Finite Group Databasebeta

← C2×#11738635 #14230447

Subgroups — C2×#11738635 #14230447

Order 1792.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90385C211yesmaximal, characteristic, complemented
2C2×#90246C211yesmaximal, characteristic
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89841C211yesmaximal, characteristic, complemented
5C2×#89790C211yesmaximal, characteristic, complemented
6#11738635C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89659C211yesmaximal, characteristic, complemented
9C2×#89640C211yesmaximal, characteristic, complemented
10C2×#89639C211yesmaximal, characteristic, complemented
11C2×#89621C211yesmaximal, characteristic, complemented
12C2×#89608C211yesmaximal, characteristic, complemented
13C2×#89555C211yesmaximal, characteristic, complemented
14C2×#89555C211yesmaximal, characteristic, complemented
15C2×#89543C211yesmaximal, characteristic, complemented
16C2×#89544C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C2×C7×#125C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C22×#1142C2211yescharacteristic
22C2×#6493—21no—
23C22×C4⋊Dic7—21no—
24C22×Dic28C2211yescharacteristic
25C22×Dic28C2211yescharacteristic
26C22×#1131C2211yescharacteristic
27C22×C8×D7C2211yescharacteristic
28#90385—24no—
29#90385C2218yescomplemented
30#90246—24no—
31#90246C2218yes—
32C2×#6461—21no—
33C2×#6460C2211yescharacteristic
34C2×#6460C2211yescharacteristic
35C2×#6460C2211yescharacteristic
36C2×#6460C2211yescharacteristic
37C2×#6457—21no—
38C2×#6455—21no—
39C2×#6455C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6453—21no—
42C2×#6449—21no—
43C2×#6449—21no—
44C2×C4×D28C2211yescharacteristic
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#478C2218yescomplemented
48C2×C7×#107C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C7×C4⋊C8C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#102C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58#89841C2218yescomplemented
59#89790C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67#89659C2218yescomplemented
68#89656C2218yescomplemented
69#89640C2218yescomplemented
70#89639C2218yescomplemented
71#89621C2218yescomplemented
72#89608C2218yescomplemented
73#89555C2218yescomplemented
74#89555C2218yescomplemented
75#89544C2218yescomplemented
76#89543C2218yescomplemented
77C2×#3315—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C23×C4×C7—21no—
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C23×Dic7—21no—
84C2×#1159—24no—
85C2×#1159—24no—
86C2×#1159—22no—
87C2×#1159—22no—
88C2×#1159—42no—
89C2×#1159—42no—
90C2×#1159C2314yes—
91C2×#1159C2314yes—
92C22×D28D411yescharacteristic
93C22×C4×D7—21no—
94C22×C4×D7C2311yescharacteristic
95C22×C4×D7C2311yescharacteristic
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C7×#125—22no—
102C7×#125C2314yes—
103C4×C7×D4—22no—
104C4×C7×D4C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C42×C7C2311yescharacteristic
112C2×#1142—24no—
113C2×#1142C2314yes—
114#6493—28no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×(C2×D7)⋊C4D411yescharacteristic
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—28no—
129C2×C4⋊Dic7D411yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C2×Dic28—42no—
138C2×Dic28—42no—
139C2×Dic28C2314yes—
140C2×Dic28C2314yes—
141C2×#1131—42no—
142C2×#1131C2314yes—
143C2×C8×D7—42no—
144C2×C8×D7C2314yes—
145#6461—28no—
146#6460—22no—
147#6460—22no—
148#6460—22no—
149#6460—22no—
150#6460C2314yes—
151#6460C2314yes—
152#6460C2314yes—
153#6460C2314yes—
154#6457—28no—
155#6455—22no—
156#6455—28no—
157#6455C2314yes—
158D7×C4⋊C4—22no—
159D7×C4⋊C4C2314yes—
160#6453—28no—
161#6449—28no—
162#6449—28no—
163C4×D28D414yes—
164C4×D28C2314yes—
165#6432—22no—
166#6432C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169C7×#107C2314yes—
170C7×#106C2314yes—
171C7×C4⋊C8C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174#6406C2314yes—
175(C2×D7)⋊C8C2314yes—
176(C2×D7)⋊C8C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6384C2314yes—
180#6384C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6381C2314yes—
185#6377C2314yes—
186C2×#552—71no—
187C2×#547—71no—
188#3315—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#478D711yescharacteristic, complemented
193C2×#470—71no—
194C2×#467—71no—
195C2×#462—71no—
196C2×#452—71no—
197C2×#452—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7—21no—
203C23×D7C2×D411yescharacteristic
204C23×D7C2×D411yescharacteristic
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4#4114yes—
208C2×C7×D4C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—44no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—44no—
220C2×C22⋊D7—44no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—24no—
227C22×Dic7—44no—
228C22×Dic7—44no—
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231#1159—28no—
232#1159—28no—
233#1159—44no—
234#1159—44no—
235#1159—48no—
236#1159—48no—
237C2×D28—42no—
238C2×D28C2×D414yes—
239C2×C4×D7—22no—
240C2×C4×D7—22no—
241C2×C4×D7—22no—
242C2×C4×D7—22no—
243C2×C4×D7—24no—
244C2×C4×D7—44no—
245C2×C4×D7C2×D412yes—
246C2×C4×D7C2×D412yes—
247C2×C4×D7C2412yes—
248C2×C4×D7C2412yes—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—22no—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—22no—
255C2×Dic14—21no—
256C2×Dic14—21no—
257C2×Dic14—21no—
258C2×Dic14C2412yes—
259C2×Dic14C2412yes—
260C2×Dic14C2412yes—
261C2×C7×C8—22no—
262C2×C7×C8—22no—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4C2412yes—
271C7×C4⋊C4C2412yes—
272C7×C4⋊C4C2412yes—
273C7×C22⋊C4—24no—
274C42×C7C2×D412yes—
275C42×C7C2412yes—
276#1142—28no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4C2×D414yes—
283(C2×D7)⋊C4C2×D414yes—
284C4⋊Dic7—21no—
285C4⋊Dic7—24no—
286C4⋊Dic7—24no—
287C4⋊Dic7—24no—
288C4⋊Dic7—24no—
289C4⋊Dic7—24no—
290C4⋊Dic7—24no—
291C4⋊Dic7C2×D414yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8C2412yes—
300C2×C7⋊C8C2412yes—
301Dic28—44no—
302Dic28—44no—
303#1131—44no—
304C8×D7—44no—
305C22×#41—71no—
306C22×#41—71no—
307C22×Q16—71no—
308C22×Q16—71no—
309C22×SD16—71no—
310C22×M16—71no—
311C23×C8—71no—
312#552—78no—
313#552—144no—
314#547—78no—
315#547—144no—
316C2×C4⋊Q8—71no—
317C2×#126—141no—
318C2×#125—141no—
319C2×#125C2×D711yescharacteristic
320C2×#123—141no—
321C2×#123—141no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—141no—
328C2×C4×Q8—71no—
329C2×C4×D4—71no—
330C2×C4×D4C2×D711yescharacteristic
331C2×#117—71no—
332C2×#117—141no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—141no—
335#491—78no—
336#485—78no—
337#484—78no—
338#478C2×D718yescomplemented
339#470—78no—
340#467—78no—
341#462—78no—
342#452—78no—
343#452—78no—
344#440—78no—
345#435—78no—
346C2×#107—71no—
347C2×#107C2×D711yescharacteristic
348C2×#106C2×D711yescharacteristic
349C2×C4⋊C8C2×D711yescharacteristic
350#417—78no—
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#102—71no—
360C2×#102C2×D711yescharacteristic
361C2×#102C2×D711yescharacteristic
362C2×C22⋊C8—71no—
363C2×C22⋊C8—71no—
364C2×#97—71no—
365C23×C7—24no—
366C23×C7—22no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7C22×D412yes—
377C22×D7C22×D412yes—
378C7×D4—24no—
379C7×D4—22no—
380C7×D4C2×#4114yes—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—48no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C2×#4112yes—
394C2×C4×C7H(5,𝔽2)12yes—
395C2×C4×C7C2511yescharacteristic
396C22⋊D7—48no—
397C22⋊D7—48no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—48no—
405C2×Dic7—48no—
406C2×Dic7—42no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—42no—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412D28—44no—
413C4×D7—24no—
414C4×D7—24no—
415C4×D7—22no—
416C4×D7—22no—
417C4×D7—22no—
418C4×D7—22no—
419C4×D7—48no—
420Dic14—22no—
421Dic14—22no—
422Dic14—22no—
423Dic14—22no—
424Dic14—22no—
425Dic14—22no—
426Dic14—42no—
427Dic14—42no—
428Dic14—42no—
429C7×C8—22no—
430C7×C8—22no—
431C7⋊C8—22no—
432C7⋊C8—22no—
433C2×#41—74no—
434C2×#41—74no—
435C2×#41—142no—
436C2×#41—142no—
437C2×#41—144no—
438C2×#41—144no—
439C2×#41—282no—
440C2×#41—282no—
441C22×Q8—71no—
442C22×Q8—71no—
443C22×Q8—71no—
444C22×D4—71no—
445C22×D4—141no—
446C22×D4—141no—
447C22×D4C22×D711yescharacteristic
448C23×C4—21no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—141no—
452C23×C4—141no—
453C23×C4—141no—
454C2×Q16—74no—
455C2×Q16—74no—
456C2×Q16—282no—
457C2×Q16—282no—
458C2×SD16—74no—
459C2×SD16—144no—
460C2×M16—74no—
461C2×M16—282no—
462C22×C8—71no—
463C22×C8—71no—
464C22×C8—74no—
465C22×C8—282no—
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D711yescharacteristic
468C4⋊Q8—74no—
469C4⋊Q8—142no—
470#126—148no—
471#125—22no—
472#125—148no—
473#125C22×D714yes—
474#123—148no—
475#123—148no—
476#123—148no—
477C22⋊Q8—74no—
478C22⋊Q8—74no—
479C22⋊Q8—74no—
480C22⋊Q8—74no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483C22⋊Q8—142no—
484C22⋊Q8—142no—
485#121—148no—
486C4×Q8—74no—
487C4×Q8—142no—
488C4×D4—22no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4C22×D714yes—
492#117—74no—
493#117—148no—
494#117—142no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—74no—
500C2×C4⋊C4—142no—
501C2×C4⋊C4—148no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4C22×D711yescharacteristic
511C2×C4⋊C4C22×D711yescharacteristic
512C2×C4⋊C4C22×D711yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—71no—
515C2×C22⋊C4—71no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C42—141no—
522C2×C42—141no—
523C2×C42C22×D711yescharacteristic
524#107—74no—
525#107C22×D714yes—
526#106C22×D714yes—
527C4⋊C8C22×D714yes—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#102—74no—
536#102C22×D714yes—
537#102C22×D714yes—
538C22⋊C8—74no—
539C22⋊C8—74no—
540#97—74no—
541C22×C7—24no—
542C22×C7—48no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7#54612yes—
546C22×C7#57512yes—
547C22×C7#57812yes—
548C22×C7C23×D411yescharacteristic
549C2×D7—22no—
550C2×D7—22no—
551C2×D7—22no—
552C2×D7—22no—
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—44no—
556C2×D7—44no—
557C4×C7—22no—
558C4×C7—22no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7#54612yes—
563C4×C7C22×#4111yescharacteristic
564C4×C7C2×H(5,𝔽2)11yescharacteristic
565Dic7—22no—
566Dic7—22no—
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—21no—
572C24—71no—
573C24—71no—
574#41—148no—
575#41—148no—
576#41—284no—
577#41—284no—
578#41—288no—
579#41—288no—
580C2×Q8—72no—
581C2×Q8—72no—
582C2×Q8—72no—
583C2×Q8—141no—
584C2×Q8—141no—
585C2×Q8—141no—
586C2×Q8—142no—
587C2×Q8—142no—
588C2×Q8—142no—
589C2×Q8—142no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—74no—
595C2×D4—144no—
596C2×D4—144no—
597C2×D4—282no—
598C2×D4—284no—
599C2×D4—284no—
600C2×D4#116114yes—
601C2×D4C23×D712yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—24no—
606C22×C4—44no—
607C22×C4—71no—
608C22×C4—71no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—284no—
625C22×C4—284no—
626C22×C4—284no—
627C22×C4D4×D711yescharacteristic
628C22×C4D4×D711yescharacteristic
629C22×C4C23×D711yescharacteristic
630Q16—284no—
631Q16—284no—
632SD16—148no—
633M16—284no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—72no—
637C2×C8—72no—
638C2×C8—142no—
639C2×C8—142no—
640C2×C8—284no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—74no—
649C4⋊C4—72no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—144no—
656C4⋊C4—141no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4C23×D712yes—
660C4⋊C4C23×D712yes—
661C4⋊C4C23×D712yes—
662C22⋊C4—24no—
663C22⋊C4—74no—
664C22⋊C4—74no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C42—144no—
671C42—144no—
672C42D4×D712yes—
673C42C23×D712yes—
674C2×C7—44no—
675C2×C7#331514yescomplemented
676C2×C7C2×#54611yescharacteristic
677C2×C7C2×#57511yescharacteristic
678C2×C7C2×#57811yescharacteristic
679D7—42no—
680D7—42no—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—72no—
686C23—72no—
687C23—142no—
688C23—142no—
689C23—142no—
690C23—142no—
691C23—142no—
692C23—142no—
693C23C2×D4×D711yescharacteristic
694Q8—142no—
695Q8—142no—
696Q8—142no—
697Q8—142no—
698Q8—142no—
699Q8—142no—
700Q8—282no—
701Q8—282no—
702Q8—282no—
703D4—24no—
704D4—22no—
705D4—284no—
706D4—288no—
707D4—288no—
708D4C2×#116114yes—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—72no—
719C2×C4—72no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—144no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—288no—
733C2×C4—288no—
734C2×C4—288no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4C2×D4×D712yes—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4C2×#116112yes—
743C2×C4#655312yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#331511yescharacteristic, complemented, Sylow
750C22—24no—
751C22—42no—
752C22—48no—
753C22—42no—
754C22—142no—
755C22—142no—
756C22—142no—
757C22—142no—
758C22—142no—
759C22—142no—
760C22—284no—
761C22—284no—
762C22#9032112yes—
763C22#9046212yes—
764C22#9046412yes—
765C22C22×D4×D711yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—142no—
772C4—142no—
773C4—282no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9032112yes—
778C4C22×#116111yescharacteristic
779C4C2×#655311yescharacteristic
780C2—44no—
781C2—282no—
782C2—282no—
783C2#1173863514yesdirect product factor
784C2C2×#9032111yescharacteristic
785C2C2×#9046211yescharacteristic
786C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
prime radicalC2×#90246C2
hypercenterC2×#478D7
hypocenterC7C2×#3315
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#90385C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89841C2semidirect
5. C2×#89790C2semidirect
6. #11738635C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89659C2semidirect
9. C2×#89640C2semidirect
10. C2×#89639C2semidirect
11. C2×#89621C2semidirect
12. C2×#89608C2semidirect
13. C2×#89555C2semidirect
14. C2×#89555C2semidirect
15. C2×#89543C2semidirect
16. C2×#89544C2semidirect
29. #90385C22semidirect
47. C7×#478C22semidirect
58. #89841C22semidirect
59. #89790C22semidirect
67. #89659C22semidirect
68. #89656C22semidirect
69. #89640C22semidirect
70. #89639C22semidirect
71. #89621C22semidirect
72. #89608C22semidirect
73. #89555C22semidirect
74. #89555C22semidirect
75. #89544C22semidirect
76. #89543C22semidirect
192. C2×#478D7semidirect
338. #478C2×D7semidirect
675. C2×C7#3315semidirect
749. C7C2×#3315semidirect
783. C2#11738635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903852
C2×#902462
C2×C7×#4782
C2×#898412
C2×#897902
#117386352
C2×#896562
C2×#896592
C2×#896402
C2×#896392
C2×#896212
C2×#896082
C2×#895552
C2×#895432
C2×#895442
C2×#33157