Finite Group Databasebeta

← C7×#23572 #13200788

Subgroups — C7×#23572 #13200788

Order 1792.

1188 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#529C211yesmaximal, characteristic
2C2×C4×C7×Q16C211yesmaximal, characteristic, complemented
3C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
4C4×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
5C7×#2059C211yesmaximal, characteristic, complemented
6C7×#2042C211yesmaximal, characteristic, complemented
7C7×#2035C211yesmaximal, characteristic, complemented
8C7×#2033C211yesmaximal, characteristic
9C7×#2026C211yesmaximal, characteristic, complemented
10C7×#2015C211yesmaximal, characteristic, complemented
11C7×#2001C211yesmaximal, characteristic, complemented
12C7×#2000C211yesmaximal, characteristic
13C4×C7×#103C211yesmaximal, characteristic, complemented
14C4×C7×#102C211yesmaximal, characteristic, complemented
15C4×C7×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×C7×Q16C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C7×#529—24no—
19C7×#529—24no—
20C2×C7×#126—21no—
21C2×C7×#125C2211yescharacteristic
22C2×C7×#124C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C4×C7×D4—21no—
30C2×C4×C7×D4C2211yescharacteristic
31C2×C7×#117—21no—
32C22×C42×C7C2211yescharacteristic
33C4×C7×Q16—24no—
34C4×C7×SD16—24no—
35C2×C7×#107C2211yescharacteristic
36C2×C7×#106C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#103C2211yescharacteristic
41C2×C7×#103C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×#102C2211yescharacteristic
44C2×C7×#102C2211yescharacteristic
45C2×C7×C22⋊C8C2211yescharacteristic
46C2×C7×C22⋊C8C2211yescharacteristic
47C2×C4×C7×C8C2211yescharacteristic
48C2×C4×C7×C8C2211yescharacteristic
49C7×#391C2211yescharacteristic
50C7×#389C2211yescharacteristic
51C7×#387—21no—
52C7×#385—21no—
53C7×#380C2211yescharacteristic
54C4×C7×C4⋊C4—21no—
55C4×C7×C4⋊C4C2211yescharacteristic
56C4×C7×C22⋊C4—21no—
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#23572C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8C2311yescharacteristic
65C22×C7×Q8C2311yescharacteristic
66C22×C7×D4—21no—
67C22×C7×D4C2311yescharacteristic
68C23×C4×C7—21no—
69C23×C4×C7D411yescharacteristic
70C23×C4×C7D411yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C2×C7×Q16—22no—
73C2×C7×Q16—22no—
74C2×C7×Q16—22no—
75C2×C7×SD16—22no—
76C2×C7×SD16—22no—
77C2×C7×SD16—22no—
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C7×#126—28no—
83C7×#125—22no—
84C7×#125—22no—
85C7×#124—22no—
86C7×#124—22no—
87C7×#123—28no—
88C7×C22⋊Q8—22no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—22no—
92C7×#121—22no—
93C7×#121—22no—
94C4×C7×Q8—22no—
95C4×C7×Q8—22no—
96C4×C7×Q8—22no—
97C4×C7×Q8D414yes—
98C4×C7×D4—28no—
99C4×C7×D4—22no—
100C4×C7×D4D414yes—
101C7×#117—28no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C42×C7—21no—
122C2×C42×C7—22no—
123C2×C42×C7—22no—
124C2×C42×C7—21no—
125C2×C42×C7—21no—
126C2×C42×C7D411yescharacteristic
127C2×C42×C7D411yescharacteristic
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C7×#107—22no—
131C7×#106—22no—
132C7×#103—22no—
133C7×#103—22no—
134C7×#103—22no—
135C7×#103—22no—
136C7×#103—22no—
137C7×#102—22no—
138C7×#102—22no—
139C7×#102—22no—
140C7×C22⋊C8—22no—
141C7×C22⋊C8—22no—
142C4×C7×C8—22no—
143C4×C7×C8—22no—
144C7×#95—21no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C2×#529C2×C711yescharacteristic
150C2×C4×Q16C2×C711yescharacteristic, complemented
151C2×C4×SD16C2×C711yescharacteristic, complemented
152C4×C22⋊Q8C2×C711yescharacteristic, complemented
153#2059C2×C711yescharacteristic, complemented
154#2042C2×C711yescharacteristic, complemented
155#2035C2×C711yescharacteristic, complemented
156#2033C2×C711yescharacteristic
157#2026C2×C711yescharacteristic, complemented
158#2015C2×C711yescharacteristic, complemented
159#2001C2×C711yescharacteristic, complemented
160#2000C2×C711yescharacteristic
161C4×#103C2×C711yescharacteristic, complemented
162C4×#102C2×C711yescharacteristic, complemented
163C4×C22⋊C8C2×C711yescharacteristic, complemented
164C24×C7—21no—
165C24×C7C2×D411yescharacteristic
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8C2×D412yes—
177C2×C7×Q8#4112yes—
178C2×C7×D4—24no—
179C2×C7×D4—21no—
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—42no—
185C2×C7×D4—42no—
186C2×C7×D4C2×D412yes—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—24no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—41no—
207C22×C4×C7—42no—
208C22×C4×C7—42no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C7×Q16—28no—
216C7×SD16—28no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—21no—
225C2×C7×C8—21no—
226C2×C7×C8—21no—
227C2×C7×C8#4112yes—
228C2×C7×C8#4112yes—
229C7×C4⋊C4—24no—
230C7×C4⋊C4—24no—
231C7×C4⋊C4—24no—
232C7×C4⋊C4—24no—
233C7×C4⋊C4—24no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—42no—
242C7×C4⋊C4—42no—
243C7×C4⋊C4C2×D412yes—
244C7×C4⋊C4C2×D412yes—
245C7×C4⋊C4#4112yes—
246C7×C22⋊C4—24no—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—42no—
253C42×C7—22no—
254C42×C7—22no—
255C42×C7—24no—
256C42×C7—21no—
257C42×C7—21no—
258C42×C7—42no—
259C42×C7—42no—
260C42×C7C2×D412yes—
261C42×C7C2×D412yes—
262C22×Q16C22×C711yescharacteristic
263C22×SD16C22×C711yescharacteristic
264#529—24no—
265#529—24no—
266C2×#126—21no—
267C2×#125C22×C711yescharacteristic
268C2×#124C22×C711yescharacteristic
269C2×#123—21no—
270C2×C22⋊Q8C22×C711yescharacteristic
271C2×C22⋊Q8C22×C711yescharacteristic
272C2×#121C22×C711yescharacteristic
273C2×C4×Q8C22×C711yescharacteristic
274C2×C4×Q8C22×C711yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4C22×C711yescharacteristic
277C2×#117—21no—
278C22×C42C22×C711yescharacteristic
279C4×Q16—24no—
280C4×SD16—24no—
281C2×#107C22×C711yescharacteristic
282C2×#106C22×C711yescharacteristic
283C2×#103C22×C711yescharacteristic
284C2×#103C22×C711yescharacteristic
285C2×#103C22×C711yescharacteristic
286C2×#103C22×C711yescharacteristic
287C2×#103C22×C711yescharacteristic
288C2×#102C22×C711yescharacteristic
289C2×#102C22×C711yescharacteristic
290C2×#102C22×C711yescharacteristic
291C2×C22⋊C8C22×C711yescharacteristic
292C2×C22⋊C8C22×C711yescharacteristic
293C2×C4×C8C22×C711yescharacteristic
294C2×C4×C8C22×C711yescharacteristic
295#391C22×C711yescharacteristic
296#389C22×C711yescharacteristic
297#387—21no—
298#385—21no—
299#380C22×C711yescharacteristic
300C4×C4⋊C4—21no—
301C4×C4⋊C4C22×C711yescharacteristic
302C4×C22⋊C4—21no—
303#340C22×C711yescharacteristic
304#340C22×C711yescharacteristic
305#340C22×C711yescharacteristic
306#340C22×C711yescharacteristic
307#336C22×C711yescharacteristic
308#336C22×C711yescharacteristic
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—22no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7#13512yes—
323C23×C7C22×D411yescharacteristic
324C7×Q8—22no—
325C7×Q8—22no—
326C7×Q8—22no—
327C7×Q8—22no—
328C7×Q8—41no—
329C7×Q8—41no—
330C7×Q8—41no—
331C7×Q8—41no—
332C7×D4—22no—
333C7×D4—22no—
334C7×D4—48no—
335C7×D4—41no—
336C7×D4—41no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—44no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—44no—
369C2×C4×C7—48no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7#12012yes—
377C2×C4×C7#12012yes—
378C2×C4×C7#13512yes—
379C2×C4×C7#13712yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4111yescharacteristic
383C2×C4×C7C2×#4111yescharacteristic
384C2×C4×C7C2×#4111yescharacteristic
385C2×C4×C7C2×#4111yescharacteristic
386C7×C8—22no—
387C7×C8—22no—
388C7×C8—41no—
389C7×C8—41no—
390C22×Q8C23×C711yescharacteristic
391C22×Q8C23×C711yescharacteristic
392C22×D4—21no—
393C22×D4C23×C711yescharacteristic
394C23×C4—21no—
395C23×C4C7×D411yescharacteristic
396C23×C4C7×D411yescharacteristic
397C23×C4C23×C711yescharacteristic
398C2×Q16—22no—
399C2×Q16—22no—
400C2×Q16—22no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—22no—
404C22×C8C23×C711yescharacteristic
405C22×C8C23×C711yescharacteristic
406C22×C8C23×C711yescharacteristic
407C22×C8C23×C711yescharacteristic
408#126—28no—
409#125—22no—
410#125—22no—
411#124—22no—
412#124—22no—
413#123—28no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418#121—22no—
419#121—22no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8C7×D414yes—
424C4×D4—28no—
425C4×D4—22no—
426C4×D4C7×D414yes—
427#117—28no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4C23×C711yescharacteristic
436C2×C4⋊C4C23×C711yescharacteristic
437C2×C4⋊C4C23×C711yescharacteristic
438C2×C4⋊C4C23×C711yescharacteristic
439C2×C4⋊C4C23×C711yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42—21no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C7×D411yescharacteristic
453C2×C42C7×D411yescharacteristic
454C2×C42C23×C711yescharacteristic
455C2×C42C23×C711yescharacteristic
456#107—22no—
457#106—22no—
458#103—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C4×C8—22no—
469C4×C8—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—81no—
486C22×C7—81no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7C2×#12011yescharacteristic
490C22×C7#52511yescharacteristic
491C22×C7#53211yescharacteristic
492C22×C7C2×#13511yescharacteristic
493C22×C7C2×#13511yescharacteristic
494C22×C7C2×#13711yescharacteristic
495C22×C7#57511yescharacteristic
496C4×C7—22no—
497C4×C7—42no—
498C4×C7—41no—
499C4×C7—42no—
500C4×C7—42no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—41no—
504C4×C7—42no—
505C4×C7—81no—
506C4×C7—81no—
507C4×C7#45214yes—
508C4×C7#52511yescharacteristic
509C4×C7#52511yescharacteristic
510C4×C7#53211yescharacteristic
511C4×C7#53211yescharacteristic
512C24—21no—
513C24C2×C7×D411yescharacteristic
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8C2×C7×D412yes—
525C2×Q8C7×#4112yes—
526C2×D4—24no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4C2×C7×D412yes—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4C2×C7×D411yescharacteristic
558C22×C4C2×C7×D411yescharacteristic
559C22×C4C2×C7×D411yescharacteristic
560C22×C4C2×C7×D411yescharacteristic
561C22×C4C2×C7×D411yescharacteristic
562C22×C4C24×C711yescharacteristic
563Q16—28no—
564SD16—28no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8C7×#4112yes—
576C2×C8C7×#4112yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4C2×C7×D412yes—
592C4⋊C4C2×C7×D412yes—
593C4⋊C4C7×#4112yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—42no—
601C42—22no—
602C42—22no—
603C42—24no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42—42no—
608C42C2×C7×D412yes—
609C42C2×C7×D412yes—
610C2×C7—42no—
611C2×C7—82no—
612C2×C7#238811yescharacteristic
613C2×C7C2×#45211yescharacteristic
614C2×C7#300211yescharacteristic
615C2×C7#310211yescharacteristic
616C2×C7#310811yescharacteristic
617C2×C7#316811yescharacteristic
618C2×C7#317211yescharacteristic
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23C7×#13512yes—
633C23C22×C7×D411yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—48no—
645D4—41no—
646D4—41no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—44no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—44no—
679C2×C4—48no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4C7×#12012yes—
687C2×C4C7×#12012yes—
688C2×C4C7×#13512yes—
689C2×C4C7×#13712yes—
690C2×C4C22×C7×D411yescharacteristic
691C2×C4C22×C7×D411yescharacteristic
692C2×C4C2×C7×#4111yescharacteristic
693C2×C4C2×C7×#4111yescharacteristic
694C2×C4C2×C7×#4111yescharacteristic
695C2×C4C2×C7×#4111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C7#2357211yescharacteristic, direct product factor, Sylow
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×C7×#12011yescharacteristic
716C22C7×#52511yescharacteristic
717C22C7×#53211yescharacteristic
718C22C2×C7×#13511yescharacteristic
719C22C2×C7×#13511yescharacteristic
720C22C2×C7×#13711yescharacteristic
721C22C7×#57511yescharacteristic
722C4—22no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4C7×#45214yes—
734C4C7×#52511yescharacteristic
735C4C7×#52511yescharacteristic
736C4C7×#53211yescharacteristic
737C4C7×#53211yescharacteristic
738C2—42no—
739C2—82no—
740C2C7×#238811yescharacteristic
741C2C2×C7×#45211yescharacteristic
742C2C7×#300211yescharacteristic
743C2C7×#310211yescharacteristic
744C2C7×#310811yescharacteristic
745C2C7×#316811yescharacteristic
746C2C7×#317211yescharacteristic
subgroupG/H
centerC22×C4×C7C2×D4
commutator, Frattini, cosocleC22×C4C24×C7
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×Q16C2semidirect
3. C2×C4×C7×SD16C2semidirect
4. C4×C7×C22⋊Q8C2semidirect
5. C7×#2059C2semidirect
6. C7×#2042C2semidirect
7. C7×#2035C2semidirect
9. C7×#2026C2semidirect
10. C7×#2015C2semidirect
11. C7×#2001C2semidirect
13. C4×C7×#103C2semidirect
14. C4×C7×#102C2semidirect
15. C4×C7×C22⋊C8C2semidirect
63. #23572C7direct (N × H)
150. C2×C4×Q16C2×C7semidirect
151. C2×C4×SD16C2×C7semidirect
152. C4×C22⋊Q8C2×C7semidirect
153. #2059C2×C7semidirect
154. #2042C2×C7semidirect
155. #2035C2×C7semidirect
157. #2026C2×C7semidirect
158. #2015C2×C7semidirect
159. #2001C2×C7semidirect
161. C4×#103C2×C7semidirect
162. C4×#102C2×C7semidirect
163. C4×C22⋊C8C2×C7semidirect
700. C7#23572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5292
C2×C4×C7×Q162
C2×C4×C7×SD162
C4×C7×C22⋊Q82
C7×#20592
C7×#20422
C7×#20352
C7×#20332
C7×#20262
C7×#20152
C7×#20012
C7×#20002
C4×C7×#1032
C4×C7×#1022
C4×C7×C22⋊C82
#235727