Finite Group Databasebeta

← C7×#18447 #13195663

Subgroups — C7×#18447 #13195663

Order 1792.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3534C211yesmaximal, characteristic
2C7×#3193C211yesmaximal, characteristic, complemented
3C7×#3190C211yesmaximal, characteristic, complemented
4C7×#2814C211yesmaximal, characteristic, complemented
5C7×#1612C211yesmaximal, characteristic, complemented
6C7×#1610C211yesmaximal, characteristic, complemented
7C7×#1609C211yesmaximal, characteristic, complemented
8C7×#1607C211yesmaximal, characteristic, complemented
9C7×#1606C211yesmaximal, characteristic, complemented
10C7×#1604C211yesmaximal, characteristic, complemented
11C7×#1603C211yesmaximal, characteristic, complemented
12C7×#1601C211yesmaximal, characteristic, complemented
13C7×#1519C211yesmaximal, characteristic, complemented
14C7×#1513C211yesmaximal, characteristic, complemented
15C7×#1468C211yesmaximal, characteristic, complemented
16C7×#562—21no—
17C7×#560—21no—
18C7×#553—21no—
19C7×#551—21no—
20C7×#546—21no—
21C7×#546—21no—
22C7×#546—21no—
23C7×D42—21no—
24C7×#540—21no—
25C7×#539—21no—
26C7×#539C2211yescharacteristic
27C7×#538—21no—
28C7×#538C2211yescharacteristic
29C7×#537C2211yescharacteristic
30C7×#534—21no—
31C7×#534C2211yescharacteristic
32C7×#525C2211yescharacteristic
33C2×C7×#123C2211yescharacteristic
34C2×C7×C22⋊Q8C2211yescharacteristic, complemented
35C2×C7×#121C2211yescharacteristic
36C7×#485—21no—
37C7×#484—21no—
38C7×#483C2211yescharacteristic, complemented
39C7×#480C2211yescharacteristic
40C7×#480C2211yescharacteristic, complemented
41C7×#480C2211yescharacteristic, complemented
42C7×#468—21no—
43C7×#468—21no—
44C7×#467—21no—
45C7×#465—21no—
46C7×#452—21no—
47C7×#451C2211yescharacteristic, complemented
48C7×#450—21no—
49C7×#448C2211yescharacteristic
50C7×#448C2211yescharacteristic, complemented
51C7×#448C2211yescharacteristic, complemented
52C7×#407C2211yescharacteristic, complemented
53C2×C7×C22⋊C8C2211yescharacteristic, complemented
54C7×#398—21no—
55C7×#398C2211yescharacteristic, complemented
56C7×#397—21no—
57C7×#397C2211yescharacteristic, complemented
58C7×#396—21no—
59C7×#395C2211yescharacteristic, complemented
60C7×#394—21no—
61C7×#393C2211yescharacteristic, complemented
62C7×#380C2211yescharacteristic, complemented
63C7×#328C2211yescharacteristic, complemented
64C7×#328C2211yescharacteristic, complemented
65C7×#327C2211yescharacteristic
66C7×#327C2211yescharacteristic
67C7×#327C2211yescharacteristic, complemented
68C7×#327C2211yescharacteristic, complemented
69C7×#327C2211yescharacteristic, complemented
70C7×#327C2211yescharacteristic, complemented
71C7×#324C2211yescharacteristic, complemented
72C7×#324C2211yescharacteristic, complemented
73C7×#323C2211yescharacteristic, complemented
74C7×#323C2211yescharacteristic, complemented
75#18447C711yesmaximal, characteristic, direct product factor, Sylow
76C2×C7×#41—21no—
77C2×C7×#41D411yescharacteristic
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4D411yescharacteristic
83C22×C7×D4D411yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C2×C7×Q16—21no—
86C2×C7×SD16—21no—
87C2×C7×SD16—21no—
88C2×C7×SD16—21no—
89C2×C7×M16—21no—
90C22×C7×C8—21no—
91C7×#127—21no—
92C7×#126—21no—
93C7×#126—21no—
94C7×#126—21no—
95C7×#126—21no—
96C7×#125—21no—
97C7×#125—21no—
98C7×#124—21no—
99C7×#124—21no—
100C7×#124—21no—
101C7×#123—21no—
102C7×#123—21no—
103C7×#123—21no—
104C7×#123—21no—
105C7×#123—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×C22⋊Q8—21no—
116C7×C22⋊Q8—21no—
117C7×C22⋊Q8—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⋊Q8D411yescharacteristic
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×#121—21no—
139C7×#121—21no—
140C7×#121—21no—
141C7×#121D411yescharacteristic
142C7×#121D411yescharacteristic
143C7×#121D411yescharacteristic
144C7×#121C2311yescharacteristic
145C7×#121C2311yescharacteristic
146C7×#121C2311yescharacteristic
147C7×#120—21no—
148C7×#120—21no—
149C7×#120—21no—
150C7×#120—21no—
151C7×#120—21no—
152C7×#120—21no—
153C7×#120—21no—
154C7×#120—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—
162C4×C7×D4—21no—
163C7×#117—21no—
164C7×#117D411yescharacteristic
165C2×C7×C4⋊C4—21no—
166C2×C7×C4⋊C4—21no—
167C2×C7×C4⋊C4—21no—
168C2×C7×C4⋊C4—21no—
169C2×C7×C4⋊C4D411yescharacteristic
170C2×C7×C4⋊C4D411yescharacteristic
171C2×C7×C4⋊C4C2311yescharacteristic
172C2×C7×C4⋊C4C2311yescharacteristic
173C2×C7×C22⋊C4—21no—
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×#107—21no—
185C7×#107—21no—
186C7×#106—21no—
187C7×#103—21no—
188C7×#103—21no—
189C7×#103—21no—
190C7×#103—21no—
191C7×#103—21no—
192C7×#102—21no—
193C7×#102—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#3534C2×C711yescharacteristic
208#3193C2×C711yescharacteristic, complemented
209#3190C2×C711yescharacteristic, complemented
210#2814C2×C711yescharacteristic, complemented
211#1612C2×C711yescharacteristic, complemented
212#1610C2×C711yescharacteristic, complemented
213#1609C2×C711yescharacteristic, complemented
214#1607C2×C711yescharacteristic, complemented
215#1606C2×C711yescharacteristic, complemented
216#1604C2×C711yescharacteristic, complemented
217#1603C2×C711yescharacteristic, complemented
218#1601C2×C711yescharacteristic, complemented
219#1519C2×C711yescharacteristic, complemented
220#1513C2×C711yescharacteristic, complemented
221#1468C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7—21no—
224C24×C7C2×D411yescharacteristic
225C24×C7C2×D411yescharacteristic
226C7×#41—81no—
227C7×#41—81no—
228C7×#41—81no—
229C2×C7×Q8—21no—
230C2×C7×Q8—21no—
231C2×C7×Q8—21no—
232C2×C7×Q8—81no—
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—21no—
244C2×C7×D4—21no—
245C2×C7×D4—21no—
246C2×C7×D4—21no—
247C2×C7×D4—21no—
248C2×C7×D4—21no—
249C2×C7×D4—21no—
250C2×C7×D4—21no—
251C2×C7×D4—81no—
252C2×C7×D4—81no—
253C2×C7×D4—81no—
254C2×C7×D4—81no—
255C2×C7×D4—81no—
256C2×C7×D4—81no—
257C2×C7×D4—82no—
258C2×C7×D4C2×D411yescharacteristic
259C2×C7×D4C2×D411yescharacteristic
260C2×C7×D4C2×D411yescharacteristic
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—81no—
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2×D411yescharacteristic
275C22×C4×C7C2×D411yescharacteristic
276C22×C4×C7C2×D411yescharacteristic
277C22×C4×C7C2×D411yescharacteristic
278C22×C4×C7C2×D411yescharacteristic
279C22×C4×C7C2×D411yescharacteristic
280C22×C4×C7C2×D411yescharacteristic
281C22×C4×C7C2411yescharacteristic
282C7×Q16—81no—
283C7×SD16—81no—
284C7×SD16—81no—
285C7×SD16—81no—
286C7×M16—81no—
287C2×C7×C8—21no—
288C2×C7×C8—21no—
289C2×C7×C8—21no—
290C2×C7×C8—21no—
291C2×C7×C8—81no—
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—41no—
308C7×C4⋊C4—41no—
309C7×C4⋊C4—81no—
310C7×C4⋊C4—81no—
311C7×C4⋊C4—81no—
312C7×C4⋊C4C2×D411yescharacteristic
313C7×C4⋊C4C2×D411yescharacteristic
314C7×C4⋊C4C2×D411yescharacteristic
315C7×C4⋊C4C2×D411yescharacteristic
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—21no—
338C7×C22⋊C4—21no—
339C7×C22⋊C4—21no—
340C7×C22⋊C4—21no—
341C7×C22⋊C4—41no—
342C7×C22⋊C4—41no—
343C7×C22⋊C4—81no—
344C7×C22⋊C4—81no—
345C7×C22⋊C4—81no—
346C42×C7—21no—
347C42×C7—21no—
348C42×C7—21no—
349#562—21no—
350#560—21no—
351#553—21no—
352#551—21no—
353#546—21no—
354#546—21no—
355#546—21no—
356D42—21no—
357#540—21no—
358#539—21no—
359#539C22×C711yescharacteristic
360#538—21no—
361#538C22×C711yescharacteristic
362#537C22×C711yescharacteristic
363#534—21no—
364#534C22×C711yescharacteristic
365#525C22×C711yescharacteristic
366C2×#123C22×C711yescharacteristic
367C2×C22⋊Q8C22×C711yescharacteristic, complemented
368C2×#121C22×C711yescharacteristic
369#485—21no—
370#484—21no—
371#483C22×C711yescharacteristic, complemented
372#480C22×C711yescharacteristic
373#480C22×C711yescharacteristic, complemented
374#480C22×C711yescharacteristic, complemented
375#468—21no—
376#468—21no—
377#467—21no—
378#465—21no—
379#452—21no—
380#451C22×C711yescharacteristic, complemented
381#450—21no—
382#448C22×C711yescharacteristic
383#448C22×C711yescharacteristic, complemented
384#448C22×C711yescharacteristic, complemented
385#407C22×C711yescharacteristic, complemented
386C2×C22⋊C8C22×C711yescharacteristic, complemented
387#398—21no—
388#398C22×C711yescharacteristic, complemented
389#397—21no—
390#397C22×C711yescharacteristic, complemented
391#396—21no—
392#395C22×C711yescharacteristic, complemented
393#394—21no—
394#393C22×C711yescharacteristic, complemented
395#380C22×C711yescharacteristic, complemented
396#328C22×C711yescharacteristic, complemented
397#328C22×C711yescharacteristic, complemented
398#327C22×C711yescharacteristic
399#327C22×C711yescharacteristic
400#327C22×C711yescharacteristic, complemented
401#327C22×C711yescharacteristic, complemented
402#327C22×C711yescharacteristic, complemented
403#327C22×C711yescharacteristic, complemented
404#324C22×C711yescharacteristic, complemented
405#324C22×C711yescharacteristic, complemented
406#323C22×C711yescharacteristic, complemented
407#323C22×C711yescharacteristic, complemented
408C23×C7—21no—
409C23×C7—21no—
410C23×C7—21no—
411C23×C7—21no—
412C23×C7—21no—
413C23×C7—21no—
414C23×C7—21no—
415C23×C7—21no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—42no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—81no—
422C23×C7—81no—
423C23×C7—81no—
424C23×C7—81no—
425C23×C7—81no—
426C23×C7#12011yescharacteristic
427C23×C7#12011yescharacteristic
428C23×C7C22×D411yescharacteristic
429C7×Q8—41no—
430C7×Q8—41no—
431C7×Q8—41no—
432C7×Q8—41no—
433C7×Q8—41no—
434C7×Q8—81no—
435C7×D4—41no—
436C7×D4—41no—
437C7×D4—41no—
438C7×D4—42no—
439C7×D4—42no—
440C7×D4—41no—
441C7×D4—41no—
442C7×D4—41no—
443C7×D4—41no—
444C7×D4—41no—
445C7×D4—41no—
446C7×D4—81no—
447C7×D4—81no—
448C7×D4—81no—
449C7×D4—81no—
450C7×D4—81no—
451C7×D4—81no—
452C7×D4—81no—
453C7×D4—81no—
454C7×D4—81no—
455C7×D4—81no—
456C7×D4—81no—
457C7×D4—81no—
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—21no—
465C2×C4×C7—21no—
466C2×C4×C7—21no—
467C2×C4×C7—21no—
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—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—81no—
489C2×C4×C7—81no—
490C2×C4×C7—81no—
491C2×C4×C7—81no—
492C2×C4×C7—81no—
493C2×C4×C7—81no—
494C2×C4×C7—81no—
495C2×C4×C7#12011yescharacteristic
496C2×C4×C7#12011yescharacteristic
497C2×C4×C7C22×D411yescharacteristic
498C2×C4×C7C22×D411yescharacteristic
499C7×C8—41no—
500C7×C8—41no—
501C7×C8—41no—
502C7×C8—41no—
503C2×#41—21no—
504C2×#41C7×D411yescharacteristic
505C22×Q8C23×C711yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C7×D411yescharacteristic
510C22×D4C7×D411yescharacteristic
511C23×C4C23×C711yescharacteristic
512C2×Q16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×M16—21no—
517C22×C8—21no—
518#127—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#125—21no—
524#125—21no—
525#124—21no—
526#124—21no—
527#124—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—
540#123—21no—
541#123—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⋊Q8C7×D411yescharacteristic
552C22⋊Q8C23×C711yescharacteristic
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121—21no—
558#121—21no—
559#121—21no—
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
569#121C7×D411yescharacteristic
570#121C7×D411yescharacteristic
571#121C23×C711yescharacteristic
572#121C23×C711yescharacteristic
573#121C23×C711yescharacteristic
574#120—21no—
575#120—21no—
576#120—21no—
577#120—21no—
578#120—21no—
579#120—21no—
580#120—21no—
581#120—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590#117—21no—
591#117C7×D411yescharacteristic
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4C7×D411yescharacteristic
597C2×C4⋊C4C7×D411yescharacteristic
598C2×C4⋊C4C23×C711yescharacteristic
599C2×C4⋊C4C23×C711yescharacteristic
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4C7×D411yescharacteristic
608C2×C22⋊C4C7×D411yescharacteristic
609C2×C22⋊C4C23×C711yescharacteristic
610#107—21no—
611#107—21no—
612#107—21no—
613#106—21no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#102—21no—
620#102—21no—
621#102—21no—
622C22⋊C8—21no—
623C22⋊C8—21no—
624C22⋊C8C23×C711yescharacteristic
625C22⋊C8C23×C711yescharacteristic
626C22⋊C8C23×C711yescharacteristic
627C22⋊C8C23×C711yescharacteristic
628#95—21no—
629#95—21no—
630#95—21no—
631#95—21no—
632#95C23×C711yescharacteristic
633#95C23×C711yescharacteristic
634C22×C7—21no—
635C22×C7—21no—
636C22×C7—21no—
637C22×C7—21no—
638C22×C7—21no—
639C22×C7—21no—
640C22×C7—21no—
641C22×C7—21no—
642C22×C7—41no—
643C22×C7—41no—
644C22×C7—41no—
645C22×C7—41no—
646C22×C7—41no—
647C22×C7—41no—
648C22×C7—41no—
649C22×C7—41no—
650C22×C7—41no—
651C22×C7—41no—
652C22×C7—41no—
653C22×C7—41no—
654C22×C7—81no—
655C22×C7—81no—
656C22×C7—81no—
657C22×C7—81no—
658C22×C7—162no—
659C22×C7—162no—
660C22×C7C2×#12011yescharacteristic
661C22×C7#57611yescharacteristic
662C22×C7#57711yescharacteristic
663C4×C7—21no—
664C4×C7—21no—
665C4×C7—21no—
666C4×C7—21no—
667C4×C7—41no—
668C4×C7—41no—
669C4×C7—41no—
670C4×C7—41no—
671C4×C7—41no—
672C4×C7—41no—
673C4×C7—41no—
674C4×C7—41no—
675C4×C7—81no—
676C4×C7—81no—
677C4×C7—81no—
678C4×C7—81no—
679C24—21no—
680C24—21no—
681C24C2×C7×D411yescharacteristic
682C24C2×C7×D411yescharacteristic
683#41—81no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×C7×D411yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—82no—
715C2×D4C2×C7×D411yescharacteristic
716C2×D4C2×C7×D411yescharacteristic
717C2×D4C2×C7×D411yescharacteristic
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—81no—
730C22×C4C2×C7×D411yescharacteristic
731C22×C4C2×C7×D411yescharacteristic
732C22×C4C2×C7×D411yescharacteristic
733C22×C4C2×C7×D411yescharacteristic
734C22×C4C2×C7×D411yescharacteristic
735C22×C4C2×C7×D411yescharacteristic
736C22×C4C2×C7×D411yescharacteristic
737C22×C4C2×C7×D411yescharacteristic
738C22×C4C24×C711yescharacteristic
739Q16—81no—
740SD16—81no—
741SD16—81no—
742SD16—81no—
743M16—81no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—81no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—41no—
765C4⋊C4—41no—
766C4⋊C4—81no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×C7×D411yescharacteristic
770C4⋊C4C2×C7×D411yescharacteristic
771C4⋊C4C2×C7×D411yescharacteristic
772C4⋊C4C2×C7×D411yescharacteristic
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—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—41no—
799C22⋊C4—41no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C2×C7—21no—
807C2×C7—21no—
808C2×C7—41no—
809C2×C7—41no—
810C2×C7—81no—
811C2×C7—81no—
812C2×C7—81no—
813C2×C7—81no—
814C2×C7#301211yescharacteristic
815C2×C7#302211yescharacteristic
816C2×C7#302611yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—41no—
829C23—41no—
830C23—81no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C7×#12011yescharacteristic
836C23C7×#12011yescharacteristic
837C23C22×C7×D411yescharacteristic
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—81no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—42no—
848D4—42no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—81no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4C7×#12011yescharacteristic
905C2×C4C7×#12011yescharacteristic
906C2×C4C22×C7×D411yescharacteristic
907C2×C4C22×C7×D411yescharacteristic
908C8—41no—
909C8—41no—
910C8—41no—
911C8—41no—
912C7#1844711yescharacteristic, direct product factor, Sylow
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C7×#12011yescharacteristic
940C22C7×#57611yescharacteristic
941C22C7×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C7×#301211yescharacteristic
967C2C7×#302211yescharacteristic
968C2C7×#302611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3534C2
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×#3193C2semidirect
3. C7×#3190C2semidirect
4. C7×#2814C2semidirect
5. C7×#1612C2semidirect
6. C7×#1610C2semidirect
7. C7×#1609C2semidirect
8. C7×#1607C2semidirect
9. C7×#1606C2semidirect
10. C7×#1604C2semidirect
11. C7×#1603C2semidirect
12. C7×#1601C2semidirect
13. C7×#1519C2semidirect
14. C7×#1513C2semidirect
15. C7×#1468C2semidirect
34. C2×C7×C22⋊Q8C22semidirect
38. C7×#483C22semidirect
40. C7×#480C22semidirect
41. C7×#480C22semidirect
47. C7×#451C22semidirect
50. C7×#448C22semidirect
51. C7×#448C22semidirect
52. C7×#407C22semidirect
53. C2×C7×C22⋊C8C22semidirect
55. C7×#398C22semidirect
57. C7×#397C22semidirect
59. C7×#395C22semidirect
61. C7×#393C22semidirect
62. C7×#380C22semidirect
63. C7×#328C22semidirect
64. C7×#328C22semidirect
67. C7×#327C22semidirect
68. C7×#327C22semidirect
69. C7×#327C22semidirect
70. C7×#327C22semidirect
71. C7×#324C22semidirect
72. C7×#324C22semidirect
73. C7×#323C22semidirect
74. C7×#323C22semidirect
75. #18447C7direct (N × H)
208. #3193C2×C7semidirect
209. #3190C2×C7semidirect
210. #2814C2×C7semidirect
211. #1612C2×C7semidirect
212. #1610C2×C7semidirect
213. #1609C2×C7semidirect
214. #1607C2×C7semidirect
215. #1606C2×C7semidirect
216. #1604C2×C7semidirect
217. #1603C2×C7semidirect
218. #1601C2×C7semidirect
219. #1519C2×C7semidirect
220. #1513C2×C7semidirect
221. #1468C2×C7semidirect
367. C2×C22⋊Q8C22×C7semidirect
371. #483C22×C7semidirect
373. #480C22×C7semidirect
374. #480C22×C7semidirect
380. #451C22×C7semidirect
383. #448C22×C7semidirect
384. #448C22×C7semidirect
385. #407C22×C7semidirect
386. C2×C22⋊C8C22×C7semidirect
388. #398C22×C7semidirect
390. #397C22×C7semidirect
392. #395C22×C7semidirect
394. #393C22×C7semidirect
395. #380C22×C7semidirect
396. #328C22×C7semidirect
397. #328C22×C7semidirect
400. #327C22×C7semidirect
401. #327C22×C7semidirect
402. #327C22×C7semidirect
403. #327C22×C7semidirect
404. #324C22×C7semidirect
405. #324C22×C7semidirect
406. #323C22×C7semidirect
407. #323C22×C7semidirect
912. C7#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35342
C7×#31932
C7×#31902
C7×#28142
C7×#16122
C7×#16102
C7×#16092
C7×#16072
C7×#16062
C7×#16042
C7×#16032
C7×#16012
C7×#15192
C7×#15132
C7×#14682
#184477