Finite Group Databasebeta

← C2×#11738223 #14230456

Subgroups — C2×#11738223 #14230456

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×#90330C211yesmaximal, characteristic, complemented
2C2×#90322C211yesmaximal, characteristic
3C2×C7×#467C211yesmaximal, characteristic, complemented
4C2×#89959C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89885C211yesmaximal, characteristic, complemented
7C2×#89883C211yesmaximal, characteristic, complemented
8C2×#89819C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10#11738223C2116yesmaximal, direct product factor
11C2×#89663C211yesmaximal, characteristic, complemented
12C2×#89656C211yesmaximal, characteristic, complemented
13C2×#89588C211yesmaximal, characteristic, complemented
14C2×#89575C211yesmaximal, characteristic, complemented
15C2×#89569C211yesmaximal, characteristic, complemented
16C2×#89589C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×#6509C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×#6507C2211yescharacteristic
26C22×#1144C2211yescharacteristic
27C22×#1143C2211yescharacteristic
28C2×C4×C22⋊D7C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×#1131C2211yescharacteristic
31#90330—24no—
32#90330C2218yescomplemented
33#90322—24no—
34#90322C2218yes—
35C2×#6460C2211yescharacteristic
36C2×#6457—21no—
37C2×#6456C2211yescharacteristic
38C2×#6455—21no—
39C2×D7×C4⋊C4—21no—
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6453C2211yescharacteristic
42C2×#6452—21no—
43C2×#6447—21no—
44C2×#6446—21no—
45C2×#6446—21no—
46C2×#6442—21no—
47C7×#467C2218yescomplemented
48C2×C7×#107C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89959C2218yescomplemented
55#89954C2218yescomplemented
56#89885C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59#89883C2218yescomplemented
60C2×(C2×D7)⋊C8C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6389C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89819C2218yescomplemented
66#89817C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89663C2218yescomplemented
72#89656C2218yescomplemented
73#89589C2218yescomplemented
74#89588C2218yescomplemented
75#89575C2218yescomplemented
76#89569C2218yescomplemented
77C2×#3315—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C2×#1161—22no—
84C2×#1161—24no—
85C2×#1161—42no—
86C2×#1161C2314yes—
87C2×#1157—22no—
88C2×#1157—24no—
89C2×#1157—42no—
90C2×#1157C2314yes—
91C22×D28—21no—
92C22×D28C2311yescharacteristic
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×C4×D7C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C2×C7×Q16—42no—
100C2×C7×Q16C2314yes—
101C22×C7×C8—42no—
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2314yes—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—22no—
107C7×C22⋊Q8C2314yes—
108C7×C22⋊Q8C2314yes—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7D411yescharacteristic
117#6509—22no—
118#6509C2314yes—
119Q8×Dic7—22no—
120Q8×Dic7C2314yes—
121#6507—22no—
122#6507C2314yes—
123C2×#1144—42no—
124C2×#1144C2314yes—
125C2×#1143—24no—
126C2×#1143C2314yes—
127C4×C22⋊D7D414yes—
128C4×C22⋊D7C2314yes—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4D411yescharacteristic
133#6489—22no—
134#6489C2314yes—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4D411yescharacteristic
146C2×C4×Dic7—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1131—42no—
152C2×#1131C2314yes—
153#6460—22no—
154#6460C2314yes—
155#6457—28no—
156#6456—22no—
157#6456C2314yes—
158#6455—28no—
159D7×C4⋊C4—22no—
160D7×C4⋊C4—28no—
161D7×C4⋊C4C2314yes—
162#6453—22no—
163#6453C2314yes—
164#6452—28no—
165#6447—28no—
166#6446—28no—
167#6446—28no—
168#6442—28no—
169C7×#107C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174C22⋊(C7⋊C8)C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180#6389C2314yes—
181Dic7⋊C8C2314yes—
182#6384C2314yes—
183#6383C2314yes—
184#6382C2314yes—
185#6381C2314yes—
186C2×#552—71no—
187C2×#547—71no—
188#3315—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#478—71no—
193C2×#470—71no—
194C2×#467D711yescharacteristic, complemented
195C2×#462—71no—
196C2×#452—71no—
197C2×#452—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8C2412yes—
212C2×C7×Q8C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2411yescharacteristic
223C2×C22⋊D7—24no—
224C2×C22⋊D7—42no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7C2×D414yes—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233#1161—28no—
234#1161—44no—
235#1161—48no—
236#1157—28no—
237#1157—44no—
238#1157—48no—
239C2×D28—21no—
240C2×D28—22no—
241C2×D28—24no—
242C2×D28—44no—
243C2×D28#4114yes—
244C2×D28C2412yes—
245C2×C4×D7—22no—
246C2×C4×D7—22no—
247C2×C4×D7—24no—
248C2×C4×D7—24no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—44no—
252C2×C4×D7—44no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C2×C4×D7C2×D412yes—
256C2×C4×D7C2412yes—
257C2×Dic14—22no—
258C2×Dic14—22no—
259C2×Dic14—21no—
260C2×Dic14C2412yes—
261C7×Q16—44no—
262C2×C7×C8—22no—
263C2×C7×C8—22no—
264C2×C7×C8—44no—
265C2×C7×C8C2412yes—
266C2×C7×C8C2412yes—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4C2412yes—
272C7×C4⋊C4C2412yes—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C22⋊Dic7—24no—
276C22⋊Dic7C2×D414yes—
277#1144—44no—
278#1143—28no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4C2×D414yes—
283C4⋊Dic7—21no—
284C4⋊Dic7—21no—
285C4⋊Dic7—24no—
286C4⋊Dic7—24no—
287C4⋊Dic7—24no—
288C4⋊Dic7C2412yes—
289C4⋊Dic7C2412yes—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4C2×D414yes—
296C4×Dic7—24no—
297C4×Dic7—24no—
298C4×Dic7C2×D412yes—
299C4×Dic7C2412yes—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304#1131—44no—
305C22×#41—71no—
306C22×#41—71no—
307C22×Q16—71no—
308C22×Q16C2×D711yescharacteristic
309C22×SD16—71no—
310C22×M16—71no—
311C23×C8C2×D711yescharacteristic
312#552—78no—
313#552—144no—
314#547—78no—
315#547—144no—
316C2×C4⋊Q8—71no—
317C2×#126—141no—
318C2×#125—71no—
319C2×#125—141no—
320C2×#123—141no—
321C2×#123—141no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8C2×D711yescharacteristic
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—141no—
328C2×C4×Q8—71no—
329C2×C4×D4—71no—
330C2×C4×D4—71no—
331C2×#117—71no—
332C2×#117—141no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—141no—
335#491—78no—
336#485—78no—
337#484—78no—
338#478—78no—
339#470—78no—
340#467C2×D718yescomplemented
341#462—78no—
342#452—78no—
343#452—78no—
344#440—78no—
345#435—78no—
346C2×#107—71no—
347C2×#107C2×D711yescharacteristic
348C2×#106—71no—
349C2×C4⋊C8—71no—
350#417—78no—
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103C2×D711yescharacteristic
358C2×#103C2×D711yescharacteristic
359C2×#102—71no—
360C2×#102—71no—
361C2×#102—71no—
362C2×C22⋊C8—71no—
363C2×C22⋊C8—71no—
364C2×#97—71no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7C22×D412yes—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—24no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—42no—
376C22×D7—42no—
377C22×D7C22×D412yes—
378C7×Q8—22no—
379C7×Q8—22no—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—42no—
383C7×Q8—42no—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C2×#4112yes—
399C2×C4×C7H(5,𝔽2)12yes—
400C2×C4×C7C2511yescharacteristic
401C22⋊D7—44no—
402C22⋊D7—48no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415D28—24no—
416D28—22no—
417D28—48no—
418D28C2×#4114yes—
419C4×D7—24no—
420C4×D7—22no—
421C4×D7—22no—
422C4×D7—48no—
423C4×D7—48no—
424C4×D7—48no—
425C4×D7—48no—
426Dic14—22no—
427Dic14—22no—
428Dic14—42no—
429C7×C8—22no—
430C7×C8—22no—
431C7⋊C8—22no—
432C7⋊C8—22no—
433C2×#41—74no—
434C2×#41—74no—
435C2×#41—144no—
436C2×#41—142no—
437C2×#41—142no—
438C2×#41—144no—
439C2×#41—282no—
440C2×#41—282no—
441C22×Q8—71no—
442C22×Q8C22×D711yescharacteristic
443C22×Q8C22×D711yescharacteristic
444C22×D4—71no—
445C22×D4—71no—
446C22×D4—141no—
447C22×D4—141no—
448C23×C4—71no—
449C23×C4—141no—
450C23×C4—141no—
451C23×C4—141no—
452C23×C4—141no—
453C23×C4C22×D711yescharacteristic
454C2×Q16—42no—
455C2×Q16—74no—
456C2×Q16—282no—
457C2×Q16C22×D714yes—
458C2×SD16—74no—
459C2×SD16—144no—
460C2×M16—74no—
461C2×M16—282no—
462C22×C8—42no—
463C22×C8—71no—
464C22×C8—71no—
465C22×C8C22×D711yescharacteristic
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D714yes—
468C4⋊Q8—74no—
469C4⋊Q8—142no—
470#126—148no—
471#125—74no—
472#125—142no—
473#125—148no—
474#123—148no—
475#123—148no—
476#123—148no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—74no—
480C22⋊Q8—74no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483C22⋊Q8C22×D714yes—
484C22⋊Q8C22×D714yes—
485#121—148no—
486C4×Q8—74no—
487C4×Q8—142no—
488C4×D4—74no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4—142no—
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—71no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—148no—
502C2×C4⋊C4—142no—
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⋊C4—141no—
511C2×C4⋊C4C22×D711yescharacteristic
512C2×C4⋊C4C22×D711yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—71no—
516C2×C22⋊C4—71no—
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C42—71no—
522C2×C42—141no—
523C2×C42—141no—
524#107—74no—
525#107C22×D714yes—
526#106—74no—
527C4⋊C8—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103C22×D714yes—
534#103C22×D714yes—
535#102—74no—
536#102—74no—
537#102—74no—
538C22⋊C8—74no—
539C22⋊C8—74no—
540#97—74no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—44no—
545C22×C7#54612yes—
546C22×C7#57512yes—
547C22×C7#57812yes—
548C22×C7C23×D411yescharacteristic
549C2×D7—22no—
550C2×D7—24no—
551C2×D7—22no—
552C2×D7—22no—
553C2×D7—44no—
554C2×D7—48no—
555C2×D7—42no—
556C2×D7—42no—
557C4×C7—22no—
558C4×C7—42no—
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—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—71no—
572C24—141no—
573C24D4×D711yescharacteristic
574#41—148no—
575#41—148no—
576#41—284no—
577#41—288no—
578#41—284no—
579#41—288no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—72no—
587C2×Q8—141no—
588C2×Q8—142no—
589C2×Q8—142no—
590C2×Q8C23×D712yes—
591C2×Q8C23×D712yes—
592C2×D4—74no—
593C2×D4—74no—
594C2×D4—72no—
595C2×D4—144no—
596C2×D4—144no—
597C2×D4—141no—
598C2×D4—142no—
599C2×D4—284no—
600C2×D4—282no—
601C2×D4—284no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—144no—
622C22×C4—284no—
623C22×C4—284no—
624C22×C4—284no—
625C22×C4—284no—
626C22×C4D4×D712yes—
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—44no—
631Q16—284no—
632SD16—148no—
633M16—284no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8—72no—
638C2×C8—72no—
639C2×C8—142no—
640C2×C8—142no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—74no—
648C4⋊C4—72no—
649C4⋊C4—72no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—144no—
656C4⋊C4—144no—
657C4⋊C4—144no—
658C4⋊C4—141no—
659C4⋊C4—141no—
660C4⋊C4C23×D712yes—
661C4⋊C4C23×D712yes—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—74no—
665C22⋊C4—74no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C42—72no—
671C42—72no—
672C42—144no—
673C42—144no—
674C2×C7—42no—
675C2×C7#331514yescomplemented
676C2×C7C2×#54611yescharacteristic
677C2×C7C2×#57511yescharacteristic
678C2×C7C2×#57811yescharacteristic
679D7—42no—
680D7—44no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—72no—
685C23—142no—
686C23—142no—
687C23—142no—
688C23—144no—
689C23—142no—
690C23—282no—
691C23—282no—
692C23C2×D4×D712yes—
693C23C2×D4×D711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—42no—
699Q8—42no—
700Q8—142no—
701Q8—142no—
702Q8—282no—
703D4—74no—
704D4—144no—
705D4—142no—
706D4—288no—
707D4—284no—
708D4—288no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—72no—
722C2×C4—72no—
723C2×C4—72no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—288no—
734C2×C4—288no—
735C2×C4—288no—
736C2×C4—288no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4#654812yes—
743C2×C4D7×#4112yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#331511yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—142no—
755C22—144no—
756C22—142no—
757C22—142no—
758C22—284no—
759C22—288no—
760C22—282no—
761C22—282no—
762C22#9030112yes—
763C22#9045712yes—
764C22#9045912yes—
765C22C22×D4×D711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—142no—
772C4—142no—
773C4—142no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9030112yes—
778C4C2×#654811yescharacteristic
779C4C2×D7×#4111yescharacteristic
780C2—42no—
781C2—282no—
782C2—284no—
783C2#1173822314yesdirect product factor
784C2C2×#9030111yescharacteristic
785C2C2×#9045711yescharacteristic
786C2C2×#9045911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#467C2
socleC23×C7C22×D4
prime radicalC2×#90322C2
hypercenterC2×#467D7
hypocenterC7C2×#3315
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#90330C2semidirect
3. C2×C7×#467C2semidirect
4. C2×#89959C2semidirect
5. C2×#89954C2semidirect
6. C2×#89885C2semidirect
7. C2×#89883C2semidirect
8. C2×#89819C2semidirect
9. C2×#89817C2semidirect
10. #11738223C2direct (N × H)
11. C2×#89663C2semidirect
12. C2×#89656C2semidirect
13. C2×#89588C2semidirect
14. C2×#89575C2semidirect
15. C2×#89569C2semidirect
16. C2×#89589C2semidirect
32. #90330C22semidirect
47. C7×#467C22semidirect
54. #89959C22semidirect
55. #89954C22semidirect
56. #89885C22semidirect
59. #89883C22semidirect
65. #89819C22semidirect
66. #89817C22semidirect
71. #89663C22semidirect
72. #89656C22semidirect
73. #89589C22semidirect
74. #89588C22semidirect
75. #89575C22semidirect
76. #89569C22semidirect
194. C2×#467D7semidirect
340. #467C2×D7semidirect
675. C2×C7#3315semidirect
749. C7C2×#3315semidirect
783. C2#11738223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903302
C2×#903222
C2×C7×#4672
C2×#899592
C2×#899542
C2×#898852
C2×#898832
C2×#898192
C2×#898172
#117382232
C2×#896632
C2×#896562
C2×#895882
C2×#895752
C2×#895692
C2×#895892
C2×#33157