Finite Group Databasebeta

← C7×#14417 #13191633

Subgroups — C7×#14417 #13191633

Order 1792.

2602 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C2×C7×#386C212yesmaximal, complemented
3C2×C7×#386C212yesmaximal, complemented
4C7×#1445C212yesmaximal, complemented
5C7×#1440C212yesmaximal, complemented
6C7×#1438C212yesmaximal, complemented
7C7×C22⋊#95C211yesmaximal, characteristic, complemented
8C7×C22⋊#95C211yesmaximal, characteristic, complemented
9C7×C22⋊#95C212yesmaximal, complemented
10C23×C7×D4C2212yes—
11C23×C7×D4C2211yescharacteristic
12C24×C4×C7C2212yes—
13C24×C4×C7C2211yescharacteristic
14C2×C7×#121—28no—
15C2×C7×#121C418yescomplemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C7×#386—28no—
25C7×#386—28no—
26C2×C7×#95C2212yes—
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7×#95C2212yes—
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2212yes—
35#14417C711yesmaximal, 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—41no—
43C22×C7×D4—42no—
44C22×C7×D4—41no—
45C22×C7×D4—42no—
46C22×C7×D4—42no—
47C22×C7×D4C2×C414yes—
48C22×C7×D4C2×C418yescomplemented
49C22×C7×D4D418yes—
50C23×C4×C7—24no—
51C23×C4×C7—24no—
52C23×C4×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7—41no—
55C23×C4×C7—41no—
56C23×C4×C7—42no—
57C23×C4×C7—42no—
58C23×C4×C7—42no—
59C23×C4×C7—42no—
60C23×C4×C7—42no—
61C23×C4×C7C2×C414yescomplemented
62C23×C4×C7C2312yes—
63C23×C4×C7C2312yes—
64C23×C4×C7C2312yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2312yes—
67C23×C4×C7C2312yes—
68C23×C4×C7C2311yescharacteristic
69C7×#121—232no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4C2×C414yescomplemented
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—24no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—41no—
83C2×C7×C22⋊C4—41no—
84C2×C7×C22⋊C4—42no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—41no—
90C2×C7×C22⋊C4—41no—
91C2×C7×C22⋊C4C2×C418yescomplemented
92C2×C7×C22⋊C4D414yescomplemented
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—41no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—41no—
101C7×#95—42no—
102C22×#121C2×C711yescharacteristic
103C2×#386C2×C712yescomplemented
104C2×#386C2×C712yescomplemented
105#1445C2×C712yescomplemented
106#1440C2×C712yescomplemented
107#1438C2×C712yescomplemented
108C22⋊#95C2×C711yescharacteristic, complemented
109C22⋊#95C2×C712yescomplemented
110C22⋊#95C2×C711yescharacteristic, complemented
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—22no—
114C24×C7—22no—
115C24×C7—22no—
116C24×C7—22no—
117C24×C7—21no—
118C24×C7—21no—
119C24×C7—21no—
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—21no—
130C24×C7—22no—
131C24×C7C22×C414yes—
132C24×C7C22×C412yes—
133C24×C7C2×D414yes—
134C24×C7C2×D414yes—
135C24×C7C2×D412yes—
136C24×C7#4112yes—
137C24×C7C2411yescharacteristic
138C2×C7×D4—216no—
139C2×C7×D4—216no—
140C2×C7×D4—44no—
141C2×C7×D4—44no—
142C2×C7×D4—48no—
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×D4C22⋊C4116yescomplemented
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
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—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
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—28no—
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—22no—
189C22×C4×C7—22no—
190C22×C4×C7—44no—
191C22×C4×C7—44no—
192C22×C4×C7—48no—
193C22×C4×C7—48no—
194C22×C4×C7—48no—
195C22×C4×C7—48no—
196C22×C4×C7—48no—
197C22×C4×C7—48no—
198C22×C4×C7—48no—
199C22×C4×C7—48no—
200C22×C4×C7—48no—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C22×C414yes—
203C22×C4×C7C22×C412yes—
204C22×C4×C7C2×D414yes—
205C22×C4×C7C2×D414yes—
206C22×C4×C7#4114yes—
207C7×C4⋊C4—28no—
208C7×C22⋊C4—216no—
209C7×C22⋊C4—44no—
210C7×C22⋊C4—48no—
211C7×C22⋊C4—48no—
212C7×C22⋊C4—48no—
213C7×C22⋊C4—48no—
214C7×C22⋊C4—44no—
215C23×D4C22×C712yes—
216C23×D4C22×C711yescharacteristic
217C24×C4C22×C712yes—
218C24×C4C22×C711yescharacteristic
219C2×#121—28no—
220C2×#121C4×C718yescomplemented
221C22×C4⋊C4C22×C711yescharacteristic
222C22×C22⋊C4C22×C712yes—
223C22×C22⋊C4C22×C712yes—
224C22×C22⋊C4C22×C712yes—
225C22×C22⋊C4C22×C712yes—
226C22×C22⋊C4C22×C711yescharacteristic
227C22×C22⋊C4C22×C712yes—
228C22×C22⋊C4C22×C711yescharacteristic
229#386—28no—
230#386—28no—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C711yescharacteristic
236C2×#95C22×C712yes—
237C2×#95C22×C712yes—
238C2×#95C22×C711yescharacteristic
239C2×#95C22×C712yes—
240C23×C7—22no—
241C23×C7—24no—
242C23×C7—24no—
243C23×C7—22no—
244C23×C7—22no—
245C23×C7—22no—
246C23×C7—22no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—24no—
250C23×C7—22no—
251C23×C7—24no—
252C23×C7—24no—
253C23×C7—22no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—24no—
268C23×C7—24no—
269C23×C7—24no—
270C23×C7—24no—
271C23×C7—24no—
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×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7C2×C22⋊C418yes—
297C23×C7C4×D414yes—
298C23×C7C23×C411yescharacteristic
299C23×C7C22×D412yes—
300C23×C7C22×D411yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4112yes—
303C23×C7H(5,𝔽2)11yescharacteristic
304C23×C7H(5,𝔽2)11yescharacteristic
305C23×C7H(5,𝔽2)12yes—
306C23×C7H(5,𝔽2)12yes—
307C23×C7H(5,𝔽2)11yescharacteristic
308C23×C72−1+411yescharacteristic
309C7×D4—416no—
310C7×D4—432no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—22no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
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—24no—
327C2×C4×C7—416no—
328C2×C4×C7—432no—
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×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—42no—
357C2×C4×C7C2×C22⋊C414yes—
358C25C23×C712yes—
359C25C23×C711yescharacteristic
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—41no—
365C22×D4—42no—
366C22×D4—41no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4C2×C4×C714yes—
370C22×D4C2×C4×C718yescomplemented
371C22×D4C7×D418yes—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4C2×C4×C714yescomplemented
384C23×C4C23×C712yes—
385C23×C4C23×C712yes—
386C23×C4C23×C711yescharacteristic
387C23×C4C23×C712yes—
388C23×C4C23×C712yes—
389C23×C4C23×C712yes—
390C23×C4C23×C711yescharacteristic
391#121—232no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4C2×C4×C714yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4C2×C4×C718yescomplemented
414C2×C22⋊C4C7×D414yescomplemented
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—41no—
420#95—42no—
421#95—42no—
422#95—41no—
423#95—42no—
424C22×C7—28no—
425C22×C7—24no—
426C22×C7—24no—
427C22×C7—28no—
428C22×C7—28no—
429C22×C7—24no—
430C22×C7—42no—
431C22×C7—44no—
432C22×C7—42no—
433C22×C7—44no—
434C22×C7—42no—
435C22×C7—44no—
436C22×C7—42no—
437C22×C7—44no—
438C22×C7—44no—
439C22×C7—44no—
440C22×C7—44no—
441C22×C7—44no—
442C22×C7—44no—
443C22×C7—44no—
444C22×C7—44no—
445C22×C7—44no—
446C22×C7—44no—
447C22×C7—44no—
448C22×C7—44no—
449C22×C7—44no—
450C22×C7C22×C22⋊C411yescharacteristic
451C22×C7C2×C4×D411yescharacteristic
452C22×C7C4×#4111yescharacteristic
453C22×C7#51811yescharacteristic
454C22×C7#51811yescharacteristic
455C22×C7#51811yescharacteristic
456C22×C7#52011yescharacteristic
457C22×C7#53412yes—
458C22×C7#53412yes—
459C22×C7#53411yescharacteristic
460C22×C7#53711yescharacteristic
461C22×C7#53811yescharacteristic
462C22×C7#53812yes—
463C22×C7#53911yescharacteristic
464C22×C7#54012yes—
465C22×C7D4212yes—
466C22×C7#54612yes—
467C22×C7#54612yes—
468C22×C7#54612yes—
469C22×C7#54712yes—
470C22×C7#55312yes—
471C22×C7#56012yes—
472C22×C7#56212yes—
473C4×C7—24no—
474C4×C7—42no—
475C4×C7—44no—
476C4×C7—44no—
477C4×C7—44no—
478C4×C7—82no—
479C4×C7—82no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—21no—
499C24—22no—
500C24C22×C4×C714yes—
501C24C22×C4×C712yes—
502C24C2×C7×D414yes—
503C24C2×C7×D414yes—
504C24C2×C7×D412yes—
505C24C7×#4112yes—
506C24C24×C711yescharacteristic
507C2×D4—216no—
508C2×D4—216no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4C7×C22⋊C4116yescomplemented
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
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—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—22no—
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—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4C22×C4×C712yes—
571C22×C4C22×C4×C714yes—
572C22×C4C22×C4×C712yes—
573C22×C4C2×C7×D414yes—
574C22×C4C2×C7×D414yes—
575C22×C4C7×#4114yes—
576C4⋊C4—28no—
577C22⋊C4—216no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—44no—
584C2×C7—48no—
585C2×C7—44no—
586C2×C7#230811yescharacteristic
587C2×C7#232511yescharacteristic
588C2×C7#233311yescharacteristic
589C2×C7D4×C22⋊C411yescharacteristic
590C2×C7#233911yescharacteristic
591C2×C7#236411yescharacteristic
592C2×C7#237711yescharacteristic
593C2×C7#266812yes—
594C2×C7#267112yes—
595C2×C7#268812yes—
596C2×C7#270812yes—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
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—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23C2×C7×C22⋊C418yes—
654C23C4×C7×D414yes—
655C23C23×C4×C711yescharacteristic
656C23C22×C7×D412yes—
657C23C22×C7×D411yescharacteristic
658C23C2×C7×#4111yescharacteristic
659C23C2×C7×#4112yes—
660C23C7×H(5,𝔽2)11yescharacteristic
661C23C7×H(5,𝔽2)11yescharacteristic
662C23C7×H(5,𝔽2)12yes—
663C23C7×H(5,𝔽2)12yes—
664C23C7×H(5,𝔽2)11yescharacteristic
665C23C7×2−1+411yescharacteristic
666D4—416no—
667D4—432no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—416no—
685C2×C4—432no—
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×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4C2×C7×C22⋊C414yes—
715C7#1441711yescharacteristic, direct product factor, Sylow
716C22—28no—
717C22—24no—
718C22—24no—
719C22—28no—
720C22—28no—
721C22—24no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—42no—
735C22—44no—
736C22—42no—
737C22—44no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—44no—
742C22C22×C7×C22⋊C411yescharacteristic
743C22C2×C4×C7×D411yescharacteristic
744C22C4×C7×#4111yescharacteristic
745C22C7×#51811yescharacteristic
746C22C7×#51811yescharacteristic
747C22C7×#51811yescharacteristic
748C22C7×#52011yescharacteristic
749C22C7×#53411yescharacteristic
750C22C7×#53412yes—
751C22C7×#53412yes—
752C22C7×#53711yescharacteristic
753C22C7×#53812yes—
754C22C7×#53811yescharacteristic
755C22C7×#53911yescharacteristic
756C22C7×#54012yes—
757C22C7×D4212yes—
758C22C7×#54612yes—
759C22C7×#54612yes—
760C22C7×#54612yes—
761C22C7×#54712yes—
762C22C7×#55312yes—
763C22C7×#56012yes—
764C22C7×#56212yes—
765C4—24no—
766C4—44no—
767C4—44no—
768C4—42no—
769C4—44no—
770C4—82no—
771C4—82no—
772C2—48no—
773C2—44no—
774C2C7×#230811yescharacteristic
775C2C7×#232511yescharacteristic
776C2C7×#233311yescharacteristic
777C2C7×D4×C22⋊C411yescharacteristic
778C2C7×#233911yescharacteristic
779C2C7×#236411yescharacteristic
780C2C7×#237711yescharacteristic
781C2C7×#266812yes—
782C2C7×#267112yes—
783C2C7×#268812yes—
784C2C7×#270812yes—
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×#386C2semidirect
3. C2×C7×#386C2semidirect
4. C7×#1445C2semidirect
5. C7×#1440C2semidirect
6. C7×#1438C2semidirect
7. C7×C22⋊#95C2semidirect
8. C7×C22⋊#95C2semidirect
9. C7×C22⋊#95C2semidirect
15. C2×C7×#121C4semidirect
35. #14417C7direct (N × H)
48. C22×C7×D4C2×C4semidirect
61. C23×C4×C7C2×C4semidirect
71. C2×C7×C4⋊C4C2×C4semidirect
91. C2×C7×C22⋊C4C2×C4semidirect
92. C2×C7×C22⋊C4D4semidirect
103. C2×#386C2×C7semidirect
104. C2×#386C2×C7semidirect
105. #1445C2×C7semidirect
106. #1440C2×C7semidirect
107. #1438C2×C7semidirect
108. C22⋊#95C2×C7semidirect
109. C22⋊#95C2×C7semidirect
110. C22⋊#95C2×C7semidirect
149. C2×C7×D4C22⋊C4semidirect
220. C2×#121C4×C7semidirect
370. C22×D4C2×C4×C7semidirect
383. C23×C4C2×C4×C7semidirect
393. C2×C4⋊C4C2×C4×C7semidirect
413. C2×C22⋊C4C2×C4×C7semidirect
414. C2×C22⋊C4C7×D4semidirect
518. C2×D4C7×C22⋊C4semidirect
715. C7#14417direct (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×#3862
C7×#14452
C7×#14402
C7×#14382
C7×C22⋊#952
#144177