Finite Group Databasebeta

← #37536675

Subgroups — #37536675

Order 23168.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153781C211yesmaximal, characteristic
2#26041183C211yesmaximal, characteristic
3#26041183C211yesmaximal, characteristic
4#26041166C211yesmaximal, characteristic
5#26041165C211yesmaximal, characteristic
6#26041160C211yesmaximal, characteristic
7#26041148C211yesmaximal, characteristic
8#26041143C211yesmaximal, characteristic
9#26041143C211yesmaximal, characteristic
10C4×#15668428C211yesmaximal, characteristic
11C4×#15668428C211yesmaximal, characteristic
12#26041130C211yesmaximal, characteristic
13#26041130C211yesmaximal, characteristic
14#26041130C211yesmaximal, characteristic
15#387×C181C211yesmaximal, characteristic
16C22×Dic362C2211yescharacteristic
17#19153781C418yescomplemented
18C2×C4⋊Dic181C2211yescharacteristic
19C2×#15668428C2211yescharacteristic
20C2×#15668428C2211yescharacteristic
21C2×#15668428C2211yescharacteristic
22C2×#15668428C2211yescharacteristic
23C2×#15668428C2211yescharacteristic
24C2×#15668428C2211yescharacteristic
25C2×#15668428C2211yescharacteristic
26C2×#15668428C2211yescharacteristic
27C2×C4×Dic181C2211yescharacteristic
28C2×C4×Dic181C2211yescharacteristic
29C2×C4×Dic181C2211yescharacteristic
30C2×C4×Dic181C2211yescharacteristic
31C2×C4×Dic181C2211yescharacteristic
32C2×C4×Dic181C2211yescharacteristic
33C2×C4×Dic181C2211yescharacteristic
34C2×C4×Dic181C2211yescharacteristic
35#19153723C2211yescharacteristic
36#19153723C2211yescharacteristic
37#19153723C2211yescharacteristic
38#19153723C2211yescharacteristic
39#19153723C2211yescharacteristic
40#19153723C2211yescharacteristic
41#19153723C2211yescharacteristic
42#19153723C2211yescharacteristic
43#19153723C2211yescharacteristic
44#19153723C2211yescharacteristic
45C2×C4⋊C4×C181C2211yescharacteristic
46C2×C4⋊C4×C181C2211yescharacteristic
47C2×C42×C181C2211yescharacteristic
48#95×C181C2211yescharacteristic
49#95×C181C2211yescharacteristic
50#95×C181C2211yescharacteristic
51#95×C181C2211yescharacteristic
52C2×Dic362—22no—
53C2×Dic362—22no—
54C2×Dic362C2×C414yes—
55C22×Dic181C2311yescharacteristic
56C22×Dic181C2311yescharacteristic
57C22×Dic181C2311yescharacteristic
58C22×Dic181C2311yescharacteristic
59C22×Dic181C2311yescharacteristic
60C22×Dic181C2311yescharacteristic
61C22×Dic181C2311yescharacteristic
62C22×Dic181C2311yescharacteristic
63C4⋊Dic181—41no—
64#15668428—22no—
65#15668428—22no—
66#15668428—22no—
67#15668428—22no—
68#15668428—22no—
69#15668428C2×C414yes—
70#15668428C2×C414yes—
71#15668428Q814yescomplemented
72C4×Dic181—22no—
73C4×Dic181—22no—
74C4×Dic181—41no—
75C4×Dic181—41no—
76C4×Dic181—41no—
77C4×Dic181C2×C414yes—
78C4×Dic181C2×C414yes—
79C4×Dic181C2×C414yes—
80C22×C4×C181C2311yescharacteristic
81C22×C4×C181C2311yescharacteristic
82C22×C4×C181C2311yescharacteristic
83C22×C4×C181C2311yescharacteristic
84C22×C4×C181C2311yescharacteristic
85C22×C4×C181C2311yescharacteristic
86C22×C4×C181C2311yescharacteristic
87C4⋊C4×C181—41no—
88C4⋊C4×C181C2×C414yes—
89C42×C181—41no—
90Dic362—28no—
91C2×Dic181—21no—
92C2×Dic181—21no—
93C2×Dic181—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×Dic181C22×C412yes—
107C2×Dic181C22×C412yes—
108C2×Dic181C22×C412yes—
109C2×Dic181C22×C412yes—
110C2×Dic181C2×Q812yes—
111C2×Dic181C2×Q812yes—
112C2×Dic181#4112yes—
113C2×Dic181#4112yes—
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×C181C22×C412yes—
134C2×C4×C181C22×C412yes—
135C2×C4×C181C22×C412yes—
136C2×C4×C181C2×Q812yes—
137C22×C181C23×C411yescharacteristic
138C22×C181C22×Q811yescharacteristic
139C22×C181C2×#4111yescharacteristic
140C22×C181C2×#4111yescharacteristic
141C22×C181C2×#4111yescharacteristic
142C22×C181H(5,𝔽2)11yescharacteristic
143C22×C1812−1+411yescharacteristic
144C4×C181—22no—
145C4×C181—22no—
146C4×C181—22no—
147C4×C181—22no—
148C4×C181—41no—
149C4×C181—41no—
150C4×C181—41no—
151Dic181—22no—
152Dic181—22no—
153Dic181—22no—
154Dic181—41no—
155Dic181—41no—
156Dic181—41no—
157Dic181#11714yes—
158Dic181C4×Q814yes—
159C2×C181C2×#11711yescharacteristic
160C2×C181C2×C4×Q811yescharacteristic
161C2×C181#52011yescharacteristic
162C2×C181#55411yescharacteristic
163C2×C181#55611yescharacteristic
164C2×C181#55711yescharacteristic
165C2×C181#55911yescharacteristic
166C181#235511yescharacteristic, complemented, Sylow
167#2355—1811nomaximal, Sylow
168C2×C4×Q8—1811no—
169#391—1811no—
170#391—1811no—
171#387—1811no—
172#387—1811no—
173#387—1811no—
174#387D18111yescharacteristic
175#384—1811no—
176#382—1811no—
177#382—1811no—
178C4×C4⋊C4—1811no—
179C4×C4⋊C4—1811no—
180C4×C4⋊C4—1811no—
181C4×C4⋊C4—1811no—
182C4×C4⋊C4—1811no—
183C22×Q8—1811no—
184C4×Q8—1818no—
185C2×C4⋊C4—1811no—
186C2×C4⋊C4—1811no—
187C2×C4⋊C4—1811no—
188C2×C4⋊C4—1811no—
189C2×C4⋊C4—1811no—
190C2×C4⋊C4—1811no—
191C2×C4⋊C4—1811no—
192C2×C4⋊C4—1811no—
193C2×C4⋊C4—1811no—
194C2×C4⋊C4C2×D18111yescharacteristic
195C2×C4⋊C4C2×D18111yescharacteristic
196C2×C42—1811no—
197C2×C42—1811no—
198C2×C42—1811no—
199C2×C42—1811no—
200C2×C42—1811no—
201C2×C42—1811no—
202C2×C42—1811no—
203C2×C42—1811no—
204C2×C42C2×D18111yescharacteristic
205#95—1811no—
206#95—1811no—
207#95—1811no—
208#95—1811no—
209#95—1811no—
210#95—1811no—
211#95—1811no—
212#95—1811no—
213#95—1811no—
214#95—1811no—
215#95C2×D18111yescharacteristic
216#95C2×D18111yescharacteristic
217#95C2×D18111yescharacteristic
218#95C2×D18111yescharacteristic
219C2×Q8—3622no—
220C2×Q8—3622no—
221C2×Q8—1814no—
222C22×C4—1811no—
223C22×C4—1811no—
224C22×C4—1811no—
225C22×C4—1811no—
226C22×C4—1811no—
227C22×C4—1811no—
228C22×C4—1811no—
229C22×C4—1811no—
230C22×C4C22×D18111yescharacteristic
231C22×C4C22×D18111yescharacteristic
232C22×C4C22×D18111yescharacteristic
233C22×C4C22×D18111yescharacteristic
234C22×C4C22×D18111yescharacteristic
235C22×C4C22×D18111yescharacteristic
236C22×C4C22×D18111yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—3622no—
239C4⋊C4—3622no—
240C4⋊C4—3622no—
241C4⋊C4—3622no—
242C4⋊C4—3622no—
243C4⋊C4—1814no—
244C4⋊C4—1814no—
245C4⋊C4—1814no—
246C4⋊C4—7241no—
247C4⋊C4C4×D18114yes—
248C42—41no—
249C42—3622no—
250C42—3622no—
251C42—1814no—
252C42—1814no—
253C42—1814no—
254C42—7241no—
255C42—7241no—
256C42—7241no—
257C23C23×D18111yescharacteristic
258Q8—3628no—
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—21no—
275C2×C4—21no—
276C2×C4—3621no—
277C2×C4—3621no—
278C2×C4—3621no—
279C2×C4—3621no—
280C2×C4—3621no—
281C2×C4—3621no—
282C2×C4—3621no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—3621no—
291C2×C4—1812no—
292C2×C4—1812no—
293C2×C4—1812no—
294C2×C4—1812no—
295C2×C4—1812no—
296C2×C4—1812no—
297C2×C4—1812no—
298C2×C4—1812no—
299C2×C4—1812no—
300C2×C4C2×C4×D18112yes—
301C2×C4C2×C4×D18112yes—
302C2×C4C2×C4×D18112yes—
303C2×C4Q8×D18112yes—
304C22C22×C4×D18111yescharacteristic
305C22C2×Q8×D18111yescharacteristic
306C22#41×D18111yescharacteristic
307C22#41×D18111yescharacteristic
308C22#41×D18111yescharacteristic
309C22#1915386111yescharacteristic
310C22#1915386311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3622no—
319C4—3622no—
320C4—3622no—
321C4—1814no—
322C4—1814no—
323C4—7241no—
324C4—7241no—
325C4—7241no—
326C2#117×D18111yescharacteristic
327C2C4×Q8×D18111yescharacteristic
328C2#2604175811yescharacteristic
329C2#2604198311yescharacteristic
330C2#2604199611yescharacteristic
331C2#2604200611yescharacteristic
332C2#2604201311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#387×C181C2
socle, prime radical, cosocleC23×C181C24
hypercenter#387D181
hypocenterC181#2355
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #19153781C4semidirect
71. #15668428Q8semidirect
166. C181#2355semidirect

Maximal subgroups

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

subgroupindex
C2×#191537812
#260411832
#260411662
#260411652
#260411602
#260411482
#260411432
C4×#156684282
#260411302
#387×C1812
#2355181