Finite Group Databasebeta

← #37575374

Subgroups — #37575374

Order 24448.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259278C211yesmaximal, characteristic
2#27132547C211yesmaximal, characteristic, complemented
3#27132547C211yesmaximal, characteristic, complemented
4#27132545C211yesmaximal, characteristic, complemented
5#27132545C211yesmaximal, characteristic, complemented
6#27132536C211yesmaximal, characteristic
7#27132535C211yesmaximal, characteristic
8#27132530C211yesmaximal, characteristic, complemented
9#27132527C211yesmaximal, characteristic, complemented
10#27132524C211yesmaximal, characteristic
11C4×Dic191⋊C4C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic191C211yesmaximal, characteristic
13#27132509C211yesmaximal, characteristic, complemented
14C2×C191⋊#95C211yesmaximal, characteristic
15C4×C22⋊C4×C191C211yesmaximal, characteristic
16C23×Dic191C2211yescharacteristic
17C23×Dic191C2211yescharacteristic
18#20259278C418yescomplemented
19C2×Dic191⋊C4C2211yescharacteristic
20C2×Dic191⋊C4C2211yescharacteristic
21C2×Dic191⋊C4C2211yescharacteristic
22C2×Dic191⋊C4C2211yescharacteristic
23C2×Dic191⋊C4C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×C22⋊Dic191C2211yescharacteristic
26C2×C22⋊Dic191C2211yescharacteristic
27C2×C4×Dic191C2211yescharacteristic
28C2×C4×Dic191C2211yescharacteristic
29C2×C4×Dic191C2211yescharacteristic
30C2×C4×Dic191C2211yescharacteristic
31C191⋊#95C2211yescharacteristic
32C191⋊#95C2211yescharacteristic
33C191⋊#95C2211yescharacteristic
34C191⋊#95C2211yescharacteristic
35C191⋊#95C2211yescharacteristic
36C191⋊#95C2211yescharacteristic
37C191⋊#95C2211yescharacteristic
38C191⋊#95C2211yescharacteristic
39C191⋊#95C2211yescharacteristic
40C191⋊#95C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C23×C4×C191C2211yescharacteristic
46C2×C22⋊C4×C191C2211yescharacteristic
47C2×C22⋊C4×C191C2211yescharacteristic
48C2×C42×C191C2211yescharacteristic
49C2×C42×C191C2211yescharacteristic
50#95×C191C2211yescharacteristic
51#95×C191C2211yescharacteristic
52C22×Dic191—22no—
53C22×Dic191—22no—
54C22×Dic191—22no—
55C22×Dic191—22no—
56C22×Dic191—41no—
57C22×Dic191C2×C414yes—
58C22×Dic191C2311yescharacteristic
59C22×Dic191C2311yescharacteristic
60C22×Dic191C2311yescharacteristic
61C22×Dic191C2311yescharacteristic
62C22×Dic191C2311yescharacteristic
63C22×Dic191C2311yescharacteristic
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66Dic191⋊C4—22no—
67Dic191⋊C4—22no—
68Dic191⋊C4—41no—
69Dic191⋊C4—41no—
70Dic191⋊C4C2×C414yescomplemented
71Dic191⋊C4C2×C414yescomplemented
72C22⋊Dic191—22no—
73C22⋊Dic191C2×C414yes—
74C4×Dic191—22no—
75C4×Dic191—41no—
76C4×Dic191C2×C414yescomplemented
77C4×Dic191C2×C414yescomplemented
78C24×C191C2311yescharacteristic
79C22×C4×C191—22no—
80C22×C4×C191—22no—
81C22×C4×C191—41no—
82C22×C4×C191C2311yescharacteristic
83C22×C4×C191C2311yescharacteristic
84C22×C4×C191C2311yescharacteristic
85C22×C4×C191C2311yescharacteristic
86C22×C4×C191C2311yescharacteristic
87C22×C4×C191C2311yescharacteristic
88C22⋊C4×C191—22no—
89C22⋊C4×C191C2×C414yes—
90C42×C191—22no—
91C42×C191—41no—
92C2×Dic191—28no—
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×Dic191—21no—
108C2×Dic191—21no—
109C2×Dic191—21no—
110C2×Dic191—21no—
111C2×Dic191—21no—
112C2×Dic191—44no—
113C2×Dic191C22×C412yes—
114C2×Dic191C22×C412yes—
115C2×Dic191C22×C412yes—
116C2×Dic191C22×C412yes—
117C2×Dic191#4112yes—
118C23×C191—21no—
119C23×C191—21no—
120C23×C191—21no—
121C23×C191—21no—
122C23×C191C22×C412yes—
123C23×C191#4112yes—
124C23×C191#4112yes—
125C23×C191C2411yescharacteristic
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×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—44no—
142C2×C4×C191C22×C412yes—
143C2×C4×C191C22×C412yes—
144C2×C4×C191#4112yes—
145C22×C191—22no—
146C22×C191—22no—
147C22×C191—22no—
148C22×C191—22no—
149C22×C191—22no—
150C22×C191—22no—
151C22×C191#11714yes—
152C22×C191C23×C411yescharacteristic
153C22×C191C2×#4111yescharacteristic
154C22×C191C2×#4111yescharacteristic
155C22×C191C2×#4111yescharacteristic
156C22×C191C2×#4111yescharacteristic
157C22×C191H(5,𝔽2)11yescharacteristic
158C22×C1912−1+411yescharacteristic
159C4×C191—22no—
160C4×C191—22no—
161C4×C191—22no—
162C4×C191—41no—
163C4×C191—41no—
164C4×C191—41no—
165Dic191—22no—
166Dic191—22no—
167Dic191—22no—
168Dic191—22no—
169Dic191—22no—
170Dic191—41no—
171Dic191—41no—
172Dic191—41no—
173C2×C191—24no—
174C2×C191C2×#11711yescharacteristic
175C2×C191C4×#4111yescharacteristic
176C2×C191#52011yescharacteristic
177C2×C191#55111yescharacteristic
178C2×C191#55111yescharacteristic
179C2×C191#55211yescharacteristic
180C2×C191#55211yescharacteristic
181C191#234311yescharacteristic, complemented, Sylow
182#2343—1911nomaximal, Sylow
183C2×#117—1911no—
184#387—1911no—
185#387—1911no—
186#387—1911no—
187#387—1911no—
188#385—1911no—
189#385—1911no—
190#383—1911no—
191#382—1911no—
192#381—1911no—
193C4×C4⋊C4—1911no—
194C4×C22⋊C4—1911no—
195C4×C22⋊C4D19111yescharacteristic
196#376—1911no—
197C2×#95—1911no—
198C23×C4—1911no—
199C23×C4—1911no—
200C23×C4C2×D19111yescharacteristic
201#117—1918no—
202C2×C4⋊C4—1911no—
203C2×C4⋊C4—1911no—
204C2×C4⋊C4—1911no—
205C2×C4⋊C4—1911no—
206C2×C4⋊C4—1911no—
207C2×C4⋊C4—1911no—
208C2×C22⋊C4—1911no—
209C2×C22⋊C4—1911no—
210C2×C22⋊C4C2×D19111yescharacteristic
211C2×C22⋊C4C2×D19111yescharacteristic
212C2×C42—1911no—
213C2×C42—1911no—
214C2×C42—1911no—
215C2×C42—1911no—
216C2×C42C2×D19111yescharacteristic
217C2×C42C2×D19111yescharacteristic
218#95—1911no—
219#95—1911no—
220#95—1911no—
221#95—1911no—
222#95—1911no—
223#95—1911no—
224#95—1911no—
225#95—1911no—
226#95—1911no—
227#95—1911no—
228#95—1911no—
229#95—1911no—
230#95—1911no—
231#95—1911no—
232#95C2×D19111yescharacteristic
233#95C2×D19111yescharacteristic
234C24C22×D19111yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—3822no—
239C22×C4—3822no—
240C22×C4—3822no—
241C22×C4—3822no—
242C22×C4—1911no—
243C22×C4—1911no—
244C22×C4—1911no—
245C22×C4—1914no—
246C22×C4—1911no—
247C22×C4—1911no—
248C22×C4—1911no—
249C22×C4—1911no—
250C22×C4—1911no—
251C22×C4—7641no—
252C22×C4C22×D19111yescharacteristic
253C22×C4C22×D19111yescharacteristic
254C22×C4C22×D19111yescharacteristic
255C22×C4C22×D19111yescharacteristic
256C22×C4C22×D19111yescharacteristic
257C22×C4C22×D19111yescharacteristic
258C4⋊C4—3822no—
259C4⋊C4—3822no—
260C4⋊C4—1914no—
261C4⋊C4—1914no—
262C4⋊C4—7641no—
263C4⋊C4—7641no—
264C22⋊C4—22no—
265C22⋊C4—3822no—
266C22⋊C4—1914no—
267C22⋊C4C4×D19114yes—
268C42—22no—
269C42—41no—
270C42—3822no—
271C42—1914no—
272C42—1914no—
273C42—7641no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D19112yes—
279C23#1569028712yes—
280C23#1569028712yes—
281C23C23×D19111yescharacteristic
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—44no—
298C2×C4—3821no—
299C2×C4—3821no—
300C2×C4—3821no—
301C2×C4—3821no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—3821no—
306C2×C4—3821no—
307C2×C4—3821no—
308C2×C4—3828no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—1912no—
319C2×C4—1912no—
320C2×C4—1912no—
321C2×C4—1912no—
322C2×C4—1912no—
323C2×C4—7644no—
324C2×C4C2×C4×D19112yes—
325C2×C4C2×C4×D19112yes—
326C2×C4#1569028612yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#2025927914yes—
334C22C22×C4×D19111yescharacteristic
335C22#41×D19111yescharacteristic
336C22C2×#1569028611yescharacteristic
337C22C2×#1569028711yescharacteristic
338C22C2×#1569028711yescharacteristic
339C22#2025936711yescharacteristic
340C22#2025936911yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3822no—
348C4—3822no—
349C4—3822no—
350C4—3822no—
351C4—3822no—
352C4—7641no—
353C4—7641no—
354C4—7641no—
355C2—24no—
356C2C2×#2025927911yescharacteristic
357C2C4×#1569028611yescharacteristic
358C2#2713314211yescharacteristic
359C2#2713333911yescharacteristic
360C2#2713334211yescharacteristic
361C2#2713334611yescharacteristic
362C2#2713335311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC4×C22⋊C4×C191C2
socle, cosocleC23×C191C24
prime radicalC24×C191C23
hypercenterC4×C22⋊C4D191
hypocenterC191#2343
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #27132547C2semidirect
3. #27132547C2semidirect
4. #27132545C2semidirect
5. #27132545C2semidirect
8. #27132530C2semidirect
9. #27132527C2semidirect
11. C4×Dic191⋊C4C2semidirect
13. #27132509C2semidirect
18. #20259278C4semidirect
70. Dic191⋊C4C2×C4semidirect
71. Dic191⋊C4C2×C4semidirect
76. C4×Dic191C2×C4semidirect
77. C4×Dic191C2×C4semidirect
181. C191#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#202592782
#271325472
#271325452
#271325362
#271325352
#271325302
#271325272
#271325242
C4×Dic191⋊C42
C22⋊C4×Dic1912
#271325092
C2×C191⋊#952
C4×C22⋊C4×C1912
#2343191