Finite Group Databasebeta

← C7×#16600 #13193816

Subgroups — C7×#16600 #13193816

Order 1792.

2010 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C7×#399C211yesmaximal, characteristic, complemented
3C2×C7×#393C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic
5C7×#1446C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1441C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C212yesmaximal
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C2×C7×C22⋊Q8—24no—
16C2×C7×C22⋊Q8—24no—
17C2×C7×C22⋊Q8—24no—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2212yes—
28C7×#399—24no—
29C7×#393—24no—
30C7×#386—24no—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#16600C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2311yescharacteristic
43C25×C7C2311yescharacteristic
44C22×C7×Q8—22no—
45C22×C7×Q8—22no—
46C22×C7×Q8—42no—
47C22×C7×Q8—42no—
48C22×C7×Q8D414yescomplemented
49C22×C7×D4—22no—
50C22×C7×D4—22no—
51C22×C7×D4—42no—
52C22×C7×D4—42no—
53C22×C7×D4Q814yescomplemented
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—42no—
57C23×C4×C7—42no—
58C23×C4×C7D414yes—
59C23×C4×C7C2312yes—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2312yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2312yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2312yes—
67C23×C4×C7C2311yescharacteristic
68C7×C22⋊Q8—232no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—42no—
77C2×C7×C4⋊C4D414yescomplemented
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4—42no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4—42no—
97C7×#95—22no—
98C7×#95—22no—
99C7×#95—24no—
100C7×#95—22no—
101C7×#95—22no—
102C7×#95—42no—
103C7×#95—42no—
104C7×#95—42no—
105C7×#95—42no—
106C7×#95—42no—
107C22×C22⋊Q8C2×C711yescharacteristic, complemented
108C2×#399C2×C711yescharacteristic, complemented
109C2×#393C2×C711yescharacteristic, complemented
110C2×#386C2×C711yescharacteristic
111#1446C2×C711yescharacteristic, complemented
112#1445C2×C711yescharacteristic, complemented
113#1441C2×C712yescomplemented
114#1439C2×C712yescomplemented
115#1439C2×C712yescomplemented
116#1438C2×C712yes—
117C22⋊#95C2×C711yescharacteristic, complemented
118C24×C7—21no—
119C24×C7—21no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—22no—
130C24×C7—21no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7C2×D412yes—
137C24×C7C2×Q812yes—
138C24×C7C2×Q812yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C2×C7×Q8—28no—
142C2×C7×Q8—48no—
143C2×C7×Q8—44no—
144C2×C7×Q8—44no—
145C2×C7×Q8—48no—
146C2×C7×D4—28no—
147C2×C7×D4—48no—
148C2×C7×D4—44no—
149C2×C7×D4—44no—
150C2×C7×D4—48no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—28no—
180C22×C4×C7—21no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—22no—
197C22×C4×C7—44no—
198C22×C4×C7—44no—
199C22×C4×C7—48no—
200C22×C4×C7—48no—
201C22×C4×C7C2×D414yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D414yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×Q812yes—
208C22×C4×C7#4114yes—
209C7×C4⋊C4—216no—
210C7×C4⋊C4—28no—
211C7×C4⋊C4—48no—
212C7×C22⋊C4—216no—
213C7×C22⋊C4—48no—
214C7×C22⋊C4—48no—
215C7×C22⋊C4—44no—
216C7×C22⋊C4—48no—
217C7×C22⋊C4—44no—
218C7×C22⋊C4—44no—
219C23×Q8C22×C711yescharacteristic
220C23×D4C22×C711yescharacteristic
221C24×C4C22×C711yescharacteristic
222C2×C22⋊Q8—24no—
223C2×C22⋊Q8—24no—
224C2×C22⋊Q8—24no—
225C22×C4⋊C4C22×C712yes—
226C22×C4⋊C4C22×C712yes—
227C22×C4⋊C4C22×C711yescharacteristic
228C22×C22⋊C4C22×C711yescharacteristic
229C22×C22⋊C4C22×C712yes—
230C22×C22⋊C4C22×C712yes—
231C22×C22⋊C4C22×C712yes—
232C22×C22⋊C4C22×C712yes—
233C22×C22⋊C4C22×C711yescharacteristic
234C22×C22⋊C4C22×C711yescharacteristic
235#399—24no—
236#393—24no—
237#386—24no—
238C2×#95C22×C711yescharacteristic
239C2×#95C22×C712yes—
240C2×#95C22×C711yescharacteristic
241C2×#95C22×C711yescharacteristic
242C2×#95C22×C711yescharacteristic
243C2×#95C22×C712yes—
244C2×#95C22×C712yes—
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C2×#95C22×C712yes—
248C23×C7—22no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—22no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—22no—
263C23×C7—24no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—24no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—41no—
278C23×C7—42no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—42no—
282C23×C7—41no—
283C23×C7—42no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7C22⋊Q814yes—
294C23×C7C22×D411yescharacteristic
295C23×C7C22×D411yescharacteristic
296C23×C7C22×D411yescharacteristic
297C23×C7C22×Q811yescharacteristic
298C23×C7C2×#4111yescharacteristic
299C23×C7C2×#4112yes—
300C23×C7H(5,𝔽2)12yes—
301C23×C7H(5,𝔽2)12yes—
302C23×C7H(5,𝔽2)12yes—
303C23×C72−1+411yescharacteristic
304C23×C72−1+411yescharacteristic
305C7×Q8—416no—
306C7×D4—416no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—24no—
317C2×C4×C7—22no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—416no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—41no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—42no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—42no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7#12014yes—
361C25C23×C711yescharacteristic
362C25C23×C711yescharacteristic
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—42no—
366C22×Q8—42no—
367C22×Q8C7×D414yescomplemented
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4C7×Q814yescomplemented
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4C7×D414yes—
378C23×C4C23×C711yescharacteristic
379C23×C4C23×C712yes—
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C712yes—
382C23×C4C23×C712yes—
383C23×C4C23×C711yescharacteristic
384C23×C4C23×C711yescharacteristic
385C23×C4C23×C712yes—
386C23×C4C23×C711yescharacteristic
387C22⋊Q8—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4C7×D414yescomplemented
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426C22×C7—24no—
427C22×C7—24no—
428C22×C7—24no—
429C22×C7—42no—
430C22×C7—42no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7—44no—
434C22×C7—44no—
435C22×C7—44no—
436C22×C7—44no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—42no—
440C22×C7—44no—
441C22×C7—44no—
442C22×C7—81no—
443C22×C7—81no—
444C22×C7—81no—
445C22×C7—81no—
446C22×C7—82no—
447C22×C7—82no—
448C22×C7C2×#12011yescharacteristic
449C22×C7C2×C22⋊Q811yescharacteristic
450C22×C7#53211yescharacteristic
451C22×C7#53411yescharacteristic
452C22×C7#53411yescharacteristic
453C22×C7#53412yes—
454C22×C7#53511yescharacteristic
455C22×C7#53512yes—
456C22×C7#53611yescharacteristic
457C22×C7#53812yes—
458C22×C7#53912yes—
459C22×C7#54212yes—
460C22×C7#54312yes—
461C22×C7#54612yes—
462C22×C7#54811yescharacteristic
463C22×C7#54811yescharacteristic
464C22×C7D4×Q811yescharacteristic
465C22×C7D4×Q811yescharacteristic
466C22×C7#55012yes—
467C22×C7#55112yes—
468C22×C7#55412yes—
469C22×C7#56212yes—
470C22×C7#56212yes—
471C4×C7—24no—
472C4×C7—42no—
473C4×C7—44no—
474C4×C7—42no—
475C4×C7—44no—
476C4×C7—44no—
477C4×C7—81no—
478C4×C7—81no—
479C4×C7—82no—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24C2×C7×D412yes—
499C24C2×C7×Q812yes—
500C24C2×C7×Q812yes—
501C24C7×#4112yes—
502C24C24×C711yescharacteristic
503C2×Q8—28no—
504C2×Q8—48no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—48no—
508C2×D4—28no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—48no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4C2×C7×D414yes—
564C22×C4C2×C7×D412yes—
565C22×C4C2×C7×D414yes—
566C22×C4C2×C7×D412yes—
567C22×C4C2×C7×D412yes—
568C22×C4C2×C7×D412yes—
569C22×C4C2×C7×Q812yes—
570C22×C4C7×#4114yes—
571C4⋊C4—216no—
572C4⋊C4—28no—
573C4⋊C4—48no—
574C22⋊C4—216no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—44no—
578C22⋊C4—48no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C2×C7—44no—
582C2×C7—82no—
583C2×C7#240911yescharacteristic
584C2×C7#243111yescharacteristic
585C2×C7#256411yescharacteristic
586C2×C7#261311yescharacteristic
587C2×C7#262611yescharacteristic
588C2×C7#266311yescharacteristic
589C2×C7#269212yes—
590C2×C7#269612yes—
591C2×C7#273012yes—
592C2×C7#273212yes—
593C2×C7#281611yescharacteristic
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C7×C22⋊Q814yes—
640C23C22×C7×D411yescharacteristic
641C23C22×C7×D411yescharacteristic
642C23C22×C7×D411yescharacteristic
643C23C22×C7×Q811yescharacteristic
644C23C2×C7×#4111yescharacteristic
645C23C2×C7×#4112yes—
646C23C7×H(5,𝔽2)12yes—
647C23C7×H(5,𝔽2)12yes—
648C23C7×H(5,𝔽2)12yes—
649C23C7×2−1+411yescharacteristic
650C23C7×2−1+411yescharacteristic
651Q8—416no—
652D4—416no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—416no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4C7×#12014yes—
707C7#1660011yescharacteristic, direct product factor, Sylow
708C22—24no—
709C22—24no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—81no—
725C22—81no—
726C22—82no—
727C22—82no—
728C22—81no—
729C22—81no—
730C22C2×C7×#12011yescharacteristic
731C22C2×C7×C22⋊Q811yescharacteristic
732C22C7×#53211yescharacteristic
733C22C7×#53411yescharacteristic
734C22C7×#53412yes—
735C22C7×#53411yescharacteristic
736C22C7×#53511yescharacteristic
737C22C7×#53512yes—
738C22C7×#53611yescharacteristic
739C22C7×#53812yes—
740C22C7×#53912yes—
741C22C7×#54212yes—
742C22C7×#54312yes—
743C22C7×#54612yes—
744C22C7×#54811yescharacteristic
745C22C7×#54811yescharacteristic
746C22C7×D4×Q811yescharacteristic
747C22C7×D4×Q811yescharacteristic
748C22C7×#55012yes—
749C22C7×#55112yes—
750C22C7×#55412yes—
751C22C7×#56212yes—
752C22C7×#56212yes—
753C4—24no—
754C4—44no—
755C4—44no—
756C4—42no—
757C4—44no—
758C4—42no—
759C4—81no—
760C4—82no—
761C4—81no—
762C2—44no—
763C2—82no—
764C2C7×#240911yescharacteristic
765C2C7×#243111yescharacteristic
766C2C7×#256411yescharacteristic
767C2C7×#261311yescharacteristic
768C2C7×#262611yescharacteristic
769C2C7×#266311yescharacteristic
770C2C7×#269212yes—
771C2C7×#269612yes—
772C2C7×#273012yes—
773C2C7×#273212yes—
774C2C7×#281611yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
2. C2×C7×#399C2semidirect
3. C2×C7×#393C2semidirect
5. C7×#1446C2semidirect
6. C7×#1445C2semidirect
7. C7×#1441C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
11. C7×C22⋊#95C2semidirect
41. #16600C7direct (N × H)
48. C22×C7×Q8D4semidirect
53. C22×C7×D4Q8semidirect
77. C2×C7×C4⋊C4D4semidirect
107. C22×C22⋊Q8C2×C7semidirect
108. C2×#399C2×C7semidirect
109. C2×#393C2×C7semidirect
111. #1446C2×C7semidirect
112. #1445C2×C7semidirect
113. #1441C2×C7semidirect
114. #1439C2×C7semidirect
115. #1439C2×C7semidirect
117. C22⋊#95C2×C7semidirect
367. C22×Q8C7×D4semidirect
372. C22×D4C7×Q8semidirect
396. C2×C4⋊C4C7×D4semidirect
707. C7#16600direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×C7×#3992
C2×C7×#3932
C2×C7×#3862
C7×#14462
C7×#14452
C7×#14412
C7×#14392
C7×#14382
C7×C22⋊#952
#166007