Finite Group Databasebeta

← #13364988

Subgroups — #13364988

Order 1792.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2297C211yesmaximal, characteristic, complemented
2C2×#90010C211yesmaximal, characteristic
3C4×#6493C211yesmaximal, characteristic, complemented
4#11729889C211yesmaximal, characteristic, complemented
5#11729340C211yesmaximal, characteristic, complemented
6#11729330C211yesmaximal, characteristic, complemented
7C4×C22⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
8#11727441C211yesmaximal, characteristic, complemented
9#11727430C211yesmaximal, characteristic, complemented
10#11727428C211yesmaximal, characteristic, complemented
11#11727421C211yesmaximal, characteristic, complemented
12#11727411C211yesmaximal, characteristic, complemented
13#11727401C211yesmaximal, characteristic, complemented
14#11727398C211yesmaximal, characteristic, complemented
15#11727391C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C22×#1141C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23C2×C4×D28C2211yescharacteristic
24C7×#391C2211yescharacteristic
25C7×#391C2211yescharacteristic
26C7×#390C2211yescharacteristic
27C7×#390C2211yescharacteristic
28C7×#386—21no—
29C7×#386—21no—
30C4×C7×C22⋊C4—21no—
31C4×C7×C22⋊C4—21no—
32#90010C418yescomplemented
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39#89985—21no—
40#89984C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×#6383C2211yescharacteristic
44C2×#6383C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89712—21no—
48#89711C2211yescharacteristic
49C4×(C2×D7)⋊C4—21no—
50C4×C4⋊Dic7C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×C4×C7⋊C8C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22045—71nomaximal, Sylow
61C2×C7×#41—22no—
62C2×C7×#41—41no—
63C2×C7×#41—41no—
64C2×C7×#41—41no—
65C2×C7×#41—41no—
66C2×C7×#41C2×C414yescomplemented
67C22×C7×Q8C2311yescharacteristic
68C22×C7×D4—21no—
69C22×C7×D4C2311yescharacteristic
70C23×C4×C7—21no—
71C23×C4×C7D411yescharacteristic
72C23×C4×C7D411yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C22×C22⋊D7—21no—
75C22×D28C2311yescharacteristic
76C22×C4×D7—21no—
77C7×#117—41no—
78C7×#117—41no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C42×C7—21no—
87C2×C42×C7—41no—
88C2×C42×C7—41no—
89C2×C42×C7D411yescharacteristic
90C2×C42×C7D411yescharacteristic
91C2×C42×C7C2311yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7—21no—
94C2×#1143—41no—
95C2×#1143—41no—
96C2×#1143C2×C414yescomplemented
97C2×#1141—41no—
98C2×#1141—41no—
99C2×#1141C2×C414yescomplemented
100#6493—22no—
101#6493C2×C414yes—
102C4×C22⋊D7—44no—
103C2×(C2×D7)⋊C4—21no—
104C2×(C2×D7)⋊C4—21no—
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×Dic7⋊C4—21no—
111C2×C4×Dic7—21no—
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C4×D28—41no—
117C4×D28—41no—
118C7×#95—21no—
119C7×#95—21no—
120C7×#95—21no—
121C7×#95—21no—
122#6409—41no—
123#6409—41no—
124#6409C2×C414yescomplemented
125#6406—41no—
126#6406—41no—
127#6406C2×C414yescomplemented
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)C2×C414yescomplemented
133#6383—41no—
134#6383—41no—
135#6382—41no—
136#6381—41no—
137C4×C7⋊C8—41no—
138C4×C7⋊C8—41no—
139C2×#449—71no—
140C4×#121—71no—
141#2297D711yescharacteristic, complemented
142#1970—71no—
143#1968—71no—
144#1934—71no—
145#1933—71no—
146#1928—71no—
147#1926—71no—
148#1879—71no—
149#1877—71no—
150#1875—71no—
151#1854—71no—
152#1788—71no—
153C4×C22⋊C8—71no—
154C24×C7—21no—
155C24×C7C2×D411yescharacteristic
156C23×D7—21no—
157C7×#41—44no—
158C7×#41—44no—
159C7×#41—44no—
160C7×#41—44no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8C22×C412yes—
167C2×C7×D4—24no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—42no—
174C2×C7×D4—42no—
175C2×C7×D4C22×C412yes—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—24no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—41no—
188C22×C4×C7—41no—
189C22×C4×C7—41no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7#4112yes—
199C22×C4×C7C2411yescharacteristic
200C2×C22⋊D7—24no—
201C2×C22⋊D7—42no—
202C2×C22⋊D7—42no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C2×D28—21no—
207C2×D28—21no—
208C2×D28—21no—
209C2×D28—21no—
210C2×D28—21no—
211C2×D28C22×C412yes—
212C2×C4×D7—42no—
213C2×C4×D7—42no—
214C2×C4×D7—42no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C22⋊C4—42no—
220C7×C22⋊C4—42no—
221C7×C22⋊C4—42no—
222C7×C22⋊C4—42no—
223C7×C22⋊C4—42no—
224C42×C7—21no—
225C42×C7—21no—
226C42×C7—21no—
227C42×C7—21no—
228C42×C7—41no—
229C42×C7—41no—
230C42×C7—42no—
231C22⋊Dic7—42no—
232#1143—44no—
233#1141—44no—
234(C2×D7)⋊C4—24no—
235(C2×D7)⋊C4—42no—
236(C2×D7)⋊C4—42no—
237(C2×D7)⋊C4—42no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7C22×C412yes—
244Dic7⋊C4—42no—
245C4×Dic7—42no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8C22×C412yes—
257C2×C7⋊C8C22×C412yes—
258C22×#41C2×D711yescharacteristic
259C22×SD16—71no—
260C22×D8—71no—
261C2×#121—71no—
262C2×C4×D4—71no—
263C2×C4×D4—141no—
264C2×#117C2×D711yescharacteristic
265C22×C42C2×D711yescharacteristic
266#449—78no—
267C2×#107—71no—
268C2×#106—71no—
269C2×#103—71no—
270C2×#103—71no—
271C2×#103—71no—
272C2×#102—71no—
273C2×#102—71no—
274C2×#102—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×C22⋊C8—71no—
278C2×C22⋊C8—71no—
279C2×C4×C8—71no—
280C2×C4×C8—71no—
281#391C2×D711yescharacteristic
282#391C2×D711yescharacteristic
283#390—71no—
284#390C2×D711yescharacteristic
285#390C2×D711yescharacteristic
286#389—71no—
287#388—141no—
288#386—21no—
289#386—21no—
290#386—141no—
291#380—71no—
292C4×C4⋊C4—71no—
293C4×C22⋊C4—21no—
294C4×C22⋊C4—21no—
295C4×C22⋊C4—141no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#336—71no—
301#336—71no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—22no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7C4×D412yes—
316C23×C7C22×D411yescharacteristic
317C22×D7—22no—
318C22×D7—41no—
319C22×D7—41no—
320C22×D7—41no—
321C22×D7—41no—
322C22×D7—41no—
323C22×D7—41no—
324C7×Q8—22no—
325C7×Q8—22no—
326C7×Q8—41no—
327C7×Q8—41no—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—48no—
331C7×D4—41no—
332C7×D4—41no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—44no—
350C2×C4×C7—44no—
351C2×C4×C7—48no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7C4×D412yes—
361C2×C4×C7#13512yes—
362C2×C4×C7#13512yes—
363C2×C4×C7AGL(1,ℤ/8)12yes—
364C2×C4×C7C23×C411yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7H(5,𝔽2)11yescharacteristic
367C2×C4×C7H(5,𝔽2)11yescharacteristic
368C2×C4×C7H(5,𝔽2)11yescharacteristic
369C2×C4×C7H(5,𝔽2)11yescharacteristic
370C22⋊D7—48no—
371C2×Dic7—22no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380D28—22no—
381D28—22no—
382D28—41no—
383D28—41no—
384C4×D7—84no—
385C7⋊C8—22no—
386C7⋊C8—22no—
387C7⋊C8—41no—
388C7⋊C8—41no—
389C2×#41—22no—
390C2×#41—41no—
391C2×#41—41no—
392C2×#41—41no—
393C2×#41—41no—
394C2×#41C4×D714yescomplemented
395C22×Q8C22×D711yescharacteristic
396C22×D4—21no—
397C22×D4—71no—
398C22×D4—141no—
399C22×D4C22×D711yescharacteristic
400C23×C4—21no—
401C23×C4—141no—
402C23×C4C22⋊D711yescharacteristic
403C23×C4C22⋊D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C2×SD16—74no—
406C2×SD16—281no—
407C2×SD16—281no—
408C2×D8—74no—
409C2×D8—281no—
410C2×D8—281no—
411C22×C8—71no—
412C22×C8—71no—
413C22×C8—71no—
414C22×C8—71no—
415#121—74no—
416#121—142no—
417C4×D4—281no—
418C4×D4—281no—
419C4×D4—284no—
420#117—41no—
421#117—41no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4C22×D711yescharacteristic
427C2×C4⋊C4C22×D711yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—141no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C42—21no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42—141no—
442C2×C42C22⋊D711yescharacteristic
443C2×C42C22⋊D711yescharacteristic
444C2×C42C22×D711yescharacteristic
445C2×C42C22×D711yescharacteristic
446#107—281no—
447#106—281no—
448#103—74no—
449#103—281no—
450#103—281no—
451#102—74no—
452#102—281no—
453#102—281no—
454#102—281no—
455#102—281no—
456C22⋊C8—74no—
457C22⋊C8—142no—
458C4×C8—281no—
459C4×C8—281no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—141no—
465#95—141no—
466#95—141no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—22no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—41no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7C2×C4×D411yescharacteristic
482C22×C7#53411yescharacteristic
483C22×C7#53511yescharacteristic
484C22×C7C2×#13511yescharacteristic
485C22×C7C2×#13511yescharacteristic
486C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C7#57511yescharacteristic
488C2×D7—42no—
489C2×D7—42no—
490C2×D7—42no—
491C2×D7—81no—
492C2×D7—81no—
493C2×D7—81no—
494C2×D7—81no—
495C4×C7—22no—
496C4×C7—22no—
497C4×C7—22no—
498C4×C7—22no—
499C4×C7—42no—
500C4×C7—41no—
501C4×C7—81no—
502C4×C7—81no—
503C4×C7#51811yescharacteristic
504C4×C7#51811yescharacteristic
505C4×C7#53811yescharacteristic
506C4×C7#53811yescharacteristic
507Dic7—42no—
508Dic7—81no—
509Dic7—81no—
510C24—21no—
511C24—141no—
512C24C2×C22⋊D711yescharacteristic
513#41—44no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8C2×C4×D712yes—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—72no—
532C2×D4—144no—
533C2×D4—141no—
534C2×D4—141no—
535C2×D4—141no—
536C2×D4—141no—
537C2×D4—141no—
538C2×D4—282no—
539C2×D4—282no—
540C2×D4C2×C4×D712yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—282no—
561C22×C4—282no—
562C22×C4—282no—
563C22×C4C2×C4×D712yes—
564C22×C4#115712yes—
565C22×C4C2×C22⋊D711yescharacteristic
566C22×C4C2×C22⋊D711yescharacteristic
567C22×C4C2×C22⋊D711yescharacteristic
568C22×C4C2×C22⋊D711yescharacteristic
569C22×C4C2×C22⋊D711yescharacteristic
570C22×C4C23×D711yescharacteristic
571SD16—284no—
572D8—284no—
573C2×C8—72no—
574C2×C8—72no—
575C2×C8—141no—
576C2×C8—141no—
577C2×C8—141no—
578C2×C8—141no—
579C2×C8—141no—
580C2×C8—141no—
581C2×C8—141no—
582C2×C8—141no—
583C2×C8—141no—
584C2×C8—141no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—72no—
590C4⋊C4—141no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—141no—
595C4⋊C4—282no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—144no—
602C22⋊C4—282no—
603C22⋊C4—282no—
604C22⋊C4—282no—
605C22⋊C4—282no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—41no—
611C42—41no—
612C42—42no—
613C42—282no—
614C2×C7—42no—
615C2×C7—82no—
616C2×C7#232111yescharacteristic
617C2×C7C4×#13511yescharacteristic
618C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
619C2×C7#318811yescharacteristic
620C2×C7#319111yescharacteristic
621C2×C7#320711yescharacteristic
622C2×C7#321211yescharacteristic
623D7—82no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—142no—
638C23—281no—
639C23—281no—
640C23—281no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23C4×C22⋊D712yes—
645C23C22×C22⋊D711yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—41no—
654D4—41no—
655D4—142no—
656D4—142no—
657D4—288no—
658D4—281no—
659D4—281no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—48no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—142no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4—281no—
691C2×C4—281no—
692C2×C4—281no—
693C2×C4—281no—
694C2×C4—281no—
695C2×C4—281no—
696C2×C4—564no—
697C2×C4C4×C22⋊D712yes—
698C2×C4#651212yes—
699C2×C4#651312yes—
700C2×C4#651312yes—
701C2×C4C22×C4×D711yescharacteristic
702C2×C4C2×#115711yescharacteristic
703C2×C4#654811yescharacteristic
704C2×C4#654811yescharacteristic
705C2×C4#654811yescharacteristic
706C2×C4#654811yescharacteristic
707C8—142no—
708C8—142no—
709C8—281no—
710C8—281no—
711C7#2204511yescharacteristic, complemented, Sylow
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—561no—
730C22—561no—
731C22—561no—
732C22—561no—
733C22C2×C4×C22⋊D711yescharacteristic
734C22#9049511yescharacteristic
735C22#9049611yescharacteristic
736C22C2×#651211yescharacteristic
737C22C2×#651311yescharacteristic
738C22C2×#651311yescharacteristic
739C22#9051311yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—42no—
745C4—41no—
746C4—81no—
747C4—81no—
748C4—282no—
749C4—561no—
750C4—561no—
751C4#9017711yescharacteristic
752C4#9017711yescharacteristic
753C4#9018511yescharacteristic
754C4#9018511yescharacteristic
755C2—42no—
756C2—82no—
757C2—562no—
758C2#1173954111yescharacteristic
759C2C4×#651311yescharacteristic
760C2C4×#651211yescharacteristic
761C2#1174037411yescharacteristic
762C2#1174037511yescharacteristic
763C2#1174074811yescharacteristic
764C2#1174075011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2297C2
socleC23×C7C22×D4
prime radicalC2×#90010C2
cosocleC22×C4×C7C24
hypercenter#2297D7
hypocenterC7#22045
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. C7×#2297C2semidirect
3. C4×#6493C2semidirect
4. #11729889C2semidirect
5. #11729340C2semidirect
6. #11729330C2semidirect
7. C4×C22⋊(C7⋊C8)C2semidirect
8. #11727441C2semidirect
9. #11727430C2semidirect
10. #11727428C2semidirect
11. #11727421C2semidirect
12. #11727411C2semidirect
13. #11727401C2semidirect
14. #11727398C2semidirect
15. #11727391C2semidirect
32. #90010C4semidirect
66. C2×C7×#41C2×C4semidirect
96. C2×#1143C2×C4semidirect
99. C2×#1141C2×C4semidirect
124. #6409C2×C4semidirect
127. #6406C2×C4semidirect
132. C22⋊(C7⋊C8)C2×C4semidirect
141. #2297D7semidirect
394. C2×#41C4×D7semidirect
711. C7#22045semidirect

Maximal subgroups

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

subgroupindex
C7×#22972
C2×#900102
C4×#64932
#117298892
#117293402
#117293302
C4×C22⋊(C7⋊C8)2
#117274412
#117274302
#117274282
#117274212
#117274112
#117274012
#117273982
#117273912
#220457