Finite Group Databasebeta

← #13374192

Subgroups — #13374192

Order 1792.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#449C211yesmaximal, characteristic
2#11741534C211yesmaximal, characteristic, complemented
3C2×#90004C211yesmaximal, characteristic, complemented
4C2×#89936C211yesmaximal, characteristic, complemented
5#11740081C211yesmaximal, characteristic, complemented
6#11729802C211yesmaximal, characteristic, complemented
7#11729792C211yesmaximal, characteristic, complemented
8#11729791C211yesmaximal, characteristic, complemented
9#11729436C211yesmaximal, characteristic, complemented
10#11727990C211yesmaximal, characteristic, complemented
11Dic7×#103C211yesmaximal, characteristic, complemented
12#11727941C211yesmaximal, characteristic, complemented
13#11727909C211yesmaximal, characteristic, complemented
14#11727703C211yesmaximal, characteristic, complemented
15#11727681C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C2×D4×Dic7—21no—
23C2×D4×Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26C7×#449C418yescomplemented
27C2×C7×#103C2211yescharacteristic
28C2×C7×#102C2211yescharacteristic
29C2×C7×C22⋊C8C2211yescharacteristic
30#90004—24no—
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33#89993—21no—
34#89993—21no—
35#89993C2211yescharacteristic
36#89993C2211yescharacteristic
37#89993C2211yescharacteristic
38#89992—21no—
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41C2×#6406C2211yescharacteristic
42C2×#6406C2211yescharacteristic
43#89984—21no—
44#89984C2211yescharacteristic
45C4×C22⋊Dic7—21no—
46C4×C22⋊Dic7C2211yescharacteristic
47#89936—24no—
48C2×#6392C2211yescharacteristic
49C2×#6392C2211yescharacteristic
50C2×#6389C2211yescharacteristic
51C2×C8×Dic7C2211yescharacteristic
52#89757C2211yescharacteristic
53C4⋊C4×Dic7C2211yescharacteristic
54#89723—21no—
55#89722—21no—
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22863—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41C2×C414yescomplemented
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4—21no—
72C22×C7×D4C2311yescharacteristic
73C22×C7×D4C2311yescharacteristic
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C23×Dic7—21no—
77C23×Dic7—21no—
78C2×C7×SD16—22no—
79C2×C7×SD16—22no—
80C2×C7×SD16C2×C414yescomplemented
81C2×C7×D8—41no—
82C2×C7×D8—41no—
83C2×C7×D8C2×C414yescomplemented
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×#121—22no—
87C7×#121C2×C414yes—
88C2×C7×C4⋊C4C2311yescharacteristic
89C2×C7×C22⋊C4—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94C2×C22⋊Dic7—21no—
95C2×C22⋊Dic7—21no—
96C2×C22⋊Dic7—21no—
97C2×C22⋊Dic7—21no—
98C2×C22⋊Dic7D411yescharacteristic
99C2×C22⋊Dic7D411yescharacteristic
100Q8×Dic7—22no—
101Q8×Dic7—22no—
102Q8×Dic7—41no—
103Q8×Dic7—41no—
104D4×Dic7—22no—
105D4×Dic7—41no—
106D4×Dic7—44no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—21no—
109C2×C4⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4×Dic7—21no—
118C2×C4×Dic7—21no—
119C2×C4×Dic7—21no—
120C2×C4×Dic7C2311yescharacteristic
121C2×C4×Dic7C2311yescharacteristic
122C2×#1136—22no—
123C2×#1136—22no—
124C2×#1136—41no—
125C22×C7⋊C8C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C7×#103C2×C414yescomplemented
128C7×#102C2×C414yescomplemented
129C7×C22⋊C8C2×C414yescomplemented
130#6409—22no—
131#6409D414yescomplemented
132#6406—22no—
133#6406—22no—
134#6406—22no—
135#6406—41no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139C7⋊#95D411yescharacteristic
140C7⋊#95D411yescharacteristic
141#6392—22no—
142#6392—41no—
143#6389—22no—
144C8×Dic7—41no—
145C2×#449D711yescharacteristic
146C2×#440—71no—
147C2×#417—71no—
148#2361—71no—
149#2341—71no—
150#1970—71no—
151#1936—71no—
152#1925—71no—
153#1895—71no—
154#1880—71no—
155#1879—71no—
156#1863—71no—
157#1852—71no—
158C4×#103—71no—
159#1753—71no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7C2×D411yescharacteristic
163C7×#41—28no—
164C7×#41—44no—
165C7×#41—44no—
166C7×#41—44no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8C22×C412yes—
171C2×C7×Q8C2×D412yes—
172C2×C7×Q8#4112yes—
173C2×C7×D4—24no—
174C2×C7×D4—24no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—42no—
186C2×C7×D4—42no—
187C2×C7×D4—42no—
188C2×C7×D4—42no—
189C2×C7×D4C22×C412yes—
190C2×C7×D4C22×C412yes—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—24no—
198C22×C4×C7—42no—
199C22×C4×C7—42no—
200C22×C4×C7C22×C412yes—
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7#4112yes—
203C22×C4×C7C2411yescharacteristic
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—42no—
209C22×Dic7—42no—
210C22×Dic7—42no—
211C22×Dic7—42no—
212C22×Dic7—81no—
213C22×Dic7—81no—
214C22×Dic7C2×D411yescharacteristic
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C22×Dic7C2×D411yescharacteristic
218C7×SD16—28no—
219C7×D8—44no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8C22×C412yes—
225C2×C7×C8C22×C412yes—
226C7×C4⋊C4—21no—
227C7×C4⋊C4C22×C412yes—
228C7×C22⋊C4—24no—
229C22⋊Dic7—22no—
230C22⋊Dic7—41no—
231C22⋊Dic7—42no—
232C22⋊Dic7—42no—
233C22⋊Dic7—42no—
234C22⋊Dic7—42no—
235C22⋊Dic7—81no—
236C22⋊Dic7—81no—
237C22⋊Dic7—81no—
238C22⋊Dic7—81no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—42no—
247C4⋊Dic7—42no—
248C4⋊Dic7—42no—
249C4⋊Dic7—42no—
250C4⋊Dic7C2×D412yes—
251C4×Dic7—21no—
252C4×Dic7—21no—
253C4×Dic7—21no—
254C4×Dic7—21no—
255C4×Dic7—42no—
256C4×Dic7—42no—
257C4×Dic7—42no—
258#1136—44no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—21no—
262C2×C7⋊C8—21no—
263C2×C7⋊C8—21no—
264C2×C7⋊C8C2×D412yes—
265C22×#41C2×D711yescharacteristic
266C22×SD16C2×D711yescharacteristic
267C22×D8C2×D711yescharacteristic
268C22×M16—71no—
269C2×#121C2×D711yescharacteristic
270C2×C4×Q8—71no—
271C2×C4×Q8—71no—
272C2×C4×D4—71no—
273C2×C4×D4—141no—
274C22×C4⋊C4—71no—
275#449Dic718yescomplemented
276#440—144no—
277C2×#107—71no—
278C2×#107—71no—
279#417—144no—
280C2×#103—71no—
281C2×#103—71no—
282C2×#103C2×D711yescharacteristic
283C2×#102—71no—
284C2×#102—71no—
285C2×#102—71no—
286C2×#102—71no—
287C2×#102C2×D711yescharacteristic
288C2×C22⋊C8C2×D711yescharacteristic
289C2×#97—71no—
290C2×C4×C8—71no—
291#390—71no—
292#390—71no—
293#390—71no—
294#390—141no—
295#390—141no—
296#389—71no—
297#388—141no—
298#386—141no—
299#385—141no—
300#380—71no—
301#380—141no—
302C4×C4⋊C4—71no—
303C4×C22⋊C4—71no—
304C4×C22⋊C4—141no—
305#340—71no—
306#340—71no—
307#340—71no—
308#340—71no—
309#336—71no—
310#336—71no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7C4×D412yes—
332C23×C7C22×D411yescharacteristic
333C7×Q8—22no—
334C7×Q8—22no—
335C7×Q8—22no—
336C7×Q8C4×D414yescomplemented
337C7×D4—22no—
338C7×D4—22no—
339C7×D4—22no—
340C7×D4—22no—
341C7×D4—48no—
342C7×D4—48no—
343C7×D4—41no—
344C7×D4—41no—
345C7×D4—41no—
346C7×D4—41no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—21no—
350C2×C4×C7—22no—
351C2×C4×C7—21no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—48no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7C4×D412yes—
361C2×C4×C7C23×C411yescharacteristic
362C2×C4×C7C22×D411yescharacteristic
363C2×C4×C7C2×#4111yescharacteristic
364C2×C4×C7C2×#4111yescharacteristic
365C2×C4×C7H(5,𝔽2)11yescharacteristic
366C2×C4×C7H(5,𝔽2)11yescharacteristic
367C2×Dic7—21no—
368C2×Dic7—21no—
369C2×Dic7—21no—
370C2×Dic7—21no—
371C2×Dic7—22no—
372C2×Dic7—21no—
373C2×Dic7—21no—
374C2×Dic7—21no—
375C2×Dic7—21no—
376C2×Dic7—21no—
377C2×Dic7—21no—
378C2×Dic7—21no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—41no—
388C2×Dic7—41no—
389C2×Dic7—41no—
390C2×Dic7—84no—
391C2×Dic7—84no—
392C2×Dic7AGL(1,ℤ/8)12yes—
393C7×C8—22no—
394C7×C8—22no—
395C7⋊C8—22no—
396C7⋊C8—41no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—41no—
401C2×#41—41no—
402C2×#41C2×Dic714yescomplemented
403C22×Q8C22×D711yescharacteristic
404C22×D4—21no—
405C22×D4—21no—
406C22×D4C22×D711yescharacteristic
407C22×D4C22×D711yescharacteristic
408C23×C4—21no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C2×SD16—22no—
413C2×SD16—22no—
414C2×SD16C2×Dic714yescomplemented
415C2×D8—41no—
416C2×D8—41no—
417C2×D8C2×Dic714yescomplemented
418C2×M16—142no—
419C2×M16—142no—
420C2×M16—281no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8C22×D711yescharacteristic
424C22×C8C22×D711yescharacteristic
425#121—22no—
426#121C2×Dic714yes—
427C4×Q8—142no—
428C4×Q8—142no—
429C4×Q8—281no—
430C4×Q8—281no—
431C4×D4—142no—
432C4×D4—281no—
433C4×D4—284no—
434C2×C4⋊C4—71no—
435C2×C4⋊C4—71no—
436C2×C4⋊C4—71no—
437C2×C4⋊C4—71no—
438C2×C4⋊C4—142no—
439C2×C4⋊C4—141no—
440C2×C4⋊C4—141no—
441C2×C4⋊C4—141no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—281no—
444C2×C4⋊C4C22×D711yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—71no—
447C2×C22⋊C4—71no—
448C2×C22⋊C4—141no—
449C2×C22⋊C4—141no—
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C42—71no—
457C2×C42—71no—
458C2×C42—141no—
459C2×C42—141no—
460C2×C42—141no—
461#107—142no—
462#107—281no—
463#103—74no—
464#103—142no—
465#103C2×Dic714yescomplemented
466#102—142no—
467#102—142no—
468#102—142no—
469#102—281no—
470#102C2×Dic714yescomplemented
471C22⋊C8C2×Dic714yescomplemented
472#97—142no—
473C4×C8—281no—
474#95—71no—
475#95—71no—
476#95—141no—
477#95—141no—
478#95—141no—
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—42no—
492C22×C7—81no—
493C22×C7—81no—
494C22×C7—81no—
495C22×C7—81no—
496C22×C7—81no—
497C22×C7—81no—
498C22×C7—81no—
499C22×C7—81no—
500C22×C7C2×C4×D411yescharacteristic
501C22×C7D4211yescharacteristic
502C22×C7#54611yescharacteristic
503C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
504C22×C7#57511yescharacteristic
505C22×C7#57611yescharacteristic
506C22×C7#57811yescharacteristic
507C4×C7—22no—
508C4×C7—24no—
509C4×C7—42no—
510C4×C7C2×C4×D411yescharacteristic
511C4×C7#51811yescharacteristic
512C4×C7#54611yescharacteristic
513C4×C7#55111yescharacteristic
514Dic7—22no—
515Dic7—41no—
516Dic7—42no—
517Dic7—41no—
518Dic7—41no—
519Dic7—81no—
520Dic7—81no—
521Dic7—81no—
522C24—21no—
523C24—21no—
524C24D4×D711yescharacteristic
525#41—28no—
526#41—44no—
527#41—44no—
528#41—44no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8D4×D712yes—
533C2×Q8#115912yes—
534C2×Q8C22×Dic712yes—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4C22×Dic712yes—
552C2×D4C22×Dic712yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—71no—
563C22×C4—71no—
564C22×C4—71no—
565C22×C4—71no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—141no—
569C22×C4—141no—
570C22×C4—282no—
571C22×C4—282no—
572C22×C4—282no—
573C22×C4—282no—
574C22×C4—561no—
575C22×C4—561no—
576C22×C4D4×D711yescharacteristic
577C22×C4#115912yes—
578C22×C4C22×Dic712yes—
579C22×C4C23×D711yescharacteristic
580SD16—28no—
581D8—44no—
582M16—284no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—72no—
588C2×C8—141no—
589C2×C8—141no—
590C2×C8—141no—
591C2×C8—141no—
592C2×C8—141no—
593C2×C8C22×Dic712yes—
594C2×C8C22×Dic712yes—
595C4⋊C4—21no—
596C4⋊C4—72no—
597C4⋊C4—141no—
598C4⋊C4—141no—
599C4⋊C4—141no—
600C4⋊C4—141no—
601C4⋊C4—141no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—282no—
605C4⋊C4—282no—
606C4⋊C4—282no—
607C4⋊C4—282no—
608C4⋊C4C22×Dic712yes—
609C22⋊C4—24no—
610C22⋊C4—142no—
611C22⋊C4—282no—
612C22⋊C4—282no—
613C22⋊C4—281no—
614C22⋊C4—282no—
615C22⋊C4—282no—
616C22⋊C4—561no—
617C22⋊C4—561no—
618C22⋊C4—561no—
619C22⋊C4—561no—
620C42—141no—
621C42—141no—
622C42—141no—
623C42—141no—
624C42—282no—
625C42—282no—
626C42—282no—
627C2×C7—42no—
628C2×C7—82no—
629C2×C7—82no—
630C2×C7#235811yescharacteristic
631C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
632C2×C7#295111yescharacteristic
633C2×C7#327411yescharacteristic
634C2×C7#327711yescharacteristic
635C2×C7#330811yescharacteristic
636C2×C7#330911yescharacteristic
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23D4×Dic712yes—
658C23C2×D4×D711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8D4×Dic714yescomplemented
663D4—22no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—72no—
687C2×C4—141no—
688C2×C4—141no—
689C2×C4—141no—
690C2×C4—141no—
691C2×C4—141no—
692C2×C4—141no—
693C2×C4—141no—
694C2×C4—141no—
695C2×C4—141no—
696C2×C4—141no—
697C2×C4—142no—
698C2×C4—141no—
699C2×C4—281no—
700C2×C4—281no—
701C2×C4—281no—
702C2×C4—281no—
703C2×C4—281no—
704C2×C4—281no—
705C2×C4—281no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—281no—
709C2×C4—281no—
710C2×C4—564no—
711C2×C4—564no—
712C2×C4D4×Dic712yes—
713C2×C4C2×D4×D711yescharacteristic
714C2×C4C2×#115911yescharacteristic
715C2×C4C2×#115911yescharacteristic
716C2×C4#654811yescharacteristic
717C2×C4#654811yescharacteristic
718C2×C4C23×Dic711yescharacteristic
719C8—22no—
720C8—22no—
721C8—142no—
722C8—281no—
723C7#2286311yescharacteristic, complemented, Sylow
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#9028111yescharacteristic
746C22#9028211yescharacteristic
747C22#9046011yescharacteristic
748C22#9046211yescharacteristic
749C22D7×AGL(1,ℤ/8)11yescharacteristic
750C22#9046411yescharacteristic
751C22C2×D4×Dic711yescharacteristic
752C4—22no—
753C4—24no—
754C4—42no—
755C4—142no—
756C4—281no—
757C4—281no—
758C4—281no—
759C4—282no—
760C4—561no—
761C4—561no—
762C4—561no—
763C4#9027811yescharacteristic
764C4#9028211yescharacteristic
765C4C2×D4×Dic711yescharacteristic
766C4#9048911yescharacteristic
767C2—42no—
768C2—82no—
769C2—82no—
770C2#1173754511yescharacteristic
771C2#1173755411yescharacteristic
772C2#1173755611yescharacteristic
773C2#1173757011yescharacteristic
774C2#1174002411yescharacteristic
775C2#1174134311yescharacteristic
776C2Dic7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#449C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#449D7
hypocenterC7#22863
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
2. #11741534C2semidirect
3. C2×#90004C2semidirect
4. C2×#89936C2semidirect
5. #11740081C2semidirect
6. #11729802C2semidirect
7. #11729792C2semidirect
8. #11729791C2semidirect
9. #11729436C2semidirect
10. #11727990C2semidirect
11. Dic7×#103C2semidirect
12. #11727941C2semidirect
13. #11727909C2semidirect
14. #11727703C2semidirect
15. #11727681C2semidirect
26. C7×#449C4semidirect
68. C2×C7×#41C2×C4semidirect
80. C2×C7×SD16C2×C4semidirect
83. C2×C7×D8C2×C4semidirect
127. C7×#103C2×C4semidirect
128. C7×#102C2×C4semidirect
129. C7×C22⋊C8C2×C4semidirect
131. #6409D4semidirect
275. #449Dic7semidirect
336. C7×Q8C4×D4semidirect
402. C2×#41C2×Dic7semidirect
414. C2×SD16C2×Dic7semidirect
417. C2×D8C2×Dic7semidirect
465. #103C2×Dic7semidirect
470. #102C2×Dic7semidirect
471. C22⋊C8C2×Dic7semidirect
662. Q8D4×Dic7semidirect
723. C7#22863semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4492
#117415342
C2×#900042
C2×#899362
#117400812
#117298022
#117297922
#117297912
#117294362
#117279902
Dic7×#1032
#117279412
#117279092
#117277032
#117276812
#228637