Finite Group Databasebeta

← #37544971

Subgroups — #37544971

Order 23168.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041909C211yesmaximal, characteristic, complemented
2#26041880C211yesmaximal, characteristic
3#26041686C211yesmaximal, characteristic, complemented
4#26041680C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041624C211yesmaximal, characteristic, complemented
7#26041606C211yesmaximal, characteristic, complemented
8#26041601C211yesmaximal, characteristic, complemented
9#26041599C211yesmaximal, characteristic, complemented
10#26041591C211yesmaximal, characteristic, complemented
11#26041576C211yesmaximal, characteristic, complemented
12#26041569C211yesmaximal, characteristic, complemented
13#26041560C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16#19153816C2211yescharacteristic
17#19153815—21no—
18#19153815C2211yescharacteristic
19#19153812C2211yescharacteristic
20#19153807C2211yescharacteristic
21#19153807C2211yescharacteristic
22#19153806—21no—
23#19153799—21no—
24#19153798—21no—
25#19153796—21no—
26#19153794—21no—
27#19153791C2211yescharacteristic
28#19153790—21no—
29#19153789—21no—
30#19153787C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153774C2211yescharacteristic
33#19153773C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35#19153750C2211yescharacteristic
36#19153750C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153747C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153747C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153738C2211yescharacteristic
43#19153738C2211yescharacteristic
44#19153737C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×D724—21no—
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426D411yescharacteristic
88#15668426D411yescharacteristic
89C4×Dic181—21no—
90C4×Dic181C2311yescharacteristic
91C2×D4×C181C2311yescharacteristic
92C22×C4×C181—21no—
93C2×C8×C181C2311yescharacteristic
94C2×C8×C181C2311yescharacteristic
95C4⋊C4×C181—21no—
96C4⋊C4×C181—21no—
97C4⋊C4×C181C2311yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C22⋊C4×C181—21no—
101C42×C181C2311yescharacteristic
102C22×D181—21no—
103C22×D181C2×D411yescharacteristic
104Dic362—81no—
105Dic362—81no—
106D724—21no—
107D724—21no—
108D724—81no—
109C22⋊D181—81no—
110C22⋊D181—81no—
111C22⋊D181—81no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—81no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124C23×C181—21no—
125D4×C181—21no—
126D4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—81no—
131C2×C4×C181C2×D411yescharacteristic
132C2×C4×C181C2×D411yescharacteristic
133C2×C4×C181C2411yescharacteristic
134C8×C181—21no—
135C8×C181—21no—
136C22×C181—41no—
137C22×C181—41no—
138C22×C181—41no—
139C22×C181C22×D411yescharacteristic
140C2×D181—21no—
141C2×D181—21no—
142C2×D181—21no—
143C2×D181—41no—
144C2×D181—41no—
145C2×D181—41no—
146C4×C181—21no—
147C4×C181—21no—
148C4×C181—41no—
149C4×C181—41no—
150C4×C181—41no—
151C4×C1812−1+411yescharacteristic
152C4×C1812−1+411yescharacteristic
153Dic181—21no—
154Dic181—21no—
155Dic181—21no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159C2×C181—81no—
160C2×C181#53611yescharacteristic
161C2×C181#57611yescharacteristic
162C2×C181#57711yescharacteristic
163D181—41no—
164D181—81no—
165C181#324111yescharacteristic, complemented, Sylow
166#3241—1811nomaximal, Sylow
167#544—1811no—
168#540—1811no—
169#501—1811no—
170#499—1811no—
171#490—1811no—
172#486—1811no—
173#482—1811no—
174#482—1811no—
175#481—1811no—
176#480—1811no—
177#478—1811no—
178#478D18111yescharacteristic, complemented
179#476—1811no—
180#474—1811no—
181#433—1811no—
182C4⋊Q8—3621no—
183C4⋊Q8—1811no—
184C4⋊Q8—1811no—
185#127—1811no—
186#125—3621no—
187#125—1811no—
188#125—1811no—
189#125C2×D18111yescharacteristic
190#123—3621no—
191#123—3621no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194#121—3621no—
195#121—3621no—
196#121—1811no—
197#121—1811no—
198C4×D4—1811no—
199C4×D4C2×D18111yescharacteristic
200#117—1811no—
201#117—1811no—
202C2×C4⋊C4—1811no—
203#107—1811no—
204#107—1811no—
205#107—1811no—
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106C2×D18111yescharacteristic
211C4⋊C8—1811no—
212C4⋊C8C2×D18111yescharacteristic
213#102—1811no—
214#102—1811no—
215#102—1811no—
216#102—1811no—
217#102—1811no—
218#102—1811no—
219#102C2×D18111yescharacteristic
220#102C2×D18111yescharacteristic
221C22⋊C8—1811no—
222C22⋊C8—1811no—
223#97—1811no—
224C4×C8—1811no—
225C2×Q8—3621no—
226C2×Q8—3621no—
227C2×D4—3621no—
228C2×D4—3621no—
229C2×D4—3621no—
230C2×D4—3621no—
231C2×D4—1811no—
232C2×D4C22×D18111yescharacteristic
233C22×C4—21no—
234C22×C4—3621no—
235C22×C4—3621no—
236C22×C4—1811no—
237C2×C8—1811no—
238C2×C8—1811no—
239C2×C8C22×D18111yescharacteristic
240C2×C8C22×D18111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—1811no—
264C22⋊C4—1811no—
265C42—3621no—
266C42—1811no—
267C42C22×D18111yescharacteristic
268C23—21no—
269C23—3621no—
270C23—1811no—
271Q8—14481no—
272Q8—14481no—
273D4—21no—
274D4—21no—
275D4—3621no—
276D4—3621no—
277D4—14481no—
278D4—14481no—
279D4—14481no—
280D4—14481no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—14481no—
291C2×C4—14481no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—1811no—
295C2×C4D4×D18111yescharacteristic
296C2×C4D4×D18111yescharacteristic
297C2×C4C23×D18111yescharacteristic
298C8—21no—
299C8—21no—
300C8—3621no—
301C8—3621no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—3621no—
306C22—3621no—
307C22—3621no—
308C22—7241no—
309C22—7241no—
310C22—7241no—
311C22C2×D4×D18111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—3621no—
318C4—3621no—
319C4—3621no—
320C4—7241no—
321C4—7241no—
322C4—7241no—
323C4#1915386311yescharacteristic
324C4#1915386411yescharacteristic
325C2—81no—
326C2—14481no—
327C2—7241no—
328C2#2604185211yescharacteristic
329C2#2604208111yescharacteristic
330C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
prime radical#26041880C2
hypercenter#478D181
hypocenterC181#3241
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041909C2semidirect
3. #26041686C2semidirect
4. #26041680C2semidirect
5. #26041642C2semidirect
6. #26041624C2semidirect
7. #26041606C2semidirect
8. #26041601C2semidirect
9. #26041599C2semidirect
10. #26041591C2semidirect
11. #26041576C2semidirect
12. #26041569C2semidirect
13. #26041560C2semidirect
14. #26041339C2semidirect
15. #478×C181C2semidirect
165. C181#3241semidirect
178. #478D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260418802
#260416862
#260416802
#260416422
#260416242
#260416062
#260416012
#260415992
#260415912
#260415762
#260415692
#260415602
#260413392
#478×C1812
#3241181