Finite Group Databasebeta

← C7×#18449 #13195665

Subgroups — C7×#18449 #13195665

Order 1792.

918 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3535C211yesmaximal, characteristic
2C7×#3195C211yesmaximal, characteristic, complemented
3C7×#3190C211yesmaximal, characteristic, complemented
4C7×#2814C211yesmaximal, characteristic, complemented
5C7×#1612C211yesmaximal, characteristic, complemented
6C7×#1611C211yesmaximal, characteristic, complemented
7C7×#1609C211yesmaximal, characteristic, complemented
8C7×#1608C211yesmaximal, characteristic, complemented
9C7×#1606C211yesmaximal, characteristic, complemented
10C7×#1605C211yesmaximal, characteristic, complemented
11C7×#1603C211yesmaximal, characteristic, complemented
12C7×#1602C211yesmaximal, 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×C22⋊Q8C2211yescharacteristic
36C7×#485—21no—
37C7×#483—21no—
38C7×#483C2211yescharacteristic
39C7×#483C2211yescharacteristic
40C7×#483C2211yescharacteristic
41C7×#480C2211yescharacteristic
42C7×#470—21no—
43C7×#470—21no—
44C7×#467—21no—
45C7×#465—21no—
46C7×#452—21no—
47C7×#451—21no—
48C7×#451C2211yescharacteristic
49C7×#451C2211yescharacteristic
50C7×#451C2211yescharacteristic
51C7×#448C2211yescharacteristic
52C7×#407C2211yescharacteristic
53C2×C7×C22⋊C8C2211yescharacteristic
54C7×#398—21no—
55C7×#398C2211yescharacteristic
56C7×#397—21no—
57C7×#397C2211yescharacteristic
58C7×#396—21no—
59C7×#395C2211yescharacteristic
60C7×#394—21no—
61C7×#393C2211yescharacteristic
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#18449C711yesmaximal, characteristic, direct product factor, Sylow
76C2×C7×#41—21no—
77C2×C7×#41D411yescharacteristic
78C22×C7×Q8D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4D411yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C2×C7×Q16—21no—
83C2×C7×Q16—21no—
84C2×C7×Q16—21no—
85C2×C7×SD16—21no—
86C2×C7×M16—21no—
87C22×C7×C8—21no—
88C7×C4⋊Q8—21no—
89C7×C4⋊Q8—21no—
90C7×C4⋊Q8—21no—
91C7×#126—21no—
92C7×#126—21no—
93C7×#126—21no—
94C7×#126—21no—
95C7×#126—21no—
96C7×#126—21no—
97C7×#125—21no—
98C7×#125—21no—
99C7×#125—21no—
100C7×#125—21no—
101C7×#125—21no—
102C7×#124—21no—
103C7×#124—21no—
104C7×#124—21no—
105C7×#124—21no—
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×#123—21no—
119C7×#123—21no—
120C7×C22⋊Q8—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⋊Q8—21no—
136C7×C22⋊Q8—21no—
137C7×C22⋊Q8—21no—
138C7×C22⋊Q8D411yescharacteristic
139C7×C22⋊Q8D411yescharacteristic
140C7×C22⋊Q8D411yescharacteristic
141C7×C22⋊Q8C2311yescharacteristic
142C7×C22⋊Q8C2311yescharacteristic
143C7×C22⋊Q8C2311yescharacteristic
144C7×#121—21no—
145C7×#121—21no—
146C7×#121—21no—
147C7×#121—21no—
148C7×#121D411yescharacteristic
149C7×#121C2311yescharacteristic
150C7×#120—21no—
151C7×#120—21no—
152C4×C7×Q8—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×D4—21no—
160C7×#117—21no—
161C7×#117—21no—
162C7×#117—21no—
163C7×#117D411yescharacteristic
164C2×C7×C4⋊C4—21no—
165C2×C7×C4⋊C4—21no—
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
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⋊C4D411yescharacteristic
181C2×C7×C22⋊C4D411yescharacteristic
182C2×C7×C22⋊C4C2311yescharacteristic
183C7×#107—21no—
184C7×#106—21no—
185C7×#106—21no—
186C7×#106—21no—
187C7×#103—21no—
188C7×#103—21no—
189C7×#103—21no—
190C7×#103—21no—
191C7×#103—21no—
192C7×#103—21no—
193C7×#103—21no—
194C7×#102—21no—
195C7×C22⋊C8—21no—
196C7×C22⋊C8—21no—
197C7×C22⋊C8C2311yescharacteristic
198C7×C22⋊C8C2311yescharacteristic
199C7×C22⋊C8C2311yescharacteristic
200C7×C22⋊C8C2311yescharacteristic
201C7×#95—21no—
202C7×#95—21no—
203C7×#95—21no—
204C7×#95—21no—
205C7×#95C2311yescharacteristic
206C7×#95C2311yescharacteristic
207#3535C2×C711yescharacteristic
208#3195C2×C711yescharacteristic, complemented
209#3190C2×C711yescharacteristic, complemented
210#2814C2×C711yescharacteristic, complemented
211#1612C2×C711yescharacteristic, complemented
212#1611C2×C711yescharacteristic, complemented
213#1609C2×C711yescharacteristic, complemented
214#1608C2×C711yescharacteristic, complemented
215#1606C2×C711yescharacteristic, complemented
216#1605C2×C711yescharacteristic, complemented
217#1603C2×C711yescharacteristic, complemented
218#1602C2×C711yescharacteristic, complemented
219#1520C2×C711yescharacteristic, complemented
220#1513C2×C711yescharacteristic, complemented
221#1468C2×C711yescharacteristic, complemented
222C24×C7C2×D411yescharacteristic
223C24×C7C2×D411yescharacteristic
224C7×#41—82no—
225C7×#41—81no—
226C2×C7×Q8—21no—
227C2×C7×Q8—21no—
228C2×C7×Q8—21no—
229C2×C7×Q8—21no—
230C2×C7×Q8—21no—
231C2×C7×Q8—81no—
232C2×C7×Q8—81no—
233C2×C7×Q8C2×D411yescharacteristic
234C2×C7×Q8C2×D411yescharacteristic
235C2×C7×Q8C2×D411yescharacteristic
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—81no—
244C2×C7×D4C2×D411yescharacteristic
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—81no—
257C22×C4×C7C2×D411yescharacteristic
258C22×C4×C7C2×D411yescharacteristic
259C22×C4×C7C2×D411yescharacteristic
260C22×C4×C7C2×D411yescharacteristic
261C22×C4×C7C2×D411yescharacteristic
262C22×C4×C7C2×D411yescharacteristic
263C22×C4×C7C2×D411yescharacteristic
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2411yescharacteristic
266C7×Q16—81no—
267C7×Q16—81no—
268C7×Q16—81no—
269C7×SD16—81no—
270C7×M16—81no—
271C2×C7×C8—21no—
272C2×C7×C8—21no—
273C2×C7×C8—21no—
274C2×C7×C8—21no—
275C2×C7×C8—81no—
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—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—41no—
302C7×C4⋊C4—41no—
303C7×C4⋊C4—81no—
304C7×C4⋊C4—81no—
305C7×C4⋊C4—81no—
306C7×C4⋊C4C2×D411yescharacteristic
307C7×C4⋊C4C2×D411yescharacteristic
308C7×C4⋊C4C2×D411yescharacteristic
309C7×C4⋊C4C2×D411yescharacteristic
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—41no—
334C7×C22⋊C4—41no—
335C7×C22⋊C4—81no—
336C7×C22⋊C4—81no—
337C7×C22⋊C4—81no—
338C42×C7—21no—
339C42×C7—21no—
340C42×C7—21no—
341C42×C7—21no—
342C42×C7—21no—
343#563—21no—
344#562—21no—
345#554—21no—
346#552—21no—
347#551—21no—
348#551—21no—
349#547—21no—
350#546—21no—
351#544C22×C711yescharacteristic
352#543C22×C711yescharacteristic
353#542—21no—
354#539—21no—
355#539—21no—
356#539C22×C711yescharacteristic
357#538C22×C711yescharacteristic
358#536—21no—
359#525C22×C711yescharacteristic
360C2×#123C22×C711yescharacteristic
361C2×C22⋊Q8C22×C711yescharacteristic
362C2×C22⋊Q8C22×C711yescharacteristic
363#485—21no—
364#483—21no—
365#483C22×C711yescharacteristic
366#483C22×C711yescharacteristic
367#483C22×C711yescharacteristic
368#480C22×C711yescharacteristic
369#470—21no—
370#470—21no—
371#467—21no—
372#465—21no—
373#452—21no—
374#451—21no—
375#451C22×C711yescharacteristic
376#451C22×C711yescharacteristic
377#451C22×C711yescharacteristic
378#448C22×C711yescharacteristic
379#407C22×C711yescharacteristic
380C2×C22⋊C8C22×C711yescharacteristic
381#398—21no—
382#398C22×C711yescharacteristic
383#397—21no—
384#397C22×C711yescharacteristic
385#396—21no—
386#395C22×C711yescharacteristic
387#394—21no—
388#393C22×C711yescharacteristic
389#380C22×C711yescharacteristic
390#328C22×C711yescharacteristic
391#328C22×C711yescharacteristic
392#328C22×C711yescharacteristic
393#328C22×C711yescharacteristic
394#328C22×C711yescharacteristic
395#328C22×C711yescharacteristic
396#327C22×C711yescharacteristic
397#327C22×C711yescharacteristic
398#324C22×C711yescharacteristic
399#324C22×C711yescharacteristic
400#323C22×C711yescharacteristic
401#323C22×C711yescharacteristic
402C23×C7—21no—
403C23×C7—21no—
404C23×C7—21no—
405C23×C7—21no—
406C23×C7—21no—
407C23×C7—21no—
408C23×C7—41no—
409C23×C7—41no—
410C23×C7—41no—
411C23×C7—41no—
412C23×C7#12011yescharacteristic
413C23×C7#12011yescharacteristic
414C23×C7C22×D411yescharacteristic
415C7×Q8—41no—
416C7×Q8—41no—
417C7×Q8—41no—
418C7×Q8—41no—
419C7×Q8—41no—
420C7×Q8—41no—
421C7×Q8—41no—
422C7×Q8—81no—
423C7×Q8—81no—
424C7×Q8—81no—
425C7×D4—41no—
426C7×D4—42no—
427C7×D4—42no—
428C7×D4—41no—
429C7×D4—41no—
430C7×D4—81no—
431C7×D4—81no—
432C7×D4—81no—
433C7×D4—81no—
434C2×C4×C7—21no—
435C2×C4×C7—21no—
436C2×C4×C7—21no—
437C2×C4×C7—21no—
438C2×C4×C7—21no—
439C2×C4×C7—21no—
440C2×C4×C7—21no—
441C2×C4×C7—21no—
442C2×C4×C7—21no—
443C2×C4×C7—21no—
444C2×C4×C7—21no—
445C2×C4×C7—21no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—42no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—81no—
468C2×C4×C7—81no—
469C2×C4×C7—81no—
470C2×C4×C7—81no—
471C2×C4×C7—81no—
472C2×C4×C7—81no—
473C2×C4×C7#12011yescharacteristic
474C2×C4×C7#12011yescharacteristic
475C2×C4×C7C22×D411yescharacteristic
476C2×C4×C7C22×D411yescharacteristic
477C7×C8—41no—
478C7×C8—41no—
479C7×C8—41no—
480C7×C8—41no—
481C2×#41—21no—
482C2×#41C7×D411yescharacteristic
483C22×Q8C7×D411yescharacteristic
484C22×Q8C23×C711yescharacteristic
485C22×D4C7×D411yescharacteristic
486C23×C4C23×C711yescharacteristic
487C2×Q16—21no—
488C2×Q16—21no—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×M16—21no—
492C22×C8—21no—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#125—21no—
507#124—21no—
508#124—21no—
509#124—21no—
510#124—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8C7×D411yescharacteristic
544C22⋊Q8C7×D411yescharacteristic
545C22⋊Q8C7×D411yescharacteristic
546C22⋊Q8C23×C711yescharacteristic
547C22⋊Q8C23×C711yescharacteristic
548C22⋊Q8C23×C711yescharacteristic
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121C7×D411yescharacteristic
554#121C23×C711yescharacteristic
555#120—21no—
556#120—21no—
557C4×Q8—21no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117—21no—
566#117—21no—
567#117—21no—
568#117C7×D411yescharacteristic
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4C7×D411yescharacteristic
576C2×C4⋊C4C7×D411yescharacteristic
577C2×C4⋊C4C23×C711yescharacteristic
578C2×C4⋊C4C23×C711yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4C7×D411yescharacteristic
586C2×C22⋊C4C7×D411yescharacteristic
587C2×C22⋊C4C23×C711yescharacteristic
588#107—21no—
589#106—21no—
590#106—21no—
591#106—21no—
592#103—21no—
593#103—21no—
594#103—21no—
595#103—21no—
596#103—21no—
597#103—21no—
598#103—21no—
599#102—21no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602C22⋊C8C23×C711yescharacteristic
603C22⋊C8C23×C711yescharacteristic
604C22⋊C8C23×C711yescharacteristic
605C22⋊C8C23×C711yescharacteristic
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95C23×C711yescharacteristic
611#95C23×C711yescharacteristic
612C22×C7—21no—
613C22×C7—21no—
614C22×C7—21no—
615C22×C7—21no—
616C22×C7—21no—
617C22×C7—21no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—41no—
621C22×C7—41no—
622C22×C7—41no—
623C22×C7—41no—
624C22×C7—41no—
625C22×C7—41no—
626C22×C7—81no—
627C22×C7—81no—
628C22×C7—81no—
629C22×C7—81no—
630C22×C7C2×#12011yescharacteristic
631C22×C7#57711yescharacteristic
632C22×C7#57811yescharacteristic
633C4×C7—21no—
634C4×C7—21no—
635C4×C7—21no—
636C4×C7—21no—
637C4×C7—41no—
638C4×C7—41no—
639C4×C7—41no—
640C4×C7—41no—
641C4×C7—41no—
642C4×C7—41no—
643C4×C7—41no—
644C4×C7—41no—
645C4×C7—41no—
646C4×C7—41no—
647C4×C7—81no—
648C4×C7—81no—
649C4×C7—81no—
650C4×C7—81no—
651C24C2×C7×D411yescharacteristic
652C24C2×C7×D411yescharacteristic
653#41—82no—
654#41—81no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8—81no—
662C2×Q8C2×C7×D411yescharacteristic
663C2×Q8C2×C7×D411yescharacteristic
664C2×Q8C2×C7×D411yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—81no—
673C2×D4C2×C7×D411yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—81no—
686C22×C4C2×C7×D411yescharacteristic
687C22×C4C2×C7×D411yescharacteristic
688C22×C4C2×C7×D411yescharacteristic
689C22×C4C2×C7×D411yescharacteristic
690C22×C4C2×C7×D411yescharacteristic
691C22×C4C2×C7×D411yescharacteristic
692C22×C4C2×C7×D411yescharacteristic
693C22×C4C2×C7×D411yescharacteristic
694C22×C4C24×C711yescharacteristic
695Q16—81no—
696Q16—81no—
697Q16—81no—
698SD16—81no—
699M16—81no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—81no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—41no—
731C4⋊C4—41no—
732C4⋊C4—81no—
733C4⋊C4—81no—
734C4⋊C4—81no—
735C4⋊C4C2×C7×D411yescharacteristic
736C4⋊C4C2×C7×D411yescharacteristic
737C4⋊C4C2×C7×D411yescharacteristic
738C4⋊C4C2×C7×D411yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
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—41no—
763C22⋊C4—41no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42—21no—
771C42—21no—
772C2×C7—21no—
773C2×C7—21no—
774C2×C7—41no—
775C2×C7—41no—
776C2×C7—81no—
777C2×C7—81no—
778C2×C7#301311yescharacteristic
779C2×C7#302211yescharacteristic
780C2×C7#302611yescharacteristic
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23C7×#12011yescharacteristic
792C23C7×#12011yescharacteristic
793C23C22×C7×D411yescharacteristic
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—81no—
802Q8—81no—
803Q8—81no—
804D4—41no—
805D4—42no—
806D4—42no—
807D4—41no—
808D4—41no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4C7×#12011yescharacteristic
853C2×C4C7×#12011yescharacteristic
854C2×C4C22×C7×D411yescharacteristic
855C2×C4C22×C7×D411yescharacteristic
856C8—41no—
857C8—41no—
858C8—41no—
859C8—41no—
860C7#1844911yescharacteristic, direct product factor, Sylow
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×C7×#12011yescharacteristic
880C22C7×#57711yescharacteristic
881C22C7×#57811yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C2—21no—
901C2—21no—
902C2—41no—
903C2—41no—
904C2—81no—
905C2—81no—
906C2C7×#301311yescharacteristic
907C2C7×#302211yescharacteristic
908C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3535C2
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
2. C7×#3195C2semidirect
3. C7×#3190C2semidirect
4. C7×#2814C2semidirect
5. C7×#1612C2semidirect
6. C7×#1611C2semidirect
7. C7×#1609C2semidirect
8. C7×#1608C2semidirect
9. C7×#1606C2semidirect
10. C7×#1605C2semidirect
11. C7×#1603C2semidirect
12. C7×#1602C2semidirect
13. C7×#1520C2semidirect
14. C7×#1513C2semidirect
15. C7×#1468C2semidirect
75. #18449C7direct (N × H)
208. #3195C2×C7semidirect
209. #3190C2×C7semidirect
210. #2814C2×C7semidirect
211. #1612C2×C7semidirect
212. #1611C2×C7semidirect
213. #1609C2×C7semidirect
214. #1608C2×C7semidirect
215. #1606C2×C7semidirect
216. #1605C2×C7semidirect
217. #1603C2×C7semidirect
218. #1602C2×C7semidirect
219. #1520C2×C7semidirect
220. #1513C2×C7semidirect
221. #1468C2×C7semidirect
860. C7#18449direct (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×#31952
C7×#31902
C7×#28142
C7×#16122
C7×#16112
C7×#16092
C7×#16082
C7×#16062
C7×#16052
C7×#16032
C7×#16022
C7×#15202
C7×#15132
C7×#14682
#184497