Finite Group Databasebeta

← C7×#23319 #13200535

Subgroups — C7×#23319 #13200535

Order 1792.

706 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2395C211yesmaximal, characteristic
2C7×#1954C211yesmaximal, characteristic
3C7×#1940C211yesmaximal, characteristic, complemented
4C7×#1939C211yesmaximal, characteristic, complemented
5C7×#1924C211yesmaximal, characteristic, complemented
6C7×#1924C211yesmaximal, characteristic, complemented
7C7×#1923C211yesmaximal, characteristic, complemented
8C7×#1923C211yesmaximal, characteristic, complemented
9C7×#1916C211yesmaximal, characteristic, complemented
10C7×#1916C211yesmaximal, characteristic, complemented
11C7×#1869C211yesmaximal, characteristic
12C7×#1850C211yesmaximal, characteristic, complemented
13C7×#1850C211yesmaximal, characteristic, complemented
14C7×#1798C211yesmaximal, characteristic, complemented
15C7×#1798C211yesmaximal, characteristic, complemented
16C23×C7×C8C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C7×#117C2211yescharacteristic
19C2×C7×C4⋊C8C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×C4⋊C8C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×C4⋊C8C2211yescharacteristic
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×C22⋊C8C2211yescharacteristic
28C2×C7×C22⋊C8C2211yescharacteristic
29C2×C7×C22⋊C8C2211yescharacteristic
30C2×C7×C22⋊C8C2211yescharacteristic
31C2×C7×C22⋊C8C2211yescharacteristic
32C2×C7×C22⋊C8C2211yescharacteristic
33C2×C7×#97C2211yescharacteristic
34C2×C4×C7×C8C2211yescharacteristic
35C2×C4×C7×C8C2211yescharacteristic
36C7×#400C411yescharacteristic
37C7×#399C411yescharacteristic
38C7×#398C411yescharacteristic
39C7×#397C411yescharacteristic
40C7×#397C411yescharacteristic
41C7×#397C411yescharacteristic
42C7×#394C411yescharacteristic
43C7×#394C411yescharacteristic
44C4×C7×C4⋊C4C2211yescharacteristic
45C4×C7×C4⋊C4C2211yescharacteristic
46C4×C7×C22⋊C4C2211yescharacteristic
47C4×C7×C22⋊C4C2211yescharacteristic
48C4×C7×C22⋊C4C2211yescharacteristic
49C7×#336C2211yescharacteristic
50C7×#336C2211yescharacteristic
51C7×#336C2211yescharacteristic
52C7×#336C2211yescharacteristic
53C7×#336C2211yescharacteristic
54C7×#336C2211yescharacteristic
55C7×#336C2211yescharacteristic
56C7×#336C2211yescharacteristic
57C7×#336C2211yescharacteristic
58C7×#336C2211yescharacteristic
59#23319C711yesmaximal, characteristic, direct product factor, Sylow
60C22×C7×D4C2×C411yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C22×C7×C8—41no—
64C22×C7×C8—41no—
65C22×C7×C8—41no—
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C22×C7×C8C2311yescharacteristic
71C22×C7×C8C2311yescharacteristic
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C4×C7×D4—41no—
75C4×C7×D4—41no—
76C7×#117—41no—
77C7×#117—41no—
78C2×C7×C4⋊C4C2×C411yescharacteristic
79C2×C7×C4⋊C4C2×C411yescharacteristic
80C2×C7×C4⋊C4C2×C411yescharacteristic
81C2×C7×C4⋊C4C2×C411yescharacteristic
82C2×C7×C4⋊C4C2×C411yescharacteristic
83C2×C7×C4⋊C4C2×C411yescharacteristic
84C2×C7×C4⋊C4C2×C411yescharacteristic
85C2×C7×C22⋊C4C2×C411yescharacteristic
86C2×C7×C22⋊C4C2×C411yescharacteristic
87C2×C7×C22⋊C4C2×C411yescharacteristic
88C2×C7×C22⋊C4C2×C411yescharacteristic
89C2×C7×C22⋊C4C2×C411yescharacteristic
90C2×C7×C22⋊C4C2×C411yescharacteristic
91C2×C7×C22⋊C4C2×C411yescharacteristic
92C2×C7×C22⋊C4C2×C411yescharacteristic
93C2×C7×C22⋊C4C2×C411yescharacteristic
94C2×C7×C22⋊C4C2×C411yescharacteristic
95C2×C42×C7C2311yescharacteristic
96C2×C42×C7C2311yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C42×C7C2311yescharacteristic
99C2×C42×C7C2311yescharacteristic
100C7×C4⋊C8—41no—
101C7×C4⋊C8—41no—
102C7×C4⋊C8—41no—
103C7×C4⋊C8—41no—
104C7×C4⋊C8—41no—
105C7×C4⋊C8—41no—
106C7×C4⋊C8—41no—
107C7×C22⋊C8—41no—
108C7×C22⋊C8—41no—
109C7×C22⋊C8—41no—
110C7×C22⋊C8—41no—
111C7×C22⋊C8—41no—
112C7×C22⋊C8—41no—
113C7×C22⋊C8—41no—
114C7×#97—41no—
115C4×C7×C8—41no—
116C4×C7×C8—41no—
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
126C7×#95C2×C411yescharacteristic
127#2395C2×C711yescharacteristic
128#1954C2×C711yescharacteristic
129#1940C2×C711yescharacteristic, complemented
130#1939C2×C711yescharacteristic, complemented
131#1924C2×C711yescharacteristic, complemented
132#1924C2×C711yescharacteristic, complemented
133#1923C2×C711yescharacteristic, complemented
134#1923C2×C711yescharacteristic, complemented
135#1916C2×C711yescharacteristic, complemented
136#1916C2×C711yescharacteristic, complemented
137#1869C2×C711yescharacteristic
138#1850C2×C711yescharacteristic, complemented
139#1850C2×C711yescharacteristic, complemented
140#1798C2×C711yescharacteristic, complemented
141#1798C2×C711yescharacteristic, complemented
142C24×C7C22×C411yescharacteristic
143C24×C7C22×C411yescharacteristic
144C2×C7×D4—22no—
145C2×C7×D4—22no—
146C2×C7×D4—41no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
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×C7C22×C411yescharacteristic
169C22×C4×C7C22×C411yescharacteristic
170C22×C4×C7C22×C411yescharacteristic
171C22×C4×C7C2411yescharacteristic
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—21no—
192C2×C7×C8—21no—
193C2×C7×C8—21no—
194C2×C7×C8—21no—
195C2×C7×C8—21no—
196C2×C7×C8—44no—
197C7×C4⋊C4—22no—
198C7×C4⋊C4—22no—
199C7×C4⋊C4—22no—
200C7×C4⋊C4—41no—
201C7×C4⋊C4—41no—
202C7×C4⋊C4—41no—
203C7×C4⋊C4—41no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—22no—
208C7×C22⋊C4—41no—
209C7×C22⋊C4—41no—
210C7×C22⋊C4—41no—
211C7×C22⋊C4—41no—
212C7×C22⋊C4—41no—
213C7×C22⋊C4—41no—
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—21no—
223C42×C7—21no—
224C23×C8C22×C711yescharacteristic
225C2×C4×D4C22×C711yescharacteristic
226C2×#117C22×C711yescharacteristic
227C2×C4⋊C8C22×C711yescharacteristic
228C2×C4⋊C8C22×C711yescharacteristic
229C2×C4⋊C8C22×C711yescharacteristic
230C2×C4⋊C8C22×C711yescharacteristic
231C2×C4⋊C8C22×C711yescharacteristic
232C2×C4⋊C8C22×C711yescharacteristic
233C2×C4⋊C8C22×C711yescharacteristic
234C2×C22⋊C8C22×C711yescharacteristic
235C2×C22⋊C8C22×C711yescharacteristic
236C2×C22⋊C8C22×C711yescharacteristic
237C2×C22⋊C8C22×C711yescharacteristic
238C2×C22⋊C8C22×C711yescharacteristic
239C2×C22⋊C8C22×C711yescharacteristic
240C2×C22⋊C8C22×C711yescharacteristic
241C2×#97C22×C711yescharacteristic
242C2×C4×C8C22×C711yescharacteristic
243C2×C4×C8C22×C711yescharacteristic
244#400C4×C711yescharacteristic
245#399C4×C711yescharacteristic
246#398C4×C711yescharacteristic
247#397C4×C711yescharacteristic
248#397C4×C711yescharacteristic
249#397C4×C711yescharacteristic
250#394C4×C711yescharacteristic
251#394C4×C711yescharacteristic
252C4×C4⋊C4C22×C711yescharacteristic
253C4×C4⋊C4C22×C711yescharacteristic
254C4×C22⋊C4C22×C711yescharacteristic
255C4×C22⋊C4C22×C711yescharacteristic
256C4×C22⋊C4C22×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×C7—21no—
272C23×C7—21no—
273C23×C7—21no—
274C23×C7—21no—
275C23×C7—21no—
276C23×C7—21no—
277C23×C7—21no—
278C23×C7—21no—
279C23×C7—21no—
280C23×C7#13112yes—
281C23×C7C23×C411yescharacteristic
282C7×D4—44no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
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—21no—
316C2×C4×C7—21no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7#13112yes—
326C2×C4×C7#13112yes—
327C2×C4×C7H(5,𝔽2)11yescharacteristic
328C2×C4×C7H(5,𝔽2)11yescharacteristic
329C2×C4×C7H(5,𝔽2)11yescharacteristic
330C2×C4×C7H(5,𝔽2)11yescharacteristic
331C2×C4×C72−1+411yescharacteristic
332C2×C4×C72−1+411yescharacteristic
333C7×C8—41no—
334C7×C8—41no—
335C7×C8—41no—
336C7×C8—41no—
337C7×C8—41no—
338C7×C8—41no—
339C7×C8—41no—
340C7×C8—41no—
341C22×D4C2×C4×C711yescharacteristic
342C23×C4C23×C711yescharacteristic
343C23×C4C23×C711yescharacteristic
344C22×C8—41no—
345C22×C8—41no—
346C22×C8—41no—
347C22×C8C23×C711yescharacteristic
348C22×C8C23×C711yescharacteristic
349C22×C8C23×C711yescharacteristic
350C22×C8C23×C711yescharacteristic
351C22×C8C23×C711yescharacteristic
352C22×C8C23×C711yescharacteristic
353C22×C8C23×C711yescharacteristic
354C22×C8C23×C711yescharacteristic
355C4×D4—41no—
356C4×D4—41no—
357#117—41no—
358#117—41no—
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×C4⋊C4C2×C4×C711yescharacteristic
366C2×C22⋊C4C2×C4×C711yescharacteristic
367C2×C22⋊C4C2×C4×C711yescharacteristic
368C2×C22⋊C4C2×C4×C711yescharacteristic
369C2×C22⋊C4C2×C4×C711yescharacteristic
370C2×C22⋊C4C2×C4×C711yescharacteristic
371C2×C22⋊C4C2×C4×C711yescharacteristic
372C2×C22⋊C4C2×C4×C711yescharacteristic
373C2×C22⋊C4C2×C4×C711yescharacteristic
374C2×C22⋊C4C2×C4×C711yescharacteristic
375C2×C22⋊C4C2×C4×C711yescharacteristic
376C2×C42C23×C711yescharacteristic
377C2×C42C23×C711yescharacteristic
378C2×C42C23×C711yescharacteristic
379C2×C42C23×C711yescharacteristic
380C2×C42C23×C711yescharacteristic
381C4⋊C8—41no—
382C4⋊C8—41no—
383C4⋊C8—41no—
384C4⋊C8—41no—
385C4⋊C8—41no—
386C4⋊C8—41no—
387C4⋊C8—41no—
388C22⋊C8—41no—
389C22⋊C8—41no—
390C22⋊C8—41no—
391C22⋊C8—41no—
392C22⋊C8—41no—
393C22⋊C8—41no—
394C22⋊C8—41no—
395#97—41no—
396C4×C8—41no—
397C4×C8—41no—
398#95C2×C4×C711yescharacteristic
399#95C2×C4×C711yescharacteristic
400#95C2×C4×C711yescharacteristic
401#95C2×C4×C711yescharacteristic
402#95C2×C4×C711yescharacteristic
403#95C2×C4×C711yescharacteristic
404#95C2×C4×C711yescharacteristic
405#95C2×C4×C711yescharacteristic
406#95C2×C4×C711yescharacteristic
407#95C2×C4×C711yescharacteristic
408C22×C7—22no—
409C22×C7—22no—
410C22×C7—22no—
411C22×C7—41no—
412C22×C7—41no—
413C22×C7—41no—
414C22×C7—41no—
415C22×C7—41no—
416C22×C7—41no—
417C22×C7—41no—
418C22×C7—41no—
419C22×C7—41no—
420C22×C7—41no—
421C22×C7—41no—
422C22×C7#51811yescharacteristic
423C22×C7#52011yescharacteristic
424C22×C7#52011yescharacteristic
425C22×C7C2×#13111yescharacteristic
426C22×C7C2×#13111yescharacteristic
427C22×C7C2×#13111yescharacteristic
428C22×C7#56811yescharacteristic
429C4×C7—22no—
430C4×C7—22no—
431C4×C7—41no—
432C4×C7—41no—
433C4×C7—41no—
434C4×C7—41no—
435C4×C7—41no—
436C4×C7—41no—
437C4×C7—41no—
438C4×C7—41no—
439C4×C7—41no—
440C4×C7—41no—
441C4×C7#56011yescharacteristic
442C4×C7#56211yescharacteristic
443C4×C7#56211yescharacteristic
444C4×C7#56311yescharacteristic
445C24C22×C4×C711yescharacteristic
446C24C22×C4×C711yescharacteristic
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—41no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4C22×C4×C711yescharacteristic
463C22×C4C22×C4×C711yescharacteristic
464C22×C4C22×C4×C711yescharacteristic
465C22×C4C22×C4×C711yescharacteristic
466C22×C4C22×C4×C711yescharacteristic
467C22×C4C22×C4×C711yescharacteristic
468C22×C4C22×C4×C711yescharacteristic
469C22×C4C22×C4×C711yescharacteristic
470C22×C4C22×C4×C711yescharacteristic
471C22×C4C22×C4×C711yescharacteristic
472C22×C4C22×C4×C711yescharacteristic
473C22×C4C22×C4×C711yescharacteristic
474C22×C4C24×C711yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—44no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C2×C7—42no—
528C2×C7—81no—
529C2×C7#237611yescharacteristic
530C2×C7#297711yescharacteristic
531C2×C7#298111yescharacteristic
532C2×C7#299211yescharacteristic
533C2×C7#299311yescharacteristic
534C2×C7#299411yescharacteristic
535C2×C7#299411yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23C7×#13112yes—
550C23C23×C4×C711yescharacteristic
551D4—44no—
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—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4C7×#13112yes—
595C2×C4C7×#13112yes—
596C2×C4C7×H(5,𝔽2)11yescharacteristic
597C2×C4C7×H(5,𝔽2)11yescharacteristic
598C2×C4C7×H(5,𝔽2)11yescharacteristic
599C2×C4C7×H(5,𝔽2)11yescharacteristic
600C2×C4C7×2−1+411yescharacteristic
601C2×C4C7×2−1+411yescharacteristic
602C8—41no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—41no—
609C8—41no—
610C7#2331911yescharacteristic, direct product factor, Sylow
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22C7×#51811yescharacteristic
626C22C7×#52011yescharacteristic
627C22C7×#52011yescharacteristic
628C22C2×C7×#13111yescharacteristic
629C22C2×C7×#13111yescharacteristic
630C22C2×C7×#13111yescharacteristic
631C22C7×#56811yescharacteristic
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4C7×#56011yescharacteristic
645C4C7×#56211yescharacteristic
646C4C7×#56211yescharacteristic
647C4C7×#56311yescharacteristic
648C2—42no—
649C2—81no—
650C2C7×#237611yescharacteristic
651C2C7×#297711yescharacteristic
652C2C7×#298111yescharacteristic
653C2C7×#299211yescharacteristic
654C2C7×#299311yescharacteristic
655C2C7×#299411yescharacteristic
656C2C7×#299411yescharacteristic
subgroupG/H
centerC22×C4×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC22×C4C24×C7
socleC23×C7C23×C4
prime radicalC22×C7×D4C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#1940C2semidirect
4. C7×#1939C2semidirect
5. C7×#1924C2semidirect
6. C7×#1924C2semidirect
7. C7×#1923C2semidirect
8. C7×#1923C2semidirect
9. C7×#1916C2semidirect
10. C7×#1916C2semidirect
12. C7×#1850C2semidirect
13. C7×#1850C2semidirect
14. C7×#1798C2semidirect
15. C7×#1798C2semidirect
59. #23319C7direct (N × H)
129. #1940C2×C7semidirect
130. #1939C2×C7semidirect
131. #1924C2×C7semidirect
132. #1924C2×C7semidirect
133. #1923C2×C7semidirect
134. #1923C2×C7semidirect
135. #1916C2×C7semidirect
136. #1916C2×C7semidirect
138. #1850C2×C7semidirect
139. #1850C2×C7semidirect
140. #1798C2×C7semidirect
141. #1798C2×C7semidirect
610. C7#23319direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#23952
C7×#19542
C7×#19402
C7×#19392
C7×#19242
C7×#19232
C7×#19162
C7×#18692
C7×#18502
C7×#17982
#233197