Finite Group Databasebeta

← C2×#11739437 #14232358

Subgroups — C2×#11739437 #14232358

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90417C211yesmaximal, characteristic, complemented
2C2×#90386C211yesmaximal, characteristic, complemented
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89838C211yesmaximal, characteristic, complemented
6#11739437C2116yesmaximal, direct product factor
7C2×#89654C211yesmaximal, characteristic, complemented
8C2×#89655C211yesmaximal, characteristic, complemented
9C2×#89653C211yesmaximal, characteristic, complemented
10C2×#89657C211yesmaximal, characteristic, complemented
11C2×#89635C211yesmaximal, characteristic, complemented
12C2×#89635C211yesmaximal, characteristic, complemented
13C2×#89637C211yesmaximal, characteristic, complemented
14C2×D7×#106C211yesmaximal, characteristic, complemented
15C2×#89483C211yesmaximal, characteristic, complemented
16C2×#89478C211yesmaximal, characteristic, complemented
17C22×#1161—21no—
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#125C2211yescharacteristic
20C2×#6509—21no—
21C22×D56C2211yescharacteristic
22C22×#1131C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90417—24no—
25#90417C2218yescomplemented
26#90386—24no—
27#90386C2218yescomplemented
28C2×#6461—21no—
29C2×#6458—21no—
30C2×#6458C2211yescharacteristic
31C2×#6458C2211yescharacteristic
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6457—21no—
36C2×#6457—21no—
37C2×#6456—21no—
38C2×#6455C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×D7×C4⋊C4C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C7×#501C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6395C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56#89856C2218yescomplemented
57#89838C2218yescomplemented
58C2×#6383C2211yescharacteristic
59C2×#6383C2211yescharacteristic
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89657C2218yescomplemented
68#89655C2218yescomplemented
69#89654C2218yescomplemented
70#89653C2218yescomplemented
71#89637C2218yescomplemented
72#89635C2218yescomplemented
73#89635C2218yescomplemented
74D7×#106C2218yescomplemented
75#89483C2218yescomplemented
76#89478C2218yescomplemented
77C2×#3345—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C2×#1161—28no—
80C2×#1161—48no—
81C22×D28—21no—
82C22×D28—21no—
83C22×D28—21no—
84C22×D28—21no—
85C22×D28D411yescharacteristic
86C22×D28C2311yescharacteristic
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×C4×D7C2311yescharacteristic
94C22×C4×D7C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8C2314yes—
99C7×#125—22no—
100C7×#125C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C42×C7C2311yescharacteristic
109#6509—28no—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×(C2×D7)⋊C4D411yescharacteristic
119C2×C4⋊Dic7D411yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×C4⋊Dic7C2311yescharacteristic
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×C4×Dic7—21no—
126C22×C7⋊C8C2311yescharacteristic
127C22×C7⋊C8C2311yescharacteristic
128C2×D56—24no—
129C2×D56C2314yes—
130C2×#1131—24no—
131C2×#1131C2314yes—
132C2×C8×D7—24no—
133C2×C8×D7C2314yes—
134#6461—28no—
135#6458—28no—
136#6458—22no—
137#6458—22no—
138#6458—22no—
139#6458—22no—
140#6458C2314yes—
141#6458C2314yes—
142#6458C2314yes—
143#6458C2314yes—
144#6457—28no—
145#6457—28no—
146#6457—28no—
147#6456—28no—
148#6455—22no—
149#6455C2314yes—
150D7×C4⋊C4—22no—
151D7×C4⋊C4—22no—
152D7×C4⋊C4—22no—
153D7×C4⋊C4C2314yes—
154D7×C4⋊C4C2314yes—
155D7×C4⋊C4C2314yes—
156C4×D28—22no—
157C4×D28—22no—
158C4×D28D414yes—
159C4×D28C2314yes—
160C4×D28C2314yes—
161C4×D28C2314yes—
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#106C2314yes—
165C7×#106C2314yes—
166C7×#97C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170(C2×D7)⋊C8C2314yes—
171#6391C2314yes—
172#6383C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6383C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6381C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C2×#553—71no—
182C2×#547—71no—
183#3345—716no—
184C2×#501D711yescharacteristic, complemented
185C2×#481—71no—
186C2×#481—71no—
187C2×#482—71no—
188C2×#480—71no—
189C2×#478—71no—
190C2×#476—71no—
191C2×#469—71no—
192C2×#466—71no—
193C2×#442—71no—
194C2×#435—71no—
195C2×#428—71no—
196C22×#106—71no—
197C23×D7—21no—
198C23×D7—21no—
199C23×D7C2×D411yescharacteristic
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—24no—
202C2×C7×Q8—44no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2411yescharacteristic
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7C2×D411yescharacteristic
213C22×Dic7C2×D411yescharacteristic
214#1161—432no—
215C2×D28—24no—
216C2×D28—22no—
217C2×D28—22no—
218C2×D28—22no—
219C2×D28—22no—
220C2×D28—24no—
221C2×D28—24no—
222C2×D28—24no—
223C2×D28—21no—
224C2×D28—21no—
225C2×D28—24no—
226C2×D28—44no—
227C2×D28—44no—
228C2×D28—44no—
229C2×D28—82no—
230C2×D28C2×D414yes—
231C2×D28C2412yes—
232C2×D28C2412yes—
233C2×C4×D7—22no—
234C2×C4×D7—22no—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—44no—
243C2×C4×D7—44no—
244C2×C4×D7—44no—
245C2×C4×D7—82no—
246C2×C4×D7—82no—
247C2×C4×D7C2×D412yes—
248C2×C4×D7C2×D412yes—
249C2×C4×D7C2412yes—
250C2×C4×D7C2412yes—
251C2×C7×C8—22no—
252C2×C7×C8#4114yescomplemented
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4C2×D414yes—
276(C2×D7)⋊C4C2×D414yes—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7C2×D414yes—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285C4×Dic7—24no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290D56—28no—
291#1131—28no—
292C8×D7—28no—
293C22×#41—141no—
294C22×D8—71no—
295C22×M16—71no—
296C23×C8—71no—
297#553—78no—
298#553—144no—
299#547—78no—
300#547—144no—
301C2×C4⋊Q8C2×D711yescharacteristic
302C2×#126—141no—
303C2×#125C2×D711yescharacteristic
304C2×#123—141no—
305C2×#123—141no—
306C2×#123—141no—
307C2×C22⋊Q8—141no—
308C2×#121—71no—
309C2×#121—71no—
310C2×#121—71no—
311C2×#121—71no—
312C2×#121—141no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—71no—
316C2×C4×D4—141no—
317C2×#117—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321#501C2×D718yescomplemented
322#482—78no—
323#481—78no—
324#481—78no—
325#480—78no—
326#478—78no—
327#476—78no—
328#469—78no—
329#466—78no—
330#442—78no—
331#435—78no—
332#428—78no—
333C2×#107—71no—
334C2×#107C2×D711yescharacteristic
335C2×#107C2×D711yescharacteristic
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106—78no—
341C2×#106C2×D711yescharacteristic
342C2×#106C2×D711yescharacteristic
343C2×C4⋊C8—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8—71no—
351C2×C22⋊C8—71no—
352C2×#97C2×D711yescharacteristic
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7AGL(1,ℤ/8)14yes—
368C22×D7C22×D412yes—
369C22×D7C22×D412yes—
370C7×Q8—48no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4112yes—
385C2×C4×C72−1+412yes—
386C2×C4×C7C2511yescharacteristic
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395D28—28no—
396D28—22no—
397D28—22no—
398D28—22no—
399D28—22no—
400D28—48no—
401D28—48no—
402D28—48no—
403D28—42no—
404D28—42no—
405D28—84no—
406C4×D7—24no—
407C4×D7—24no—
408C4×D7—22no—
409C4×D7—22no—
410C4×D7—22no—
411C4×D7—22no—
412C4×D7—48no—
413C4×D7—48no—
414C4×D7—48no—
415C4×D7—84no—
416C4×D7—84no—
417C7×C8—22no—
418C7×C8C2×#4114yescomplemented
419C7⋊C8—22no—
420C7⋊C8—22no—
421C2×#41—148no—
422C2×#41—288no—
423C22×Q8—21no—
424C22×D4—71no—
425C22×D4—71no—
426C22×D4—71no—
427C22×D4—141no—
428C22×D4—141no—
429C22×D4—141no—
430C22×D4—141no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C2×D8—74no—
439C2×D8—144no—
440C2×M16—74no—
441C2×M16—144no—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8—74no—
445C22×C8—144no—
446C22×C8C22×D711yescharacteristic
447C22×C8C22×D711yescharacteristic
448C4⋊Q8—22no—
449C4⋊Q8C22×D714yes—
450#126—148no—
451#125—22no—
452#125C22×D714yes—
453#123—148no—
454#123—148no—
455#123—148no—
456C22⋊Q8—148no—
457#121—74no—
458#121—74no—
459#121—74no—
460#121—74no—
461#121—142no—
462#121—142no—
463#121—142no—
464#121—142no—
465#121—148no—
466C4×D4—74no—
467C4×D4—74no—
468C4×D4—74no—
469C4×D4—74no—
470C4×D4—148no—
471C4×D4—142no—
472C4×D4—142no—
473#117—74no—
474#117—142no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D711yescharacteristic
492C2×C4⋊C4C22×D711yescharacteristic
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C22⋊C4—71no—
495C2×C22⋊C4—71no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C42—141no—
504C2×C42C22×D711yescharacteristic
505#107—74no—
506#107C22×D714yes—
507#107C22×D714yes—
508#106—74no—
509#106—74no—
510#106—74no—
511#106—74no—
512#106C22×D714yes—
513#106C22×D714yes—
514C4⋊C8—74no—
515#102—74no—
516#102—74no—
517#102—74no—
518#102—74no—
519#102—74no—
520#102—74no—
521C22⋊C8—74no—
522C22⋊C8—74no—
523#97C22×D714yes—
524C22×C7#54712yes—
525C22×C7C2×AGL(1,ℤ/8)12yes—
526C22×C7#57712yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—28no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—22no—
533C2×D7—22no—
534C2×D7—44no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—84no—
542C2×D7—84no—
543C2×D7C2×AGL(1,ℤ/8)14yes—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7#54712yes—
551C4×C7C22×#4111yescharacteristic
552C4×C7C2×2−1+411yescharacteristic
553Dic7—22no—
554Dic7—22no—
555Dic7—42no—
556Dic7—42no—
557C24—71no—
558C24—71no—
559C24—141no—
560C24—141no—
561#41—2832no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—72no—
567C2×D4—144no—
568C2×D4—144no—
569C2×D4—144no—
570C2×D4—144no—
571C2×D4—144no—
572C2×D4—141no—
573C2×D4—141no—
574C2×D4—142no—
575C2×D4—142no—
576C2×D4—142no—
577C2×D4—142no—
578C2×D4—284no—
579C2×D4—284no—
580C2×D4—284no—
581C2×D4—562no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—71no—
587C22×C4—71no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—144no—
593C22×C4—144no—
594C22×C4—144no—
595C22×C4—142no—
596C22×C4—142no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—144no—
602C22×C4—144no—
603C22×C4—284no—
604C22×C4—284no—
605C22×C4—284no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4D4×D711yescharacteristic
609C22×C4D4×D711yescharacteristic
610C22×C4C23×D711yescharacteristic
611D8—148no—
612M16—148no—
613C2×C8—22no—
614C2×C8—72no—
615C2×C8—72no—
616C2×C8—142no—
617C2×C8—142no—
618C2×C8—148no—
619C2×C8#116114yescomplemented
620C2×C8C23×D712yes—
621C2×C8C23×D712yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—74no—
630C4⋊C4—72no—
631C4⋊C4—72no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—141no—
636C4⋊C4—141no—
637C4⋊C4C23×D712yes—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C4⋊C4C23×D712yes—
641C22⋊C4—74no—
642C22⋊C4—74no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C42—144no—
651C42D4×D712yes—
652C42C23×D712yes—
653C2×C7#334514yescomplemented
654C2×C7C2×#54711yescharacteristic
655C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
656C2×C7C2×#57711yescharacteristic
657D7—24no—
658D7—42no—
659D7—82no—
660D7—82no—
661C23—74no—
662C23—72no—
663C23—72no—
664C23—142no—
665C23—142no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23—282no—
675C23—282no—
676C23—282no—
677C23C2×D4×D711yescharacteristic
678Q8—48no—
679D4—148no—
680D4—142no—
681D4—142no—
682D4—142no—
683D4—142no—
684D4—288no—
685D4—288no—
686D4—288no—
687D4—282no—
688D4—282no—
689D4—564no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—72no—
701C2×C4—72no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—144no—
705C2×C4—144no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—288no—
713C2×C4—288no—
714C2×C4—288no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4C2×#116112yes—
723C2×C4#655112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—142no—
727C8—142no—
728C8C2×#116114yescomplemented
729C7C2×#334511yescharacteristic, complemented, Sylow
730C22—74no—
731C22—142no—
732C22—148no—
733C22—142no—
734C22—142no—
735C22—142no—
736C22—142no—
737C22—284no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—282no—
742C22—282no—
743C22—282no—
744C22—564no—
745C22—564no—
746C22#9041712yes—
747C22D7×AGL(1,ℤ/8)12yes—
748C22#9046912yes—
749C22C22×D4×D711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—142no—
757C4—142no—
758C4—282no—
759C4—282no—
760C4#9041712yes—
761C4C22×#116111yescharacteristic
762C4C2×#655111yescharacteristic
763C2—144no—
764C2—282no—
765C2—562no—
766C2—562no—
767C2#1173943714yesdirect product factor
768C2C2×#9041711yescharacteristic
769C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#501C2
socleC23×C7C22×D4
hypercenterC2×#501D7
hypocenterC7C2×#3345
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#90417C2semidirect
2. C2×#90386C2semidirect
3. C2×C7×#501C2semidirect
4. C2×#89856C2semidirect
5. C2×#89838C2semidirect
6. #11739437C2direct (N × H)
7. C2×#89654C2semidirect
8. C2×#89655C2semidirect
9. C2×#89653C2semidirect
10. C2×#89657C2semidirect
11. C2×#89635C2semidirect
12. C2×#89635C2semidirect
13. C2×#89637C2semidirect
14. C2×D7×#106C2semidirect
15. C2×#89483C2semidirect
16. C2×#89478C2semidirect
25. #90417C22semidirect
27. #90386C22semidirect
45. C7×#501C22semidirect
56. #89856C22semidirect
57. #89838C22semidirect
67. #89657C22semidirect
68. #89655C22semidirect
69. #89654C22semidirect
70. #89653C22semidirect
71. #89637C22semidirect
72. #89635C22semidirect
73. #89635C22semidirect
74. D7×#106C22semidirect
75. #89483C22semidirect
76. #89478C22semidirect
184. C2×#501D7semidirect
252. C2×C7×C8#41semidirect
321. #501C2×D7semidirect
418. C7×C8C2×#41semidirect
619. C2×C8#1161semidirect
653. C2×C7#3345semidirect
728. C8C2×#1161semidirect
729. C7C2×#3345semidirect
767. C2#11739437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904172
C2×#903862
C2×C7×#5012
C2×#898562
C2×#898382
#117394372
C2×#896542
C2×#896552
C2×#896532
C2×#896572
C2×#896352
C2×#896372
C2×D7×#1062
C2×#894832
C2×#894782
C2×#33457