Finite Group Databasebeta

← #37536466

Subgroups — #37536466

Order 23168.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153815C211yesmaximal, characteristic
2#26041185C211yesmaximal, characteristic
3#26041184C211yesmaximal, characteristic
4#26041183C211yesmaximal, characteristic
5#26041183C211yesmaximal, characteristic
6#26041176C211yesmaximal, characteristic
7#26041174C211yesmaximal, characteristic
8#26041165C211yesmaximal, characteristic
9#26041164C211yesmaximal, characteristic
10#26041162C211yesmaximal, characteristic
11#26041143C211yesmaximal, characteristic
12C4×#15668428C211yesmaximal, characteristic
13#26041130C211yesmaximal, characteristic
14#26041124C211yesmaximal, characteristic
15#387×C181C211yesmaximal, characteristic
16C22×Dic362C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18#19153815C418yescomplemented
19C2×C4⋊Dic181C2211yescharacteristic
20C2×C4⋊Dic181C2211yescharacteristic
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
33#19153723C2211yescharacteristic
34#19153723C2211yescharacteristic
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—41no—
53C2×Dic362—41no—
54C2×Dic362—41no—
55C2×Dic362—41no—
56C2×Dic362C2×C414yes—
57C2×Dic362C2×C414yes—
58C22×Dic181C2311yescharacteristic
59C22×Dic181C2311yescharacteristic
60C22×Dic181C2311yescharacteristic
61C22×Dic181C2311yescharacteristic
62C22×Dic181C2311yescharacteristic
63C22×Dic181C2311yescharacteristic
64C22×Dic181C2311yescharacteristic
65C22×Dic181C2311yescharacteristic
66C4⋊Dic181—41no—
67C4⋊Dic181C2×C414yes—
68#15668428—22no—
69#15668428—22no—
70#15668428—41no—
71#15668428—41no—
72#15668428C2×C414yes—
73#15668428C2×C414yes—
74C4×Dic181—22no—
75C4×Dic181—41no—
76C4×Dic181—41no—
77C4×Dic181—41no—
78C4×Dic181C2×C414yes—
79C4×Dic181Q814yescomplemented
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—44no—
91Dic362—44no—
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×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181C22×C412yes—
110C2×Dic181C22×C412yes—
111C2×Dic181C22×C412yes—
112C2×Dic181C22×C412yes—
113C2×Dic181C2×Q812yes—
114C2×Dic181C2×Q812yes—
115C2×Dic181#4112yes—
116C23×C181C2411yescharacteristic
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×C181C22×C412yes—
135C2×C4×C181C22×C412yes—
136C2×C4×C181C22×C412yes—
137C2×C4×C181C2×Q812yes—
138C22×C181C23×C411yescharacteristic
139C22×C181C22×Q811yescharacteristic
140C22×C181C2×#4111yescharacteristic
141C22×C181H(5,𝔽2)11yescharacteristic
142C22×C181H(5,𝔽2)11yescharacteristic
143C22×C1812−1+411yescharacteristic
144C22×C1812−1+411yescharacteristic
145C4×C181—22no—
146C4×C181—22no—
147C4×C181—22no—
148C4×C181—22no—
149C4×C181—41no—
150C4×C181—41no—
151C4×C181—41no—
152Dic181—22no—
153Dic181—22no—
154Dic181—22no—
155Dic181—22no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159Dic181C4×Q814yes—
160C2×C181C2×C4×Q811yescharacteristic
161C2×C181#51811yescharacteristic
162C2×C181#51911yescharacteristic
163C2×C181#54211yescharacteristic
164C2×C181#54211yescharacteristic
165C2×C181#54411yescharacteristic
166C2×C181#54411yescharacteristic
167C181#233111yescharacteristic, complemented, Sylow
168#2331—1811nomaximal, Sylow
169C2×C4⋊Q8—1811no—
170#391—1811no—
171#391—1811no—
172#391—1811no—
173#391—1811no—
174#389—1811no—
175#389—1811no—
176#387—1811no—
177#387—1811no—
178#387—1811no—
179#387D18111yescharacteristic
180#382—1811no—
181C4×C4⋊C4—1811no—
182C4×C4⋊C4—1811no—
183#376—1811no—
184C22×Q8—1811no—
185C22×Q8—1811no—
186C4⋊Q8—1818no—
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⋊C4—1811no—
195C2×C4⋊C4C2×D18111yescharacteristic
196C2×C4⋊C4C2×D18111yescharacteristic
197C2×C42—1811no—
198C2×C42—1811no—
199C2×C42—1811no—
200C2×C42—1811no—
201C2×C42—1811no—
202C2×C42—1811no—
203C2×C42C2×D18111yescharacteristic
204#95—1811no—
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#95—1811no—
216#95C2×D18111yescharacteristic
217#95C2×D18111yescharacteristic
218#95C2×D18111yescharacteristic
219#95C2×D18111yescharacteristic
220C2×Q8—1814no—
221C2×Q8—1814no—
222C2×Q8—7241no—
223C2×Q8—7241no—
224C2×Q8—7241no—
225C2×Q8—7241no—
226C22×C4—1811no—
227C22×C4—1811no—
228C22×C4—1811no—
229C22×C4—1811no—
230C22×C4—1811no—
231C22×C4—1811no—
232C22×C4—1811no—
233C22×C4—1811no—
234C22×C4C22×D18111yescharacteristic
235C22×C4C22×D18111yescharacteristic
236C22×C4C22×D18111yescharacteristic
237C22×C4C22×D18111yescharacteristic
238C22×C4C22×D18111yescharacteristic
239C22×C4C22×D18111yescharacteristic
240C22×C4C22×D18111yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—3622no—
243C4⋊C4—3622no—
244C4⋊C4—1814no—
245C4⋊C4—1814no—
246C4⋊C4—1814no—
247C4⋊C4—7241no—
248C4⋊C4—7241no—
249C4⋊C4—7241no—
250C4⋊C4C4×D18114yes—
251C42—41no—
252C42—3622no—
253C42—1814no—
254C42—1814no—
255C42—7241no—
256C42—7241no—
257C42—7241no—
258C23C23×D18111yescharacteristic
259Q8—7244no—
260Q8—7244no—
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—21no—
277C2×C4—21no—
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—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—1812no—
296C2×C4—1812no—
297C2×C4—1812no—
298C2×C4—1812no—
299C2×C4—1812no—
300C2×C4—1812no—
301C2×C4—1812no—
302C2×C4C2×C4×D18112yes—
303C2×C4C2×C4×D18112yes—
304C2×C4C2×C4×D18112yes—
305C2×C4Q8×D18112yes—
306C22C22×C4×D18111yescharacteristic
307C22C2×Q8×D18111yescharacteristic
308C22#41×D18111yescharacteristic
309C22#1915386111yescharacteristic
310C22#1915386211yescharacteristic
311C22#1915386311yescharacteristic
312C22#1915386311yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—3622no—
321C4—3622no—
322C4—3622no—
323C4—3622no—
324C4—1814no—
325C4—7241no—
326C4—7241no—
327C4—7241no—
328C2C4×Q8×D18111yescharacteristic
329C2#2604175111yescharacteristic
330C2#2604175611yescharacteristic
331C2#2604189511yescharacteristic
332C2#2604189711yescharacteristic
333C2#2604190811yescharacteristic
334C2#2604190911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#387×C181C2
socle, prime radical, cosocleC23×C181C24
hypercenter#387D181
hypocenterC181#2331
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #19153815C4semidirect
79. C4×Dic181Q8semidirect
167. C181#2331semidirect

Maximal subgroups

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

subgroupindex
C2×#191538152
#260411852
#260411842
#260411832
#260411762
#260411742
#260411652
#260411642
#260411622
#260411432
C4×#156684282
#260411302
#260411242
#387×C1812
#2331181