Finite Group Databasebeta

← C7×#62862 #13240078

Subgroups — C7×#62862 #13240078

Order 1792.

7498 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3545C214yesmaximal, complemented
2C7×#3543C214yesmaximal, complemented
3C7×#3542C2116yesmaximal, complemented
4C7×#3534C218yesmaximal, complemented
5C7×#3533C218yesmaximal, complemented
6C7×#3532C218yesmaximal, complemented
7C7×#3491C212yesmaximal, complemented
8C7×#3490C214yesmaximal, complemented
9C7×#3485C212yesmaximal, complemented
10C7×#3484C214yesmaximal, complemented
11C2×C7×#535C211yesmaximal, characteristic, complemented
12C2×C7×#534C212yesmaximal, complemented
13C2×C7×H(5,𝔽2)C2212yescomplemented
14C22×C7×#41C2211yescharacteristic, complemented
15C23×C7×D4C2211yescharacteristic, complemented
16C23×C7×D4C2212yescomplemented
17C7×#563C2214yescomplemented
18C7×#562C22116yescomplemented
19C7×#562C2218yescomplemented
20C7×H(3,𝔽4)C2214yescomplemented
21C7×#560C2218yescomplemented
22C7×#560C22116yescomplemented
23C7×#560C2218yescomplemented
24C7×#559C2214yescomplemented
25C7×#555C2218yescomplemented
26C7×#553C22116yescomplemented
27C7×#552C22116yescomplemented
28C7×#551C22116yescomplemented
29C7×#551C22116yescomplemented
30C7×#551C2218yescomplemented
31C7×#551C22116yescomplemented
32C7×#550C2218yescomplemented
33C7×#547C22116yescomplemented
34C7×#546C22116yescomplemented
35C7×#546C22116yescomplemented
36C7×#546C22116yescomplemented
37C7×#546C22116yescomplemented
38C7×#546C22116yescomplemented
39C7×#546C22116yescomplemented
40C7×D42C22116yescomplemented
41C7×D42C2214yescomplemented
42C7×D42C22116yescomplemented
43C7×#543C2212yescomplemented
44C7×#542C22116yescomplemented
45C7×#540C22116yescomplemented
46C7×#540C22116yescomplemented
47C7×#539C2218yescomplemented
48C7×#539C2218yescomplemented
49C7×#538C22116yescomplemented
50C7×#538C22116yescomplemented
51C7×#538C22116yescomplemented
52C7×#538C2218yescomplemented
53C7×#537C2218yescomplemented
54C7×#536C2214yescomplemented
55C7×#535C2218yescomplemented
56C7×#535C2218yescomplemented
57C7×#535C2218yescomplemented
58C7×#535C22116yescomplemented
59C7×#534C2212yes—
60C7×#534C2218yescomplemented
61C7×#534C2218yescomplemented
62C7×#534C2214yescomplemented
63C7×#534C2218yescomplemented
64C7×#534C2218yescomplemented
65C7×#534C2218yescomplemented
66C7×#534C2218yescomplemented
67C7×#534C2214yescomplemented
68C2×C7×#127C2212yescomplemented
69C7×#529C2218yescomplemented
70C2×C7×#124C2212yescomplemented
71C7×#525C22116yescomplemented
72C7×#525C2218yescomplemented
73C7×#525C2214yescomplemented
74C2×C7×#123C2214yescomplemented
75C2×C7×#123C2214yescomplemented
76C2×C7×#123C2214yescomplemented
77C2×C7×#121C2218yescomplemented
78C2×C7×#121C2214yescomplemented
79C2×C7×#120C2214yescomplemented
80C2×C7×#120C2214yescomplemented
81C2×C7×#120C2214yescomplemented
82C2×C7×#120C2218yescomplemented
83C7×#518C2214yescomplemented
84C7×#518C2212yescomplemented
85C2×C7×#117C2211yescharacteristic, complemented
86C22×C7×C22⋊C4C2212yescomplemented
87#62862C711yesmaximal, characteristic, direct product factor, Sylow
88C25×C7C2312yes—
89C25×C7C2312yescomplemented
90C7×H(5,𝔽2)—48no—
91C2×C7×#41—44no—
92C2×C7×#41C2318yes—
93C2×C7×#41C2314yes—
94C2×C7×#41C2318yescomplemented
95C2×C7×#41C23116yescomplemented
96C22×C7×Q8C2311yescharacteristic, complemented
97C22×C7×D4—44no—
98C22×C7×D4—48no—
99C22×C7×D4C2314yes—
100C22×C7×D4C2312yes—
101C22×C7×D4C2314yes—
102C22×C7×D4C2312yes—
103C22×C7×D4C2314yes—
104C22×C7×D4C2312yes—
105C22×C7×D4C2318yes—
106C22×C7×D4C2318yes—
107C22×C7×D4C2314yes—
108C22×C7×D4C2318yes—
109C22×C7×D4C2314yescomplemented
110C22×C7×D4C2318yescomplemented
111C22×C7×D4C2311yescharacteristic, complemented
112C22×C7×D4C2318yescomplemented
113C22×C7×D4C23116yescomplemented
114C23×C4×C7C2311yescharacteristic
115C23×C4×C7C2312yescomplemented
116C23×C4×C7C2312yescomplemented
117C23×C4×C7C2314yescomplemented
118C7×C4⋊Q8C2318yescomplemented
119C7×#127C2314yes—
120C7×#127C2318yescomplemented
121C7×#127C2314yescomplemented
122C7×#127C23116yescomplemented
123C7×#126C23116yescomplemented
124C7×#126C23116yescomplemented
125C7×#126C23116yescomplemented
126C7×#126C23116yescomplemented
127C7×#125C2318yescomplemented
128C7×#125C23116yescomplemented
129C7×#124C2314yes—
130C7×#124C2318yescomplemented
131C7×#124C2314yescomplemented
132C7×#124C2318yescomplemented
133C7×#124C23116yescomplemented
134C7×#124C23116yescomplemented
135C7×#124C2318yescomplemented
136C7×#124C23116yescomplemented
137C7×#123C2318yes—
138C7×#123C23116yes—
139C7×#123C2318yes—
140C7×#123C2318yes—
141C7×#123C2318yescomplemented
142C7×#123C2318yescomplemented
143C7×#123C2318yescomplemented
144C7×#123C2318yescomplemented
145C7×#123C2318yescomplemented
146C7×#123C23116yescomplemented
147C7×#123C2318yescomplemented
148C7×#123C23116yescomplemented
149C7×#123C23116yescomplemented
150C7×#123C23116yescomplemented
151C7×#123C23116yescomplemented
152C7×#123C2318yescomplemented
153C7×#123C23116yescomplemented
154C7×#123C23116yescomplemented
155C7×C22⋊Q8C23116yescomplemented
156C7×C22⋊Q8C2318yescomplemented
157C7×C22⋊Q8C23116yescomplemented
158C7×C22⋊Q8C23116yescomplemented
159C7×C22⋊Q8C2318yescomplemented
160C7×C22⋊Q8C23116yescomplemented
161C7×C22⋊Q8C23116yescomplemented
162C7×#121C23116yes—
163C7×#121C23116yes—
164C7×#121C2318yes—
165C7×#121C23116yes—
166C7×#121C2318yes—
167C7×#121C23116yescomplemented
168C7×#121C23116yescomplemented
169C7×#121C2318yescomplemented
170C7×#121C23116yescomplemented
171C7×#121C2318yescomplemented
172C7×#121C23116yescomplemented
173C7×#121C23116yescomplemented
174C7×#121C23116yescomplemented
175C7×#121C23116yescomplemented
176C7×#121C23116yescomplemented
177C7×#121C23116yescomplemented
178C7×#121C23116yescomplemented
179C7×#121C23116yescomplemented
180C7×#121C23116yescomplemented
181C7×#120C2318yes—
182C7×#120C2318yes—
183C7×#120C2318yes—
184C7×#120C2318yes—
185C7×#120C23116yes—
186C7×#120C2318yes—
187C7×#120C23116yes—
188C7×#120C2318yescomplemented
189C7×#120C2318yescomplemented
190C7×#120C2318yescomplemented
191C7×#120C2318yescomplemented
192C7×#120C2318yescomplemented
193C7×#120C23116yescomplemented
194C7×#120C23116yescomplemented
195C7×#120C2318yescomplemented
196C7×#120C2318yescomplemented
197C7×#120C23116yescomplemented
198C4×C7×Q8C2318yescomplemented
199C4×C7×D4C23116yes—
200C4×C7×D4C23116yescomplemented
201C4×C7×D4C23116yescomplemented
202C4×C7×D4C23116yescomplemented
203C4×C7×D4C23116yescomplemented
204C4×C7×D4C23116yescomplemented
205C4×C7×D4C23116yescomplemented
206C4×C7×D4C23116yescomplemented
207C4×C7×D4C2318yescomplemented
208C7×#117C2318yescomplemented
209C7×#117C2318yescomplemented
210C7×#117C2314yescomplemented
211C7×#117C23116yescomplemented
212C7×#117C23116yescomplemented
213C2×C7×C4⋊C4C2312yescomplemented
214C2×C7×C4⋊C4C2318yescomplemented
215C2×C7×C4⋊C4C2318yescomplemented
216C2×C7×C22⋊C4C2314yes—
217C2×C7×C22⋊C4C2318yes—
218C2×C7×C22⋊C4C2312yes—
219C2×C7×C22⋊C4C2318yes—
220C2×C7×C22⋊C4C2314yescomplemented
221C2×C7×C22⋊C4C2318yescomplemented
222C2×C7×C22⋊C4C2318yescomplemented
223C2×C7×C22⋊C4C2314yescomplemented
224C2×C7×C22⋊C4C2318yescomplemented
225C2×C7×C22⋊C4C2318yescomplemented
226C2×C7×C22⋊C4C23116yescomplemented
227C2×C7×C22⋊C4C2318yescomplemented
228C2×C42×C7C2312yescomplemented
229#3545C2×C714yescomplemented
230#3543C2×C714yescomplemented
231#3542C2×C7116yescomplemented
232#3534C2×C718yescomplemented
233#3533C2×C718yescomplemented
234#3532C2×C718yescomplemented
235#3491C2×C712yescomplemented
236#3490C2×C714yescomplemented
237#3485C2×C712yescomplemented
238#3484C2×C714yescomplemented
239C2×#535C2×C711yescharacteristic, complemented
240C2×#534C2×C712yescomplemented
241C24×C7—28no—
242C24×C7—44no—
243C24×C7—84no—
244C24×C7—84no—
245C24×C7C2414yes—
246C24×C7C2414yes—
247C24×C7C2414yes—
248C24×C7C2412yes—
249C24×C7C2412yes—
250C24×C7C2412yes—
251C24×C7C2418yes—
252C24×C7C2414yes—
253C24×C7C2411yescharacteristic
254C7×#41—416no—
255C7×#41—416no—
256C7×#41—48no—
257C7×#41—816no—
258C2×C7×Q8—42no—
259C2×C7×Q8C2418yes—
260C2×C7×Q8C2414yes—
261C2×C7×Q8C2414yes—
262C2×C7×D4—216no—
263C2×C7×D4—28no—
264C2×C7×D4—44no—
265C2×C7×D4—44no—
266C2×C7×D4—48no—
267C2×C7×D4—48no—
268C2×C7×D4—48no—
269C2×C7×D4—42no—
270C2×C7×D4—416no—
271C2×C7×D4—416no—
272C2×C7×D4—48no—
273C2×C7×D4—416no—
274C2×C7×D4—88no—
275C2×C7×D4—88no—
276C2×C7×D4—816no—
277C2×C7×D4C2418yes—
278C2×C7×D4C2418yes—
279C2×C7×D4C2418yes—
280C2×C7×D4C24116yes—
281C2×C7×D4C24116yes—
282C2×C7×D4C2418yes—
283C2×C7×D4C24116yes—
284C2×C7×D4C24116yes—
285C2×C7×D4C24116yes—
286C2×C7×D4C2412yes—
287C2×C7×D4C2412yes—
288C2×C7×D4C2414yes—
289C2×C7×D4C2414yes—
290C2×C7×D4C2414yes—
291C2×C7×D4C2418yes—
292C2×C7×D4C2414yes—
293C2×C7×D4C24116yes—
294C2×C7×D4C2412yes—
295C2×C7×D4C2412yes—
296C22×C4×C7—24no—
297C22×C4×C7—44no—
298C22×C4×C7—44no—
299C22×C4×C7—84no—
300C22×C4×C7C2411yescharacteristic
301C22×C4×C7C2414yes—
302C22×C4×C7C2412yes—
303C22×C4×C7C2414yes—
304C22×C4×C7C2411yescharacteristic
305C22×C4×C7C2414yes—
306C22×C4×C7C2418yes—
307C22×C4×C7C24116yes—
308C22×C4×C7C2418yes—
309C22×C4×C7C24116yes—
310C22×C4×C7C2418yes—
311C22×C4×C7C2418yes—
312C22×C4×C7C2414yes—
313C22×C4×C7C2418yes—
314C7×C4⋊C4C24116yes—
315C7×C4⋊C4C2418yes—
316C7×C4⋊C4C24116yes—
317C7×C4⋊C4C24116yes—
318C7×C4⋊C4C24116yes—
319C7×C4⋊C4C24116yes—
320C7×C4⋊C4C2418yes—
321C7×C4⋊C4C2418yes—
322C7×C4⋊C4C2418yes—
323C7×C22⋊C4C2418yes—
324C7×C22⋊C4C2418yes—
325C7×C22⋊C4C2418yes—
326C7×C22⋊C4C2418yes—
327C7×C22⋊C4C2418yes—
328C7×C22⋊C4C24116yes—
329C7×C22⋊C4C24116yes—
330C7×C22⋊C4C24116yes—
331C7×C22⋊C4C24116yes—
332C7×C22⋊C4C24116yes—
333C7×C22⋊C4C24116yes—
334C7×C22⋊C4C24116yes—
335C7×C22⋊C4C24116yes—
336C7×C22⋊C4C24116yes—
337C7×C22⋊C4C2418yes—
338C7×C22⋊C4C24116yes—
339C42×C7C2414yes—
340C42×C7C2414yes—
341C42×C7C24116yes—
342C42×C7C2418yes—
343C2×H(5,𝔽2)C22×C712yescomplemented
344C22×#41C22×C711yescharacteristic, complemented
345C23×D4C22×C711yescharacteristic, complemented
346C23×D4C22×C712yescomplemented
347#563C22×C714yescomplemented
348#562C22×C7116yescomplemented
349#562C22×C718yescomplemented
350H(3,𝔽4)C22×C714yescomplemented
351#560C22×C718yescomplemented
352#560C22×C7116yescomplemented
353#560C22×C718yescomplemented
354#559C22×C714yescomplemented
355#555C22×C718yescomplemented
356#553C22×C7116yescomplemented
357#552C22×C7116yescomplemented
358#551C22×C7116yescomplemented
359#551C22×C7116yescomplemented
360#551C22×C718yescomplemented
361#551C22×C7116yescomplemented
362#550C22×C718yescomplemented
363#547C22×C7116yescomplemented
364#546C22×C7116yescomplemented
365#546C22×C7116yescomplemented
366#546C22×C7116yescomplemented
367#546C22×C7116yescomplemented
368#546C22×C7116yescomplemented
369#546C22×C7116yescomplemented
370D42C22×C7116yescomplemented
371D42C22×C714yescomplemented
372D42C22×C7116yescomplemented
373#543C22×C712yescomplemented
374#542C22×C7116yescomplemented
375#540C22×C7116yescomplemented
376#540C22×C7116yescomplemented
377#539C22×C718yescomplemented
378#539C22×C718yescomplemented
379#538C22×C7116yescomplemented
380#538C22×C7116yescomplemented
381#538C22×C7116yescomplemented
382#538C22×C718yescomplemented
383#537C22×C718yescomplemented
384#536C22×C714yescomplemented
385#535C22×C718yescomplemented
386#535C22×C718yescomplemented
387#535C22×C718yescomplemented
388#535C22×C7116yescomplemented
389#534C22×C712yes—
390#534C22×C718yescomplemented
391#534C22×C718yescomplemented
392#534C22×C714yescomplemented
393#534C22×C718yescomplemented
394#534C22×C718yescomplemented
395#534C22×C718yescomplemented
396#534C22×C718yescomplemented
397#534C22×C714yescomplemented
398C2×#127C22×C712yescomplemented
399#529C22×C718yescomplemented
400C2×#124C22×C712yescomplemented
401#525C22×C7116yescomplemented
402#525C22×C718yescomplemented
403#525C22×C714yescomplemented
404C2×#123C22×C714yescomplemented
405C2×#123C22×C714yescomplemented
406C2×#123C22×C714yescomplemented
407C2×#121C22×C718yescomplemented
408C2×#121C22×C714yescomplemented
409C2×#120C22×C714yescomplemented
410C2×#120C22×C714yescomplemented
411C2×#120C22×C714yescomplemented
412C2×#120C22×C718yescomplemented
413#518C22×C714yescomplemented
414#518C22×C712yescomplemented
415C2×#117C22×C711yescharacteristic, complemented
416C22×C22⋊C4C22×C712yescomplemented
417C23×C7—24no—
418C23×C7—24no—
419C23×C7—24no—
420C23×C7—28no—
421C23×C7—28no—
422C23×C7—28no—
423C23×C7—44no—
424C23×C7—42no—
425C23×C7—44no—
426C23×C7—48no—
427C23×C7—44no—
428C23×C7—48no—
429C23×C7—48no—
430C23×C7—48no—
431C23×C7—416no—
432C23×C7—44no—
433C23×C7—48no—
434C23×C7—816no—
435C23×C7—816no—
436C23×C7H(5,𝔽2)14yes—
437C23×C7C2514yes—
438C23×C7C2518yes—
439C23×C7C2514yes—
440C23×C7C2514yes—
441C23×C7C2512yes—
442C23×C7C2511yescharacteristic
443C7×Q8—44no—
444C7×Q8—44no—
445C7×Q8—48no—
446C7×D4—216no—
447C7×D4—216no—
448C7×D4—216no—
449C7×D4—42no—
450C7×D4—44no—
451C7×D4—42no—
452C7×D4—42no—
453C7×D4—44no—
454C7×D4—42no—
455C7×D4—416no—
456C7×D4—48no—
457C7×D4—44no—
458C7×D4—44no—
459C7×D4—416no—
460C7×D4—416no—
461C7×D4—48no—
462C7×D4—416no—
463C7×D4—416no—
464C7×D4—416no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—28no—
468C2×C4×C7—28no—
469C2×C4×C7—24no—
470C2×C4×C7—48no—
471C2×C4×C7—48no—
472C2×C4×C7—48no—
473C2×C4×C7—416no—
474C2×C4×C7—44no—
475C2×C4×C7—48no—
476C2×C4×C7—44no—
477C2×C4×C7—416no—
478C2×C4×C7—48no—
479C2×C4×C7C2518yes—
480C2×C4×C7C2512yes—
481C2×C4×C7C25116yes—
482C2×C4×C7C2514yes—
483C2×C4×C7C2518yes—
484C2×C4×C7C2512yes—
485C25C23×C712yes—
486C25C23×C712yescomplemented
487H(5,𝔽2)—48no—
488C2×#41—44no—
489C2×#41C23×C718yes—
490C2×#41C23×C714yes—
491C2×#41C23×C718yescomplemented
492C2×#41C23×C7116yescomplemented
493C22×Q8C23×C711yescharacteristic, complemented
494C22×D4—44no—
495C22×D4—48no—
496C22×D4C23×C712yes—
497C22×D4C23×C714yes—
498C22×D4C23×C714yes—
499C22×D4C23×C718yes—
500C22×D4C23×C712yes—
501C22×D4C23×C714yes—
502C22×D4C23×C714yes—
503C22×D4C23×C712yes—
504C22×D4C23×C718yes—
505C22×D4C23×C718yes—
506C22×D4C23×C714yescomplemented
507C22×D4C23×C711yescharacteristic, complemented
508C22×D4C23×C718yescomplemented
509C22×D4C23×C718yescomplemented
510C22×D4C23×C7116yescomplemented
511C23×C4C23×C711yescharacteristic
512C23×C4C23×C712yescomplemented
513C23×C4C23×C712yescomplemented
514C23×C4C23×C714yescomplemented
515C4⋊Q8C23×C718yescomplemented
516#127C23×C714yes—
517#127C23×C718yescomplemented
518#127C23×C714yescomplemented
519#127C23×C7116yescomplemented
520#126C23×C7116yescomplemented
521#126C23×C7116yescomplemented
522#126C23×C7116yescomplemented
523#126C23×C7116yescomplemented
524#125C23×C718yescomplemented
525#125C23×C7116yescomplemented
526#124C23×C714yes—
527#124C23×C718yescomplemented
528#124C23×C714yescomplemented
529#124C23×C718yescomplemented
530#124C23×C7116yescomplemented
531#124C23×C7116yescomplemented
532#124C23×C718yescomplemented
533#124C23×C7116yescomplemented
534#123C23×C718yes—
535#123C23×C7116yes—
536#123C23×C718yes—
537#123C23×C718yes—
538#123C23×C718yescomplemented
539#123C23×C718yescomplemented
540#123C23×C718yescomplemented
541#123C23×C718yescomplemented
542#123C23×C718yescomplemented
543#123C23×C7116yescomplemented
544#123C23×C718yescomplemented
545#123C23×C7116yescomplemented
546#123C23×C7116yescomplemented
547#123C23×C7116yescomplemented
548#123C23×C7116yescomplemented
549#123C23×C718yescomplemented
550#123C23×C7116yescomplemented
551#123C23×C7116yescomplemented
552C22⋊Q8C23×C7116yescomplemented
553C22⋊Q8C23×C718yescomplemented
554C22⋊Q8C23×C7116yescomplemented
555C22⋊Q8C23×C7116yescomplemented
556C22⋊Q8C23×C718yescomplemented
557C22⋊Q8C23×C7116yescomplemented
558C22⋊Q8C23×C7116yescomplemented
559#121C23×C7116yes—
560#121C23×C7116yes—
561#121C23×C718yes—
562#121C23×C7116yes—
563#121C23×C718yes—
564#121C23×C7116yescomplemented
565#121C23×C7116yescomplemented
566#121C23×C718yescomplemented
567#121C23×C7116yescomplemented
568#121C23×C718yescomplemented
569#121C23×C7116yescomplemented
570#121C23×C7116yescomplemented
571#121C23×C7116yescomplemented
572#121C23×C7116yescomplemented
573#121C23×C7116yescomplemented
574#121C23×C7116yescomplemented
575#121C23×C7116yescomplemented
576#121C23×C7116yescomplemented
577#121C23×C7116yescomplemented
578#120C23×C718yes—
579#120C23×C718yes—
580#120C23×C718yes—
581#120C23×C718yes—
582#120C23×C7116yes—
583#120C23×C718yes—
584#120C23×C7116yes—
585#120C23×C718yescomplemented
586#120C23×C718yescomplemented
587#120C23×C718yescomplemented
588#120C23×C718yescomplemented
589#120C23×C718yescomplemented
590#120C23×C7116yescomplemented
591#120C23×C7116yescomplemented
592#120C23×C718yescomplemented
593#120C23×C718yescomplemented
594#120C23×C7116yescomplemented
595C4×Q8C23×C718yescomplemented
596C4×D4C23×C7116yes—
597C4×D4C23×C7116yescomplemented
598C4×D4C23×C7116yescomplemented
599C4×D4C23×C7116yescomplemented
600C4×D4C23×C7116yescomplemented
601C4×D4C23×C7116yescomplemented
602C4×D4C23×C7116yescomplemented
603C4×D4C23×C7116yescomplemented
604C4×D4C23×C718yescomplemented
605#117C23×C718yescomplemented
606#117C23×C718yescomplemented
607#117C23×C714yescomplemented
608#117C23×C7116yescomplemented
609#117C23×C7116yescomplemented
610C2×C4⋊C4C23×C712yescomplemented
611C2×C4⋊C4C23×C718yescomplemented
612C2×C4⋊C4C23×C718yescomplemented
613C2×C22⋊C4C23×C714yes—
614C2×C22⋊C4C23×C718yes—
615C2×C22⋊C4C23×C712yes—
616C2×C22⋊C4C23×C718yes—
617C2×C22⋊C4C23×C714yescomplemented
618C2×C22⋊C4C23×C718yescomplemented
619C2×C22⋊C4C23×C718yescomplemented
620C2×C22⋊C4C23×C714yescomplemented
621C2×C22⋊C4C23×C718yescomplemented
622C2×C22⋊C4C23×C718yescomplemented
623C2×C22⋊C4C23×C7116yescomplemented
624C2×C22⋊C4C23×C718yescomplemented
625C2×C42C23×C712yescomplemented
626C22×C7—24no—
627C22×C7—22no—
628C22×C7—24no—
629C22×C7—24no—
630C22×C7—28no—
631C22×C7—24no—
632C22×C7—28no—
633C22×C7—28no—
634C22×C7—216no—
635C22×C7—28no—
636C22×C7—44no—
637C22×C7—48no—
638C22×C7—48no—
639C22×C7—84no—
640C22×C7—88no—
641C22×C7—88no—
642C22×C7—88no—
643C22×C7—816no—
644C22×C7—164no—
645C22×C7C2×H(5,𝔽2)14yes—
646C22×C7C2×H(5,𝔽2)12yes—
647C22×C7C2611yescharacteristic
648C4×C7—22no—
649C4×C7—22no—
650C4×C7—28no—
651C4×C7—24no—
652C4×C7—216no—
653C4×C7—28no—
654C24—28no—
655C24—44no—
656C24—84no—
657C24—84no—
658C24C24×C714yes—
659C24C24×C714yes—
660C24C24×C714yes—
661C24C24×C712yes—
662C24C24×C712yes—
663C24C24×C712yes—
664C24C24×C718yes—
665C24C24×C714yes—
666C24C24×C711yescharacteristic
667#41—416no—
668#41—416no—
669#41—48no—
670#41—816no—
671C2×Q8—42no—
672C2×Q8C24×C718yes—
673C2×Q8C24×C714yes—
674C2×Q8C24×C714yes—
675C2×D4—216no—
676C2×D4—28no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—42no—
683C2×D4—416no—
684C2×D4—416no—
685C2×D4—48no—
686C2×D4—416no—
687C2×D4—88no—
688C2×D4—88no—
689C2×D4—816no—
690C2×D4C24×C718yes—
691C2×D4C24×C718yes—
692C2×D4C24×C718yes—
693C2×D4C24×C7116yes—
694C2×D4C24×C7116yes—
695C2×D4C24×C718yes—
696C2×D4C24×C7116yes—
697C2×D4C24×C7116yes—
698C2×D4C24×C7116yes—
699C2×D4C24×C712yes—
700C2×D4C24×C712yes—
701C2×D4C24×C714yes—
702C2×D4C24×C714yes—
703C2×D4C24×C714yes—
704C2×D4C24×C718yes—
705C2×D4C24×C714yes—
706C2×D4C24×C7116yes—
707C2×D4C24×C712yes—
708C2×D4C24×C712yes—
709C22×C4—24no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—84no—
713C22×C4C24×C711yescharacteristic
714C22×C4C24×C714yes—
715C22×C4C24×C712yes—
716C22×C4C24×C714yes—
717C22×C4C24×C711yescharacteristic
718C22×C4C24×C714yes—
719C22×C4C24×C718yes—
720C22×C4C24×C7116yes—
721C22×C4C24×C718yes—
722C22×C4C24×C7116yes—
723C22×C4C24×C718yes—
724C22×C4C24×C718yes—
725C22×C4C24×C714yes—
726C22×C4C24×C718yes—
727C4⋊C4C24×C7116yes—
728C4⋊C4C24×C718yes—
729C4⋊C4C24×C7116yes—
730C4⋊C4C24×C7116yes—
731C4⋊C4C24×C7116yes—
732C4⋊C4C24×C7116yes—
733C4⋊C4C24×C718yes—
734C4⋊C4C24×C718yes—
735C4⋊C4C24×C718yes—
736C22⋊C4C24×C718yes—
737C22⋊C4C24×C718yes—
738C22⋊C4C24×C718yes—
739C22⋊C4C24×C718yes—
740C22⋊C4C24×C718yes—
741C22⋊C4C24×C7116yes—
742C22⋊C4C24×C7116yes—
743C22⋊C4C24×C7116yes—
744C22⋊C4C24×C7116yes—
745C22⋊C4C24×C7116yes—
746C22⋊C4C24×C7116yes—
747C22⋊C4C24×C7116yes—
748C22⋊C4C24×C7116yes—
749C22⋊C4C24×C7116yes—
750C22⋊C4C24×C718yes—
751C22⋊C4C24×C7116yes—
752C42C24×C714yes—
753C42C24×C714yes—
754C42C24×C7116yes—
755C42C24×C718yes—
756C2×C7—24no—
757C2×C7—22no—
758C2×C7—44no—
759C2×C7—44no—
760C2×C7—48no—
761C2×C7—44no—
762C2×C7C22×H(5,𝔽2)11yescharacteristic
763C2×C7H(7,𝔽2)12yes—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—28no—
768C23—28no—
769C23—28no—
770C23—44no—
771C23—42no—
772C23—44no—
773C23—48no—
774C23—44no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—416no—
779C23—44no—
780C23—48no—
781C23—816no—
782C23—816no—
783C23C7×H(5,𝔽2)14yes—
784C23C25×C714yes—
785C23C25×C718yes—
786C23C25×C714yes—
787C23C25×C714yes—
788C23C25×C712yes—
789C23C25×C711yescharacteristic
790Q8—44no—
791Q8—44no—
792Q8—48no—
793D4—216no—
794D4—216no—
795D4—216no—
796D4—42no—
797D4—44no—
798D4—42no—
799D4—42no—
800D4—44no—
801D4—42no—
802D4—416no—
803D4—48no—
804D4—44no—
805D4—44no—
806D4—416no—
807D4—416no—
808D4—48no—
809D4—416no—
810D4—416no—
811D4—416no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—48no—
820C2×C4—416no—
821C2×C4—44no—
822C2×C4—48no—
823C2×C4—44no—
824C2×C4—416no—
825C2×C4—48no—
826C2×C4C25×C718yes—
827C2×C4C25×C712yes—
828C2×C4C25×C7116yes—
829C2×C4C25×C714yes—
830C2×C4C25×C718yes—
831C2×C4C25×C712yes—
832C7#6286211yescharacteristic, direct product factor, Sylow
833C22—24no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—24no—
839C22—28no—
840C22—28no—
841C22—216no—
842C22—28no—
843C22—44no—
844C22—48no—
845C22—48no—
846C22—88no—
847C22—88no—
848C22—88no—
849C22—84no—
850C22—816no—
851C22—164no—
852C22C2×C7×H(5,𝔽2)14yes—
853C22C2×C7×H(5,𝔽2)12yes—
854C22C26×C711yescharacteristic
855C4—22no—
856C4—22no—
857C4—28no—
858C4—24no—
859C4—216no—
860C4—28no—
861C2—24no—
862C2—22no—
863C2—44no—
864C2—44no—
865C2—48no—
866C2—44no—
867C2C22×C7×H(5,𝔽2)11yescharacteristic
868C2C7×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×#3545C2semidirect
2. C7×#3543C2semidirect
3. C7×#3542C2semidirect
4. C7×#3534C2semidirect
5. C7×#3533C2semidirect
6. C7×#3532C2semidirect
7. C7×#3491C2semidirect
8. C7×#3490C2semidirect
9. C7×#3485C2semidirect
10. C7×#3484C2semidirect
11. C2×C7×#535C2semidirect
12. C2×C7×#534C2semidirect
13. C2×C7×H(5,𝔽2)C22semidirect
14. C22×C7×#41C22semidirect
15. C23×C7×D4C22semidirect
16. C23×C7×D4C22semidirect
17. C7×#563C22semidirect
18. C7×#562C22semidirect
19. C7×#562C22semidirect
20. C7×H(3,𝔽4)C22semidirect
21. C7×#560C22semidirect
22. C7×#560C22semidirect
23. C7×#560C22semidirect
24. C7×#559C22semidirect
25. C7×#555C22semidirect
26. C7×#553C22semidirect
27. C7×#552C22semidirect
28. C7×#551C22semidirect
29. C7×#551C22semidirect
30. C7×#551C22semidirect
31. C7×#551C22semidirect
32. C7×#550C22semidirect
33. C7×#547C22semidirect
34. C7×#546C22semidirect
35. C7×#546C22semidirect
36. C7×#546C22semidirect
37. C7×#546C22semidirect
38. C7×#546C22semidirect
39. C7×#546C22semidirect
40. C7×D42C22semidirect
41. C7×D42C22semidirect
42. C7×D42C22semidirect
43. C7×#543C22semidirect
44. C7×#542C22semidirect
45. C7×#540C22semidirect
46. C7×#540C22semidirect
47. C7×#539C22semidirect
48. C7×#539C22semidirect
49. C7×#538C22semidirect
50. C7×#538C22semidirect
51. C7×#538C22semidirect
52. C7×#538C22semidirect
53. C7×#537C22semidirect
54. C7×#536C22semidirect
55. C7×#535C22semidirect
56. C7×#535C22semidirect
57. C7×#535C22semidirect
58. C7×#535C22semidirect
60. C7×#534C22semidirect
61. C7×#534C22semidirect
62. C7×#534C22semidirect
63. C7×#534C22semidirect
64. C7×#534C22semidirect
65. C7×#534C22semidirect
66. C7×#534C22semidirect
67. C7×#534C22semidirect
68. C2×C7×#127C22semidirect
69. C7×#529C22semidirect
70. C2×C7×#124C22semidirect
71. C7×#525C22semidirect
72. C7×#525C22semidirect
73. C7×#525C22semidirect
74. C2×C7×#123C22semidirect
75. C2×C7×#123C22semidirect
76. C2×C7×#123C22semidirect
77. C2×C7×#121C22semidirect
78. C2×C7×#121C22semidirect
79. C2×C7×#120C22semidirect
80. C2×C7×#120C22semidirect
81. C2×C7×#120C22semidirect
82. C2×C7×#120C22semidirect
83. C7×#518C22semidirect
84. C7×#518C22semidirect
85. C2×C7×#117C22semidirect
86. C22×C7×C22⋊C4C22semidirect
87. #62862C7direct (N × H)
89. C25×C7C23semidirect
94. C2×C7×#41C23semidirect
95. C2×C7×#41C23semidirect
96. C22×C7×Q8C23semidirect
109. C22×C7×D4C23semidirect
110. C22×C7×D4C23semidirect
111. C22×C7×D4C23semidirect
112. C22×C7×D4C23semidirect
113. C22×C7×D4C23semidirect
115. C23×C4×C7C23semidirect
116. C23×C4×C7C23semidirect
117. C23×C4×C7C23semidirect
118. C7×C4⋊Q8C23semidirect
120. C7×#127C23semidirect
121. C7×#127C23semidirect
122. C7×#127C23semidirect
123. C7×#126C23semidirect
124. C7×#126C23semidirect
125. C7×#126C23semidirect
126. C7×#126C23semidirect
127. C7×#125C23semidirect
128. C7×#125C23semidirect
130. C7×#124C23semidirect
131. C7×#124C23semidirect
132. C7×#124C23semidirect
133. C7×#124C23semidirect
134. C7×#124C23semidirect
135. C7×#124C23semidirect
136. C7×#124C23semidirect
141. C7×#123C23semidirect
142. C7×#123C23semidirect
143. C7×#123C23semidirect
144. C7×#123C23semidirect
145. C7×#123C23semidirect
146. C7×#123C23semidirect
147. C7×#123C23semidirect
148. C7×#123C23semidirect
149. C7×#123C23semidirect
150. C7×#123C23semidirect
151. C7×#123C23semidirect
152. C7×#123C23semidirect
153. C7×#123C23semidirect
154. C7×#123C23semidirect
155. C7×C22⋊Q8C23semidirect
156. C7×C22⋊Q8C23semidirect
157. C7×C22⋊Q8C23semidirect
158. C7×C22⋊Q8C23semidirect
159. C7×C22⋊Q8C23semidirect
160. C7×C22⋊Q8C23semidirect
161. C7×C22⋊Q8C23semidirect
167. C7×#121C23semidirect
168. C7×#121C23semidirect
169. C7×#121C23semidirect
170. C7×#121C23semidirect
171. C7×#121C23semidirect
172. C7×#121C23semidirect
173. C7×#121C23semidirect
174. C7×#121C23semidirect
175. C7×#121C23semidirect
176. C7×#121C23semidirect
177. C7×#121C23semidirect
178. C7×#121C23semidirect
179. C7×#121C23semidirect
180. C7×#121C23semidirect
188. C7×#120C23semidirect
189. C7×#120C23semidirect
190. C7×#120C23semidirect
191. C7×#120C23semidirect
192. C7×#120C23semidirect
193. C7×#120C23semidirect
194. C7×#120C23semidirect
195. C7×#120C23semidirect
196. C7×#120C23semidirect
197. C7×#120C23semidirect
198. C4×C7×Q8C23semidirect
200. C4×C7×D4C23semidirect
201. C4×C7×D4C23semidirect
202. C4×C7×D4C23semidirect
203. C4×C7×D4C23semidirect
204. C4×C7×D4C23semidirect
205. C4×C7×D4C23semidirect
206. C4×C7×D4C23semidirect
207. C4×C7×D4C23semidirect
208. C7×#117C23semidirect
209. C7×#117C23semidirect
210. C7×#117C23semidirect
211. C7×#117C23semidirect
212. C7×#117C23semidirect
213. C2×C7×C4⋊C4C23semidirect
214. C2×C7×C4⋊C4C23semidirect
215. C2×C7×C4⋊C4C23semidirect
220. C2×C7×C22⋊C4C23semidirect
221. C2×C7×C22⋊C4C23semidirect
222. C2×C7×C22⋊C4C23semidirect
223. C2×C7×C22⋊C4C23semidirect
224. C2×C7×C22⋊C4C23semidirect
225. C2×C7×C22⋊C4C23semidirect
226. C2×C7×C22⋊C4C23semidirect
227. C2×C7×C22⋊C4C23semidirect
228. C2×C42×C7C23semidirect
229. #3545C2×C7semidirect
230. #3543C2×C7semidirect
231. #3542C2×C7semidirect
232. #3534C2×C7semidirect
233. #3533C2×C7semidirect
234. #3532C2×C7semidirect
235. #3491C2×C7semidirect
236. #3490C2×C7semidirect
237. #3485C2×C7semidirect
238. #3484C2×C7semidirect
239. C2×#535C2×C7semidirect
240. C2×#534C2×C7semidirect
343. C2×H(5,𝔽2)C22×C7semidirect
344. C22×#41C22×C7semidirect
345. C23×D4C22×C7semidirect
346. C23×D4C22×C7semidirect
347. #563C22×C7semidirect
348. #562C22×C7semidirect
349. #562C22×C7semidirect
350. H(3,𝔽4)C22×C7semidirect
351. #560C22×C7semidirect
352. #560C22×C7semidirect
353. #560C22×C7semidirect
354. #559C22×C7semidirect
355. #555C22×C7semidirect
356. #553C22×C7semidirect
357. #552C22×C7semidirect
358. #551C22×C7semidirect
359. #551C22×C7semidirect
360. #551C22×C7semidirect
361. #551C22×C7semidirect
362. #550C22×C7semidirect
363. #547C22×C7semidirect
364. #546C22×C7semidirect
365. #546C22×C7semidirect
366. #546C22×C7semidirect
367. #546C22×C7semidirect
368. #546C22×C7semidirect
369. #546C22×C7semidirect
370. D42C22×C7semidirect
371. D42C22×C7semidirect
372. D42C22×C7semidirect
373. #543C22×C7semidirect
374. #542C22×C7semidirect
375. #540C22×C7semidirect
376. #540C22×C7semidirect
377. #539C22×C7semidirect
378. #539C22×C7semidirect
379. #538C22×C7semidirect
380. #538C22×C7semidirect
381. #538C22×C7semidirect
382. #538C22×C7semidirect
383. #537C22×C7semidirect
384. #536C22×C7semidirect
385. #535C22×C7semidirect
386. #535C22×C7semidirect
387. #535C22×C7semidirect
388. #535C22×C7semidirect
390. #534C22×C7semidirect
391. #534C22×C7semidirect
392. #534C22×C7semidirect
393. #534C22×C7semidirect
394. #534C22×C7semidirect
395. #534C22×C7semidirect
396. #534C22×C7semidirect
397. #534C22×C7semidirect
398. C2×#127C22×C7semidirect
399. #529C22×C7semidirect
400. C2×#124C22×C7semidirect
401. #525C22×C7semidirect
402. #525C22×C7semidirect
403. #525C22×C7semidirect
404. C2×#123C22×C7semidirect
405. C2×#123C22×C7semidirect
406. C2×#123C22×C7semidirect
407. C2×#121C22×C7semidirect
408. C2×#121C22×C7semidirect
409. C2×#120C22×C7semidirect
410. C2×#120C22×C7semidirect
411. C2×#120C22×C7semidirect
412. C2×#120C22×C7semidirect
413. #518C22×C7semidirect
414. #518C22×C7semidirect
415. C2×#117C22×C7semidirect
416. C22×C22⋊C4C22×C7semidirect
486. C25C23×C7semidirect
491. C2×#41C23×C7semidirect
492. C2×#41C23×C7semidirect
493. C22×Q8C23×C7semidirect
506. C22×D4C23×C7semidirect
507. C22×D4C23×C7semidirect
508. C22×D4C23×C7semidirect
509. C22×D4C23×C7semidirect
510. C22×D4C23×C7semidirect
512. C23×C4C23×C7semidirect
513. C23×C4C23×C7semidirect
514. C23×C4C23×C7semidirect
515. C4⋊Q8C23×C7semidirect
517. #127C23×C7semidirect
518. #127C23×C7semidirect
519. #127C23×C7semidirect
520. #126C23×C7semidirect
521. #126C23×C7semidirect
522. #126C23×C7semidirect
523. #126C23×C7semidirect
524. #125C23×C7semidirect
525. #125C23×C7semidirect
527. #124C23×C7semidirect
528. #124C23×C7semidirect
529. #124C23×C7semidirect
530. #124C23×C7semidirect
531. #124C23×C7semidirect
532. #124C23×C7semidirect
533. #124C23×C7semidirect
538. #123C23×C7semidirect
539. #123C23×C7semidirect
540. #123C23×C7semidirect
541. #123C23×C7semidirect
542. #123C23×C7semidirect
543. #123C23×C7semidirect
544. #123C23×C7semidirect
545. #123C23×C7semidirect
546. #123C23×C7semidirect
547. #123C23×C7semidirect
548. #123C23×C7semidirect
549. #123C23×C7semidirect
550. #123C23×C7semidirect
551. #123C23×C7semidirect
552. C22⋊Q8C23×C7semidirect
553. C22⋊Q8C23×C7semidirect
554. C22⋊Q8C23×C7semidirect
555. C22⋊Q8C23×C7semidirect
556. C22⋊Q8C23×C7semidirect
557. C22⋊Q8C23×C7semidirect
558. C22⋊Q8C23×C7semidirect
564. #121C23×C7semidirect
565. #121C23×C7semidirect
566. #121C23×C7semidirect
567. #121C23×C7semidirect
568. #121C23×C7semidirect
569. #121C23×C7semidirect
570. #121C23×C7semidirect
571. #121C23×C7semidirect
572. #121C23×C7semidirect
573. #121C23×C7semidirect
574. #121C23×C7semidirect
575. #121C23×C7semidirect
576. #121C23×C7semidirect
577. #121C23×C7semidirect
585. #120C23×C7semidirect
586. #120C23×C7semidirect
587. #120C23×C7semidirect
588. #120C23×C7semidirect
589. #120C23×C7semidirect
590. #120C23×C7semidirect
591. #120C23×C7semidirect
592. #120C23×C7semidirect
593. #120C23×C7semidirect
594. #120C23×C7semidirect
595. C4×Q8C23×C7semidirect
597. C4×D4C23×C7semidirect
598. C4×D4C23×C7semidirect
599. C4×D4C23×C7semidirect
600. C4×D4C23×C7semidirect
601. C4×D4C23×C7semidirect
602. C4×D4C23×C7semidirect
603. C4×D4C23×C7semidirect
604. C4×D4C23×C7semidirect
605. #117C23×C7semidirect
606. #117C23×C7semidirect
607. #117C23×C7semidirect
608. #117C23×C7semidirect
609. #117C23×C7semidirect
610. C2×C4⋊C4C23×C7semidirect
611. C2×C4⋊C4C23×C7semidirect
612. C2×C4⋊C4C23×C7semidirect
617. C2×C22⋊C4C23×C7semidirect
618. C2×C22⋊C4C23×C7semidirect
619. C2×C22⋊C4C23×C7semidirect
620. C2×C22⋊C4C23×C7semidirect
621. C2×C22⋊C4C23×C7semidirect
622. C2×C22⋊C4C23×C7semidirect
623. C2×C22⋊C4C23×C7semidirect
624. C2×C22⋊C4C23×C7semidirect
625. C2×C42C23×C7semidirect
832. C7#62862direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35452
C7×#35432
C7×#35422
C7×#35342
C7×#35332
C7×#35322
C7×#34912
C7×#34902
C7×#34852
C7×#34842
C2×C7×#5352
C2×C7×#5342
#628627