Finite Group Databasebeta

← #37575235

Subgroups — #37575235

Order 24448.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259321C211yesmaximal, characteristic
2C2×C4×Dic382C211yesmaximal, characteristic
3C2×#20259287C211yesmaximal, characteristic
4#27132567C211yesmaximal, characteristic
5#27132567C211yesmaximal, characteristic
6#27132550C211yesmaximal, characteristic
7#27132549C211yesmaximal, characteristic
8#27132548C211yesmaximal, characteristic
9#27132547C211yesmaximal, characteristic
10#27132546C211yesmaximal, characteristic
11#27132545C211yesmaximal, characteristic
12#27132544C211yesmaximal, characteristic
13#27132527C211yesmaximal, characteristic
14#27132508C211yesmaximal, characteristic
15#387×C191C211yesmaximal, characteristic
16C22×Dic382C2211yescharacteristic
17C22×Dic382C2211yescharacteristic
18#20259321C418yescomplemented
19C4×Dic382—24no—
20#20259287—24no—
21C2×C4⋊Dic191C2211yescharacteristic
22C2×C4⋊Dic191C2211yescharacteristic
23C2×Dic191⋊C4C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×C4×Dic191C2211yescharacteristic
30C2×C4×Dic191C2211yescharacteristic
31C2×C4×Dic191C2211yescharacteristic
32C2×C4×Dic191C2211yescharacteristic
33C2×C4×Dic191C2211yescharacteristic
34C2×C4×Dic191C2211yescharacteristic
35C191⋊#95C2211yescharacteristic
36C191⋊#95C2211yescharacteristic
37C191⋊#95C2211yescharacteristic
38C191⋊#95C2211yescharacteristic
39C191⋊#95C2211yescharacteristic
40C191⋊#95C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C2×C4⋊C4×C191C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic
49C2×C42×C191C2211yescharacteristic
50#95×C191C2211yescharacteristic
51#95×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54C2×Dic382—22no—
55C2×Dic382—22no—
56C2×Dic382—22no—
57C2×Dic382—22no—
58C2×Dic382C2×C414yes—
59C2×Dic382C2×C414yes—
60C22×Dic191C2311yescharacteristic
61C22×Dic191C2311yescharacteristic
62C22×Dic191C2311yescharacteristic
63C22×Dic191C2311yescharacteristic
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C4⋊Dic191—22no—
69C4⋊Dic191C2×C414yes—
70Dic191⋊C4—22no—
71Dic191⋊C4—22no—
72Dic191⋊C4—22no—
73Dic191⋊C4—22no—
74Dic191⋊C4C2×C414yes—
75Dic191⋊C4C2×C414yes—
76C4×Dic191—22no—
77C4×Dic191—22no—
78C4×Dic191—22no—
79C4×Dic191—22no—
80C4×Dic191C2×C414yes—
81C4×Dic191D414yes—
82C22×C4×C191C2311yescharacteristic
83C22×C4×C191C2311yescharacteristic
84C22×C4×C191C2311yescharacteristic
85C22×C4×C191C2311yescharacteristic
86C22×C4×C191C2311yescharacteristic
87C22×C4×C191C2311yescharacteristic
88C22×C4×C191C2311yescharacteristic
89C4⋊C4×C191—22no—
90C4⋊C4×C191C2×C414yes—
91C42×C191—22no—
92Dic382—28no—
93Dic382—28no—
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×Dic191—21no—
108C2×Dic191—21no—
109C2×Dic191—21no—
110C2×Dic191—21no—
111C2×Dic191C22×C412yes—
112C2×Dic191C22×C412yes—
113C2×Dic191C22×C412yes—
114C2×Dic191C22×C412yes—
115C2×Dic191C2×D412yes—
116C2×Dic191C2×D412yes—
117C2×Dic191#4112yes—
118C23×C191C2411yescharacteristic
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×C191—21no—
133C2×C4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191C22×C412yes—
137C2×C4×C191C22×C412yes—
138C2×C4×C191C22×C412yes—
139C2×C4×C191C2×D412yes—
140C22×C191C23×C411yescharacteristic
141C22×C191C22×D411yescharacteristic
142C22×C191C2×#4111yescharacteristic
143C22×C1912−1+411yescharacteristic
144C22×C1912−1+411yescharacteristic
145C22×C1912−1+411yescharacteristic
146C22×C1912−1+411yescharacteristic
147C4×C191—22no—
148C4×C191—22no—
149C4×C191—22no—
150C4×C191—22no—
151C4×C191—41no—
152C4×C191—41no—
153C4×C191—41no—
154Dic191—22no—
155Dic191—22no—
156Dic191—22no—
157Dic191—22no—
158Dic191—41no—
159Dic191—41no—
160Dic191—41no—
161Dic191C4×D414yes—
162C2×C191C2×C4×D411yescharacteristic
163C2×C191#51911yescharacteristic
164C2×C191#51911yescharacteristic
165C2×C191#53611yescharacteristic
166C2×C191#53611yescharacteristic
167C2×C191#54111yescharacteristic
168C2×C191#54111yescharacteristic
169C191#232711yescharacteristic, complemented, Sylow
170#2327—1911nomaximal, Sylow
171C2×C4⋊Q8—1911no—
172C2×C4×Q8—1911no—
173C2×C4×Q8—1911no—
174#391—1911no—
175#391—1911no—
176#387—1911no—
177#387—1911no—
178#387—1911no—
179#387—1911no—
180#387—1911no—
181#387—1911no—
182#387—1911no—
183#387D19111yescharacteristic
184#382—1911no—
185#376—1911no—
186C22×Q8—1911no—
187C22×Q8—1911no—
188C4⋊Q8—1918no—
189C4×Q8—3824no—
190C4×Q8—3824no—
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⋊C4—1911no—
198C2×C4⋊C4—1911no—
199C2×C4⋊C4C2×D19111yescharacteristic
200C2×C4⋊C4C2×D19111yescharacteristic
201C2×C42—1911no—
202C2×C42—1911no—
203C2×C42—1911no—
204C2×C42—1911no—
205C2×C42—1911no—
206C2×C42—1911no—
207C2×C42C2×D19111yescharacteristic
208#95—1911no—
209#95—1911no—
210#95—1911no—
211#95—1911no—
212#95—1911no—
213#95—1911no—
214#95—1911no—
215#95—1911no—
216#95—1911no—
217#95—1911no—
218#95—1911no—
219#95—1911no—
220#95C2×D19111yescharacteristic
221#95C2×D19111yescharacteristic
222#95C2×D19111yescharacteristic
223#95C2×D19111yescharacteristic
224C2×Q8—3822no—
225C2×Q8—3822no—
226C2×Q8—3822no—
227C2×Q8—3822no—
228C2×Q8—1914no—
229C2×Q8—1914no—
230C22×C4—1911no—
231C22×C4—1911no—
232C22×C4—1911no—
233C22×C4—1911no—
234C22×C4—1911no—
235C22×C4—1911no—
236C22×C4—1911no—
237C22×C4—1911no—
238C22×C4C22×D19111yescharacteristic
239C22×C4C22×D19111yescharacteristic
240C22×C4C22×D19111yescharacteristic
241C22×C4C22×D19111yescharacteristic
242C22×C4C22×D19111yescharacteristic
243C22×C4C22×D19111yescharacteristic
244C22×C4C22×D19111yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—3822no—
247C4⋊C4—3822no—
248C4⋊C4—3822no—
249C4⋊C4—3822no—
250C4⋊C4—3822no—
251C4⋊C4—1914no—
252C4⋊C4—1914no—
253C4⋊C4—1914no—
254C4⋊C4C4×D19114yes—
255C42—22no—
256C42—3822no—
257C42—3822no—
258C42—3822no—
259C42—3822no—
260C42—1914no—
261C42—1914no—
262C23C23×D19111yescharacteristic
263Q8—3828no—
264Q8—3828no—
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—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
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—3821no—
292C2×C4—3821no—
293C2×C4—3821no—
294C2×C4—3821no—
295C2×C4—3821no—
296C2×C4—3821no—
297C2×C4—3821no—
298C2×C4—3821no—
299C2×C4—1912no—
300C2×C4—1912no—
301C2×C4—1912no—
302C2×C4—1912no—
303C2×C4—1912no—
304C2×C4—1912no—
305C2×C4—1912no—
306C2×C4C2×C4×D19112yes—
307C2×C4C2×C4×D19112yes—
308C2×C4C2×C4×D19112yes—
309C2×C4D4×D19112yes—
310C22C22×C4×D19111yescharacteristic
311C22C2×D4×D19111yescharacteristic
312C22#41×D19111yescharacteristic
313C22#2025936911yescharacteristic
314C22#2025936911yescharacteristic
315C22#2025936911yescharacteristic
316C22#2025937011yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3822no—
325C4—3822no—
326C4—3822no—
327C4—3822no—
328C4—1914no—
329C4—7641no—
330C4—7641no—
331C4—7641no—
332C2C4×D4×D19111yescharacteristic
333C2#2713313911yescharacteristic
334C2#2713314011yescharacteristic
335C2#2713323511yescharacteristic
336C2#2713323611yescharacteristic
337C2#2713327011yescharacteristic
338C2#2713327211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#387×C191C2
socle, prime radical, cosocleC23×C191C24
hypercenter#387D191
hypocenterC191#2327
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #20259321C4semidirect
169. C191#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#202593212
C2×C4×Dic3822
C2×#202592872
#271325672
#271325502
#271325492
#271325482
#271325472
#271325462
#271325452
#271325442
#271325272
#271325082
#387×C1912
#2327191