Finite Group Databasebeta

← #13370146

Subgroups — #13370146

Order 1792.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90246C211yesmaximal, characteristic
2C2×C7×#435C211yesmaximal, characteristic, complemented
3#11739780C211yesmaximal, characteristic, complemented
4#11729744C211yesmaximal, characteristic, complemented
5#11729739C211yesmaximal, characteristic, complemented
6#11729727C211yesmaximal, characteristic, complemented
7C2×#89346C211yesmaximal, characteristic, complemented
8#11728234C211yesmaximal, characteristic, complemented
9#11728213C211yesmaximal, characteristic, complemented
10#11727687C211yesmaximal, characteristic, complemented
11#11727686C211yesmaximal, characteristic, complemented
12#11727679C211yesmaximal, characteristic, complemented
13#11727678C211yesmaximal, characteristic, complemented
14#11727582C211yesmaximal, characteristic, complemented
15#11727566C211yesmaximal, characteristic, complemented
16C22×#1159—21no—
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26#90246—24no—
27#90246C418yescomplemented
28C2×#6460—21no—
29C2×#6449—21no—
30C2×#6449—21no—
31C2×C4×D28C2211yescharacteristic
32C2×#6432C2211yescharacteristic
33C7×#435—24no—
34C2×C7×C4⋊C8C2211yescharacteristic
35C2×C7×C22⋊C8C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×#97C2211yescharacteristic
38#89992—21no—
39#89984C2211yescharacteristic
40#89984C2211yescharacteristic
41C2×#6395C2211yescharacteristic
42C2×#6395C2211yescharacteristic
43C2×#6395C2211yescharacteristic
44C2×#6395C2211yescharacteristic
45#89753—21no—
46#89723—21no—
47C22⋊C4×Dic7—21no—
48#89708C2211yescharacteristic
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#22495—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—
71C2×#1159—28no—
72C2×#1159—44no—
73C2×#1159—44no—
74C22×D28C2311yescharacteristic
75C22×C4×D7—21no—
76C22×Dic14—21no—
77C2×C7×M16—22no—
78C2×C7×M16—22no—
79C2×C7×M16—41no—
80C22×C7×C8—22no—
81C22×C7×C8—22no—
82C22×C7×C8—41no—
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C4×C7×D4C2×C414yes—
88C4×C7×D4D414yes—
89C2×C7×C4⋊C4D411yescharacteristic
90C2×C7×C22⋊C4D411yescharacteristic
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×C22⋊Dic7—21no—
94C2×C22⋊Dic7—21no—
95C2×C22⋊Dic7—21no—
96#6493—22no—
97#6493—22no—
98#6493C2×C414yes—
99#6493C2×C414yescomplemented
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103#6489—22no—
104#6489—41no—
105C2×C4⋊Dic7—21no—
106C2×C4⋊Dic7—21no—
107C2×C4⋊Dic7—21no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7C2×C414yes—
114C2×C4⋊Dic7C2×C414yescomplemented
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4×Dic7—21no—
123C2×C4×Dic7—21no—
124#6460—28no—
125#6449—28no—
126#6449—28no—
127C4×D28—22no—
128C4×D28C2×C414yescomplemented
129#6432—22no—
130#6432C2×C414yescomplemented
131C7×C4⋊C8—22no—
132C7×C22⋊C8—22no—
133C7×C22⋊C8—22no—
134C7×#97—22no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139C7⋊#95—21no—
140#6395—22no—
141#6395—22no—
142#6395—41no—
143#6395—41no—
144C2×#547—71no—
145C2×#435D711yescharacteristic, complemented
146#2352—71no—
147#1993—71no—
148#1987—71no—
149#1895—71no—
150#1893—71no—
151#1875—71no—
152#1874—71no—
153#1824—71no—
154#1823—71no—
155#1804—71no—
156#1762—71no—
157#1736—71no—
158C2×#340—71no—
159C24×C7C2×D411yescharacteristic
160C24×C7C2×D411yescharacteristic
161C23×D7—21no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4C22⋊C414yes—
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×C7—21no—
173C22×C4×C7C22×C412yes—
174C22×C4×C7C22×C412yes—
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2411yescharacteristic
182C2×C22⋊D7—24no—
183C2×C22⋊D7—24no—
184C2×C22⋊D7—42no—
185C2×C22⋊D7—42no—
186C2×C22⋊D7—42no—
187C2×C22⋊D7—42no—
188C22×Dic7—24no—
189C22×Dic7—24no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7—21no—
197C22×Dic7—42no—
198C22×Dic7—42no—
199C22×Dic7—42no—
200C22×Dic7—42no—
201C22×Dic7—42no—
202C22×Dic7—42no—
203C22×Dic7—81no—
204#1159—432no—
205C2×D28—21no—
206C2×D28—21no—
207C2×D28—21no—
208C2×D28—21no—
209C2×D28—21no—
210C2×D28C22×C412yes—
211C2×C4×D7—24no—
212C2×C4×D7—42no—
213C2×C4×D7—42no—
214C2×Dic14—24no—
215C2×Dic14—42no—
216C2×Dic14—42no—
217C7×M16—44no—
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—21no—
225C2×C7×C8—21no—
226C2×C7×C8—21no—
227C2×C7×C8—21no—
228C2×C7×C8—21no—
229C2×C7×C8—44no—
230C2×C7×C8#4112yescomplemented
231C7×C4⋊C4C22⋊C414yes—
232C7×C22⋊C4C22⋊C414yes—
233C7×C22⋊C4C22⋊C414yes—
234C42×C7C22×C412yes—
235C42×C7C2×D412yes—
236C22⋊Dic7—42no—
237C22⋊Dic7—42no—
238C22⋊Dic7—81no—
239(C2×D7)⋊C4—24no—
240(C2×D7)⋊C4—24no—
241(C2×D7)⋊C4—24no—
242C4⋊Dic7—24no—
243C4⋊Dic7—24no—
244C4⋊Dic7—24no—
245C4⋊Dic7—21no—
246C4⋊Dic7—21no—
247C4⋊Dic7—21no—
248C4⋊Dic7—21no—
249C4⋊Dic7—21no—
250C4⋊Dic7—21no—
251C4⋊Dic7—21no—
252C4⋊Dic7—21no—
253C4⋊Dic7—21no—
254C4⋊Dic7—21no—
255C4⋊Dic7—42no—
256C4⋊Dic7C22×C412yes—
257C4⋊Dic7C22×C412yes—
258C4⋊Dic7C22×C412yes—
259C4⋊Dic7#4112yescomplemented
260C4×Dic7—42no—
261C4×Dic7—81no—
262C22×#41—141no—
263C22×M16C2×D711yescharacteristic
264C23×C8C2×D711yescharacteristic
265#547—78no—
266#547—144no—
267C2×C4⋊Q8—71no—
268C2×#123—141no—
269C2×#123—141no—
270C2×C22⋊Q8—141no—
271C2×#121—71no—
272C2×#121—71no—
273C2×C4×D4—71no—
274C2×C4×D4C2×D711yescharacteristic
275C2×#117—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279#435—24no—
280C2×C4⋊C8C2×D711yescharacteristic
281C2×#102—71no—
282C2×#102—71no—
283C2×#102—71no—
284C2×#102—71no—
285C2×C22⋊C8C2×D711yescharacteristic
286C2×C22⋊C8C2×D711yescharacteristic
287C2×#97C2×D711yescharacteristic
288#388—141no—
289#387—141no—
290#386—141no—
291#382—71no—
292#380—71no—
293#380—71no—
294C4×C4⋊C4—71no—
295C4×C22⋊C4—141no—
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—
306#340—71no—
307#340—71no—
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×C7—21no—
317C23×C7—21no—
318C23×C7C2×C22⋊C412yes—
319C23×C7C2×C22⋊C412yes—
320C23×C7AGL(1,ℤ/8)12yes—
321C23×C7AGL(1,ℤ/8)12yes—
322C23×C7C22×D411yescharacteristic
323C22×D7—22no—
324C22×D7—41no—
325C22×D7—41no—
326C22×D7—41no—
327C22×D7—41no—
328C22×D7—41no—
329C22×D7—41no—
330C7×D4—28no—
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—21no—
338C2×C4×C7—21no—
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×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7C2×C22⋊C412yes—
348C2×C4×C7C2×C22⋊C412yes—
349C2×C4×C7C2×C22⋊C412yes—
350C2×C4×C7C2×C22⋊C412yes—
351C2×C4×C7C23×C411yescharacteristic
352C2×C4×C7C22×D411yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7C2×#4111yescharacteristic
355C2×C4×C7H(5,𝔽2)11yescharacteristic
356C2×C4×C72−1+411yescharacteristic
357C22⋊D7—48no—
358C22⋊D7—48no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—48no—
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—48no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—84no—
383D28—22no—
384D28—22no—
385D28—41no—
386D28—41no—
387C4×D7—48no—
388Dic14—48no—
389C7×C8—22no—
390C7×C8—41no—
391C7×C8—41no—
392C7×C8—41no—
393C2×#41—148no—
394C2×#41—284no—
395C2×#41—284no—
396C22×Q8—141no—
397C22×D4—71no—
398C22×D4—141no—
399C22×D4—141no—
400C22×D4D2811yescharacteristic
401C23×C4—141no—
402C23×C4—141no—
403C23×C4—141no—
404C23×C4—141no—
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D711yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—41no—
413C22×C8C22×D711yescharacteristic
414C22×C8C22×D711yescharacteristic
415C22×C8C22×D711yescharacteristic
416C22×C8C22×D711yescharacteristic
417C4⋊Q8—74no—
418C4⋊Q8—142no—
419#123—148no—
420#123—148no—
421C22⋊Q8—148no—
422#121—74no—
423#121—74no—
424#121—142no—
425#121—142no—
426C4×D4—74no—
427C4×D4—142no—
428C4×D4C4×D714yes—
429C4×D4C22⋊D714yes—
430#117—142no—
431#117—281no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—74no—
434C2×C4⋊C4—71no—
435C2×C4⋊C4—71no—
436C2×C4⋊C4—71no—
437C2×C4⋊C4—71no—
438C2×C4⋊C4—71no—
439C2×C4⋊C4—71no—
440C2×C4⋊C4—71no—
441C2×C4⋊C4—142no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4—141no—
445C2×C4⋊C4—142no—
446C2×C4⋊C4—142no—
447C2×C4⋊C4—141no—
448C2×C4⋊C4—281no—
449C2×C4⋊C4D2811yescharacteristic
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C22⋊C4D2811yescharacteristic
457C2×C22⋊C4D2811yescharacteristic
458C2×C42—141no—
459C2×C42—141no—
460C2×C42C22×D711yescharacteristic
461C4⋊C8—22no—
462#102—142no—
463#102—142no—
464#102—281no—
465#102—281no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468#97—22no—
469#95—141no—
470#95—141no—
471#95—141no—
472#95—141no—
473#95—141no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—22no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7#41814yes—
488C22×C7C22×C22⋊C411yescharacteristic
489C22×C7#54611yescharacteristic
490C22×C7#54711yescharacteristic
491C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
492C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C7#57711yescharacteristic
494C22×C7#57811yescharacteristic
495C2×D7—42no—
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—81no—
499C2×D7—81no—
500C2×D7—81no—
501C2×D7—81no—
502C4×C7—22no—
503C4×C7—22no—
504C4×C7—22no—
505C4×C7—22no—
506C4×C7C4×#4111yescharacteristic
507C4×C7#52011yescharacteristic
508C4×C7#54611yescharacteristic
509C4×C7#54711yescharacteristic
510Dic7—42no—
511Dic7—42no—
512Dic7—42no—
513Dic7—42no—
514Dic7—81no—
515Dic7—81no—
516Dic7—81no—
517C24—141no—
518C24C2×D2811yescharacteristic
519C24C2×D2811yescharacteristic
520#41—2832no—
521C2×Q8—144no—
522C2×Q8—282no—
523C2×Q8—282no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—72no—
527C2×D4—144no—
528C2×D4—144no—
529C2×D4—141no—
530C2×D4—141no—
531C2×D4—141no—
532C2×D4—141no—
533C2×D4—141no—
534C2×D4—282no—
535C2×D4—282no—
536C2×D4—282no—
537C2×D4—282no—
538C2×D4(C2×D7)⋊C414yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—144no—
548C22×C4—144no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—144no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—141no—
557C22×C4—282no—
558C22×C4—282no—
559C22×C4—282no—
560C22×C4—282no—
561C22×C4—282no—
562C22×C4—282no—
563C22×C4—282no—
564C22×C4—282no—
565C22×C4—561no—
566C22×C4C2×C4×D712yes—
567C22×C4C2×C4×D712yes—
568C22×C4C2×D2811yescharacteristic
569C22×C4C2×D2811yescharacteristic
570C22×C4C2×D2811yescharacteristic
571C22×C4C2×D2811yescharacteristic
572C22×C4C2×C22⋊D712yes—
573C22×C4C2×C22⋊D712yes—
574C22×C4C23×D711yescharacteristic
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8#115912yescomplemented
589C4⋊C4—72no—
590C4⋊C4—72no—
591C4⋊C4—72no—
592C4⋊C4—72no—
593C4⋊C4—144no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—141no—
597C4⋊C4—141no—
598C4⋊C4—141no—
599C4⋊C4—141no—
600C4⋊C4—141no—
601C4⋊C4—141no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—282no—
607C4⋊C4(C2×D7)⋊C414yes—
608C22⋊C4—144no—
609C22⋊C4—144no—
610C22⋊C4—144no—
611C22⋊C4—282no—
612C22⋊C4—282no—
613C22⋊C4—561no—
614C22⋊C4(C2×D7)⋊C414yes—
615C22⋊C4(C2×D7)⋊C414yes—
616C42—282no—
617C42—561no—
618C42C2×C4×D712yes—
619C42C2×C22⋊D712yes—
620C2×C7—24no—
621C2×C7—42no—
622C2×C7#233911yescharacteristic
623C2×C7C2×#41811yescharacteristic
624C2×C7#289811yescharacteristic
625C2×C7#330611yescharacteristic
626C2×C7#330811yescharacteristic
627C2×C7#334311yescharacteristic
628C2×C7#334511yescharacteristic
629D7—82no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—142no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23—281no—
645C23—281no—
646C23—281no—
647C23#647112yes—
648C23#647112yes—
649C23C2×(C2×D7)⋊C412yes—
650C23C2×(C2×D7)⋊C412yes—
651C23C22×D2811yescharacteristic
652Q8—288no—
653D4—28no—
654D4—142no—
655D4—142no—
656D4—288no—
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—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—288no—
681C2×C4—288no—
682C2×C4—288no—
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—281no—
692C2×C4—281no—
693C2×C4—281no—
694C2×C4—281no—
695C2×C4—281no—
696C2×C4—281no—
697C2×C4—281no—
698C2×C4—281no—
699C2×C4—281no—
700C2×C4—564no—
701C2×C4C2×(C2×D7)⋊C412yes—
702C2×C4C2×(C2×D7)⋊C412yes—
703C2×C4C2×(C2×D7)⋊C412yes—
704C2×C4C2×(C2×D7)⋊C412yes—
705C2×C4C22×C4×D711yescharacteristic
706C2×C4C2×#115911yescharacteristic
707C2×C4#654811yescharacteristic
708C2×C4D7×#4111yescharacteristic
709C2×C4#655411yescharacteristic
710C2×C4C22×C22⋊D711yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C7#2249511yescharacteristic, complemented, Sylow
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—561no—
733C22—561no—
734C22—561no—
735C22—561no—
736C22#8990314yes—
737C22#9024511yescharacteristic
738C22#9024611yescharacteristic
739C22C2×#647111yescharacteristic
740C22C2×#647111yescharacteristic
741C22#9044211yescharacteristic
742C22#9044411yescharacteristic
743C22C22×(C2×D7)⋊C411yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—282no—
749C4—282no—
750C4—282no—
751C4—282no—
752C4—561no—
753C4—561no—
754C4—561no—
755C4C4×#115911yescharacteristic
756C4#9023711yescharacteristic
757C4#9049711yescharacteristic
758C4#9051511yescharacteristic
759C2—24no—
760C2—42no—
761C2—562no—
762C2#1173691411yescharacteristic
763C2#1173691611yescharacteristic
764C2#1173694411yescharacteristic
765C2#1173695411yescharacteristic
766C2#1173977511yescharacteristic
767C2C2×#8990311yescharacteristic
768C2#1174125111yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90246C2
cosocleC22×C4×C7C24
hypercenterC2×#435D7
hypocenterC7#22495
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. #11739780C2semidirect
4. #11729744C2semidirect
5. #11729739C2semidirect
6. #11729727C2semidirect
7. C2×#89346C2semidirect
8. #11728234C2semidirect
9. #11728213C2semidirect
10. #11727687C2semidirect
11. #11727686C2semidirect
12. #11727679C2semidirect
13. #11727678C2semidirect
14. #11727582C2semidirect
15. #11727566C2semidirect
27. #90246C4semidirect
99. #6493C2×C4semidirect
114. C2×C4⋊Dic7C2×C4semidirect
128. C4×D28C2×C4semidirect
130. #6432C2×C4semidirect
145. C2×#435D7semidirect
230. C2×C7×C8#41semidirect
259. C4⋊Dic7#41semidirect
588. C2×C8#1159semidirect
715. C7#22495semidirect

Maximal subgroups

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

subgroupindex
C2×#902462
C2×C7×#4352
#117397802
#117297442
#117297392
#117297272
C2×#893462
#117282342
#117282132
#117276872
#117276862
#117276792
#117276782
#117275822
#117275662
#224957