Finite Group Databasebeta

← #37546063

Subgroups — #37546063

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041930C211yesmaximal, characteristic, complemented
2#26041929C211yesmaximal, characteristic, complemented
3#26041683C211yesmaximal, characteristic, complemented
4#26041594C211yesmaximal, characteristic, complemented
5#26041593C211yesmaximal, characteristic, complemented
6#26041591C211yesmaximal, characteristic, complemented
7#26041558C211yesmaximal, characteristic, complemented
8#26041557C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041513C211yesmaximal, characteristic, complemented
11#26041359C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13C2×#19153749C211yesmaximal, characteristic, complemented
14#107×D181C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668448—21no—
18C2×#15668434C2211yescharacteristic
19C22×#13089678C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153815C2211yescharacteristic
23#19153801—21no—
24#19153799—21no—
25#19153798—21no—
26#19153797—21no—
27#19153794—21no—
28#19153793—21no—
29#19153791C2211yescharacteristic
30#19153790C2211yescharacteristic
31#19153787C2211yescharacteristic
32D4×Dic181C2211yescharacteristic
33#19153778C2211yescharacteristic
34C4×C22⋊D181C2211yescharacteristic
35C2×C4⋊Dic181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153749C2211yescharacteristic
43#19153749C2211yescharacteristic
44#19153749C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—44no—
60#15668448—44no—
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181D411yescharacteristic
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74#15668434—22no—
75C2×#13089678—22no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C8×D181—22no—
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181D411yescharacteristic
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181C2311yescharacteristic
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C22×C4×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C22×D181—21no—
108C22×D181C2×D411yescharacteristic
109Dic362—42no—
110Dic362—42no—
111D724—21no—
112D724—21no—
113D724—42no—
114C22⋊D181—42no—
115C22⋊D181—42no—
116C22⋊D181D814yescomplemented
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—42no—
121C2×Dic181—42no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—21no—
126C4×D181—21no—
127C4×D181—42no—
128C4×D181—42no—
129C4×D181—42no—
130#13089678—21no—
131#13089678#4112yescomplemented
132C23×C181—21no—
133C23×C181C2×D411yescharacteristic
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—42no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—42no—
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2411yescharacteristic
145C8×C181—21no—
146C8×C181—21no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181C2×D812yes—
153C22×C181C22×D411yescharacteristic
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181C2×D812yes—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181C2×#4111yescharacteristic
165C4×C1812−1+411yescharacteristic
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171Dic181C2×D812yes—
172C2×C181—22no—
173C2×C181—81no—
174C2×C181#54711yescharacteristic
175C2×C181C22×D811yescharacteristic
176C2×C181#57811yescharacteristic
177D181—22no—
178D181—81no—
179C181#333411yescharacteristic, complemented, Sylow
180#3334—1811nomaximal, Sylow
181#547—1811no—
182#547—1811no—
183#500—1811no—
184#480—1811no—
185#480—1811no—
186#480—1811no—
187#480D18111yescharacteristic, complemented
188#474—1811no—
189#474—1811no—
190#466—1811no—
191#466—1811no—
192C4×D8—1811no—
193C8×D4—1811no—
194C2×#107—1811no—
195C2×#107—1811no—
196C2×#41—3621no—
197C2×#41—3621no—
198C2×D8—1811no—
199C22×C8—1811no—
200C22×C8—1811no—
201C4⋊Q8—1811no—
202C4⋊Q8—1811no—
203#123—3621no—
204#123—3621no—
205#123—3621no—
206#123—3621no—
207C22⋊Q8—3621no—
208C22⋊Q8—3621no—
209#121—1811no—
210#121—1811no—
211#121—1811no—
212#121C2×D18111yescharacteristic
213C4×D4—1811no—
214C4×D4—1811no—
215C4×D4—1811no—
216C2×C4⋊C4—1811no—
217C2×C4⋊C4—1811no—
218C2×C4⋊C4—1811no—
219C2×C4⋊C4C2×D18111yescharacteristic
220#107—1811no—
221#107—1811no—
222#107—1811no—
223#107—1811no—
224#107—1811no—
225#107—1811no—
226#107—1811no—
227#107C2×D18111yescharacteristic
228#107C2×D18111yescharacteristic
229C4⋊C8—1811no—
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102C2×D18111yescharacteristic
235#102C2×D18111yescharacteristic
236C22⋊C8—1811no—
237C22⋊C8C2×D18111yescharacteristic
238C4×C8—1811no—
239#41—7244no—
240#41—7244no—
241C2×Q8—3621no—
242C2×Q8—3621no—
243C2×D4—21no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—1811no—
248C2×D4—1811no—
249C2×D4C22×D18111yescharacteristic
250C22×C4—21no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—1811no—
257C22×C4C22×D18111yescharacteristic
258D8—3622no—
259C2×C8—3622no—
260C2×C8—3622no—
261C2×C8—1811no—
262C2×C8—1811no—
263C2×C8C22×D18111yescharacteristic
264C2×C8C22×D18111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4—1811no—
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C4⋊C4C22×D18111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—1811no—
285C22⋊C4—1811no—
286C42—1811no—
287C23—21no—
288C23—3621no—
289C23—1811no—
290C23D4×D18111yescharacteristic
291Q8—7242no—
292Q8—7242no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—3621no—
297D4—3621no—
298D4—1814no—
299D4—7242no—
300D4—7242no—
301D4—7242no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—1811no—
314C2×C4—1811no—
315C2×C4—1811no—
316C2×C4—7242no—
317C2×C4—7242no—
318C2×C4—7242no—
319C2×C4—7242no—
320C2×C4—7242no—
321C2×C4D4×D18111yescharacteristic
322C2×C4C23×D18111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3621no—
326C8—1812no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3621no—
333C22—3621no—
334C22—1812no—
335C22—7241no—
336C22—7241no—
337C22—7241no—
338C22D8×D18112yes—
339C22C2×D4×D18111yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3621no—
345C4—3621no—
346C4—1812no—
347C4—7241no—
348C4—7241no—
349C4—7241no—
350C4#41×D18111yescharacteristic
351C4#1915386311yescharacteristic
352C2—22no—
353C2—81no—
354C2—3622no—
355C2—14481no—
356C2#2604192711yescharacteristic
357C2C2×D8×D18111yescharacteristic
358C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
hypercenter#480D181
hypocenterC181#3334
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #26041930C2semidirect
2. #26041929C2semidirect
3. #26041683C2semidirect
4. #26041594C2semidirect
5. #26041593C2semidirect
6. #26041591C2semidirect
7. #26041558C2semidirect
8. #26041557C2semidirect
9. #26041514C2semidirect
10. #26041513C2semidirect
11. #26041359C2semidirect
12. #26041342C2semidirect
13. C2×#19153749C2semidirect
14. #107×D181C2semidirect
15. #480×C181C2semidirect
116. C22⋊D181D8semidirect
131. #13089678#41semidirect
179. C181#3334semidirect
187. #480D181semidirect

Maximal subgroups

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

subgroupindex
#260419302
#260419292
#260416832
#260415942
#260415932
#260415912
#260415582
#260415572
#260415142
#260415132
#260413592
#260413422
C2×#191537492
#107×D1812
#480×C1812
#3334181