Finite Group Databasebeta

← C7×#18283 #13195499

Subgroups — C7×#18283 #13195499

Order 1792.

886 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3564C211yesmaximal, characteristic
2C7×#3117C211yesmaximal, characteristic, complemented
3C7×#3104C211yesmaximal, characteristic, complemented
4C7×#2604C211yesmaximal, characteristic, complemented
5C7×#1618C211yesmaximal, characteristic
6C7×#1617C211yesmaximal, characteristic, complemented
7C7×#1615C211yesmaximal, characteristic, complemented
8C7×#1614C211yesmaximal, characteristic, complemented
9C7×#1606C211yesmaximal, characteristic
10C7×#1605C211yesmaximal, characteristic, complemented
11C7×#1603C211yesmaximal, characteristic, complemented
12C7×#1602C211yesmaximal, characteristic, complemented
13C7×#1506C211yesmaximal, characteristic, complemented
14C7×#1500C211yesmaximal, characteristic, complemented
15C7×#1473C211yesmaximal, characteristic, complemented
16C7×#563—21no—
17C7×#563—21no—
18C7×#556—21no—
19C7×#554—21no—
20C7×#552—21no—
21C7×#552—21no—
22C7×#551—21no—
23C7×#551—21no—
24C7×#544C2211yescharacteristic
25C7×#543C2211yescharacteristic
26C7×#542—21no—
27C7×#541—21no—
28C7×#541—21no—
29C7×#539—21no—
30C7×#539C2211yescharacteristic
31C7×#538C2211yescharacteristic
32C7×#533C2211yescharacteristic
33C7×#529C2211yescharacteristic
34C2×C7×#126C2211yescharacteristic
35C2×C4×C7×Q8C2211yescharacteristic
36C7×#484C2211yescharacteristic
37C7×#484C2211yescharacteristic
38C7×#484C2211yescharacteristic
39C7×#481C2211yescharacteristic
40C7×#479—21no—
41C7×#477—21no—
42C7×#464—21no—
43C7×#462—21no—
44C7×#451C2211yescharacteristic
45C7×#451C2211yescharacteristic
46C7×#451C2211yescharacteristic
47C7×#448C2211yescharacteristic
48C7×#441—21no—
49C7×#440—21no—
50C4×C7×Q16—21no—
51C4×C7×Q16—21no—
52C7×#432C2211yescharacteristic
53C7×#431C2211yescharacteristic
54C7×#400C2211yescharacteristic
55C7×#399C2211yescharacteristic
56C7×#395C2211yescharacteristic
57C7×#393C2211yescharacteristic
58C7×#389—21no—
59C7×#388—21no—
60C7×#388—21no—
61C7×#387—21no—
62C7×#376C2211yescharacteristic
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#18283C711yesmaximal, characteristic, direct product factor, Sylow
76C22×C7×Q8C2311yescharacteristic
77C2×C7×Q16—21no—
78C2×C7×Q16—21no—
79C2×C7×Q16—21no—
80C2×C7×SD16—21no—
81C7×C4⋊Q8—21no—
82C7×C4⋊Q8—21no—
83C7×C4⋊Q8—21no—
84C7×C4⋊Q8D411yescharacteristic
85C7×C4⋊Q8D411yescharacteristic
86C7×#126—21no—
87C7×#126—21no—
88C7×#126—21no—
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×#126—21no—
99C7×#125—21no—
100C7×#125—21no—
101C7×#125—21no—
102C7×#125—21no—
103C7×#125—21no—
104C7×#125—21no—
105C7×#125—21no—
106C7×#125—21no—
107C7×#125—21no—
108C7×#125D411yescharacteristic
109C7×#124—21no—
110C7×#124—21no—
111C7×#124—21no—
112C7×#124D411yescharacteristic
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×C22⋊Q8—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⋊Q8C2311yescharacteristic
136C7×C22⋊Q8C2311yescharacteristic
137C7×C22⋊Q8C2311yescharacteristic
138C7×#121—21no—
139C7×#121C2311yescharacteristic
140C7×#120—21no—
141C4×C7×Q8—21no—
142C4×C7×Q8—21no—
143C4×C7×Q8—21no—
144C4×C7×Q8—21no—
145C4×C7×Q8—21no—
146C4×C7×Q8—21no—
147C4×C7×Q8—21no—
148C4×C7×Q8D411yescharacteristic
149C4×C7×Q8D411yescharacteristic
150C4×C7×Q8D411yescharacteristic
151C4×C7×D4—21no—
152C4×C7×D4—21no—
153C4×C7×D4—21no—
154C4×C7×D4—21no—
155C4×C7×D4—21no—
156C4×C7×D4D411yescharacteristic
157C7×#117—21no—
158C7×#117—21no—
159C7×#117—21no—
160C7×#117—21no—
161C7×#117—21no—
162C7×#117—21no—
163C2×C7×C4⋊C4—21no—
164C2×C7×C4⋊C4—21no—
165C2×C7×C4⋊C4—21no—
166C2×C7×C4⋊C4—21no—
167C2×C7×C4⋊C4D411yescharacteristic
168C2×C7×C4⋊C4D411yescharacteristic
169C2×C7×C4⋊C4C2311yescharacteristic
170C2×C7×C4⋊C4C2311yescharacteristic
171C2×C7×C22⋊C4—21no—
172C2×C7×C22⋊C4—21no—
173C2×C7×C22⋊C4—21no—
174C2×C7×C22⋊C4D411yescharacteristic
175C2×C7×C22⋊C4D411yescharacteristic
176C2×C7×C22⋊C4C2311yescharacteristic
177C2×C42×C7—21no—
178C2×C42×C7—21no—
179C2×C42×C7C2311yescharacteristic
180C7×#107—21no—
181C7×#107—21no—
182C7×#107—21no—
183C7×#106—21no—
184C7×C4⋊C8—21no—
185C7×C4⋊C8—21no—
186C7×#103—21no—
187C7×#103—21no—
188C7×#103—21no—
189C7×#103—21no—
190C7×#103—21no—
191C7×#103—21no—
192C7×#103—21no—
193C7×#102—21no—
194C7×C22⋊C8C2311yescharacteristic
195C7×C22⋊C8C2311yescharacteristic
196C7×C22⋊C8C2311yescharacteristic
197C7×C22⋊C8C2311yescharacteristic
198C7×#97—21no—
199C4×C7×C8—21no—
200C7×#95—21no—
201C7×#95—21no—
202C7×#95—21no—
203C7×#95—21no—
204C7×#95—21no—
205C7×#95C2311yescharacteristic
206C7×#95C2311yescharacteristic
207#3564C2×C711yescharacteristic
208#3117C2×C711yescharacteristic, complemented
209#3104C2×C711yescharacteristic, complemented
210#2604C2×C711yescharacteristic, complemented
211#1618C2×C711yescharacteristic
212#1617C2×C711yescharacteristic, complemented
213#1615C2×C711yescharacteristic, complemented
214#1614C2×C711yescharacteristic, complemented
215#1606C2×C711yescharacteristic
216#1605C2×C711yescharacteristic, complemented
217#1603C2×C711yescharacteristic, complemented
218#1602C2×C711yescharacteristic, complemented
219#1506C2×C711yescharacteristic, complemented
220#1500C2×C711yescharacteristic, complemented
221#1473C2×C711yescharacteristic, complemented
222C24×C7C2×D411yescharacteristic
223C2×C7×Q8—21no—
224C2×C7×Q8—21no—
225C2×C7×Q8—21no—
226C2×C7×Q8—21no—
227C2×C7×Q8—21no—
228C2×C7×Q8—42no—
229C2×C7×Q8C2×D411yescharacteristic
230C2×C7×Q8C2×D411yescharacteristic
231C2×C7×Q8C2×D411yescharacteristic
232C2×C7×D4—21no—
233C2×C7×D4—21no—
234C2×C7×D4—21no—
235C2×C7×D4C2×D411yescharacteristic
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C7×Q16—42no—
252C7×Q16—42no—
253C7×Q16—42no—
254C7×SD16—42no—
255C2×C7×C8—21no—
256C2×C7×C8—21no—
257C2×C7×C8—21no—
258C2×C7×C8—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4—21no—
276C7×C4⋊C4—21no—
277C7×C4⋊C4—21no—
278C7×C4⋊C4—21no—
279C7×C4⋊C4—21no—
280C7×C4⋊C4—21no—
281C7×C4⋊C4—21no—
282C7×C4⋊C4—21no—
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—42no—
291C7×C4⋊C4—42no—
292C7×C4⋊C4—41no—
293C7×C4⋊C4—41no—
294C7×C4⋊C4C2×D411yescharacteristic
295C7×C4⋊C4C2×D411yescharacteristic
296C7×C4⋊C4C2×D411yescharacteristic
297C7×C4⋊C4C2×D411yescharacteristic
298C7×C22⋊C4—21no—
299C7×C22⋊C4—21no—
300C7×C22⋊C4—21no—
301C7×C22⋊C4—21no—
302C7×C22⋊C4—21no—
303C7×C22⋊C4—21no—
304C7×C22⋊C4—21no—
305C7×C22⋊C4—21no—
306C7×C22⋊C4—21no—
307C7×C22⋊C4—21no—
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—42no—
320C7×C22⋊C4—42no—
321C42×C7—21no—
322C42×C7—21no—
323C42×C7—21no—
324C42×C7—21no—
325C42×C7—21no—
326C42×C7—21no—
327C42×C7—21no—
328C42×C7—42no—
329C42×C7—41no—
330C42×C7—41no—
331C42×C7C2×D411yescharacteristic
332C42×C7C2×D411yescharacteristic
333C42×C7C2×D411yescharacteristic
334C42×C7C2×D411yescharacteristic
335#563—21no—
336#563—21no—
337#556—21no—
338#554—21no—
339#552—21no—
340#552—21no—
341#551—21no—
342#551—21no—
343#544C22×C711yescharacteristic
344#543C22×C711yescharacteristic
345#542—21no—
346#541—21no—
347#541—21no—
348#539—21no—
349#539C22×C711yescharacteristic
350#538C22×C711yescharacteristic
351#533C22×C711yescharacteristic
352#529C22×C711yescharacteristic
353C2×#126C22×C711yescharacteristic
354C2×C4×Q8C22×C711yescharacteristic
355#484C22×C711yescharacteristic
356#484C22×C711yescharacteristic
357#484C22×C711yescharacteristic
358#481C22×C711yescharacteristic
359#479—21no—
360#477—21no—
361#464—21no—
362#462—21no—
363#451C22×C711yescharacteristic
364#451C22×C711yescharacteristic
365#451C22×C711yescharacteristic
366#448C22×C711yescharacteristic
367#441—21no—
368#440—21no—
369C4×Q16—21no—
370C4×Q16—21no—
371#432C22×C711yescharacteristic
372#431C22×C711yescharacteristic
373#400C22×C711yescharacteristic
374#399C22×C711yescharacteristic
375#395C22×C711yescharacteristic
376#393C22×C711yescharacteristic
377#389—21no—
378#388—21no—
379#388—21no—
380#387—21no—
381#376C22×C711yescharacteristic
382#328C22×C711yescharacteristic
383#328C22×C711yescharacteristic
384#328C22×C711yescharacteristic
385#328C22×C711yescharacteristic
386#328C22×C711yescharacteristic
387#328C22×C711yescharacteristic
388#327C22×C711yescharacteristic
389#327C22×C711yescharacteristic
390#324C22×C711yescharacteristic
391#324C22×C711yescharacteristic
392#323C22×C711yescharacteristic
393#323C22×C711yescharacteristic
394C23×C7—21no—
395C23×C7—21no—
396C23×C7—21no—
397C23×C7—21no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7C22×D411yescharacteristic
401C7×Q8—22no—
402C7×Q8—22no—
403C7×Q8—41no—
404C7×Q8—41no—
405C7×Q8—41no—
406C7×Q8—41no—
407C7×Q8—41no—
408C7×Q8—81no—
409C7×Q8—81no—
410C7×Q8—81no—
411C7×D4—41no—
412C7×D4—41no—
413C7×D4—41no—
414C7×D4—81no—
415C7×D4—81no—
416C2×C4×C7—21no—
417C2×C4×C7—21no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—21no—
421C2×C4×C7—21no—
422C2×C4×C7—21no—
423C2×C4×C7—21no—
424C2×C4×C7—21no—
425C2×C4×C7—21no—
426C2×C4×C7—21no—
427C2×C4×C7—21no—
428C2×C4×C7—21no—
429C2×C4×C7—21no—
430C2×C4×C7—21no—
431C2×C4×C7—21no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—81no—
447C2×C4×C7—81no—
448C2×C4×C7—81no—
449C2×C4×C7—81no—
450C2×C4×C7—81no—
451C2×C4×C7#12011yescharacteristic
452C2×C4×C7#12011yescharacteristic
453C2×C4×C7#12011yescharacteristic
454C2×C4×C7#12011yescharacteristic
455C2×C4×C7C22×D411yescharacteristic
456C2×C4×C7C22×D411yescharacteristic
457C7×C8—41no—
458C7×C8—41no—
459C7×C8—41no—
460C7×C8—41no—
461C22×Q8C23×C711yescharacteristic
462C2×Q16—21no—
463C2×Q16—21no—
464C2×Q16—21no—
465C2×SD16—21no—
466C4⋊Q8—21no—
467C4⋊Q8—21no—
468C4⋊Q8—21no—
469C4⋊Q8C7×D411yescharacteristic
470C4⋊Q8C7×D411yescharacteristic
471#126—21no—
472#126—21no—
473#126—21no—
474#126—21no—
475#126—21no—
476#126—21no—
477#126—21no—
478#126—21no—
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#126—21no—
484#125—21no—
485#125—21no—
486#125—21no—
487#125—21no—
488#125—21no—
489#125—21no—
490#125—21no—
491#125—21no—
492#125—21no—
493#125C7×D411yescharacteristic
494#124—21no—
495#124—21no—
496#124—21no—
497#124C7×D411yescharacteristic
498#123—21no—
499#123—21no—
500#123—21no—
501#123—21no—
502#123—21no—
503#123—21no—
504#123—21no—
505#123—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8C23×C711yescharacteristic
521C22⋊Q8C23×C711yescharacteristic
522C22⋊Q8C23×C711yescharacteristic
523#121—21no—
524#121C23×C711yescharacteristic
525#120—21no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8—21no—
529C4×Q8—21no—
530C4×Q8—21no—
531C4×Q8—21no—
532C4×Q8—21no—
533C4×Q8C7×D411yescharacteristic
534C4×Q8C7×D411yescharacteristic
535C4×Q8C7×D411yescharacteristic
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4C7×D411yescharacteristic
542#117—21no—
543#117—21no—
544#117—21no—
545#117—21no—
546#117—21no—
547#117—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C7×D411yescharacteristic
553C2×C4⋊C4C7×D411yescharacteristic
554C2×C4⋊C4C23×C711yescharacteristic
555C2×C4⋊C4C23×C711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4C7×D411yescharacteristic
560C2×C22⋊C4C7×D411yescharacteristic
561C2×C22⋊C4C23×C711yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C711yescharacteristic
565#107—21no—
566#107—21no—
567#107—21no—
568#106—21no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#103—21no—
572#103—21no—
573#103—21no—
574#103—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579C22⋊C8C23×C711yescharacteristic
580C22⋊C8C23×C711yescharacteristic
581C22⋊C8C23×C711yescharacteristic
582C22⋊C8C23×C711yescharacteristic
583#97—21no—
584C4×C8—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95C23×C711yescharacteristic
591#95C23×C711yescharacteristic
592C22×C7—21no—
593C22×C7—21no—
594C22×C7—41no—
595C22×C7—41no—
596C22×C7—41no—
597C22×C7—41no—
598C22×C7—41no—
599C22×C7—41no—
600C22×C7—81no—
601C22×C7—81no—
602C22×C7C2×#12011yescharacteristic
603C22×C7#57811yescharacteristic
604C22×C7#57811yescharacteristic
605C4×C7—21no—
606C4×C7—21no—
607C4×C7—21no—
608C4×C7—21no—
609C4×C7—21no—
610C4×C7—21no—
611C4×C7—42no—
612C4×C7—41no—
613C4×C7—41no—
614C4×C7—41no—
615C4×C7—41no—
616C4×C7—41no—
617C4×C7—41no—
618C4×C7—42no—
619C4×C7—41no—
620C4×C7—41no—
621C4×C7—41no—
622C4×C7—41no—
623C4×C7—81no—
624C4×C7—81no—
625C24C2×C7×D411yescharacteristic
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—42no—
632C2×Q8C2×C7×D411yescharacteristic
633C2×Q8C2×C7×D411yescharacteristic
634C2×Q8C2×C7×D411yescharacteristic
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4C2×C7×D411yescharacteristic
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4C2×C7×D411yescharacteristic
649C22×C4C2×C7×D411yescharacteristic
650C22×C4C2×C7×D411yescharacteristic
651C22×C4C2×C7×D411yescharacteristic
652C22×C4C2×C7×D411yescharacteristic
653C22×C4C24×C711yescharacteristic
654Q16—42no—
655Q16—42no—
656Q16—42no—
657SD16—42no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4C2×C7×D411yescharacteristic
698C4⋊C4C2×C7×D411yescharacteristic
699C4⋊C4C2×C7×D411yescharacteristic
700C4⋊C4C2×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—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42—41no—
733C42—41no—
734C42C2×C7×D411yescharacteristic
735C42C2×C7×D411yescharacteristic
736C42C2×C7×D411yescharacteristic
737C42C2×C7×D411yescharacteristic
738C2×C7—21no—
739C2×C7—21no—
740C2×C7—81no—
741C2×C7—81no—
742C2×C7#301111yescharacteristic
743C2×C7#301811yescharacteristic
744C2×C7#302511yescharacteristic
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—41no—
750C23—41no—
751C23C22×C7×D411yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—81no—
760Q8—81no—
761Q8—81no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—81no—
766D4—81no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4C7×#12011yescharacteristic
803C2×C4C7×#12011yescharacteristic
804C2×C4C7×#12011yescharacteristic
805C2×C4C7×#12011yescharacteristic
806C2×C4C22×C7×D411yescharacteristic
807C2×C4C22×C7×D411yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C7#1828311yescharacteristic, direct product factor, Sylow
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—81no—
822C22—81no—
823C22C2×C7×#12011yescharacteristic
824C22C7×#57811yescharacteristic
825C22C7×#57811yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C4—81no—
846C2—21no—
847C2—21no—
848C2—81no—
849C2—81no—
850C2C7×#301111yescharacteristic
851C2C7×#301811yescharacteristic
852C2C7×#302511yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#538C22
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
2. C7×#3117C2semidirect
3. C7×#3104C2semidirect
4. C7×#2604C2semidirect
6. C7×#1617C2semidirect
7. C7×#1615C2semidirect
8. C7×#1614C2semidirect
10. C7×#1605C2semidirect
11. C7×#1603C2semidirect
12. C7×#1602C2semidirect
13. C7×#1506C2semidirect
14. C7×#1500C2semidirect
15. C7×#1473C2semidirect
75. #18283C7direct (N × H)
208. #3117C2×C7semidirect
209. #3104C2×C7semidirect
210. #2604C2×C7semidirect
212. #1617C2×C7semidirect
213. #1615C2×C7semidirect
214. #1614C2×C7semidirect
216. #1605C2×C7semidirect
217. #1603C2×C7semidirect
218. #1602C2×C7semidirect
219. #1506C2×C7semidirect
220. #1500C2×C7semidirect
221. #1473C2×C7semidirect
812. C7#18283direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35642
C7×#31172
C7×#31042
C7×#26042
C7×#16182
C7×#16172
C7×#16152
C7×#16142
C7×#16062
C7×#16052
C7×#16032
C7×#16022
C7×#15062
C7×#15002
C7×#14732
#182837