Finite Group Databasebeta

← C7×#62788 #13240004

Subgroups — C7×#62788 #13240004

Order 1792.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3523C214yesmaximal, complemented
2C7×#3522C214yesmaximal, complemented
3C7×#3516C218yesmaximal, complemented
4C7×#3507C216yesmaximal, complemented
5C7×#3502C211yesmaximal, characteristic, complemented
6C7×#3497C211yesmaximal, characteristic, complemented
7C7×#3492C216yesmaximal, complemented
8C7×#3486C212yesmaximal, complemented
9C7×#3482C218yesmaximal, complemented
10C7×#3480C214yesmaximal, complemented
11C7×Q8×#41C214yesmaximal, complemented
12C7×#3461C216yesmaximal, complemented
13C7×#3444C216yesmaximal, complemented
14C4×C7×2−1+4C212yesmaximal, complemented
15C22×C4×C7×Q8C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2212yes—
17C23×C7×Q8C2211yescharacteristic
18C7×#559C22112yescomplemented
19C7×Q82C2214yescomplemented
20C7×#557C22112yescomplemented
21C7×#557C2214yescomplemented
22C7×#557C2218yescomplemented
23C7×#556C22112yescomplemented
24C7×#556C22124yescomplemented
25C7×#554C22124yes—
26C7×#554C22112yescomplemented
27C7×#553C22124yes—
28C7×#552C22124yes—
29C7×#552C22124yescomplemented
30C7×#550C2214yescomplemented
31C7×D4×Q8C2218yes—
32C7×D4×Q8C2218yes—
33C7×D4×Q8C2214yescomplemented
34C7×#548C2218yes—
35C7×#548C2218yes—
36C7×#548C2218yescomplemented
37C7×#547C22124yes—
38C7×#544C2216yes—
39C7×#542C22124yescomplemented
40C7×#541C22124yescomplemented
41C7×#539C22124yes—
42C7×#537C2216yes—
43C7×#536C22112yes—
44C7×#533C2216yes—
45C7×#533C2216yes—
46C7×#533C2216yes—
47C7×#533C22124yescomplemented
48C7×#532C2216yes—
49C7×#532C2216yes—
50C7×#532C2216yes—
51C7×#529C22112yes—
52C7×#529C22112yes—
53C7×#529C22112yes—
54C7×#529C22112yes—
55C7×#529C22112yes—
56C7×#529C22112yes—
57C7×#529C22124yescomplemented
58C7×#525C2214yes—
59C7×#525C22112yes—
60C7×#525C22112yes—
61C7×#520C22112yes—
62C7×#520C2218yescomplemented
63C7×#519C2212yes—
64C7×#519C2218yescomplemented
65C4×C7×#41C22112yes—
66C4×C7×#41C22112yes—
67C4×C7×#41C22112yes—
68C4×C7×#41C2218yescomplemented
69C2×C4×C7×Q8C2211yescharacteristic
70C2×C4×C7×Q8C2213yes—
71C2×C4×C7×Q8C2214yes—
72C2×C4×C7×Q8C2214yes—
73C2×C4×C7×Q8C2211yescharacteristic
74C2×C4×C7×Q8C2213yes—
75C2×C4×C7×Q8C2214yes—
76C2×C4×C7×Q8C2214yes—
77C2×C4×C7×Q8C2218yescomplemented
78C22×C7×C4⋊C4C2213yes—
79C22×C42×C7C2213yes—
80#62788C711yesmaximal, characteristic, direct product factor, Sylow
81C7×2−1+4—216no—
82C2×C7×#41C23112yes—
83C2×C7×#41C2318yes—
84C2×C7×#41C2314yes—
85C2×C7×#41C23112yes—
86C22×C7×Q8—28no—
87C22×C7×Q8C2313yes—
88C22×C7×Q8C2314yes—
89C22×C7×Q8C2314yes—
90C22×C7×Q8C2318yes—
91C22×C7×Q8C2311yescharacteristic
92C23×C4×C7C2313yes—
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2313yes—
95C7×C4⋊Q8C2316yes—
96C7×C4⋊Q8C2316yes—
97C7×C4⋊Q8C2316yes—
98C7×C4⋊Q8C23124yes—
99C7×C4⋊Q8C23124yes—
100C7×#127C2316yes—
101C7×#126C23124yes—
102C7×#126C23124yes—
103C7×#126C23148yes—
104C7×#125C23112yes—
105C7×#125C23112yes—
106C7×#125C23112yes—
107C7×#125C23124yes—
108C7×#125C23148yes—
109C7×#124C23112yes—
110C7×#124C23112yes—
111C7×#124C23112yes—
112C7×#124C23124yes—
113C7×#123C2318yes—
114C7×#123C23124yes—
115C7×#123C23124yes—
116C7×#123C23148yes—
117C7×C22⋊Q8C2314yes—
118C7×C22⋊Q8C2314yes—
119C7×C22⋊Q8C23112yes—
120C7×C22⋊Q8C23112yes—
121C7×C22⋊Q8C23112yes—
122C7×C22⋊Q8C23112yes—
123C7×C22⋊Q8C23124yes—
124C7×C22⋊Q8C23124yes—
125C7×C22⋊Q8C23124yes—
126C7×C22⋊Q8C23148yes—
127C7×#121C2314yes—
128C7×#121C2314yes—
129C7×#121C23112yes—
130C7×#121C23112yes—
131C7×#121C23112yes—
132C7×#121C23112yes—
133C7×#121C23124yes—
134C7×#120C2318yes—
135C4×C7×Q8C2314yes—
136C4×C7×Q8C2314yes—
137C4×C7×Q8C23112yes—
138C4×C7×Q8C23112yes—
139C4×C7×Q8C2314yes—
140C4×C7×Q8C2314yes—
141C4×C7×Q8C23112yes—
142C4×C7×Q8C23112yes—
143C4×C7×Q8C23112yes—
144C4×C7×Q8C2318yes—
145C4×C7×Q8C23124yes—
146C4×C7×Q8C23112yes—
147C4×C7×Q8C23112yes—
148C4×C7×Q8C23112yes—
149C4×C7×Q8C23112yes—
150C4×C7×Q8C23112yes—
151C4×C7×Q8C2318yes—
152C4×C7×D4C2318yes—
153C4×C7×D4C2318yes—
154C4×C7×D4C23112yes—
155C4×C7×D4C23124yes—
156C4×C7×D4C23112yes—
157C4×C7×D4C23124yes—
158C4×C7×D4C23124yes—
159C4×C7×D4C23124yes—
160C4×C7×D4C23112yes—
161C4×C7×D4C23112yes—
162C4×C7×D4C23112yes—
163C4×C7×D4C23112yes—
164C4×C7×D4C23124yes—
165C7×#117C2314yes—
166C7×#117C23112yes—
167C7×#117C23124yes—
168C7×#117C23112yes—
169C7×#117C23124yes—
170C7×#117C23124yes—
171C7×#117C23124yes—
172C2×C7×C4⋊C4C2313yes—
173C2×C7×C4⋊C4C2313yes—
174C2×C7×C4⋊C4C2316yes—
175C2×C7×C4⋊C4C23112yes—
176C2×C7×C4⋊C4C23112yes—
177C2×C7×C4⋊C4C23124yes—
178C2×C42×C7C2313yes—
179C2×C42×C7C2316yes—
180C2×C42×C7C2316yes—
181C2×C42×C7C2316yes—
182C2×C42×C7C2313yes—
183C2×C42×C7C2313yes—
184C2×C42×C7C2316yes—
185C2×C42×C7C2313yes—
186C2×C42×C7C23124yes—
187#3523C2×C714yescomplemented
188#3522C2×C714yescomplemented
189#3516C2×C718yescomplemented
190#3507C2×C716yescomplemented
191#3502C2×C711yescharacteristic, complemented
192#3497C2×C711yescharacteristic, complemented
193#3492C2×C716yescomplemented
194#3486C2×C712yescomplemented
195#3482C2×C718yescomplemented
196#3480C2×C714yescomplemented
197Q8×#41C2×C714yescomplemented
198#3461C2×C716yescomplemented
199#3444C2×C716yescomplemented
200C4×2−1+4C2×C712yescomplemented
201C22×C4×Q8C2×C711yescharacteristic, complemented
202C24×C7C2411yescharacteristic
203C7×#41—232no—
204C7×#41—248no—
205C7×#41—216no—
206C7×#41—424no—
207C2×C7×Q8—216no—
208C2×C7×Q8—216no—
209C2×C7×Q8—232no—
210C2×C7×Q8—212no—
211C2×C7×Q8#4118yescomplemented
212C2×C7×Q8C2414yes—
213C2×C7×Q8C24112yes—
214C2×C7×Q8C24112yes—
215C2×C7×Q8C24112yes—
216C2×C7×Q8C2414yes—
217C2×C7×D4C2418yes—
218C2×C7×D4C2414yes—
219C2×C7×D4C2418yes—
220C2×C7×D4C2418yes—
221C2×C7×D4C24112yes—
222C2×C7×D4C24112yes—
223C22×C4×C7—212no—
224C22×C4×C7—24no—
225C22×C4×C7—46no—
226C22×C4×C7C2411yescharacteristic
227C22×C4×C7C2411yescharacteristic
228C22×C4×C7C2411yescharacteristic
229C22×C4×C7C2416yes—
230C22×C4×C7C2416yes—
231C22×C4×C7C2416yes—
232C22×C4×C7C2413yes—
233C22×C4×C7C24124yes—
234C22×C4×C7C2411yescharacteristic
235C22×C4×C7C2411yescharacteristic
236C22×C4×C7C2418yes—
237C22×C4×C7C2413yes—
238C22×C4×C7C2416yes—
239C22×C4×C7C2413yes—
240C22×C4×C7C24124yes—
241C22×C4×C7C2413yes—
242C22×C4×C7C2411yescharacteristic
243C7×C4⋊C4C24112yes—
244C7×C4⋊C4C24112yes—
245C7×C4⋊C4C24124yes—
246C7×C4⋊C4C24112yes—
247C7×C4⋊C4C24124yes—
248C7×C4⋊C4C24112yes—
249C7×C4⋊C4C2418yes—
250C7×C4⋊C4C2418yes—
251C7×C4⋊C4C2414yes—
252C7×C4⋊C4C2414yes—
253C7×C4⋊C4C24112yes—
254C7×C4⋊C4C24112yes—
255C7×C4⋊C4C24124yes—
256C7×C4⋊C4C24124yes—
257C7×C4⋊C4C24124yes—
258C7×C22⋊C4C2418yes—
259C7×C22⋊C4C2418yes—
260C7×C22⋊C4C24124yes—
261C7×C22⋊C4C2418yes—
262C7×C22⋊C4C2418yes—
263C7×C22⋊C4C2418yes—
264C7×C22⋊C4C24124yes—
265C7×C22⋊C4C24124yes—
266C7×C22⋊C4C24124yes—
267C42×C7C2416yes—
268C42×C7C2416yes—
269C42×C7C2416yes—
270C42×C7C2416yes—
271C42×C7C2416yes—
272C42×C7C2416yes—
273C42×C7C24124yes—
274C42×C7C24124yes—
275C42×C7C2416yes—
276C42×C7C2416yes—
277C42×C7C2418yes—
278C2×2−1+4C22×C712yes—
279C23×Q8C22×C711yescharacteristic
280#559C22×C7112yescomplemented
281Q82C22×C714yescomplemented
282#557C22×C7112yescomplemented
283#557C22×C714yescomplemented
284#557C22×C718yescomplemented
285#556C22×C7112yescomplemented
286#556C22×C7124yescomplemented
287#554C22×C7124yes—
288#554C22×C7112yescomplemented
289#553C22×C7124yes—
290#552C22×C7124yes—
291#552C22×C7124yescomplemented
292#550C22×C714yescomplemented
293D4×Q8C22×C718yes—
294D4×Q8C22×C718yes—
295D4×Q8C22×C714yescomplemented
296#548C22×C718yes—
297#548C22×C718yes—
298#548C22×C718yescomplemented
299#547C22×C7124yes—
300#544C22×C716yes—
301#542C22×C7124yescomplemented
302#541C22×C7124yescomplemented
303#539C22×C7124yes—
304#537C22×C716yes—
305#536C22×C7112yes—
306#533C22×C716yes—
307#533C22×C716yes—
308#533C22×C716yes—
309#533C22×C7124yescomplemented
310#532C22×C716yes—
311#532C22×C716yes—
312#532C22×C716yes—
313#529C22×C7112yes—
314#529C22×C7112yes—
315#529C22×C7112yes—
316#529C22×C7112yes—
317#529C22×C7112yes—
318#529C22×C7112yes—
319#529C22×C7124yescomplemented
320#525C22×C714yes—
321#525C22×C7112yes—
322#525C22×C7112yes—
323#520C22×C7112yes—
324#520C22×C718yescomplemented
325#519C22×C712yes—
326#519C22×C718yescomplemented
327C4×#41C22×C7112yes—
328C4×#41C22×C7112yes—
329C4×#41C22×C7112yes—
330C4×#41C22×C718yescomplemented
331C2×C4×Q8C22×C711yescharacteristic
332C2×C4×Q8C22×C713yes—
333C2×C4×Q8C22×C714yes—
334C2×C4×Q8C22×C714yes—
335C2×C4×Q8C22×C711yescharacteristic
336C2×C4×Q8C22×C713yes—
337C2×C4×Q8C22×C714yes—
338C2×C4×Q8C22×C714yes—
339C2×C4×Q8C22×C718yescomplemented
340C22×C4⋊C4C22×C713yes—
341C22×C42C22×C713yes—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7C2518yes—
346C23×C7C2511yescharacteristic
347C23×C7C2511yescharacteristic
348C23×C7C2511yescharacteristic
349C7×Q8—224no—
350C7×Q8—224no—
351C7×Q8—28no—
352C7×Q8—412no—
353C7×Q8C2×#41116yes—
354C7×D4—216no—
355C7×D4—216no—
356C7×D4—216no—
357C7×D4—224no—
358C7×D4—28no—
359C7×D4—412no—
360C2×C4×C7—26no—
361C2×C4×C7—22no—
362C2×C4×C7—212no—
363C2×C4×C7—212no—
364C2×C4×C7—212no—
365C2×C4×C7—248no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—216no—
371C2×C4×C7—43no—
372C2×C4×C7—46no—
373C2×C4×C7—43no—
374C2×C4×C7—424no—
375C2×C4×C7C2×#41112yes—
376C2×C4×C72−1+414yescomplemented
377C2×C4×C7C2511yescharacteristic
378C2×C4×C7C2511yescharacteristic
379C2×C4×C7C2516yes—
380C2×C4×C7C2518yes—
381C2×C4×C7C2516yes—
382C2×C4×C7C2518yes—
383C2×C4×C7C2518yes—
384C2×C4×C7C2516yes—
385C2×C4×C7C2516yes—
386C2×C4×C7C2511yescharacteristic
387C2×C4×C7C2511yescharacteristic
3882−1+4—216no—
389C2×#41C23×C714yes—
390C2×#41C23×C7112yes—
391C2×#41C23×C718yes—
392C2×#41C23×C7112yes—
393C22×Q8—28no—
394C22×Q8C23×C713yes—
395C22×Q8C23×C714yes—
396C22×Q8C23×C714yes—
397C22×Q8C23×C718yes—
398C22×Q8C23×C711yescharacteristic
399C23×C4C23×C713yes—
400C23×C4C23×C711yescharacteristic
401C23×C4C23×C713yes—
402C4⋊Q8C23×C716yes—
403C4⋊Q8C23×C716yes—
404C4⋊Q8C23×C716yes—
405C4⋊Q8C23×C7124yes—
406C4⋊Q8C23×C7124yes—
407#127C23×C716yes—
408#126C23×C7124yes—
409#126C23×C7124yes—
410#126C23×C7148yes—
411#125C23×C7112yes—
412#125C23×C7112yes—
413#125C23×C7112yes—
414#125C23×C7124yes—
415#125C23×C7148yes—
416#124C23×C7112yes—
417#124C23×C7112yes—
418#124C23×C7112yes—
419#124C23×C7124yes—
420#123C23×C718yes—
421#123C23×C7124yes—
422#123C23×C7124yes—
423#123C23×C7148yes—
424C22⋊Q8C23×C714yes—
425C22⋊Q8C23×C714yes—
426C22⋊Q8C23×C7112yes—
427C22⋊Q8C23×C7112yes—
428C22⋊Q8C23×C7112yes—
429C22⋊Q8C23×C7112yes—
430C22⋊Q8C23×C7124yes—
431C22⋊Q8C23×C7124yes—
432C22⋊Q8C23×C7124yes—
433C22⋊Q8C23×C7148yes—
434#121C23×C714yes—
435#121C23×C714yes—
436#121C23×C7112yes—
437#121C23×C7112yes—
438#121C23×C7112yes—
439#121C23×C7112yes—
440#121C23×C7124yes—
441#120C23×C718yes—
442C4×Q8C23×C714yes—
443C4×Q8C23×C714yes—
444C4×Q8C23×C7112yes—
445C4×Q8C23×C7112yes—
446C4×Q8C23×C714yes—
447C4×Q8C23×C714yes—
448C4×Q8C23×C7112yes—
449C4×Q8C23×C7112yes—
450C4×Q8C23×C7112yes—
451C4×Q8C23×C718yes—
452C4×Q8C23×C7124yes—
453C4×Q8C23×C7112yes—
454C4×Q8C23×C7112yes—
455C4×Q8C23×C7112yes—
456C4×Q8C23×C7112yes—
457C4×Q8C23×C7112yes—
458C4×Q8C23×C718yes—
459C4×D4C23×C718yes—
460C4×D4C23×C718yes—
461C4×D4C23×C7112yes—
462C4×D4C23×C7124yes—
463C4×D4C23×C7112yes—
464C4×D4C23×C7124yes—
465C4×D4C23×C7124yes—
466C4×D4C23×C7124yes—
467C4×D4C23×C7112yes—
468C4×D4C23×C7112yes—
469C4×D4C23×C7112yes—
470C4×D4C23×C7112yes—
471C4×D4C23×C7124yes—
472#117C23×C714yes—
473#117C23×C7112yes—
474#117C23×C7124yes—
475#117C23×C7112yes—
476#117C23×C7124yes—
477#117C23×C7124yes—
478#117C23×C7124yes—
479C2×C4⋊C4C23×C713yes—
480C2×C4⋊C4C23×C713yes—
481C2×C4⋊C4C23×C716yes—
482C2×C4⋊C4C23×C7112yes—
483C2×C4⋊C4C23×C7112yes—
484C2×C4⋊C4C23×C7124yes—
485C2×C42C23×C713yes—
486C2×C42C23×C716yes—
487C2×C42C23×C716yes—
488C2×C42C23×C713yes—
489C2×C42C23×C716yes—
490C2×C42C23×C713yes—
491C2×C42C23×C716yes—
492C2×C42C23×C713yes—
493C2×C42C23×C7124yes—
494C22×C7—28no—
495C22×C7—21no—
496C22×C7—21no—
497C22×C7—21no—
498C22×C7—21no—
499C22×C7—21no—
500C22×C7—21no—
501C22×C7—28no—
502C22×C7—28no—
503C22×C7—28no—
504C22×C7C22×#4112yes—
505C22×C7C2×2−1+412yes—
506C22×C7#58512yes—
507C22×C7C2611yescharacteristic
508C4×C7—28no—
509C4×C7—26no—
510C4×C7—21no—
511C4×C7—21no—
512C4×C7—28no—
513C4×C7—26no—
514C4×C7—26no—
515C4×C7—28no—
516C4×C7C22×#41112yes—
517C4×C7C2×2−1+412yes—
518C4×C7C2×2−1+412yes—
519C24C24×C711yescharacteristic
520#41—232no—
521#41—248no—
522#41—216no—
523#41—424no—
524C2×Q8—216no—
525C2×Q8—216no—
526C2×Q8—232no—
527C2×Q8—212no—
528C2×Q8C7×#4118yescomplemented
529C2×Q8C24×C714yes—
530C2×Q8C24×C7112yes—
531C2×Q8C24×C7112yes—
532C2×Q8C24×C7112yes—
533C2×Q8C24×C714yes—
534C2×D4C24×C718yes—
535C2×D4C24×C714yes—
536C2×D4C24×C718yes—
537C2×D4C24×C718yes—
538C2×D4C24×C7112yes—
539C2×D4C24×C7112yes—
540C22×C4—212no—
541C22×C4—24no—
542C22×C4—46no—
543C22×C4C24×C711yescharacteristic
544C22×C4C24×C711yescharacteristic
545C22×C4C24×C711yescharacteristic
546C22×C4C24×C711yescharacteristic
547C22×C4C24×C711yescharacteristic
548C22×C4C24×C718yes—
549C22×C4C24×C716yes—
550C22×C4C24×C716yes—
551C22×C4C24×C716yes—
552C22×C4C24×C713yes—
553C22×C4C24×C7124yes—
554C22×C4C24×C713yes—
555C22×C4C24×C716yes—
556C22×C4C24×C713yes—
557C22×C4C24×C7124yes—
558C22×C4C24×C713yes—
559C22×C4C24×C711yescharacteristic
560C4⋊C4C24×C7112yes—
561C4⋊C4C24×C7112yes—
562C4⋊C4C24×C7124yes—
563C4⋊C4C24×C7112yes—
564C4⋊C4C24×C7124yes—
565C4⋊C4C24×C7112yes—
566C4⋊C4C24×C718yes—
567C4⋊C4C24×C718yes—
568C4⋊C4C24×C714yes—
569C4⋊C4C24×C714yes—
570C4⋊C4C24×C7112yes—
571C4⋊C4C24×C7112yes—
572C4⋊C4C24×C7124yes—
573C4⋊C4C24×C7124yes—
574C4⋊C4C24×C7124yes—
575C22⋊C4C24×C718yes—
576C22⋊C4C24×C718yes—
577C22⋊C4C24×C7124yes—
578C22⋊C4C24×C718yes—
579C22⋊C4C24×C718yes—
580C22⋊C4C24×C718yes—
581C22⋊C4C24×C7124yes—
582C22⋊C4C24×C7124yes—
583C22⋊C4C24×C7124yes—
584C42C24×C716yes—
585C42C24×C716yes—
586C42C24×C716yes—
587C42C24×C718yes—
588C42C24×C716yes—
589C42C24×C716yes—
590C42C24×C716yes—
591C42C24×C716yes—
592C42C24×C716yes—
593C42C24×C7124yes—
594C42C24×C7124yes—
595C2×C7—22no—
596C2×C7—22no—
597C2×C7—22no—
598C2×C7—48no—
599C2×C7C23×#4111yescharacteristic
600C2×C7C22×2−1+411yescharacteristic
601C2×C7C2×#58511yescharacteristic
602C23—22no—
603C23—22no—
604C23—22no—
605C23C25×C718yes—
606C23C25×C711yescharacteristic
607C23C25×C711yescharacteristic
608C23C25×C711yescharacteristic
609Q8—224no—
610Q8—224no—
611Q8—28no—
612Q8—412no—
613Q8C2×C7×#41116yes—
614D4—216no—
615D4—216no—
616D4—216no—
617D4—224no—
618D4—28no—
619D4—412no—
620C2×C4—26no—
621C2×C4—22no—
622C2×C4—212no—
623C2×C4—212no—
624C2×C4—212no—
625C2×C4—248no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—216no—
631C2×C4—43no—
632C2×C4—46no—
633C2×C4—43no—
634C2×C4—424no—
635C2×C4C2×C7×#41112yes—
636C2×C4C7×2−1+414yescomplemented
637C2×C4C25×C711yescharacteristic
638C2×C4C25×C711yescharacteristic
639C2×C4C25×C716yes—
640C2×C4C25×C718yes—
641C2×C4C25×C716yes—
642C2×C4C25×C718yes—
643C2×C4C25×C718yes—
644C2×C4C25×C716yes—
645C2×C4C25×C716yes—
646C2×C4C25×C711yescharacteristic
647C2×C4C25×C711yescharacteristic
648C7#6278811yescharacteristic, direct product factor, Sylow
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C22×C7×#4112yes—
660C22C2×C7×2−1+412yes—
661C22C7×#58512yes—
662C22C26×C711yescharacteristic
663C4—28no—
664C4—26no—
665C4—21no—
666C4—21no—
667C4—28no—
668C4—26no—
669C4—26no—
670C4—28no—
671C4C22×C7×#41112yes—
672C4C2×C7×2−1+412yes—
673C4C2×C7×2−1+412yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—48no—
678C2C23×C7×#4111yescharacteristic
679C2C22×C7×2−1+411yescharacteristic
680C2C2×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×#3523C2semidirect
2. C7×#3522C2semidirect
3. C7×#3516C2semidirect
4. C7×#3507C2semidirect
5. C7×#3502C2semidirect
6. C7×#3497C2semidirect
7. C7×#3492C2semidirect
8. C7×#3486C2semidirect
9. C7×#3482C2semidirect
10. C7×#3480C2semidirect
11. C7×Q8×#41C2semidirect
12. C7×#3461C2semidirect
13. C7×#3444C2semidirect
14. C4×C7×2−1+4C2semidirect
15. C22×C4×C7×Q8C2semidirect
18. C7×#559C22semidirect
19. C7×Q82C22semidirect
20. C7×#557C22semidirect
21. C7×#557C22semidirect
22. C7×#557C22semidirect
23. C7×#556C22semidirect
24. C7×#556C22semidirect
26. C7×#554C22semidirect
29. C7×#552C22semidirect
30. C7×#550C22semidirect
33. C7×D4×Q8C22semidirect
36. C7×#548C22semidirect
39. C7×#542C22semidirect
40. C7×#541C22semidirect
47. C7×#533C22semidirect
57. C7×#529C22semidirect
62. C7×#520C22semidirect
64. C7×#519C22semidirect
68. C4×C7×#41C22semidirect
77. C2×C4×C7×Q8C22semidirect
80. #62788C7direct (N × H)
187. #3523C2×C7semidirect
188. #3522C2×C7semidirect
189. #3516C2×C7semidirect
190. #3507C2×C7semidirect
191. #3502C2×C7semidirect
192. #3497C2×C7semidirect
193. #3492C2×C7semidirect
194. #3486C2×C7semidirect
195. #3482C2×C7semidirect
196. #3480C2×C7semidirect
197. Q8×#41C2×C7semidirect
198. #3461C2×C7semidirect
199. #3444C2×C7semidirect
200. C4×2−1+4C2×C7semidirect
201. C22×C4×Q8C2×C7semidirect
211. C2×C7×Q8#41semidirect
280. #559C22×C7semidirect
281. Q82C22×C7semidirect
282. #557C22×C7semidirect
283. #557C22×C7semidirect
284. #557C22×C7semidirect
285. #556C22×C7semidirect
286. #556C22×C7semidirect
288. #554C22×C7semidirect
291. #552C22×C7semidirect
292. #550C22×C7semidirect
295. D4×Q8C22×C7semidirect
298. #548C22×C7semidirect
301. #542C22×C7semidirect
302. #541C22×C7semidirect
309. #533C22×C7semidirect
319. #529C22×C7semidirect
324. #520C22×C7semidirect
326. #519C22×C7semidirect
330. C4×#41C22×C7semidirect
339. C2×C4×Q8C22×C7semidirect
376. C2×C4×C72−1+4semidirect
528. C2×Q8C7×#41semidirect
636. C2×C4C7×2−1+4semidirect
648. C7#62788direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35232
C7×#35222
C7×#35162
C7×#35072
C7×#35022
C7×#34972
C7×#34922
C7×#34862
C7×#34822
C7×#34802
C7×Q8×#412
C7×#34612
C7×#34442
C4×C7×2−1+42
C22×C4×C7×Q82
#627887