Finite Group Databasebeta

← C7×#14723 #13191939

Subgroups — C7×#14723 #13191939

Order 1792.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C4×C7×D4C211yesmaximal, characteristic
3C2×C7×#395C211yesmaximal, characteristic, complemented
4C2×C7×#393C211yesmaximal, characteristic, complemented
5C2×C7×#385C212yesmaximal, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1439C211yesmaximal, characteristic, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1438C212yesmaximal
10C7×#1436C212yesmaximal, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C2×C7×C22⋊Q8—24no—
17C2×C7×C22⋊Q8—28no—
18C2×C4×C7×D4—24no—
19C2×C4×C7×D4—24no—
20C2×C4×C7×D4—24no—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2212yes—
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C7×#395—24no—
33C7×#393—24no—
34C7×#385—28no—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43#14723C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C25×C7C2311yescharacteristic
46C22×C7×Q8—24no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8—42no—
51C22×C7×D4—22no—
52C22×C7×D4—22no—
53C22×C7×D4—22no—
54C22×C7×D4—22no—
55C22×C7×D4—22no—
56C22×C7×D4—22no—
57C22×C7×D4Q814yescomplemented
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—24no—
64C23×C4×C7—24no—
65C23×C4×C7—42no—
66C23×C4×C7—42no—
67C23×C4×C7D414yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2312yes—
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2312yes—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2312yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C7×C22⋊Q8—232no—
78C4×C7×D4—232no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—24no—
84C2×C7×C4⋊C4—24no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—24no—
87C2×C7×C4⋊C4—42no—
88C2×C7×C4⋊C4D414yes—
89C2×C7×C4⋊C4D418yescomplemented
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4D414yes—
108C2×C42×C7—22no—
109C2×C42×C7—22no—
110C2×C42×C7—22no—
111C7×#95—24no—
112C7×#95—24no—
113C7×#95—24no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—24no—
117C7×#95—24no—
118C7×#95—24no—
119C22×C22⋊Q8C2×C711yescharacteristic, complemented
120C22×C4×D4C2×C711yescharacteristic
121C2×#395C2×C711yescharacteristic, complemented
122C2×#393C2×C711yescharacteristic, complemented
123C2×#385C2×C712yescomplemented
124#1441C2×C711yescharacteristic, complemented
125#1439C2×C712yescomplemented
126#1439C2×C711yescharacteristic, complemented
127#1438C2×C712yes—
128#1436C2×C712yescomplemented
129C22⋊#95C2×C711yescharacteristic, complemented
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7C2×D412yes—
147C24×C7C2×D412yes—
148C24×C7C2×Q812yes—
149C24×C7C2×Q812yes—
150C24×C7#4112yes—
151C24×C7#4112yes—
152C24×C7C2411yescharacteristic
153C2×C7×Q8—28no—
154C2×C7×Q8—48no—
155C2×C7×Q8—48no—
156C2×C7×Q8—44no—
157C2×C7×Q8—44no—
158C2×C7×D4—28no—
159C2×C7×D4—28no—
160C2×C7×D4—28no—
161C2×C7×D4—28no—
162C2×C7×D4—28no—
163C2×C7×D4—28no—
164C2×C7×D4—28no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—28no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
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—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—28no—
202C22×C4×C7—28no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—44no—
211C22×C4×C7—48no—
212C22×C4×C7—48no—
213C22×C4×C7—48no—
214C22×C4×C7—48no—
215C22×C4×C7—44no—
216C22×C4×C7—44no—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D414yes—
219C22×C4×C7C2×D414yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D414yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×Q812yes—
228C22×C4×C7#4114yes—
229C22×C4×C7#4112yes—
230C7×C4⋊C4—28no—
231C7×C4⋊C4—28no—
232C7×C4⋊C4—216no—
233C7×C4⋊C4—48no—
234C7×C22⋊C4—216no—
235C7×C22⋊C4—28no—
236C7×C22⋊C4—216no—
237C7×C22⋊C4—28no—
238C7×C22⋊C4—48no—
239C7×C22⋊C4—48no—
240C42×C7—28no—
241C23×Q8C22×C711yescharacteristic
242C23×D4C22×C711yescharacteristic
243C24×C4C22×C711yescharacteristic
244C24×C4C22×C711yescharacteristic
245C2×C22⋊Q8—24no—
246C2×C22⋊Q8—28no—
247C2×C4×D4—24no—
248C2×C4×D4—24no—
249C2×C4×D4—24no—
250C22×C4⋊C4C22×C711yescharacteristic
251C22×C4⋊C4C22×C712yes—
252C22×C4⋊C4C22×C711yescharacteristic
253C22×C4⋊C4C22×C712yes—
254C22×C22⋊C4C22×C711yescharacteristic
255C22×C22⋊C4C22×C712yes—
256C22×C22⋊C4C22×C712yes—
257C22×C22⋊C4C22×C712yes—
258C22×C22⋊C4C22×C712yes—
259C22×C22⋊C4C22×C711yescharacteristic
260C22×C42C22×C711yescharacteristic
261#395—24no—
262#393—24no—
263#385—28no—
264C2×#95C22×C711yescharacteristic
265C2×#95C22×C712yes—
266C2×#95C22×C711yescharacteristic
267C2×#95C22×C712yes—
268C2×#95C22×C712yes—
269C2×#95C22×C712yes—
270C2×#95C22×C712yes—
271C2×#95C22×C712yes—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—24no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—24no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—41no—
299C23×C7—42no—
300C23×C7—41no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7—42no—
310C23×C7—42no—
311C23×C7—42no—
312C23×C7—42no—
313C23×C7—42no—
314C23×C7—42no—
315C23×C7—42no—
316C23×C7C22⋊Q814yes—
317C23×C7C22⋊Q814yescomplemented
318C23×C7C22×D411yescharacteristic
319C23×C7C22×D411yescharacteristic
320C23×C7C22×D411yescharacteristic
321C23×C7C22×D412yes—
322C23×C7C22×Q811yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4112yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C7×Q8—416no—
330C7×D4—232no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—24no—
342C2×C4×C7—24no—
343C2×C4×C7—24no—
344C2×C4×C7—24no—
345C2×C4×C7—22no—
346C2×C4×C7—24no—
347C2×C4×C7—22no—
348C2×C4×C7—24no—
349C2×C4×C7—24no—
350C2×C4×C7—24no—
351C2×C4×C7—24no—
352C2×C4×C7—24no—
353C2×C4×C7—24no—
354C2×C4×C7—24no—
355C2×C4×C7—24no—
356C2×C4×C7—24no—
357C2×C4×C7—24no—
358C2×C4×C7—416no—
359C2×C4×C7—416no—
360C2×C4×C7—41no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—42no—
370C2×C4×C7—41no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7#12014yes—
386C2×C4×C7#12014yes—
387C2×C4×C7C22⋊Q814yescomplemented
388C25C23×C711yescharacteristic
389C25C23×C711yescharacteristic
390C22×Q8—24no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—42no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4C7×Q814yescomplemented
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4C7×D414yes—
412C23×C4C23×C712yes—
413C23×C4C23×C712yes—
414C23×C4C23×C712yes—
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C711yescharacteristic
417C23×C4C23×C712yes—
418C23×C4C23×C711yescharacteristic
419C23×C4C23×C711yescharacteristic
420C23×C4C23×C711yescharacteristic
421C22⋊Q8—232no—
422C4×D4—232no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4C7×D414yes—
433C2×C4⋊C4C7×D418yescomplemented
434C2×C22⋊C4—22no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4C7×D414yes—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—22no—
459#95—22no—
460#95—24no—
461#95—24no—
462#95—24no—
463C22×C7—24no—
464C22×C7—24no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—28no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7—44no—
483C22×C7—44no—
484C22×C7—44no—
485C22×C7C2×#12011yescharacteristic
486C22×C7C2×#12011yescharacteristic
487C22×C7C2×C22⋊Q811yescharacteristic
488C22×C7C2×C22⋊Q811yescharacteristic
489C22×C7C2×C22⋊Q811yescharacteristic
490C22×C7#52511yescharacteristic
491C22×C7#52511yescharacteristic
492C22×C7#52511yescharacteristic
493C22×C7#52512yes—
494C22×C7#53211yescharacteristic
495C22×C7#53212yes—
496C22×C7#53411yescharacteristic
497C22×C7#53611yescharacteristic
498C22×C7#53912yes—
499C22×C7#54212yes—
500C22×C7D4212yes—
501C22×C7D4212yes—
502C22×C7#54712yes—
503C22×C7#54812yes—
504C22×C7#54812yes—
505C22×C7D4×Q812yes—
506C22×C7#55112yes—
507C22×C7#55412yes—
508C4×C7—24no—
509C4×C7—24no—
510C4×C7—24no—
511C4×C7—44no—
512C4×C7—42no—
513C4×C7—44no—
514C4×C7—42no—
515C4×C7—44no—
516C4×C7—82no—
517C24—22no—
518C24—22no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24C2×C7×D412yes—
534C24C2×C7×D412yes—
535C24C2×C7×Q812yes—
536C24C2×C7×Q812yes—
537C24C7×#4112yes—
538C24C7×#4112yes—
539C24C24×C711yescharacteristic
540C2×Q8—28no—
541C2×Q8—48no—
542C2×Q8—48no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4C2×C7×D412yes—
605C22×C4C2×C7×D414yes—
606C22×C4C2×C7×D414yes—
607C22×C4C2×C7×D412yes—
608C22×C4C2×C7×D412yes—
609C22×C4C2×C7×D412yes—
610C22×C4C2×C7×D414yes—
611C22×C4C2×C7×D412yes—
612C22×C4C2×C7×D412yes—
613C22×C4C2×C7×D412yes—
614C22×C4C2×C7×Q812yes—
615C22×C4C7×#4114yes—
616C22×C4C7×#4112yes—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—216no—
620C4⋊C4—48no—
621C22⋊C4—28no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—28no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C42—28no—
628C2×C7—44no—
629C2×C7—44no—
630C2×C7#238811yescharacteristic
631C2×C7#240311yescharacteristic
632C2×C7#240911yescharacteristic
633C2×C7#243211yescharacteristic
634C2×C7#244912yes—
635C2×C7#245212yes—
636C2×C7#246112yes—
637C2×C7#246312yes—
638C2×C7#256411yescharacteristic
639C2×C7#263811yescharacteristic
640C2×C7#284811yescharacteristic
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C7×C22⋊Q814yes—
686C23C7×C22⋊Q814yescomplemented
687C23C22×C7×D411yescharacteristic
688C23C22×C7×D411yescharacteristic
689C23C22×C7×D411yescharacteristic
690C23C22×C7×D412yes—
691C23C22×C7×Q811yescharacteristic
692C23C2×C7×#4111yescharacteristic
693C23C2×C7×#4111yescharacteristic
694C23C2×C7×#4111yescharacteristic
695C23C2×C7×#4112yes—
696C23C7×H(5,𝔽2)12yes—
697C23C7×2−1+412yes—
698Q8—416no—
699D4—232no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—416no—
728C2×C4—416no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4C7×#12014yes—
755C2×C4C7×#12014yes—
756C2×C4C7×C22⋊Q814yescomplemented
757C7#1472311yescharacteristic, direct product factor, Sylow
758C22—24no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22C2×C7×#12011yescharacteristic
781C22C2×C7×#12011yescharacteristic
782C22C2×C7×C22⋊Q811yescharacteristic
783C22C2×C7×C22⋊Q811yescharacteristic
784C22C2×C7×C22⋊Q811yescharacteristic
785C22C7×#52512yes—
786C22C7×#52511yescharacteristic
787C22C7×#52511yescharacteristic
788C22C7×#52511yescharacteristic
789C22C7×#53211yescharacteristic
790C22C7×#53212yes—
791C22C7×#53411yescharacteristic
792C22C7×#53611yescharacteristic
793C22C7×#53912yes—
794C22C7×#54212yes—
795C22C7×D4212yes—
796C22C7×D4212yes—
797C22C7×#54712yes—
798C22C7×#54812yes—
799C22C7×#54812yes—
800C22C7×D4×Q812yes—
801C22C7×#55112yes—
802C22C7×#55412yes—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—42no—
810C4—44no—
811C4—82no—
812C2—44no—
813C2—44no—
814C2C7×#238811yescharacteristic
815C2C7×#240311yescharacteristic
816C2C7×#240911yescharacteristic
817C2C7×#243211yescharacteristic
818C2C7×#244912yes—
819C2C7×#245212yes—
820C2C7×#246112yes—
821C2C7×#246312yes—
822C2C7×#256411yescharacteristic
823C2C7×#263811yescharacteristic
824C2C7×#284811yescharacteristic
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
3. C2×C7×#395C2semidirect
4. C2×C7×#393C2semidirect
5. C2×C7×#385C2semidirect
6. C7×#1441C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
10. C7×#1436C2semidirect
11. C7×C22⋊#95C2semidirect
43. #14723C7direct (N × H)
57. C22×C7×D4Q8semidirect
89. C2×C7×C4⋊C4D4semidirect
119. C22×C22⋊Q8C2×C7semidirect
121. C2×#395C2×C7semidirect
122. C2×#393C2×C7semidirect
123. C2×#385C2×C7semidirect
124. #1441C2×C7semidirect
125. #1439C2×C7semidirect
126. #1439C2×C7semidirect
128. #1436C2×C7semidirect
129. C22⋊#95C2×C7semidirect
317. C23×C7C22⋊Q8semidirect
387. C2×C4×C7C22⋊Q8semidirect
401. C22×D4C7×Q8semidirect
433. C2×C4⋊C4C7×D4semidirect
686. C23C7×C22⋊Q8semidirect
756. C2×C4C7×C22⋊Q8semidirect
757. C7#14723direct (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
C22×C4×C7×D42
C2×C7×#3952
C2×C7×#3932
C2×C7×#3852
C7×#14412
C7×#14392
C7×#14382
C7×#14362
C7×C22⋊#952
#147237