Finite Group Databasebeta

← #47986358

Subgroups — #47986358

Order 35456.

456 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579875C211yesmaximal, characteristic
2#31799898C211yesmaximal, characteristic, complemented
3#31799897C211yesmaximal, characteristic, complemented
4#31799893C211yesmaximal, characteristic
5#31799892C211yesmaximal, characteristic
6#31799891C211yesmaximal, characteristic
7#31799888C211yesmaximal, characteristic, complemented
8#31799887C211yesmaximal, characteristic, complemented
9#31799886C211yesmaximal, characteristic, complemented
10#31799876C211yesmaximal, characteristic
11#31799873C211yesmaximal, characteristic
12#31799873C211yesmaximal, characteristic
13#31799871C211yesmaximal, characteristic, complemented
14#31799869C211yesmaximal, characteristic, complemented
15#389×C277C211yesmaximal, characteristic, complemented
16C22×C4×D277C2211yescharacteristic
17#22579875C418yescomplemented
18C2×C4⋊Dic277C2211yescharacteristic
19C2×C4⋊Dic277C2211yescharacteristic
20C2×#17984542C2211yescharacteristic
21C2×#17984542C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×#17984540C2211yescharacteristic
27C2×#17984540C2211yescharacteristic
28C2×#17984540C2211yescharacteristic
29C2×#17984540C2211yescharacteristic
30C2×#17984540C2211yescharacteristic
31C2×#17984540C2211yescharacteristic
32C2×C4×Dic277C2211yescharacteristic
33C2×C4×Dic277C2211yescharacteristic
34C2×C4×Dic277C2211yescharacteristic
35#22579787C2211yescharacteristic
36#22579787C2211yescharacteristic
37#22579787C2211yescharacteristic
38#22579787C2211yescharacteristic
39#22579787C2211yescharacteristic
40#22579787C2211yescharacteristic
41#22579787C2211yescharacteristic
42#22579787C2211yescharacteristic
43#22579787C2211yescharacteristic
44#22579787C2211yescharacteristic
45C2×C4⋊C4×C277C2211yescharacteristic
46C2×C4⋊C4×C277C2211yescharacteristic
47C2×C4⋊C4×C277C2211yescharacteristic
48C2×C4⋊C4×C277C2211yescharacteristic
49C2×C42×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52C23×D277C2311yescharacteristic
53C22×Dic277C2311yescharacteristic
54C22×Dic277C2311yescharacteristic
55C22×Dic277C2311yescharacteristic
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C2×C4×D277—41no—
61C2×C4×D277—41no—
62C2×C4×D277—41no—
63C4⋊Dic277—41no—
64C4⋊Dic277C2×C414yescomplemented
65#17984542—41no—
66#17984542—41no—
67#17984542—41no—
68#17984542—41no—
69#17984542—41no—
70#17984542C2×C414yescomplemented
71#17984540—41no—
72#17984540—41no—
73#17984540—41no—
74#17984540C2×C414yes—
75#17984540C2×C414yes—
76#17984540C2×C414yes—
77C4×Dic277—41no—
78C4×Dic277—41no—
79C4×Dic277C2×C414yescomplemented
80C22×C4×C277C2311yescharacteristic
81C22×C4×C277C2311yescharacteristic
82C22×C4×C277C2311yescharacteristic
83C22×C4×C277C2311yescharacteristic
84C22×C4×C277C2311yescharacteristic
85C22×C4×C277C2311yescharacteristic
86C22×C4×C277C2311yescharacteristic
87C4⋊C4×C277—41no—
88C4⋊C4×C277—41no—
89C4⋊C4×C277—41no—
90C4⋊C4×C277C2×C414yescomplemented
91C42×C277—41no—
92C22×D277—21no—
93C22×D277—21no—
94C22×D277—21no—
95C22×D277—21no—
96C22×D277—21no—
97C22×D277—21no—
98C22×D277C22×C412yes—
99C2×Dic277—21no—
100C2×Dic277—21no—
101C2×Dic277—21no—
102C2×Dic277—21no—
103C2×Dic277—21no—
104C2×Dic277—21no—
105C2×Dic277—21no—
106C2×Dic277—21no—
107C2×Dic277—21no—
108C2×Dic277—21no—
109C2×Dic277—21no—
110C2×Dic277—21no—
111C2×Dic277—21no—
112C2×Dic277—21no—
113C2×Dic277—21no—
114C2×Dic277—21no—
115C2×Dic277—21no—
116C2×Dic277—21no—
117C2×Dic277C22×C412yes—
118C2×Dic277C22×C412yes—
119C2×Dic277C22×C412yes—
120C4×D277—44no—
121C23×C277C2411yescharacteristic
122C2×C4×C277—21no—
123C2×C4×C277—21no—
124C2×C4×C277—21no—
125C2×C4×C277—21no—
126C2×C4×C277—21no—
127C2×C4×C277—21no—
128C2×C4×C277—21no—
129C2×C4×C277—21no—
130C2×C4×C277—21no—
131C2×C4×C277—21no—
132C2×C4×C277—21no—
133C2×C4×C277—21no—
134C2×C4×C277—21no—
135C2×C4×C277—21no—
136C2×C4×C277—21no—
137C2×C4×C277—21no—
138C2×C4×C277—21no—
139C2×C4×C277—21no—
140C2×C4×C277C22×C412yes—
141C2×C4×C277C22×C412yes—
142C2×C4×C277C22×C412yes—
143C22×C277C23×C411yescharacteristic
144C22×C277H(5,𝔽2)11yescharacteristic
145C22×C277H(5,𝔽2)11yescharacteristic
146C22×C277H(5,𝔽2)11yescharacteristic
147C22×C2772−1+411yescharacteristic
148C22×C2772−1+411yescharacteristic
149C22×C2772−1+411yescharacteristic
150C2×D277—22no—
151C2×D277—22no—
152C2×D277—22no—
153C2×D277—41no—
154C2×D277—41no—
155C2×D277—41no—
156C2×D277—41no—
157C4×C277—22no—
158C4×C277—22no—
159C4×C277—22no—
160C4×C277—41no—
161C4×C277—41no—
162C4×C277—41no—
163C4×C277—41no—
164Dic277—22no—
165Dic277—22no—
166Dic277—22no—
167Dic277—41no—
168Dic277—41no—
169Dic277—41no—
170Dic277—41no—
171C2×C277#52011yescharacteristic
172C2×C277#52011yescharacteristic
173C2×C277#52011yescharacteristic
174C2×C277#56011yescharacteristic
175C2×C277#56311yescharacteristic
176C2×C277#56311yescharacteristic
177C2×C277#56311yescharacteristic
178D277—42no—
179C277#238311yescharacteristic, complemented, Sylow
180#2383—2771nomaximal, Sylow
181C2×#126—2771no—
182#389—2771no—
183#389—2771no—
184#389D27711yescharacteristic, complemented
185#388—2771no—
186#388—2771no—
187#388—2771no—
188#387—2771no—
189#387—2771no—
190#387—2771no—
191#385—2771no—
192#385—2771no—
193#385—2771no—
194#384—2771no—
195#383—2771no—
196C23×C4—2771no—
197#126—2778no—
198C2×C4⋊C4—2771no—
199C2×C4⋊C4—2771no—
200C2×C4⋊C4—2771no—
201C2×C4⋊C4—2771no—
202C2×C4⋊C4—2771no—
203C2×C4⋊C4—2771no—
204C2×C4⋊C4—2771no—
205C2×C4⋊C4—2771no—
206C2×C4⋊C4C2×D27711yescharacteristic
207C2×C4⋊C4C2×D27711yescharacteristic
208C2×C4⋊C4C2×D27711yescharacteristic
209C2×C4⋊C4C2×D27711yescharacteristic
210C2×C22⋊C4—2771no—
211C2×C22⋊C4—2771no—
212C2×C22⋊C4—2771no—
213C2×C22⋊C4—2771no—
214C2×C22⋊C4—2771no—
215C2×C22⋊C4—2771no—
216C2×C42—2771no—
217C2×C42—2771no—
218C2×C42—2771no—
219C2×C42C2×D27711yescharacteristic
220#95—2771no—
221#95—2771no—
222#95—2771no—
223#95—2771no—
224#95—2771no—
225#95—2771no—
226#95—2771no—
227#95—2771no—
228#95—2771no—
229#95—2771no—
230#95C2×D27711yescharacteristic
231#95C2×D27711yescharacteristic
232C24—2771no—
233C22×C4—2771no—
234C22×C4—2771no—
235C22×C4—2771no—
236C22×C4—2771no—
237C22×C4—2771no—
238C22×C4—2771no—
239C22×C4—2771no—
240C22×C4—11081no—
241C22×C4—11081no—
242C22×C4—11081no—
243C22×C4C22×D27711yescharacteristic
244C22×C4C22×D27711yescharacteristic
245C22×C4C22×D27711yescharacteristic
246C22×C4C22×D27711yescharacteristic
247C22×C4C22×D27711yescharacteristic
248C22×C4C22×D27711yescharacteristic
249C22×C4C22×D27711yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2774no—
254C4⋊C4—2774no—
255C4⋊C4—11081no—
256C4⋊C4—11081no—
257C4⋊C4—11081no—
258C4⋊C4—11081no—
259C4⋊C4—11081no—
260C4⋊C4—11081no—
261C4⋊C4C4×D27714yescomplemented
262C22⋊C4—2774no—
263C22⋊C4—2774no—
264C22⋊C4—2774no—
265C22⋊C4—11081no—
266C22⋊C4—11081no—
267C22⋊C4—11081no—
268C42—41no—
269C42—2774no—
270C42—11081no—
271C42—11081no—
272C23—2772no—
273C23—5541no—
274C23—5541no—
275C23—5541no—
276C23—5541no—
277C23—5541no—
278C23—5541no—
279C23C23×D27711yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—2772no—
299C2×C4—2772no—
300C2×C4—2772no—
301C2×C4—5541no—
302C2×C4—5541no—
303C2×C4—5541no—
304C2×C4—5541no—
305C2×C4—5541no—
306C2×C4—5541no—
307C2×C4—5541no—
308C2×C4—5541no—
309C2×C4—5541no—
310C2×C4—5541no—
311C2×C4—5541no—
312C2×C4—5541no—
313C2×C4—5541no—
314C2×C4—5541no—
315C2×C4—5541no—
316C2×C4—5541no—
317C2×C4—5541no—
318C2×C4—5541no—
319C2×C4—11084no—
320C2×C4C2×C4×D27712yes—
321C2×C4C2×C4×D27712yes—
322C2×C4C2×C4×D27712yes—
323C22—5542no—
324C22—5542no—
325C22—5542no—
326C22—11081no—
327C22—11081no—
328C22—11081no—
329C22—11081no—
330C22C22×C4×D27711yescharacteristic
331C22#2257992511yescharacteristic
332C22#2257992511yescharacteristic
333C22#2257992611yescharacteristic
334C22#2257992711yescharacteristic
335C22#2257992811yescharacteristic
336C22#2257992811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—5542no—
345C4—5542no—
346C4—5542no—
347C4—11081no—
348C4—11081no—
349C4—11081no—
350C4—11081no—
351C2—11082no—
352C2#3180048111yescharacteristic
353C2#3180048311yescharacteristic
354C2#3180048411yescharacteristic
355C2#3180074011yescharacteristic
356C2#3180075111yescharacteristic
357C2#3180075311yescharacteristic
358C2#3180075611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#389×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenter#389D277
hypocenterC277#2383
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #31799898C2semidirect
3. #31799897C2semidirect
7. #31799888C2semidirect
8. #31799887C2semidirect
9. #31799886C2semidirect
13. #31799871C2semidirect
14. #31799869C2semidirect
15. #389×C277C2semidirect
17. #22579875C4semidirect
64. C4⋊Dic277C2×C4semidirect
70. #17984542C2×C4semidirect
79. C4×Dic277C2×C4semidirect
90. C4⋊C4×C277C2×C4semidirect
179. C277#2383semidirect
184. #389D277semidirect
261. C4⋊C4C4×D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225798752
#317998982
#317998972
#317998932
#317998922
#317998912
#317998882
#317998872
#317998862
#317998762
#317998732
#317998712
#317998692
#389×C2772
#2383277