Finite Group Databasebeta

← #13281769

Subgroups — #13281769

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#385C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×#89982C211yesmaximal, characteristic
4C2×#89748C211yesmaximal, characteristic, complemented
5C2×#89717C211yesmaximal, characteristic
6C2×#89716C211yesmaximal, characteristic
7C2×#89419C211yesmaximal, characteristic, complemented
8#11729322C211yesmaximal, characteristic, complemented
9#11729322C211yesmaximal, characteristic, complemented
10#11729320C211yesmaximal, characteristic, complemented
11#11729301C211yesmaximal, characteristic
12#11729300C211yesmaximal, characteristic
13#11727167C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C7×#385—24no—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38#89982—24no—
39#89982—24no—
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89748—24no—
55#89717C418yescomplemented
56#89716—24no—
57#89419—24no—
58#14405—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—41no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
66C23×C4×C7—41no—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4—41no—
86C2×C7×C4⋊C4—41no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—41no—
92C2×C7×C22⋊C4C2×C414yes—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7C2×C414yes—
102C2×C22⋊Dic7C2×C414yes—
103C2×C22⋊Dic7D414yes—
104C2×C22⋊Dic7Q814yes—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—41no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4—41no—
121C2×Dic7⋊C4—41no—
122C2×Dic7⋊C4—41no—
123C2×Dic7⋊C4—41no—
124C2×Dic7⋊C4—41no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4C2×C414yescomplemented
128C2×Dic7⋊C4D414yes—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—22no—
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—41no—
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95D414yes—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95C2×C414yescomplemented
150C7⋊#95C2×C414yescomplemented
151C2×#389—71no—
152C2×#388—71no—
153C2×#388—71no—
154C2×#385—71no—
155C2×#385—71no—
156C2×#385D711yescharacteristic
157C2×#384—71no—
158#1444—71no—
159#1444—71no—
160#1442—71no—
161#1441—71no—
162#1439—71no—
163#1439—71no—
164#1436—71no—
165#1434—71no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7C22×C412yes—
179C24×C7C2×D412yes—
180C24×C7C2×Q812yes—
181C24×C7C2411yescharacteristic
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—44no—
218C22×C4×C7—44no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7—44no—
222C22×C4×C7—44no—
223C22×C4×C7—44no—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7#4112yes—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×Q812yes—
285C22×Dic7C2×Q812yes—
286C22×Dic7#4112yes—
287C7×C4⋊C4—44no—
288C7×C4⋊C4—44no—
289C7×C22⋊C4—28no—
290C7×C22⋊C4—44no—
291C22⋊Dic7—28no—
292C22⋊Dic7—44no—
293C22⋊Dic7—44no—
294C22⋊Dic7C4⋊C4116yescomplemented
295C4⋊Dic7—44no—
296Dic7⋊C4—28no—
297Dic7⋊C4—44no—
298Dic7⋊C4—44no—
299Dic7⋊C4—44no—
300Dic7⋊C4—44no—
301Dic7⋊C4—44no—
302Dic7⋊C4—44no—
303C4×Dic7—28no—
304C4×Dic7—44no—
305C24×C4C2×D711yescharacteristic
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C4⋊C4C2×D711yescharacteristic
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4—71no—
319C22×C22⋊C4—71no—
320C22×C22⋊C4C2×D711yescharacteristic
321C22×C22⋊C4C2×D711yescharacteristic
322C22×C42—71no—
323C22×C42—71no—
324#389—144no—
325#388—78no—
326#388—144no—
327#385—24no—
328#385—144no—
329#385—144no—
330#384—144no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7C2×C4⋊C414yes—
382C23×C7C23×C411yescharacteristic
383C23×C7C22×D411yescharacteristic
384C23×C7C22×D411yescharacteristic
385C23×C7C22×D411yescharacteristic
386C23×C7C22×Q811yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7H(5,𝔽2)11yescharacteristic
390C23×C7H(5,𝔽2)11yescharacteristic
391C23×C7H(5,𝔽2)11yescharacteristic
392C23×C7H(5,𝔽2)11yescharacteristic
393C23×C72−1+411yescharacteristic
394C23×C72−1+411yescharacteristic
395C23×C72−1+411yescharacteristic
396C23×C72−1+411yescharacteristic
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—416no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7C4×D414yes—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7C2×C4⋊C414yes—
494C2×Dic7C2×C4⋊C414yes—
495C2×Dic7C4×D414yes—
496C25C22×D711yescharacteristic
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—41no—
501C23×C4—41no—
502C23×C4—41no—
503C23×C4—41no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—74no—
525C2×C4⋊C4—74no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—142no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—142no—
535C2×C4⋊C4—142no—
536C2×C4⋊C4—142no—
537C2×C4⋊C4—142no—
538C2×C4⋊C4—142no—
539C2×C4⋊C4—281no—
540C2×C4⋊C4—281no—
541C2×C4⋊C4—281no—
542C2×C4⋊C4—281no—
543C2×C4⋊C4—281no—
544C2×C4⋊C4—281no—
545C2×C4⋊C4—281no—
546C2×C4⋊C4—281no—
547C2×C4⋊C4—281no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—74no—
554C2×C22⋊C4—74no—
555C2×C22⋊C4—74no—
556C2×C22⋊C4—74no—
557C2×C22⋊C4—142no—
558C2×C22⋊C4—142no—
559C2×C22⋊C4—142no—
560C2×C22⋊C4—142no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—281no—
563C2×C22⋊C4—281no—
564C2×C22⋊C4—281no—
565C2×C22⋊C4C4×D714yes—
566C2×C42—74no—
567C2×C42—142no—
568C2×C42—142no—
569C2×C42—142no—
570C2×C42—142no—
571C2×C42—281no—
572#95—22no—
573#95—74no—
574#95—74no—
575#95—142no—
576#95—142no—
577#95—142no—
578#95—142no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—281no—
585#95—281no—
586#95—281no—
587#95C22⋊D714yes—
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—42no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7C22×C4⋊C411yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7C2×C4×D411yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7#52011yescharacteristic
608C22×C7#52011yescharacteristic
609C22×C7#52011yescharacteristic
610C22×C7#53411yescharacteristic
611C22×C7#53511yescharacteristic
612C22×C7#53511yescharacteristic
613C22×C7#53611yescharacteristic
614C22×C7#53611yescharacteristic
615C22×C7#53611yescharacteristic
616C22×C7#53911yescharacteristic
617C22×C7#53911yescharacteristic
618C22×C7#54211yescharacteristic
619C22×C7#54211yescharacteristic
620C22×C7#54411yescharacteristic
621C22×C7#54411yescharacteristic
622C22×C7D4211yescharacteristic
623C22×C7D4211yescharacteristic
624C22×C7D4211yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54711yescharacteristic
628C22×C7#54811yescharacteristic
629C22×C7D4×Q811yescharacteristic
630C22×C7D4×Q811yescharacteristic
631C22×C7#55311yescharacteristic
632C22×C7#55411yescharacteristic
633C22×C7#55411yescharacteristic
634C22×C7#56011yescharacteristic
635C22×C7#56311yescharacteristic
636C22×C7#56311yescharacteristic
637C22×C7#56311yescharacteristic
638C4×C7—24no—
639C4×C7—42no—
640C4×C7—42no—
641C4×C7—42no—
642C4×C7—42no—
643C4×C7—81no—
644Dic7—24no—
645Dic7—24no—
646Dic7—24no—
647Dic7—42no—
648Dic7—42no—
649Dic7—81no—
650Dic7—81no—
651Dic7—81no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C2×C4×D712yes—
665C24D4×D712yes—
666C24Q8×D712yes—
667C24C23×D711yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—72no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
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—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4C2×C4×D712yes—
767C22×C4C2×C4×D712yes—
768C22×C4#115712yes—
769C22×C4D4×D712yes—
770C22×C4C2×C22⋊D712yes—
771C22×C4C2×C22⋊D712yes—
772C22×C4C2×C22⋊D712yes—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—148no—
776C4⋊C4—284no—
777C4⋊C4—284no—
778C4⋊C4—284no—
779C4⋊C4—284no—
780C4⋊C4—284no—
781C4⋊C4—284no—
782C4⋊C4—284no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—716no—
786C22⋊C4—148no—
787C22⋊C4—284no—
788C22⋊C4—284no—
789C42—148no—
790C42—284no—
791C2×C7—44no—
792C2×C7#231711yescharacteristic
793C2×C7#232211yescharacteristic
794C2×C7#232611yescharacteristic
795C2×C7D4×C4⋊C411yescharacteristic
796C2×C7D4×C4⋊C411yescharacteristic
797C2×C7#236111yescharacteristic
798C2×C7#238311yescharacteristic
799C2×C7#266911yescharacteristic
800C2×C7#267411yescharacteristic
801C2×C7#267711yescharacteristic
802C2×C7#268011yescharacteristic
803C2×C7#271811yescharacteristic
804C2×C7#272011yescharacteristic
805C2×C7#272911yescharacteristic
806C2×C7#279011yescharacteristic
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23D7×C4⋊C414yes—
842C23C22×C4×D711yescharacteristic
843C23C2×#115711yescharacteristic
844C23C2×D4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23#654811yescharacteristic
847C23#654811yescharacteristic
848C23#654811yescharacteristic
849C23#654811yescharacteristic
850C23C2×Q8×D711yescharacteristic
851C23#655111yescharacteristic
852C23D7×#4111yescharacteristic
853C23#655411yescharacteristic
854C23#655411yescharacteristic
855C23#655411yescharacteristic
856C23C22×C22⋊D711yescharacteristic
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—416no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—74no—
900C2×C4—74no—
901C2×C4—74no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4C4×C22⋊D714yes—
956C7#1440511yescharacteristic, complemented, Sylow
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×D7×C4⋊C411yescharacteristic
973C22#9019511yescharacteristic
974C22#9019811yescharacteristic
975C22#9020211yescharacteristic
976C22#9023111yescharacteristic
977C22C4×D4×D711yescharacteristic
978C22#9023711yescharacteristic
979C22#9023711yescharacteristic
980C22#9023711yescharacteristic
981C22#9024311yescharacteristic
982C22#9025211yescharacteristic
983C22#9025211yescharacteristic
984C22#9028011yescharacteristic
985C22#9028111yescharacteristic
986C22#9028311yescharacteristic
987C22#9028611yescharacteristic
988C22#9031411yescharacteristic
989C22#9031411yescharacteristic
990C22#9031911yescharacteristic
991C22#9032311yescharacteristic
992C22#9032711yescharacteristic
993C22#9032911yescharacteristic
994C22#9033711yescharacteristic
995C22#9033711yescharacteristic
996C22#9033911yescharacteristic
997C22#9034211yescharacteristic
998C22#9034611yescharacteristic
999C22#9035111yescharacteristic
1000C22C2×C4×C22⋊D711yescharacteristic
1001C22D4×C22⋊D711yescharacteristic
1002C22D4×C22⋊D711yescharacteristic
1003C22#9049611yescharacteristic
1004C22Q8×C22⋊D711yescharacteristic
1005C22#9051511yescharacteristic
1006C22#9051611yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—81no—
1013C4—144no—
1014C4—144no—
1015C4—144no—
1016C4—282no—
1017C4—282no—
1018C4—561no—
1019C4—561no—
1020C4—561no—
1021C2—44no—
1022C2#1173182711yescharacteristic
1023C2#1173183811yescharacteristic
1024C2#1173184811yescharacteristic
1025C2#1173195311yescharacteristic
1026C2#1173197811yescharacteristic
1027C2#1173198411yescharacteristic
1028C2#1173202111yescharacteristic
1029C2#1173203811yescharacteristic
1030C2C4⋊C4×C22⋊D711yescharacteristic
1031C2#1173977311yescharacteristic
1032C2#1173978511yescharacteristic
1033C2#1174005411yescharacteristic
1034C2#1174023611yescharacteristic
1035C2#1174024811yescharacteristic
1036C2#1174031611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#385C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14405
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#89748C2semidirect
7. C2×#89419C2semidirect
8. #11729322C2semidirect
9. #11729322C2semidirect
10. #11729320C2semidirect
13. #11727167C2semidirect
14. #11727160C2semidirect
15. #11727155C2semidirect
55. #89717C4semidirect
127. C2×Dic7⋊C4C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
149. C7⋊#95C2×C4semidirect
150. C7⋊#95C2×C4semidirect
294. C22⋊Dic7C4⋊C4semidirect
956. C7#14405semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3852
C2×#899822
C2×#897482
C2×#897172
C2×#897162
C2×#894192
#117293222
#117293202
#117293012
#117293002
#117271672
#117271602
#117271552
#144057