Finite Group Databasebeta

← #37541927

Subgroups — #37541927

Order 23168.

358 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041220C211yesmaximal, characteristic, complemented
2#26041218C211yesmaximal, characteristic, complemented
3#26041214C211yesmaximal, characteristic
4#26041212C211yesmaximal, characteristic, complemented
5#26041210C211yesmaximal, characteristic, complemented
6#26041210C211yesmaximal, characteristic, complemented
7#26041208C211yesmaximal, characteristic
8#26041208C211yesmaximal, characteristic
9#26041208C211yesmaximal, characteristic
10#26041201C211yesmaximal, characteristic
11#26041201C211yesmaximal, characteristic
12#26041176C211yesmaximal, characteristic, complemented
13#26041169C211yesmaximal, characteristic
14#26041164C211yesmaximal, characteristic, complemented
15#398×C181C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic181C2211yescharacteristic
17C2×C4⋊Dic181C2211yescharacteristic
18C2×#15668428C2211yescharacteristic
19C2×#15668428C2211yescharacteristic
20C2×#15668428C2211yescharacteristic
21C2×#15668428C2211yescharacteristic
22C2×#15668428C2211yescharacteristic
23C2×#15668428C2211yescharacteristic
24C2×#15668428C2211yescharacteristic
25C2×#15668426C2211yescharacteristic
26C2×#15668426C2211yescharacteristic
27C2×#15668426C2211yescharacteristic
28C2×#15668426C2211yescharacteristic
29C2×#15668426C2211yescharacteristic
30C2×#15668426C2211yescharacteristic
31C2×#15668426C2211yescharacteristic
32C2×C4×Dic181C2211yescharacteristic
33#19153723C2211yescharacteristic
34#19153723C2211yescharacteristic
35#19153723C2211yescharacteristic
36#19153723C2211yescharacteristic
37#19153723C2211yescharacteristic
38#19153723C2211yescharacteristic
39#19153723C2211yescharacteristic
40#19153723C2211yescharacteristic
41#19153723C2211yescharacteristic
42#19153723C2211yescharacteristic
43#19153723C2211yescharacteristic
44C2×C4⋊C4×C181C2211yescharacteristic
45C2×C4⋊C4×C181C2211yescharacteristic
46C2×C4⋊C4×C181C2211yescharacteristic
47C2×C4⋊C4×C181C2211yescharacteristic
48#95×C181C2211yescharacteristic
49#95×C181C2211yescharacteristic
50#95×C181C2211yescharacteristic
51C23×D181C2311yescharacteristic
52C22×Dic181C2311yescharacteristic
53C22×Dic181C2311yescharacteristic
54C22×Dic181C2311yescharacteristic
55C22×Dic181C2311yescharacteristic
56C22×Dic181C2311yescharacteristic
57C22×Dic181C2311yescharacteristic
58C22×Dic181C2311yescharacteristic
59C4⋊Dic181—22no—
60C4⋊Dic181—41no—
61#15668428—22no—
62#15668428—41no—
63#15668428—41no—
64#15668428—41no—
65#15668428—41no—
66#15668428—41no—
67#15668428—41no—
68#15668426—22no—
69#15668426—41no—
70#15668426—41no—
71#15668426—41no—
72#15668426—41no—
73#15668426—41no—
74#15668426—41no—
75C4×Dic181—41no—
76C22×C4×C181C2311yescharacteristic
77C22×C4×C181C2311yescharacteristic
78C22×C4×C181C2311yescharacteristic
79C22×C4×C181C2311yescharacteristic
80C22×C4×C181C2311yescharacteristic
81C22×C4×C181C2311yescharacteristic
82C22×C4×C181C2311yescharacteristic
83C4⋊C4×C181—41no—
84C4⋊C4×C181—41no—
85C4⋊C4×C181—41no—
86C4⋊C4×C181—41no—
87C22×D181—21no—
88C22×D181—21no—
89C22×D181—21no—
90C22×D181—21no—
91C22×D181—21no—
92C22×D181—21no—
93C22×D181—21no—
94C2×Dic181—21no—
95C2×Dic181—21no—
96C2×Dic181—21no—
97C2×Dic181—21no—
98C2×Dic181—21no—
99C2×Dic181—21no—
100C2×Dic181—21no—
101C2×Dic181—21no—
102C2×Dic181—21no—
103C2×Dic181—21no—
104C2×Dic181—21no—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181#4112yes—
115C23×C181C2411yescharacteristic
116C2×C4×C181—21no—
117C2×C4×C181—21no—
118C2×C4×C181—21no—
119C2×C4×C181—21no—
120C2×C4×C181—21no—
121C2×C4×C181—21no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C22×C181C2×#4111yescharacteristic
138C22×C181H(5,𝔽2)11yescharacteristic
139C22×C181H(5,𝔽2)11yescharacteristic
140C22×C181H(5,𝔽2)11yescharacteristic
141C22×C1812−1+411yescharacteristic
142C22×C1812−1+411yescharacteristic
143C22×C1812−1+411yescharacteristic
144C2×D181—41no—
145C2×D181—41no—
146C2×D181—41no—
147C2×D181—41no—
148C2×D181—41no—
149C2×D181—41no—
150C2×D181—41no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181—41no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181—41no—
158Dic181—22no—
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163Dic181—41no—
164Dic181—41no—
165C2×C181#53911yescharacteristic
166C2×C181#54011yescharacteristic
167C2×C181#54111yescharacteristic
168C2×C181#56211yescharacteristic
169C2×C181#56211yescharacteristic
170C2×C181#56311yescharacteristic
171C2×C181#56311yescharacteristic
172D181—81no—
173C181#283611yescharacteristic, complemented, Sylow
174#2836—1811nomaximal, Sylow
175#400—1811no—
176#400—1811no—
177#399—1811no—
178#398—1811no—
179#398—1811no—
180#398—1811no—
181#398D18111yescharacteristic, complemented
182#397—1811no—
183#397—1811no—
184#397—1811no—
185#396—1811no—
186#396—1811no—
187#389—1811no—
188#388—1811no—
189#387—1811no—
190C2×C4⋊C4—1811no—
191C2×C4⋊C4—1811no—
192C2×C4⋊C4—1811no—
193C2×C4⋊C4—1811no—
194C2×C4⋊C4—1811no—
195C2×C4⋊C4—1811no—
196C2×C4⋊C4—1811no—
197C2×C4⋊C4—1811no—
198C2×C4⋊C4—1811no—
199C2×C4⋊C4C2×D18111yescharacteristic
200C2×C4⋊C4C2×D18111yescharacteristic
201C2×C4⋊C4C2×D18111yescharacteristic
202C2×C4⋊C4C2×D18111yescharacteristic
203C2×C22⋊C4—1811no—
204C2×C22⋊C4—1811no—
205C2×C22⋊C4—1811no—
206C2×C22⋊C4—1811no—
207C2×C22⋊C4—1811no—
208C2×C22⋊C4—1811no—
209C2×C22⋊C4—1811no—
210C2×C42—1811no—
211#95—1811no—
212#95—1811no—
213#95—1811no—
214#95—1811no—
215#95—1811no—
216#95—1811no—
217#95—1811no—
218#95—1811no—
219#95—1811no—
220#95—1811no—
221#95—1811no—
222#95C2×D18111yescharacteristic
223#95C2×D18111yescharacteristic
224#95C2×D18111yescharacteristic
225C24—1811no—
226C22×C4—1811no—
227C22×C4—1811no—
228C22×C4—1811no—
229C22×C4—1811no—
230C22×C4—1811no—
231C22×C4—1811no—
232C22×C4—1811no—
233C22×C4C22×D18111yescharacteristic
234C22×C4C22×D18111yescharacteristic
235C22×C4C22×D18111yescharacteristic
236C22×C4C22×D18111yescharacteristic
237C22×C4C22×D18111yescharacteristic
238C22×C4C22×D18111yescharacteristic
239C22×C4C22×D18111yescharacteristic
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—3622no—
245C4⋊C4—3622no—
246C4⋊C4—7241no—
247C4⋊C4—7241no—
248C4⋊C4—7241no—
249C4⋊C4—7241no—
250C4⋊C4—7241no—
251C4⋊C4—7241no—
252C4⋊C4—7241no—
253C22⋊C4—3622no—
254C22⋊C4—7241no—
255C22⋊C4—7241no—
256C22⋊C4—7241no—
257C22⋊C4—7241no—
258C22⋊C4—7241no—
259C22⋊C4—7241no—
260C42—7241no—
261C23—3621no—
262C23—3621no—
263C23—3621no—
264C23—3621no—
265C23—3621no—
266C23—3621no—
267C23—3621no—
268C23C23×D18111yescharacteristic
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—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—3621no—
291C2×C4—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—3621no—
306C2×C4—3621no—
307C2×C4—3621no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—1812no—
311C22—7241no—
312C22—7241no—
313C22—7241no—
314C22—7241no—
315C22—7241no—
316C22—7241no—
317C22—7241no—
318C22#41×D18111yescharacteristic
319C22#1915386111yescharacteristic
320C22#1915386111yescharacteristic
321C22#1915386211yescharacteristic
322C22#1915386311yescharacteristic
323C22#1915386411yescharacteristic
324C22#1915386411yescharacteristic
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—3622no—
333C4—7241no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4—7241no—
338C4—7241no—
339C2—14481no—
340C2#2604187711yescharacteristic
341C2#2604187911yescharacteristic
342C2#2604188811yescharacteristic
343C2#2604202511yescharacteristic
344C2#2604202611yescharacteristic
345C2#2604202811yescharacteristic
346C2#2604203011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#398×C181C2
prime radicalC23×D181C23
hypercenter#398D181
hypocenterC181#2836
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #26041220C2semidirect
2. #26041218C2semidirect
4. #26041212C2semidirect
5. #26041210C2semidirect
6. #26041210C2semidirect
12. #26041176C2semidirect
14. #26041164C2semidirect
15. #398×C181C2semidirect
173. C181#2836semidirect
181. #398D181semidirect

Maximal subgroups

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

subgroupindex
#260412202
#260412182
#260412142
#260412122
#260412102
#260412082
#260412012
#260411762
#260411692
#260411642
#398×C1812
#2836181