic
1164C2×C4C2×C22⋊Dic711yescharacteristic
1165C2×C4C2×C22⋊Dic711yescharacteristic
1166C2×C4C2×C22⋊Dic711yescharacteristic
1167C2×C4C2×D4×D711yescharacteristic
1168C2×C4C2×#115911yescharacteristic
1169C2×C4#654811yescharacteristic
1170C2×C4#654811yescharacteristic
1171C2×C4C23×Dic711yescharacteristic
1172C2×C4C22×C22⋊D711yescharacteristic
1173C8—142no—
1174C8—281no—
1175C8—281no—
1176C8—281no—
1177C7#2243411yescharacteristic, complemented, Sylow
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—22no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#9000812yescomplemented
1207C22D4×C22⋊D711yescharacteristic
1208C22#9049711yescharacteristic
1209C22C22×C22⋊Dic711yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—282no—
1224C4—282no—
1225C4—561no—
1226C4—561no—
1227C4C2×D4×Dic711yescharacteristic
1228C4#9048911yescharacteristic
1229C4D4×C22⋊D711yescharacteristic
1230C4#9049711yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic711yescharacteristic
1241C2C2×#9000811yescharacteristic
1242C2#1174156511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC7×D4×#41C2
socleC22×C7C22×C22⋊C4
cosocleC22×C4×C7C24
hypercenterD4×#41D7
hypocenterC7#22434
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#90008C2semidirect
3. C22×#6411C2semidirect
4. #11739763C2semidirect
5. D4×#1136C2semidirect
6. #11729892C2semidirect
7. #11729892C2semidirect
8. #11729572C2semidirect
9. #11729570C2semidirect
10. #11729467C2semidirect
11. #11729467C2semidirect
12. #11729466C2semidirect
13. #11729465C2semidirect
14. #11729400C2semidirect
15. #11729397C2semidirect
18. C7×#550C4semidirect
19. C7×D4×Q8C4semidirect
20. C7×#548C4semidirect
21. C7×#548C4semidirect
23. C7×#547C4semidirect
26. C7×#546C4semidirect
27. C7×#546C4semidirect
29. C7×D42C4semidirect
39. C2×#6489C22semidirect
40. C22×C4×Dic7C22semidirect
41. C22×#1136C22semidirect
42. C22×#1136C22semidirect
49. C2×#6411C22semidirect
50. C2×#6411C22semidirect
51. C2×#6411C22semidirect
52. C2×#6411C22semidirect
53. C2×#6411C22semidirect
54. C2×#6411C22semidirect
55. C2×#6411C22semidirect
56. C2×#6411C22semidirect
58. C4×C22⋊Dic7C22semidirect
59. C4×C22⋊Dic7C22semidirect
60. #89979C22semidirect
61. #89979C22semidirect
69. C4×C4⋊Dic7C22semidirect
70. #89704C22semidirect
71. #89696C22semidirect
72. C4×#1136C22semidirect
73. #89327C22semidirect
74. #89327C22semidirect
75. #89327C22semidirect
76. #89327C22semidirect
92. C2×C7×#41C2×C4semidirect
93. C2×C7×#41C2×C4semidirect
98. C22×C7×Q8C2×C4semidirect
103. C22×C7×D4C2×C4semidirect
111. C7×C4⋊Q8C2×C4semidirect
113. C7×#127C2×C4semidirect
116. C7×#124C2×C4semidirect
117. C7×#124C2×C4semidirect
130. C7×C22⋊Q8C2×C4semidirect
131. C7×C22⋊Q8C2×C4semidirect
144. C7×#121C2×C4semidirect
145. C7×#121C2×C4semidirect
152. C4×C7×Q8C2×C4semidirect
153. C4×C7×Q8C2×C4semidirect
170. C4×C7×D4C2×C4semidirect
171. C4×C7×D4C2×C4semidirect
223. #6411D4semidirect
425. C4×Dic7C2×D4semidirect
435. #1136C2×D4semidirect
446. #550Dic7semidirect
447. D4×Q8Dic7semidirect
448. #548Dic7semidirect
449. #548Dic7semidirect
451. #547Dic7semidirect
454. #546Dic7semidirect
455. #546Dic7semidirect
457. D42Dic7semidirect
647. C2×#41C2×Dic7semidirect
648. C2×#41C2×Dic7semidirect
653. C22×Q8C2×Dic7semidirect
658. C22×D4C2×Dic7semidirect
678. C4⋊Q8C2×Dic7semidirect
680. #127C2×Dic7semidirect
683. #124C2×Dic7semidirect
684. #124C2×Dic7semidirect
697. C22⋊Q8C2×Dic7semidirect
698. C22⋊Q8C2×Dic7semidirect
711. #121C2×Dic7semidirect
712. #121C2×Dic7semidirect
719. C4×Q8C2×Dic7semidirect
720. C4×Q8C2×Dic7semidirect
737. C4×D4C2×Dic7semidirect
738. C4×D4C2×Dic7semidirect
820. C22×C7#421semidirect
1177. C7#22434semidirect
1206. C22#90008semidirect

Maximal subgroups

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

subgroupindex
C7×D4×#412
C2×#900082
C22×#64112
#117397632
D4×#11362
#117298922
#117295722
#117295702
#117294672
#117294662
#117294652
#117294002
#117293972
#224347