Finite Group Databasebeta

← C7×#14043 #13191259

Subgroups — C7×#14043 #13191259

Order 1792.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C4⋊C4C211yesmaximal, characteristic
2C2×C7×#389C212yesmaximal, complemented
3C2×C7×#385C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
7C7×#1444C212yesmaximal, complemented
8C7×#1441C212yesmaximal, complemented
9C7×#1436C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic
11C7×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4—24no—
16C22×C7×C4⋊C4—28no—
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C4⋊C4C2212yes—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2212yes—
28C7×#389—28no—
29C7×#385—24no—
30C7×#385—24no—
31C7×#385C418yescomplemented
32C4×C7×C22⋊C4—24no—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42#14043C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7C2311yescharacteristic
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—24no—
47C23×C4×C7—24no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—24no—
52C23×C4×C7—24no—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—42no—
56C23×C4×C7—42no—
57C23×C4×C7C2×C414yes—
58C23×C4×C7D414yes—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2312yes—
65C23×C4×C7C2312yes—
66C23×C4×C7C2312yes—
67C23×C4×C7C2312yes—
68C23×C4×C7C2311yescharacteristic
69C2×C7×C4⋊C4—232no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—24no—
82C2×C7×C4⋊C4—42no—
83C2×C7×C4⋊C4—42no—
84C2×C7×C4⋊C4C2×C418yescomplemented
85C2×C7×C4⋊C4D418yes—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4C2×C414yes—
94C2×C7×C22⋊C4C2×C414yes—
95C2×C7×C22⋊C4D414yes—
96C2×C7×C22⋊C4Q814yes—
97C2×C7×C22⋊C4Q814yes—
98C2×C42×C7—24no—
99C2×C42×C7—24no—
100C2×C42×C7—42no—
101C7×#95—24no—
102C7×#95—22no—
103C7×#95—22no—
104C7×#95—24no—
105C7×#95—24no—
106C7×#95—24no—
107C7×#95—24no—
108C7×#95—42no—
109C7×#95C2×C418yescomplemented
110C23×C4⋊C4C2×C711yescharacteristic
111C2×#389C2×C712yescomplemented
112C2×#385C2×C711yescharacteristic
113C2×#385C2×C711yescharacteristic
114C2×#385C2×C711yescharacteristic
115C2×C4×C22⋊C4C2×C711yescharacteristic
116#1444C2×C712yescomplemented
117#1441C2×C712yescomplemented
118#1436C2×C712yescomplemented
119C22⋊#95C2×C711yescharacteristic
120C22⋊#95C2×C711yescharacteristic
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7C22×C412yes—
126C24×C7C2×D412yes—
127C24×C7C2×D412yes—
128C24×C7C2×Q812yes—
129C24×C7C2×Q812yes—
130C24×C7#4112yes—
131C24×C7#4112yes—
132C24×C7C2411yescharacteristic
133C22×C4×C7—28no—
134C22×C4×C7—216no—
135C22×C4×C7—28no—
136C22×C4×C7—28no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—216no—
149C22×C4×C7—28no—
150C22×C4×C7—28no—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
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—21no—
163C22×C4×C7—21no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
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—21no—
177C22×C4×C7—21no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—44no—
187C22×C4×C7—48no—
188C22×C4×C7—48no—
189C22×C4×C7—48no—
190C22×C4×C7—48no—
191C22×C4×C7—44no—
192C22×C4×C7—44no—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C22×C412yes—
195C22×C4×C7C22×C414yes—
196C22×C4×C7C22×C414yes—
197C22×C4×C7C2×D412yes—
198C22×C4×C7C2×D414yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D414yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D414yes—
203C22×C4×C7C2×Q814yes—
204C22×C4×C7C2×Q814yes—
205C22×C4×C7#4114yes—
206C7×C4⋊C4—216no—
207C7×C4⋊C4—216no—
208C7×C4⋊C4—216no—
209C7×C4⋊C4—48no—
210C7×C4⋊C4—44no—
211C7×C4⋊C4—44no—
212C7×C22⋊C4—28no—
213C7×C22⋊C4—28no—
214C7×C22⋊C4—44no—
215C7×C22⋊C4C4⋊C4116yescomplemented
216C42×C7—48no—
217C24×C4C22×C711yescharacteristic
218C24×C4C22×C711yescharacteristic
219C24×C4C22×C711yescharacteristic
220C22×C4⋊C4—24no—
221C22×C4⋊C4—28no—
222C22×C4⋊C4C22×C712yes—
223C22×C4⋊C4C22×C711yescharacteristic
224C22×C4⋊C4C22×C712yes—
225C22×C4⋊C4C22×C712yes—
226C22×C4⋊C4C22×C712yes—
227C22×C4⋊C4C22×C711yescharacteristic
228C22×C22⋊C4C22×C711yescharacteristic
229C22×C22⋊C4C22×C711yescharacteristic
230C22×C22⋊C4C22×C711yescharacteristic
231C22×C22⋊C4C22×C711yescharacteristic
232C22×C42C22×C712yes—
233#389—28no—
234#385—24no—
235#385—24no—
236#385C4×C718yescomplemented
237C4×C22⋊C4—24no—
238C2×#95C22×C712yes—
239C2×#95C22×C712yes—
240C2×#95C22×C712yes—
241C2×#95C22×C711yescharacteristic
242C2×#95C22×C712yes—
243C2×#95C22×C711yescharacteristic
244C2×#95C22×C712yes—
245C2×#95C22×C712yes—
246C2×#95C22×C712yes—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7—22no—
250C23×C7—22no—
251C23×C7—24no—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—24no—
258C23×C7—24no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7C2×C4⋊C414yes—
264C23×C7C4×D414yes—
265C23×C7C4×Q814yes—
266C23×C7#12114yes—
267C23×C7C22⋊Q814yes—
268C23×C7#12514yes—
269C23×C7C4⋊Q814yes—
270C23×C7C23×C411yescharacteristic
271C23×C7C22×D411yescharacteristic
272C23×C7C22×D411yescharacteristic
273C23×C7C22×D412yes—
274C23×C7C22×Q811yescharacteristic
275C23×C7C22×Q811yescharacteristic
276C23×C7C2×#4111yescharacteristic
277C23×C7C2×#4112yes—
278C23×C7C2×#4111yescharacteristic
279C23×C7H(5,𝔽2)12yes—
280C23×C72−1+412yes—
281C2×C4×C7—232no—
282C2×C4×C7—24no—
283C2×C4×C7—24no—
284C2×C4×C7—24no—
285C2×C4×C7—24no—
286C2×C4×C7—24no—
287C2×C4×C7—22no—
288C2×C4×C7—24no—
289C2×C4×C7—24no—
290C2×C4×C7—24no—
291C2×C4×C7—22no—
292C2×C4×C7—24no—
293C2×C4×C7—24no—
294C2×C4×C7—24no—
295C2×C4×C7—24no—
296C2×C4×C7—24no—
297C2×C4×C7—24no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—22no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
305C2×C4×C7—24no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—416no—
312C2×C4×C7—416no—
313C2×C4×C7—41no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—41no—
317C2×C4×C7—42no—
318C2×C4×C7—41no—
319C2×C4×C7—42no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7C2×C4⋊C418yescomplemented
340C2×C4×C7C4×D418yes—
341C2×C4×C7#12014yes—
342C25C23×C711yescharacteristic
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4C2×C4×C714yes—
357C23×C4C7×D414yes—
358C23×C4C23×C711yescharacteristic
359C23×C4C23×C711yescharacteristic
360C23×C4C23×C711yescharacteristic
361C23×C4C23×C711yescharacteristic
362C23×C4C23×C711yescharacteristic
363C23×C4C23×C712yes—
364C23×C4C23×C712yes—
365C23×C4C23×C712yes—
366C23×C4C23×C712yes—
367C23×C4C23×C711yescharacteristic
368C2×C4⋊C4—232no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4C2×C4×C718yescomplemented
384C2×C4⋊C4C7×D418yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4C2×C4×C714yes—
393C2×C22⋊C4C2×C4×C714yes—
394C2×C22⋊C4C7×D414yes—
395C2×C22⋊C4C7×Q814yes—
396C2×C22⋊C4C7×Q814yes—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400#95—24no—
401#95—22no—
402#95—22no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95C2×C4×C718yescomplemented
409C22×C7—24no—
410C22×C7—24no—
411C22×C7—28no—
412C22×C7—28no—
413C22×C7—24no—
414C22×C7—24no—
415C22×C7—24no—
416C22×C7—28no—
417C22×C7—28no—
418C22×C7—24no—
419C22×C7#38918yescomplemented
420C22×C7C22×C4⋊C411yescharacteristic
421C22×C7C2×C4×D411yescharacteristic
422C22×C7C2×C4×D412yes—
423C22×C7C2×C4×Q811yescharacteristic
424C22×C7#52012yes—
425C22×C7C2×#12011yescharacteristic
426C22×C7C2×#12111yescharacteristic
427C22×C7C2×C22⋊Q811yescharacteristic
428C22×C7#52511yescharacteristic
429C22×C7#52512yes—
430C22×C7C2×#12511yescharacteristic
431C22×C7C2×C4⋊Q811yescharacteristic
432C22×C7#53411yescharacteristic
433C22×C7#53611yescharacteristic
434C22×C7#53912yes—
435C22×C7D4212yes—
436C22×C7#54612yes—
437C22×C7#54712yes—
438C22×C7D4×Q812yes—
439C22×C7D4×Q812yes—
440C22×C7#55212yes—
441C22×C7#55412yes—
442C22×C7#55412yes—
443C4×C7—28no—
444C4×C7—24no—
445C4×C7—28no—
446C4×C7—42no—
447C4×C7—42no—
448C4×C7—44no—
449C4×C7—44no—
450C4×C7—42no—
451C4×C7—81no—
452C4×C7—81no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22×C4×C712yes—
458C24C2×C7×D412yes—
459C24C2×C7×D412yes—
460C24C2×C7×Q812yes—
461C24C2×C7×Q812yes—
462C24C7×#4112yes—
463C24C7×#4112yes—
464C24C24×C711yescharacteristic
465C22×C4—28no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4C22×C4×C712yes—
526C22×C4C22×C4×C712yes—
527C22×C4C22×C4×C714yes—
528C22×C4C22×C4×C714yes—
529C22×C4C2×C7×D412yes—
530C22×C4C2×C7×D414yes—
531C22×C4C2×C7×D414yes—
532C22×C4C2×C7×D414yes—
533C22×C4C2×C7×D412yes—
534C22×C4C2×C7×D414yes—
535C22×C4C2×C7×Q814yes—
536C22×C4C2×C7×Q814yes—
537C22×C4C7×#4114yes—
538C4⋊C4—216no—
539C4⋊C4—216no—
540C4⋊C4—216no—
541C4⋊C4—48no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C22⋊C4—28no—
545C22⋊C4—28no—
546C22⋊C4—44no—
547C22⋊C4C7×C4⋊C4116yescomplemented
548C42—48no—
549C2×C7—28no—
550C2×C7C2×#38911yescharacteristic
551C2×C7C4×#12011yescharacteristic
552C2×C7#232211yescharacteristic
553C2×C7D4×C4⋊C412yes—
554C2×C7#236012yes—
555C2×C7#241011yescharacteristic
556C2×C7#241311yescharacteristic
557C2×C7#243411yescharacteristic
558C2×C7#244912yes—
559C2×C7#247312yes—
560C2×C7#258311yescharacteristic
561C23—24no—
562C23—24no—
563C23—22no—
564C23—22no—
565C23—24no—
566C23—22no—
567C23—22no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23C2×C7×C4⋊C414yes—
578C23C4×C7×D414yes—
579C23C4×C7×Q814yes—
580C23C7×#12114yes—
581C23C7×C22⋊Q814yes—
582C23C7×#12514yes—
583C23C7×C4⋊Q814yes—
584C23C23×C4×C711yescharacteristic
585C23C22×C7×D411yescharacteristic
586C23C22×C7×D411yescharacteristic
587C23C22×C7×D412yes—
588C23C22×C7×Q811yescharacteristic
589C23C22×C7×Q811yescharacteristic
590C23C2×C7×#4111yescharacteristic
591C23C2×C7×#4112yes—
592C23C2×C7×#4111yescharacteristic
593C23C7×H(5,𝔽2)12yes—
594C23C7×2−1+412yes—
595C2×C4—232no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—416no—
626C2×C4—416no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4C2×C7×C4⋊C418yescomplemented
654C2×C4C4×C7×D418yes—
655C2×C4C7×#12014yes—
656C7#1404311yescharacteristic, direct product factor, Sylow
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—28no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22C7×#38918yescomplemented
668C22C22×C7×C4⋊C411yescharacteristic
669C22C2×C4×C7×D411yescharacteristic
670C22C2×C4×C7×D412yes—
671C22C2×C4×C7×Q811yescharacteristic
672C22C7×#52012yes—
673C22C2×C7×#12011yescharacteristic
674C22C2×C7×#12111yescharacteristic
675C22C2×C7×C22⋊Q811yescharacteristic
676C22C7×#52511yescharacteristic
677C22C7×#52512yes—
678C22C2×C7×#12511yescharacteristic
679C22C2×C7×C4⋊Q811yescharacteristic
680C22C7×#53411yescharacteristic
681C22C7×#53611yescharacteristic
682C22C7×#53912yes—
683C22C7×D4212yes—
684C22C7×#54612yes—
685C22C7×#54712yes—
686C22C7×D4×Q812yes—
687C22C7×D4×Q812yes—
688C22C7×#55212yes—
689C22C7×#55412yes—
690C22C7×#55412yes—
691C4—24no—
692C4—28no—
693C4—28no—
694C4—42no—
695C4—44no—
696C4—44no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C2—28no—
702C2C2×C7×#38911yescharacteristic
703C2C4×C7×#12011yescharacteristic
704C2C7×#232211yescharacteristic
705C2C7×D4×C4⋊C412yes—
706C2C7×#236012yes—
707C2C7×#241011yescharacteristic
708C2C7×#241311yescharacteristic
709C2C7×#243411yescharacteristic
710C2C7×#244912yes—
711C2C7×#247312yes—
712C2C7×#258311yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#389C2semidirect
7. C7×#1444C2semidirect
8. C7×#1441C2semidirect
9. C7×#1436C2semidirect
31. C7×#385C4semidirect
42. #14043C7direct (N × H)
84. C2×C7×C4⋊C4C2×C4semidirect
109. C7×#95C2×C4semidirect
111. C2×#389C2×C7semidirect
116. #1444C2×C7semidirect
117. #1441C2×C7semidirect
118. #1436C2×C7semidirect
215. C7×C22⋊C4C4⋊C4semidirect
236. #385C4×C7semidirect
339. C2×C4×C7C2×C4⋊C4semidirect
383. C2×C4⋊C4C2×C4×C7semidirect
408. #95C2×C4×C7semidirect
419. C22×C7#389semidirect
547. C22⋊C4C7×C4⋊C4semidirect
653. C2×C4C2×C7×C4⋊C4semidirect
656. C7#14043direct (N × H)
667. C22C7×#389semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C4⋊C42
C2×C7×#3892
C2×C7×#3852
C2×C4×C7×C22⋊C42
C7×#14442
C7×#14412
C7×#14362
C7×C22⋊#952
#140437