Finite Group Databasebeta

← C2×#11729416 #13355686

Subgroups — C2×#11729416 #13355686

Order 1792.

1678 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×C7×#519C211yesmaximal, characteristic, complemented
2C22×#6505C211yesmaximal, characteristic
3C2×#89997C211yesmaximal, characteristic, complemented
4C2×#89778C211yesmaximal, characteristic
5C2×#89777C211yesmaximal, characteristic
6#11729416C218yesmaximal, direct product factor
7C2×#89328C211yesmaximal, characteristic, complemented
8C2×#89326C211yesmaximal, characteristic, complemented
9C23×C7×Q8C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C7×#519—22no—
12C7×#519—22no—
13C7×#519—22no—
14C7×#519C2214yescomplemented
15C2×C4×C7×Q8—22no—
16C2×C4×C7×Q8—22no—
17C2×C7×#117—22no—
18C2×C7×#117C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C22×#1144C412yescomplemented
21C2×#6505—22no—
22C2×#6505—22no—
23C2×#6505—22no—
24C2×#6505—22no—
25C2×#6505C414yescomplemented
26C2×#6505C2214yes—
27C22×#1143C412yescomplemented
28C2×#6489C2211yescharacteristic
29C22×#1136C2211yescharacteristic
30C22×#1136C2211yescharacteristic
31#89997—22no—
32#89997C2214yescomplemented
33C2×#6409—22no—
34#89778—22no—
35#89778C2214yes—
36#89777—22no—
37#89777C2214yes—
38C2×#6380—22no—
39C2×#6379—22no—
40#89328C2214yescomplemented
41#89326C2214yescomplemented
42C2×#1905—71nomaximal, Sylow
43C22×C7×Q8—21no—
44C22×C7×Q8—21no—
45C22×C7×Q8—21no—
46C22×C7×Q8—21no—
47C22×C7×Q8—21no—
48C22×C7×Q8—21no—
49C22×C7×Q8—21no—
50C22×C7×Q8C2×C412yes—
51C22×C7×Q8C2×C412yes—
52C22×C7×Q8D412yes—
53C22×C7×Q8D412yes—
54C22×C7×Q8D412yes—
55C22×C7×Q8D412yes—
56C22×C7×Q8C2312yes—
57C23×C4×C7—21no—
58C23×C4×C7C2311yescharacteristic
59C22×C22⋊D7—21no—
60C2×#1157—21no—
61C2×#1157—21no—
62C2×#1157—21no—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157C2×C412yes—
71C2×#1157C2312yes—
72C22×D28C2×C411yescharacteristic
73C22×C4×D7—21no—
74C22×Dic14C2×C411yescharacteristic
75C4×C7×Q8—28no—
76C4×C7×Q8—28no—
77C4×C7×Q8—28no—
78C4×C7×Q8—28no—
79C7×#117—28no—
80C7×#117—21no—
81C7×#117—21no—
82C7×#117—21no—
83C7×#117—21no—
84C7×#117—28no—
85C7×#117D412yes—
86C7×#117D412yes—
87C7×#117C2312yes—
88C7×#117C2312yes—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4D412yes—
94C2×C42×C7—24no—
95C2×C42×C7—21no—
96C2×C42×C7D412yes—
97C2×C22⋊Dic7—21no—
98C2×#1144—24no—
99C2×#1144—24no—
100C2×#1144C2×C418yescomplemented
101#6505—28no—
102#6505—28no—
103#6505—28no—
104#6505—28no—
105C2×#1143—24no—
106C2×#1143—24no—
107C2×#1143C2×C418yescomplemented
108#6489—21no—
109#6489—21no—
110#6489—21no—
111#6489C2312yes—
112C2×C4⋊Dic7—21no—
113C2×C4×Dic7—21no—
114C2×#1136—21no—
115C2×#1136—21no—
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136—21no—
123C2×#1136C2×C412yes—
124C2×#1136C2312yes—
125C2×#1136C2312yes—
126C22×C7⋊C8—21no—
127C22×C7⋊C8C2×C412yes—
128#6409—28no—
129#6380—28no—
130#6379—28no—
131C22×#137—71no—
132C2×#519D711yescharacteristic, complemented
133C2×#421—71no—
134C2×#419—71no—
135C2×#410—71no—
136#1905—78no—
137C2×#344—71no—
138C2×H(3,ℤ/4)—71no—
139C24×C7C2×D411yescharacteristic
140C23×D7—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8—22no—
145C2×C7×Q8—22no—
146C2×C7×Q8—22no—
147C2×C7×Q8—22no—
148C2×C7×Q8—22no—
149C2×C7×Q8—22no—
150C2×C7×Q8—22no—
151C2×C7×Q8—22no—
152C2×C7×Q8—22no—
153C2×C7×Q8—22no—
154C2×C7×Q8—22no—
155C2×C7×Q8—22no—
156C2×C7×Q8—22no—
157C2×C7×Q8—22no—
158C2×C7×Q8—22no—
159C2×C7×Q8—22no—
160C2×C7×Q8—22no—
161C2×C7×Q8—22no—
162C2×C7×Q8C22⋊C414yes—
163C2×C7×Q8C22⋊C414yes—
164C2×C7×Q8C22⋊C414yes—
165C2×C7×Q8C22⋊C414yes—
166C2×C7×Q8C22×C414yes—
167C2×C7×Q8C2×D414yes—
168C2×C7×Q8C2×D414yes—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7C22×C411yescharacteristic
179C22×C4×C7C22×C411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7#4111yescharacteristic
188C22×C4×C7#4111yescharacteristic
189C22×C4×C7#4111yescharacteristic
190C22×C4×C7#4111yescharacteristic
191C22×C4×C7C2411yescharacteristic
192C2×C22⋊D7—22no—
193C2×C22⋊D7—22no—
194C2×C22⋊D7—41no—
195C2×C22⋊D7—41no—
196C2×C22⋊D7—41no—
197C2×C22⋊D7—41no—
198C22×Dic7—21no—
199C22×Dic7—41no—
200#1157—22no—
201#1157—22no—
202#1157—22no—
203#1157—22no—
204#1157—22no—
205#1157—22no—
206#1157—22no—
207#1157—22no—
208#1157—41no—
209#1157—41no—
210#1157—41no—
211#1157—41no—
212#1157—41no—
213#1157—41no—
214#1157—41no—
215#1157—41no—
216C2×D28—21no—
217C2×D28—21no—
218C2×D28—21no—
219C2×D28—21no—
220C2×D28—21no—
221C2×D28C22×C412yes—
222C2×C4×D7—22no—
223C2×C4×D7—22no—
224C2×C4×D7—41no—
225C2×C4×D7—41no—
226C2×C4×D7—41no—
227C2×C4×D7—41no—
228C2×Dic14—21no—
229C2×Dic14—21no—
230C2×Dic14—21no—
231C2×Dic14—21no—
232C2×Dic14—21no—
233C2×Dic14C22×C412yes—
234C7×C4⋊C4—216no—
235C7×C4⋊C4—22no—
236C7×C4⋊C4—22no—
237C7×C4⋊C4—22no—
238C7×C4⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4C2×D414yes—
243C42×C7—216no—
244C42×C7—22no—
245C42×C7—22no—
246C42×C7—22no—
247C42×C7C2×D414yes—
248C22⋊Dic7—22no—
249C22⋊Dic7—41no—
250#1144—216no—
251#1143—216no—
252C4⋊Dic7—22no—
253C4⋊Dic7—41no—
254C4×Dic7—22no—
255C4×Dic7—41no—
256#1136—22no—
257#1136—22no—
258#1136—22no—
259#1136—22no—
260#1136—22no—
261#1136—22no—
262#1136—41no—
263#1136—41no—
264C2×C7⋊C8—22no—
265C2×C7⋊C8—22no—
266C2×C7⋊C8—22no—
267C2×C7⋊C8—41no—
268C2×C7⋊C8—41no—
269C2×C7⋊C8C22×C414yes—
270C22×#41—71no—
271C23×Q8C2×D711yescharacteristic
272C2×#137—74no—
273C2×#137—74no—
274C2×#137—142no—
275C2×#137—142no—
276C2×#137—142no—
277C2×#137—142no—
278C22×Q16—72no—
279C22×SD16—72no—
280C22×M16—71no—
281C22×M16—71no—
282#519—22no—
283#519—22no—
284#519—22no—
285#519C2×D714yescomplemented
286C2×C4×Q8—22no—
287C2×C4×Q8—22no—
288C2×#117—22no—
289C2×#117—71no—
290C2×#117C2×D711yescharacteristic
291C2×#117C2×D711yescharacteristic
292#421—74no—
293#421—142no—
294C2×#104—142no—
295#419—74no—
296#419—142no—
297C2×#103—142no—
298#410—74no—
299#410—142no—
300C2×#99—142no—
301#344—74no—
302H(3,ℤ/4)—74no—
303C23×C7—42no—
304C23×C7C4×D411yescharacteristic
305C23×C7C4×D411yescharacteristic
306C23×C7#12011yescharacteristic
307C23×C7#12011yescharacteristic
308C23×C7#12111yescharacteristic
309C23×C7#12111yescharacteristic
310C23×C7C22×D411yescharacteristic
311C22×D7—22no—
312C22×D7—41no—
313C22×D7—41no—
314C22×D7—82no—
315C7×Q8—24no—
316C7×Q8—24no—
317C7×Q8—24no—
318C7×Q8—24no—
319C7×Q8—24no—
320C7×Q8—24no—
321C7×Q8—24no—
322C7×Q8C2×C22⋊C418yes—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—24no—
327C2×C4×C7—24no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—24no—
331C2×C4×C7—24no—
332C2×C4×C7—44no—
333C2×C4×C7—44no—
334C2×C4×C7C2×C22⋊C411yescharacteristic
335C2×C4×C7C2×C22⋊C411yescharacteristic
336C2×C4×C7C2×C22⋊C411yescharacteristic
337C2×C4×C7C2×C22⋊C411yescharacteristic
338C2×C4×C7C4×D411yescharacteristic
339C2×C4×C7C4×D411yescharacteristic
340C2×C4×C7C4×D411yescharacteristic
341C2×C4×C7C4×D411yescharacteristic
342C2×C4×C7C4×D411yescharacteristic
343C2×C4×C7C4×D411yescharacteristic
344C2×C4×C7#12011yescharacteristic
345C2×C4×C7#12011yescharacteristic
346C2×C4×C7#12111yescharacteristic
347C2×C4×C7#12111yescharacteristic
348C2×C4×C7#12111yescharacteristic
349C2×C4×C7#12111yescharacteristic
350C2×C4×C7#12111yescharacteristic
351C2×C4×C7#12111yescharacteristic
352C2×C4×C7#12311yescharacteristic
353C2×C4×C7#12311yescharacteristic
354C2×C4×C7#12311yescharacteristic
355C2×C4×C7#12311yescharacteristic
356C2×C4×C7C23×C411yescharacteristic
357C2×C4×C7C22×D411yescharacteristic
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C22×D411yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C22⋊D7—42no—
363C22⋊D7—42no—
364C22⋊D7—42no—
365C22⋊D7—42no—
366C2×Dic7—22no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—42no—
370C2×Dic7—82no—
371D28—22no—
372D28—22no—
373D28—41no—
374D28—41no—
375C4×D7—42no—
376C4×D7—42no—
377C4×D7—42no—
378C4×D7—42no—
379Dic14—22no—
380Dic14—22no—
381Dic14—41no—
382Dic14—41no—
383C7⋊C8—24no—
384C7⋊C8—42no—
385C2×#41—72no—
386C2×#41—72no—
387C2×#41—141no—
388C2×#41—141no—
389C2×#41—141no—
390C2×#41—141no—
391C2×#41—141no—
392C2×#41—141no—
393C2×#41—141no—
394C2×#41—141no—
395C2×#41—141no—
396C2×#41—141no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—71no—
405C22×Q8C4×D712yes—
406C22×Q8C4×D712yes—
407C22×Q8D2812yes—
408C22×Q8D2812yes—
409C22×Q8C22⋊D712yes—
410C22×Q8C22⋊D712yes—
411C22×Q8C22×D712yes—
412C22×D4—71no—
413C22×D4—141no—
414C23×C4—21no—
415C23×C4—141no—
416C23×C4C22×D711yescharacteristic
417#137—148no—
418#137—148no—
419#137—148no—
420#137—148no—
421C2×Q16—78no—
422C2×Q16—144no—
423C2×Q16—144no—
424C2×SD16—78no—
425C2×SD16—144no—
426C2×SD16—144no—
427C2×M16—72no—
428C2×M16—72no—
429C2×M16—72no—
430C2×M16—141no—
431C2×M16—141no—
432C2×M16—141no—
433C2×M16—141no—
434C2×M16—141no—
435C2×M16—141no—
436C2×M16—141no—
437C2×M16—141no—
438C2×M16—141no—
439C22×C8—72no—
440C22×C8—141no—
441C4×Q8—28no—
442C4×Q8—28no—
443C4×Q8—28no—
444C4×Q8—28no—
445#117—28no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117—21no—
450#117—28no—
451#117—72no—
452#117—141no—
453#117—141no—
454#117—141no—
455#117C22⋊D712yes—
456#117C22⋊D712yes—
457#117C22×D712yes—
458#117C22×D712yes—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—141no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—141no—
465C2×C22⋊C4C22⋊D712yes—
466C2×C42—24no—
467C2×C42—21no—
468C2×C42—141no—
469C2×C42C22⋊D712yes—
470#104—148no—
471#103—148no—
472#99—148no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7#38611yescharacteristic
481C22×C7#38611yescharacteristic
482C22×C7#38611yescharacteristic
483C22×C7#38611yescharacteristic
484C22×C7C2×C4×D411yescharacteristic
485C22×C7C2×#12011yescharacteristic
486C22×C7C2×#12111yescharacteristic
487C2×D7—42no—
488C2×D7—82no—
489C2×D7—82no—
490C2×D7—82no—
491C4×C7—28no—
492C4×C7—44no—
493C4×C7—44no—
494C4×C7#38611yescharacteristic
495C4×C7#38611yescharacteristic
496C4×C7#38611yescharacteristic
497C4×C7#38611yescharacteristic
498C4×C7C22×C22⋊C411yescharacteristic
499C4×C7C2×C4×D411yescharacteristic
500C4×C7C2×#12111yescharacteristic
501C4×C7C2×#12311yescharacteristic
502Dic7—42no—
503Dic7—82no—
504C24—141no—
505C24C2×C22⋊D711yescharacteristic
506#41—142no—
507#41—142no—
508#41—142no—
509#41—142no—
510#41—142no—
511#41—142no—
512#41—142no—
513#41—142no—
514#41—281no—
515#41—281no—
516#41—281no—
517#41—281no—
518#41—281no—
519#41—281no—
520#41—281no—
521#41—281no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—72no—
544C2×Q8—141no—
545C2×Q8—141no—
546C2×Q8—141no—
547C2×Q8—141no—
548C2×Q8—141no—
549C2×Q8(C2×D7)⋊C414yes—
550C2×Q8(C2×D7)⋊C414yes—
551C2×Q8(C2×D7)⋊C414yes—
552C2×Q8(C2×D7)⋊C414yes—
553C2×Q8C2×C4×D714yes—
554C2×Q8C2×D2814yes—
555C2×Q8C2×C22⋊D714yes—
556C2×D4—72no—
557C2×D4—142no—
558C2×D4—142no—
559C2×D4—141no—
560C2×D4—141no—
561C2×D4—141no—
562C2×D4—141no—
563C2×D4—141no—
564C2×D4—281no—
565C2×D4—281no—
566C2×D4—281no—
567C2×D4—281no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—141no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—281no—
581C22×C4—281no—
582C22×C4—281no—
583C22×C4—281no—
584C22×C4—281no—
585C22×C4C2×C4×D711yescharacteristic
586C22×C4C2×C4×D711yescharacteristic
587C22×C4C2×D2811yescharacteristic
588C22×C4C2×D2811yescharacteristic
589C22×C4#115711yescharacteristic
590C22×C4#115711yescharacteristic
591C22×C4#115711yescharacteristic
592C22×C4#115711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C2×C22⋊D711yescharacteristic
595C22×C4C2×C22⋊D711yescharacteristic
596C22×C4C2×C22⋊D711yescharacteristic
597C22×C4C2×C22⋊D711yescharacteristic
598C22×C4C23×D711yescharacteristic
599Q16—1416no—
600SD16—1416no—
601M16—142no—
602M16—142no—
603M16—142no—
604M16—142no—
605M16—142no—
606M16—142no—
607M16—281no—
608M16—281no—
609C2×C8—74no—
610C2×C8—142no—
611C2×C8—142no—
612C2×C8—142no—
613C2×C8—281no—
614C2×C8—281no—
615C4⋊C4—216no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—142no—
621C4⋊C4—281no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—142no—
626C22⋊C4—281no—
627C22⋊C4C2×C22⋊D714yes—
628C42—216no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—142no—
633C42—281no—
634C42C2×C22⋊D714yes—
635C2×C7—21no—
636C2×C7—21no—
637C2×C7—21no—
638C2×C7—21no—
639C2×C7—21no—
640C2×C7—21no—
641C2×C7#190512yescomplemented
642C2×C7C2×#38611yescharacteristic
643D7—82no—
644C23—42no—
645C23—142no—
646C23—281no—
647C23—281no—
648C23—562no—
649C23C4×C22⋊D711yescharacteristic
650C23C4×C22⋊D711yescharacteristic
651C23#649311yescharacteristic
652C23#649311yescharacteristic
653C23#651611yescharacteristic
654C23#651611yescharacteristic
655C23C22×C22⋊D711yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—142no—
664Q8—142no—
665Q8—281no—
666Q8—281no—
667Q8C2×(C2×D7)⋊C418yes—
668D4—142no—
669D4—142no—
670D4—282no—
671D4—282no—
672D4—282no—
673D4—282no—
674D4—281no—
675D4—281no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—142no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—562no—
696C2×C4C2×(C2×D7)⋊C411yescharacteristic
697C2×C4C2×(C2×D7)⋊C411yescharacteristic
698C2×C4C2×(C2×D7)⋊C411yescharacteristic
699C2×C4C2×(C2×D7)⋊C411yescharacteristic
700C2×C4C4×C22⋊D711yescharacteristic
701C2×C4C4×C22⋊D711yescharacteristic
702C2×C4C4×C22⋊D711yescharacteristic
703C2×C4C4×C22⋊D711yescharacteristic
704C2×C4C4×C22⋊D711yescharacteristic
705C2×C4C4×C22⋊D711yescharacteristic
706C2×C4#649211yescharacteristic
707C2×C4#649211yescharacteristic
708C2×C4#649211yescharacteristic
709C2×C4#649211yescharacteristic
710C2×C4#649311yescharacteristic
711C2×C4#649311yescharacteristic
712C2×C4#649311yescharacteristic
713C2×C4#649311yescharacteristic
714C2×C4#649311yescharacteristic
715C2×C4#649311yescharacteristic
716C2×C4#651611yescharacteristic
717C2×C4#651611yescharacteristic
718C2×C4C22×C4×D711yescharacteristic
719C2×C4C22×D2811yescharacteristic
720C2×C4C2×#115711yescharacteristic
721C2×C4C2×#115711yescharacteristic
722C2×C4C22×C22⋊D711yescharacteristic
723C2×C4C22×C22⋊D711yescharacteristic
724C8—144no—
725C8—282no—
726C7C2×#190511yescharacteristic, complemented, Sylow
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—282no—
735C22—562no—
736C22—562no—
737C22—562no—
738C22#8998511yescharacteristic
739C22#8998511yescharacteristic
740C22#8998511yescharacteristic
741C22#8998511yescharacteristic
742C22C2×C4×C22⋊D711yescharacteristic
743C22C2×#649311yescharacteristic
744C22C2×#651611yescharacteristic
745C4—28no—
746C4—44no—
747C4—44no—
748C4—282no—
749C4—562no—
750C4#8998511yescharacteristic
751C4#8998511yescharacteristic
752C4#8998511yescharacteristic
753C4#8998511yescharacteristic
754C4C22×(C2×D7)⋊C411yescharacteristic
755C4C2×C4×C22⋊D711yescharacteristic
756C4C2×#649211yescharacteristic
757C4C2×#649311yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—562no—
765C2#1172941612yesdirect product factor
766C2C2×#8998511yescharacteristic
subgroupG/H
centerC22#89985
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#519C2
socleC22×C7#386
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenterC2×#519D7
hypocenterC7C2×#1905
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. C2×C7×#519C2semidirect
3. C2×#89997C2semidirect
6. #11729416C2direct (N × H)
7. C2×#89328C2semidirect
8. C2×#89326C2semidirect
14. C7×#519C22semidirect
20. C22×#1144C4semidirect
25. C2×#6505C4semidirect
27. C22×#1143C4semidirect
32. #89997C22semidirect
40. #89328C22semidirect
41. #89326C22semidirect
100. C2×#1144C2×C4semidirect
107. C2×#1143C2×C4semidirect
132. C2×#519D7semidirect
285. #519C2×D7semidirect
641. C2×C7#1905semidirect
726. C7C2×#1905semidirect
765. C2#11729416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5192
C22×#65052
C2×#899972
C2×#897782
C2×#897772
#117294162
C2×#893282
C2×#893262
C2×#19057