Finite Group Databasebeta

← C2×#11736790 #14221978

Subgroups — C2×#11736790 #14221978

Order 1792.

2182 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×#90170C211yesmaximal, characteristic, complemented
2C2×C4×#1157C211yesmaximal, characteristic, complemented
3C2×C7×#432C211yesmaximal, characteristic, complemented
4#11736790C2116yesmaximal, direct product factor
5C2×#89601C211yesmaximal, characteristic, complemented
6C2×#89617C211yesmaximal, characteristic, complemented
7C2×#89619C211yesmaximal, characteristic, complemented
8C2×#89616C211yesmaximal, characteristic, complemented
9C2×#89505C211yesmaximal, characteristic, complemented
10C2×#89506C211yesmaximal, characteristic
11C2×#89495C211yesmaximal, characteristic, complemented
12C2×#89509C211yesmaximal, characteristic, complemented
13C2×#89488C211yesmaximal, characteristic, complemented
14C2×#89483C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89482C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C2×#6493C2211yescharacteristic
20C2×#6492—21no—
21C2×C4×C22⋊D7—21no—
22C2×C4×C22⋊D7—21no—
23C2×C4×C22⋊D7—21no—
24C2×#6489C2211yescharacteristic
25C2×#6487C2211yescharacteristic
26C22×Dic28C2211yescharacteristic
27C22×D56C2211yescharacteristic
28C22×#1132C2211yescharacteristic
29C22×#1132C2211yescharacteristic
30#90170—24no—
31#90170C2218yescomplemented
32C2×#6439—21no—
33C2×#6438C2211yescharacteristic
34C4×#1157—24no—
35C4×#1157C2218yescomplemented
36C2×C4×D28C2211yescharacteristic
37C2×C4×D28C2211yescharacteristic
38C2×C4×D28C2211yescharacteristic
39C2×#6435—21no—
40C2×#6435—21no—
41C2×C42×D7—21no—
42C2×#6433C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#432C2218yescomplemented
47C2×C7×C4⋊C8C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52C2×C7×#97C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65#89619C2218yescomplemented
66#89617C2218yescomplemented
67#89616C2218yescomplemented
68#89601C2218yescomplemented
69#89509C2218yescomplemented
70#89506C2218yes—
71#89505C2218yescomplemented
72#89495C2218yescomplemented
73#89488C2218yescomplemented
74#89483C2218yescomplemented
75#89482C2218yescomplemented
76#89482C2218yescomplemented
77C2×#3111—71nomaximal, Sylow
78C23×C4×C7D411yescharacteristic
79C23×C4×C7D411yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C2×#1157—22no—
84C2×#1157—24no—
85C2×#1157—24no—
86C2×#1157C2314yes—
87C22×D28C2311yescharacteristic
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7—21no—
93C22×Dic14C2311yescharacteristic
94C22×Dic14C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C2×C42×C7D411yescharacteristic
100C2×C42×C7D411yescharacteristic
101C2×C42×C7D414yes—
102C2×C42×C7C2311yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C42×C7C2314yes—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107#6493—22no—
108#6493C2314yes—
109#6492—28no—
110C4×C22⋊D7—28no—
111C4×C22⋊D7—28no—
112C4×C22⋊D7—28no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119#6489—22no—
120#6489C2314yes—
121C2×C4⋊Dic7C2311yescharacteristic
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125#6487—22no—
126#6487C2314yes—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×Dic28—24no—
138C2×Dic28C2314yes—
139C2×D56—24no—
140C2×D56C2314yes—
141C2×#1132—24no—
142C2×#1132—24no—
143C2×#1132C2314yes—
144C2×#1132C2314yes—
145#6439—28no—
146#6438—22no—
147#6438C2314yes—
148C4×D28—22no—
149C4×D28—22no—
150C4×D28—22no—
151C4×D28C2314yes—
152C4×D28C2314yes—
153C4×D28C2314yes—
154#6435—28no—
155#6435—28no—
156C42×D7—28no—
157#6433—22no—
158#6433C2314yes—
159C4×Dic14—22no—
160C4×Dic14—22no—
161C4×Dic14—22no—
162C4×Dic14C2314yes—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165C7×C4⋊C8C2314yes—
166C7×C4⋊C8C2314yes—
167C7×C22⋊C8C2314yes—
168C7×C22⋊C8C2314yes—
169C7×#97C2314yes—
170C7×#97C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6392C2314yes—
176#6392C2314yes—
177#6391C2314yes—
178#6391C2314yes—
179#6390C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183C2×#529—71no—
184C2×C4×#41—71no—
185#3111—716no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#464—71no—
191C2×#463—71no—
192C2×#452—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×#440—71no—
197C2×#440—71no—
198C2×#432D711yescharacteristic, complemented
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C23×D7—21no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—42no—
205C22×C4×C7—42no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D414yes—
213C22×C4×C7C2×D414yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—28no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—44no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226#1157—216no—
227#1157—28no—
228#1157—28no—
229C2×D28—21no—
230C2×D28—22no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—21no—
234C2×D28#4114yes—
235C2×D28C2412yes—
236C2×D28C2412yes—
237C2×C4×D7—28no—
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×Dic14—21no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—21no—
250C2×Dic14#4114yes—
251C2×Dic14C2412yes—
252C2×Dic14C2412yes—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8—22no—
257C2×C7×C8C2412yes—
258C2×C7×C8C2412yes—
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C42×C7C2×D412yes—
262C42×C7C2×D412yes—
263C42×C7C2×D414yes—
264C42×C7C2×D414yes—
265C42×C7C2412yes—
266C42×C7C2412yes—
267C22⋊Dic7—24no—
268C22⋊Dic7—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—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282C4⋊Dic7C2412yes—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289C4×Dic7—24no—
290C4×Dic7—24no—
291C4×Dic7—24no—
292C4×Dic7—24no—
293Dic28—28no—
294D56—28no—
295#1132—28no—
296#1132—28no—
297C22×#41—71no—
298C22×Q16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×D8—71no—
302#529—78no—
303#529—144no—
304C2×#126—141no—
305C2×#125—71no—
306C2×#124—71no—
307C2×#123—141no—
308C2×C22⋊Q8—71no—
309C2×#121—71no—
310C4×#41—78no—
311C4×#41—144no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—71no—
318C2×C4×D4—141no—
319C2×C4×D4—141no—
320C2×C4×D4—141no—
321C2×#117—71no—
322C2×#117—141no—
323C2×#117—141no—
324C22×C42—141no—
325C22×C42C2×D711yescharacteristic
326#485—78no—
327#482—78no—
328#479—78no—
329#478—78no—
330#464—78no—
331#463—78no—
332#452—78no—
333#449—78no—
334#442—78no—
335#441—78no—
336#440—78no—
337#440—78no—
338#432C2×D718yescomplemented
339C2×#107—71no—
340C2×#107—71no—
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8C2×D711yescharacteristic
344C2×C4⋊C8C2×D711yescharacteristic
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×C22⋊C8C2×D711yescharacteristic
354C2×C22⋊C8C2×D711yescharacteristic
355C2×#97C2×D711yescharacteristic
356C2×#97C2×D711yescharacteristic
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—24no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2×#4112yes—
388C2×C4×C7C2511yescharacteristic
389C22⋊D7—216no—
390C22⋊D7—48no—
391C2×Dic7—24no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403D28—24no—
404D28—22no—
405D28—22no—
406D28—22no—
407D28—42no—
408D28C2×#4114yes—
409C4×D7—216no—
410C4×D7—48no—
411C4×D7—48no—
412C4×D7—48no—
413Dic14—24no—
414Dic14—22no—
415Dic14—22no—
416Dic14—22no—
417Dic14—42no—
418Dic14C2×#4114yes—
419C7×C8—22no—
420C7×C8—22no—
421C7×C8—22no—
422C7×C8—22no—
423C2×#41—74no—
424C2×#41—144no—
425C2×#41—144no—
426C2×#41—142no—
427C22×Q8—71no—
428C22×Q8—71no—
429C22×D4—71no—
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4D2811yescharacteristic
438C23×C4D2811yescharacteristic
439C23×C4C22×D711yescharacteristic
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×C8C22×D711yescharacteristic
449C22×C8C22×D711yescharacteristic
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452#126—148no—
453#125—74no—
454#125—142no—
455#124—74no—
456#124—142no—
457#123—148no—
458C22⋊Q8—74no—
459C22⋊Q8—142no—
460#121—74no—
461#121—142no—
462C4×Q8—74no—
463C4×Q8—74no—
464C4×Q8—74no—
465C4×Q8—142no—
466C4×Q8—142no—
467C4×Q8—142no—
468C4×D4—74no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—148no—
472C4×D4—148no—
473C4×D4—148no—
474C4×D4—142no—
475C4×D4—142no—
476C4×D4—142no—
477#117—74no—
478#117—142no—
479#117—148no—
480#117—148no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42—141no—
502C2×C42—141no—
503C2×C42—148no—
504C2×C42D2811yescharacteristic
505C2×C42D2814yes—
506C2×C42D2811yescharacteristic
507C2×C42C22×D711yescharacteristic
508C2×C42C22×D711yescharacteristic
509C2×C42C22×D714yes—
510#107—74no—
511#107—74no—
512#106—74no—
513#106—74no—
514C4⋊C8C22×D714yes—
515C4⋊C8C22×D714yes—
516#103—74no—
517#103—74no—
518#103—74no—
519#103—74no—
520#102—74no—
521#102—74no—
522#102—74no—
523#102—74no—
524C22⋊C8C22×D714yes—
525C22⋊C8C22×D714yes—
526#97C22×D714yes—
527#97C22×D714yes—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—44no—
532C22×C7#52512yes—
533C22×C7#57512yes—
534C22×C7#57512yes—
535C22×C7C23×D411yescharacteristic
536C2×D7—24no—
537C2×D7—48no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7—22no—
549C4×C7#52512yes—
550C4×C7C22×#4111yescharacteristic
551C4×C7C22×#4111yescharacteristic
552Dic7—24no—
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558C24—141no—
559C24—141no—
560C24C2×D2811yescharacteristic
561#41—148no—
562#41—148no—
563#41—1416no—
564C2×Q8—74no—
565C2×Q8—72no—
566C2×Q8—72no—
567C2×Q8—141no—
568C2×Q8—141no—
569C2×Q8—142no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×D4—74no—
573C2×D4—72no—
574C2×D4—72no—
575C2×D4—148no—
576C2×D4—144no—
577C2×D4—144no—
578C2×D4—141no—
579C2×D4—141no—
580C2×D4—142no—
581C2×D4—142no—
582C2×D4—142no—
583C2×D4—284no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—148no—
589C22×C4—141no—
590C22×C4—144no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—284no—
600C22×C4—284no—
601C22×C4—284no—
602C22×C4C2×D2812yes—
603C22×C4C2×D2811yescharacteristic
604C22×C4C2×D2811yescharacteristic
605C22×C4C2×D2811yescharacteristic
606C22×C4C2×D2811yescharacteristic
607C22×C4C2×D2811yescharacteristic
608C22×C4C2×D2814yes—
609C22×C4C2×D2814yes—
610C22×C4C23×D712yes—
611C22×C4C23×D711yescharacteristic
612Q16—148no—
613SD16—148no—
614SD16—148no—
615D8—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C23×D712yes—
621C2×C8C23×D712yes—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—72no—
625C4⋊C4—72no—
626C4⋊C4—72no—
627C4⋊C4—72no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—141no—
635C4⋊C4—141no—
636C4⋊C4—141no—
637C4⋊C4—141no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C42—144no—
647C42—144no—
648C42—144no—
649C42—144no—
650C42C2×D2814yes—
651C42C2×D2814yes—
652C42C2×D2812yes—
653C42C2×D2812yes—
654C42C23×D712yes—
655C42C23×D712yes—
656C2×C7—42no—
657C2×C7#311114yescomplemented
658C2×C7C2×#52511yescharacteristic
659C2×C7C2×#57511yescharacteristic
660C2×C7C2×#57511yescharacteristic
661D7—44no—
662D7—82no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—144no—
667C23—142no—
668C23—142no—
669C23—282no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23C22×D2812yes—
675C23C22×D2811yescharacteristic
676Q8—74no—
677Q8—144no—
678Q8—142no—
679Q8—142no—
680Q8—142no—
681Q8—282no—
682D4—74no—
683D4—1416no—
684D4—144no—
685D4—142no—
686D4—142no—
687D4—142no—
688D4—288no—
689D4—282no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—1416no—
701C2×C4—144no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—288no—
709C2×C4—288no—
710C2×C4—288no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4C22×D2812yes—
717C2×C4C22×D2812yes—
718C2×C4C22×D2812yes—
719C2×C4C22×D2812yes—
720C2×C4C22×D2812yes—
721C2×C4C22×D2811yescharacteristic
722C2×C4D7×#4112yes—
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—22no—
729C7C2×#311111yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—144no—
735C22—288no—
736C22—282no—
737C22—282no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9021512yes—
743C22#9043912yes—
744C22#9043912yes—
745C22C23×D2811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—144no—
752C4—282no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4#9021512yes—
758C4C2×D7×#4111yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—42no—
761C2—284no—
762C2—562no—
763C2#1173679014yesdirect product factor
764C2C2×#9021511yescharacteristic
765C2C2×#9043911yescharacteristic
766C2C2×#9043911yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#432C2
socleC23×C7C22×D4
prime radicalC2×#89506C2
hypercenterC2×#432D7
hypocenterC7C2×#3111
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#90170C2semidirect
2. C2×C4×#1157C2semidirect
3. C2×C7×#432C2semidirect
4. #11736790C2direct (N × H)
5. C2×#89601C2semidirect
6. C2×#89617C2semidirect
7. C2×#89619C2semidirect
8. C2×#89616C2semidirect
9. C2×#89505C2semidirect
11. C2×#89495C2semidirect
12. C2×#89509C2semidirect
13. C2×#89488C2semidirect
14. C2×#89483C2semidirect
15. C2×#89482C2semidirect
16. C2×#89482C2semidirect
31. #90170C22semidirect
35. C4×#1157C22semidirect
46. C7×#432C22semidirect
65. #89619C22semidirect
66. #89617C22semidirect
67. #89616C22semidirect
68. #89601C22semidirect
69. #89509C22semidirect
71. #89505C22semidirect
72. #89495C22semidirect
73. #89488C22semidirect
74. #89483C22semidirect
75. #89482C22semidirect
76. #89482C22semidirect
198. C2×#432D7semidirect
338. #432C2×D7semidirect
657. C2×C7#3111semidirect
729. C7C2×#3111semidirect
763. C2#11736790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#901702
C2×C4×#11572
C2×C7×#4322
#117367902
C2×#896012
C2×#896172
C2×#896192
C2×#896162
C2×#895052
C2×#895062
C2×#894952
C2×#895092
C2×#894882
C2×#894832
C2×#894822
C2×#31117