Finite Group Databasebeta

← #37544983

Subgroups — #37544983

Order 23168.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041907C211yesmaximal, characteristic
2#26041689C211yesmaximal, characteristic, complemented
3#26041678C211yesmaximal, characteristic, complemented
4#26041647C211yesmaximal, characteristic, complemented
5#26041629C211yesmaximal, characteristic, complemented
6#26041617C211yesmaximal, characteristic
7#26041617C211yesmaximal, characteristic
8#26041612C211yesmaximal, characteristic
9#26041607C211yesmaximal, characteristic
10#26041586C211yesmaximal, characteristic, complemented
11#26041586C211yesmaximal, characteristic, complemented
12#26041574C211yesmaximal, characteristic, complemented
13#26041564C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic
15#541×C181C211yesmaximal, characteristic
16#19153816C2211yescharacteristic
17#19153816C2211yescharacteristic
18#19153815—21no—
19#19153808C2211yescharacteristic
20#19153808C2211yescharacteristic
21#19153807—21no—
22#19153793—21no—
23#19153793—21no—
24#19153775C2211yescharacteristic
25C2×C4⋊Dic181C2211yescharacteristic
26#19153749C2211yescharacteristic
27#19153749C2211yescharacteristic
28#19153749C2211yescharacteristic
29#19153749C2211yescharacteristic
30#19153747C2211yescharacteristic
31#19153747C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153740C2211yescharacteristic
39#19153740C2211yescharacteristic
40#19153740C2211yescharacteristic
41#19153740C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153740C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48C4⋊Q8×C181C2211yescharacteristic
49#126×C181—21no—
50#126×C181—21no—
51#125×C181—21no—
52#125×C181—21no—
53#125×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56C4×Q8×C181C2211yescharacteristic
57C4×Q8×C181C2211yescharacteristic
58#117×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C22×Dic181—21no—
62C2×#13089678C2311yescharacteristic
63C2×#13089678C2311yescharacteristic
64C2×#13089678C2311yescharacteristic
65C2×#13089678C2311yescharacteristic
66C4⋊Dic181—21no—
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181C2311yescharacteristic
70C4⋊Dic181C2311yescharacteristic
71C4⋊Dic181C2311yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73#15668428—21no—
74#15668428—21no—
75#15668428—21no—
76#15668428—21no—
77C22⋊Dic181—21no—
78C4×Dic181—21no—
79C2×Q8×C181C2311yescharacteristic
80C2×Q8×C181C2311yescharacteristic
81C22×C4×C181C2311yescharacteristic
82C4⋊C4×C181—21no—
83C4⋊C4×C181—21no—
84C4⋊C4×C181—21no—
85C4⋊C4×C181—21no—
86C4⋊C4×C181—21no—
87C4⋊C4×C181—21no—
88C4⋊C4×C181—21no—
89C4⋊C4×C181—21no—
90C4⋊C4×C181D411yescharacteristic
91C4⋊C4×C181D411yescharacteristic
92C4⋊C4×C181C2311yescharacteristic
93C4⋊C4×C181C2311yescharacteristic
94C22⋊C4×C181—21no—
95C22⋊C4×C181—21no—
96C22⋊C4×C181D411yescharacteristic
97C22⋊C4×C181D411yescharacteristic
98C42×C181—21no—
99C42×C181—21no—
100C42×C181C2311yescharacteristic
101C42×C181C2311yescharacteristic
102Dic362—81no—
103Dic362—81no—
104C2×Dic181—21no—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—81no—
109#13089678—21no—
110#13089678—21no—
111#13089678—21no—
112#13089678—21no—
113C23×C181C2×D411yescharacteristic
114Q8×C181—21no—
115Q8×C181—21no—
116Q8×C181—21no—
117Q8×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×C181C2×D411yescharacteristic
125C2×C4×C181C2×D411yescharacteristic
126C2×C4×C181C2×D411yescharacteristic
127C2×C4×C181C2×D411yescharacteristic
128C2×C4×C181C2×D411yescharacteristic
129C2×C4×C181C2411yescharacteristic
130C22×C181—21no—
131C22×C181—21no—
132C22×C181—21no—
133C22×C181C22×D411yescharacteristic
134C4×C181—21no—
135C4×C181—21no—
136C4×C181—21no—
137C4×C181—21no—
138C4×C181—21no—
139C4×C181—41no—
140C4×C181—41no—
141C4×C181—41no—
142C4×C181—41no—
143C4×C1812−1+411yescharacteristic
144C4×C1812−1+411yescharacteristic
145Dic181—41no—
146Dic181—41no—
147Dic181—41no—
148Dic181—41no—
149C2×C181—41no—
150C2×C181#53611yescharacteristic
151C2×C181#57711yescharacteristic
152C2×C181#57811yescharacteristic
153C181#324211yescharacteristic, complemented, Sylow
154#3242—1811nomaximal, Sylow
155#544—1811no—
156#541D18111yescharacteristic
157#501—1811no—
158#499—1811no—
159#491—1811no—
160#487—1811no—
161#485—1811no—
162#485—1811no—
163#484—1811no—
164#483—1811no—
165#479—1811no—
166#479—1811no—
167#477—1811no—
168#475—1811no—
169#433—1811no—
170C4⋊Q8—3621no—
171C4⋊Q8—1811no—
172C4⋊Q8—1811no—
173C4⋊Q8C2×D18111yescharacteristic
174#126—21no—
175#126—21no—
176#125—21no—
177#125—21no—
178#125—3621no—
179#125—1811no—
180#125—1811no—
181#125C2×D18111yescharacteristic
182C22⋊Q8—3621no—
183C22⋊Q8—3621no—
184C22⋊Q8C2×D18111yescharacteristic
185C22⋊Q8C2×D18111yescharacteristic
186C4×Q8C2×D18111yescharacteristic
187C4×Q8C2×D18111yescharacteristic
188#117—1811no—
189#117C2×D18111yescharacteristic
190C2×C4⋊C4—1811no—
191#107—1811no—
192#107—1811no—
193#107—1811no—
194#107—1811no—
195#106—1811no—
196#106—1811no—
197#106—1811no—
198#106—1811no—
199C4⋊C8—1811no—
200C4⋊C8—1811no—
201#103—1811no—
202#103—1811no—
203#103—1811no—
204#103—1811no—
205#103—1811no—
206#103—1811no—
207#103—1811no—
208#103—1811no—
209C22⋊C8—1811no—
210C22⋊C8—1811no—
211#97—1811no—
212C4×C8—1811no—
213C2×Q8—3621no—
214C2×Q8—3621no—
215C2×Q8C22×D18111yescharacteristic
216C2×Q8C22×D18111yescharacteristic
217C22×C4—3621no—
218C22×C4C22×D18111yescharacteristic
219C2×C8—1811no—
220C2×C8—1811no—
221C2×C8—1811no—
222C2×C8—1811no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—3621no—
232C4⋊C4—3621no—
233C4⋊C4—3621no—
234C4⋊C4—3621no—
235C4⋊C4—3621no—
236C4⋊C4—3621no—
237C4⋊C4—3621no—
238C4⋊C4—1811no—
239C4⋊C4—1811no—
240C4⋊C4—1811no—
241C4⋊C4—1811no—
242C4⋊C4C22⋊D18111yescharacteristic
243C4⋊C4C22⋊D18111yescharacteristic
244C4⋊C4C22×D18111yescharacteristic
245C4⋊C4C22×D18111yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—3621no—
249C22⋊C4C22⋊D18111yescharacteristic
250C22⋊C4C22⋊D18111yescharacteristic
251C42—21no—
252C42—21no—
253C42—3621no—
254C42C22×D18111yescharacteristic
255C42C22×D18111yescharacteristic
256C23C2×C22⋊D18111yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—21no—
260Q8—21no—
261Q8—14481no—
262Q8—14481no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—3621no—
270C2×C4—3621no—
271C2×C4—3621no—
272C2×C4—3621no—
273C2×C4—14481no—
274C2×C4C2×C22⋊D18111yescharacteristic
275C2×C4C2×C22⋊D18111yescharacteristic
276C2×C4C2×C22⋊D18111yescharacteristic
277C2×C4C2×C22⋊D18111yescharacteristic
278C2×C4C2×C22⋊D18111yescharacteristic
279C2×C4C23×D18111yescharacteristic
280C8—3621no—
281C8—3621no—
282C8—3621no—
283C8—3621no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×C22⋊D18111yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—7241no—
298C4—7241no—
299C4—7241no—
300C4—7241no—
301C4#1915386311yescharacteristic
302C4#1915386311yescharacteristic
303C2—41no—
304C2#2604185011yescharacteristic
305C2#2604208711yescharacteristic
306C2#2604209411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#541×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenter#541D181
hypocenterC181#3242
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #26041689C2semidirect
3. #26041678C2semidirect
4. #26041647C2semidirect
5. #26041629C2semidirect
10. #26041586C2semidirect
11. #26041586C2semidirect
12. #26041574C2semidirect
13. #26041564C2semidirect
153. C181#3242semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260416892
#260416782
#260416472
#260416292
#260416172
#260416122
#260416072
#260415862
#260415742
#260415642
#260413402
#541×C1812
#3242181