Finite Group Databasebeta

← #37546409

Subgroups — #37546409

Order 23168.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042006C211yesmaximal, characteristic, complemented
2#26042001C211yesmaximal, characteristic
3#26041636C211yesmaximal, characteristic
4#26041635C211yesmaximal, characteristic
5#26041628C211yesmaximal, characteristic, complemented
6#26041589C211yesmaximal, characteristic, complemented
7#26041558C211yesmaximal, characteristic
8#26041504C211yesmaximal, characteristic
9#26041502C211yesmaximal, characteristic
10#26041488C211yesmaximal, characteristic, complemented
11#26041403C211yesmaximal, characteristic, complemented
12#26041373C211yesmaximal, characteristic, complemented
13C4×#15668439C211yesmaximal, characteristic, complemented
14#26041366C211yesmaximal, characteristic
15#479×C181C211yesmaximal, characteristic, complemented
16C2×Dic724C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19#19153815—21no—
20#19153815C2211yescharacteristic
21#19153814C2211yescharacteristic
22#19153811—21no—
23#19153810—21no—
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153806—21no—
27#19153805C2211yescharacteristic
28#19153804C2211yescharacteristic
29#19153794—21no—
30C4×Dic362C2211yescharacteristic
31C4×Dic362C2211yescharacteristic
32#19153781—21no—
33#19153781C2211yescharacteristic
34#19153781C2211yescharacteristic
35#19153781C2211yescharacteristic
36#19153778C2211yescharacteristic
37#19153773—21no—
38#19153749C2211yescharacteristic
39#19153745C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153741C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C4×#13089678C2211yescharacteristic
50C8×Dic181C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362D411yescharacteristic
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C4×D181—21no—
65Dic724—22no—
66#15668439—22no—
67#15668438—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C4⋊Dic181—21no—
71C4⋊Dic181D411yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73#15668428—21no—
74#15668428—21no—
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88C4×Dic181—21no—
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181C2311yescharacteristic
93C4×Dic181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C42×C181—21no—
104C42×C181C2311yescharacteristic
105C22×D181—21no—
106Dic362—21no—
107Dic362—22no—
108Dic362—21no—
109Dic362—21no—
110Dic362—42no—
111Dic362#4112yes—
112D724—21no—
113D724—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—42no—
122#13089678—21no—
123#13089678—21no—
124Q8×C181—21no—
125Q8×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181C2×D411yescharacteristic
131C2×C4×C181C2×D411yescharacteristic
132C2×C4×C181C2411yescharacteristic
133C8×C181—21no—
134C8×C181—21no—
135C22×C181C22×D411yescharacteristic
136C2×D181—41no—
137C2×D181—41no—
138C2×D181—41no—
139C4×C181—21no—
140C4×C181—21no—
141C4×C181—41no—
142C4×C181—41no—
143C4×C181—41no—
144C4×C181—41no—
145C4×C181C2×#4111yescharacteristic
146C4×C1812−1+411yescharacteristic
147Dic181—22no—
148Dic181—21no—
149Dic181—21no—
150Dic181—21no—
151Dic181—41no—
152Dic181—41no—
153Dic181#13512yes—
154C2×C181#54811yescharacteristic
155C2×C181C2×#13511yescharacteristic
156C2×C181#57811yescharacteristic
157D181—81no—
158C181#336411yescharacteristic, complemented, Sylow
159#3364—1811nomaximal, Sylow
160#557—1811no—
161#556—1811no—
162#488—1811no—
163#488—1811no—
164#487—1811no—
165#479—1811no—
166#479D18111yescharacteristic, complemented
167#474—1811no—
168#464—1811no—
169#464—1811no—
170#462—1811no—
171C8×Q8—1811no—
172C4×Q16—1811no—
173C4×Q16—1811no—
174C4×SD16—1811no—
175C2×Q16—1811no—
176C2×Q16—1811no—
177C2×SD16—1811no—
178C4⋊Q8—3621no—
179C4⋊Q8—1811no—
180C4⋊Q8—1811no—
181#126—3621no—
182#126—3621no—
183#125—3621no—
184#125—3621no—
185#125—1811no—
186#125C2×D18111yescharacteristic
187#124—1811no—
188#124—1811no—
189C22⋊Q8—3621no—
190C4×Q8—3621no—
191C4×Q8—1811no—
192C4×Q8—1811no—
193C4×Q8—1811no—
194C4×Q8—1811no—
195C4×Q8—1811no—
196C4×Q8C2×D18111yescharacteristic
197C4×D4—1811no—
198#117—3621no—
199#107—1811no—
200#107C2×D18111yescharacteristic
201#106C2×D18111yescharacteristic
202C4⋊C8—1811no—
203C4⋊C8—1811no—
204C4⋊C8C2×D18111yescharacteristic
205#103—1811no—
206#103—1811no—
207#103—1811no—
208#103—1811no—
209#103—1811no—
210#103C2×D18111yescharacteristic
211#103C2×D18111yescharacteristic
212#102—1811no—
213#102—1811no—
214#102—1811no—
215C4×C8—1811no—
216C4×C8—1811no—
217C4×C8—1811no—
218C2×Q8—3621no—
219C2×Q8—1811no—
220C2×Q8—1811no—
221C2×Q8—1811no—
222C2×Q8C22×D18111yescharacteristic
223C2×D4—1811no—
224C22×C4—3621no—
225Q16—3622no—
226Q16—3622no—
227SD16—3622no—
228C2×C8—1811no—
229C2×C8—1811no—
230C2×C8C22×D18111yescharacteristic
231C2×C8C22×D18111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—3621no—
236C4⋊C4—3621no—
237C4⋊C4—3621no—
238C4⋊C4—3621no—
239C4⋊C4—3621no—
240C4⋊C4—3621no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—1811no—
245C4⋊C4—1811no—
246C4⋊C4—1811no—
247C4⋊C4—1811no—
248C4⋊C4C22×D18111yescharacteristic
249C4⋊C4C22×D18111yescharacteristic
250C4⋊C4C22×D18111yescharacteristic
251C22⋊C4—3621no—
252C22⋊C4—3621no—
253C22⋊C4—3621no—
254C22⋊C4—3621no—
255C22⋊C4—3621no—
256C42—21no—
257C42—3621no—
258C42—3621no—
259C42—3621no—
260C42—3621no—
261C42—1811no—
262C42—1811no—
263C42C22×D18111yescharacteristic
264C23—3621no—
265Q8—21no—
266Q8—21no—
267Q8—3622no—
268Q8—3621no—
269Q8—3621no—
270Q8—3621no—
271Q8—1812no—
272Q8—7242no—
273D4—3621no—
274D4—3621no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—3621no—
280C2×C4—3621no—
281C2×C4—3621no—
282C2×C4—1811no—
283C2×C4—1811no—
284C2×C4—1811no—
285C2×C4—1811no—
286C2×C4—7242no—
287C2×C4D4×D18111yescharacteristic
288C2×C4D4×D18111yescharacteristic
289C2×C4C23×D18111yescharacteristic
290C8—21no—
291C8—21no—
292C8—3621no—
293C8—3621no—
294C22—7241no—
295C22—7241no—
296C22—7241no—
297C22C2×D4×D18111yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—3622no—
305C4—3621no—
306C4—3621no—
307C4—3621no—
308C4—1812no—
309C4—7241no—
310C4—7241no—
311C4#41×D18111yescharacteristic
312C4#1915386411yescharacteristic
313C2—14481no—
314C2#2604193911yescharacteristic
315C2#135×D18111yescharacteristic
316C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#479×C181C2
socleC22×C181C22×D4
prime radicalC2×D724C23
hypercenter#479D181
hypocenterC181#3364
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #26042006C2semidirect
5. #26041628C2semidirect
6. #26041589C2semidirect
10. #26041488C2semidirect
11. #26041403C2semidirect
12. #26041373C2semidirect
13. C4×#15668439C2semidirect
15. #479×C181C2semidirect
158. C181#3364semidirect
166. #479D181semidirect

Maximal subgroups

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

subgroupindex
#260420062
#260420012
#260416362
#260416352
#260416282
#260415892
#260415582
#260415042
#260415022
#260414882
#260414032
#260413732
C4×#156684392
#260413662
#479×C1812
#3364181