Finite Group Databasebeta

← C7×#14418 #13191634

Subgroups — C7×#14418 #13191634

Order 1792.

2386 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×#121C211yesmaximal, characteristic
2C2×C7×#390C212yesmaximal, complemented
3C2×C7×#387C212yesmaximal, complemented
4C7×#1439C212yesmaximal, complemented
5C7×#1438C212yesmaximal, complemented
6C7×#1438C212yesmaximal, complemented
7C7×#1437C212yesmaximal, complemented
8C7×C22⋊#95C211yesmaximal, characteristic, complemented
9C7×C22⋊#95C211yesmaximal, characteristic, complemented
10C23×C7×D4C2212yes—
11C23×C7×D4C2211yescharacteristic
12C24×C4×C7C2211yescharacteristic
13C2×C7×#121—28no—
14C2×C7×#121C418yescomplemented
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2212yes—
26C7×#390—28no—
27C7×#387—28no—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35#14418C711yesmaximal, characteristic, direct product factor, Sylow
36C25×C7C2312yes—
37C25×C7C2311yescharacteristic
38C22×C7×D4—24no—
39C22×C7×D4—24no—
40C22×C7×D4—24no—
41C22×C7×D4—24no—
42C22×C7×D4—24no—
43C22×C7×D4—42no—
44C22×C7×D4—42no—
45C22×C7×D4—41no—
46C22×C7×D4—41no—
47C22×C7×D4—42no—
48C22×C7×D4C2×C418yes—
49C22×C7×D4C2×C414yes—
50C23×C4×C7—24no—
51C23×C4×C7—41no—
52C23×C4×C7—41no—
53C23×C4×C7—42no—
54C23×C4×C7C2×C414yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2312yes—
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2311yescharacteristic
62C7×#121—232no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—42no—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C7×C4⋊C4D418yes—
68C2×C7×C22⋊C4—24no—
69C2×C7×C22⋊C4—24no—
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—41no—
78C2×C7×C22⋊C4—41no—
79C2×C7×C22⋊C4—42no—
80C2×C7×C22⋊C4—42no—
81C2×C7×C22⋊C4—42no—
82C2×C7×C22⋊C4—42no—
83C2×C7×C22⋊C4—42no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4C2×C418yes—
91C2×C7×C22⋊C4D414yescomplemented
92C2×C42×C7—24no—
93C2×C42×C7—24no—
94C2×C42×C7—42no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—24no—
99C7×#95—41no—
100C7×#95—42no—
101C7×#95—41no—
102C22×#121C2×C711yescharacteristic
103C2×#390C2×C712yescomplemented
104C2×#387C2×C712yescomplemented
105#1439C2×C712yescomplemented
106#1438C2×C712yescomplemented
107#1438C2×C712yescomplemented
108#1437C2×C712yescomplemented
109C22⋊#95C2×C711yescharacteristic, complemented
110C22⋊#95C2×C711yescharacteristic, complemented
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—21no—
114C24×C7—21no—
115C24×C7—21no—
116C24×C7—22no—
117C24×C7—22no—
118C24×C7—21no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7C22×C414yes—
134C24×C7C22×C412yes—
135C24×C7C2×D412yes—
136C24×C7#4112yes—
137C24×C7C2411yescharacteristic
138C2×C7×D4—216no—
139C2×C7×D4—216no—
140C2×C7×D4—28no—
141C2×C7×D4—44no—
142C2×C7×D4—44no—
143C2×C7×D4—48no—
144C2×C7×D4—48no—
145C2×C7×D4—48no—
146C2×C7×D4—48no—
147C2×C7×D4—48no—
148C2×C7×D4—48no—
149C2×C7×D4—48no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
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—28no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—48no—
191C22×C4×C7—48no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C414yes—
194C22×C4×C7C22×C412yes—
195C22×C4×C7C2×D414yes—
196C22×C4×C7C2×D414yes—
197C22×C4×C7C2×D414yes—
198C22×C4×C7C2×D414yes—
199C22×C4×C7#4114yes—
200C7×C4⋊C4—48no—
201C7×C4⋊C4C22⋊C4116yescomplemented
202C7×C22⋊C4—216no—
203C7×C22⋊C4—44no—
204C7×C22⋊C4—48no—
205C7×C22⋊C4—48no—
206C7×C22⋊C4—48no—
207C7×C22⋊C4—48no—
208C7×C22⋊C4—44no—
209C7×C22⋊C4—48no—
210C42×C7—48no—
211C23×D4C22×C712yes—
212C23×D4C22×C711yescharacteristic
213C24×C4C22×C711yescharacteristic
214C2×#121—28no—
215C2×#121C4×C718yescomplemented
216C22×C4⋊C4C22×C712yes—
217C22×C4⋊C4C22×C711yescharacteristic
218C22×C22⋊C4C22×C712yes—
219C22×C22⋊C4C22×C712yes—
220C22×C22⋊C4C22×C712yes—
221C22×C22⋊C4C22×C711yescharacteristic
222C22×C22⋊C4C22×C712yes—
223C22×C22⋊C4C22×C712yes—
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C711yescharacteristic
226C22×C42C22×C712yes—
227#390—28no—
228#387—28no—
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C711yescharacteristic
234C2×#95C22×C712yes—
235C2×#95C22×C711yescharacteristic
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—22no—
239C23×C7—22no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—22no—
243C23×C7—22no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—24no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
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—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7C4×D414yes—
294C23×C7C23×C411yescharacteristic
295C23×C7C22×D412yes—
296C23×C7C22×D411yescharacteristic
297C23×C7C2×#4111yescharacteristic
298C23×C7C2×#4112yes—
299C23×C7H(5,𝔽2)11yescharacteristic
300C23×C7H(5,𝔽2)11yescharacteristic
301C23×C7H(5,𝔽2)12yes—
302C23×C7H(5,𝔽2)12yes—
303C23×C7H(5,𝔽2)11yescharacteristic
304C23×C72−1+411yescharacteristic
305C7×D4—432no—
306C7×D4—416no—
307C2×C4×C7—24no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—416no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
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—42no—
344C2×C4×C7—42no—
345C2×C4×C7—42no—
346C2×C4×C7—42no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—42no—
350C2×C4×C7—42no—
351C2×C4×C7C2×C22⋊C418yes—
352C2×C4×C7C2×C22⋊C414yes—
353C25C23×C712yes—
354C25C23×C711yescharacteristic
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4—42no—
365C22×D4C2×C4×C718yes—
366C22×D4C2×C4×C714yes—
367C23×C4—24no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—42no—
371C23×C4C2×C4×C714yes—
372C23×C4C23×C712yes—
373C23×C4C23×C712yes—
374C23×C4C23×C711yescharacteristic
375C23×C4C23×C712yes—
376C23×C4C23×C712yes—
377C23×C4C23×C712yes—
378C23×C4C23×C711yescharacteristic
379#121—232no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4C2×C4×C714yes—
384C2×C4⋊C4C7×D418yes—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×C4×C718yes—
408C2×C22⋊C4C7×D414yescomplemented
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—42no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—41no—
417#95—42no—
418#95—41no—
419C22×C7—24no—
420C22×C7—24no—
421C22×C7—24no—
422C22×C7—42no—
423C22×C7—42no—
424C22×C7—42no—
425C22×C7—42no—
426C22×C7—44no—
427C22×C7—44no—
428C22×C7—44no—
429C22×C7—44no—
430C22×C7—44no—
431C22×C7—44no—
432C22×C7—44no—
433C22×C7—44no—
434C22×C7—44no—
435C22×C7—44no—
436C22×C7—44no—
437C22×C7—82no—
438C22×C7—82no—
439C22×C7—82no—
440C22×C7—82no—
441C22×C7—82no—
442C22×C7—82no—
443C22×C7—82no—
444C22×C7—82no—
445C22×C7C22×C22⋊C411yescharacteristic
446C22×C7C2×C4×D411yescharacteristic
447C22×C7C4×#4111yescharacteristic
448C22×C7#51811yescharacteristic
449C22×C7#51811yescharacteristic
450C22×C7#51811yescharacteristic
451C22×C7#52011yescharacteristic
452C22×C7#53411yescharacteristic
453C22×C7#53512yes—
454C22×C7#53512yes—
455C22×C7#53711yescharacteristic
456C22×C7#53811yescharacteristic
457C22×C7#53812yes—
458C22×C7#53911yescharacteristic
459C22×C7#54012yes—
460C22×C7D4212yes—
461C22×C7#54612yes—
462C22×C7#54612yes—
463C22×C7#54812yes—
464C22×C7#55012yes—
465C22×C7#55312yes—
466C22×C7#56012yes—
467C22×C7#56212yes—
468C4×C7—24no—
469C4×C7—28no—
470C4×C7—42no—
471C4×C7—44no—
472C4×C7—44no—
473C4×C7—82no—
474C4×C7—82no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24C22×C4×C714yes—
498C24C22×C4×C712yes—
499C24C2×C7×D412yes—
500C24C7×#4112yes—
501C24C24×C711yescharacteristic
502C2×D4—216no—
503C2×D4—216no—
504C2×D4—28no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4C22×C4×C712yes—
557C22×C4C22×C4×C714yes—
558C22×C4C22×C4×C712yes—
559C22×C4C2×C7×D414yes—
560C22×C4C2×C7×D414yes—
561C22×C4C2×C7×D414yes—
562C22×C4C2×C7×D414yes—
563C22×C4C7×#4114yes—
564C4⋊C4—48no—
565C4⋊C4C7×C22⋊C4116yescomplemented
566C22⋊C4—216no—
567C22⋊C4—44no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—44no—
573C22⋊C4—48no—
574C42—48no—
575C2×C7—44no—
576C2×C7—84no—
577C2×C7#230911yescharacteristic
578C2×C7#232511yescharacteristic
579C2×C7#233311yescharacteristic
580C2×C7D4×C22⋊C411yescharacteristic
581C2×C7#234111yescharacteristic
582C2×C7#236411yescharacteristic
583C2×C7#237711yescharacteristic
584C2×C7#267312yes—
585C2×C7#267612yes—
586C2×C7#271112yes—
587C2×C7#271412yes—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C4×C7×D414yes—
646C23C23×C4×C711yescharacteristic
647C23C22×C7×D412yes—
648C23C22×C7×D411yescharacteristic
649C23C2×C7×#4111yescharacteristic
650C23C2×C7×#4112yes—
651C23C7×H(5,𝔽2)11yescharacteristic
652C23C7×H(5,𝔽2)11yescharacteristic
653C23C7×H(5,𝔽2)12yes—
654C23C7×H(5,𝔽2)12yes—
655C23C7×H(5,𝔽2)11yescharacteristic
656C23C7×2−1+411yescharacteristic
657D4—432no—
658D4—416no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
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—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4C2×C7×C22⋊C418yes—
704C2×C4C2×C7×C22⋊C414yes—
705C7#1441811yescharacteristic, direct product factor, Sylow
706C22—24no—
707C22—24no—
708C22—24no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—82no—
725C22—82no—
726C22—82no—
727C22—82no—
728C22—82no—
729C22—82no—
730C22—82no—
731C22—82no—
732C22C22×C7×C22⋊C411yescharacteristic
733C22C2×C4×C7×D411yescharacteristic
734C22C4×C7×#4111yescharacteristic
735C22C7×#51811yescharacteristic
736C22C7×#51811yescharacteristic
737C22C7×#51811yescharacteristic
738C22C7×#52011yescharacteristic
739C22C7×#53411yescharacteristic
740C22C7×#53512yes—
741C22C7×#53512yes—
742C22C7×#53711yescharacteristic
743C22C7×#53812yes—
744C22C7×#53811yescharacteristic
745C22C7×#53911yescharacteristic
746C22C7×#54012yes—
747C22C7×D4212yes—
748C22C7×#54612yes—
749C22C7×#54612yes—
750C22C7×#54812yes—
751C22C7×#55012yes—
752C22C7×#55312yes—
753C22C7×#56012yes—
754C22C7×#56212yes—
755C4—24no—
756C4—28no—
757C4—44no—
758C4—44no—
759C4—42no—
760C4—82no—
761C4—82no—
762C2—44no—
763C2—84no—
764C2C7×#230911yescharacteristic
765C2C7×#232511yescharacteristic
766C2C7×#233311yescharacteristic
767C2C7×D4×C22⋊C411yescharacteristic
768C2C7×#234111yescharacteristic
769C2C7×#236411yescharacteristic
770C2C7×#237711yescharacteristic
771C2C7×#267312yes—
772C2C7×#267612yes—
773C2C7×#271112yes—
774C2C7×#271412yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#390C2semidirect
3. C2×C7×#387C2semidirect
4. C7×#1439C2semidirect
5. C7×#1438C2semidirect
6. C7×#1438C2semidirect
7. C7×#1437C2semidirect
8. C7×C22⋊#95C2semidirect
9. C7×C22⋊#95C2semidirect
14. C2×C7×#121C4semidirect
35. #14418C7direct (N × H)
91. C2×C7×C22⋊C4D4semidirect
103. C2×#390C2×C7semidirect
104. C2×#387C2×C7semidirect
105. #1439C2×C7semidirect
106. #1438C2×C7semidirect
107. #1438C2×C7semidirect
108. #1437C2×C7semidirect
109. C22⋊#95C2×C7semidirect
110. C22⋊#95C2×C7semidirect
201. C7×C4⋊C4C22⋊C4semidirect
215. C2×#121C4×C7semidirect
408. C2×C22⋊C4C7×D4semidirect
565. C4⋊C4C7×C22⋊C4semidirect
705. C7#14418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C2×C7×#3902
C2×C7×#3872
C7×#14392
C7×#14382
C7×#14372
C7×C22⋊#952
#144187