Finite Group Databasebeta

← C2×#11738446 #14222134

Subgroups — C2×#11738446 #14222134

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90424C211yesmaximal, characteristic, complemented
2C2×#90265C211yesmaximal, characteristic, complemented
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89800C211yesmaximal, characteristic, complemented
6#11738446C2116yesmaximal, direct product factor
7C2×#89635C211yesmaximal, characteristic, complemented
8C2×#89634C211yesmaximal, characteristic, complemented
9C2×#89641C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89616C211yesmaximal, characteristic, complemented
12C2×#89612C211yesmaximal, characteristic, complemented
13C2×#89582C211yesmaximal, characteristic, complemented
14C2×#89583C211yesmaximal, characteristic
15C2×#89561C211yesmaximal, characteristic, complemented
16C2×#89560C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×#6510—21no—
21C2×#6509—21no—
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25C22×D56C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27#90424—24no—
28#90424C2218yescomplemented
29#90265—24no—
30#90265C2218yescomplemented
31C2×#6461—21no—
32C2×#6460C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456—21no—
36C2×#6456C2211yescharacteristic
37C2×#6456C2211yescharacteristic
38C2×D7×C4⋊C4—21no—
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6438C2211yescharacteristic
42C2×C4×D28—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6435—21no—
45C2×#6435C2211yescharacteristic
46C7×#475C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×C8×Dic7C2211yescharacteristic
58#89856C2218yescomplemented
59#89800C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89641C2218yescomplemented
68#89635C2218yescomplemented
69#89634C2218yescomplemented
70#89624C2218yescomplemented
71#89616C2218yescomplemented
72#89612C2218yescomplemented
73#89583C2218yes—
74#89582C2218yescomplemented
75#89561C2218yescomplemented
76#89560C2218yescomplemented
77C2×#3125—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C2×#1161—24no—
81C2×#1161—24no—
82C2×#1161—22no—
83C2×#1161C2314yes—
84C22×D28—21no—
85C22×D28—21no—
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×Dic14C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8C2314yes—
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C42×C7—21no—
107C2×C42×C7C2311yescharacteristic
108#6510—28no—
109#6509—28no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112C2×#1144—24no—
113C2×#1144C2314yes—
114C2×#1143—24no—
115C2×#1143C2314yes—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
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)⋊C4D411yescharacteristic
124C2×(C2×D7)⋊C4D411yescharacteristic
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4D411yescharacteristic
131C2×Dic7⋊C4D411yescharacteristic
132C2×C4×Dic7—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C2×D56—24no—
138C2×D56C2314yes—
139C2×#1132—24no—
140C2×#1132C2314yes—
141#6461—28no—
142#6460—22no—
143#6460C2314yes—
144#6458—22no—
145#6458C2314yes—
146#6457—28no—
147#6456—28no—
148#6456—22no—
149#6456—22no—
150#6456C2314yes—
151#6456C2314yes—
152D7×C4⋊C4—22no—
153D7×C4⋊C4—28no—
154D7×C4⋊C4C2314yes—
155#6450—22no—
156#6450C2314yes—
157#6438—22no—
158#6438C2314yes—
159C4×D28—22no—
160C4×D28—28no—
161C4×D28C2314yes—
162#6435—28no—
163#6435D414yes—
164#6435C2314yes—
165C7×#106C2314yes—
166C7×#106C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170#6395C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6390C2314yes—
174#6389C2314yes—
175C8×Dic7C2314yes—
176#6384C2314yes—
177#6383C2314yes—
178#6383C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6382C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542—71no—
184C2×#520—71no—
185#3125—716no—
186C2×#481—71no—
187C2×#483—71no—
188C2×#475D711yescharacteristic, complemented
189C2×#476—71no—
190C2×#464—71no—
191C2×#463—71no—
192C2×#452—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C23×D7—21no—
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×Q8—21no—
203C2×C7×Q8—24no—
204C2×C7×Q8—22no—
205C2×C7×Q8—82no—
206C2×C7×Q8#4114yes—
207C2×C7×Q8C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7C2×D411yescharacteristic
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220#1161—216no—
221#1161—28no—
222#1161—28no—
223C2×D28—28no—
224C2×D28—24no—
225C2×D28—21no—
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—21no—
230C2×D28—24no—
231C2×D28—82no—
232C2×D28#4114yes—
233C2×D28C2412yes—
234C2×D28C2412yes—
235C2×C4×D7—28no—
236C2×C4×D7—22no—
237C2×C4×D7—22no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—24no—
243C2×C4×D7—82no—
244C2×C4×D7—82no—
245C2×C4×D7—82no—
246C2×C4×D7—82no—
247C2×C4×D7C2×D412yes—
248C2×C4×D7C2412yes—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—21no—
252C2×Dic14C2412yes—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C42×C7—24no—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268#1144—28no—
269#1143—28no—
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)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4C2×D414yes—
278(C2×D7)⋊C4C2×D414yes—
279C4⋊Dic7—21no—
280C4⋊Dic7—24no—
281C4⋊Dic7—24no—
282C4⋊Dic7C2412yes—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4C2×D414yes—
286Dic7⋊C4C2×D414yes—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295D56—28no—
296#1132—28no—
297C22×#41—71no—
298C22×Q16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×D8—71no—
302#542—78no—
303#542—144no—
304C2×C4⋊Q8C2×D711yescharacteristic
305C2×#126—141no—
306C2×#124—71no—
307C2×#124—141no—
308C2×#123—141no—
309C2×C22⋊Q8—71no—
310C2×C22⋊Q8—141no—
311C2×#121—71no—
312#520—78no—
313#520—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8C2×D711yescharacteristic
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×C4×D4—141no—
322C2×#117—71no—
323C2×#117—141no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—141no—
326#483—78no—
327#481—78no—
328#476—78no—
329#475C2×D718yescomplemented
330#464—78no—
331#463—78no—
332#452—78no—
333#449—78no—
334#442—78no—
335#441—78no—
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#106—71no—
340C2×#106—71no—
341C2×#106C2×D711yescharacteristic
342C2×#106C2×D711yescharacteristic
343C2×C4⋊C8—71no—
344C2×C4⋊C8C2×D711yescharacteristic
345C2×#103—71no—
346C2×#103—71no—
347C2×#103C2×D711yescharacteristic
348C2×#103C2×D711yescharacteristic
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×C22⋊C8—71no—
354C2×C22⋊C8—71no—
355C2×#97—71no—
356C2×C4×C8—71no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—24no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7C22×D412yes—
370C7×Q8—24no—
371C7×Q8—22no—
372C7×Q8—84no—
373C7×Q8C2×#4114yes—
374C2×C4×C7—24no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C7C2×#4112yes—
388C2×C4×C7C2×#4112yes—
389C2×C4×C7C2511yescharacteristic
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400D28—216no—
401D28—24no—
402D28—22no—
403D28—22no—
404D28—22no—
405D28—42no—
406D28—84no—
407D28C2×#4114yes—
408C4×D7—216no—
409C4×D7—24no—
410C4×D7—22no—
411C4×D7—22no—
412C4×D7—84no—
413C4×D7—84no—
414C4×D7—84no—
415C4×D7—84no—
416Dic14—22no—
417Dic14—22no—
418Dic14—42no—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C2×#41—74no—
424C2×#41—142no—
425C2×#41—144no—
426C2×#41—144no—
427C22×Q8—21no—
428C22×Q8—71no—
429C22×Q8C22×D711yescharacteristic
430C22×D4—71no—
431C22×D4—71no—
432C22×D4—141no—
433C22×D4—141no—
434C23×C4—71no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4—141no—
440C2×Q16—74no—
441C2×Q16—144no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×D8—74no—
447C2×D8—144no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452C4⋊Q8—22no—
453C4⋊Q8C22×D714yes—
454#126—148no—
455#124—74no—
456#124—148no—
457#124—142no—
458#123—148no—
459C22⋊Q8—74no—
460C22⋊Q8—142no—
461C22⋊Q8—148no—
462#121—74no—
463#121—142no—
464C4×Q8—22no—
465C4×Q8—74no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×Q8—142no—
469C4×Q8C22×D714yes—
470C4×D4—74no—
471C4×D4—74no—
472C4×D4—74no—
473C4×D4—148no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—148no—
477C4×D4—142no—
478#117—74no—
479#117—74no—
480#117—148no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—148no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4C22×D711yescharacteristic
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C4⋊C4C22×D711yescharacteristic
496C2×C22⋊C4—71no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C42—21no—
506C2×C42—71no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42C22×D711yescharacteristic
510#106—74no—
511#106—74no—
512#106C22×D714yes—
513#106C22×D714yes—
514C4⋊C8—74no—
515C4⋊C8C22×D714yes—
516#103—74no—
517#103—74no—
518#103C22×D714yes—
519#103C22×D714yes—
520#102—74no—
521#102—74no—
522#102—74no—
523#102—74no—
524C22⋊C8—74no—
525C22⋊C8—74no—
526#97—74no—
527C4×C8—74no—
528C22×C7#52512yes—
529C22×C7#57712yes—
530C22×C7#57712yes—
531C22×C7C23×D411yescharacteristic
532C2×D7—22no—
533C2×D7—24no—
534C2×D7—22no—
535C2×D7—22no—
536C2×D7—44no—
537C2×D7—48no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—24no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7#52512yes—
551C4×C7C22×#4111yescharacteristic
552C4×C7C22×#4111yescharacteristic
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558C24—71no—
559C24—141no—
560C24—141no—
561#41—148no—
562#41—1416no—
563#41—148no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—72no—
568C2×Q8—82no—
569C2×Q8—141no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8#116114yes—
573C2×Q8C23×D712yes—
574C2×D4—74no—
575C2×D4—72no—
576C2×D4—72no—
577C2×D4—144no—
578C2×D4—148no—
579C2×D4—144no—
580C2×D4—141no—
581C2×D4—141no—
582C2×D4—142no—
583C2×D4—142no—
584C2×D4—142no—
585C2×D4—562no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
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—148no—
599C22×C4—144no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—144no—
605C22×C4—562no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4—562no—
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4C23×D711yescharacteristic
612Q16—148no—
613SD16—148no—
614SD16—148no—
615D8—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—74no—
630C4⋊C4—74no—
631C4⋊C4—72no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—141no—
637C4⋊C4C23×D712yes—
638C4⋊C4C23×D712yes—
639C4⋊C4C23×D712yes—
640C22⋊C4—74no—
641C22⋊C4—74no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C42—24no—
650C42—72no—
651C42—72no—
652C42—144no—
653C42—144no—
654C42D4×D712yes—
655C42C23×D712yes—
656C2×C7#312514yescomplemented
657C2×C7C2×#52511yescharacteristic
658C2×C7C2×#57711yescharacteristic
659C2×C7C2×#57711yescharacteristic
660D7—42no—
661D7—44no—
662D7—82no—
663C23—72no—
664C23—142no—
665C23—142no—
666C23—144no—
667C23—142no—
668C23—142no—
669C23—142no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23—282no—
675C23C2×D4×D711yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—84no—
679Q8—142no—
680Q8—142no—
681Q8—282no—
682Q8C2×#116114yes—
683D4—74no—
684D4—1416no—
685D4—144no—
686D4—142no—
687D4—142no—
688D4—142no—
689D4—282no—
690D4—564no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—72no—
702C2×C4—72no—
703C2×C4—72no—
704C2×C4—1416no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—144no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—564no—
716C2×C4—564no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4C2×#116112yes—
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#312511yescharacteristic, complemented, Sylow
730C22—142no—
731C22—144no—
732C22—142no—
733C22—142no—
734C22—282no—
735C22—284no—
736C22—288no—
737C22—282no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9031812yes—
743C22#9045312yes—
744C22#9046912yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—24no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—142no—
753C4—142no—
754C4—142no—
755C4—282no—
756C4—282no—
757C4#9031812yes—
758C4C22×#116111yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—282no—
761C2—284no—
762C2—562no—
763C2#1173844614yesdirect product factor
764C2C2×#9031811yescharacteristic
765C2C2×#9045311yescharacteristic
766C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC2×#89583C2
hypercenterC2×#475D7
hypocenterC7C2×#3125
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#90424C2semidirect
2. C2×#90265C2semidirect
3. C2×C7×#475C2semidirect
4. C2×#89856C2semidirect
5. C2×#89800C2semidirect
6. #11738446C2direct (N × H)
7. C2×#89635C2semidirect
8. C2×#89634C2semidirect
9. C2×#89641C2semidirect
10. C2×#89624C2semidirect
11. C2×#89616C2semidirect
12. C2×#89612C2semidirect
13. C2×#89582C2semidirect
15. C2×#89561C2semidirect
16. C2×#89560C2semidirect
28. #90424C22semidirect
30. #90265C22semidirect
46. C7×#475C22semidirect
58. #89856C22semidirect
59. #89800C22semidirect
67. #89641C22semidirect
68. #89635C22semidirect
69. #89634C22semidirect
70. #89624C22semidirect
71. #89616C22semidirect
72. #89612C22semidirect
74. #89582C22semidirect
75. #89561C22semidirect
76. #89560C22semidirect
188. C2×#475D7semidirect
329. #475C2×D7semidirect
656. C2×C7#3125semidirect
729. C7C2×#3125semidirect
763. C2#11738446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904242
C2×#902652
C2×C7×#4752
C2×#898562
C2×#898002
#117384462
C2×#896352
C2×#896342
C2×#896412
C2×#896242
C2×#896162
C2×#896122
C2×#895822
C2×#895832
C2×#895612
C2×#895602
C2×#31257