Finite Group Databasebeta

← #47986264

Subgroups — #47986264

Order 35456.

464 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22579870C211yesmaximal, characteristic
2#31799900C211yesmaximal, characteristic
3#31799899C211yesmaximal, characteristic
4#31799897C211yesmaximal, characteristic
5#31799897C211yesmaximal, characteristic
6#31799888C211yesmaximal, characteristic
7#31799887C211yesmaximal, characteristic
8#31799886C211yesmaximal, characteristic
9#31799886C211yesmaximal, characteristic
10C4×#17984542C211yesmaximal, characteristic
11C4×#17984542C211yesmaximal, characteristic
12C4×#17984542C211yesmaximal, characteristic
13#31799853C211yesmaximal, characteristic
14#31799853C211yesmaximal, characteristic
15C4×C4⋊C4×C277C211yesmaximal, characteristic
16#22579870C418yescomplemented
17C2×C4⋊Dic277C2211yescharacteristic
18C2×C4⋊Dic277C2211yescharacteristic
19C2×#17984542C2211yescharacteristic
20C2×#17984542C2211yescharacteristic
21C2×#17984542C2211yescharacteristic
22C2×#17984542C2211yescharacteristic
23C2×#17984542C2211yescharacteristic
24C2×#17984542C2211yescharacteristic
25C2×#17984542C2211yescharacteristic
26C2×#17984542C2211yescharacteristic
27C2×#17984542C2211yescharacteristic
28C2×#17984542C2211yescharacteristic
29C2×C4×Dic277C2211yescharacteristic
30C2×C4×Dic277C2211yescharacteristic
31C2×C4×Dic277C2211yescharacteristic
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×C42×C277C2211yescharacteristic
48C2×C42×C277C2211yescharacteristic
49C2×C42×C277C2211yescharacteristic
50#95×C277C2211yescharacteristic
51#95×C277C2211yescharacteristic
52C22×Dic277C2311yescharacteristic
53C22×Dic277C2311yescharacteristic
54C22×Dic277C2311yescharacteristic
55C22×Dic277C2311yescharacteristic
56C22×Dic277C2311yescharacteristic
57C22×Dic277C2311yescharacteristic
58C22×Dic277C2311yescharacteristic
59C22×Dic277C2311yescharacteristic
60C4⋊Dic277—41no—
61C4⋊Dic277C2×C414yes—
62#17984542—22no—
63#17984542—22no—
64#17984542—22no—
65#17984542—22no—
66#17984542—41no—
67#17984542C2×C414yes—
68#17984542C2×C414yes—
69#17984542C2×C414yes—
70#17984542C2×C414yes—
71#17984542Q814yes—
72C4×Dic277—22no—
73C4×Dic277—22no—
74C4×Dic277—22no—
75C4×Dic277—41no—
76C4×Dic277—41no—
77C4×Dic277C2×C414yes—
78C22×C4×C277C2311yescharacteristic
79C22×C4×C277C2311yescharacteristic
80C22×C4×C277C2311yescharacteristic
81C22×C4×C277C2311yescharacteristic
82C22×C4×C277C2311yescharacteristic
83C22×C4×C277C2311yescharacteristic
84C22×C4×C277C2311yescharacteristic
85C4⋊C4×C277—22no—
86C4⋊C4×C277C2×C414yes—
87C42×C277—22no—
88C42×C277—41no—
89C42×C277—41no—
90C2×Dic277—21no—
91C2×Dic277—21no—
92C2×Dic277—21no—
93C2×Dic277—21no—
94C2×Dic277—21no—
95C2×Dic277—21no—
96C2×Dic277—21no—
97C2×Dic277—21no—
98C2×Dic277—21no—
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×Dic277C22×C412yes—
108C2×Dic277C22×C412yes—
109C2×Dic277C22×C412yes—
110C2×Dic277C22×C412yes—
111C2×Dic277C2×Q812yes—
112C2×Dic277C2×Q812yes—
113C2×Dic277#4112yes—
114C23×C277C2411yescharacteristic
115C2×C4×C277—21no—
116C2×C4×C277—21no—
117C2×C4×C277—21no—
118C2×C4×C277—21no—
119C2×C4×C277—21no—
120C2×C4×C277—21no—
121C2×C4×C277—21no—
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×C277C22×C412yes—
131C2×C4×C277C22×C412yes—
132C2×C4×C277C22×C412yes—
133C2×C4×C277C2×Q812yes—
134C2×C4×C277#4112yes—
135C2×C4×C277#4112yes—
136C22×C277C23×C411yescharacteristic
137C22×C277C22×Q811yescharacteristic
138C22×C277C2×#4111yescharacteristic
139C22×C277C2×#4111yescharacteristic
140C22×C277C2×#4111yescharacteristic
141C22×C277H(5,𝔽2)11yescharacteristic
142C22×C2772−1+411yescharacteristic
143C4×C277—22no—
144C4×C277—22no—
145C4×C277—22no—
146C4×C277—22no—
147C4×C277—22no—
148C4×C277—22no—
149C4×C277—41no—
150Dic277—22no—
151Dic277—22no—
152Dic277—22no—
153Dic277—22no—
154Dic277—41no—
155Dic277—41no—
156Dic277—41no—
157Dic277C4×Q814yes—
158C2×C277C2×C4×Q811yescharacteristic
159C2×C277C4×#4111yescharacteristic
160C2×C277#52011yescharacteristic
161C2×C277#55211yescharacteristic
162C2×C277#55311yescharacteristic
163C2×C277#55411yescharacteristic
164C2×C277#55711yescharacteristic
165C277#237011yescharacteristic, complemented, Sylow
166#2370—2771nomaximal, Sylow
167C2×#125—2771no—
168#389—2771no—
169#389—2771no—
170#389—2771no—
171#389—2771no—
172#387—2771no—
173#387—2771no—
174#387—2771no—
175#387—2771no—
176C4×C4⋊C4—2771no—
177C4×C4⋊C4—2771no—
178C4×C4⋊C4—2771no—
179C4×C4⋊C4—2771no—
180C4×C4⋊C4—2771no—
181C4×C4⋊C4D27711yescharacteristic
182#125—2778no—
183C2×C4⋊C4—2771no—
184C2×C4⋊C4—2771no—
185C2×C4⋊C4—2771no—
186C2×C4⋊C4—2771no—
187C2×C4⋊C4—2771no—
188C2×C4⋊C4—2771no—
189C2×C4⋊C4—2771no—
190C2×C4⋊C4—2771no—
191C2×C4⋊C4—2771no—
192C2×C4⋊C4—2771no—
193C2×C4⋊C4—2771no—
194C2×C4⋊C4—2771no—
195C2×C4⋊C4C2×D27711yescharacteristic
196C2×C4⋊C4C2×D27711yescharacteristic
197C2×C42—2771no—
198C2×C42—2771no—
199C2×C42—2771no—
200C2×C42—2771no—
201C2×C42—2771no—
202C2×C42—2771no—
203C2×C42C2×D27711yescharacteristic
204C2×C42C2×D27711yescharacteristic
205C2×C42C2×D27711yescharacteristic
206#95—2771no—
207#95—2771no—
208#95—2771no—
209#95—2771no—
210#95—2771no—
211#95—2771no—
212#95—2771no—
213#95—2771no—
214#95—2771no—
215#95—2771no—
216#95C2×D27711yescharacteristic
217#95C2×D27711yescharacteristic
218C22×C4—2771no—
219C22×C4—2771no—
220C22×C4—2771no—
221C22×C4—2771no—
222C22×C4—2771no—
223C22×C4—2771no—
224C22×C4—2771no—
225C22×C4—2771no—
226C22×C4C22×D27711yescharacteristic
227C22×C4C22×D27711yescharacteristic
228C22×C4C22×D27711yescharacteristic
229C22×C4C22×D27711yescharacteristic
230C22×C4C22×D27711yescharacteristic
231C22×C4C22×D27711yescharacteristic
232C22×C4C22×D27711yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—2774no—
235C4⋊C4—2774no—
236C4⋊C4—2774no—
237C4⋊C4—2774no—
238C4⋊C4—2774no—
239C4⋊C4—2774no—
240C4⋊C4—5542no—
241C4⋊C4—5542no—
242C4⋊C4—5542no—
243C4⋊C4—5542no—
244C4⋊C4—11081no—
245C4⋊C4—11081no—
246C4⋊C4C4×D27714yes—
247C42—22no—
248C42—41no—
249C42—41no—
250C42—2774no—
251C42—5542no—
252C42—5542no—
253C42—5542no—
254C42—11081no—
255C42—11081no—
256C23C23×D27711yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—2772no—
273C2×C4—2772no—
274C2×C4—2772no—
275C2×C4—2772no—
276C2×C4—2772no—
277C2×C4—2772no—
278C2×C4—2772no—
279C2×C4—5541no—
280C2×C4—5541no—
281C2×C4—5541no—
282C2×C4—5541no—
283C2×C4—5541no—
284C2×C4—5541no—
285C2×C4—5541no—
286C2×C4—5541no—
287C2×C4—5541no—
288C2×C4—5541no—
289C2×C4—5541no—
290C2×C4—5541no—
291C2×C4—5541no—
292C2×C4—5541no—
293C2×C4—5541no—
294C2×C4—5541no—
295C2×C4—5541no—
296C2×C4C2×C4×D27712yes—
297C2×C4C2×C4×D27712yes—
298C2×C4C2×C4×D27712yes—
299C2×C4Q8×D27712yes—
300C2×C4#1798456312yes—
301C2×C4#1798456312yes—
302C22C22×C4×D27711yescharacteristic
303C22C2×Q8×D27711yescharacteristic
304C22#41×D27711yescharacteristic
305C22C2×#1798456311yescharacteristic
306C22C2×#1798456311yescharacteristic
307C22#2257992511yescharacteristic
308C22#2257992711yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—2774no—
317C4—5542no—
318C4—5542no—
319C4—5542no—
320C4—5542no—
321C4—11081no—
322C4—11081no—
323C4—11081no—
324C2C4×Q8×D27711yescharacteristic
325C2C4×#1798456311yescharacteristic
326C2#3180048111yescharacteristic
327C2#3180068511yescharacteristic
328C2#3180070111yescharacteristic
329C2#3180070711yescharacteristic
330C2#3180073011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
FittingC4×C4⋊C4×C277C2
socle, prime radical, cosocleC23×C277C24
hypercenterC4×C4⋊C4D277
hypocenterC277#2370
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #22579870C4semidirect
165. C277#2370semidirect

Maximal subgroups

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

subgroupindex
C2×#225798702
#317999002
#317998992
#317998972
#317998882
#317998872
#317998862
C4×#179845422
#317998532
C4×C4⋊C4×C2772
#2370277