Finite Group Databasebeta

← C7×#62793 #13240009

Subgroups — C7×#62793 #13240009

Order 1792.

7190 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3524C218yesmaximal, complemented
2C7×#3518C214yesmaximal, complemented
3C7×#3517C214yesmaximal, complemented
4C7×#3506C216yesmaximal, complemented
5C7×#3502C211yesmaximal, characteristic, complemented
6C7×#3497C211yesmaximal, characteristic, complemented
7C7×#3493C216yesmaximal, complemented
8C7×#3487C212yesmaximal, complemented
9C7×#3483C214yesmaximal, complemented
10C7×#3482C214yesmaximal, complemented
11C7×#3480C218yesmaximal, complemented
12C7×#3460C216yesmaximal, complemented
13C7×#3444C216yesmaximal, complemented
14C4×C7×2−1+4C212yesmaximal, complemented
15C2×C4×C7×#41C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2212yes—
17C22×C7×#41C2211yescharacteristic
18C7×#559C22124yescomplemented
19C7×Q82C2214yescomplemented
20C7×#557C2218yescomplemented
21C7×#557C2214yescomplemented
22C7×#556C22124yescomplemented
23C7×#556C22112yescomplemented
24C7×#555C22124yescomplemented
25C7×#555C22112yescomplemented
26C7×#553C22124yescomplemented
27C7×#553C22124yescomplemented
28C7×#552C22124yescomplemented
29C7×#550C2218yes—
30C7×#550C2218yes—
31C7×#550C2214yescomplemented
32C7×#550C22112yescomplemented
33C7×D4×Q8C2214yescomplemented
34C7×#548C2218yes—
35C7×#548C2218yes—
36C7×#548C2218yescomplemented
37C7×#547C22112yescomplemented
38C7×#544C2216yes—
39C7×#542C22124yescomplemented
40C7×#540C22124yescomplemented
41C7×#538C22124yes—
42C7×#537C2216yes—
43C7×#535C22112yes—
44C7×#533C2216yes—
45C7×#533C2216yescomplemented
46C7×#533C2216yescomplemented
47C7×#532C2216yes—
48C7×#532C2216yescomplemented
49C7×#532C2216yescomplemented
50C7×#532C22124yescomplemented
51C7×#529C2214yes—
52C7×#529C22112yes—
53C7×#529C22112yescomplemented
54C7×#529C22112yescomplemented
55C7×#529C22112yescomplemented
56C7×#529C22112yescomplemented
57C7×#529C22124yescomplemented
58C7×#525C22112yes—
59C7×#525C22112yes—
60C7×#525C22112yes—
61C7×#520C22112yes—
62C7×#520C2218yescomplemented
63C7×#519C2212yes—
64C7×#519C2218yescomplemented
65C4×C7×#41C2214yes—
66C4×C7×#41C2214yes—
67C4×C7×#41C2214yes—
68C4×C7×#41C2214yes—
69C4×C7×#41C22112yes—
70C4×C7×#41C2218yescomplemented
71C4×C7×#41C22112yescomplemented
72C4×C7×#41C22112yescomplemented
73C2×C4×C7×Q8C2211yescharacteristic
74C2×C4×C7×Q8C2211yescharacteristic
75C2×C4×C7×Q8C2218yescomplemented
76C2×C4×C7×D4C2213yes—
77C2×C4×C7×D4C2213yes—
78C2×C7×#117C2213yes—
79C22×C42×C7C2213yes—
80#62793C711yesmaximal, characteristic, direct product factor, Sylow
81C7×2−1+4—216no—
82C2×C7×#41—28no—
83C2×C7×#41C2314yes—
84C2×C7×#41C2314yes—
85C2×C7×#41C23112yes—
86C2×C7×#41C2318yes—
87C2×C7×#41C23112yes—
88C2×C7×#41C23112yes—
89C22×C7×Q8C2318yes—
90C22×C7×Q8C2311yescharacteristic
91C22×C7×D4C2313yes—
92C23×C4×C7C2313yes—
93C23×C4×C7C2313yes—
94C23×C4×C7C2313yes—
95C7×C4⋊Q8C2316yes—
96C7×C4⋊Q8C2316yes—
97C7×C4⋊Q8C2316yes—
98C7×C4⋊Q8C23124yes—
99C7×#127C2316yes—
100C7×#127C23124yes—
101C7×#126C2318yes—
102C7×#126C23124yes—
103C7×#126C23148yes—
104C7×#125C2314yes—
105C7×#125C23112yes—
106C7×#125C23112yes—
107C7×#125C23124yes—
108C7×#124C2314yes—
109C7×#124C23112yes—
110C7×#124C23112yes—
111C7×#124C23124yes—
112C7×#124C23148yes—
113C7×#123C2318yes—
114C7×#123C23124yes—
115C7×#123C23124yes—
116C7×#123C23148yes—
117C7×C22⋊Q8C2314yes—
118C7×C22⋊Q8C23112yes—
119C7×C22⋊Q8C23112yes—
120C7×C22⋊Q8C23112yes—
121C7×C22⋊Q8C23112yes—
122C7×C22⋊Q8C23112yes—
123C7×C22⋊Q8C23124yes—
124C7×#121C2314yes—
125C7×#121C23112yes—
126C7×#121C23112yes—
127C7×#121C23112yes—
128C7×#121C23112yes—
129C7×#121C23112yes—
130C7×#121C23124yes—
131C7×#121C23124yes—
132C7×#121C23124yes—
133C7×#121C23148yes—
134C7×#120C23124yes—
135C4×C7×Q8C2314yes—
136C4×C7×Q8C2314yes—
137C4×C7×Q8C2314yes—
138C4×C7×Q8C2314yes—
139C4×C7×Q8C23112yes—
140C4×C7×Q8C2318yes—
141C4×C7×Q8C23124yes—
142C4×C7×Q8C23112yes—
143C4×C7×Q8C2314yes—
144C4×C7×Q8C2318yes—
145C4×C7×Q8C23112yes—
146C4×C7×Q8C23112yes—
147C4×C7×Q8C23112yes—
148C4×C7×D4C23112yes—
149C4×C7×D4C23112yes—
150C4×C7×D4C23112yes—
151C4×C7×D4C23112yes—
152C4×C7×D4C2318yes—
153C4×C7×D4C23112yes—
154C4×C7×D4C23124yes—
155C4×C7×D4C23112yes—
156C4×C7×D4C2314yes—
157C4×C7×D4C23124yes—
158C4×C7×D4C23124yes—
159C4×C7×D4C23124yes—
160C4×C7×D4C23124yes—
161C4×C7×D4C23124yes—
162C4×C7×D4C23112yes—
163C4×C7×D4C23112yes—
164C4×C7×D4C23112yes—
165C7×#117C23112yes—
166C7×#117C23112yes—
167C7×#117C23112yes—
168C7×#117C23124yes—
169C7×#117C2318yes—
170C7×#117C23124yes—
171C7×#117C23112yes—
172C7×#117C23112yes—
173C7×#117C23124yes—
174C2×C7×C4⋊C4C2313yes—
175C2×C7×C4⋊C4C2313yes—
176C2×C7×C4⋊C4C23124yes—
177C2×C7×C22⋊C4C2316yes—
178C2×C42×C7C2311yescharacteristic
179C2×C42×C7C2313yes—
180C2×C42×C7C2313yes—
181C2×C42×C7C2313yes—
182C2×C42×C7C2316yes—
183C2×C42×C7C2316yes—
184C2×C42×C7C2316yes—
185C2×C42×C7C2316yes—
186C2×C42×C7C23124yes—
187#3524C2×C718yescomplemented
188#3518C2×C714yescomplemented
189#3517C2×C714yescomplemented
190#3506C2×C716yescomplemented
191#3502C2×C711yescharacteristic, complemented
192#3497C2×C711yescharacteristic, complemented
193#3493C2×C716yescomplemented
194#3487C2×C712yescomplemented
195#3483C2×C714yescomplemented
196#3482C2×C714yescomplemented
197#3480C2×C718yescomplemented
198#3460C2×C716yescomplemented
199#3444C2×C716yescomplemented
200C4×2−1+4C2×C712yescomplemented
201C2×C4×#41C2×C711yescharacteristic, complemented
202C24×C7C2413yes—
203C7×#41—216no—
204C7×#41—216no—
205C7×#41—232no—
206C7×#41—248no—
207C7×#41—424no—
208C7×#41—424no—
209C2×C7×Q8—232no—
210C2×C7×Q8#4118yescomplemented
211C2×C7×Q8C24112yes—
212C2×C7×Q8C2414yes—
213C2×C7×Q8C24112yes—
214C2×C7×Q8C2414yes—
215C2×C7×D4—212no—
216C2×C7×D4C2418yes—
217C2×C7×D4C24112yes—
218C2×C7×D4C24112yes—
219C2×C7×D4C2414yes—
220C2×C7×D4C24124yes—
221C2×C7×D4C24124yes—
222C2×C7×D4C24112yes—
223C22×C4×C7—212no—
224C22×C4×C7—46no—
225C22×C4×C7—46no—
226C22×C4×C7C2411yescharacteristic
227C22×C4×C7C2411yescharacteristic
228C22×C4×C7C2416yes—
229C22×C4×C7C2416yes—
230C22×C4×C7C2416yes—
231C22×C4×C7C24124yes—
232C22×C4×C7C2411yescharacteristic
233C22×C4×C7C2418yes—
234C22×C4×C7C2416yes—
235C22×C4×C7C2413yes—
236C22×C4×C7C2413yes—
237C22×C4×C7C2416yes—
238C22×C4×C7C2416yes—
239C22×C4×C7C24124yes—
240C22×C4×C7C2413yes—
241C7×C4⋊C4C24112yes—
242C7×C4⋊C4C24112yes—
243C7×C4⋊C4C24124yes—
244C7×C4⋊C4C24112yes—
245C7×C4⋊C4C2414yes—
246C7×C4⋊C4C2418yes—
247C7×C4⋊C4C24112yes—
248C7×C4⋊C4C2414yes—
249C7×C4⋊C4C2418yes—
250C7×C4⋊C4C2418yes—
251C7×C4⋊C4C2418yes—
252C7×C4⋊C4C24124yes—
253C7×C4⋊C4C24112yes—
254C7×C4⋊C4C24112yes—
255C7×C22⋊C4C24124yes—
256C7×C22⋊C4C2418yes—
257C7×C22⋊C4C2418yes—
258C7×C22⋊C4C24124yes—
259C7×C22⋊C4C2418yes—
260C7×C22⋊C4C2418yes—
261C7×C22⋊C4C2418yes—
262C7×C22⋊C4C24124yes—
263C7×C22⋊C4C24124yes—
264C7×C22⋊C4C24124yes—
265C42×C7C2411yescharacteristic
266C42×C7C2411yescharacteristic
267C42×C7C2416yes—
268C42×C7C2416yes—
269C42×C7C2416yes—
270C42×C7C2416yes—
271C42×C7C2416yes—
272C42×C7C24124yes—
273C42×C7C24124yes—
274C42×C7C2411yescharacteristic
275C42×C7C2416yes—
276C42×C7C2411yescharacteristic
277C42×C7C2418yes—
278C2×2−1+4C22×C712yes—
279C22×#41C22×C711yescharacteristic
280#559C22×C7124yescomplemented
281Q82C22×C714yescomplemented
282#557C22×C718yescomplemented
283#557C22×C714yescomplemented
284#556C22×C7124yescomplemented
285#556C22×C7112yescomplemented
286#555C22×C7124yescomplemented
287#555C22×C7112yescomplemented
288#553C22×C7124yescomplemented
289#553C22×C7124yescomplemented
290#552C22×C7124yescomplemented
291#550C22×C718yes—
292#550C22×C718yes—
293#550C22×C714yescomplemented
294#550C22×C7112yescomplemented
295D4×Q8C22×C714yescomplemented
296#548C22×C718yes—
297#548C22×C718yes—
298#548C22×C718yescomplemented
299#547C22×C7112yescomplemented
300#544C22×C716yes—
301#542C22×C7124yescomplemented
302#540C22×C7124yescomplemented
303#538C22×C7124yes—
304#537C22×C716yes—
305#535C22×C7112yes—
306#533C22×C716yes—
307#533C22×C716yescomplemented
308#533C22×C716yescomplemented
309#532C22×C716yes—
310#532C22×C716yescomplemented
311#532C22×C716yescomplemented
312#532C22×C7124yescomplemented
313#529C22×C714yes—
314#529C22×C7112yes—
315#529C22×C7112yescomplemented
316#529C22×C7112yescomplemented
317#529C22×C7112yescomplemented
318#529C22×C7112yescomplemented
319#529C22×C7124yescomplemented
320#525C22×C7112yes—
321#525C22×C7112yes—
322#525C22×C7112yes—
323#520C22×C7112yes—
324#520C22×C718yescomplemented
325#519C22×C712yes—
326#519C22×C718yescomplemented
327C4×#41C22×C714yes—
328C4×#41C22×C714yes—
329C4×#41C22×C714yes—
330C4×#41C22×C714yes—
331C4×#41C22×C7112yes—
332C4×#41C22×C718yescomplemented
333C4×#41C22×C7112yescomplemented
334C4×#41C22×C7112yescomplemented
335C2×C4×Q8C22×C711yescharacteristic
336C2×C4×Q8C22×C711yescharacteristic
337C2×C4×Q8C22×C718yescomplemented
338C2×C4×D4C22×C713yes—
339C2×C4×D4C22×C713yes—
340C2×#117C22×C713yes—
341C22×C42C22×C713yes—
342C23×C7—26no—
343C23×C7—43no—
344C23×C7—43no—
345C23×C7C2516yes—
346C23×C7C2518yes—
347C23×C7C2511yescharacteristic
348C7×Q8—224no—
349C7×Q8—28no—
350C7×Q8—412no—
351C7×Q8C2×#41116yes—
352C7×D4—216no—
353C7×D4—224no—
354C7×D4—224no—
355C7×D4—28no—
356C7×D4—412no—
357C7×D4—424no—
358C7×D4—424no—
359C2×C4×C7—22no—
360C2×C4×C7—212no—
361C2×C4×C7—212no—
362C2×C4×C7—248no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—212no—
366C2×C4×C7—212no—
367C2×C4×C7—216no—
368C2×C4×C7—43no—
369C2×C4×C7—46no—
370C2×C4×C7—46no—
371C2×C4×C7—43no—
372C2×C4×C7—424no—
373C2×C4×C7C2×#41112yes—
374C2×C4×C7C2511yescharacteristic
375C2×C4×C7C2511yescharacteristic
376C2×C4×C7C2511yescharacteristic
377C2×C4×C7C2511yescharacteristic
378C2×C4×C7C2516yes—
379C2×C4×C7C2518yes—
380C2×C4×C7C2518yes—
381C2×C4×C7C2516yes—
382C2×C4×C7C2518yes—
383C2×C4×C7C2516yes—
384C2×C4×C7C2511yescharacteristic
385C2×C4×C7C2511yescharacteristic
3862−1+4—216no—
387C2×#41—28no—
388C2×#41C23×C714yes—
389C2×#41C23×C714yes—
390C2×#41C23×C7112yes—
391C2×#41C23×C718yes—
392C2×#41C23×C7112yes—
393C2×#41C23×C7112yes—
394C22×Q8C23×C718yes—
395C22×Q8C23×C711yescharacteristic
396C22×D4C23×C713yes—
397C23×C4C23×C713yes—
398C23×C4C23×C713yes—
399C23×C4C23×C713yes—
400C4⋊Q8C23×C716yes—
401C4⋊Q8C23×C716yes—
402C4⋊Q8C23×C716yes—
403C4⋊Q8C23×C7124yes—
404#127C23×C716yes—
405#127C23×C7124yes—
406#126C23×C718yes—
407#126C23×C7124yes—
408#126C23×C7148yes—
409#125C23×C714yes—
410#125C23×C7112yes—
411#125C23×C7112yes—
412#125C23×C7124yes—
413#124C23×C714yes—
414#124C23×C7112yes—
415#124C23×C7112yes—
416#124C23×C7124yes—
417#124C23×C7148yes—
418#123C23×C718yes—
419#123C23×C7124yes—
420#123C23×C7124yes—
421#123C23×C7148yes—
422C22⋊Q8C23×C714yes—
423C22⋊Q8C23×C7112yes—
424C22⋊Q8C23×C7112yes—
425C22⋊Q8C23×C7112yes—
426C22⋊Q8C23×C7112yes—
427C22⋊Q8C23×C7112yes—
428C22⋊Q8C23×C7124yes—
429#121C23×C714yes—
430#121C23×C7112yes—
431#121C23×C7112yes—
432#121C23×C7112yes—
433#121C23×C7112yes—
434#121C23×C7112yes—
435#121C23×C7124yes—
436#121C23×C7124yes—
437#121C23×C7124yes—
438#121C23×C7148yes—
439#120C23×C7124yes—
440C4×Q8C23×C714yes—
441C4×Q8C23×C714yes—
442C4×Q8C23×C714yes—
443C4×Q8C23×C714yes—
444C4×Q8C23×C7112yes—
445C4×Q8C23×C718yes—
446C4×Q8C23×C7124yes—
447C4×Q8C23×C7112yes—
448C4×Q8C23×C714yes—
449C4×Q8C23×C718yes—
450C4×Q8C23×C7112yes—
451C4×Q8C23×C7112yes—
452C4×Q8C23×C7112yes—
453C4×D4C23×C7112yes—
454C4×D4C23×C7112yes—
455C4×D4C23×C7112yes—
456C4×D4C23×C7112yes—
457C4×D4C23×C718yes—
458C4×D4C23×C7112yes—
459C4×D4C23×C7124yes—
460C4×D4C23×C7112yes—
461C4×D4C23×C714yes—
462C4×D4C23×C7124yes—
463C4×D4C23×C7124yes—
464C4×D4C23×C7124yes—
465C4×D4C23×C7124yes—
466C4×D4C23×C7124yes—
467C4×D4C23×C7112yes—
468C4×D4C23×C7112yes—
469C4×D4C23×C7112yes—
470#117C23×C7112yes—
471#117C23×C7112yes—
472#117C23×C7112yes—
473#117C23×C7124yes—
474#117C23×C718yes—
475#117C23×C7124yes—
476#117C23×C7112yes—
477#117C23×C7112yes—
478#117C23×C7124yes—
479C2×C4⋊C4C23×C713yes—
480C2×C4⋊C4C23×C713yes—
481C2×C4⋊C4C23×C7124yes—
482C2×C22⋊C4C23×C716yes—
483C2×C42C23×C713yes—
484C2×C42C23×C713yes—
485C2×C42C23×C713yes—
486C2×C42C23×C7124yes—
487C2×C42C23×C716yes—
488C2×C42C23×C716yes—
489C2×C42C23×C716yes—
490C2×C42C23×C716yes—
491C2×C42C23×C711yescharacteristic
492C22×C7—21no—
493C22×C7—21no—
494C22×C7—28no—
495C22×C7—26no—
496C22×C7—26no—
497C22×C7—26no—
498C22×C7—28no—
499C22×C7—28no—
500C22×C7—412no—
501C22×C7C22×#4112yes—
502C22×C7C2611yescharacteristic
503C4×C7—21no—
504C4×C7—21no—
505C4×C7—28no—
506C4×C7—21no—
507C4×C7—21no—
508C4×C7—26no—
509C4×C7—26no—
510C4×C7—28no—
511C4×C7—28no—
512C4×C7C22×#41112yes—
513C4×C7#58512yes—
514C4×C7#58512yes—
515C24C24×C713yes—
516#41—216no—
517#41—216no—
518#41—232no—
519#41—248no—
520#41—424no—
521#41—424no—
522C2×Q8—232no—
523C2×Q8C7×#4118yescomplemented
524C2×Q8C24×C7112yes—
525C2×Q8C24×C714yes—
526C2×Q8C24×C7112yes—
527C2×Q8C24×C714yes—
528C2×D4—212no—
529C2×D4C24×C718yes—
530C2×D4C24×C7112yes—
531C2×D4C24×C7112yes—
532C2×D4C24×C714yes—
533C2×D4C24×C7124yes—
534C2×D4C24×C7124yes—
535C2×D4C24×C7112yes—
536C22×C4—212no—
537C22×C4—46no—
538C22×C4—46no—
539C22×C4C24×C711yescharacteristic
540C22×C4C24×C711yescharacteristic
541C22×C4C24×C711yescharacteristic
542C22×C4C24×C718yes—
543C22×C4C24×C716yes—
544C22×C4C24×C716yes—
545C22×C4C24×C716yes—
546C22×C4C24×C716yes—
547C22×C4C24×C7124yes—
548C22×C4C24×C713yes—
549C22×C4C24×C713yes—
550C22×C4C24×C716yes—
551C22×C4C24×C716yes—
552C22×C4C24×C7124yes—
553C22×C4C24×C713yes—
554C4⋊C4C24×C7112yes—
555C4⋊C4C24×C7112yes—
556C4⋊C4C24×C7124yes—
557C4⋊C4C24×C7112yes—
558C4⋊C4C24×C714yes—
559C4⋊C4C24×C718yes—
560C4⋊C4C24×C7112yes—
561C4⋊C4C24×C714yes—
562C4⋊C4C24×C718yes—
563C4⋊C4C24×C718yes—
564C4⋊C4C24×C718yes—
565C4⋊C4C24×C7124yes—
566C4⋊C4C24×C7112yes—
567C4⋊C4C24×C7112yes—
568C22⋊C4C24×C7124yes—
569C22⋊C4C24×C718yes—
570C22⋊C4C24×C718yes—
571C22⋊C4C24×C7124yes—
572C22⋊C4C24×C718yes—
573C22⋊C4C24×C718yes—
574C22⋊C4C24×C718yes—
575C22⋊C4C24×C7124yes—
576C22⋊C4C24×C7124yes—
577C22⋊C4C24×C7124yes—
578C42C24×C711yescharacteristic
579C42C24×C716yes—
580C42C24×C711yescharacteristic
581C42C24×C711yescharacteristic
582C42C24×C711yescharacteristic
583C42C24×C716yes—
584C42C24×C716yes—
585C42C24×C718yes—
586C42C24×C716yes—
587C42C24×C716yes—
588C42C24×C716yes—
589C42C24×C7124yes—
590C42C24×C7124yes—
591C2×C7—22no—
592C2×C7—48no—
593C2×C7—46no—
594C2×C7C23×#4111yescharacteristic
595C2×C7C2×#58511yescharacteristic
596C2×C7C2×#58511yescharacteristic
597C23—26no—
598C23—43no—
599C23—43no—
600C23C25×C716yes—
601C23C25×C718yes—
602C23C25×C711yescharacteristic
603Q8—224no—
604Q8—28no—
605Q8—412no—
606Q8C2×C7×#41116yes—
607D4—216no—
608D4—224no—
609D4—224no—
610D4—28no—
611D4—412no—
612D4—424no—
613D4—424no—
614C2×C4—22no—
615C2×C4—212no—
616C2×C4—212no—
617C2×C4—248no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—212no—
621C2×C4—212no—
622C2×C4—216no—
623C2×C4—43no—
624C2×C4—46no—
625C2×C4—46no—
626C2×C4—43no—
627C2×C4—424no—
628C2×C4C2×C7×#41112yes—
629C2×C4C25×C711yescharacteristic
630C2×C4C25×C711yescharacteristic
631C2×C4C25×C711yescharacteristic
632C2×C4C25×C716yes—
633C2×C4C25×C711yescharacteristic
634C2×C4C25×C718yes—
635C2×C4C25×C718yes—
636C2×C4C25×C716yes—
637C2×C4C25×C718yes—
638C2×C4C25×C716yes—
639C2×C4C25×C711yescharacteristic
640C2×C4C25×C711yescharacteristic
641C7#6279311yescharacteristic, direct product factor, Sylow
642C22—21no—
643C22—21no—
644C22—28no—
645C22—26no—
646C22—26no—
647C22—26no—
648C22—28no—
649C22—28no—
650C22—412no—
651C22C22×C7×#4112yes—
652C22C26×C711yescharacteristic
653C4—21no—
654C4—21no—
655C4—28no—
656C4—21no—
657C4—21no—
658C4—26no—
659C4—26no—
660C4—28no—
661C4—28no—
662C4C22×C7×#41112yes—
663C4C7×#58512yes—
664C4C7×#58512yes—
665C2—22no—
666C2—46no—
667C2—48no—
668C2C23×C7×#4111yescharacteristic
669C2C2×C7×#58511yescharacteristic
670C2C2×C7×#58511yescharacteristic
subgroupG/H
centerC2×C4×C7C25
commutator, Frattini, cosocleC22C26×C7
socleC22×C7C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3524C2semidirect
2. C7×#3518C2semidirect
3. C7×#3517C2semidirect
4. C7×#3506C2semidirect
5. C7×#3502C2semidirect
6. C7×#3497C2semidirect
7. C7×#3493C2semidirect
8. C7×#3487C2semidirect
9. C7×#3483C2semidirect
10. C7×#3482C2semidirect
11. C7×#3480C2semidirect
12. C7×#3460C2semidirect
13. C7×#3444C2semidirect
14. C4×C7×2−1+4C2semidirect
15. C2×C4×C7×#41C2semidirect
18. C7×#559C22semidirect
19. C7×Q82C22semidirect
20. C7×#557C22semidirect
21. C7×#557C22semidirect
22. C7×#556C22semidirect
23. C7×#556C22semidirect
24. C7×#555C22semidirect
25. C7×#555C22semidirect
26. C7×#553C22semidirect
27. C7×#553C22semidirect
28. C7×#552C22semidirect
31. C7×#550C22semidirect
32. C7×#550C22semidirect
33. C7×D4×Q8C22semidirect
36. C7×#548C22semidirect
37. C7×#547C22semidirect
39. C7×#542C22semidirect
40. C7×#540C22semidirect
45. C7×#533C22semidirect
46. C7×#533C22semidirect
48. C7×#532C22semidirect
49. C7×#532C22semidirect
50. C7×#532C22semidirect
53. C7×#529C22semidirect
54. C7×#529C22semidirect
55. C7×#529C22semidirect
56. C7×#529C22semidirect
57. C7×#529C22semidirect
62. C7×#520C22semidirect
64. C7×#519C22semidirect
70. C4×C7×#41C22semidirect
71. C4×C7×#41C22semidirect
72. C4×C7×#41C22semidirect
75. C2×C4×C7×Q8C22semidirect
80. #62793C7direct (N × H)
187. #3524C2×C7semidirect
188. #3518C2×C7semidirect
189. #3517C2×C7semidirect
190. #3506C2×C7semidirect
191. #3502C2×C7semidirect
192. #3497C2×C7semidirect
193. #3493C2×C7semidirect
194. #3487C2×C7semidirect
195. #3483C2×C7semidirect
196. #3482C2×C7semidirect
197. #3480C2×C7semidirect
198. #3460C2×C7semidirect
199. #3444C2×C7semidirect
200. C4×2−1+4C2×C7semidirect
201. C2×C4×#41C2×C7semidirect
210. C2×C7×Q8#41semidirect
280. #559C22×C7semidirect
281. Q82C22×C7semidirect
282. #557C22×C7semidirect
283. #557C22×C7semidirect
284. #556C22×C7semidirect
285. #556C22×C7semidirect
286. #555C22×C7semidirect
287. #555C22×C7semidirect
288. #553C22×C7semidirect
289. #553C22×C7semidirect
290. #552C22×C7semidirect
293. #550C22×C7semidirect
294. #550C22×C7semidirect
295. D4×Q8C22×C7semidirect
298. #548C22×C7semidirect
299. #547C22×C7semidirect
301. #542C22×C7semidirect
302. #540C22×C7semidirect
307. #533C22×C7semidirect
308. #533C22×C7semidirect
310. #532C22×C7semidirect
311. #532C22×C7semidirect
312. #532C22×C7semidirect
315. #529C22×C7semidirect
316. #529C22×C7semidirect
317. #529C22×C7semidirect
318. #529C22×C7semidirect
319. #529C22×C7semidirect
324. #520C22×C7semidirect
326. #519C22×C7semidirect
332. C4×#41C22×C7semidirect
333. C4×#41C22×C7semidirect
334. C4×#41C22×C7semidirect
337. C2×C4×Q8C22×C7semidirect
523. C2×Q8C7×#41semidirect
641. C7#62793direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35242
C7×#35182
C7×#35172
C7×#35062
C7×#35022
C7×#34972
C7×#34932
C7×#34872
C7×#34832
C7×#34822
C7×#34802
C7×#34602
C7×#34442
C4×C7×2−1+42
C2×C4×C7×#412
#627937