Finite Group Databasebeta

← C7×#22506 #13199722

Subgroups — C7×#22506 #13199722

Order 1792.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3475C211yesmaximal, characteristic
2C7×D4×M16C211yesmaximal, characteristic, complemented
3C7×#2290C211yesmaximal, characteristic, complemented
4C7×#1995C211yesmaximal, characteristic, complemented
5C7×#1986C211yesmaximal, characteristic, complemented
6C7×#1897C211yesmaximal, characteristic, complemented
7C7×#1896C211yesmaximal, characteristic, complemented
8C7×#1871C211yesmaximal, characteristic, complemented
9C7×#1871C211yesmaximal, characteristic, complemented
10C7×#1826C211yesmaximal, characteristic, complemented
11C7×#1826C211yesmaximal, characteristic, complemented
12C7×#1806C211yesmaximal, characteristic, complemented
13C7×#1759C211yesmaximal, characteristic, complemented
14C7×#1733C211yesmaximal, characteristic, complemented
15C2×C7×#339C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C7×#556C411yescharacteristic, complemented
19C7×#555C411yescharacteristic, complemented
20C7×#554C411yescharacteristic, complemented
21C7×#553C411yescharacteristic, complemented
22C7×#553C411yescharacteristic, complemented
23C7×#552—21no—
24C7×#552C411yescharacteristic, complemented
25C7×#552C411yescharacteristic, complemented
26C7×#551—21no—
27C7×#551—21no—
28C7×#547C411yescharacteristic, complemented
29C7×#546—21no—
30C7×#533C2211yescharacteristic
31C7×#529—21no—
32C7×#529—21no—
33C7×#529—21no—
34C7×#525C2211yescharacteristic
35C7×#525C2211yescharacteristic
36C4×C7×#41—21no—
37C4×C7×#41C2211yescharacteristic
38C2×C4×C7×D4C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C2×C7×#117C2211yescharacteristic
41C2×C7×#117C2211yescharacteristic
42C22×C42×C7C2211yescharacteristic
43C7×#436—21no—
44C7×#435—21no—
45C7×#435—21no—
46C7×C8×D4—21no—
47C7×#423C2211yescharacteristic
48C2×C7×#104C2211yescharacteristic
49C2×C7×#104C2211yescharacteristic
50C2×C7×#104C2211yescharacteristic
51C2×C7×#104C2211yescharacteristic
52C7×#407C2211yescharacteristic
53C7×#407C2211yescharacteristic
54C4×C7×M16C2211yescharacteristic
55C7×#388—21no—
56C7×#387—21no—
57C7×#386—21no—
58C7×#385—21no—
59C4×C7×C4⋊C4C2211yescharacteristic
60C4×C7×C22⋊C4C2211yescharacteristic
61C4×C7×C22⋊C4C2211yescharacteristic
62C7×#376C2211yescharacteristic
63C7×#339C2211yescharacteristic
64C7×#339C2211yescharacteristic
65C7×#339C2211yescharacteristic
66C7×#339C2211yescharacteristic
67C7×#339C2211yescharacteristic
68C7×#339C2211yescharacteristic
69C7×#339C2211yescharacteristic
70C7×#339C2211yescharacteristic
71C7×#339C2211yescharacteristic
72C7×#339C2211yescharacteristic
73C7×#339C2211yescharacteristic
74C7×#339C2211yescharacteristic
75#22506C711yesmaximal, characteristic, direct product factor, Sylow
76C2×C7×#41—21no—
77C2×C7×#41C2311yescharacteristic
78C22×C7×D4D411yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C2×C7×M16—22no—
85C2×C7×M16—22no—
86C2×C7×M16—41no—
87C2×C7×M16—41no—
88C2×C7×M16C2311yescharacteristic
89C2×C7×M16C2311yescharacteristic
90C2×C7×M16C2311yescharacteristic
91C2×C7×M16C2311yescharacteristic
92C22×C7×C8—21no—
93C22×C7×C8—21no—
94C7×C4⋊Q8C2×C411yescharacteristic, complemented
95C7×C4⋊Q8C2×C411yescharacteristic, complemented
96C7×#126—21no—
97C7×#126—21no—
98C7×#126—21no—
99C7×#126—21no—
100C7×#126—21no—
101C7×#126—21no—
102C7×#125—21no—
103C7×#125—21no—
104C7×#125—21no—
105C7×#125C2×C411yescharacteristic, complemented
106C7×#125C2×C411yescharacteristic, complemented
107C7×#124—21no—
108C7×#124—21no—
109C7×#124—21no—
110C7×#123—21no—
111C7×#123—21no—
112C7×#123—21no—
113C7×#123—21no—
114C7×#123—21no—
115C7×#123—21no—
116C7×#123—21no—
117C7×#123—21no—
118C7×C22⋊Q8—21no—
119C7×C22⋊Q8—21no—
120C7×C22⋊Q8—21no—
121C7×C22⋊Q8—21no—
122C7×C22⋊Q8—21no—
123C7×C22⋊Q8C2×C411yescharacteristic
124C7×C22⋊Q8C2×C411yescharacteristic
125C7×C22⋊Q8C2×C411yescharacteristic, complemented
126C7×C22⋊Q8C2×C411yescharacteristic, complemented
127C7×#121—21no—
128C7×#121—21no—
129C7×#121—21no—
130C7×#121C2×C411yescharacteristic
131C7×#121C2×C411yescharacteristic
132C7×#121C2×C411yescharacteristic, complemented
133C7×#121C2×C411yescharacteristic, complemented
134C7×#120—21no—
135C7×#120—21no—
136C4×C7×Q8—21no—
137C4×C7×Q8—21no—
138C4×C7×Q8—21no—
139C4×C7×Q8C2×C411yescharacteristic, complemented
140C4×C7×Q8C2×C411yescharacteristic, complemented
141C4×C7×D4—21no—
142C4×C7×D4—21no—
143C4×C7×D4—21no—
144C4×C7×D4—21no—
145C4×C7×D4—21no—
146C4×C7×D4—21no—
147C4×C7×D4—21no—
148C4×C7×D4—21no—
149C4×C7×D4—21no—
150C4×C7×D4C2×C411yescharacteristic
151C4×C7×D4C2×C411yescharacteristic
152C4×C7×D4C2×C411yescharacteristic
153C4×C7×D4C2×C411yescharacteristic
154C4×C7×D4C2×C411yescharacteristic, complemented
155C4×C7×D4C2×C411yescharacteristic, complemented
156C4×C7×D4D411yescharacteristic
157C4×C7×D4D411yescharacteristic
158C4×C7×D4D411yescharacteristic
159C4×C7×D4D411yescharacteristic
160C7×#117—21no—
161C7×#117—21no—
162C7×#117—21no—
163C7×#117—21no—
164C7×#117—21no—
165C7×#117—21no—
166C7×#117—21no—
167C7×#117—21no—
168C7×#117—22no—
169C7×#117—41no—
170C7×#117C2×C411yescharacteristic
171C7×#117C2×C411yescharacteristic
172C7×#117C2×C411yescharacteristic, complemented
173C7×#117C2×C411yescharacteristic, complemented
174C7×#117C2311yescharacteristic
175C7×#117C2311yescharacteristic
176C7×#117C2311yescharacteristic
177C2×C7×C4⋊C4—21no—
178C2×C7×C4⋊C4—21no—
179C2×C7×C4⋊C4C2×C411yescharacteristic
180C2×C7×C4⋊C4C2×C411yescharacteristic
181C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
182C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
183C2×C7×C4⋊C4D411yescharacteristic
184C2×C7×C22⋊C4—21no—
185C2×C7×C22⋊C4—21no—
186C2×C7×C22⋊C4—21no—
187C2×C7×C22⋊C4—21no—
188C2×C7×C22⋊C4—21no—
189C2×C7×C22⋊C4D411yescharacteristic
190C2×C7×C22⋊C4D411yescharacteristic
191C2×C42×C7—21no—
192C2×C42×C7—21no—
193C2×C42×C7—21no—
194C2×C42×C7—22no—
195C2×C42×C7—21no—
196C2×C42×C7—41no—
197C2×C42×C7C2311yescharacteristic
198C2×C42×C7C2311yescharacteristic
199C2×C42×C7C2311yescharacteristic
200C2×C42×C7C2311yescharacteristic
201C2×C42×C7C2311yescharacteristic
202C7×C4⋊C8—21no—
203C7×C4⋊C8—21no—
204C7×#104—22no—
205C7×#104—22no—
206C7×#104—41no—
207C7×#104—41no—
208C7×C22⋊C8—21no—
209C7×C22⋊C8—21no—
210C7×C22⋊C8—21no—
211C7×C22⋊C8—21no—
212C7×#97—21no—
213C4×C7×C8—21no—
214C7×#95—21no—
215C7×#95—21no—
216C7×#95—21no—
217C7×#95—21no—
218C7×#95—21no—
219#3475C2×C711yescharacteristic
220D4×M16C2×C711yescharacteristic, complemented
221#2290C2×C711yescharacteristic, complemented
222#1995C2×C711yescharacteristic, complemented
223#1986C2×C711yescharacteristic, complemented
224#1897C2×C711yescharacteristic, complemented
225#1896C2×C711yescharacteristic, complemented
226#1871C2×C711yescharacteristic, complemented
227#1871C2×C711yescharacteristic, complemented
228#1826C2×C711yescharacteristic, complemented
229#1826C2×C711yescharacteristic, complemented
230#1806C2×C711yescharacteristic, complemented
231#1759C2×C711yescharacteristic, complemented
232#1733C2×C711yescharacteristic, complemented
233C2×#339C2×C711yescharacteristic, complemented
234C24×C7C2×D411yescharacteristic
235C24×C7C2×D411yescharacteristic
236C7×#41—21no—
237C7×#41—21no—
238C7×#41—21no—
239C7×#41—21no—
240C7×#41—44no—
241C2×C7×Q8—21no—
242C2×C7×Q8—21no—
243C2×C7×Q8C22×C411yescharacteristic
244C2×C7×D4—21no—
245C2×C7×D4—21no—
246C2×C7×D4—21no—
247C2×C7×D4—21no—
248C2×C7×D4—21no—
249C2×C7×D4—42no—
250C2×C7×D4C22⋊C411yescharacteristic
251C2×C7×D4C22⋊C411yescharacteristic
252C2×C7×D4C22⋊C411yescharacteristic
253C2×C7×D4C22⋊C411yescharacteristic
254C2×C7×D4C22×C411yescharacteristic
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—42no—
275C22×C4×C7—42no—
276C22×C4×C7—42no—
277C22×C4×C7C22×C411yescharacteristic
278C22×C4×C7C22×C411yescharacteristic
279C22×C4×C7C22×C411yescharacteristic
280C22×C4×C7C22×C411yescharacteristic
281C22×C4×C7C2×D411yescharacteristic
282C22×C4×C7C2×D411yescharacteristic
283C22×C4×C7C2×D411yescharacteristic
284C22×C4×C7C2×D411yescharacteristic
285C22×C4×C7C2×D411yescharacteristic
286C22×C4×C7C2×D411yescharacteristic
287C22×C4×C7C2×D411yescharacteristic
288C22×C4×C7C2×D411yescharacteristic
289C22×C4×C7C2411yescharacteristic
290C7×M16—21no—
291C7×M16—21no—
292C7×M16—21no—
293C7×M16—21no—
294C7×M16—21no—
295C7×M16—21no—
296C7×M16—21no—
297C7×M16—42no—
298C7×M16—42no—
299C7×M16#4112yescomplemented
300C2×C7×C8—21no—
301C2×C7×C8—21no—
302C2×C7×C8—21no—
303C2×C7×C8—21no—
304C2×C7×C8—42no—
305C2×C7×C8—42no—
306C7×C4⋊C4—21no—
307C7×C4⋊C4—21no—
308C7×C4⋊C4—21no—
309C7×C4⋊C4—21no—
310C7×C4⋊C4—21no—
311C7×C4⋊C4—21no—
312C7×C4⋊C4—21no—
313C7×C4⋊C4—21no—
314C7×C4⋊C4—21no—
315C7×C4⋊C4—21no—
316C7×C4⋊C4—21no—
317C7×C4⋊C4—21no—
318C7×C4⋊C4—21no—
319C7×C4⋊C4—21no—
320C7×C4⋊C4—21no—
321C7×C4⋊C4—21no—
322C7×C4⋊C4—42no—
323C7×C4⋊C4—42no—
324C7×C4⋊C4C22⋊C411yescharacteristic
325C7×C4⋊C4C22⋊C411yescharacteristic
326C7×C4⋊C4C22⋊C411yescharacteristic
327C7×C4⋊C4C22⋊C411yescharacteristic
328C7×C4⋊C4C22×C411yescharacteristic
329C7×C4⋊C4C22×C411yescharacteristic
330C7×C4⋊C4C22×C411yescharacteristic
331C7×C4⋊C4C22×C411yescharacteristic
332C7×C4⋊C4C22×C411yescharacteristic
333C7×C4⋊C4C22×C411yescharacteristic
334C7×C22⋊C4—21no—
335C7×C22⋊C4—21no—
336C7×C22⋊C4—21no—
337C7×C22⋊C4—21no—
338C7×C22⋊C4—21no—
339C7×C22⋊C4—21no—
340C7×C22⋊C4—21no—
341C7×C22⋊C4—21no—
342C7×C22⋊C4—21no—
343C7×C22⋊C4—21no—
344C7×C22⋊C4—21no—
345C7×C22⋊C4—21no—
346C7×C22⋊C4—21no—
347C7×C22⋊C4—21no—
348C7×C22⋊C4—21no—
349C7×C22⋊C4—21no—
350C7×C22⋊C4—21no—
351C7×C22⋊C4—42no—
352C7×C22⋊C4—42no—
353C7×C22⋊C4—42no—
354C7×C22⋊C4C22⋊C411yescharacteristic
355C7×C22⋊C4C22⋊C411yescharacteristic
356C7×C22⋊C4C22⋊C411yescharacteristic
357C7×C22⋊C4C22⋊C411yescharacteristic
358C7×C22⋊C4C22⋊C411yescharacteristic
359C7×C22⋊C4C22⋊C411yescharacteristic
360C7×C22⋊C4C22⋊C411yescharacteristic
361C7×C22⋊C4C22⋊C411yescharacteristic
362C42×C7—21no—
363C42×C7—21no—
364C42×C7—21no—
365C42×C7—21no—
366C42×C7—21no—
367C42×C7—21no—
368C42×C7—21no—
369C42×C7—21no—
370C42×C7—21no—
371C42×C7—21no—
372C42×C7—21no—
373C42×C7—21no—
374C42×C7—21no—
375C42×C7—21no—
376C42×C7—21no—
377C42×C7—21no—
378C42×C7—42no—
379C42×C7C22×C411yescharacteristic
380C42×C7C22×C411yescharacteristic
381C42×C7C2×D411yescharacteristic
382C42×C7C2×D411yescharacteristic
383C42×C7#4112yescomplemented
384C22×M16C22×C711yescharacteristic
385C22×M16C22×C711yescharacteristic
386#556C4×C711yescharacteristic, complemented
387#555C4×C711yescharacteristic, complemented
388#554C4×C711yescharacteristic, complemented
389#553C4×C711yescharacteristic, complemented
390#553C4×C711yescharacteristic, complemented
391#552—21no—
392#552C4×C711yescharacteristic, complemented
393#552C4×C711yescharacteristic, complemented
394#551—21no—
395#551—21no—
396#547C4×C711yescharacteristic, complemented
397#546—21no—
398#533C22×C711yescharacteristic
399#529—21no—
400#529—21no—
401#529—21no—
402#525C22×C711yescharacteristic
403#525C22×C711yescharacteristic
404C4×#41—21no—
405C4×#41C22×C711yescharacteristic
406C2×C4×D4C22×C711yescharacteristic
407C2×#117C22×C711yescharacteristic
408C2×#117C22×C711yescharacteristic
409C2×#117C22×C711yescharacteristic
410C22×C42C22×C711yescharacteristic
411#436—21no—
412#435—21no—
413#435—21no—
414C8×D4—21no—
415#423C22×C711yescharacteristic
416C2×#104C22×C711yescharacteristic
417C2×#104C22×C711yescharacteristic
418C2×#104C22×C711yescharacteristic
419C2×#104C22×C711yescharacteristic
420#407C22×C711yescharacteristic
421#407C22×C711yescharacteristic
422C4×M16C22×C711yescharacteristic
423#388—21no—
424#387—21no—
425#386—21no—
426#385—21no—
427C4×C4⋊C4C22×C711yescharacteristic
428C4×C22⋊C4C22×C711yescharacteristic
429C4×C22⋊C4C22×C711yescharacteristic
430#376C22×C711yescharacteristic
431#339C22×C711yescharacteristic
432#339C22×C711yescharacteristic
433#339C22×C711yescharacteristic
434#339C22×C711yescharacteristic
435#339C22×C711yescharacteristic
436#339C22×C711yescharacteristic
437#339C22×C711yescharacteristic
438#339C22×C711yescharacteristic
439#339C22×C711yescharacteristic
440#339C22×C711yescharacteristic
441#339C22×C711yescharacteristic
442#339C22×C711yescharacteristic
443C23×C7—21no—
444C23×C7—21no—
445C23×C7—22no—
446C23×C7—21no—
447C23×C7—21no—
448C23×C7—21no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—41no—
452C23×C7C2×C22⋊C411yescharacteristic
453C23×C7C2×C22⋊C411yescharacteristic
454C23×C7C2×C22⋊C411yescharacteristic
455C23×C7C2×C22⋊C411yescharacteristic
456C23×C7C22×D411yescharacteristic
457C7×Q8—21no—
458C7×Q8—21no—
459C7×Q8—42no—
460C7×Q8—81no—
461C7×D4—22no—
462C7×D4—22no—
463C7×D4—21no—
464C7×D4—21no—
465C7×D4—41no—
466C7×D4—41no—
467C7×D4—42no—
468C7×D4—41no—
469C7×D4—41no—
470C7×D4—42no—
471C7×D4—81no—
472C7×D4—81no—
473C2×C4×C7—21no—
474C2×C4×C7—21no—
475C2×C4×C7—21no—
476C2×C4×C7—21no—
477C2×C4×C7—21no—
478C2×C4×C7—21no—
479C2×C4×C7—21no—
480C2×C4×C7—21no—
481C2×C4×C7—21no—
482C2×C4×C7—21no—
483C2×C4×C7—21no—
484C2×C4×C7—21no—
485C2×C4×C7—21no—
486C2×C4×C7—21no—
487C2×C4×C7—21no—
488C2×C4×C7—21no—
489C2×C4×C7—21no—
490C2×C4×C7—21no—
491C2×C4×C7—21no—
492C2×C4×C7—21no—
493C2×C4×C7—22no—
494C2×C4×C7—21no—
495C2×C4×C7—21no—
496C2×C4×C7—21no—
497C2×C4×C7—21no—
498C2×C4×C7—21no—
499C2×C4×C7—21no—
500C2×C4×C7—21no—
501C2×C4×C7—22no—
502C2×C4×C7—41no—
503C2×C4×C7—41no—
504C2×C4×C7—42no—
505C2×C4×C7—41no—
506C2×C4×C7—41no—
507C2×C4×C7—41no—
508C2×C4×C7—42no—
509C2×C4×C7—48no—
510C2×C4×C7—41no—
511C2×C4×C7—42no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—41no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—81no—
521C2×C4×C7—81no—
522C2×C4×C7—81no—
523C2×C4×C7C2×C22⋊C411yescharacteristic
524C2×C4×C7C2×C22⋊C411yescharacteristic
525C2×C4×C7C2×C22⋊C411yescharacteristic
526C2×C4×C7C2×C22⋊C411yescharacteristic
527C2×C4×C7C2×C22⋊C411yescharacteristic
528C2×C4×C7C2×C22⋊C411yescharacteristic
529C2×C4×C7C2×C22⋊C411yescharacteristic
530C2×C4×C7C2×C22⋊C411yescharacteristic
531C2×C4×C7C23×C411yescharacteristic
532C2×C4×C7C22×D411yescharacteristic
533C2×C4×C7C2×#4111yescharacteristic
534C2×C4×C7C2×#4111yescharacteristic
535C2×C4×C7H(5,𝔽2)11yescharacteristic
536C2×C4×C72−1+411yescharacteristic
537C7×C8—22no—
538C7×C8—41no—
539C7×C8—41no—
540C7×C8—41no—
541C2×#41—21no—
542C2×#41C23×C711yescharacteristic
543C22×D4C7×D411yescharacteristic
544C23×C4—21no—
545C23×C4C23×C711yescharacteristic
546C23×C4C23×C711yescharacteristic
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C711yescharacteristic
554C2×M16C23×C711yescharacteristic
555C2×M16C23×C711yescharacteristic
556C2×M16C23×C711yescharacteristic
557C22×C8—21no—
558C22×C8—21no—
559C4⋊Q8C2×C4×C711yescharacteristic, complemented
560C4⋊Q8C2×C4×C711yescharacteristic, complemented
561#126—21no—
562#126—21no—
563#126—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#125—21no—
568#125—21no—
569#125—21no—
570#125C2×C4×C711yescharacteristic, complemented
571#125C2×C4×C711yescharacteristic, complemented
572#124—21no—
573#124—21no—
574#124—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8C2×C4×C711yescharacteristic
589C22⋊Q8C2×C4×C711yescharacteristic
590C22⋊Q8C2×C4×C711yescharacteristic, complemented
591C22⋊Q8C2×C4×C711yescharacteristic, complemented
592#121—21no—
593#121—21no—
594#121—21no—
595#121C2×C4×C711yescharacteristic
596#121C2×C4×C711yescharacteristic
597#121C2×C4×C711yescharacteristic, complemented
598#121C2×C4×C711yescharacteristic, complemented
599#120—21no—
600#120—21no—
601C4×Q8—21no—
602C4×Q8—21no—
603C4×Q8—21no—
604C4×Q8C2×C4×C711yescharacteristic, complemented
605C4×Q8C2×C4×C711yescharacteristic, complemented
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4C2×C4×C711yescharacteristic
616C4×D4C2×C4×C711yescharacteristic
617C4×D4C2×C4×C711yescharacteristic
618C4×D4C2×C4×C711yescharacteristic
619C4×D4C2×C4×C711yescharacteristic, complemented
620C4×D4C2×C4×C711yescharacteristic, complemented
621C4×D4C7×D411yescharacteristic
622C4×D4C7×D411yescharacteristic
623C4×D4C7×D411yescharacteristic
624C4×D4C7×D411yescharacteristic
625#117—21no—
626#117—21no—
627#117—21no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117—22no—
634#117—41no—
635#117C2×C4×C711yescharacteristic
636#117C2×C4×C711yescharacteristic
637#117C2×C4×C711yescharacteristic, complemented
638#117C2×C4×C711yescharacteristic, complemented
639#117C23×C711yescharacteristic
640#117C23×C711yescharacteristic
641#117C23×C711yescharacteristic
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4C2×C4×C711yescharacteristic
645C2×C4⋊C4C2×C4×C711yescharacteristic
646C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
647C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
648C2×C4⋊C4C7×D411yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4C7×D411yescharacteristic
655C2×C22⋊C4C7×D411yescharacteristic
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—22no—
660C2×C42—21no—
661C2×C42—41no—
662C2×C42C23×C711yescharacteristic
663C2×C42C23×C711yescharacteristic
664C2×C42C23×C711yescharacteristic
665C2×C42C23×C711yescharacteristic
666C2×C42C23×C711yescharacteristic
667C4⋊C8—21no—
668C4⋊C8—21no—
669#104—22no—
670#104—22no—
671#104—41no—
672#104—41no—
673C22⋊C8—21no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676C22⋊C8—21no—
677#97—21no—
678C4×C8—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684C22×C7—21no—
685C22×C7—21no—
686C22×C7—21no—
687C22×C7—21no—
688C22×C7—21no—
689C22×C7—21no—
690C22×C7—21no—
691C22×C7—21no—
692C22×C7—21no—
693C22×C7—21no—
694C22×C7—21no—
695C22×C7—21no—
696C22×C7—21no—
697C22×C7—42no—
698C22×C7—42no—
699C22×C7—41no—
700C22×C7—41no—
701C22×C7—41no—
702C22×C7—81no—
703C22×C7—81no—
704C22×C7#42112yes—
705C22×C7C22×C22⋊C411yescharacteristic
706C22×C7#54611yescharacteristic
707C22×C7#54711yescharacteristic
708C4×C7—21no—
709C4×C7—21no—
710C4×C7—21no—
711C4×C7—21no—
712C4×C7—21no—
713C4×C7—21no—
714C4×C7—21no—
715C4×C7—21no—
716C4×C7—42no—
717C4×C7—42no—
718C4×C7—41no—
719C4×C7—41no—
720C4×C7—41no—
721C4×C7—41no—
722C4×C7—41no—
723C4×C7—41no—
724C4×C7—41no—
725C4×C7—81no—
726C4×C7—81no—
727C4×C7C4×#4111yescharacteristic
728C4×C7#52011yescharacteristic
729C4×C7#54611yescharacteristic
730C4×C7#54711yescharacteristic
731C24C2×C7×D411yescharacteristic
732C24C2×C7×D411yescharacteristic
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—44no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C22×C4×C711yescharacteristic
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—42no—
747C2×D4C7×C22⋊C411yescharacteristic
748C2×D4C7×C22⋊C411yescharacteristic
749C2×D4C7×C22⋊C411yescharacteristic
750C2×D4C7×C22⋊C411yescharacteristic
751C2×D4C22×C4×C711yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4C22×C4×C711yescharacteristic
775C22×C4C22×C4×C711yescharacteristic
776C22×C4C22×C4×C711yescharacteristic
777C22×C4C22×C4×C711yescharacteristic
778C22×C4C2×C7×D411yescharacteristic
779C22×C4C2×C7×D411yescharacteristic
780C22×C4C2×C7×D411yescharacteristic
781C22×C4C2×C7×D411yescharacteristic
782C22×C4C2×C7×D411yescharacteristic
783C22×C4C2×C7×D411yescharacteristic
784C22×C4C2×C7×D411yescharacteristic
785C22×C4C2×C7×D411yescharacteristic
786C22×C4C24×C711yescharacteristic
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—21no—
794M16—42no—
795M16—42no—
796M16C7×#4112yescomplemented
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—42no—
802C2×C8—42no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4C7×C22⋊C411yescharacteristic
822C4⋊C4C7×C22⋊C411yescharacteristic
823C4⋊C4C7×C22⋊C411yescharacteristic
824C4⋊C4C7×C22⋊C411yescharacteristic
825C4⋊C4C22×C4×C711yescharacteristic
826C4⋊C4C22×C4×C711yescharacteristic
827C4⋊C4C22×C4×C711yescharacteristic
828C4⋊C4C22×C4×C711yescharacteristic
829C4⋊C4C22×C4×C711yescharacteristic
830C4⋊C4C22×C4×C711yescharacteristic
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—42no—
849C22⋊C4—42no—
850C22⋊C4—42no—
851C22⋊C4C7×C22⋊C411yescharacteristic
852C22⋊C4C7×C22⋊C411yescharacteristic
853C22⋊C4C7×C22⋊C411yescharacteristic
854C22⋊C4C7×C22⋊C411yescharacteristic
855C22⋊C4C7×C22⋊C411yescharacteristic
856C22⋊C4C7×C22⋊C411yescharacteristic
857C22⋊C4C7×C22⋊C411yescharacteristic
858C22⋊C4C7×C22⋊C411yescharacteristic
859C42—21no—
860C42—21no—
861C42—21no—
862C42—21no—
863C42—21no—
864C42—21no—
865C42—21no—
866C42—21no—
867C42—21no—
868C42—21no—
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—42no—
876C42C22×C4×C711yescharacteristic
877C42C22×C4×C711yescharacteristic
878C42C2×C7×D411yescharacteristic
879C42C2×C7×D411yescharacteristic
880C42C7×#4112yescomplemented
881C2×C7—21no—
882C2×C7—21no—
883C2×C7—22no—
884C2×C7—41no—
885C2×C7—41no—
886C2×C7—41no—
887C2×C7—81no—
888C2×C7#233911yescharacteristic
889C2×C7C2×#42111yescharacteristic
890C2×C7#290111yescharacteristic
891C23—21no—
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23C2×C7×C22⋊C411yescharacteristic
901C23C2×C7×C22⋊C411yescharacteristic
902C23C2×C7×C22⋊C411yescharacteristic
903C23C2×C7×C22⋊C411yescharacteristic
904C23C22×C7×D411yescharacteristic
905Q8—21no—
906Q8—21no—
907Q8—42no—
908Q8—81no—
909D4—22no—
910D4—22no—
911D4—21no—
912D4—21no—
913D4—41no—
914D4—41no—
915D4—42no—
916D4—41no—
917D4—41no—
918D4—42no—
919D4—81no—
920D4—81no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—42no—
957C2×C4—48no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4C2×C7×C22⋊C411yescharacteristic
972C2×C4C2×C7×C22⋊C411yescharacteristic
973C2×C4C2×C7×C22⋊C411yescharacteristic
974C2×C4C2×C7×C22⋊C411yescharacteristic
975C2×C4C2×C7×C22⋊C411yescharacteristic
976C2×C4C2×C7×C22⋊C411yescharacteristic
977C2×C4C2×C7×C22⋊C411yescharacteristic
978C2×C4C2×C7×C22⋊C411yescharacteristic
979C2×C4C23×C4×C711yescharacteristic
980C2×C4C22×C7×D411yescharacteristic
981C2×C4C2×C7×#4111yescharacteristic
982C2×C4C2×C7×#4111yescharacteristic
983C2×C4C7×H(5,𝔽2)11yescharacteristic
984C2×C4C7×2−1+411yescharacteristic
985C8—22no—
986C8—41no—
987C8—41no—
988C8—41no—
989C7#2250611yescharacteristic, direct product factor, Sylow
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22C7×#42112yes—
1011C22C22×C7×C22⋊C411yescharacteristic
1012C22C7×#54611yescharacteristic
1013C22C7×#54711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—41no—
1030C4—41no—
1031C4—81no—
1032C4—81no—
1033C4C4×C7×#4111yescharacteristic
1034C4C7×#52011yescharacteristic
1035C4C7×#54611yescharacteristic
1036C4C7×#54711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2C7×#233911yescharacteristic
1045C2C2×C7×#42111yescharacteristic
1046C2C7×#290111yescharacteristic
subgroupG/H
centerC2×C4×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
socleC22×C7C22×C22⋊C4
prime radicalC7×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×D4×M16C2semidirect
3. C7×#2290C2semidirect
4. C7×#1995C2semidirect
5. C7×#1986C2semidirect
6. C7×#1897C2semidirect
7. C7×#1896C2semidirect
8. C7×#1871C2semidirect
9. C7×#1871C2semidirect
10. C7×#1826C2semidirect
11. C7×#1826C2semidirect
12. C7×#1806C2semidirect
13. C7×#1759C2semidirect
14. C7×#1733C2semidirect
15. C2×C7×#339C2semidirect
18. C7×#556C4semidirect
19. C7×#555C4semidirect
20. C7×#554C4semidirect
21. C7×#553C4semidirect
22. C7×#553C4semidirect
24. C7×#552C4semidirect
25. C7×#552C4semidirect
28. C7×#547C4semidirect
75. #22506C7direct (N × H)
94. C7×C4⋊Q8C2×C4semidirect
95. C7×C4⋊Q8C2×C4semidirect
105. C7×#125C2×C4semidirect
106. C7×#125C2×C4semidirect
125. C7×C22⋊Q8C2×C4semidirect
126. C7×C22⋊Q8C2×C4semidirect
132. C7×#121C2×C4semidirect
133. C7×#121C2×C4semidirect
139. C4×C7×Q8C2×C4semidirect
140. C4×C7×Q8C2×C4semidirect
154. C4×C7×D4C2×C4semidirect
155. C4×C7×D4C2×C4semidirect
172. C7×#117C2×C4semidirect
173. C7×#117C2×C4semidirect
181. C2×C7×C4⋊C4C2×C4semidirect
182. C2×C7×C4⋊C4C2×C4semidirect
220. D4×M16C2×C7semidirect
221. #2290C2×C7semidirect
222. #1995C2×C7semidirect
223. #1986C2×C7semidirect
224. #1897C2×C7semidirect
225. #1896C2×C7semidirect
226. #1871C2×C7semidirect
227. #1871C2×C7semidirect
228. #1826C2×C7semidirect
229. #1826C2×C7semidirect
230. #1806C2×C7semidirect
231. #1759C2×C7semidirect
232. #1733C2×C7semidirect
233. C2×#339C2×C7semidirect
299. C7×M16#41semidirect
383. C42×C7#41semidirect
386. #556C4×C7semidirect
387. #555C4×C7semidirect
388. #554C4×C7semidirect
389. #553C4×C7semidirect
390. #553C4×C7semidirect
392. #552C4×C7semidirect
393. #552C4×C7semidirect
396. #547C4×C7semidirect
559. C4⋊Q8C2×C4×C7semidirect
560. C4⋊Q8C2×C4×C7semidirect
570. #125C2×C4×C7semidirect
571. #125C2×C4×C7semidirect
590. C22⋊Q8C2×C4×C7semidirect
591. C22⋊Q8C2×C4×C7semidirect
597. #121C2×C4×C7semidirect
598. #121C2×C4×C7semidirect
604. C4×Q8C2×C4×C7semidirect
605. C4×Q8C2×C4×C7semidirect
619. C4×D4C2×C4×C7semidirect
620. C4×D4C2×C4×C7semidirect
637. #117C2×C4×C7semidirect
638. #117C2×C4×C7semidirect
646. C2×C4⋊C4C2×C4×C7semidirect
647. C2×C4⋊C4C2×C4×C7semidirect
796. M16C7×#41semidirect
880. C42C7×#41semidirect
989. C7#22506direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34752
C7×D4×M162
C7×#22902
C7×#19952
C7×#19862
C7×#18972
C7×#18962
C7×#18712
C7×#18262
C7×#18062
C7×#17592
C7×#17332
C2×C7×#3392
#225067