Finite Group Databasebeta

← C7×#18280 #13195496

Subgroups — C7×#18280 #13195496

Order 1792.

1002 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3560C211yesmaximal, characteristic, complemented
2C7×#3114C211yesmaximal, characteristic, complemented
3C7×#3100C211yesmaximal, characteristic, complemented
4C7×#2603C211yesmaximal, characteristic, complemented
5C7×#1612C211yesmaximal, characteristic, complemented
6C7×#1610C211yesmaximal, characteristic, complemented
7C7×#1609C211yesmaximal, characteristic, complemented
8C7×#1607C211yesmaximal, characteristic, complemented
9C7×#1600C211yesmaximal, characteristic, complemented
10C7×#1598C211yesmaximal, characteristic, complemented
11C7×#1597C211yesmaximal, characteristic, complemented
12C7×#1595C211yesmaximal, characteristic, complemented
13C7×#1505C211yesmaximal, characteristic, complemented
14C7×#1500C211yesmaximal, characteristic, complemented
15C7×#1473C211yesmaximal, characteristic, complemented
16C7×#563—21no—
17C7×#560—21no—
18C7×#553—21no—
19C7×#553—21no—
20C7×#551—21no—
21C7×#547—21no—
22C7×#546—21no—
23C7×#546—21no—
24C7×#542—21no—
25C7×#539—21no—
26C7×#539C2211yescharacteristic
27C7×#538—21no—
28C7×#538—21no—
29C7×#538C2211yescharacteristic
30C7×#537C2211yescharacteristic
31C7×#534C2211yescharacteristic
32C7×#532C2211yescharacteristic
33C7×#529C2211yescharacteristic
34C2×C7×#126C2211yescharacteristic
35C2×C4×C7×D4C2211yescharacteristic, complemented
36C7×#483C2211yescharacteristic, complemented
37C7×#480C2211yescharacteristic
38C7×#480C2211yescharacteristic
39C7×#480C2211yescharacteristic, complemented
40C7×#478—21no—
41C7×#474—21no—
42C7×#463—21no—
43C7×#459—21no—
44C7×#450C2211yescharacteristic, complemented
45C7×#447C2211yescharacteristic
46C7×#447C2211yescharacteristic
47C7×#447C2211yescharacteristic, complemented
48C7×#442—21no—
49C7×#440—21no—
50C4×C7×D8—21no—
51C4×C7×D8—21no—
52C7×#432C2211yescharacteristic, complemented
53C7×#431C2211yescharacteristic, complemented
54C7×#398C2211yescharacteristic, complemented
55C7×#397C2211yescharacteristic
56C7×#394C2211yescharacteristic, complemented
57C7×#392C2211yescharacteristic
58C7×#390—21no—
59C7×#388—21no—
60C7×#386—21no—
61C7×#385—21no—
62C7×#376C2211yescharacteristic, complemented
63C7×#328C2211yescharacteristic, complemented
64C7×#328C2211yescharacteristic, complemented
65C7×#327C2211yescharacteristic
66C7×#327C2211yescharacteristic
67C7×#327C2211yescharacteristic
68C7×#327C2211yescharacteristic
69C7×#327C2211yescharacteristic, complemented
70C7×#327C2211yescharacteristic, complemented
71C7×#324C2211yescharacteristic, complemented
72C7×#324C2211yescharacteristic, complemented
73C7×#323C2211yescharacteristic
74C7×#323C2211yescharacteristic
75#18280C711yesmaximal, characteristic, direct product factor, Sylow
76C2×C7×#41—21no—
77C2×C7×#41—21no—
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C2×C7×SD16—21no—
83C2×C7×D8—21no—
84C2×C7×D8—21no—
85C2×C7×D8—21no—
86C7×C4⋊Q8—21no—
87C7×C4⋊Q8D411yescharacteristic, complemented
88C7×#127D411yescharacteristic, complemented
89C7×#126—21no—
90C7×#126—21no—
91C7×#126—21no—
92C7×#126—21no—
93C7×#126—21no—
94C7×#126—21no—
95C7×#126—21no—
96C7×#126—21no—
97C7×#126—21no—
98C7×#125—21no—
99C7×#125—21no—
100C7×#125D411yescharacteristic, complemented
101C7×#124—21no—
102C7×#124—21no—
103C7×#124—21no—
104C7×#124—21no—
105C7×#124D411yescharacteristic, complemented
106C7×#123—21no—
107C7×#123—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×C22⋊Q8—21no—
119C7×C22⋊Q8—21no—
120C7×C22⋊Q8—21no—
121C7×C22⋊Q8—21no—
122C7×C22⋊Q8—21no—
123C7×C22⋊Q8—21no—
124C7×C22⋊Q8—21no—
125C7×C22⋊Q8C2311yescharacteristic
126C7×#121—21no—
127C7×#121—21no—
128C7×#121—21no—
129C7×#121—21no—
130C7×#121—21no—
131C7×#121—21no—
132C7×#121—21no—
133C7×#121—21no—
134C7×#121—21no—
135C7×#121—21no—
136C7×#121—21no—
137C7×#121—21no—
138C7×#121C2311yescharacteristic
139C7×#121C2311yescharacteristic
140C7×#121C2311yescharacteristic
141C7×#120—21no—
142C7×#120—21no—
143C7×#120—21no—
144C7×#120—21no—
145C7×#120—21no—
146C4×C7×Q8D411yescharacteristic, complemented
147C4×C7×D4—21no—
148C4×C7×D4—21no—
149C4×C7×D4—21no—
150C4×C7×D4—21no—
151C4×C7×D4—21no—
152C4×C7×D4—21no—
153C4×C7×D4—21no—
154C4×C7×D4—21no—
155C4×C7×D4—21no—
156C4×C7×D4—21no—
157C4×C7×D4—21no—
158C4×C7×D4—21no—
159C4×C7×D4D411yescharacteristic, complemented
160C4×C7×D4D411yescharacteristic, complemented
161C4×C7×D4D411yescharacteristic, complemented
162C7×#117—21no—
163C7×#117—21no—
164C2×C7×C4⋊C4—21no—
165C2×C7×C4⋊C4—21no—
166C2×C7×C4⋊C4D411yescharacteristic
167C2×C7×C4⋊C4D411yescharacteristic
168C2×C7×C4⋊C4C2311yescharacteristic
169C2×C7×C4⋊C4C2311yescharacteristic
170C2×C7×C22⋊C4—21no—
171C2×C7×C22⋊C4—21no—
172C2×C7×C22⋊C4—21no—
173C2×C7×C22⋊C4—21no—
174C2×C7×C22⋊C4—21no—
175C2×C7×C22⋊C4—21no—
176C2×C7×C22⋊C4—21no—
177C2×C7×C22⋊C4D411yescharacteristic
178C2×C7×C22⋊C4D411yescharacteristic
179C2×C7×C22⋊C4C2311yescharacteristic
180C2×C42×C7—21no—
181C2×C42×C7C2311yescharacteristic
182C7×#107—21no—
183C7×#107—21no—
184C7×#107—21no—
185C7×#106—21no—
186C7×C4⋊C8—21no—
187C7×C4⋊C8—21no—
188C7×#103—21no—
189C7×#102—21no—
190C7×#102—21no—
191C7×#102—21no—
192C7×#102—21no—
193C7×#102—21no—
194C7×#102—21no—
195C7×#102—21no—
196C7×C22⋊C8C2311yescharacteristic
197C7×C22⋊C8C2311yescharacteristic
198C7×C22⋊C8C2311yescharacteristic
199C7×C22⋊C8C2311yescharacteristic
200C7×#97—21no—
201C4×C7×C8—21no—
202C7×#95—21no—
203C7×#95—21no—
204C7×#95—21no—
205C7×#95C2311yescharacteristic
206C7×#95C2311yescharacteristic
207#3560C2×C711yescharacteristic, complemented
208#3114C2×C711yescharacteristic, complemented
209#3100C2×C711yescharacteristic, complemented
210#2603C2×C711yescharacteristic, complemented
211#1612C2×C711yescharacteristic, complemented
212#1610C2×C711yescharacteristic, complemented
213#1609C2×C711yescharacteristic, complemented
214#1607C2×C711yescharacteristic, complemented
215#1600C2×C711yescharacteristic, complemented
216#1598C2×C711yescharacteristic, complemented
217#1597C2×C711yescharacteristic, complemented
218#1595C2×C711yescharacteristic, complemented
219#1505C2×C711yescharacteristic, complemented
220#1500C2×C711yescharacteristic, complemented
221#1473C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7—21no—
224C24×C7C2×D411yescharacteristic
225C7×#41—81no—
226C7×#41—81no—
227C7×#41—81no—
228C7×#41—81no—
229C2×C7×Q8—21no—
230C2×C7×Q8—21no—
231C2×C7×Q8C2×D411yescharacteristic
232C2×C7×D4—21no—
233C2×C7×D4—21no—
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—21no—
244C2×C7×D4—21no—
245C2×C7×D4—21no—
246C2×C7×D4—42no—
247C2×C7×D4—42no—
248C2×C7×D4—42no—
249C2×C7×D4—81no—
250C2×C7×D4—81no—
251C2×C7×D4—81no—
252C2×C7×D4C2×D411yescharacteristic
253C2×C7×D4C2×D411yescharacteristic
254C2×C7×D4C2×D411yescharacteristic
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—41no—
267C22×C4×C7—41no—
268C22×C4×C7—81no—
269C22×C4×C7—81no—
270C22×C4×C7C2×D411yescharacteristic
271C22×C4×C7C2×D411yescharacteristic
272C22×C4×C7C2×D411yescharacteristic
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2×D411yescharacteristic
275C22×C4×C7C2411yescharacteristic
276C7×SD16—42no—
277C7×D8—42no—
278C7×D8—42no—
279C7×D8—42no—
280C2×C7×C8—21no—
281C2×C7×C8—21no—
282C2×C7×C8—21no—
283C2×C7×C8—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—81no—
304C7×C4⋊C4C2×D411yescharacteristic
305C7×C4⋊C4C2×D411yescharacteristic
306C7×C4⋊C4C2×D411yescharacteristic
307C7×C4⋊C4C2×D411yescharacteristic
308C7×C22⋊C4—21no—
309C7×C22⋊C4—21no—
310C7×C22⋊C4—21no—
311C7×C22⋊C4—21no—
312C7×C22⋊C4—21no—
313C7×C22⋊C4—21no—
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—42no—
334C7×C22⋊C4—42no—
335C7×C22⋊C4—41no—
336C7×C22⋊C4—41no—
337C7×C22⋊C4—81no—
338C7×C22⋊C4—81no—
339C42×C7—21no—
340C42×C7—21no—
341C42×C7—21no—
342C42×C7—42no—
343C42×C7C2×D411yescharacteristic
344C42×C7C2×D411yescharacteristic
345C42×C7C2×D411yescharacteristic
346C42×C7C2×D411yescharacteristic
347#563—21no—
348#560—21no—
349#553—21no—
350#553—21no—
351#551—21no—
352#547—21no—
353#546—21no—
354#546—21no—
355#542—21no—
356#539—21no—
357#539C22×C711yescharacteristic
358#538—21no—
359#538—21no—
360#538C22×C711yescharacteristic
361#537C22×C711yescharacteristic
362#534C22×C711yescharacteristic
363#532C22×C711yescharacteristic
364#529C22×C711yescharacteristic
365C2×#126C22×C711yescharacteristic
366C2×C4×D4C22×C711yescharacteristic, complemented
367#483C22×C711yescharacteristic, complemented
368#480C22×C711yescharacteristic
369#480C22×C711yescharacteristic
370#480C22×C711yescharacteristic, complemented
371#478—21no—
372#474—21no—
373#463—21no—
374#459—21no—
375#450C22×C711yescharacteristic, complemented
376#447C22×C711yescharacteristic
377#447C22×C711yescharacteristic
378#447C22×C711yescharacteristic, complemented
379#442—21no—
380#440—21no—
381C4×D8—21no—
382C4×D8—21no—
383#432C22×C711yescharacteristic, complemented
384#431C22×C711yescharacteristic, complemented
385#398C22×C711yescharacteristic, complemented
386#397C22×C711yescharacteristic
387#394C22×C711yescharacteristic, complemented
388#392C22×C711yescharacteristic
389#390—21no—
390#388—21no—
391#386—21no—
392#385—21no—
393#376C22×C711yescharacteristic, complemented
394#328C22×C711yescharacteristic, complemented
395#328C22×C711yescharacteristic, complemented
396#327C22×C711yescharacteristic
397#327C22×C711yescharacteristic
398#327C22×C711yescharacteristic
399#327C22×C711yescharacteristic
400#327C22×C711yescharacteristic, complemented
401#327C22×C711yescharacteristic, complemented
402#324C22×C711yescharacteristic, complemented
403#324C22×C711yescharacteristic, complemented
404#323C22×C711yescharacteristic
405#323C22×C711yescharacteristic
406C23×C7—22no—
407C23×C7—21no—
408C23×C7—21no—
409C23×C7—21no—
410C23×C7—21no—
411C23×C7—21no—
412C23×C7—21no—
413C23×C7—41no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—81no—
422C23×C7—81no—
423C23×C7—81no—
424C23×C7C22×D411yescharacteristic
425C7×Q8—41no—
426C7×Q8—81no—
427C7×Q8—81no—
428C7×D4—22no—
429C7×D4—22no—
430C7×D4—41no—
431C7×D4—41no—
432C7×D4—41no—
433C7×D4—41no—
434C7×D4—41no—
435C7×D4—41no—
436C7×D4—41no—
437C7×D4—41no—
438C7×D4—41no—
439C7×D4—41no—
440C7×D4—41no—
441C7×D4—81no—
442C7×D4—81no—
443C7×D4—81no—
444C7×D4—81no—
445C7×D4—81no—
446C7×D4—81no—
447C7×D4—81no—
448C7×D4—81no—
449C7×D4—81no—
450C7×D4—84no—
451C2×C4×C7—21no—
452C2×C4×C7—21no—
453C2×C4×C7—22no—
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—21no—
463C2×C4×C7—21no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
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—81no—
477C2×C4×C7—81no—
478C2×C4×C7—81no—
479C2×C4×C7—82no—
480C2×C4×C7—82no—
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×C7#12011yescharacteristic
489C2×C4×C7#12011yescharacteristic
490C2×C4×C7C22×D411yescharacteristic
491C2×C4×C7C22×D411yescharacteristic
492C7×C8—41no—
493C7×C8—41no—
494C7×C8—41no—
495C7×C8—41no—
496C2×#41—21no—
497C2×#41—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C711yescharacteristic
501C23×C4—21no—
502C2×SD16—21no—
503C2×D8—21no—
504C2×D8—21no—
505C2×D8—21no—
506C4⋊Q8—21no—
507C4⋊Q8C7×D411yescharacteristic, complemented
508#127C7×D411yescharacteristic, complemented
509#126—21no—
510#126—21no—
511#126—21no—
512#126—21no—
513#126—21no—
514#126—21no—
515#126—21no—
516#126—21no—
517#126—21no—
518#125—21no—
519#125—21no—
520#125C7×D411yescharacteristic, complemented
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#124C7×D411yescharacteristic, complemented
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—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8C23×C711yescharacteristic
546#121—21no—
547#121—21no—
548#121—21no—
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121—21no—
558#121C23×C711yescharacteristic
559#121C23×C711yescharacteristic
560#121C23×C711yescharacteristic
561#120—21no—
562#120—21no—
563#120—21no—
564#120—21no—
565#120—21no—
566C4×Q8C7×D411yescharacteristic, complemented
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4C7×D411yescharacteristic, complemented
580C4×D4C7×D411yescharacteristic, complemented
581C4×D4C7×D411yescharacteristic, complemented
582#117—21no—
583#117—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C7×D411yescharacteristic
587C2×C4⋊C4C7×D411yescharacteristic
588C2×C4⋊C4C23×C711yescharacteristic
589C2×C4⋊C4C23×C711yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4C7×D411yescharacteristic
598C2×C22⋊C4C7×D411yescharacteristic
599C2×C22⋊C4C23×C711yescharacteristic
600C2×C42—21no—
601C2×C42C23×C711yescharacteristic
602#107—21no—
603#107—21no—
604#107—21no—
605#106—21no—
606C4⋊C8—21no—
607C4⋊C8—21no—
608#103—21no—
609#102—21no—
610#102—21no—
611#102—21no—
612#102—21no—
613#102—21no—
614#102—21no—
615#102—21no—
616C22⋊C8C23×C711yescharacteristic
617C22⋊C8C23×C711yescharacteristic
618C22⋊C8C23×C711yescharacteristic
619C22⋊C8C23×C711yescharacteristic
620#97—21no—
621C4×C8—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95C23×C711yescharacteristic
626#95C23×C711yescharacteristic
627C22×C7—21no—
628C22×C7—21no—
629C22×C7—42no—
630C22×C7—42no—
631C22×C7—41no—
632C22×C7—41no—
633C22×C7—41no—
634C22×C7—41no—
635C22×C7—41no—
636C22×C7—41no—
637C22×C7—41no—
638C22×C7—41no—
639C22×C7—41no—
640C22×C7—42no—
641C22×C7—41no—
642C22×C7—41no—
643C22×C7—41no—
644C22×C7—81no—
645C22×C7—81no—
646C22×C7—81no—
647C22×C7—81no—
648C22×C7—81no—
649C22×C7—81no—
650C22×C7—162no—
651C22×C7C2×#12011yescharacteristic
652C22×C7#57611yescharacteristic
653C22×C7#57611yescharacteristic
654C4×C7—21no—
655C4×C7—21no—
656C4×C7—21no—
657C4×C7—21no—
658C4×C7—21no—
659C4×C7—21no—
660C4×C7—42no—
661C4×C7—41no—
662C4×C7—41no—
663C4×C7—41no—
664C4×C7—41no—
665C4×C7—41no—
666C4×C7—41no—
667C4×C7—41no—
668C4×C7—41no—
669C4×C7—81no—
670C4×C7—81no—
671C24—21no—
672C24—21no—
673C24C2×C7×D411yescharacteristic
674#41—81no—
675#41—81no—
676#41—81no—
677#41—81no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8C2×C7×D411yescharacteristic
681C2×D4—21no—
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—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4C2×C7×D411yescharacteristic
702C2×D4C2×C7×D411yescharacteristic
703C2×D4C2×C7×D411yescharacteristic
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4C2×C7×D411yescharacteristic
720C22×C4C2×C7×D411yescharacteristic
721C22×C4C2×C7×D411yescharacteristic
722C22×C4C2×C7×D411yescharacteristic
723C22×C4C2×C7×D411yescharacteristic
724C22×C4C24×C711yescharacteristic
725SD16—42no—
726D8—42no—
727D8—42no—
728D8—42no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—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—81no—
753C4⋊C4C2×C7×D411yescharacteristic
754C4⋊C4C2×C7×D411yescharacteristic
755C4⋊C4C2×C7×D411yescharacteristic
756C4⋊C4C2×C7×D411yescharacteristic
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—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—42no—
783C22⋊C4—42no—
784C22⋊C4—41no—
785C22⋊C4—41no—
786C22⋊C4—81no—
787C22⋊C4—81no—
788C42—21no—
789C42—21no—
790C42—21no—
791C42—42no—
792C42C2×C7×D411yescharacteristic
793C42C2×C7×D411yescharacteristic
794C42C2×C7×D411yescharacteristic
795C42C2×C7×D411yescharacteristic
796C2×C7—21no—
797C2×C7—21no—
798C2×C7—81no—
799C2×C7—82no—
800C2×C7—81no—
801C2×C7—81no—
802C2×C7—81no—
803C2×C7#300811yescharacteristic
804C2×C7#301811yescharacteristic
805C2×C7#302511yescharacteristic
806C23—22no—
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—81no—
822C23—81no—
823C23—81no—
824C23C22×C7×D411yescharacteristic
825Q8—41no—
826Q8—81no—
827Q8—81no—
828D4—22no—
829D4—22no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—84no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
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—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C7×#12011yescharacteristic
887C2×C4C7×#12011yescharacteristic
888C2×C4C7×#12011yescharacteristic
889C2×C4C7×#12011yescharacteristic
890C2×C4C22×C7×D411yescharacteristic
891C2×C4C22×C7×D411yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C7#1828011yescharacteristic, direct product factor, Sylow
897C22—21no—
898C22—21no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—162no—
921C22C2×C7×#12011yescharacteristic
922C22C7×#57611yescharacteristic
923C22C7×#57611yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—81no—
940C4—81no—
941C2—21no—
942C2—21no—
943C2—82no—
944C2—81no—
945C2—81no—
946C2—81no—
947C2—81no—
948C2C7×#300811yescharacteristic
949C2C7×#301811yescharacteristic
950C2C7×#302511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3560C2semidirect
2. C7×#3114C2semidirect
3. C7×#3100C2semidirect
4. C7×#2603C2semidirect
5. C7×#1612C2semidirect
6. C7×#1610C2semidirect
7. C7×#1609C2semidirect
8. C7×#1607C2semidirect
9. C7×#1600C2semidirect
10. C7×#1598C2semidirect
11. C7×#1597C2semidirect
12. C7×#1595C2semidirect
13. C7×#1505C2semidirect
14. C7×#1500C2semidirect
15. C7×#1473C2semidirect
35. C2×C4×C7×D4C22semidirect
36. C7×#483C22semidirect
39. C7×#480C22semidirect
44. C7×#450C22semidirect
47. C7×#447C22semidirect
52. C7×#432C22semidirect
53. C7×#431C22semidirect
54. C7×#398C22semidirect
56. C7×#394C22semidirect
62. C7×#376C22semidirect
63. C7×#328C22semidirect
64. C7×#328C22semidirect
69. C7×#327C22semidirect
70. C7×#327C22semidirect
71. C7×#324C22semidirect
72. C7×#324C22semidirect
75. #18280C7direct (N × H)
87. C7×C4⋊Q8D4semidirect
88. C7×#127D4semidirect
100. C7×#125D4semidirect
105. C7×#124D4semidirect
146. C4×C7×Q8D4semidirect
159. C4×C7×D4D4semidirect
160. C4×C7×D4D4semidirect
161. C4×C7×D4D4semidirect
207. #3560C2×C7semidirect
208. #3114C2×C7semidirect
209. #3100C2×C7semidirect
210. #2603C2×C7semidirect
211. #1612C2×C7semidirect
212. #1610C2×C7semidirect
213. #1609C2×C7semidirect
214. #1607C2×C7semidirect
215. #1600C2×C7semidirect
216. #1598C2×C7semidirect
217. #1597C2×C7semidirect
218. #1595C2×C7semidirect
219. #1505C2×C7semidirect
220. #1500C2×C7semidirect
221. #1473C2×C7semidirect
366. C2×C4×D4C22×C7semidirect
367. #483C22×C7semidirect
370. #480C22×C7semidirect
375. #450C22×C7semidirect
378. #447C22×C7semidirect
383. #432C22×C7semidirect
384. #431C22×C7semidirect
385. #398C22×C7semidirect
387. #394C22×C7semidirect
393. #376C22×C7semidirect
394. #328C22×C7semidirect
395. #328C22×C7semidirect
400. #327C22×C7semidirect
401. #327C22×C7semidirect
402. #324C22×C7semidirect
403. #324C22×C7semidirect
507. C4⋊Q8C7×D4semidirect
508. #127C7×D4semidirect
520. #125C7×D4semidirect
525. #124C7×D4semidirect
566. C4×Q8C7×D4semidirect
579. C4×D4C7×D4semidirect
580. C4×D4C7×D4semidirect
581. C4×D4C7×D4semidirect
896. C7#18280direct (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×#31142
C7×#31002
C7×#26032
C7×#16122
C7×#16102
C7×#16092
C7×#16072
C7×#16002
C7×#15982
C7×#15972
C7×#15952
C7×#15052
C7×#15002
C7×#14732
#182807