Finite Group Databasebeta

← #37575256

Subgroups — #37575256

Order 24448.

444 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×#20259312C211yesmaximal, characteristic
2#27132562C211yesmaximal, characteristic
3#27132561C211yesmaximal, characteristic
4#27132560C211yesmaximal, characteristic
5#27132560C211yesmaximal, characteristic
6#27132560C211yesmaximal, characteristic
7#27132558C211yesmaximal, characteristic
8#27132550C211yesmaximal, characteristic
9#27132548C211yesmaximal, characteristic
10#27132545C211yesmaximal, characteristic
11#27132532C211yesmaximal, characteristic
12C4×Dic191⋊C4C211yesmaximal, characteristic
13#27132514C211yesmaximal, characteristic
14#27132508C211yesmaximal, characteristic
15#387×C191C211yesmaximal, characteristic
16#20259312C418yescomplemented
17C2×C4⋊Dic191C2211yescharacteristic
18C2×C4⋊Dic191C2211yescharacteristic
19C2×C4⋊Dic191C2211yescharacteristic
20C2×C4⋊Dic191C2211yescharacteristic
21C2×Dic191⋊C4C2211yescharacteristic
22C2×Dic191⋊C4C2211yescharacteristic
23C2×Dic191⋊C4C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×Dic191⋊C4C2211yescharacteristic
30C2×Dic191⋊C4C2211yescharacteristic
31C2×C4×Dic191C2211yescharacteristic
32C2×C4×Dic191C2211yescharacteristic
33C2×C4×Dic191C2211yescharacteristic
34C2×C4×Dic191C2211yescharacteristic
35C2×C4×Dic191C2211yescharacteristic
36C2×C4×Dic191C2211yescharacteristic
37C191⋊#95C2211yescharacteristic
38C191⋊#95C2211yescharacteristic
39C191⋊#95C2211yescharacteristic
40C191⋊#95C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C2×C4⋊C4×C191C2211yescharacteristic
46C2×C4⋊C4×C191C2211yescharacteristic
47C2×C42×C191C2211yescharacteristic
48#95×C191C2211yescharacteristic
49#95×C191C2211yescharacteristic
50#95×C191C2211yescharacteristic
51#95×C191C2211yescharacteristic
52C22×Dic191C2311yescharacteristic
53C22×Dic191C2311yescharacteristic
54C22×Dic191C2311yescharacteristic
55C22×Dic191C2311yescharacteristic
56C22×Dic191C2311yescharacteristic
57C22×Dic191C2311yescharacteristic
58C22×Dic191C2311yescharacteristic
59C22×Dic191C2311yescharacteristic
60C4⋊Dic191—41no—
61C4⋊Dic191—41no—
62C4⋊Dic191—41no—
63C4⋊Dic191C2×C414yes—
64Dic191⋊C4—22no—
65Dic191⋊C4—22no—
66Dic191⋊C4—41no—
67Dic191⋊C4—41no—
68Dic191⋊C4—41no—
69Dic191⋊C4—41no—
70Dic191⋊C4C2×C414yes—
71Dic191⋊C4C2×C414yes—
72Dic191⋊C4C2×C414yes—
73Dic191⋊C4C2×C414yes—
74C4×Dic191—22no—
75C4×Dic191—41no—
76C4×Dic191—41no—
77C4×Dic191—41no—
78C4×Dic191C2×C414yes—
79C4×Dic191Q814yes—
80C22×C4×C191C2311yescharacteristic
81C22×C4×C191C2311yescharacteristic
82C22×C4×C191C2311yescharacteristic
83C22×C4×C191C2311yescharacteristic
84C22×C4×C191C2311yescharacteristic
85C22×C4×C191C2311yescharacteristic
86C22×C4×C191C2311yescharacteristic
87C4⋊C4×C191—41no—
88C4⋊C4×C191C2×C414yes—
89C42×C191—41no—
90C2×Dic191—21no—
91C2×Dic191—21no—
92C2×Dic191—21no—
93C2×Dic191—21no—
94C2×Dic191—21no—
95C2×Dic191—21no—
96C2×Dic191—21no—
97C2×Dic191—21no—
98C2×Dic191—21no—
99C2×Dic191—21no—
100C2×Dic191—21no—
101C2×Dic191—21no—
102C2×Dic191—21no—
103C2×Dic191—21no—
104C2×Dic191—21no—
105C2×Dic191—21no—
106C2×Dic191—21no—
107C2×Dic191C22×C412yes—
108C2×Dic191C22×C412yes—
109C2×Dic191C22×C412yes—
110C2×Dic191C22×C412yes—
111C2×Dic191C2×Q812yes—
112C2×Dic191C2×Q812yes—
113C2×Dic191#4112yes—
114C23×C191C2411yescharacteristic
115C2×C4×C191—21no—
116C2×C4×C191—21no—
117C2×C4×C191—21no—
118C2×C4×C191—21no—
119C2×C4×C191—21no—
120C2×C4×C191—21no—
121C2×C4×C191—21no—
122C2×C4×C191—21no—
123C2×C4×C191—21no—
124C2×C4×C191—21no—
125C2×C4×C191—21no—
126C2×C4×C191—21no—
127C2×C4×C191—21no—
128C2×C4×C191—21no—
129C2×C4×C191—21no—
130C2×C4×C191—21no—
131C2×C4×C191—21no—
132C2×C4×C191C22×C412yes—
133C2×C4×C191C22×C412yes—
134C2×C4×C191C22×C412yes—
135C2×C4×C191C2×Q812yes—
136C22×C191C23×C411yescharacteristic
137C22×C191C22×Q811yescharacteristic
138C22×C191C2×#4111yescharacteristic
139C22×C191H(5,𝔽2)11yescharacteristic
140C22×C191H(5,𝔽2)11yescharacteristic
141C22×C1912−1+411yescharacteristic
142C22×C1912−1+411yescharacteristic
143C4×C191—22no—
144C4×C191—22no—
145C4×C191—22no—
146C4×C191—22no—
147C4×C191—41no—
148C4×C191—41no—
149C4×C191—41no—
150Dic191—22no—
151Dic191—22no—
152Dic191—22no—
153Dic191—22no—
154Dic191—41no—
155Dic191—41no—
156Dic191—41no—
157Dic191C4×Q814yes—
158C2×C191C2×C4×Q811yescharacteristic
159C2×C191#52011yescharacteristic
160C2×C191#52011yescharacteristic
161C2×C191#54011yescharacteristic
162C2×C191#54111yescharacteristic
163C2×C191#54411yescharacteristic
164C2×C191#54411yescharacteristic
165C191#233011yescharacteristic, complemented, Sylow
166#2330—1911nomaximal, Sylow
167C2×#125—1911no—
168#389—1911no—
169#389—1911no—
170#389—1911no—
171#389—1911no—
172#389—1911no—
173#389—1911no—
174#387—1911no—
175#387—1911no—
176#387—1911no—
177#387D19111yescharacteristic
178#384—1911no—
179C4×C4⋊C4—1911no—
180C4×C4⋊C4—1911no—
181#376—1911no—
182#125—1918no—
183C2×C4⋊C4—1911no—
184C2×C4⋊C4—1911no—
185C2×C4⋊C4—1911no—
186C2×C4⋊C4—1911no—
187C2×C4⋊C4—1911no—
188C2×C4⋊C4—1911no—
189C2×C4⋊C4—1911no—
190C2×C4⋊C4—1911no—
191C2×C4⋊C4—1911no—
192C2×C4⋊C4—1911no—
193C2×C4⋊C4—1911no—
194C2×C4⋊C4—1911no—
195C2×C4⋊C4—1911no—
196C2×C4⋊C4—1911no—
197C2×C4⋊C4C2×D19111yescharacteristic
198C2×C4⋊C4C2×D19111yescharacteristic
199C2×C42—1911no—
200C2×C42—1911no—
201C2×C42—1911no—
202C2×C42—1911no—
203C2×C42—1911no—
204C2×C42—1911no—
205C2×C42C2×D19111yescharacteristic
206#95—1911no—
207#95—1911no—
208#95—1911no—
209#95—1911no—
210#95—1911no—
211#95—1911no—
212#95—1911no—
213#95—1911no—
214#95C2×D19111yescharacteristic
215#95C2×D19111yescharacteristic
216#95C2×D19111yescharacteristic
217#95C2×D19111yescharacteristic
218C22×C4—1911no—
219C22×C4—1911no—
220C22×C4—1911no—
221C22×C4—1911no—
222C22×C4—1911no—
223C22×C4—1911no—
224C22×C4—1911no—
225C22×C4—1911no—
226C22×C4C22×D19111yescharacteristic
227C22×C4C22×D19111yescharacteristic
228C22×C4C22×D19111yescharacteristic
229C22×C4C22×D19111yescharacteristic
230C22×C4C22×D19111yescharacteristic
231C22×C4C22×D19111yescharacteristic
232C22×C4C22×D19111yescharacteristic
233C4⋊C4—41no—
234C4⋊C4—3822no—
235C4⋊C4—3822no—
236C4⋊C4—1914no—
237C4⋊C4—1914no—
238C4⋊C4—1914no—
239C4⋊C4—1914no—
240C4⋊C4—1914no—
241C4⋊C4—7641no—
242C4⋊C4—7641no—
243C4⋊C4—7641no—
244C4⋊C4—7641no—
245C4⋊C4—7641no—
246C4⋊C4—7641no—
247C4⋊C4—7641no—
248C4⋊C4C4×D19114yes—
249C42—41no—
250C42—3822no—
251C42—1914no—
252C42—1914no—
253C42—7641no—
254C42—7641no—
255C42—7641no—
256C23C23×D19111yescharacteristic
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—21no—
273C2×C4—21no—
274C2×C4—3821no—
275C2×C4—3821no—
276C2×C4—3821no—
277C2×C4—3821no—
278C2×C4—3821no—
279C2×C4—3821no—
280C2×C4—3821no—
281C2×C4—3821no—
282C2×C4—3821no—
283C2×C4—3821no—
284C2×C4—3821no—
285C2×C4—3821no—
286C2×C4—3821no—
287C2×C4—3821no—
288C2×C4—3821no—
289C2×C4—3821no—
290C2×C4—3821no—
291C2×C4—1912no—
292C2×C4—1912no—
293C2×C4—1912no—
294C2×C4—1912no—
295C2×C4—1912no—
296C2×C4—1912no—
297C2×C4—1912no—
298C2×C4C2×C4×D19112yes—
299C2×C4C2×C4×D19112yes—
300C2×C4C2×C4×D19112yes—
301C2×C4Q8×D19112yes—
302C22C22×C4×D19111yescharacteristic
303C22C2×Q8×D19111yescharacteristic
304C22#41×D19111yescharacteristic
305C22#2025936711yescharacteristic
306C22#2025936811yescharacteristic
307C22#2025936911yescharacteristic
308C22#2025936911yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—3822no—
317C4—3822no—
318C4—3822no—
319C4—3822no—
320C4—1914no—
321C4—7641no—
322C4—7641no—
323C4—7641no—
324C2C4×Q8×D19111yescharacteristic
325C2#2713314211yescharacteristic
326C2#2713314311yescharacteristic
327C2#2713326511yescharacteristic
328C2#2713327011yescharacteristic
329C2#2713329211yescharacteristic
330C2#2713329311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#387×C191C2
socle, prime radical, cosocleC23×C191C24
hypercenter#387D191
hypocenterC191#2330
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #20259312C4semidirect
165. C191#2330semidirect

Maximal subgroups

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

subgroupindex
C2×#202593122
#271325622
#271325612
#271325602
#271325582
#271325502
#271325482
#271325452
#271325322
C4×Dic191⋊C42
#271325142
#271325082
#387×C1912
#2330191