Finite Group Databasebeta

← #11735149

Subgroups — #11735149

Order 896.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#397C211yesmaximal, characteristic, complemented
2#89766C211yesmaximal, characteristic, complemented
3#89762C211yesmaximal, characteristic, complemented
4#89727C211yesmaximal, characteristic
5#89727C211yesmaximal, characteristic
6#89727C211yesmaximal, characteristic
7#89723C211yesmaximal, characteristic, complemented
8#89723C211yesmaximal, characteristic, complemented
9#89720C211yesmaximal, characteristic, complemented
10#89449C211yesmaximal, characteristic, complemented
11#89447C211yesmaximal, characteristic, complemented
12#89447C211yesmaximal, characteristic, complemented
13#89442C211yesmaximal, characteristic, complemented
14#89442C211yesmaximal, characteristic, complemented
15#89441C211yesmaximal, characteristic, complemented
16C24×D7C2211yescharacteristic
17C2×C7×C4⋊C4C2211yescharacteristic, complemented
18C2×C7×C22⋊C4C2211yescharacteristic
19C2×C7×C22⋊C4C2211yescharacteristic
20C2×C7×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic7C2211yescharacteristic
22C2×C22⋊Dic7C2211yescharacteristic
23C2×C22⋊Dic7C2211yescharacteristic
24C2×(C2×D7)⋊C4C2211yescharacteristic
25C2×(C2×D7)⋊C4C2211yescharacteristic
26C2×(C2×D7)⋊C4C2211yescharacteristic
27C2×(C2×D7)⋊C4C2211yescharacteristic
28C2×(C2×D7)⋊C4C2211yescharacteristic
29C2×(C2×D7)⋊C4C2211yescharacteristic
30C2×(C2×D7)⋊C4C2211yescharacteristic
31C2×(C2×D7)⋊C4C2211yescharacteristic
32C2×(C2×D7)⋊C4C2211yescharacteristic
33C2×(C2×D7)⋊C4C2211yescharacteristic
34C2×(C2×D7)⋊C4C2211yescharacteristic
35C2×(C2×D7)⋊C4C2211yescharacteristic
36C2×C4⋊Dic7C2211yescharacteristic, complemented
37C2×C4⋊Dic7C2211yescharacteristic, complemented
38C2×C4⋊Dic7C2211yescharacteristic, complemented
39C2×Dic7⋊C4C2211yescharacteristic, complemented
40C2×Dic7⋊C4C2211yescharacteristic, complemented
41C2×C4×Dic7C2211yescharacteristic, complemented
42C2×C4×Dic7C2211yescharacteristic, complemented
43C7×#95C2211yescharacteristic, complemented
44C7×#95C2211yescharacteristic, complemented
45C7×#95C2211yescharacteristic, complemented
46C7⋊#95C2211yescharacteristic, complemented
47C7⋊#95C2211yescharacteristic, complemented
48C7⋊#95C2211yescharacteristic, complemented
49C7⋊#95C2211yescharacteristic, complemented
50C7⋊#95C2211yescharacteristic, complemented
51#2735—71nomaximal, Sylow
52C24×C7C2311yescharacteristic
53C23×D7—22no—
54C23×D7—22no—
55C23×D7—22no—
56C23×D7—41no—
57C23×D7—41no—
58C23×D7—41no—
59C23×D7—41no—
60C23×D7C2311yescharacteristic
61C23×D7C2311yescharacteristic
62C22×C4×C7C2311yescharacteristic
63C22×C4×C7C2311yescharacteristic
64C22×C4×C7C2311yescharacteristic
65C22×C4×C7C2311yescharacteristic
66C22×C4×C7C2311yescharacteristic
67C22×C4×C7C2311yescharacteristic
68C22×Dic7C2311yescharacteristic
69C22×Dic7C2311yescharacteristic
70C22×Dic7C2311yescharacteristic
71C22×Dic7C2311yescharacteristic
72C22×Dic7C2311yescharacteristic
73C22×Dic7C2311yescharacteristic
74C7×C4⋊C4—41no—
75C7×C22⋊C4—22no—
76C7×C22⋊C4—22no—
77C7×C22⋊C4—41no—
78C22⋊Dic7—41no—
79C22⋊Dic7—41no—
80C22⋊Dic7—41no—
81(C2×D7)⋊C4—22no—
82(C2×D7)⋊C4—22no—
83(C2×D7)⋊C4—22no—
84(C2×D7)⋊C4—22no—
85(C2×D7)⋊C4—41no—
86(C2×D7)⋊C4—41no—
87(C2×D7)⋊C4—41no—
88(C2×D7)⋊C4—41no—
89(C2×D7)⋊C4—41no—
90(C2×D7)⋊C4—41no—
91(C2×D7)⋊C4—41no—
92(C2×D7)⋊C4—41no—
93C4⋊Dic7—41no—
94C4⋊Dic7—41no—
95C4⋊Dic7—41no—
96Dic7⋊C4—41no—
97Dic7⋊C4—41no—
98C4×Dic7—41no—
99C4×Dic7—41no—
100#399—71no—
101#397—71no—
102#397—71no—
103#397D711yescharacteristic, complemented
104#396—71no—
105#396—71no—
106#388—71no—
107#388—71no—
108#388—71no—
109#388—71no—
110#388—71no—
111#388—71no—
112#379—71no—
113#379—71no—
114#379—71no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7#4112yes—
122C23×C7C2411yescharacteristic
123C22×D7—21no—
124C22×D7—21no—
125C22×D7—21no—
126C22×D7—21no—
127C22×D7—21no—
128C22×D7—21no—
129C22×D7—21no—
130C22×D7—21no—
131C22×D7—21no—
132C22×D7—21no—
133C22×D7—21no—
134C22×D7—21no—
135C22×D7—44no—
136C22×D7—44no—
137C22×D7—44no—
138C22×D7—44no—
139C22×D7—44no—
140C22×D7—44no—
141C22×D7—44no—
142C22×D7#4112yes—
143C22×D7#4112yes—
144C2×C4×C7—21no—
145C2×C4×C7—21no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—21no—
159C2×C4×C7—21no—
160C2×C4×C7—21no—
161C2×C4×C7—21no—
162C2×Dic7—21no—
163C2×Dic7—21no—
164C2×Dic7—21no—
165C2×Dic7—21no—
166C2×Dic7—21no—
167C2×Dic7—21no—
168C2×Dic7—21no—
169C2×Dic7—21no—
170C2×Dic7—21no—
171C2×Dic7—21no—
172C2×Dic7—21no—
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176C2×Dic7—21no—
177C2×Dic7—21no—
178C2×Dic7—21no—
179C2×Dic7—21no—
180C25—71no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—71no—
183C2×C4⋊C4—71no—
184C2×C4⋊C4—71no—
185C2×C4⋊C4—71no—
186C2×C4⋊C4C2×D711yescharacteristic, complemented
187C2×C22⋊C4—71no—
188C2×C22⋊C4—71no—
189C2×C22⋊C4—71no—
190C2×C22⋊C4—71no—
191C2×C22⋊C4—71no—
192C2×C22⋊C4—71no—
193C2×C22⋊C4—71no—
194C2×C22⋊C4—71no—
195C2×C22⋊C4—71no—
196C2×C22⋊C4—71no—
197C2×C22⋊C4—71no—
198C2×C22⋊C4—71no—
199C2×C22⋊C4—71no—
200C2×C22⋊C4—71no—
201C2×C22⋊C4—71no—
202C2×C22⋊C4C2×D711yescharacteristic
203C2×C22⋊C4C2×D711yescharacteristic
204C2×C22⋊C4C2×D711yescharacteristic
205C2×C42—71no—
206C2×C42—71no—
207#95—71no—
208#95—71no—
209#95—71no—
210#95—71no—
211#95—71no—
212#95C2×D711yescharacteristic, complemented
213#95C2×D711yescharacteristic, complemented
214#95C2×D711yescharacteristic, complemented
215C22×C7—22no—
216C22×C7—22no—
217C22×C7—22no—
218C22×C7—41no—
219C22×C7—41no—
220C22×C7—41no—
221C22×C7—41no—
222C22×C7C2×#4111yescharacteristic
223C22×C7C2×#4111yescharacteristic
224C22×C7C2×#4111yescharacteristic
225C22×C7H(5,𝔽2)11yescharacteristic
226C22×C7H(5,𝔽2)11yescharacteristic
227C22×C7H(5,𝔽2)11yescharacteristic
228C22×C7H(5,𝔽2)11yescharacteristic
229C2×D7—22no—
230C2×D7—22no—
231C2×D7—22no—
232C2×D7—22no—
233C2×D7—22no—
234C2×D7—22no—
235C2×D7—416no—
236C2×D7—41no—
237C2×D7—41no—
238C2×D7—41no—
239C2×D7—41no—
240C2×D7—41no—
241C2×D7—41no—
242C2×D7—41no—
243C2×D7—41no—
244C4×C7—41no—
245C4×C7—41no—
246C4×C7—41no—
247C4×C7—41no—
248C4×C7—41no—
249C4×C7—41no—
250Dic7—41no—
251Dic7—41no—
252Dic7—41no—
253Dic7—41no—
254Dic7—41no—
255Dic7—41no—
256C24—71no—
257C24—71no—
258C24—142no—
259C24—142no—
260C24—142no—
261C24—281no—
262C24—281no—
263C24—281no—
264C24—281no—
265C24C22×D711yescharacteristic
266C22×C4—71no—
267C22×C4—71no—
268C22×C4—71no—
269C22×C4—71no—
270C22×C4—71no—
271C22×C4—71no—
272C22×C4C22×D711yescharacteristic
273C22×C4C22×D711yescharacteristic
274C22×C4C22×D711yescharacteristic
275C22×C4C22×D711yescharacteristic
276C22×C4C22×D711yescharacteristic
277C22×C4C22×D711yescharacteristic
278C4⋊C4—41no—
279C4⋊C4—281no—
280C4⋊C4—281no—
281C4⋊C4—281no—
282C4⋊C4—281no—
283C4⋊C4—281no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—142no—
288C22⋊C4—142no—
289C22⋊C4—142no—
290C22⋊C4—142no—
291C22⋊C4—281no—
292C22⋊C4—281no—
293C22⋊C4—281no—
294C22⋊C4—281no—
295C22⋊C4—281no—
296C22⋊C4—281no—
297C22⋊C4—281no—
298C22⋊C4—281no—
299C22⋊C4—281no—
300C22⋊C4—281no—
301C22⋊C4—281no—
302C42—281no—
303C42—281no—
304C2×C7—42no—
305C2×C7#53811yescharacteristic
306C2×C7#53811yescharacteristic
307C2×C7#53811yescharacteristic
308C2×C7#55111yescharacteristic
309C2×C7#55111yescharacteristic
310C2×C7#55111yescharacteristic
311C2×C7#56011yescharacteristic
312D7—42no—
313D7—42no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—72no—
321C23—72no—
322C23—141no—
323C23—141no—
324C23—141no—
325C23—141no—
326C23—141no—
327C23—141no—
328C23—141no—
329C23—141no—
330C23—141no—
331C23—141no—
332C23—141no—
333C23—141no—
334C23—284no—
335C23—284no—
336C23—284no—
337C23—284no—
338C23—284no—
339C23—284no—
340C23—284no—
341C23#115912yes—
342C23C23×D711yescharacteristic
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—141no—
362C2×C4—141no—
363C2×C4—141no—
364C2×C4—141no—
365C2×C4—141no—
366C2×C4—141no—
367C2×C4—141no—
368C2×C4—141no—
369C2×C4—141no—
370C2×C4—141no—
371C2×C4—141no—
372C2×C4—141no—
373C2×C4—141no—
374C2×C4—141no—
375C2×C4—141no—
376C2×C4—141no—
377C2×C4—141no—
378C2×C4—141no—
379C7#273511yescharacteristic, complemented, Sylow
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—142no—
388C22—142no—
389C22—142no—
390C22—142no—
391C22—142no—
392C22—142no—
393C22—2816no—
394C22—281no—
395C22—281no—
396C22—281no—
397C22—281no—
398C22—281no—
399C22—281no—
400C22—281no—
401C22—281no—
402C22C2×#115911yescharacteristic
403C22#654811yescharacteristic
404C22D7×#4111yescharacteristic
405C22D7×#4111yescharacteristic
406C22#655311yescharacteristic
407C22#655311yescharacteristic
408C22#655311yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—281no—
416C4—281no—
417C4—281no—
418C4—281no—
419C4—281no—
420C4—281no—
421C2—42no—
422C2—282no—
423C2—282no—
424C2#9030811yescharacteristic
425C2#9034811yescharacteristic
426C2#9034911yescharacteristic
427C2#9034911yescharacteristic
428C2#9036911yescharacteristic
429C2#9039611yescharacteristic
430C2#9040211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC7×#397C2
prime radicalC24×D7C22
hypercenter#397D7
hypocenterC7#2735
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C7×#397C2semidirect
2. #89766C2semidirect
3. #89762C2semidirect
7. #89723C2semidirect
8. #89723C2semidirect
9. #89720C2semidirect
10. #89449C2semidirect
11. #89447C2semidirect
12. #89447C2semidirect
13. #89442C2semidirect
14. #89442C2semidirect
15. #89441C2semidirect
17. C2×C7×C4⋊C4C22semidirect
36. C2×C4⋊Dic7C22semidirect
37. C2×C4⋊Dic7C22semidirect
38. C2×C4⋊Dic7C22semidirect
39. C2×Dic7⋊C4C22semidirect
40. C2×Dic7⋊C4C22semidirect
41. C2×C4×Dic7C22semidirect
42. C2×C4×Dic7C22semidirect
43. C7×#95C22semidirect
44. C7×#95C22semidirect
45. C7×#95C22semidirect
46. C7⋊#95C22semidirect
47. C7⋊#95C22semidirect
48. C7⋊#95C22semidirect
49. C7⋊#95C22semidirect
50. C7⋊#95C22semidirect
103. #397D7semidirect
186. C2×C4⋊C4C2×D7semidirect
212. #95C2×D7semidirect
213. #95C2×D7semidirect
214. #95C2×D7semidirect
379. C7#2735semidirect

Maximal subgroups

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

subgroupindex
C7×#3972
#897662
#897622
#897272
#897232
#897202
#894492
#894472
#894422
#894412
#27357