Finite Group Databasebeta

← C7×#23238 #13200454

Subgroups — C7×#23238 #13200454

Order 1792.

796 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2C7×#1985C211yesmaximal, characteristic, complemented
3C7×#1984C211yesmaximal, characteristic, complemented
4C7×#1917C211yesmaximal, characteristic, complemented
5C7×#1917C211yesmaximal, characteristic, complemented
6C7×#1917C211yesmaximal, characteristic, complemented
7C7×#1916C211yesmaximal, characteristic, complemented
8C7×#1850C211yesmaximal, characteristic
9C7×#1850C211yesmaximal, characteristic
10C7×#1771C211yesmaximal, characteristic, complemented
11C7×#1770C211yesmaximal, characteristic, complemented
12C7×#1752C211yesmaximal, characteristic
13C7×C8×C22⋊C4C211yesmaximal, characteristic
14C7×#1749C211yesmaximal, characteristic
15C2×C7×#336C211yesmaximal, characteristic
16C23×C7×C8C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C7×C22⋊Q8C411yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×C4⋊C8C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×#97C2211yescharacteristic
28C2×C7×#97C2211yescharacteristic
29C2×C7×#97C2211yescharacteristic
30C2×C7×#97C2211yescharacteristic
31C2×C4×C7×C8C2211yescharacteristic
32C2×C4×C7×C8C2211yescharacteristic
33C7×#391C411yescharacteristic
34C7×#389C411yescharacteristic
35C7×#387C411yescharacteristic
36C7×#387C411yescharacteristic
37C7×#385C411yescharacteristic
38C7×#385C411yescharacteristic
39C7×#380C411yescharacteristic
40C4×C7×C4⋊C4C2211yescharacteristic
41C4×C7×C4⋊C4C2211yescharacteristic
42C4×C7×C4⋊C4C2211yescharacteristic
43C4×C7×C22⋊C4C2211yescharacteristic
44C4×C7×C22⋊C4C2211yescharacteristic
45C7×#336C2211yescharacteristic
46C7×#336C2211yescharacteristic
47C7×#336C2211yescharacteristic
48C7×#336C2211yescharacteristic
49C7×#336C2211yescharacteristic
50C7×#336C2211yescharacteristic
51C7×#336C2211yescharacteristic
52C7×#336C2211yescharacteristic
53C7×#336C2211yescharacteristic
54C7×#336C2211yescharacteristic
55C7×#336C2211yescharacteristic
56C7×#336C2211yescharacteristic
57C7×#336C2211yescharacteristic
58C7×#336C2211yescharacteristic
59#23238C711yesmaximal, characteristic, direct product factor, Sylow
60C22×C7×Q8C2×C411yescharacteristic
61C23×C4×C7C2×C411yescharacteristic
62C23×C4×C7C2×C411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C22×C7×C8—22no—
65C22×C7×C8—22no—
66C22×C7×C8—22no—
67C22×C7×C8—22no—
68C22×C7×C8—41no—
69C22×C7×C8—41no—
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C7×C22⋊Q8—24no—
79C4×C7×Q8—41no—
80C4×C7×Q8—41no—
81C2×C7×C4⋊C4C2×C411yescharacteristic
82C2×C7×C4⋊C4C2×C411yescharacteristic
83C2×C7×C4⋊C4C2×C411yescharacteristic
84C2×C7×C4⋊C4C2×C411yescharacteristic
85C2×C7×C4⋊C4C2×C411yescharacteristic
86C2×C7×C4⋊C4C2×C411yescharacteristic
87C2×C7×C4⋊C4C2×C411yescharacteristic
88C2×C7×C4⋊C4C2×C411yescharacteristic
89C2×C7×C4⋊C4C2×C411yescharacteristic
90C2×C7×C22⋊C4C2×C411yescharacteristic
91C2×C7×C22⋊C4C2×C411yescharacteristic
92C2×C7×C22⋊C4C2×C411yescharacteristic
93C2×C7×C22⋊C4C2×C411yescharacteristic
94C2×C42×C7—41no—
95C2×C42×C7—41no—
96C2×C42×C7C2×C411yescharacteristic
97C2×C42×C7C2×C411yescharacteristic
98C2×C42×C7C2311yescharacteristic
99C2×C42×C7C2311yescharacteristic
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C42×C7C2311yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C7×C4⋊C8—22no—
105C7×C4⋊C8—22no—
106C7×C4⋊C8—41no—
107C7×C4⋊C8—41no—
108C7×C22⋊C8—22no—
109C7×C22⋊C8Q814yescomplemented
110C7×#97—22no—
111C7×#97—41no—
112C7×#97—41no—
113C7×#97—41no—
114C4×C7×C8—22no—
115C4×C7×C8—41no—
116C7×#95C2×C411yescharacteristic
117C7×#95C2×C411yescharacteristic
118C7×#95C2×C411yescharacteristic
119C7×#95C2×C411yescharacteristic
120C7×#95C2×C411yescharacteristic
121C7×#95C2×C411yescharacteristic
122C7×#95C2×C411yescharacteristic
123C7×#95C2×C411yescharacteristic
124C7×#95C2×C411yescharacteristic
125C7×#95C2×C411yescharacteristic
126C4×C22⋊Q8C2×C711yescharacteristic
127#1985C2×C711yescharacteristic, complemented
128#1984C2×C711yescharacteristic, complemented
129#1917C2×C711yescharacteristic, complemented
130#1917C2×C711yescharacteristic, complemented
131#1917C2×C711yescharacteristic, complemented
132#1916C2×C711yescharacteristic, complemented
133#1850C2×C711yescharacteristic
134#1850C2×C711yescharacteristic
135#1771C2×C711yescharacteristic, complemented
136#1770C2×C711yescharacteristic, complemented
137#1752C2×C711yescharacteristic
138C8×C22⋊C4C2×C711yescharacteristic
139#1749C2×C711yescharacteristic
140C2×#336C2×C711yescharacteristic
141C24×C7C22×C411yescharacteristic
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8—41no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—41no—
153C22×C4×C7—41no—
154C22×C4×C7—41no—
155C22×C4×C7C22×C411yescharacteristic
156C22×C4×C7C22×C411yescharacteristic
157C22×C4×C7C22×C411yescharacteristic
158C22×C4×C7C22×C411yescharacteristic
159C22×C4×C7C22×C411yescharacteristic
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C22×C411yescharacteristic
162C22×C4×C7C22×C411yescharacteristic
163C22×C4×C7C22×C411yescharacteristic
164C22×C4×C7C22×C411yescharacteristic
165C22×C4×C7C22×C411yescharacteristic
166C22×C4×C7C22×C411yescharacteristic
167C22×C4×C7C22×C411yescharacteristic
168C22×C4×C7C2×Q812yes—
169C22×C4×C7#4112yes—
170C22×C4×C7C2411yescharacteristic
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—44no—
192C2×C7×C8—44no—
193C2×C7×C8C2×Q812yes—
194C2×C7×C8C2×Q812yes—
195C2×C7×C8#4112yes—
196C2×C7×C8#4112yes—
197C7×C4⋊C4—22no—
198C7×C4⋊C4—22no—
199C7×C4⋊C4—22no—
200C7×C4⋊C4—22no—
201C7×C4⋊C4—41no—
202C7×C4⋊C4—41no—
203C7×C4⋊C4—41no—
204C7×C4⋊C4—41no—
205C7×C4⋊C4—41no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4—22no—
209C7×C22⋊C4M1614yes—
210C42×C7—21no—
211C42×C7—21no—
212C42×C7—21no—
213C42×C7—21no—
214C42×C7—21no—
215C42×C7—21no—
216C42×C7—21no—
217C42×C7—21no—
218C42×C7—21no—
219C42×C7—21no—
220C42×C7—21no—
221C42×C7—21no—
222C42×C7—41no—
223C42×C7—41no—
224C23×C8C22×C711yescharacteristic
225C23×C8C22×C711yescharacteristic
226C2×C22⋊Q8C4×C711yescharacteristic
227C2×C4×Q8C22×C711yescharacteristic
228C22×C42C22×C711yescharacteristic
229C2×C4⋊C8C22×C711yescharacteristic
230C2×C4⋊C8C22×C711yescharacteristic
231C2×C4⋊C8C22×C711yescharacteristic
232C2×C4⋊C8C22×C711yescharacteristic
233C2×C22⋊C8C22×C711yescharacteristic
234C2×C22⋊C8C22×C711yescharacteristic
235C2×#97C22×C711yescharacteristic
236C2×#97C22×C711yescharacteristic
237C2×#97C22×C711yescharacteristic
238C2×#97C22×C711yescharacteristic
239C2×C4×C8C22×C711yescharacteristic
240C2×C4×C8C22×C711yescharacteristic
241#391C4×C711yescharacteristic
242#389C4×C711yescharacteristic
243#387C4×C711yescharacteristic
244#387C4×C711yescharacteristic
245#385C4×C711yescharacteristic
246#385C4×C711yescharacteristic
247#380C4×C711yescharacteristic
248C4×C4⋊C4C22×C711yescharacteristic
249C4×C4⋊C4C22×C711yescharacteristic
250C4×C4⋊C4C22×C711yescharacteristic
251C4×C22⋊C4C22×C711yescharacteristic
252C4×C22⋊C4C22×C711yescharacteristic
253#336C22×C711yescharacteristic
254#336C22×C711yescharacteristic
255#336C22×C711yescharacteristic
256#336C22×C711yescharacteristic
257#336C22×C711yescharacteristic
258#336C22×C711yescharacteristic
259#336C22×C711yescharacteristic
260#336C22×C711yescharacteristic
261#336C22×C711yescharacteristic
262#336C22×C711yescharacteristic
263#336C22×C711yescharacteristic
264#336C22×C711yescharacteristic
265#336C22×C711yescharacteristic
266#336C22×C711yescharacteristic
267C23×C7—21no—
268C23×C7—21no—
269C23×C7—21no—
270C23×C7—21no—
271C23×C7C4×Q812yes—
272C23×C7C2×M1612yes—
273C23×C7#13112yes—
274C23×C7C23×C411yescharacteristic
275C7×Q8—44no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—44no—
316C2×C4×C7—44no—
317C2×C4×C7C4×Q812yes—
318C2×C4×C7C2×M1612yes—
319C2×C4×C7C2×M1612yes—
320C2×C4×C7#13112yes—
321C2×C4×C7C22×Q811yescharacteristic
322C2×C4×C7C2×#4111yescharacteristic
323C2×C4×C7C2×#4111yescharacteristic
324C2×C4×C7C2×#4111yescharacteristic
325C2×C4×C7H(5,𝔽2)11yescharacteristic
326C2×C4×C7H(5,𝔽2)11yescharacteristic
327C7×C8—22no—
328C7×C8—22no—
329C7×C8—22no—
330C7×C8—22no—
331C7×C8—41no—
332C7×C8—41no—
333C7×C8—41no—
334C7×C8—41no—
335C22×Q8C2×C4×C711yescharacteristic
336C23×C4C2×C4×C711yescharacteristic
337C23×C4C2×C4×C711yescharacteristic
338C23×C4C23×C711yescharacteristic
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—41no—
344C22×C8—41no—
345C22×C8C23×C711yescharacteristic
346C22×C8C23×C711yescharacteristic
347C22×C8C23×C711yescharacteristic
348C22×C8C23×C711yescharacteristic
349C22×C8C23×C711yescharacteristic
350C22×C8C23×C711yescharacteristic
351C22×C8C23×C711yescharacteristic
352C22×C8C23×C711yescharacteristic
353C22⋊Q8—24no—
354C4×Q8—41no—
355C4×Q8—41no—
356C2×C4⋊C4C2×C4×C711yescharacteristic
357C2×C4⋊C4C2×C4×C711yescharacteristic
358C2×C4⋊C4C2×C4×C711yescharacteristic
359C2×C4⋊C4C2×C4×C711yescharacteristic
360C2×C4⋊C4C2×C4×C711yescharacteristic
361C2×C4⋊C4C2×C4×C711yescharacteristic
362C2×C4⋊C4C2×C4×C711yescharacteristic
363C2×C4⋊C4C2×C4×C711yescharacteristic
364C2×C4⋊C4C2×C4×C711yescharacteristic
365C2×C22⋊C4C2×C4×C711yescharacteristic
366C2×C22⋊C4C2×C4×C711yescharacteristic
367C2×C22⋊C4C2×C4×C711yescharacteristic
368C2×C22⋊C4C2×C4×C711yescharacteristic
369C2×C42—41no—
370C2×C42—41no—
371C2×C42C2×C4×C711yescharacteristic
372C2×C42C2×C4×C711yescharacteristic
373C2×C42C23×C711yescharacteristic
374C2×C42C23×C711yescharacteristic
375C2×C42C23×C711yescharacteristic
376C2×C42C23×C711yescharacteristic
377C2×C42C23×C711yescharacteristic
378C2×C42C23×C711yescharacteristic
379C4⋊C8—22no—
380C4⋊C8—22no—
381C4⋊C8—41no—
382C4⋊C8—41no—
383C22⋊C8—22no—
384C22⋊C8C7×Q814yescomplemented
385#97—22no—
386#97—41no—
387#97—41no—
388#97—41no—
389C4×C8—22no—
390C4×C8—41no—
391#95C2×C4×C711yescharacteristic
392#95C2×C4×C711yescharacteristic
393#95C2×C4×C711yescharacteristic
394#95C2×C4×C711yescharacteristic
395#95C2×C4×C711yescharacteristic
396#95C2×C4×C711yescharacteristic
397#95C2×C4×C711yescharacteristic
398#95C2×C4×C711yescharacteristic
399#95C2×C4×C711yescharacteristic
400#95C2×C4×C711yescharacteristic
401C22×C7—22no—
402C22×C7—22no—
403C22×C7—22no—
404C22×C7—22no—
405C22×C7—22no—
406C22×C7—22no—
407C22×C7#44614yes—
408C22×C7C2×C4×Q811yescharacteristic
409C22×C7C4×#4111yescharacteristic
410C22×C7#51811yescharacteristic
411C22×C7C22×M1611yescharacteristic
412C22×C7C2×#13111yescharacteristic
413C22×C7C2×#13111yescharacteristic
414C22×C7#56811yescharacteristic
415C4×C7—22no—
416C4×C7—22no—
417C4×C7—22no—
418C4×C7—22no—
419C4×C7—41no—
420C4×C7—41no—
421C4×C7—41no—
422C4×C7—41no—
423C4×C7—41no—
424C4×C7—41no—
425C4×C7—41no—
426C4×C7—41no—
427C4×C7—41no—
428C4×C7#55111yescharacteristic
429C4×C7#55111yescharacteristic
430C4×C7#55411yescharacteristic
431C4×C7#55411yescharacteristic
432C24C22×C4×C711yescharacteristic
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—41no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C22×C4×C711yescharacteristic
447C22×C4C22×C4×C711yescharacteristic
448C22×C4C22×C4×C711yescharacteristic
449C22×C4C22×C4×C711yescharacteristic
450C22×C4C22×C4×C711yescharacteristic
451C22×C4C22×C4×C711yescharacteristic
452C22×C4C22×C4×C711yescharacteristic
453C22×C4C22×C4×C711yescharacteristic
454C22×C4C22×C4×C711yescharacteristic
455C22×C4C22×C4×C711yescharacteristic
456C22×C4C22×C4×C711yescharacteristic
457C22×C4C22×C4×C711yescharacteristic
458C22×C4C22×C4×C711yescharacteristic
459C22×C4C2×C7×Q812yes—
460C22×C4C7×#4112yes—
461C22×C4C24×C711yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—44no—
483C2×C8—44no—
484C2×C8C2×C7×Q812yes—
485C2×C8C2×C7×Q812yes—
486C2×C8C7×#4112yes—
487C2×C8C7×#4112yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4C7×M1614yes—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42—41no—
515C2×C7—24no—
516C2×C7#236811yescharacteristic
517C2×C7C2×#44611yescharacteristic
518C2×C7#296211yescharacteristic
519C2×C7#296611yescharacteristic
520C2×C7#297011yescharacteristic
521C2×C7#297411yescharacteristic
522C2×C7#297611yescharacteristic
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C4×C7×Q812yes—
528C23C2×C7×M1612yes—
529C23C7×#13112yes—
530C23C23×C4×C711yescharacteristic
531Q8—44no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4C4×C7×Q812yes—
574C2×C4C2×C7×M1612yes—
575C2×C4C2×C7×M1612yes—
576C2×C4C7×#13112yes—
577C2×C4C22×C7×Q811yescharacteristic
578C2×C4C2×C7×#4111yescharacteristic
579C2×C4C2×C7×#4111yescharacteristic
580C2×C4C2×C7×#4111yescharacteristic
581C2×C4C7×H(5,𝔽2)11yescharacteristic
582C2×C4C7×H(5,𝔽2)11yescharacteristic
583C8—22no—
584C8—22no—
585C8—22no—
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C7#2323811yescharacteristic, direct product factor, Sylow
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22C7×#44614yes—
599C22C2×C4×C7×Q811yescharacteristic
600C22C4×C7×#4111yescharacteristic
601C22C7×#51811yescharacteristic
602C22C22×C7×M1611yescharacteristic
603C22C2×C7×#13111yescharacteristic
604C22C2×C7×#13111yescharacteristic
605C22C7×#56811yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4C7×#55111yescharacteristic
620C4C7×#55111yescharacteristic
621C4C7×#55411yescharacteristic
622C4C7×#55411yescharacteristic
623C2—24no—
624C2C7×#236811yescharacteristic
625C2C2×C7×#44611yescharacteristic
626C2C7×#296211yescharacteristic
627C2C7×#296611yescharacteristic
628C2C7×#297011yescharacteristic
629C2C7×#297411yescharacteristic
630C2C7×#297611yescharacteristic
subgroupG/H
centerC22×C4×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC22×C4C24×C7
socleC23×C7C23×C4
prime radicalC24×C7C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#1985C2semidirect
3. C7×#1984C2semidirect
4. C7×#1917C2semidirect
5. C7×#1917C2semidirect
6. C7×#1917C2semidirect
7. C7×#1916C2semidirect
10. C7×#1771C2semidirect
11. C7×#1770C2semidirect
59. #23238C7direct (N × H)
109. C7×C22⋊C8Q8semidirect
127. #1985C2×C7semidirect
128. #1984C2×C7semidirect
129. #1917C2×C7semidirect
130. #1917C2×C7semidirect
131. #1917C2×C7semidirect
132. #1916C2×C7semidirect
135. #1771C2×C7semidirect
136. #1770C2×C7semidirect
384. C22⋊C8C7×Q8semidirect
591. C7#23238direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊Q82
C7×#19852
C7×#19842
C7×#19172
C7×#19162
C7×#18502
C7×#17712
C7×#17702
C7×#17522
C7×C8×C22⋊C42
C7×#17492
C2×C7×#3362
#232387