Finite Group Databasebeta

← C7×#18448 #13195664

Subgroups — C7×#18448 #13195664

Order 1792.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3535C211yesmaximal, characteristic, complemented
2C7×#3193C211yesmaximal, characteristic, complemented
3C7×#3188C211yesmaximal, characteristic, complemented
4C7×#2813C211yesmaximal, characteristic, complemented
5C7×#1618C211yesmaximal, characteristic, complemented
6C7×#1617C211yesmaximal, characteristic, complemented
7C7×#1615C211yesmaximal, characteristic, complemented
8C7×#1614C211yesmaximal, characteristic, complemented
9C7×#1600C211yesmaximal, characteristic, complemented
10C7×#1599C211yesmaximal, characteristic, complemented
11C7×#1597C211yesmaximal, characteristic, complemented
12C7×#1596C211yesmaximal, characteristic, complemented
13C7×#1520C211yesmaximal, characteristic, complemented
14C7×#1513C211yesmaximal, characteristic, complemented
15C7×#1468C211yesmaximal, characteristic, complemented
16C7×#563—21no—
17C7×#562—21no—
18C7×#554—21no—
19C7×#552—21no—
20C7×#551—21no—
21C7×#551—21no—
22C7×#547—21no—
23C7×#546—21no—
24C7×#544C2211yescharacteristic
25C7×#543C2211yescharacteristic
26C7×#542—21no—
27C7×#539—21no—
28C7×#539—21no—
29C7×#539C2211yescharacteristic
30C7×#538C2211yescharacteristic
31C7×#536—21no—
32C7×#525C2211yescharacteristic
33C2×C7×#123C2211yescharacteristic
34C2×C7×C22⋊Q8C2211yescharacteristic
35C2×C7×#121C2211yescharacteristic
36C7×#484C2211yescharacteristic
37C7×#484C2211yescharacteristic
38C7×#484C2211yescharacteristic
39C7×#482—21no—
40C7×#481C2211yescharacteristic
41C7×#480—21no—
42C7×#468—21no—
43C7×#468—21no—
44C7×#466—21no—
45C7×#465—21no—
46C7×#450C2211yescharacteristic
47C7×#450C2211yescharacteristic
48C7×#450C2211yescharacteristic
49C7×#449—21no—
50C7×#448—21no—
51C7×#447C2211yescharacteristic
52C7×#407C2211yescharacteristic
53C2×C7×C22⋊C8C2211yescharacteristic
54C7×#400C2211yescharacteristic
55C7×#399C2211yescharacteristic
56C7×#396—21no—
57C7×#394—21no—
58C7×#394—21no—
59C7×#394C2211yescharacteristic
60C7×#392—21no—
61C7×#392C2211yescharacteristic
62C7×#380C2211yescharacteristic
63C7×#328C2211yescharacteristic
64C7×#328C2211yescharacteristic
65C7×#328C2211yescharacteristic
66C7×#328C2211yescharacteristic
67C7×#328C2211yescharacteristic
68C7×#328C2211yescharacteristic
69C7×#327C2211yescharacteristic
70C7×#327C2211yescharacteristic
71C7×#324C2211yescharacteristic
72C7×#324C2211yescharacteristic
73C7×#323C2211yescharacteristic
74C7×#323C2211yescharacteristic
75#18448C711yesmaximal, characteristic, direct product factor, Sylow
76C2×C7×#41—21no—
77C2×C7×#41D411yescharacteristic, complemented
78C22×C7×Q8D411yescharacteristic, complemented
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4D411yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C2×C7×SD16—21no—
85C2×C7×SD16—21no—
86C2×C7×SD16—21no—
87C2×C7×D8—21no—
88C2×C7×M16—21no—
89C22×C7×C8—21no—
90C7×C4⋊Q8—21no—
91C7×C4⋊Q8—21no—
92C7×C4⋊Q8—21no—
93C7×#126—21no—
94C7×#126—21no—
95C7×#126—21no—
96C7×#126—21no—
97C7×#126—21no—
98C7×#126—21no—
99C7×#125—21no—
100C7×#125—21no—
101C7×#125—21no—
102C7×#125—21no—
103C7×#125—21no—
104C7×#124—21no—
105C7×#124—21no—
106C7×#124—21no—
107C7×#124—21no—
108C7×#123—21no—
109C7×#123—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×#123—21no—
119C7×#123—21no—
120C7×#123—21no—
121C7×#123—21no—
122C7×C22⋊Q8—21no—
123C7×C22⋊Q8—21no—
124C7×C22⋊Q8—21no—
125C7×C22⋊Q8—21no—
126C7×C22⋊Q8—21no—
127C7×C22⋊Q8—21no—
128C7×C22⋊Q8—21no—
129C7×C22⋊Q8—21no—
130C7×C22⋊Q8—21no—
131C7×C22⋊Q8—21no—
132C7×C22⋊Q8—21no—
133C7×C22⋊Q8—21no—
134C7×C22⋊Q8—21no—
135C7×C22⋊Q8—21no—
136C7×C22⋊Q8D411yescharacteristic, complemented
137C7×C22⋊Q8D411yescharacteristic, complemented
138C7×C22⋊Q8D411yescharacteristic, complemented
139C7×C22⋊Q8C2311yescharacteristic
140C7×C22⋊Q8C2311yescharacteristic
141C7×C22⋊Q8C2311yescharacteristic
142C7×#121—21no—
143C7×#121—21no—
144C7×#121—21no—
145C7×#121—21no—
146C7×#121—21no—
147C7×#121—21no—
148C7×#121—21no—
149C7×#121—21no—
150C7×#121D411yescharacteristic, complemented
151C7×#121C2311yescharacteristic
152C7×#120—21no—
153C7×#120—21no—
154C4×C7×Q8—21no—
155C4×C7×D4—21no—
156C4×C7×D4—21no—
157C4×C7×D4—21no—
158C4×C7×D4—21no—
159C4×C7×D4—21no—
160C4×C7×D4—21no—
161C4×C7×D4—21no—
162C7×#117—21no—
163C7×#117—21no—
164C7×#117—21no—
165C7×#117D411yescharacteristic, complemented
166C2×C7×C4⋊C4—21no—
167C2×C7×C4⋊C4—21no—
168C2×C7×C4⋊C4—21no—
169C2×C7×C4⋊C4—21no—
170C2×C7×C4⋊C4D411yescharacteristic
171C2×C7×C4⋊C4D411yescharacteristic, complemented
172C2×C7×C4⋊C4C2311yescharacteristic
173C2×C7×C4⋊C4C2311yescharacteristic
174C2×C7×C22⋊C4—21no—
175C2×C7×C22⋊C4—21no—
176C2×C7×C22⋊C4—21no—
177C2×C7×C22⋊C4—21no—
178C2×C7×C22⋊C4—21no—
179C2×C7×C22⋊C4—21no—
180C2×C7×C22⋊C4—21no—
181C2×C7×C22⋊C4—21no—
182C2×C7×C22⋊C4D411yescharacteristic
183C2×C7×C22⋊C4D411yescharacteristic
184C2×C7×C22⋊C4C2311yescharacteristic
185C7×#107—21no—
186C7×#107—21no—
187C7×#107—21no—
188C7×#106—21no—
189C7×#103—21no—
190C7×#103—21no—
191C7×#103—21no—
192C7×#102—21no—
193C7×#102—21no—
194C7×#102—21no—
195C7×#102—21no—
196C7×#102—21no—
197C7×C22⋊C8—21no—
198C7×C22⋊C8—21no—
199C7×C22⋊C8C2311yescharacteristic
200C7×C22⋊C8C2311yescharacteristic
201C7×C22⋊C8C2311yescharacteristic
202C7×C22⋊C8C2311yescharacteristic
203C7×#95—21no—
204C7×#95—21no—
205C7×#95C2311yescharacteristic
206C7×#95C2311yescharacteristic
207#3535C2×C711yescharacteristic, complemented
208#3193C2×C711yescharacteristic, complemented
209#3188C2×C711yescharacteristic, complemented
210#2813C2×C711yescharacteristic, complemented
211#1618C2×C711yescharacteristic, complemented
212#1617C2×C711yescharacteristic, complemented
213#1615C2×C711yescharacteristic, complemented
214#1614C2×C711yescharacteristic, complemented
215#1600C2×C711yescharacteristic, complemented
216#1599C2×C711yescharacteristic, complemented
217#1597C2×C711yescharacteristic, complemented
218#1596C2×C711yescharacteristic, complemented
219#1520C2×C711yescharacteristic, complemented
220#1513C2×C711yescharacteristic, complemented
221#1468C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7C2×D411yescharacteristic
224C24×C7C2×D411yescharacteristic
225C7×#41—82no—
226C7×#41—81no—
227C2×C7×Q8—21no—
228C2×C7×Q8—21no—
229C2×C7×Q8—21no—
230C2×C7×Q8—81no—
231C2×C7×Q8C2×D411yescharacteristic
232C2×C7×Q8C2×D411yescharacteristic
233C2×C7×Q8C2×D411yescharacteristic
234C2×C7×D4—21no—
235C2×C7×D4—21no—
236C2×C7×D4—21no—
237C2×C7×D4—21no—
238C2×C7×D4—21no—
239C2×C7×D4—21no—
240C2×C7×D4—21no—
241C2×C7×D4—21no—
242C2×C7×D4—21no—
243C2×C7×D4—41no—
244C2×C7×D4—41no—
245C2×C7×D4—81no—
246C2×C7×D4—81no—
247C2×C7×D4—81no—
248C2×C7×D4—81no—
249C2×C7×D4—81no—
250C2×C7×D4—81no—
251C2×C7×D4—81no—
252C2×C7×D4C2×D411yescharacteristic
253C22×C4×C7—21no—
254C22×C4×C7—21no—
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—81no—
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2×D411yescharacteristic
266C22×C4×C7C2×D411yescharacteristic
267C22×C4×C7C2×D411yescharacteristic
268C22×C4×C7C2×D411yescharacteristic
269C22×C4×C7C2×D411yescharacteristic
270C22×C4×C7C2×D411yescharacteristic
271C22×C4×C7C2×D411yescharacteristic
272C22×C4×C7C2411yescharacteristic
273C7×SD16—81no—
274C7×SD16—81no—
275C7×SD16—81no—
276C7×D8—81no—
277C7×M16—81no—
278C2×C7×C8—21no—
279C2×C7×C8—21no—
280C2×C7×C8—21no—
281C2×C7×C8—21no—
282C2×C7×C8—81no—
283C7×C4⋊C4—21no—
284C7×C4⋊C4—21no—
285C7×C4⋊C4—21no—
286C7×C4⋊C4—21no—
287C7×C4⋊C4—21no—
288C7×C4⋊C4—21no—
289C7×C4⋊C4—21no—
290C7×C4⋊C4—21no—
291C7×C4⋊C4—21no—
292C7×C4⋊C4—21no—
293C7×C4⋊C4—21no—
294C7×C4⋊C4—21no—
295C7×C4⋊C4—21no—
296C7×C4⋊C4—21no—
297C7×C4⋊C4—21no—
298C7×C4⋊C4—21no—
299C7×C4⋊C4—21no—
300C7×C4⋊C4—21no—
301C7×C4⋊C4—21no—
302C7×C4⋊C4—21no—
303C7×C4⋊C4—21no—
304C7×C4⋊C4—21no—
305C7×C4⋊C4—21no—
306C7×C4⋊C4—21no—
307C7×C4⋊C4—21no—
308C7×C4⋊C4—81no—
309C7×C4⋊C4—81no—
310C7×C4⋊C4C2×D411yescharacteristic
311C7×C4⋊C4C2×D411yescharacteristic
312C7×C4⋊C4C2×D411yescharacteristic
313C7×C4⋊C4C2×D411yescharacteristic
314C7×C22⋊C4—21no—
315C7×C22⋊C4—21no—
316C7×C22⋊C4—21no—
317C7×C22⋊C4—21no—
318C7×C22⋊C4—21no—
319C7×C22⋊C4—21no—
320C7×C22⋊C4—21no—
321C7×C22⋊C4—21no—
322C7×C22⋊C4—21no—
323C7×C22⋊C4—21no—
324C7×C22⋊C4—21no—
325C7×C22⋊C4—21no—
326C7×C22⋊C4—21no—
327C7×C22⋊C4—21no—
328C7×C22⋊C4—21no—
329C7×C22⋊C4—21no—
330C7×C22⋊C4—21no—
331C7×C22⋊C4—21no—
332C7×C22⋊C4—21no—
333C7×C22⋊C4—21no—
334C7×C22⋊C4—21no—
335C7×C22⋊C4—21no—
336C7×C22⋊C4—21no—
337C7×C22⋊C4—41no—
338C7×C22⋊C4—41no—
339C7×C22⋊C4—81no—
340C7×C22⋊C4—81no—
341C7×C22⋊C4—81no—
342C7×C22⋊C4—81no—
343C7×C22⋊C4—81no—
344C42×C7—21no—
345C42×C7—21no—
346C42×C7—21no—
347C42×C7—21no—
348C42×C7—21no—
349#563—21no—
350#562—21no—
351#554—21no—
352#552—21no—
353#551—21no—
354#551—21no—
355#547—21no—
356#546—21no—
357#544C22×C711yescharacteristic
358#543C22×C711yescharacteristic
359#542—21no—
360#539—21no—
361#539—21no—
362#539C22×C711yescharacteristic
363#538C22×C711yescharacteristic
364#536—21no—
365#525C22×C711yescharacteristic
366C2×#123C22×C711yescharacteristic
367C2×C22⋊Q8C22×C711yescharacteristic
368C2×#121C22×C711yescharacteristic
369#484C22×C711yescharacteristic
370#484C22×C711yescharacteristic
371#484C22×C711yescharacteristic
372#482—21no—
373#481C22×C711yescharacteristic
374#480—21no—
375#468—21no—
376#468—21no—
377#466—21no—
378#465—21no—
379#450C22×C711yescharacteristic
380#450C22×C711yescharacteristic
381#450C22×C711yescharacteristic
382#449—21no—
383#448—21no—
384#447C22×C711yescharacteristic
385#407C22×C711yescharacteristic
386C2×C22⋊C8C22×C711yescharacteristic
387#400C22×C711yescharacteristic
388#399C22×C711yescharacteristic
389#396—21no—
390#394—21no—
391#394—21no—
392#394C22×C711yescharacteristic
393#392—21no—
394#392C22×C711yescharacteristic
395#380C22×C711yescharacteristic
396#328C22×C711yescharacteristic
397#328C22×C711yescharacteristic
398#328C22×C711yescharacteristic
399#328C22×C711yescharacteristic
400#328C22×C711yescharacteristic
401#328C22×C711yescharacteristic
402#327C22×C711yescharacteristic
403#327C22×C711yescharacteristic
404#324C22×C711yescharacteristic
405#324C22×C711yescharacteristic
406#323C22×C711yescharacteristic
407#323C22×C711yescharacteristic
408C23×C7—21no—
409C23×C7—21no—
410C23×C7—21no—
411C23×C7—21no—
412C23×C7—21no—
413C23×C7—21no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—41no—
422C23×C7—41no—
423C23×C7—41no—
424C23×C7—41no—
425C23×C7#12011yescharacteristic
426C23×C7#12011yescharacteristic
427C23×C7C22×D411yescharacteristic
428C7×Q8—41no—
429C7×Q8—41no—
430C7×Q8—41no—
431C7×Q8—81no—
432C7×Q8—81no—
433C7×Q8—81no—
434C7×D4—41no—
435C7×D4—41no—
436C7×D4—41no—
437C7×D4—41no—
438C7×D4—41no—
439C7×D4—42no—
440C7×D4—42no—
441C7×D4—41no—
442C7×D4—41no—
443C7×D4—81no—
444C7×D4—81no—
445C7×D4—81no—
446C7×D4—81no—
447C7×D4—82no—
448C7×D4—82no—
449C7×D4—84no—
450C2×C4×C7—21no—
451C2×C4×C7—21no—
452C2×C4×C7—21no—
453C2×C4×C7—21no—
454C2×C4×C7—21no—
455C2×C4×C7—21no—
456C2×C4×C7—21no—
457C2×C4×C7—21no—
458C2×C4×C7—21no—
459C2×C4×C7—21no—
460C2×C4×C7—21no—
461C2×C4×C7—21no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—42no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—81no—
481C2×C4×C7—81no—
482C2×C4×C7—81no—
483C2×C4×C7—81no—
484C2×C4×C7—81no—
485C2×C4×C7—81no—
486C2×C4×C7#12011yescharacteristic
487C2×C4×C7#12011yescharacteristic
488C2×C4×C7C22×D411yescharacteristic
489C2×C4×C7C22×D411yescharacteristic
490C7×C8—41no—
491C7×C8—41no—
492C7×C8—41no—
493C7×C8—41no—
494C2×#41—21no—
495C2×#41C7×D411yescharacteristic, complemented
496C22×Q8C7×D411yescharacteristic, complemented
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C7×D411yescharacteristic
500C22×D4C23×C711yescharacteristic
501C23×C4C23×C711yescharacteristic
502C2×SD16—21no—
503C2×SD16—21no—
504C2×SD16—21no—
505C2×D8—21no—
506C2×M16—21no—
507C22×C8—21no—
508C4⋊Q8—21no—
509C4⋊Q8—21no—
510C4⋊Q8—21no—
511#126—21no—
512#126—21no—
513#126—21no—
514#126—21no—
515#126—21no—
516#126—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#124—21no—
526#123—21no—
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8C7×D411yescharacteristic, complemented
555C22⋊Q8C7×D411yescharacteristic, complemented
556C22⋊Q8C7×D411yescharacteristic, complemented
557C22⋊Q8C23×C711yescharacteristic
558C22⋊Q8C23×C711yescharacteristic
559C22⋊Q8C23×C711yescharacteristic
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121C7×D411yescharacteristic, complemented
569#121C23×C711yescharacteristic
570#120—21no—
571#120—21no—
572C4×Q8—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580#117—21no—
581#117—21no—
582#117—21no—
583#117C7×D411yescharacteristic, complemented
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4C7×D411yescharacteristic
589C2×C4⋊C4C7×D411yescharacteristic, complemented
590C2×C4⋊C4C23×C711yescharacteristic
591C2×C4⋊C4C23×C711yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4C7×D411yescharacteristic
601C2×C22⋊C4C7×D411yescharacteristic
602C2×C22⋊C4C23×C711yescharacteristic
603#107—21no—
604#107—21no—
605#107—21no—
606#106—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#102—21no—
611#102—21no—
612#102—21no—
613#102—21no—
614#102—21no—
615C22⋊C8—21no—
616C22⋊C8—21no—
617C22⋊C8C23×C711yescharacteristic
618C22⋊C8C23×C711yescharacteristic
619C22⋊C8C23×C711yescharacteristic
620C22⋊C8C23×C711yescharacteristic
621#95—21no—
622#95—21no—
623#95C23×C711yescharacteristic
624#95C23×C711yescharacteristic
625C22×C7—21no—
626C22×C7—21no—
627C22×C7—21no—
628C22×C7—21no—
629C22×C7—21no—
630C22×C7—21no—
631C22×C7—21no—
632C22×C7—21no—
633C22×C7—41no—
634C22×C7—41no—
635C22×C7—41no—
636C22×C7—41no—
637C22×C7—41no—
638C22×C7—41no—
639C22×C7—81no—
640C22×C7—81no—
641C22×C7—81no—
642C22×C7—81no—
643C22×C7—81no—
644C22×C7—81no—
645C22×C7—81no—
646C22×C7—81no—
647C22×C7—81no—
648C22×C7—81no—
649C22×C7—81no—
650C22×C7C2×#12011yescharacteristic
651C22×C7#57711yescharacteristic
652C22×C7#57811yescharacteristic
653C4×C7—21no—
654C4×C7—21no—
655C4×C7—21no—
656C4×C7—21no—
657C4×C7—41no—
658C4×C7—41no—
659C4×C7—41no—
660C4×C7—41no—
661C4×C7—41no—
662C4×C7—41no—
663C4×C7—41no—
664C4×C7—41no—
665C4×C7—41no—
666C4×C7—41no—
667C4×C7—81no—
668C4×C7—81no—
669C4×C7—81no—
670C24—21no—
671C24C2×C7×D411yescharacteristic
672C24C2×C7×D411yescharacteristic
673#41—82no—
674#41—81no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—81no—
679C2×Q8C2×C7×D411yescharacteristic
680C2×Q8C2×C7×D411yescharacteristic
681C2×Q8C2×C7×D411yescharacteristic
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—41no—
692C2×D4—41no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4C2×C7×D411yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—81no—
712C22×C4C2×C7×D411yescharacteristic
713C22×C4C2×C7×D411yescharacteristic
714C22×C4C2×C7×D411yescharacteristic
715C22×C4C2×C7×D411yescharacteristic
716C22×C4C2×C7×D411yescharacteristic
717C22×C4C2×C7×D411yescharacteristic
718C22×C4C2×C7×D411yescharacteristic
719C22×C4C2×C7×D411yescharacteristic
720C22×C4C24×C711yescharacteristic
721SD16—81no—
722SD16—81no—
723SD16—81no—
724D8—81no—
725M16—81no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—81no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—81no—
757C4⋊C4—81no—
758C4⋊C4C2×C7×D411yescharacteristic
759C4⋊C4C2×C7×D411yescharacteristic
760C4⋊C4C2×C7×D411yescharacteristic
761C4⋊C4C2×C7×D411yescharacteristic
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—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—41no—
786C22⋊C4—41no—
787C22⋊C4—81no—
788C22⋊C4—81no—
789C22⋊C4—81no—
790C22⋊C4—81no—
791C22⋊C4—81no—
792C42—21no—
793C42—21no—
794C42—21no—
795C42—21no—
796C42—21no—
797C2×C7—21no—
798C2×C7—21no—
799C2×C7—41no—
800C2×C7—41no—
801C2×C7—81no—
802C2×C7—81no—
803C2×C7—161no—
804C2×C7#301311yescharacteristic
805C2×C7#302111yescharacteristic
806C2×C7#302611yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23C7×#12011yescharacteristic
825C23C7×#12011yescharacteristic
826C23C22×C7×D411yescharacteristic
827Q8—41no—
828Q8—41no—
829Q8—41no—
830Q8—81no—
831Q8—81no—
832Q8—81no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—41no—
841D4—41no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—82no—
847D4—82no—
848D4—84no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4C7×#12011yescharacteristic
886C2×C4C7×#12011yescharacteristic
887C2×C4C22×C7×D411yescharacteristic
888C2×C4C22×C7×D411yescharacteristic
889C8—41no—
890C8—41no—
891C8—41no—
892C8—41no—
893C7#1844811yescharacteristic, direct product factor, Sylow
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C7×#12011yescharacteristic
920C22C7×#57711yescharacteristic
921C22C7×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C7×#301311yescharacteristic
947C2C7×#302111yescharacteristic
948C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3535C2semidirect
2. C7×#3193C2semidirect
3. C7×#3188C2semidirect
4. C7×#2813C2semidirect
5. C7×#1618C2semidirect
6. C7×#1617C2semidirect
7. C7×#1615C2semidirect
8. C7×#1614C2semidirect
9. C7×#1600C2semidirect
10. C7×#1599C2semidirect
11. C7×#1597C2semidirect
12. C7×#1596C2semidirect
13. C7×#1520C2semidirect
14. C7×#1513C2semidirect
15. C7×#1468C2semidirect
75. #18448C7direct (N × H)
77. C2×C7×#41D4semidirect
78. C22×C7×Q8D4semidirect
136. C7×C22⋊Q8D4semidirect
137. C7×C22⋊Q8D4semidirect
138. C7×C22⋊Q8D4semidirect
150. C7×#121D4semidirect
165. C7×#117D4semidirect
171. C2×C7×C4⋊C4D4semidirect
207. #3535C2×C7semidirect
208. #3193C2×C7semidirect
209. #3188C2×C7semidirect
210. #2813C2×C7semidirect
211. #1618C2×C7semidirect
212. #1617C2×C7semidirect
213. #1615C2×C7semidirect
214. #1614C2×C7semidirect
215. #1600C2×C7semidirect
216. #1599C2×C7semidirect
217. #1597C2×C7semidirect
218. #1596C2×C7semidirect
219. #1520C2×C7semidirect
220. #1513C2×C7semidirect
221. #1468C2×C7semidirect
495. C2×#41C7×D4semidirect
496. C22×Q8C7×D4semidirect
554. C22⋊Q8C7×D4semidirect
555. C22⋊Q8C7×D4semidirect
556. C22⋊Q8C7×D4semidirect
568. #121C7×D4semidirect
583. #117C7×D4semidirect
589. C2×C4⋊C4C7×D4semidirect
893. C7#18448direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35352
C7×#31932
C7×#31882
C7×#28132
C7×#16182
C7×#16172
C7×#16152
C7×#16142
C7×#16002
C7×#15992
C7×#15972
C7×#15962
C7×#15202
C7×#15132
C7×#14682
#184487