Finite Group Databasebeta

← C7×#62863 #13240079

Subgroups — C7×#62863 #13240079

Order 1792.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3560C218yesmaximal, complemented
2C7×#3558C218yesmaximal, complemented
3C7×#3537C218yesmaximal, complemented
4C7×#3534C218yesmaximal, complemented
5C7×#3533C218yesmaximal, complemented
6C7×#3532C218yesmaximal, complemented
7C7×#3505C214yesmaximal, complemented
8C7×#3496C214yesmaximal, complemented
9C7×#3484C214yesmaximal, complemented
10C2×C7×#538C212yesmaximal, complemented
11C2×C7×#534C211yesmaximal, characteristic, complemented
12C2×C7×H(5,𝔽2)C2214yescomplemented
13C23×C7×D4C2212yescomplemented
14C7×#563C2218yescomplemented
15C7×#562C22116yescomplemented
16C7×H(3,𝔽4)C2218yescomplemented
17C7×#560C22116yescomplemented
18C7×#560C2218yescomplemented
19C7×#560C2218yescomplemented
20C7×#559C2218yescomplemented
21C7×#553C22116yescomplemented
22C7×#553C22116yescomplemented
23C7×#553C2218yescomplemented
24C7×#552C2218yescomplemented
25C7×#551C22116yescomplemented
26C7×#551C2218yescomplemented
27C7×#551C2218yescomplemented
28C7×#548C2218yescomplemented
29C7×#547C2218yescomplemented
30C7×#547C2218yescomplemented
31C7×#546C2218yescomplemented
32C7×#546C22116yescomplemented
33C7×#546C22116yescomplemented
34C7×#546C22116yescomplemented
35C7×#546C22116yescomplemented
36C7×#546C22116yescomplemented
37C7×D42C2218yescomplemented
38C7×D42C22116yescomplemented
39C7×D42C22116yescomplemented
40C7×D42C2218yescomplemented
41C7×D42C2218yescomplemented
42C7×#542C22116yescomplemented
43C7×#540C22116yescomplemented
44C7×#539C22116yescomplemented
45C7×#539C2218yescomplemented
46C7×#538C22116yescomplemented
47C7×#538C2218yescomplemented
48C7×#538C2218yescomplemented
49C7×#538C22116yescomplemented
50C7×#538C22116yescomplemented
51C7×#538C22116yescomplemented
52C7×#538C2218yescomplemented
53C7×#537C2218yescomplemented
54C7×#535C2218yescomplemented
55C7×#535C22116yescomplemented
56C7×#534C2218yescomplemented
57C7×#534C2218yescomplemented
58C7×#534C2218yescomplemented
59C7×#534C2218yescomplemented
60C7×#534C22116yescomplemented
61C7×#534C2218yescomplemented
62C7×#532C2218yescomplemented
63C7×#529C2218yescomplemented
64C2×C7×#126C2214yescomplemented
65C2×C7×#124C2214yescomplemented
66C7×#525C2218yescomplemented
67C7×#525C2218yescomplemented
68C2×C7×#123C2214yescomplemented
69C2×C7×#123C2214yescomplemented
70C2×C7×C22⋊Q8C2212yescomplemented
71C2×C7×#121C2214yescomplemented
72C2×C7×#121C2214yescomplemented
73C2×C7×#121C2212yescomplemented
74C2×C7×#121C2218yescomplemented
75C2×C7×#120C2214yescomplemented
76C2×C7×#120C2214yescomplemented
77C2×C7×#120C2218yescomplemented
78C7×#518C2214yescomplemented
79C2×C4×C7×D4C2214yescomplemented
80C22×C7×C22⋊C4C2211yescharacteristic, complemented
81#62863C711yesmaximal, characteristic, direct product factor, Sylow
82C25×C7C2311yescharacteristic
83C25×C7C2312yes—
84C7×H(5,𝔽2)—416no—
85C2×C7×#41C2318yes—
86C2×C7×#41C23116yescomplemented
87C2×C7×#41C2318yescomplemented
88C22×C7×Q8C2312yescomplemented
89C22×C7×D4—48no—
90C22×C7×D4C2314yes—
91C22×C7×D4C2314yes—
92C22×C7×D4C2314yes—
93C22×C7×D4C23116yes—
94C22×C7×D4C2318yes—
95C22×C7×D4C2314yes—
96C22×C7×D4C2314yes—
97C22×C7×D4C2314yes—
98C22×C7×D4C23116yescomplemented
99C22×C7×D4C23116yescomplemented
100C22×C7×D4C2312yescomplemented
101C22×C7×D4C2318yescomplemented
102C23×C4×C7C2312yes—
103C23×C4×C7C2312yes—
104C23×C4×C7C2314yescomplemented
105C7×C4⋊Q8C2318yescomplemented
106C7×#127C2318yes—
107C7×#127C2318yes—
108C7×#127C2318yescomplemented
109C7×#126C23116yescomplemented
110C7×#126C23116yescomplemented
111C7×#126C23116yescomplemented
112C7×#126C23116yescomplemented
113C7×#126C23116yescomplemented
114C7×#125C2318yescomplemented
115C7×#125C23116yescomplemented
116C7×#124C2318yes—
117C7×#124C2318yes—
118C7×#124C23116yescomplemented
119C7×#124C23116yescomplemented
120C7×#124C2318yescomplemented
121C7×#124C23116yescomplemented
122C7×#124C23116yescomplemented
123C7×#123C23116yes—
124C7×#123C2318yes—
125C7×#123C2318yes—
126C7×#123C23116yes—
127C7×#123C2318yes—
128C7×#123C2318yes—
129C7×#123C23116yescomplemented
130C7×#123C23116yescomplemented
131C7×#123C23116yescomplemented
132C7×#123C23116yescomplemented
133C7×#123C23116yescomplemented
134C7×#123C23116yescomplemented
135C7×#123C23116yescomplemented
136C7×#123C23116yescomplemented
137C7×C22⋊Q8C2318yes—
138C7×C22⋊Q8C2318yescomplemented
139C7×C22⋊Q8C2318yescomplemented
140C7×C22⋊Q8C23116yescomplemented
141C7×C22⋊Q8C23116yescomplemented
142C7×C22⋊Q8C23116yescomplemented
143C7×C22⋊Q8C23116yescomplemented
144C7×#121C2318yes—
145C7×#121C2318yes—
146C7×#121C2318yes—
147C7×#121C2318yes—
148C7×#121C2318yes—
149C7×#121C23116yes—
150C7×#121C23116yes—
151C7×#121C23116yes—
152C7×#121C23116yes—
153C7×#121C2318yescomplemented
154C7×#121C23116yescomplemented
155C7×#121C23116yescomplemented
156C7×#121C23116yescomplemented
157C7×#121C2318yescomplemented
158C7×#121C23116yescomplemented
159C7×#121C2318yescomplemented
160C7×#121C2318yescomplemented
161C7×#121C23116yescomplemented
162C7×#121C23116yescomplemented
163C7×#121C23116yescomplemented
164C7×#121C23116yescomplemented
165C7×#121C23116yescomplemented
166C7×#120C23116yes—
167C7×#120C23116yes—
168C7×#120C2318yes—
169C7×#120C2318yes—
170C7×#120C23116yes—
171C7×#120C23116yes—
172C7×#120C2318yes—
173C7×#120C2318yes—
174C7×#120C23116yescomplemented
175C7×#120C23116yescomplemented
176C7×#120C23116yescomplemented
177C7×#120C23116yescomplemented
178C7×#120C23116yescomplemented
179C4×C7×Q8C2318yescomplemented
180C4×C7×D4C2318yes—
181C4×C7×D4C2318yes—
182C4×C7×D4C2318yescomplemented
183C4×C7×D4C2318yescomplemented
184C4×C7×D4C23116yescomplemented
185C4×C7×D4C23116yescomplemented
186C4×C7×D4C23116yescomplemented
187C4×C7×D4C23116yescomplemented
188C4×C7×D4C23116yescomplemented
189C4×C7×D4C2318yescomplemented
190C4×C7×D4C2318yescomplemented
191C4×C7×D4C2318yescomplemented
192C4×C7×D4C23116yescomplemented
193C7×#117C2318yes—
194C7×#117C2318yescomplemented
195C7×#117C23116yescomplemented
196C2×C7×C4⋊C4C2314yes—
197C2×C7×C4⋊C4C2314yescomplemented
198C2×C7×C4⋊C4C2314yescomplemented
199C2×C7×C4⋊C4C2312yescomplemented
200C2×C7×C4⋊C4C2318yescomplemented
201C2×C7×C4⋊C4C2312yescomplemented
202C2×C7×C22⋊C4C2314yes—
203C2×C7×C22⋊C4C2314yes—
204C2×C7×C22⋊C4C2314yes—
205C2×C7×C22⋊C4C2314yes—
206C2×C7×C22⋊C4C2318yes—
207C2×C7×C22⋊C4C2318yes—
208C2×C7×C22⋊C4C2314yes—
209C2×C7×C22⋊C4C2314yes—
210C2×C7×C22⋊C4C2314yescomplemented
211C2×C7×C22⋊C4C23116yescomplemented
212C2×C7×C22⋊C4C2314yescomplemented
213C2×C7×C22⋊C4C23116yescomplemented
214C2×C42×C7C2314yescomplemented
215#3560C2×C718yescomplemented
216#3558C2×C718yescomplemented
217#3537C2×C718yescomplemented
218#3534C2×C718yescomplemented
219#3533C2×C718yescomplemented
220#3532C2×C718yescomplemented
221#3505C2×C714yescomplemented
222#3496C2×C714yescomplemented
223#3484C2×C714yescomplemented
224C2×#538C2×C712yescomplemented
225C2×#534C2×C711yescharacteristic, complemented
226C24×C7—24no—
227C24×C7—44no—
228C24×C7—82no—
229C24×C7—84no—
230C24×C7C2414yes—
231C24×C7C2414yes—
232C24×C7C2412yes—
233C24×C7C2414yes—
234C24×C7C2418yes—
235C24×C7C2418yes—
236C24×C7C2411yescharacteristic
237C7×#41—416no—
238C7×#41—432no—
239C7×#41—88no—
240C2×C7×Q8—82no—
241C2×C7×Q8C2418yes—
242C2×C7×Q8C2418yes—
243C2×C7×D4—216no—
244C2×C7×D4—216no—
245C2×C7×D4—48no—
246C2×C7×D4—432no—
247C2×C7×D4—416no—
248C2×C7×D4—432no—
249C2×C7×D4—84no—
250C2×C7×D4—84no—
251C2×C7×D4—84no—
252C2×C7×D4—82no—
253C2×C7×D4—88no—
254C2×C7×D4—816no—
255C2×C7×D4C2418yes—
256C2×C7×D4C2418yes—
257C2×C7×D4C24116yes—
258C2×C7×D4C2418yes—
259C2×C7×D4C2418yes—
260C2×C7×D4C24116yes—
261C2×C7×D4C24116yes—
262C2×C7×D4C24116yes—
263C2×C7×D4C24116yes—
264C2×C7×D4C2418yes—
265C2×C7×D4C2418yes—
266C2×C7×D4C2418yes—
267C2×C7×D4C24116yes—
268C2×C7×D4C2418yes—
269C22×C4×C7—44no—
270C22×C4×C7—82no—
271C22×C4×C7—84no—
272C22×C4×C7C2414yes—
273C22×C4×C7C2414yes—
274C22×C4×C7C2414yes—
275C22×C4×C7C2414yes—
276C22×C4×C7C2414yes—
277C22×C4×C7C2412yes—
278C22×C4×C7C2412yes—
279C22×C4×C7C2414yes—
280C22×C4×C7C24116yes—
281C22×C4×C7C2418yes—
282C22×C4×C7C2418yes—
283C22×C4×C7C24116yes—
284C22×C4×C7C2418yes—
285C22×C4×C7C2418yes—
286C7×C4⋊C4C2418yes—
287C7×C4⋊C4C2418yes—
288C7×C4⋊C4C2418yes—
289C7×C4⋊C4C24116yes—
290C7×C4⋊C4C24116yes—
291C7×C4⋊C4C2418yes—
292C7×C4⋊C4C2418yes—
293C7×C4⋊C4C2418yes—
294C7×C4⋊C4C24116yes—
295C7×C4⋊C4C24116yes—
296C7×C22⋊C4C2418yes—
297C7×C22⋊C4C2414yes—
298C7×C22⋊C4C2418yes—
299C7×C22⋊C4C2414yes—
300C7×C22⋊C4C24116yes—
301C7×C22⋊C4C24116yes—
302C7×C22⋊C4C24116yes—
303C7×C22⋊C4C24116yes—
304C7×C22⋊C4C2418yes—
305C7×C22⋊C4C2418yes—
306C7×C22⋊C4C2418yes—
307C7×C22⋊C4C24116yes—
308C7×C22⋊C4C24116yes—
309C7×C22⋊C4C24116yes—
310C7×C22⋊C4C24116yes—
311C7×C22⋊C4C2418yes—
312C7×C22⋊C4C2418yes—
313C7×C22⋊C4C24116yes—
314C42×C7C2418yes—
315C42×C7C2418yes—
316C42×C7C2418yes—
317C42×C7C2418yes—
318C2×H(5,𝔽2)C22×C714yescomplemented
319C23×D4C22×C712yescomplemented
320#563C22×C718yescomplemented
321#562C22×C7116yescomplemented
322H(3,𝔽4)C22×C718yescomplemented
323#560C22×C7116yescomplemented
324#560C22×C718yescomplemented
325#560C22×C718yescomplemented
326#559C22×C718yescomplemented
327#553C22×C7116yescomplemented
328#553C22×C718yescomplemented
329#553C22×C7116yescomplemented
330#552C22×C718yescomplemented
331#551C22×C7116yescomplemented
332#551C22×C718yescomplemented
333#551C22×C718yescomplemented
334#548C22×C718yescomplemented
335#547C22×C718yescomplemented
336#547C22×C718yescomplemented
337#546C22×C718yescomplemented
338#546C22×C7116yescomplemented
339#546C22×C7116yescomplemented
340#546C22×C7116yescomplemented
341#546C22×C7116yescomplemented
342#546C22×C7116yescomplemented
343D42C22×C718yescomplemented
344D42C22×C7116yescomplemented
345D42C22×C7116yescomplemented
346D42C22×C718yescomplemented
347D42C22×C718yescomplemented
348#542C22×C7116yescomplemented
349#540C22×C7116yescomplemented
350#539C22×C7116yescomplemented
351#539C22×C718yescomplemented
352#538C22×C7116yescomplemented
353#538C22×C718yescomplemented
354#538C22×C718yescomplemented
355#538C22×C7116yescomplemented
356#538C22×C7116yescomplemented
357#538C22×C7116yescomplemented
358#538C22×C718yescomplemented
359#537C22×C718yescomplemented
360#535C22×C718yescomplemented
361#535C22×C7116yescomplemented
362#534C22×C718yescomplemented
363#534C22×C718yescomplemented
364#534C22×C718yescomplemented
365#534C22×C718yescomplemented
366#534C22×C7116yescomplemented
367#534C22×C718yescomplemented
368#532C22×C718yescomplemented
369#529C22×C718yescomplemented
370C2×#126C22×C714yescomplemented
371C2×#124C22×C714yescomplemented
372#525C22×C718yescomplemented
373#525C22×C718yescomplemented
374C2×#123C22×C714yescomplemented
375C2×#123C22×C714yescomplemented
376C2×C22⋊Q8C22×C712yescomplemented
377C2×#121C22×C714yescomplemented
378C2×#121C22×C714yescomplemented
379C2×#121C22×C712yescomplemented
380C2×#121C22×C718yescomplemented
381C2×#120C22×C714yescomplemented
382C2×#120C22×C714yescomplemented
383C2×#120C22×C718yescomplemented
384#518C22×C714yescomplemented
385C2×C4×D4C22×C714yescomplemented
386C22×C22⋊C4C22×C711yescharacteristic, complemented
387C23×C7—24no—
388C23×C7—28no—
389C23×C7—28no—
390C23×C7—28no—
391C23×C7—42no—
392C23×C7—44no—
393C23×C7—44no—
394C23×C7—48no—
395C23×C7—44no—
396C23×C7—44no—
397C23×C7—44no—
398C23×C7—48no—
399C23×C7—416no—
400C23×C7—48no—
401C23×C7—416no—
402C23×C7—88no—
403C23×C7—816no—
404C23×C7H(5,𝔽2)14yes—
405C23×C7C2514yes—
406C23×C7C2518yes—
407C23×C7C2518yes—
408C23×C7C2511yescharacteristic
409C23×C7C2512yes—
410C7×Q8—48no—
411C7×Q8—48no—
412C7×D4—232no—
413C7×D4—216no—
414C7×D4—216no—
415C7×D4—48no—
416C7×D4—48no—
417C7×D4—48no—
418C7×D4—416no—
419C7×D4—416no—
420C7×D4—48no—
421C7×D4—416no—
422C7×D4—48no—
423C7×D4—416no—
424C7×D4—48no—
425C7×D4—416no—
426C2×C4×C7—28no—
427C2×C4×C7—28no—
428C2×C4×C7—48no—
429C2×C4×C7—44no—
430C2×C4×C7—42no—
431C2×C4×C7—44no—
432C2×C4×C7—48no—
433C2×C4×C7—44no—
434C2×C4×C7—42no—
435C2×C4×C7—48no—
436C2×C4×C7—416no—
437C2×C4×C7—48no—
438C2×C4×C7—44no—
439C2×C4×C7—416no—
440C2×C4×C7C2518yes—
441C2×C4×C7C2514yes—
442C2×C4×C7C2514yes—
443C2×C4×C7C2518yes—
444C2×C4×C7C2518yes—
445C2×C4×C7C2518yes—
446C25C23×C711yescharacteristic
447C25C23×C712yes—
448H(5,𝔽2)—416no—
449C2×#41C23×C718yes—
450C2×#41C23×C7116yescomplemented
451C2×#41C23×C718yescomplemented
452C22×Q8C23×C712yescomplemented
453C22×D4—48no—
454C22×D4C23×C714yes—
455C22×D4C23×C714yes—
456C22×D4C23×C714yes—
457C22×D4C23×C718yes—
458C22×D4C23×C7116yes—
459C22×D4C23×C714yes—
460C22×D4C23×C714yes—
461C22×D4C23×C714yes—
462C22×D4C23×C7116yescomplemented
463C22×D4C23×C7116yescomplemented
464C22×D4C23×C712yescomplemented
465C22×D4C23×C718yescomplemented
466C23×C4C23×C712yes—
467C23×C4C23×C712yes—
468C23×C4C23×C714yescomplemented
469C4⋊Q8C23×C718yescomplemented
470#127C23×C718yes—
471#127C23×C718yes—
472#127C23×C718yescomplemented
473#126C23×C7116yescomplemented
474#126C23×C7116yescomplemented
475#126C23×C7116yescomplemented
476#126C23×C7116yescomplemented
477#126C23×C7116yescomplemented
478#125C23×C718yescomplemented
479#125C23×C7116yescomplemented
480#124C23×C718yes—
481#124C23×C718yes—
482#124C23×C7116yescomplemented
483#124C23×C7116yescomplemented
484#124C23×C718yescomplemented
485#124C23×C7116yescomplemented
486#124C23×C7116yescomplemented
487#123C23×C7116yes—
488#123C23×C718yes—
489#123C23×C718yes—
490#123C23×C7116yes—
491#123C23×C718yes—
492#123C23×C718yes—
493#123C23×C7116yescomplemented
494#123C23×C7116yescomplemented
495#123C23×C7116yescomplemented
496#123C23×C7116yescomplemented
497#123C23×C7116yescomplemented
498#123C23×C7116yescomplemented
499#123C23×C7116yescomplemented
500#123C23×C7116yescomplemented
501C22⋊Q8C23×C718yes—
502C22⋊Q8C23×C718yescomplemented
503C22⋊Q8C23×C718yescomplemented
504C22⋊Q8C23×C7116yescomplemented
505C22⋊Q8C23×C7116yescomplemented
506C22⋊Q8C23×C7116yescomplemented
507C22⋊Q8C23×C7116yescomplemented
508#121C23×C718yes—
509#121C23×C718yes—
510#121C23×C718yes—
511#121C23×C718yes—
512#121C23×C718yes—
513#121C23×C7116yes—
514#121C23×C7116yes—
515#121C23×C7116yes—
516#121C23×C7116yes—
517#121C23×C718yescomplemented
518#121C23×C7116yescomplemented
519#121C23×C7116yescomplemented
520#121C23×C7116yescomplemented
521#121C23×C718yescomplemented
522#121C23×C7116yescomplemented
523#121C23×C718yescomplemented
524#121C23×C718yescomplemented
525#121C23×C7116yescomplemented
526#121C23×C7116yescomplemented
527#121C23×C7116yescomplemented
528#121C23×C7116yescomplemented
529#121C23×C7116yescomplemented
530#120C23×C7116yes—
531#120C23×C7116yes—
532#120C23×C718yes—
533#120C23×C718yes—
534#120C23×C7116yes—
535#120C23×C7116yes—
536#120C23×C718yes—
537#120C23×C718yes—
538#120C23×C7116yescomplemented
539#120C23×C7116yescomplemented
540#120C23×C7116yescomplemented
541#120C23×C7116yescomplemented
542#120C23×C7116yescomplemented
543C4×Q8C23×C718yescomplemented
544C4×D4C23×C718yes—
545C4×D4C23×C718yes—
546C4×D4C23×C718yescomplemented
547C4×D4C23×C718yescomplemented
548C4×D4C23×C7116yescomplemented
549C4×D4C23×C7116yescomplemented
550C4×D4C23×C7116yescomplemented
551C4×D4C23×C7116yescomplemented
552C4×D4C23×C7116yescomplemented
553C4×D4C23×C718yescomplemented
554C4×D4C23×C718yescomplemented
555C4×D4C23×C718yescomplemented
556C4×D4C23×C7116yescomplemented
557#117C23×C718yes—
558#117C23×C718yescomplemented
559#117C23×C7116yescomplemented
560C2×C4⋊C4C23×C714yes—
561C2×C4⋊C4C23×C714yescomplemented
562C2×C4⋊C4C23×C714yescomplemented
563C2×C4⋊C4C23×C712yescomplemented
564C2×C4⋊C4C23×C718yescomplemented
565C2×C4⋊C4C23×C712yescomplemented
566C2×C22⋊C4C23×C714yes—
567C2×C22⋊C4C23×C714yes—
568C2×C22⋊C4C23×C714yes—
569C2×C22⋊C4C23×C714yes—
570C2×C22⋊C4C23×C718yes—
571C2×C22⋊C4C23×C718yes—
572C2×C22⋊C4C23×C714yes—
573C2×C22⋊C4C23×C714yes—
574C2×C22⋊C4C23×C714yescomplemented
575C2×C22⋊C4C23×C7116yescomplemented
576C2×C22⋊C4C23×C714yescomplemented
577C2×C22⋊C4C23×C7116yescomplemented
578C2×C42C23×C714yescomplemented
579C22×C7—22no—
580C22×C7—22no—
581C22×C7—22no—
582C22×C7—28no—
583C22×C7—24no—
584C22×C7—28no—
585C22×C7—28no—
586C22×C7—216no—
587C22×C7—28no—
588C22×C7—28no—
589C22×C7—44no—
590C22×C7—48no—
591C22×C7—88no—
592C22×C7—88no—
593C22×C7—88no—
594C22×C7—816no—
595C22×C7—168no—
596C22×C7C2×H(5,𝔽2)12yes—
597C22×C7C2×H(5,𝔽2)14yes—
598C22×C7C2611yescharacteristic
599C4×C7—28no—
600C4×C7—28no—
601C4×C7—24no—
602C4×C7—28no—
603C4×C7—24no—
604C4×C7—28no—
605C24—24no—
606C24—44no—
607C24—82no—
608C24—84no—
609C24C24×C714yes—
610C24C24×C714yes—
611C24C24×C712yes—
612C24C24×C714yes—
613C24C24×C718yes—
614C24C24×C718yes—
615C24C24×C711yescharacteristic
616#41—416no—
617#41—432no—
618#41—88no—
619C2×Q8—82no—
620C2×Q8C24×C718yes—
621C2×Q8C24×C718yes—
622C2×D4—216no—
623C2×D4—216no—
624C2×D4—48no—
625C2×D4—432no—
626C2×D4—416no—
627C2×D4—432no—
628C2×D4—84no—
629C2×D4—84no—
630C2×D4—84no—
631C2×D4—82no—
632C2×D4—88no—
633C2×D4—816no—
634C2×D4C24×C718yes—
635C2×D4C24×C718yes—
636C2×D4C24×C7116yes—
637C2×D4C24×C718yes—
638C2×D4C24×C718yes—
639C2×D4C24×C7116yes—
640C2×D4C24×C7116yes—
641C2×D4C24×C7116yes—
642C2×D4C24×C7116yes—
643C2×D4C24×C718yes—
644C2×D4C24×C718yes—
645C2×D4C24×C718yes—
646C2×D4C24×C7116yes—
647C2×D4C24×C718yes—
648C22×C4—44no—
649C22×C4—82no—
650C22×C4—84no—
651C22×C4C24×C714yes—
652C22×C4C24×C714yes—
653C22×C4C24×C714yes—
654C22×C4C24×C714yes—
655C22×C4C24×C714yes—
656C22×C4C24×C712yes—
657C22×C4C24×C712yes—
658C22×C4C24×C714yes—
659C22×C4C24×C7116yes—
660C22×C4C24×C718yes—
661C22×C4C24×C718yes—
662C22×C4C24×C7116yes—
663C22×C4C24×C718yes—
664C22×C4C24×C718yes—
665C4⋊C4C24×C718yes—
666C4⋊C4C24×C718yes—
667C4⋊C4C24×C718yes—
668C4⋊C4C24×C7116yes—
669C4⋊C4C24×C7116yes—
670C4⋊C4C24×C718yes—
671C4⋊C4C24×C718yes—
672C4⋊C4C24×C718yes—
673C4⋊C4C24×C7116yes—
674C4⋊C4C24×C7116yes—
675C22⋊C4C24×C718yes—
676C22⋊C4C24×C714yes—
677C22⋊C4C24×C718yes—
678C22⋊C4C24×C714yes—
679C22⋊C4C24×C7116yes—
680C22⋊C4C24×C7116yes—
681C22⋊C4C24×C7116yes—
682C22⋊C4C24×C7116yes—
683C22⋊C4C24×C718yes—
684C22⋊C4C24×C718yes—
685C22⋊C4C24×C718yes—
686C22⋊C4C24×C7116yes—
687C22⋊C4C24×C7116yes—
688C22⋊C4C24×C7116yes—
689C22⋊C4C24×C7116yes—
690C22⋊C4C24×C718yes—
691C22⋊C4C24×C718yes—
692C22⋊C4C24×C7116yes—
693C42C24×C718yes—
694C42C24×C718yes—
695C42C24×C718yes—
696C42C24×C718yes—
697C2×C7—22no—
698C2×C7—24no—
699C2×C7—44no—
700C2×C7—48no—
701C2×C7—48no—
702C2×C7C22×H(5,𝔽2)11yescharacteristic
703C2×C7H(7,𝔽2)12yes—
704C23—24no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—48no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—48no—
716C23—416no—
717C23—48no—
718C23—416no—
719C23—88no—
720C23—816no—
721C23C7×H(5,𝔽2)14yes—
722C23C25×C714yes—
723C23C25×C718yes—
724C23C25×C718yes—
725C23C25×C711yescharacteristic
726C23C25×C712yes—
727Q8—48no—
728Q8—48no—
729D4—232no—
730D4—216no—
731D4—216no—
732D4—48no—
733D4—48no—
734D4—48no—
735D4—416no—
736D4—416no—
737D4—48no—
738D4—416no—
739D4—48no—
740D4—416no—
741D4—48no—
742D4—416no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—48no—
753C2×C4—416no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—416no—
757C2×C4C25×C718yes—
758C2×C4C25×C714yes—
759C2×C4C25×C714yes—
760C2×C4C25×C718yes—
761C2×C4C25×C718yes—
762C2×C4C25×C718yes—
763C7#6286311yescharacteristic, direct product factor, Sylow
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×C7×H(5,𝔽2)12yes—
782C22C2×C7×H(5,𝔽2)14yes—
783C22C26×C711yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×C7×H(5,𝔽2)11yescharacteristic
796C2C7×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C7C26
commutator, Frattini, cosocleC22C26×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3560C2semidirect
2. C7×#3558C2semidirect
3. C7×#3537C2semidirect
4. C7×#3534C2semidirect
5. C7×#3533C2semidirect
6. C7×#3532C2semidirect
7. C7×#3505C2semidirect
8. C7×#3496C2semidirect
9. C7×#3484C2semidirect
10. C2×C7×#538C2semidirect
11. C2×C7×#534C2semidirect
12. C2×C7×H(5,𝔽2)C22semidirect
13. C23×C7×D4C22semidirect
14. C7×#563C22semidirect
15. C7×#562C22semidirect
16. C7×H(3,𝔽4)C22semidirect
17. C7×#560C22semidirect
18. C7×#560C22semidirect
19. C7×#560C22semidirect
20. C7×#559C22semidirect
21. C7×#553C22semidirect
22. C7×#553C22semidirect
23. C7×#553C22semidirect
24. C7×#552C22semidirect
25. C7×#551C22semidirect
26. C7×#551C22semidirect
27. C7×#551C22semidirect
28. C7×#548C22semidirect
29. C7×#547C22semidirect
30. C7×#547C22semidirect
31. C7×#546C22semidirect
32. C7×#546C22semidirect
33. C7×#546C22semidirect
34. C7×#546C22semidirect
35. C7×#546C22semidirect
36. C7×#546C22semidirect
37. C7×D42C22semidirect
38. C7×D42C22semidirect
39. C7×D42C22semidirect
40. C7×D42C22semidirect
41. C7×D42C22semidirect
42. C7×#542C22semidirect
43. C7×#540C22semidirect
44. C7×#539C22semidirect
45. C7×#539C22semidirect
46. C7×#538C22semidirect
47. C7×#538C22semidirect
48. C7×#538C22semidirect
49. C7×#538C22semidirect
50. C7×#538C22semidirect
51. C7×#538C22semidirect
52. C7×#538C22semidirect
53. C7×#537C22semidirect
54. C7×#535C22semidirect
55. C7×#535C22semidirect
56. C7×#534C22semidirect
57. C7×#534C22semidirect
58. C7×#534C22semidirect
59. C7×#534C22semidirect
60. C7×#534C22semidirect
61. C7×#534C22semidirect
62. C7×#532C22semidirect
63. C7×#529C22semidirect
64. C2×C7×#126C22semidirect
65. C2×C7×#124C22semidirect
66. C7×#525C22semidirect
67. C7×#525C22semidirect
68. C2×C7×#123C22semidirect
69. C2×C7×#123C22semidirect
70. C2×C7×C22⋊Q8C22semidirect
71. C2×C7×#121C22semidirect
72. C2×C7×#121C22semidirect
73. C2×C7×#121C22semidirect
74. C2×C7×#121C22semidirect
75. C2×C7×#120C22semidirect
76. C2×C7×#120C22semidirect
77. C2×C7×#120C22semidirect
78. C7×#518C22semidirect
79. C2×C4×C7×D4C22semidirect
80. C22×C7×C22⋊C4C22semidirect
81. #62863C7direct (N × H)
86. C2×C7×#41C23semidirect
87. C2×C7×#41C23semidirect
88. C22×C7×Q8C23semidirect
98. C22×C7×D4C23semidirect
99. C22×C7×D4C23semidirect
100. C22×C7×D4C23semidirect
101. C22×C7×D4C23semidirect
104. C23×C4×C7C23semidirect
105. C7×C4⋊Q8C23semidirect
108. C7×#127C23semidirect
109. C7×#126C23semidirect
110. C7×#126C23semidirect
111. C7×#126C23semidirect
112. C7×#126C23semidirect
113. C7×#126C23semidirect
114. C7×#125C23semidirect
115. C7×#125C23semidirect
118. C7×#124C23semidirect
119. C7×#124C23semidirect
120. C7×#124C23semidirect
121. C7×#124C23semidirect
122. C7×#124C23semidirect
129. C7×#123C23semidirect
130. C7×#123C23semidirect
131. C7×#123C23semidirect
132. C7×#123C23semidirect
133. C7×#123C23semidirect
134. C7×#123C23semidirect
135. C7×#123C23semidirect
136. C7×#123C23semidirect
138. C7×C22⋊Q8C23semidirect
139. C7×C22⋊Q8C23semidirect
140. C7×C22⋊Q8C23semidirect
141. C7×C22⋊Q8C23semidirect
142. C7×C22⋊Q8C23semidirect
143. C7×C22⋊Q8C23semidirect
153. C7×#121C23semidirect
154. C7×#121C23semidirect
155. C7×#121C23semidirect
156. C7×#121C23semidirect
157. C7×#121C23semidirect
158. C7×#121C23semidirect
159. C7×#121C23semidirect
160. C7×#121C23semidirect
161. C7×#121C23semidirect
162. C7×#121C23semidirect
163. C7×#121C23semidirect
164. C7×#121C23semidirect
165. C7×#121C23semidirect
174. C7×#120C23semidirect
175. C7×#120C23semidirect
176. C7×#120C23semidirect
177. C7×#120C23semidirect
178. C7×#120C23semidirect
179. C4×C7×Q8C23semidirect
182. C4×C7×D4C23semidirect
183. C4×C7×D4C23semidirect
184. C4×C7×D4C23semidirect
185. C4×C7×D4C23semidirect
186. C4×C7×D4C23semidirect
187. C4×C7×D4C23semidirect
188. C4×C7×D4C23semidirect
189. C4×C7×D4C23semidirect
190. C4×C7×D4C23semidirect
191. C4×C7×D4C23semidirect
192. C4×C7×D4C23semidirect
194. C7×#117C23semidirect
195. C7×#117C23semidirect
197. C2×C7×C4⋊C4C23semidirect
198. C2×C7×C4⋊C4C23semidirect
199. C2×C7×C4⋊C4C23semidirect
200. C2×C7×C4⋊C4C23semidirect
201. C2×C7×C4⋊C4C23semidirect
210. C2×C7×C22⋊C4C23semidirect
211. C2×C7×C22⋊C4C23semidirect
212. C2×C7×C22⋊C4C23semidirect
213. C2×C7×C22⋊C4C23semidirect
214. C2×C42×C7C23semidirect
215. #3560C2×C7semidirect
216. #3558C2×C7semidirect
217. #3537C2×C7semidirect
218. #3534C2×C7semidirect
219. #3533C2×C7semidirect
220. #3532C2×C7semidirect
221. #3505C2×C7semidirect
222. #3496C2×C7semidirect
223. #3484C2×C7semidirect
224. C2×#538C2×C7semidirect
225. C2×#534C2×C7semidirect
318. C2×H(5,𝔽2)C22×C7semidirect
319. C23×D4C22×C7semidirect
320. #563C22×C7semidirect
321. #562C22×C7semidirect
322. H(3,𝔽4)C22×C7semidirect
323. #560C22×C7semidirect
324. #560C22×C7semidirect
325. #560C22×C7semidirect
326. #559C22×C7semidirect
327. #553C22×C7semidirect
328. #553C22×C7semidirect
329. #553C22×C7semidirect
330. #552C22×C7semidirect
331. #551C22×C7semidirect
332. #551C22×C7semidirect
333. #551C22×C7semidirect
334. #548C22×C7semidirect
335. #547C22×C7semidirect
336. #547C22×C7semidirect
337. #546C22×C7semidirect
338. #546C22×C7semidirect
339. #546C22×C7semidirect
340. #546C22×C7semidirect
341. #546C22×C7semidirect
342. #546C22×C7semidirect
343. D42C22×C7semidirect
344. D42C22×C7semidirect
345. D42C22×C7semidirect
346. D42C22×C7semidirect
347. D42C22×C7semidirect
348. #542C22×C7semidirect
349. #540C22×C7semidirect
350. #539C22×C7semidirect
351. #539C22×C7semidirect
352. #538C22×C7semidirect
353. #538C22×C7semidirect
354. #538C22×C7semidirect
355. #538C22×C7semidirect
356. #538C22×C7semidirect
357. #538C22×C7semidirect
358. #538C22×C7semidirect
359. #537C22×C7semidirect
360. #535C22×C7semidirect
361. #535C22×C7semidirect
362. #534C22×C7semidirect
363. #534C22×C7semidirect
364. #534C22×C7semidirect
365. #534C22×C7semidirect
366. #534C22×C7semidirect
367. #534C22×C7semidirect
368. #532C22×C7semidirect
369. #529C22×C7semidirect
370. C2×#126C22×C7semidirect
371. C2×#124C22×C7semidirect
372. #525C22×C7semidirect
373. #525C22×C7semidirect
374. C2×#123C22×C7semidirect
375. C2×#123C22×C7semidirect
376. C2×C22⋊Q8C22×C7semidirect
377. C2×#121C22×C7semidirect
378. C2×#121C22×C7semidirect
379. C2×#121C22×C7semidirect
380. C2×#121C22×C7semidirect
381. C2×#120C22×C7semidirect
382. C2×#120C22×C7semidirect
383. C2×#120C22×C7semidirect
384. #518C22×C7semidirect
385. C2×C4×D4C22×C7semidirect
386. C22×C22⋊C4C22×C7semidirect
450. C2×#41C23×C7semidirect
451. C2×#41C23×C7semidirect
452. C22×Q8C23×C7semidirect
462. C22×D4C23×C7semidirect
463. C22×D4C23×C7semidirect
464. C22×D4C23×C7semidirect
465. C22×D4C23×C7semidirect
468. C23×C4C23×C7semidirect
469. C4⋊Q8C23×C7semidirect
472. #127C23×C7semidirect
473. #126C23×C7semidirect
474. #126C23×C7semidirect
475. #126C23×C7semidirect
476. #126C23×C7semidirect
477. #126C23×C7semidirect
478. #125C23×C7semidirect
479. #125C23×C7semidirect
482. #124C23×C7semidirect
483. #124C23×C7semidirect
484. #124C23×C7semidirect
485. #124C23×C7semidirect
486. #124C23×C7semidirect
493. #123C23×C7semidirect
494. #123C23×C7semidirect
495. #123C23×C7semidirect
496. #123C23×C7semidirect
497. #123C23×C7semidirect
498. #123C23×C7semidirect
499. #123C23×C7semidirect
500. #123C23×C7semidirect
502. C22⋊Q8C23×C7semidirect
503. C22⋊Q8C23×C7semidirect
504. C22⋊Q8C23×C7semidirect
505. C22⋊Q8C23×C7semidirect
506. C22⋊Q8C23×C7semidirect
507. C22⋊Q8C23×C7semidirect
517. #121C23×C7semidirect
518. #121C23×C7semidirect
519. #121C23×C7semidirect
520. #121C23×C7semidirect
521. #121C23×C7semidirect
522. #121C23×C7semidirect
523. #121C23×C7semidirect
524. #121C23×C7semidirect
525. #121C23×C7semidirect
526. #121C23×C7semidirect
527. #121C23×C7semidirect
528. #121C23×C7semidirect
529. #121C23×C7semidirect
538. #120C23×C7semidirect
539. #120C23×C7semidirect
540. #120C23×C7semidirect
541. #120C23×C7semidirect
542. #120C23×C7semidirect
543. C4×Q8C23×C7semidirect
546. C4×D4C23×C7semidirect
547. C4×D4C23×C7semidirect
548. C4×D4C23×C7semidirect
549. C4×D4C23×C7semidirect
550. C4×D4C23×C7semidirect
551. C4×D4C23×C7semidirect
552. C4×D4C23×C7semidirect
553. C4×D4C23×C7semidirect
554. C4×D4C23×C7semidirect
555. C4×D4C23×C7semidirect
556. C4×D4C23×C7semidirect
558. #117C23×C7semidirect
559. #117C23×C7semidirect
561. C2×C4⋊C4C23×C7semidirect
562. C2×C4⋊C4C23×C7semidirect
563. C2×C4⋊C4C23×C7semidirect
564. C2×C4⋊C4C23×C7semidirect
565. C2×C4⋊C4C23×C7semidirect
574. C2×C22⋊C4C23×C7semidirect
575. C2×C22⋊C4C23×C7semidirect
576. C2×C22⋊C4C23×C7semidirect
577. C2×C22⋊C4C23×C7semidirect
578. C2×C42C23×C7semidirect
763. C7#62863direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35602
C7×#35582
C7×#35372
C7×#35342
C7×#35332
C7×#35322
C7×#35052
C7×#34962
C7×#34842
C2×C7×#5382
C2×C7×#5342
#628637