Finite Group Databasebeta

← #13370116

Subgroups — #13370116

Order 1792.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90256C211yesmaximal, characteristic
2C2×C7×#435C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic7C211yesmaximal, characteristic, complemented
4#11729744C211yesmaximal, characteristic, complemented
5#11729739C211yesmaximal, characteristic, complemented
6#11729727C211yesmaximal, characteristic, complemented
7C2×#89346C211yesmaximal, characteristic, complemented
8#11728233C211yesmaximal, characteristic, complemented
9#11728215C211yesmaximal, characteristic, complemented
10#11727686C211yesmaximal, characteristic, complemented
11#11727686C211yesmaximal, characteristic, complemented
12#11727680C211yesmaximal, characteristic, complemented
13#11727679C211yesmaximal, characteristic, complemented
14#11727581C211yesmaximal, characteristic, complemented
15#11727566C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×#6502—21no—
20C2×D4×Dic7—21no—
21C2×#6493C2211yescharacteristic
22C2×#6493C2211yescharacteristic
23C2×#6489C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27#90256—24no—
28#90256C418yescomplemented
29C2×#6461—21no—
30C2×#6446—21no—
31C2×(C22⋊D7)⋊C4—21no—
32C2×C4×D28C2211yescharacteristic
33C2×#6433C2211yescharacteristic
34C7×#435—24no—
35C2×C7×C4⋊C8C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39#89984C2211yescharacteristic
40#89984C2211yescharacteristic
41C2×#6395C2211yescharacteristic
42C2×#6395C2211yescharacteristic
43C2×#6395C2211yescharacteristic
44C2×#6395C2211yescharacteristic
45#89757—21no—
46#89722—21no—
47#89722—21no—
48#89707C2211yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#89346C2211yescharacteristic
62#22493—71nomaximal, Sylow
63C22×C7×D4D411yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C22×C22⋊D7—21no—
67C22×C22⋊D7—21no—
68C23×Dic7—21no—
69C23×Dic7—21no—
70C23×Dic7—21no—
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C2×C7×M16—22no—
74C2×C7×M16—22no—
75C2×C7×M16—41no—
76C22×C7×C8—22no—
77C22×C7×C8—22no—
78C22×C7×C8—41no—
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C4×C7×D4C2×C414yes—
84C4×C7×D4D414yes—
85C2×C7×C4⋊C4D411yescharacteristic
86C2×C7×C22⋊C4D411yescharacteristic
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92#6502—28no—
93D4×Dic7—44no—
94#6493—22no—
95#6493—22no—
96#6493C2×C414yescomplemented
97#6493C2×C414yescomplemented
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101#6489—22no—
102#6489C2×C414yescomplemented
103C2×C4⋊Dic7—21no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—21no—
108C2×C4⋊Dic7—21no—
109C2×C4⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7C2×C414yescomplemented
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×C4×Dic7—21no—
124C2×C4×Dic7—21no—
125#6461—28no—
126#6446—28no—
127(C22⋊D7)⋊C4—28no—
128C4×D28—22no—
129C4×D28C2×C414yescomplemented
130#6433—22no—
131#6433C2×C414yescomplemented
132C7×C4⋊C8—22no—
133C7×C22⋊C8—22no—
134C7×C22⋊C8—22no—
135C7×#97—22no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139#6395—22no—
140#6395—22no—
141#6395—41no—
142#6395—41no—
143C2×#553—71no—
144C2×#435D711yescharacteristic, complemented
145D4×C4⋊C4—71no—
146#1992—71no—
147#1989—71no—
148#1895—71no—
149#1893—71no—
150#1874—71no—
151#1874—71no—
152#1825—71no—
153#1824—71no—
154#1802—71no—
155#1762—71no—
156#1736—71no—
157C2×#340—71no—
158C24×C7C2×D411yescharacteristic
159C24×C7C2×D411yescharacteristic
160C23×D7—21no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4C22⋊C414yes—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7C22×C412yes—
173C22×C4×C7C22×C412yes—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D412yes—
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2411yescharacteristic
181C2×C22⋊D7—24no—
182C2×C22⋊D7—24no—
183C2×C22⋊D7—42no—
184C2×C22⋊D7—42no—
185C2×C22⋊D7—81no—
186C2×C22⋊D7—81no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C22×Dic7—21no—
191C22×Dic7—24no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—42no—
196C22×Dic7—42no—
197C22×Dic7—42no—
198C22×Dic7—42no—
199C22×Dic7—81no—
200C22×Dic7—81no—
201C22×Dic7—81no—
202C22×Dic7—81no—
203C2×D28—21no—
204C2×D28—21no—
205C2×D28—21no—
206C2×D28—21no—
207C2×D28—21no—
208C2×D28C22×C412yes—
209C2×C4×D7—24no—
210C2×C4×D7—81no—
211C2×C4×D7—81no—
212C7×M16—44no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—44no—
225C2×C7×C8#4112yes—
226C7×C4⋊C4C22⋊C414yes—
227C7×C22⋊C4C22⋊C414yes—
228C7×C22⋊C4C22⋊C414yes—
229C42×C7C22×C412yes—
230C42×C7C2×D412yes—
231C22⋊Dic7—24no—
232C22⋊Dic7—42no—
233C22⋊Dic7—42no—
234(C2×D7)⋊C4—24no—
235(C2×D7)⋊C4—24no—
236(C2×D7)⋊C4—24no—
237C4⋊Dic7—24no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—21no—
247C4⋊Dic7—21no—
248C4⋊Dic7—42no—
249C4⋊Dic7—42no—
250C4⋊Dic7—42no—
251C4⋊Dic7—81no—
252C4⋊Dic7C22×C412yes—
253C4⋊Dic7C22×C412yes—
254C4⋊Dic7C22×C412yes—
255C4⋊Dic7#4112yes—
256Dic7⋊C4—24no—
257Dic7⋊C4—24no—
258C4×Dic7—24no—
259C4×Dic7—42no—
260C22×M16C2×D711yescharacteristic
261C23×C8C2×D711yescharacteristic
262#553—78no—
263#553—144no—
264C2×#126—141no—
265C2×#125—71no—
266C2×#123—141no—
267C2×#121—71no—
268C2×#121—71no—
269C2×#121—141no—
270C2×C4×D4—71no—
271C2×C4×D4—141no—
272C2×C4×D4—141no—
273C2×C4×D4C2×D711yescharacteristic
274C2×#117—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278#435—24no—
279C2×C4⋊C8C2×D711yescharacteristic
280C2×#102—71no—
281C2×#102—71no—
282C2×#102—71no—
283C2×#102—71no—
284C2×C22⋊C8C2×D711yescharacteristic
285C2×C22⋊C8C2×D711yescharacteristic
286C2×#97C2×D711yescharacteristic
287#389—141no—
288#385—141no—
289#385—141no—
290#384—71no—
291#380—71no—
292#380—71no—
293C4×C4⋊C4—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#340—71no—
303#340—71no—
304#340—71no—
305#340—71no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7C2×C22⋊C412yes—
317C23×C7C2×C22⋊C412yes—
318C23×C7AGL(1,ℤ/8)12yes—
319C23×C7#13712yes—
320C23×C7C22×D411yescharacteristic
321C22×D7—22no—
322C22×D7—41no—
323C22×D7—41no—
324C22×D7—41no—
325C22×D7—41no—
326C22×D7—41no—
327C22×D7—41no—
328C7×D4—28no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7C2×C22⋊C412yes—
346C2×C4×C7C2×C22⋊C412yes—
347C2×C4×C7C2×C22⋊C412yes—
348C2×C4×C7C2×C22⋊C412yes—
349C2×C4×C7C23×C411yescharacteristic
350C2×C4×C7C22×D411yescharacteristic
351C2×C4×C7C2×#4111yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7H(5,𝔽2)11yescharacteristic
354C2×C4×C72−1+411yescharacteristic
355C22⋊D7—48no—
356C22⋊D7—84no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—84no—
379C2×Dic7—84no—
380C2×Dic7—84no—
381D28—22no—
382D28—22no—
383D28—41no—
384D28—41no—
385C4×D7—84no—
386C7×C8—22no—
387C7×C8—41no—
388C7×C8—41no—
389C7×C8—41no—
390C22×D4—71no—
391C22×D4—141no—
392C22×D4—141no—
393C22×D4D2811yescharacteristic
394C23×C4—141no—
395C23×C4—141no—
396C23×C4—141no—
397C23×C4—141no—
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—41no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—41no—
406C22×C8C22×D711yescharacteristic
407C22×C8C22×D711yescharacteristic
408C22×C8C22×D711yescharacteristic
409C22×C8C22×D711yescharacteristic
410#126—148no—
411#125—74no—
412#125—142no—
413#123—148no—
414#121—74no—
415#121—74no—
416#121—148no—
417#121—142no—
418#121—142no—
419C4×D4—74no—
420C4×D4—148no—
421C4×D4—142no—
422C4×D4—284no—
423C4×D4C4×D714yes—
424C4×D4C22⋊D714yes—
425#117—74no—
426#117—142no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—71no—
429C2×C4⋊C4—71no—
430C2×C4⋊C4—71no—
431C2×C4⋊C4—71no—
432C2×C4⋊C4—71no—
433C2×C4⋊C4—71no—
434C2×C4⋊C4—71no—
435C2×C4⋊C4—142no—
436C2×C4⋊C4—142no—
437C2×C4⋊C4—141no—
438C2×C4⋊C4—141no—
439C2×C4⋊C4—141no—
440C2×C4⋊C4—142no—
441C2×C4⋊C4—141no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4—141no—
445C2×C4⋊C4—281no—
446C2×C4⋊C4—281no—
447C2×C4⋊C4D2811yescharacteristic
448C2×C22⋊C4—141no—
449C2×C22⋊C4—141no—
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4D2811yescharacteristic
455C2×C22⋊C4D2811yescharacteristic
456C2×C42—141no—
457C2×C42—141no—
458C2×C42C22×D711yescharacteristic
459C4⋊C8—22no—
460#102—142no—
461#102—142no—
462#102—281no—
463#102—281no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466#97—22no—
467#95—141no—
468#95—141no—
469#95—141no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7#41714yes—
484C22×C7C22×C22⋊C411yescharacteristic
485C22×C7#54611yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
488C22×C7C2×#13711yescharacteristic
489C22×C7#57611yescharacteristic
490C22×C7#57711yescharacteristic
491C2×D7—42no—
492C2×D7—42no—
493C2×D7—42no—
494C2×D7—81no—
495C2×D7—81no—
496C2×D7—81no—
497C2×D7—81no—
498C4×C7—22no—
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—22no—
502C4×C7C4×#4111yescharacteristic
503C4×C7#52011yescharacteristic
504C4×C7#54611yescharacteristic
505C4×C7#54711yescharacteristic
506Dic7—42no—
507Dic7—42no—
508Dic7—42no—
509Dic7—42no—
510Dic7—81no—
511Dic7—81no—
512Dic7—81no—
513C24—141no—
514C24C2×D2811yescharacteristic
515C24C2×D2811yescharacteristic
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—72no—
519C2×D4—144no—
520C2×D4—144no—
521C2×D4—141no—
522C2×D4—141no—
523C2×D4—141no—
524C2×D4—141no—
525C2×D4—141no—
526C2×D4—282no—
527C2×D4—282no—
528C2×D4—561no—
529C2×D4—561no—
530C2×D4(C2×D7)⋊C414yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—141no—
540C22×C4—141no—
541C22×C4—141no—
542C22×C4—141no—
543C22×C4—144no—
544C22×C4—144no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—282no—
549C22×C4—282no—
550C22×C4—282no—
551C22×C4—282no—
552C22×C4—561no—
553C22×C4—561no—
554C22×C4—561no—
555C22×C4—561no—
556C22×C4—561no—
557C22×C4—561no—
558C22×C4C2×C4×D712yes—
559C22×C4C2×C4×D712yes—
560C22×C4C2×D2811yescharacteristic
561C22×C4C2×D2811yescharacteristic
562C22×C4C2×D2811yescharacteristic
563C22×C4C2×D2811yescharacteristic
564C22×C4C2×C22⋊D712yes—
565C22×C4C2×C22⋊D712yes—
566C22×C4C23×D711yescharacteristic
567M16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—44no—
580C2×C8#115912yes—
581C4⋊C4—72no—
582C4⋊C4—72no—
583C4⋊C4—72no—
584C4⋊C4—72no—
585C4⋊C4—144no—
586C4⋊C4—144no—
587C4⋊C4—144no—
588C4⋊C4—141no—
589C4⋊C4—141no—
590C4⋊C4—141no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—141no—
595C4⋊C4—141no—
596C4⋊C4—141no—
597C4⋊C4—141no—
598C4⋊C4—282no—
599C4⋊C4—282no—
600C4⋊C4—282no—
601C4⋊C4—561no—
602C4⋊C4(C2×D7)⋊C414yes—
603C22⋊C4—144no—
604C22⋊C4—144no—
605C22⋊C4—144no—
606C22⋊C4—144no—
607C22⋊C4—282no—
608C22⋊C4—282no—
609C22⋊C4(C2×D7)⋊C414yes—
610C22⋊C4(C2×D7)⋊C414yes—
611C42—144no—
612C42—282no—
613C42C2×C4×D712yes—
614C42C2×C22⋊D712yes—
615C2×C7—24no—
616C2×C7—42no—
617C2×C7#233911yescharacteristic
618C2×C7C2×#41711yescharacteristic
619C2×C7#289711yescharacteristic
620C2×C7#331811yescharacteristic
621C2×C7#332011yescharacteristic
622C2×C7#334511yescharacteristic
623C2×C7#334611yescharacteristic
624D7—82no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—142no—
636C23—281no—
637C23—281no—
638C23—281no—
639C23—281no—
640C23—281no—
641C23—281no—
642C23#647112yes—
643C23#647212yes—
644C23C2×(C2×D7)⋊C412yes—
645C23C2×(C2×D7)⋊C412yes—
646C23C22×D2811yescharacteristic
647D4—28no—
648D4—142no—
649D4—142no—
650D4—288no—
651D4—281no—
652D4—281no—
653D4—564no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—281no—
678C2×C4—281no—
679C2×C4—281no—
680C2×C4—281no—
681C2×C4—281no—
682C2×C4—281no—
683C2×C4—281no—
684C2×C4—281no—
685C2×C4—281no—
686C2×C4—281no—
687C2×C4—281no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4—281no—
691C2×C4—564no—
692C2×C4—564no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4C2×(C2×D7)⋊C412yes—
696C2×C4C2×(C2×D7)⋊C412yes—
697C2×C4C2×(C2×D7)⋊C412yes—
698C2×C4C2×(C2×D7)⋊C412yes—
699C2×C4C22×C4×D711yescharacteristic
700C2×C4C2×#115911yescharacteristic
701C2×C4#654811yescharacteristic
702C2×C4D7×#4111yescharacteristic
703C2×C4#655411yescharacteristic
704C2×C4C22×C22⋊D711yescharacteristic
705C8—22no—
706C8—41no—
707C8—41no—
708C8—41no—
709C7#2249311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—282no—
724C22—282no—
725C22—282no—
726C22—561no—
727C22—561no—
728C22—561no—
729C22—561no—
730C22#8990514yes—
731C22#9024511yescharacteristic
732C22#9024611yescharacteristic
733C22C2×#647111yescharacteristic
734C22C2×#647211yescharacteristic
735C22#9044211yescharacteristic
736C22#9044311yescharacteristic
737C22C22×(C2×D7)⋊C411yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4—282no—
746C4—561no—
747C4—561no—
748C4—561no—
749C4C4×#115911yescharacteristic
750C4#9023711yescharacteristic
751C4#9049711yescharacteristic
752C4#9051511yescharacteristic
753C2—24no—
754C2—42no—
755C2—562no—
756C2#1173691611yescharacteristic
757C2#1173691711yescharacteristic
758C2#1173695011yescharacteristic
759C2#1173696011yescharacteristic
760C2#1173977511yescharacteristic
761C2C2×#8990511yescharacteristic
762C2#1174124211yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90256C2
cosocleC22×C4×C7C24
hypercenterC2×#435D7
hypocenterC7#22493
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×C7×#435C2semidirect
3. D4×C4⋊Dic7C2semidirect
4. #11729744C2semidirect
5. #11729739C2semidirect
6. #11729727C2semidirect
7. C2×#89346C2semidirect
8. #11728233C2semidirect
9. #11728215C2semidirect
10. #11727686C2semidirect
11. #11727686C2semidirect
12. #11727680C2semidirect
13. #11727679C2semidirect
14. #11727581C2semidirect
15. #11727566C2semidirect
28. #90256C4semidirect
96. #6493C2×C4semidirect
97. #6493C2×C4semidirect
102. #6489C2×C4semidirect
113. C2×C4⋊Dic7C2×C4semidirect
129. C4×D28C2×C4semidirect
131. #6433C2×C4semidirect
144. C2×#435D7semidirect
709. C7#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#902562
C2×C7×#4352
D4×C4⋊Dic72
#117297442
#117297392
#117297272
C2×#893462
#117282332
#117282152
#117276862
#117276802
#117276792
#117275812
#117275662
#224937