Finite Group Databasebeta

← #11738093

Subgroups — #11738093

Order 896.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#90326C211yesmaximal, characteristic, complemented
2#90302C211yesmaximal, characteristic
3C7×#465C211yesmaximal, characteristic, complemented
4#89943C211yesmaximal, characteristic, complemented
5SD16×Dic7C211yesmaximal, characteristic, complemented
6C8×C22⋊D7C211yesmaximal, characteristic, complemented
7C2×#6391C211yesmaximal, characteristic, complemented
8#89815C211yesmaximal, characteristic, complemented
9#89806C211yesmaximal, characteristic, complemented
10D7×#106C211yesmaximal, characteristic, complemented
11#89627C211yesmaximal, characteristic, complemented
12#89577C211yesmaximal, characteristic, complemented
13#89563C211yesmaximal, characteristic, complemented
14#89549C211yesmaximal, characteristic, complemented
15#89533C211yesmaximal, characteristic, complemented
16C2×#1159—21no—
17C2×C7×SD16C2211yescharacteristic
18C22×C7×C8C2211yescharacteristic
19C7×C22⋊Q8C2211yescharacteristic
20C7×#121C2211yescharacteristic
21#6509C2211yescharacteristic
22Q8×Dic7C2211yescharacteristic
23#6501C2211yescharacteristic
24#6498—21no—
25D4×Dic7C2211yescharacteristic
26C4×C22⋊D7C2211yescharacteristic
27C2×C4⋊Dic7C2211yescharacteristic
28C2×C4⋊Dic7C2211yescharacteristic
29C2×C8×D7C2211yescharacteristic
30#6460—21no—
31D7×C4⋊C4C2211yescharacteristic
32D7×C4⋊C4C2211yescharacteristic
33#6452—21no—
34#6451C2211yescharacteristic
35#6451C2211yescharacteristic
36#6446—21no—
37(C22⋊D7)⋊C4—21no—
38#6441—21no—
39#6441—21no—
40C7×#106C2211yescharacteristic
41C7×#103C2211yescharacteristic
42C7×#102C2211yescharacteristic
43#6409C2211yescharacteristic
44#6409C2211yescharacteristic
45#6406C2211yescharacteristic
46#6406C2211yescharacteristic
47C22⋊(C7⋊C8)C2211yescharacteristic
48(C2×D7)⋊C8C2211yescharacteristic
49#6391C2211yescharacteristic
50#6391C2211yescharacteristic
51#6391C2211yescharacteristic
52#6391C2211yescharacteristic
53Dic7⋊C8C2211yescharacteristic
54C8×Dic7C2211yescharacteristic
55#6382C2211yescharacteristic
56#6382C2211yescharacteristic
57#6382C2211yescharacteristic
58#6382C2211yescharacteristic
59#3335—71nomaximal, Sylow
60C2×C7×Q8C2311yescharacteristic
61C2×C7×D4—21no—
62C2×C7×D4C2311yescharacteristic
63C22×C4×C7C2311yescharacteristic
64C2×C22⋊D7—21no—
65C2×C22⋊D7D411yescharacteristic
66C22×Dic7—21no—
67C22×Dic7—21no—
68C22×Dic7—21no—
69#1159—44no—
70C2×C4×D7—21no—
71C2×C4×D7—21no—
72C2×C4×D7C2311yescharacteristic
73C2×Dic14—21no—
74C2×Dic14—21no—
75C7×SD16—22no—
76C2×C7×C8—22no—
77C2×C7×C8C2311yescharacteristic
78C2×C7×C8C2311yescharacteristic
79C7×C4⋊C4—21no—
80C7×C4⋊C4C2311yescharacteristic
81C7×C4⋊C4C2311yescharacteristic
82C7×C22⋊C4—21no—
83C7×C22⋊C4—21no—
84C22⋊Dic7—21no—
85C22⋊Dic7—21no—
86C22⋊Dic7D411yescharacteristic
87(C2×D7)⋊C4—21no—
88(C2×D7)⋊C4D411yescharacteristic
89C4⋊Dic7—21no—
90C4⋊Dic7—21no—
91C4⋊Dic7—21no—
92C4⋊Dic7C2311yescharacteristic
93C4⋊Dic7C2311yescharacteristic
94C4⋊Dic7C2311yescharacteristic
95C4⋊Dic7C2311yescharacteristic
96Dic7⋊C4—21no—
97Dic7⋊C4—21no—
98Dic7⋊C4—21no—
99Dic7⋊C4—21no—
100Dic7⋊C4—21no—
101Dic7⋊C4D411yescharacteristic
102C4×Dic7—21no—
103C4×Dic7C2311yescharacteristic
104C2×C7⋊C8C2311yescharacteristic
105C2×C7⋊C8C2311yescharacteristic
106C8×D7—22no—
107#554—71no—
108#547—71no—
109#498—71no—
110#483—71no—
111#483—71no—
112#481—71no—
113#481—71no—
114#476—71no—
115#475—71no—
116#465—71no—
117#465D711yescharacteristic, complemented
118C4×SD16—71no—
119C8×D4—71no—
120C2×#106—71no—
121C2×#106—71no—
122C23×C7—21no—
123C23×C7C2×D411yescharacteristic
124C22×D7C2×D411yescharacteristic
125C7×Q8—21no—
126C7×Q8—21no—
127C7×D4—21no—
128C7×D4—21no—
129C7×D4—42no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7C2×D411yescharacteristic
136C2×C4×C7C2411yescharacteristic
137C22⋊D7—42no—
138C22⋊D7SD1614yescomplemented
139C2×Dic7—21no—
140C2×Dic7—21no—
141C2×Dic7—21no—
142C2×Dic7—21no—
143C2×Dic7—42no—
144C2×Dic7—42no—
145C2×Dic7—81no—
146C2×Dic7C2×D411yescharacteristic
147C2×Dic7C2×D411yescharacteristic
148C2×Dic7C2×D411yescharacteristic
149C4×D7—21no—
150C4×D7—21no—
151C4×D7—42no—
152C4×D7—81no—
153Dic14—42no—
154Dic14—81no—
155C7×C8—21no—
156C7×C8#4112yescomplemented
157C7⋊C8—21no—
158C7⋊C8—21no—
159C2×#41—141no—
160C2×SD16C2×D711yescharacteristic
161C22×C8—71no—
162C22×C8C2×D711yescharacteristic
163C4⋊Q8—71no—
164C4⋊Q8—71no—
165#125—141no—
166#123—141no—
167#123—141no—
168C22⋊Q8—71no—
169C22⋊Q8—141no—
170C22⋊Q8—141no—
171C22⋊Q8—141no—
172C22⋊Q8C2×D711yescharacteristic
173#121—71no—
174#121C2×D711yescharacteristic
175C4×Q8—71no—
176C4×D4—71no—
177C4×D4—71no—
178C4×D4—141no—
179C2×C4⋊C4—71no—
180C2×C4⋊C4—71no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—71no—
183#106—71no—
184#106—71no—
185#106—71no—
186#106—71no—
187#106—71no—
188#106—71no—
189#106—71no—
190#106—71no—
191#106C2×D711yescharacteristic
192C4⋊C8—71no—
193#103—71no—
194#103—71no—
195#103C2×D711yescharacteristic
196#102—71no—
197#102—71no—
198#102C2×D711yescharacteristic
199C22⋊C8—71no—
200C22⋊C8—71no—
201C4×C8—71no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7C2×SD1612yes—
208C22×C7C22×D411yescharacteristic
209C2×D7—21no—
210C2×D7—21no—
211C2×D7C2×SD1612yes—
212C4×C7—21no—
213C4×C7—41no—
214C4×C7—41no—
215C4×C7—41no—
216C4×C7C2×#4111yescharacteristic
217C4×C72−1+411yescharacteristic
218Dic7—21no—
219Dic7—21no—
220Dic7—41no—
221Dic7—41no—
222Dic7—41no—
223Dic7—41no—
224Dic7C2×SD1612yes—
225#41—284no—
226C2×Q8—141no—
227C2×Q8—141no—
228C2×Q8C22×D711yescharacteristic
229C2×D4—21no—
230C2×D4—71no—
231C2×D4—141no—
232C2×D4C22×D711yescharacteristic
233C22×C4—71no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4—141no—
237C22×C4—141no—
238C22×C4—141no—
239C22×C4C22×D711yescharacteristic
240SD16—22no—
241C2×C8—22no—
242C2×C8—71no—
243C2×C8—71no—
244C2×C8—142no—
245C2×C8C22×D711yescharacteristic
246C2×C8C22×D711yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—71no—
249C4⋊C4—71no—
250C4⋊C4—71no—
251C4⋊C4—71no—
252C4⋊C4—71no—
253C4⋊C4—141no—
254C4⋊C4—141no—
255C4⋊C4—141no—
256C4⋊C4—141no—
257C4⋊C4—141no—
258C4⋊C4—141no—
259C4⋊C4—141no—
260C4⋊C4—141no—
261C4⋊C4C22×D711yescharacteristic
262C4⋊C4C22×D711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—71no—
266C22⋊C4—71no—
267C22⋊C4—141no—
268C22⋊C4—141no—
269C22⋊C4—141no—
270C42—71no—
271C42—141no—
272C2×C7—22no—
273C2×C7—81no—
274C2×C7#54711yescharacteristic
275C2×C7C22×SD1611yescharacteristic
276C2×C7#57711yescharacteristic
277D7—22no—
278C23—21no—
279C23—71no—
280C23D4×D711yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—282no—
284Q8—561no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—74no—
289D4—282no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—71no—
296C2×C4—71no—
297C2×C4—71no—
298C2×C4—141no—
299C2×C4—141no—
300C2×C4—141no—
301C2×C4—141no—
302C2×C4—141no—
303C2×C4—141no—
304C2×C4—282no—
305C2×C4—282no—
306C2×C4—282no—
307C2×C4—561no—
308C2×C4—561no—
309C2×C4D4×D711yescharacteristic
310C2×C4C23×D711yescharacteristic
311C8—21no—
312C8—141no—
313C8—141no—
314C8#115912yescomplemented
315C7#333511yescharacteristic, complemented, Sylow
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—72no—
322C22—141no—
323C22—141no—
324C22D7×SD1612yes—
325C22C2×D4×D711yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—72no—
331C4—141no—
332C4—141no—
333C4—281no—
334C4—281no—
335C4—281no—
336C4—281no—
337C4C2×#115911yescharacteristic
338C4#655411yescharacteristic
339C2—22no—
340C2—81no—
341C2—142no—
342C2#9030211yescharacteristic
343C2C2×D7×SD1611yescharacteristic
344C2#9046111yescharacteristic
subgroupG/H
centerC22C2×D4×D7
commutator, cosocleC2×C4×C7C24
FrattiniC2×C4C23×D7
FittingC7×#465C2
socleC22×C7C22×D4
prime radical#90302C2
hypercenter#465D7
hypocenterC7#3335
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #90326C2semidirect
3. C7×#465C2semidirect
4. #89943C2semidirect
5. SD16×Dic7C2semidirect
6. C8×C22⋊D7C2semidirect
7. C2×#6391C2semidirect
8. #89815C2semidirect
9. #89806C2semidirect
10. D7×#106C2semidirect
11. #89627C2semidirect
12. #89577C2semidirect
13. #89563C2semidirect
14. #89549C2semidirect
15. #89533C2semidirect
117. #465D7semidirect
138. C22⋊D7SD16semidirect
156. C7×C8#41semidirect
314. C8#1159semidirect
315. C7#3335semidirect

Maximal subgroups

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

subgroupindex
#903262
#903022
C7×#4652
#899432
SD16×Dic72
C8×C22⋊D72
C2×#63912
#898152
#898062
D7×#1062
#896272
#895772
#895632
#895492
#895332
#33357