Finite Group Databasebeta

← C7×#14549 #13191765

Subgroups — C7×#14549 #13191765

Order 1792.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C2×C7×#389C211yesmaximal, characteristic, complemented
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×C7×#385C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic
6C7×#1444C211yesmaximal, characteristic, complemented
7C7×#1443C211yesmaximal, characteristic, complemented
8C7×#1441C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×C4⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C7×#396C418yescomplemented
34C7×#389—24no—
35C7×#387—24no—
36C7×#385—24no—
37C7×#385—24no—
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#14549C711yesmaximal, characteristic, direct product factor, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—41no—
62C23×C4×C7—41no—
63C23×C4×C7—41no—
64C23×C4×C7—41no—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—41no—
90C2×C7×C4⋊C4—41no—
91C2×C7×C4⋊C4—41no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4—41no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4C2×C414yescomplemented
100C2×C7×C4⋊C4C2×C414yescomplemented
101C2×C7×C4⋊C4C2×C414yescomplemented
102C2×C7×C4⋊C4D414yes—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—41no—
112C2×C7×C22⋊C4—41no—
113C2×C7×C22⋊C4—41no—
114C2×C7×C22⋊C4—41no—
115C2×C7×C22⋊C4—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4C2×C414yes—
118C2×C7×C22⋊C4C2×C414yes—
119C2×C7×C22⋊C4C2×C414yes—
120C2×C7×C22⋊C4Q814yes—
121C2×C42×C7—22no—
122C2×C42×C7—22no—
123C2×C42×C7—22no—
124C2×C42×C7—41no—
125C2×C42×C7—41no—
126C2×C42×C7—41no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—41no—
137C7×#95—41no—
138C7×#95—41no—
139C7×#95—41no—
140C7×#95—41no—
141C7×#95—41no—
142C7×#95—41no—
143C7×#95C2×C414yescomplemented
144C7×#95D414yes—
145C2×#396C2×C711yescharacteristic
146C2×#389C2×C711yescharacteristic, complemented
147C2×#387C2×C711yescharacteristic, complemented
148C2×#385C2×C711yescharacteristic
149C2×#385C2×C711yescharacteristic
150#1444C2×C711yescharacteristic, complemented
151#1443C2×C711yescharacteristic, complemented
152#1441C2×C711yescharacteristic, complemented
153#1441C2×C711yescharacteristic, complemented
154#1439C2×C711yescharacteristic
155#1437C2×C711yescharacteristic
156#1437C2×C711yescharacteristic
157#1436C2×C711yescharacteristic, complemented
158C4⋊#95C2×C711yescharacteristic, complemented
159C22⋊#95C2×C711yescharacteristic
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7C22×C412yes—
173C24×C7C2×Q812yes—
174C24×C7#4112yes—
175C24×C7C2411yescharacteristic
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—44no—
259C22×C4×C7—44no—
260C22×C4×C7—44no—
261C22×C4×C7—44no—
262C22×C4×C7—44no—
263C22×C4×C7—44no—
264C22×C4×C7—44no—
265C22×C4×C7C22×C412yes—
266C22×C4×C7C22×C412yes—
267C22×C4×C7C22×C412yes—
268C22×C4×C7C22×C412yes—
269C22×C4×C7C22×C412yes—
270C22×C4×C7C22×C412yes—
271C22×C4×C7C2×D412yes—
272C22×C4×C7C2×D412yes—
273C22×C4×C7C2×D412yes—
274C22×C4×C7C2×D412yes—
275C22×C4×C7C2×D412yes—
276C22×C4×C7C2×D412yes—
277C22×C4×C7C2×Q812yes—
278C22×C4×C7C2×Q812yes—
279C22×C4×C7#4112yes—
280C22×C4×C7#4112yes—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—28no—
283C7×C4⋊C4—44no—
284C7×C4⋊C4—44no—
285C7×C4⋊C4—44no—
286C7×C4⋊C4—44no—
287C7×C4⋊C4—44no—
288C7×C4⋊C4—44no—
289C7×C22⋊C4—28no—
290C7×C22⋊C4—28no—
291C7×C22⋊C4—44no—
292C7×C22⋊C4—44no—
293C7×C22⋊C4—44no—
294C7×C22⋊C4—44no—
295C42×C7—44no—
296C42×C7—44no—
297C24×C4C22×C711yescharacteristic
298C22×C4⋊C4C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300C22×C4⋊C4C22×C711yescharacteristic
301C22×C4⋊C4C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303C22×C4⋊C4C22×C711yescharacteristic
304C22×C4⋊C4C22×C711yescharacteristic
305C22×C4⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C711yescharacteristic
308C22×C22⋊C4C22×C711yescharacteristic
309C22×C22⋊C4C22×C711yescharacteristic
310C22×C22⋊C4C22×C711yescharacteristic
311C22×C22⋊C4C22×C711yescharacteristic
312C22×C42C22×C711yescharacteristic
313C22×C42C22×C711yescharacteristic
314#396C4×C718yescomplemented
315#389—24no—
316#387—24no—
317#385—24no—
318#385—24no—
319C2×#95C22×C711yescharacteristic
320C2×#95C22×C711yescharacteristic
321C2×#95C22×C711yescharacteristic
322C2×#95C22×C711yescharacteristic
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C2×#95C22×C711yescharacteristic
331C2×#95C22×C711yescharacteristic
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C2×#95C22×C711yescharacteristic
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7C4×Q814yes—
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×Q811yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C7H(5,𝔽2)11yescharacteristic
381C23×C7H(5,𝔽2)11yescharacteristic
382C23×C7H(5,𝔽2)11yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C72−1+411yescharacteristic
385C23×C72−1+411yescharacteristic
386C23×C72−1+411yescharacteristic
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—416no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7C4×D414yes—
485C2×C4×C7C4×D414yes—
486C25C23×C711yescharacteristic
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—41no—
491C23×C4—41no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4C23×C711yescharacteristic
495C23×C4C23×C711yescharacteristic
496C23×C4C23×C711yescharacteristic
497C23×C4C23×C711yescharacteristic
498C23×C4C23×C711yescharacteristic
499C23×C4C23×C711yescharacteristic
500C23×C4C23×C711yescharacteristic
501C23×C4C23×C711yescharacteristic
502C23×C4C23×C711yescharacteristic
503C23×C4C23×C711yescharacteristic
504C23×C4C23×C711yescharacteristic
505C23×C4C23×C711yescharacteristic
506C23×C4C23×C711yescharacteristic
507C23×C4C23×C711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4C2×C4×C714yescomplemented
529C2×C4⋊C4C2×C4×C714yescomplemented
530C2×C4⋊C4C2×C4×C714yescomplemented
531C2×C4⋊C4C7×D414yes—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4C2×C4×C714yes—
547C2×C22⋊C4C2×C4×C714yes—
548C2×C22⋊C4C2×C4×C714yes—
549C2×C22⋊C4C7×Q814yes—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—41no—
554C2×C42—41no—
555C2×C42—41no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—41no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95—41no—
571#95—41no—
572#95C2×C4×C714yescomplemented
573#95C7×D414yes—
574C22×C7—24no—
575C22×C7—24no—
576C22×C7—24no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7C2×C4×D411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C2×C4×Q811yescharacteristic
592C22×C7#51811yescharacteristic
593C22×C7#52011yescharacteristic
594C22×C7#52011yescharacteristic
595C22×C7#52011yescharacteristic
596C22×C7#53411yescharacteristic
597C22×C7#53511yescharacteristic
598C22×C7#53711yescharacteristic
599C22×C7#53711yescharacteristic
600C22×C7#53811yescharacteristic
601C22×C7#53811yescharacteristic
602C22×C7#53911yescharacteristic
603C22×C7#53911yescharacteristic
604C22×C7#54011yescharacteristic
605C22×C7#54211yescharacteristic
606C22×C7#54311yescharacteristic
607C22×C7#54411yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7#54811yescharacteristic
613C22×C7D4×Q811yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7#55211yescharacteristic
616C22×C7#55211yescharacteristic
617C22×C7#55311yescharacteristic
618C22×C7#55411yescharacteristic
619C22×C7#55411yescharacteristic
620C22×C7#56011yescharacteristic
621C22×C7#56311yescharacteristic
622C22×C7#56311yescharacteristic
623C22×C7#56311yescharacteristic
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631C4×C7—42no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7—42no—
635C4×C7—42no—
636C4×C7—81no—
637C4×C7—81no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24C22×C4×C712yes—
651C24C2×C7×Q812yes—
652C24C7×#4112yes—
653C24C24×C711yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4C22×C4×C712yes—
744C22×C4C22×C4×C712yes—
745C22×C4C22×C4×C712yes—
746C22×C4C22×C4×C712yes—
747C22×C4C22×C4×C712yes—
748C22×C4C22×C4×C712yes—
749C22×C4C2×C7×D412yes—
750C22×C4C2×C7×D412yes—
751C22×C4C2×C7×D412yes—
752C22×C4C2×C7×D412yes—
753C22×C4C2×C7×D412yes—
754C22×C4C2×C7×D412yes—
755C22×C4C2×C7×Q812yes—
756C22×C4C2×C7×Q812yes—
757C22×C4C7×#4112yes—
758C22×C4C7×#4112yes—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C42—44no—
774C42—44no—
775C2×C7—44no—
776C2×C7#232411yescharacteristic
777C2×C7#232511yescharacteristic
778C2×C7#232911yescharacteristic
779C2×C7#236011yescharacteristic
780C2×C7#236011yescharacteristic
781C2×C7#236111yescharacteristic
782C2×C7#238311yescharacteristic
783C2×C7#267811yescharacteristic
784C2×C7#268311yescharacteristic
785C2×C7#269511yescharacteristic
786C2×C7#270711yescharacteristic
787C2×C7#272011yescharacteristic
788C2×C7#272911yescharacteristic
789C2×C7#276511yescharacteristic
790C2×C7#278011yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C4×C7×Q814yes—
826C23C23×C4×C711yescharacteristic
827C23C22×C7×D411yescharacteristic
828C23C22×C7×D411yescharacteristic
829C23C22×C7×Q811yescharacteristic
830C23C2×C7×#4111yescharacteristic
831C23C2×C7×#4111yescharacteristic
832C23C2×C7×#4111yescharacteristic
833C23C7×H(5,𝔽2)11yescharacteristic
834C23C7×H(5,𝔽2)11yescharacteristic
835C23C7×H(5,𝔽2)11yescharacteristic
836C23C7×H(5,𝔽2)11yescharacteristic
837C23C7×H(5,𝔽2)11yescharacteristic
838C23C7×2−1+411yescharacteristic
839C23C7×2−1+411yescharacteristic
840C23C7×2−1+411yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—416no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C4×C7×D414yes—
939C2×C4C4×C7×D414yes—
940C7#1454911yescharacteristic, direct product factor, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×C7×D411yescharacteristic
957C22C2×C4×C7×D411yescharacteristic
958C22C2×C4×C7×Q811yescharacteristic
959C22C7×#51811yescharacteristic
960C22C7×#52011yescharacteristic
961C22C7×#52011yescharacteristic
962C22C7×#52011yescharacteristic
963C22C7×#53411yescharacteristic
964C22C7×#53511yescharacteristic
965C22C7×#53711yescharacteristic
966C22C7×#53711yescharacteristic
967C22C7×#53811yescharacteristic
968C22C7×#53811yescharacteristic
969C22C7×#53911yescharacteristic
970C22C7×#53911yescharacteristic
971C22C7×#54011yescharacteristic
972C22C7×#54211yescharacteristic
973C22C7×#54311yescharacteristic
974C22C7×#54411yescharacteristic
975C22C7×D4211yescharacteristic
976C22C7×#54611yescharacteristic
977C22C7×#54611yescharacteristic
978C22C7×#54711yescharacteristic
979C22C7×#54811yescharacteristic
980C22C7×D4×Q811yescharacteristic
981C22C7×D4×Q811yescharacteristic
982C22C7×#55211yescharacteristic
983C22C7×#55211yescharacteristic
984C22C7×#55311yescharacteristic
985C22C7×#55411yescharacteristic
986C22C7×#55411yescharacteristic
987C22C7×#56011yescharacteristic
988C22C7×#56311yescharacteristic
989C22C7×#56311yescharacteristic
990C22C7×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C7×#232411yescharacteristic
1007C2C7×#232511yescharacteristic
1008C2C7×#232911yescharacteristic
1009C2C7×#236011yescharacteristic
1010C2C7×#236011yescharacteristic
1011C2C7×#236111yescharacteristic
1012C2C7×#238311yescharacteristic
1013C2C7×#267811yescharacteristic
1014C2C7×#268311yescharacteristic
1015C2C7×#269511yescharacteristic
1016C2C7×#270711yescharacteristic
1017C2C7×#272011yescharacteristic
1018C2C7×#272911yescharacteristic
1019C2C7×#276511yescharacteristic
1020C2C7×#278011yescharacteristic
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
3. C2×C7×#387C2semidirect
6. C7×#1444C2semidirect
7. C7×#1443C2semidirect
8. C7×#1441C2semidirect
9. C7×#1441C2semidirect
13. C7×#1436C2semidirect
14. C7×C4⋊#95C2semidirect
33. C7×#396C4semidirect
56. #14549C7direct (N × H)
99. C2×C7×C4⋊C4C2×C4semidirect
100. C2×C7×C4⋊C4C2×C4semidirect
101. C2×C7×C4⋊C4C2×C4semidirect
143. C7×#95C2×C4semidirect
146. C2×#389C2×C7semidirect
147. C2×#387C2×C7semidirect
150. #1444C2×C7semidirect
151. #1443C2×C7semidirect
152. #1441C2×C7semidirect
153. #1441C2×C7semidirect
157. #1436C2×C7semidirect
158. C4⋊#95C2×C7semidirect
314. #396C4×C7semidirect
528. C2×C4⋊C4C2×C4×C7semidirect
529. C2×C4⋊C4C2×C4×C7semidirect
530. C2×C4⋊C4C2×C4×C7semidirect
572. #95C2×C4×C7semidirect
940. C7#14549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×C7×#3892
C2×C7×#3872
C2×C7×#3852
C7×#14442
C7×#14432
C7×#14412
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
C7×C22⋊#952
#145497