Finite Group Databasebeta

← #45667411

Subgroups — #45667411

Order 32896.

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×#22551582C211yesmaximal, characteristic
2#30656634C211yesmaximal, characteristic
3#30656634C211yesmaximal, characteristic
4#30656633C211yesmaximal, characteristic
5#30656632C211yesmaximal, characteristic
6#30656620C211yesmaximal, characteristic
7#30656619C211yesmaximal, characteristic
8#30656619C211yesmaximal, characteristic
9C4⋊C4×Dic257C211yesmaximal, characteristic
10C4×#16861597C211yesmaximal, characteristic
11C4×#16861597C211yesmaximal, characteristic
12#30656588C211yesmaximal, characteristic
13#30656588C211yesmaximal, characteristic
14#30656588C211yesmaximal, characteristic
15#387×C257C211yesmaximal, characteristic
16#22551582C418yescomplemented
17C2×C4⋊Dic257C2211yescharacteristic
18C2×C4⋊Dic257C2211yescharacteristic
19C2×#16861597C2211yescharacteristic
20C2×#16861597C2211yescharacteristic
21C2×#16861597C2211yescharacteristic
22C2×#16861597C2211yescharacteristic
23C2×#16861597C2211yescharacteristic
24C2×#16861597C2211yescharacteristic
25C2×#16861597C2211yescharacteristic
26C2×#16861597C2211yescharacteristic
27C2×#16861597C2211yescharacteristic
28C2×#16861597C2211yescharacteristic
29C2×C4×Dic257C2211yescharacteristic
30C2×C4×Dic257C2211yescharacteristic
31C2×C4×Dic257C2211yescharacteristic
32C2×C4×Dic257C2211yescharacteristic
33C2×C4×Dic257C2211yescharacteristic
34C2×C4×Dic257C2211yescharacteristic
35C2×C4×Dic257C2211yescharacteristic
36C2×C4×Dic257C2211yescharacteristic
37#22551499C2211yescharacteristic
38#22551499C2211yescharacteristic
39#22551499C2211yescharacteristic
40#22551499C2211yescharacteristic
41#22551499C2211yescharacteristic
42#22551499C2211yescharacteristic
43#22551499C2211yescharacteristic
44#22551499C2211yescharacteristic
45C2×C4⋊C4×C257C2211yescharacteristic
46C2×C4⋊C4×C257C2211yescharacteristic
47C2×C42×C257C2211yescharacteristic
48#95×C257C2211yescharacteristic
49#95×C257C2211yescharacteristic
50#95×C257C2211yescharacteristic
51#95×C257C2211yescharacteristic
52C22×Dic257C2311yescharacteristic
53C22×Dic257C2311yescharacteristic
54C22×Dic257C2311yescharacteristic
55C22×Dic257C2311yescharacteristic
56C22×Dic257C2311yescharacteristic
57C22×Dic257C2311yescharacteristic
58C22×Dic257C2311yescharacteristic
59C22×Dic257C2311yescharacteristic
60C4⋊Dic257—22no—
61C4⋊Dic257C2×C414yes—
62#16861597—22no—
63#16861597—22no—
64#16861597—22no—
65#16861597—22no—
66#16861597—41no—
67#16861597C2×C414yes—
68#16861597C2×C414yes—
69#16861597C2×C414yes—
70#16861597C2×C414yes—
71#16861597Q814yes—
72C4×Dic257—22no—
73C4×Dic257—22no—
74C4×Dic257—22no—
75C4×Dic257—22no—
76C4×Dic257—41no—
77C4×Dic257—41no—
78C4×Dic257—41no—
79C4×Dic257C2×C414yes—
80C22×C4×C257C2311yescharacteristic
81C22×C4×C257C2311yescharacteristic
82C22×C4×C257C2311yescharacteristic
83C22×C4×C257C2311yescharacteristic
84C22×C4×C257C2311yescharacteristic
85C22×C4×C257C2311yescharacteristic
86C22×C4×C257C2311yescharacteristic
87C4⋊C4×C257—41no—
88C4⋊C4×C257C2×C414yes—
89C42×C257—41no—
90C2×Dic257—21no—
91C2×Dic257—21no—
92C2×Dic257—21no—
93C2×Dic257—21no—
94C2×Dic257—21no—
95C2×Dic257—21no—
96C2×Dic257—21no—
97C2×Dic257—21no—
98C2×Dic257—21no—
99C2×Dic257—21no—
100C2×Dic257—21no—
101C2×Dic257—21no—
102C2×Dic257—21no—
103C2×Dic257—21no—
104C2×Dic257—21no—
105C2×Dic257C22×C412yes—
106C2×Dic257C22×C412yes—
107C2×Dic257C22×C412yes—
108C2×Dic257C22×C412yes—
109C2×Dic257C2×Q812yes—
110C2×Dic257C2×Q812yes—
111C2×Dic257#4112yes—
112C2×Dic257#4112yes—
113C2×Dic257#4112yes—
114C23×C257C2411yescharacteristic
115C2×C4×C257—21no—
116C2×C4×C257—21no—
117C2×C4×C257—21no—
118C2×C4×C257—21no—
119C2×C4×C257—21no—
120C2×C4×C257—21no—
121C2×C4×C257—21no—
122C2×C4×C257—21no—
123C2×C4×C257—21no—
124C2×C4×C257—21no—
125C2×C4×C257—21no—
126C2×C4×C257—21no—
127C2×C4×C257—21no—
128C2×C4×C257—21no—
129C2×C4×C257—21no—
130C2×C4×C257—21no—
131C2×C4×C257—21no—
132C2×C4×C257C22×C412yes—
133C2×C4×C257C22×C412yes—
134C2×C4×C257C22×C412yes—
135C2×C4×C257C2×Q812yes—
136C22×C257C23×C411yescharacteristic
137C22×C257C22×Q811yescharacteristic
138C22×C257C2×#4111yescharacteristic
139C22×C257C2×#4111yescharacteristic
140C22×C257C2×#4111yescharacteristic
141C22×C257H(5,𝔽2)11yescharacteristic
142C22×C2572−1+411yescharacteristic
143C4×C257—22no—
144C4×C257—22no—
145C4×C257—22no—
146C4×C257—22no—
147C4×C257—41no—
148C4×C257—41no—
149C4×C257—41no—
150Dic257—22no—
151Dic257—22no—
152Dic257—22no—
153Dic257—22no—
154Dic257—22no—
155Dic257—22no—
156Dic257—41no—
157Dic257C4×Q814yes—
158C2×C257C2×C4×Q811yescharacteristic
159C2×C257C4×#4111yescharacteristic
160C2×C257#52011yescharacteristic
161C2×C257#55211yescharacteristic
162C2×C257#55311yescharacteristic
163C2×C257#55411yescharacteristic
164C2×C257#55711yescharacteristic
165C257#237011yescharacteristic, complemented, Sylow
166#2370—2571nomaximal, Sylow
167C2×#125—2571no—
168#389—2571no—
169#389—2571no—
170#389—2571no—
171#389—2571no—
172#387—2571no—
173#387—2571no—
174#387—2571no—
175#387D25711yescharacteristic
176C4×C4⋊C4—2571no—
177C4×C4⋊C4—2571no—
178C4×C4⋊C4—2571no—
179C4×C4⋊C4—2571no—
180C4×C4⋊C4—2571no—
181C4×C4⋊C4—2571no—
182#125—2578no—
183C2×C4⋊C4—2571no—
184C2×C4⋊C4—2571no—
185C2×C4⋊C4—2571no—
186C2×C4⋊C4—2571no—
187C2×C4⋊C4—2571no—
188C2×C4⋊C4—2571no—
189C2×C4⋊C4—2571no—
190C2×C4⋊C4—2571no—
191C2×C4⋊C4—2571no—
192C2×C4⋊C4—2571no—
193C2×C4⋊C4—2571no—
194C2×C4⋊C4—2571no—
195C2×C4⋊C4C2×D25711yescharacteristic
196C2×C4⋊C4C2×D25711yescharacteristic
197C2×C42—2571no—
198C2×C42—2571no—
199C2×C42—2571no—
200C2×C42—2571no—
201C2×C42—2571no—
202C2×C42—2571no—
203C2×C42—2571no—
204C2×C42—2571no—
205C2×C42C2×D25711yescharacteristic
206#95—2571no—
207#95—2571no—
208#95—2571no—
209#95—2571no—
210#95—2571no—
211#95—2571no—
212#95—2571no—
213#95—2571no—
214#95C2×D25711yescharacteristic
215#95C2×D25711yescharacteristic
216#95C2×D25711yescharacteristic
217#95C2×D25711yescharacteristic
218C22×C4—2571no—
219C22×C4—2571no—
220C22×C4—2571no—
221C22×C4—2571no—
222C22×C4—2571no—
223C22×C4—2571no—
224C22×C4—2571no—
225C22×C4—2571no—
226C22×C4C22×D25711yescharacteristic
227C22×C4C22×D25711yescharacteristic
228C22×C4C22×D25711yescharacteristic
229C22×C4C22×D25711yescharacteristic
230C22×C4C22×D25711yescharacteristic
231C22×C4C22×D25711yescharacteristic
232C22×C4C22×D25711yescharacteristic
233C4⋊C4—2574no—
234C4⋊C4—2574no—
235C4⋊C4—2574no—
236C4⋊C4—2574no—
237C4⋊C4—2574no—
238C4⋊C4—2574no—
239C4⋊C4—5142no—
240C4⋊C4—5142no—
241C4⋊C4—5142no—
242C4⋊C4—5142no—
243C4⋊C4—5142no—
244C4⋊C4—41no—
245C4⋊C4—10281no—
246C4⋊C4C4×D25714yes—
247C42—2574no—
248C42—5142no—
249C42—5142no—
250C42—5142no—
251C42—5142no—
252C42—41no—
253C42—10281no—
254C42—10281no—
255C42—10281no—
256C23C23×D25711yescharacteristic
257C2×C4—2572no—
258C2×C4—2572no—
259C2×C4—2572no—
260C2×C4—2572no—
261C2×C4—2572no—
262C2×C4—2572no—
263C2×C4—2572no—
264C2×C4—2572no—
265C2×C4—2572no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—5141no—
284C2×C4—5141no—
285C2×C4—5141no—
286C2×C4—5141no—
287C2×C4—5141no—
288C2×C4—5141no—
289C2×C4—5141no—
290C2×C4—5141no—
291C2×C4—5141no—
292C2×C4—5141no—
293C2×C4—5141no—
294C2×C4—5141no—
295C2×C4—5141no—
296C2×C4—5141no—
297C2×C4—5141no—
298C2×C4C2×C4×D25712yes—
299C2×C4C2×C4×D25712yes—
300C2×C4C2×C4×D25712yes—
301C2×C4Q8×D25712yes—
302C22C22×C4×D25711yescharacteristic
303C22C2×Q8×D25711yescharacteristic
304C22#41×D25711yescharacteristic
305C22#41×D25711yescharacteristic
306C22#41×D25711yescharacteristic
307C22#2255163711yescharacteristic
308C22#2255163911yescharacteristic
309C4—2574no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—5142no—
315C4—5142no—
316C4—5142no—
317C4—5142no—
318C4—5142no—
319C4—5142no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—10281no—
324C2C4×Q8×D25711yescharacteristic
325C2#3065720511yescharacteristic
326C2#3065721611yescharacteristic
327C2#3065742311yescharacteristic
328C2#3065743211yescharacteristic
329C2#3065744111yescharacteristic
330C2#3065746411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D257
commutatorC22×C257C23×C4
Fitting#387×C257C2
socle, prime radical, cosocleC23×C257C24
hypercenter#387D257
hypocenterC257#2370
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #22551582C4semidirect
165. C257#2370semidirect

Maximal subgroups

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

subgroupindex
C2×#225515822
#306566342
#306566332
#306566322
#306566202
#306566192
C4⋊C4×Dic2572
C4×#168615972
#306565882
#387×C2572
#2370257