Finite Group Databasebeta

← C2×#11736670 #14232360

Subgroups — C2×#11736670 #14232360

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×#90221C211yesmaximal, characteristic, complemented
2C2×#90198C211yesmaximal, characteristic, complemented
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89899C211yesmaximal, characteristic, complemented
6C2×#89775C211yesmaximal, characteristic, complemented
7C2×#89740C211yesmaximal, characteristic, complemented
8#11736670C2116yesmaximal, direct product factor
9C2×#89663C211yesmaximal, characteristic, complemented
10C2×#89654C211yesmaximal, characteristic, complemented
11C2×#89655C211yesmaximal, characteristic, complemented
12C2×#89648C211yesmaximal, characteristic, complemented
13C2×#89642C211yesmaximal, characteristic, complemented
14C2×#89635C211yesmaximal, characteristic, complemented
15C2×D7×#106C211yesmaximal, characteristic, complemented
16C2×#89641C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×M16C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6493C2211yescharacteristic
23C2×#6492—21no—
24C2×C4×C22⋊D7C2211yescharacteristic
25C22×D56C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90221—24no—
28#90221C2218yescomplemented
29C2×#6459—21no—
30#90198—24no—
31#90198C2218yescomplemented
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456C2211yescharacteristic
36C2×#6456C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6447—21no—
42C2×#6446—21no—
43C2×#6439—21no—
44C2×C4×D28—21no—
45C7×#428C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89907C2218yescomplemented
52#89899C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59#89775C2218yescomplemented
60#89740C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89663C2218yescomplemented
70#89655C2218yescomplemented
71#89654C2218yescomplemented
72#89648C2218yescomplemented
73#89642C2218yescomplemented
74#89641C2218yescomplemented
75#89635C2218yescomplemented
76D7×#106C2218yescomplemented
77C2×#3345—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C2×#1157—28no—
84C2×#1157—48no—
85C22×D28—21no—
86C22×D28—21no—
87C22×D28C2311yescharacteristic
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×C4×D7C2311yescharacteristic
94C22×Dic14—21no—
95C2×C7×M16—24no—
96C2×C7×M16C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C7×#117—22no—
100C7×#117C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C22⋊C4—21no—
109C2×C42×C7—21no—
110C2×C22⋊Dic7D411yescharacteristic
111#6493—22no—
112#6493—22no—
113#6493C2314yes—
114#6493C2314yes—
115#6492—28no—
116C4×C22⋊D7D414yes—
117C4×C22⋊D7C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4D411yescharacteristic
133C2×C4×Dic7C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C2×D56—24no—
137C2×D56C2314yes—
138C2×C8×D7—24no—
139C2×C8×D7C2314yes—
140#6459—28no—
141#6458—22no—
142#6458—22no—
143#6458C2314yes—
144#6458C2314yes—
145#6457—28no—
146#6456—22no—
147#6456—22no—
148#6456C2314yes—
149#6456C2314yes—
150D7×C4⋊C4—22no—
151D7×C4⋊C4—22no—
152D7×C4⋊C4C2314yes—
153D7×C4⋊C4C2314yes—
154#6453—22no—
155#6453C2314yes—
156#6451—22no—
157#6451C2314yes—
158#6447—28no—
159#6446—28no—
160#6439—28no—
161C4×D28—28no—
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#106C2314yes—
165C7×#106C2314yes—
166C22⋊(C7⋊C8)C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6391C2314yes—
171#6389C2314yes—
172Dic7⋊C8C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6383C2314yes—
176#6383C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6381C2314yes—
181C2×#553—71no—
182C2×#547—71no—
183#3345—716no—
184C2×#501—71no—
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×#428D711yescharacteristic, complemented
196C22×#106—71no—
197C24×C7C2×D411yescharacteristic
198C23×D7—21no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—24no—
208C22×C4×C7—44no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2411yescharacteristic
213C2×C22⋊D7—24no—
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—44no—
217C2×C22⋊D7—82no—
218C2×C22⋊D7C2×D414yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7C2×D411yescharacteristic
222C22×Dic7C2×D411yescharacteristic
223C22×Dic7C2×D411yescharacteristic
224#1157—432no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—24no—
230C2×D28—24no—
231C2×D28—21no—
232C2×D28—21no—
233C2×D28—44no—
234C2×D28—44no—
235C2×D28C2412yes—
236C2×D28C2412yes—
237C2×C4×D7—22no—
238C2×C4×D7—22no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—24no—
243C2×C4×D7—44no—
244C2×C4×D7—44no—
245C2×C4×D7—82no—
246C2×C4×D7—82no—
247C2×C4×D7C2×D412yes—
248C2×C4×D7C2412yes—
249C2×Dic14—24no—
250C2×Dic14—44no—
251C7×M16—28no—
252C2×C7×C8—22no—
253C2×C7×C8#4114yescomplemented
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C22⋊C4—24no—
266C42×C7—24no—
267C22⋊Dic7C2×D414yes—
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)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4C2×D414yes—
285C4×Dic7C2×D412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291D56—28no—
292C8×D7—28no—
293C22×#41—141no—
294C22×D8—71no—
295C22×M16C2×D711yescharacteristic
296C23×C8—71no—
297#553—78no—
298#553—144no—
299#547—78no—
300#547—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#125—71no—
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×#117C2×D711yescharacteristic
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4C2×D711yescharacteristic
321#501—78no—
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#428C2×D718yescomplemented
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×#97—71no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7C22×D412yes—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7AGL(1,ℤ/8)14yes—
369C22×D7C22×D412yes—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—48no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C72−1+412yes—
387C2×C4×C7C2511yescharacteristic
388C22⋊D7—28no—
389C22⋊D7—48no—
390C22⋊D7—84no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—42no—
397C2×Dic7—42no—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401D28—22no—
402D28—22no—
403D28—22no—
404D28—22no—
405D28—48no—
406D28—48no—
407D28—42no—
408D28—42no—
409C4×D7—24no—
410C4×D7—22no—
411C4×D7—22no—
412C4×D7—48no—
413C4×D7—48no—
414C4×D7—84no—
415C4×D7—84no—
416Dic14—48no—
417C7×C8—22no—
418C7×C8C2×#4114yescomplemented
419C7⋊C8—22no—
420C7⋊C8—22no—
421C2×#41—148no—
422C2×#41—288no—
423C22×Q8—141no—
424C22×D4—71no—
425C22×D4—71no—
426C22×D4—71no—
427C22×D4—141no—
428C22×D4—141no—
429C22×D4—141no—
430C22×D4—141no—
431C23×C4—21no—
432C23×C4—71no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4C22×D711yescharacteristic
438C2×D8—74no—
439C2×D8—144no—
440C2×M16—24no—
441C2×M16C22×D714yes—
442C22×C8—71no—
443C22×C8—71no—
444C22×C8—74no—
445C22×C8—144no—
446C22×C8C22×D711yescharacteristic
447C22×C8C22×D711yescharacteristic
448C4⋊Q8—74no—
449C4⋊Q8—142no—
450#126—148no—
451#125—74no—
452#125—142no—
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—148no—
462#121—142no—
463#121—142no—
464#121—142no—
465#121—142no—
466C4×D4—74no—
467C4×D4—74no—
468C4×D4—74no—
469C4×D4—74no—
470C4×D4—148no—
471C4×D4—142no—
472C4×D4—142no—
473#117—22no—
474#117C22×D714yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—71no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—142no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D711yescharacteristic
492C2×C4⋊C4C22×D714yes—
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—71no—
496C2×C22⋊C4—71no—
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—21no—
504C2×C42—71no—
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#97—74no—
524C22×C7—22no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—44no—
528C22×C7#54712yes—
529C22×C7C2×AGL(1,ℤ/8)12yes—
530C22×C7#57712yes—
531C22×C7C23×D411yescharacteristic
532C2×D7—28no—
533C2×D7—22no—
534C2×D7—22no—
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—42no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7#54712yes—
550C4×C7C22×#4111yescharacteristic
551C4×C7C2×2−1+411yescharacteristic
552Dic7—22no—
553Dic7—22no—
554Dic7—22no—
555Dic7—42no—
556Dic7—42no—
557C24—71no—
558C24—141no—
559C24—141no—
560C24D4×D711yescharacteristic
561#41—2832no—
562C2×Q8—144no—
563C2×Q8—284no—
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—142no—
573C2×D4—142no—
574C2×D4—141no—
575C2×D4—141no—
576C2×D4—142no—
577C2×D4—142no—
578C2×D4—284no—
579C2×D4—284no—
580C2×D4—284no—
581C2×D4—562no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—44no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—71no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—284no—
604C22×C4—284no—
605C22×C4—562no—
606C22×C4—562no—
607C22×C4D4×D712yes—
608C22×C4D4×D711yescharacteristic
609C22×C4C23×D712yes—
610C22×C4C23×D711yescharacteristic
611D8—148no—
612M16—28no—
613C2×C8—22no—
614C2×C8—72no—
615C2×C8—72no—
616C2×C8—142no—
617C2×C8—142no—
618C2×C8—148no—
619C2×C8#115714yescomplemented
620C2×C8C23×D712yes—
621C2×C8C23×D712yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—74no—
628C4⋊C4—72no—
629C4⋊C4—72no—
630C4⋊C4—144no—
631C4⋊C4—144no—
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—24no—
642C22⋊C4—74no—
643C22⋊C4—74no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C42—24no—
651C42—72no—
652C42—72no—
653C2×C7—42no—
654C2×C7#334514yescomplemented
655C2×C7C2×#54711yescharacteristic
656C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
657C2×C7C2×#57711yescharacteristic
658D7—24no—
659D7—82no—
660D7—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—74no—
665C23—72no—
666C23—142no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23—282no—
675C23—282no—
676C23C2×D4×D712yes—
677C23C2×D4×D711yescharacteristic
678Q8—288no—
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—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—48no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—72no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—144no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—288no—
715C2×C4—288no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—564no—
719C2×C4—564no—
720C2×C4C2×#115712yes—
721C2×C4C2×D4×D712yes—
722C2×C4C2×D4×D711yescharacteristic
723C2×C4#655112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—142no—
727C8—142no—
728C8C2×#115714yescomplemented
729C7C2×#334511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—74no—
735C22—142no—
736C22—142no—
737C22—148no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—282no—
742C22—282no—
743C22—282no—
744C22—564no—
745C22—564no—
746C22#9019812yes—
747C22D7×AGL(1,ℤ/8)12yes—
748C22#9046912yes—
749C22C22×D4×D711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—142no—
756C4—142no—
757C4—142no—
758C4—282no—
759C4—282no—
760C4#9019812yes—
761C4C22×#115711yescharacteristic
762C4C2×#655111yescharacteristic
763C2—42no—
764C2—144no—
765C2—562no—
766C2—562no—
767C2#1173667014yesdirect product factor
768C2C2×#9019811yescharacteristic
769C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#428C2
socleC23×C7C22×D4
hypercenterC2×#428D7
hypocenterC7C2×#3345
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#90221C2semidirect
2. C2×#90198C2semidirect
3. C2×C7×#428C2semidirect
4. C2×#89907C2semidirect
5. C2×#89899C2semidirect
6. C2×#89775C2semidirect
7. C2×#89740C2semidirect
8. #11736670C2direct (N × H)
9. C2×#89663C2semidirect
10. C2×#89654C2semidirect
11. C2×#89655C2semidirect
12. C2×#89648C2semidirect
13. C2×#89642C2semidirect
14. C2×#89635C2semidirect
15. C2×D7×#106C2semidirect
16. C2×#89641C2semidirect
28. #90221C22semidirect
31. #90198C22semidirect
45. C7×#428C22semidirect
51. #89907C22semidirect
52. #89899C22semidirect
59. #89775C22semidirect
60. #89740C22semidirect
69. #89663C22semidirect
70. #89655C22semidirect
71. #89654C22semidirect
72. #89648C22semidirect
73. #89642C22semidirect
74. #89641C22semidirect
75. #89635C22semidirect
76. D7×#106C22semidirect
195. C2×#428D7semidirect
253. C2×C7×C8#41semidirect
332. #428C2×D7semidirect
418. C7×C8C2×#41semidirect
619. C2×C8#1157semidirect
654. C2×C7#3345semidirect
728. C8C2×#1157semidirect
729. C7C2×#3345semidirect
767. C2#11736670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902212
C2×#901982
C2×C7×#4282
C2×#899072
C2×#898992
C2×#897752
C2×#897402
#117366702
C2×#896632
C2×#896542
C2×#896552
C2×#896482
C2×#896422
C2×#896352
C2×D7×#1062
C2×#896412
C2×#33457