Finite Group Databasebeta

← C7×#23581 #13200797

Subgroups — C7×#23581 #13200797

Order 1792.

1122 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2C2×C7×#441C211yesmaximal, characteristic, complemented
3C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
4C7×#2323C211yesmaximal, characteristic, complemented
5C7×#2058C211yesmaximal, characteristic, complemented
6C7×#2042C211yesmaximal, characteristic, complemented
7C7×#2035C211yesmaximal, characteristic, complemented
8C7×#2034C211yesmaximal, characteristic
9C7×#2024C211yesmaximal, characteristic, complemented
10C7×#2015C211yesmaximal, characteristic, complemented
11C7×#2001C211yesmaximal, characteristic, complemented
12C7×#2000C211yesmaximal, characteristic
13C7×#1762C211yesmaximal, characteristic, complemented
14C4×C7×#103C211yesmaximal, characteristic, complemented
15C7×#1750C211yesmaximal, characteristic, complemented
16C22×C7×Q16C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C7×#542—24no—
19C7×#542—24no—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#126—21no—
22C2×C7×#124—21no—
23C2×C7×#124C2211yescharacteristic
24C2×C7×#123—21no—
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8C2211yescharacteristic
27C2×C7×C22⋊Q8C2211yescharacteristic
28C2×C7×#121C2211yescharacteristic
29C2×C4×C7×Q8C2211yescharacteristic
30C2×C4×C7×Q8C2211yescharacteristic
31C2×C4×C7×D4C2211yescharacteristic
32C2×C7×#117C2211yescharacteristic
33C7×#441—24no—
34C4×C7×SD16—24no—
35C2×C7×#106C2211yescharacteristic
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×C7×#97C2211yescharacteristic
48C2×C4×C7×C8C2211yescharacteristic
49C7×#391C2211yescharacteristic
50C7×#389—21no—
51C7×#389C2211yescharacteristic
52C7×#388—21no—
53C7×#388—21no—
54C7×#387—21no—
55C7×#380C2211yescharacteristic
56C4×C7×C4⋊C4C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#23581C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8—21no—
65C22×C7×Q8C2311yescharacteristic
66C22×C7×Q8C2311yescharacteristic
67C22×C7×D4—21no—
68C22×C7×D4C2311yescharacteristic
69C23×C4×C7—21no—
70C23×C4×C7C2311yescharacteristic
71C2×C7×Q16—22no—
72C2×C7×Q16—22no—
73C2×C7×Q16—22no—
74C2×C7×SD16—22no—
75C2×C7×SD16—22no—
76C2×C7×SD16—22no—
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C7×C4⋊Q8—22no—
82C7×C4⋊Q8—22no—
83C7×#126—28no—
84C7×#124—28no—
85C7×#124—22no—
86C7×#124—22no—
87C7×#123—28no—
88C7×C22⋊Q8—28no—
89C7×C22⋊Q8—22no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—22no—
93C7×#121—22no—
94C7×#121—22no—
95C4×C7×Q8—22no—
96C4×C7×Q8—22no—
97C4×C7×Q8—22no—
98C4×C7×Q8D414yes—
99C4×C7×D4—22no—
100C4×C7×D4D414yes—
101C7×#117—22no—
102C7×#117—22no—
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⋊C4D411yescharacteristic
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
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×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C42×C7—21no—
126C2×C42×C7—21no—
127C2×C42×C7—21no—
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C7×#106—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—
142C7×#97—22no—
143C4×C7×C8—22no—
144C7×#95—21no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C2×#542C2×C711yescharacteristic
150C2×#441C2×C711yescharacteristic, complemented
151C2×C4×SD16C2×C711yescharacteristic, complemented
152#2323C2×C711yescharacteristic, complemented
153#2058C2×C711yescharacteristic, complemented
154#2042C2×C711yescharacteristic, complemented
155#2035C2×C711yescharacteristic, complemented
156#2034C2×C711yescharacteristic
157#2024C2×C711yescharacteristic, complemented
158#2015C2×C711yescharacteristic, complemented
159#2001C2×C711yescharacteristic, complemented
160#2000C2×C711yescharacteristic
161#1762C2×C711yescharacteristic, complemented
162C4×#103C2×C711yescharacteristic, complemented
163#1750C2×C711yescharacteristic, complemented
164C24×C7—21no—
165C24×C7C2×D411yescharacteristic
166C2×C7×Q8—24no—
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×Q8—21no—
177C2×C7×Q8—81no—
178C2×C7×Q8—81no—
179C2×C7×Q8C2×D412yes—
180C2×C7×Q8#4112yes—
181C2×C7×D4—24no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
187C2×C7×D4—81no—
188C2×C7×D4—81no—
189C2×C7×D4C2×D412yes—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—24no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—81no—
205C22×C4×C7—81no—
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2411yescharacteristic
212C7×Q16—28no—
213C7×SD16—28no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
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#4112yes—
225C2×C7×C8#4112yes—
226C7×C4⋊C4—24no—
227C7×C4⋊C4—24no—
228C7×C4⋊C4—24no—
229C7×C4⋊C4—24no—
230C7×C4⋊C4—22no—
231C7×C4⋊C4—22no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—42no—
240C7×C4⋊C4—81no—
241C7×C4⋊C4C2×D412yes—
242C7×C4⋊C4C2×D412yes—
243C7×C4⋊C4#4112yes—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—24no—
246C7×C22⋊C4—24no—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—24no—
250C7×C22⋊C4—22no—
251C7×C22⋊C4—22no—
252C7×C22⋊C4—81no—
253C42×C7—24no—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—42no—
257C42×C7—81no—
258C42×C7C2×D412yes—
259C42×C7C2×D412yes—
260C22×Q16C22×C711yescharacteristic
261C22×SD16C22×C711yescharacteristic
262#542—24no—
263#542—24no—
264C2×C4⋊Q8C22×C711yescharacteristic
265C2×#126—21no—
266C2×#124—21no—
267C2×#124C22×C711yescharacteristic
268C2×#123—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8C22×C711yescharacteristic
271C2×C22⋊Q8C22×C711yescharacteristic
272C2×#121C22×C711yescharacteristic
273C2×C4×Q8C22×C711yescharacteristic
274C2×C4×Q8C22×C711yescharacteristic
275C2×C4×D4C22×C711yescharacteristic
276C2×#117C22×C711yescharacteristic
277#441—24no—
278C4×SD16—24no—
279C2×#106C22×C711yescharacteristic
280C2×#106C22×C711yescharacteristic
281C2×#103C22×C711yescharacteristic
282C2×#103C22×C711yescharacteristic
283C2×#103C22×C711yescharacteristic
284C2×#103C22×C711yescharacteristic
285C2×#103C22×C711yescharacteristic
286C2×#102C22×C711yescharacteristic
287C2×#102C22×C711yescharacteristic
288C2×#102C22×C711yescharacteristic
289C2×C22⋊C8C22×C711yescharacteristic
290C2×C22⋊C8C22×C711yescharacteristic
291C2×#97C22×C711yescharacteristic
292C2×C4×C8C22×C711yescharacteristic
293#391C22×C711yescharacteristic
294#389—21no—
295#389C22×C711yescharacteristic
296#388—21no—
297#388—21no—
298#387—21no—
299#380C22×C711yescharacteristic
300C4×C4⋊C4C22×C711yescharacteristic
301#340C22×C711yescharacteristic
302#340C22×C711yescharacteristic
303#340C22×C711yescharacteristic
304#340C22×C711yescharacteristic
305#336C22×C711yescharacteristic
306#336C22×C711yescharacteristic
307C23×C7—21no—
308C23×C7—22no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7C22×D411yescharacteristic
322C7×Q8—22no—
323C7×Q8—22no—
324C7×Q8—22no—
325C7×Q8—22no—
326C7×Q8—41no—
327C7×Q8—41no—
328C7×Q8—41no—
329C7×Q8—41no—
330C7×Q8—84no—
331C7×D4—22no—
332C7×D4—22no—
333C7×D4—41no—
334C7×D4—41no—
335C7×D4—84no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—22no—
342C2×C4×C7—21no—
343C2×C4×C7—22no—
344C2×C4×C7—21no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
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—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—84no—
375C2×C4×C7#12012yes—
376C2×C4×C7#12012yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C2×#4111yescharacteristic
380C2×C4×C7C2×#4111yescharacteristic
381C2×C4×C7C2×#4111yescharacteristic
382C2×C4×C7C2×#4111yescharacteristic
383C7×C8—22no—
384C7×C8—22no—
385C7×C8—41no—
386C7×C8—41no—
387C22×Q8—21no—
388C22×Q8C23×C711yescharacteristic
389C22×Q8C23×C711yescharacteristic
390C22×D4—21no—
391C22×D4C23×C711yescharacteristic
392C23×C4—21no—
393C23×C4C23×C711yescharacteristic
394C2×Q16—22no—
395C2×Q16—22no—
396C2×Q16—22no—
397C2×SD16—22no—
398C2×SD16—22no—
399C2×SD16—22no—
400C22×C8C23×C711yescharacteristic
401C22×C8C23×C711yescharacteristic
402C22×C8C23×C711yescharacteristic
403C22×C8C23×C711yescharacteristic
404C4⋊Q8—22no—
405C4⋊Q8—22no—
406#126—28no—
407#124—28no—
408#124—22no—
409#124—22no—
410#123—28no—
411C22⋊Q8—28no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416#121—22no—
417#121—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8C7×D414yes—
422C4×D4—22no—
423C4×D4C7×D414yes—
424#117—22no—
425#117—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4C7×D411yescharacteristic
433C2×C4⋊C4C7×D411yescharacteristic
434C2×C4⋊C4C23×C711yescharacteristic
435C2×C4⋊C4C23×C711yescharacteristic
436C2×C4⋊C4C23×C711yescharacteristic
437C2×C4⋊C4C23×C711yescharacteristic
438C2×C4⋊C4C23×C711yescharacteristic
439C2×C22⋊C4—21no—
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⋊C4C7×D411yescharacteristic
447C2×C22⋊C4C7×D411yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C711yescharacteristic
452C2×C42C23×C711yescharacteristic
453#106—22no—
454#106—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#102—22no—
461#102—22no—
462#102—22no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465#97—22no—
466C4×C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C22×C7—41no—
473C22×C7—41no—
474C22×C7—41no—
475C22×C7—42no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—42no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—42no—
482C22×C7—81no—
483C22×C7—81no—
484C22×C7—81no—
485C22×C7—81no—
486C22×C7C2×#12011yescharacteristic
487C22×C7#52511yescharacteristic
488C22×C7#53211yescharacteristic
489C22×C7#57711yescharacteristic
490C22×C7#57711yescharacteristic
491C22×C7#57711yescharacteristic
492C22×C7#57811yescharacteristic
493C4×C7—22no—
494C4×C7—22no—
495C4×C7—42no—
496C4×C7—41no—
497C4×C7—42no—
498C4×C7—42no—
499C4×C7—41no—
500C4×C7—42no—
501C4×C7—42no—
502C4×C7—41no—
503C4×C7—81no—
504C4×C7—81no—
505C4×C7#52511yescharacteristic
506C4×C7#52511yescharacteristic
507C4×C7#53211yescharacteristic
508C4×C7#53211yescharacteristic
509C24—21no—
510C24C2×C7×D411yescharacteristic
511C2×Q8—24no—
512C2×Q8—21no—
513C2×Q8—21no—
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—81no—
523C2×Q8—81no—
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—81no—
533C2×D4—81no—
534C2×D4C2×C7×D412yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4C2×C7×D411yescharacteristic
552C22×C4C2×C7×D411yescharacteristic
553C22×C4C2×C7×D411yescharacteristic
554C22×C4C2×C7×D411yescharacteristic
555C22×C4C2×C7×D411yescharacteristic
556C22×C4C24×C711yescharacteristic
557Q16—28no—
558SD16—28no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8C7×#4112yes—
570C2×C8C7×#4112yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—81no—
586C4⋊C4C2×C7×D412yes—
587C4⋊C4C2×C7×D412yes—
588C4⋊C4C7×#4112yes—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—81no—
598C42—24no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—81no—
603C42C2×C7×D412yes—
604C42C2×C7×D412yes—
605C2×C7—81no—
606C2×C7—82no—
607C2×C7#238811yescharacteristic
608C2×C7#300911yescharacteristic
609C2×C7#301311yescharacteristic
610C2×C7#312111yescharacteristic
611C2×C7#312511yescharacteristic
612C2×C7#317311yescharacteristic
613C2×C7#317811yescharacteristic
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×C7×D411yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—84no—
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—84no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
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—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4C7×#12012yes—
683C2×C4C7×#12012yes—
684C2×C4C22×C7×D411yescharacteristic
685C2×C4C22×C7×D411yescharacteristic
686C2×C4C2×C7×#4111yescharacteristic
687C2×C4C2×C7×#4111yescharacteristic
688C2×C4C2×C7×#4111yescharacteristic
689C2×C4C2×C7×#4111yescharacteristic
690C8—22no—
691C8—22no—
692C8—41no—
693C8—41no—
694C7#2358111yescharacteristic, direct product factor, Sylow
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—41no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×C7×#12011yescharacteristic
710C22C7×#52511yescharacteristic
711C22C7×#53211yescharacteristic
712C22C7×#57711yescharacteristic
713C22C7×#57711yescharacteristic
714C22C7×#57711yescharacteristic
715C22C7×#57811yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4C7×#52511yescharacteristic
729C4C7×#52511yescharacteristic
730C4C7×#53211yescharacteristic
731C4C7×#53211yescharacteristic
732C2—81no—
733C2—82no—
734C2C7×#238811yescharacteristic
735C2C7×#300911yescharacteristic
736C2C7×#301311yescharacteristic
737C2C7×#312111yescharacteristic
738C2C7×#312511yescharacteristic
739C2C7×#317311yescharacteristic
740C2C7×#317811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#441C2semidirect
3. C2×C4×C7×SD16C2semidirect
4. C7×#2323C2semidirect
5. C7×#2058C2semidirect
6. C7×#2042C2semidirect
7. C7×#2035C2semidirect
9. C7×#2024C2semidirect
10. C7×#2015C2semidirect
11. C7×#2001C2semidirect
13. C7×#1762C2semidirect
14. C4×C7×#103C2semidirect
15. C7×#1750C2semidirect
63. #23581C7direct (N × H)
150. C2×#441C2×C7semidirect
151. C2×C4×SD16C2×C7semidirect
152. #2323C2×C7semidirect
153. #2058C2×C7semidirect
154. #2042C2×C7semidirect
155. #2035C2×C7semidirect
157. #2024C2×C7semidirect
158. #2015C2×C7semidirect
159. #2001C2×C7semidirect
161. #1762C2×C7semidirect
162. C4×#103C2×C7semidirect
163. #1750C2×C7semidirect
694. C7#23581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×C7×#4412
C2×C4×C7×SD162
C7×#23232
C7×#20582
C7×#20422
C7×#20352
C7×#20342
C7×#20242
C7×#20152
C7×#20012
C7×#20002
C7×#17622
C4×C7×#1032
C7×#17502
#235817