Finite Group Databasebeta

← #37544916

Subgroups — #37544916

Order 23168.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041832C211yesmaximal, characteristic, complemented
2#26041824C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041686C211yesmaximal, characteristic, complemented
5#26041642C211yesmaximal, characteristic, complemented
6#26041642C211yesmaximal, characteristic, complemented
7#26041604C211yesmaximal, characteristic, complemented
8#26041603C211yesmaximal, characteristic, complemented
9#26041600C211yesmaximal, characteristic, complemented
10#26041568C211yesmaximal, characteristic, complemented
11#26041567C211yesmaximal, characteristic, complemented
12#26041558C211yesmaximal, characteristic, complemented
13#26041557C211yesmaximal, characteristic, complemented
14#26041333C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668448—21no—
17#19153815C2211yescharacteristic
18#19153815C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153812C2211yescharacteristic
21#19153807C2211yescharacteristic
22#19153807C2211yescharacteristic
23#19153802—21no—
24#19153793—21no—
25#19153793—21no—
26#19153790C2211yescharacteristic
27#19153788—21no—
28C4×Dic362—21no—
29C4×Dic362—21no—
30D4×Dic181C2211yescharacteristic
31#19153778C2211yescharacteristic
32#19153776—21no—
33#19153775C2211yescharacteristic
34C2×C4×Dic181C2211yescharacteristic
35#19153750C2211yescharacteristic
36#19153749C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51#19153726C2211yescharacteristic
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668448—44no—
60C2×Dic362—21no—
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C22×Dic181D411yescharacteristic
69C22×Dic181D411yescharacteristic
70C2×C4×D181—21no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85#15668426—21no—
86#15668426—21no—
87C4×Dic181—21no—
88C4×Dic181D411yescharacteristic
89C4×Dic181D411yescharacteristic
90C4×Dic181C2311yescharacteristic
91C4×Dic181C2311yescharacteristic
92C2×D4×C181—21no—
93C2×D4×C181C2311yescharacteristic
94C22×C4×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C4⋊C4×C181C2311yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C42×C181—21no—
103C22×D181—21no—
104Dic362—42no—
105Dic362—42no—
106Dic362—42no—
107D724—21no—
108D724—21no—
109C22⋊D181—42no—
110C22⋊D181—42no—
111C22⋊D181—42no—
112C2×Dic181—22no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—41no—
117C2×Dic181—42no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C4×D181—42no—
123#13089678—21no—
124#13089678—21no—
125C23×C181—21no—
126C23×C181C2×D411yescharacteristic
127D4×C181—21no—
128D4×C181—21no—
129D4×C181—42no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181C2×D411yescharacteristic
136C2×C4×C181C2411yescharacteristic
137C8×C181—21no—
138C8×C181—21no—
139C22×C181—21no—
140C22×C181—21no—
141C22×C181—21no—
142C22×C181—41no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181C22×D411yescharacteristic
146C2×D181—41no—
147C2×D181—41no—
148C2×D181—41no—
149C4×C181—21no—
150C4×C181—41no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C1812−1+411yescharacteristic
154C4×C1812−1+411yescharacteristic
155Dic181—21no—
156Dic181—21no—
157Dic181—21no—
158Dic181—41no—
159Dic181—41no—
160Dic181—41no—
161Dic181AGL(1,ℤ/8)12yes—
162C2×C181—41no—
163C2×C181—81no—
164C2×C181#53611yescharacteristic
165C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
166C2×C181#57511yescharacteristic
167D181—81no—
168C181#323511yescharacteristic, complemented, Sylow
169#3235—1811nomaximal, Sylow
170#533—1811no—
171#532—1811no—
172#501—1811no—
173#501—1811no—
174#490—1811no—
175#490—1811no—
176#482—1811no—
177#482—1811no—
178#482—1811no—
179#482D18111yescharacteristic, complemented
180#476—1811no—
181#476—1811no—
182#474—1811no—
183#474—1811no—
184#432—1811no—
185C2×#41—3621no—
186C4⋊Q8—1811no—
187C4⋊Q8—1811no—
188C4⋊Q8—1811no—
189#127—1811no—
190#125—1811no—
191#125—1811no—
192#124—3621no—
193C22⋊Q8—3621no—
194C22⋊Q8—3621no—
195#121—3621no—
196#121—1811no—
197#121C2×D18111yescharacteristic
198C4×Q8—3621no—
199C4×Q8—3621no—
200C4×D4—3621no—
201C4×D4—1811no—
202C4×D4—1811no—
203#117—1811no—
204#117C2×D18111yescharacteristic
205C2×C42—1811no—
206#107—1811no—
207#107—1811no—
208#107—1811no—
209#107C2×D18111yescharacteristic
210#106—1811no—
211#106—1811no—
212#106—1811no—
213#106C2×D18111yescharacteristic
214C4⋊C8—1811no—
215C4⋊C8—1811no—
216#102—1811no—
217#102—1811no—
218#102—1811no—
219#102—1811no—
220#102—1811no—
221#102—1811no—
222#102C2×D18111yescharacteristic
223#102C2×D18111yescharacteristic
224C22⋊C8—1811no—
225C22⋊C8C2×D18111yescharacteristic
226#97—1811no—
227#97—1811no—
228#41—7244no—
229C2×Q8—3621no—
230C2×Q8—3621no—
231C2×Q8—3621no—
232C2×D4—21no—
233C2×D4—3621no—
234C2×D4—3621no—
235C2×D4—3621no—
236C2×D4—1811no—
237C2×D4C22×D18111yescharacteristic
238C22×C4—3621no—
239C22×C4—3621no—
240C22×C4—1811no—
241C22×C4—1811no—
242C22×C4C22×D18111yescharacteristic
243C2×C8—1811no—
244C2×C8—1811no—
245C2×C8C22×D18111yescharacteristic
246C2×C8C22×D18111yescharacteristic
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—3621no—
254C4⋊C4—1811no—
255C4⋊C4—1811no—
256C4⋊C4—1811no—
257C4⋊C4C22×D18111yescharacteristic
258C4⋊C4C22×D18111yescharacteristic
259C4⋊C4C22×D18111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C22⋊C4—3621no—
266C42—21no—
267C42—3621no—
268C42—1811no—
269C42—1811no—
270C42—1811no—
271C42—1811no—
272C23—21no—
273C23—3621no—
274C23D4×D18111yescharacteristic
275Q8—7242no—
276Q8—7242no—
277Q8—7242no—
278D4—21no—
279D4—21no—
280D4—42no—
281D4—3621no—
282D4—3621no—
283D4—7242no—
284D4—7242no—
285D4—7242no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—3622no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—1811no—
296C2×C4—1811no—
297C2×C4—1811no—
298C2×C4—1811no—
299C2×C4—7242no—
300C2×C4—7241no—
301C2×C4—7242no—
302C2×C4D4×D18111yescharacteristic
303C2×C4C23×D18111yescharacteristic
304C8—21no—
305C8—21no—
306C8—3621no—
307C8—3621no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—7241no—
315C22—7241no—
316C22—7241no—
317C22C2×D4×D18111yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—3621no—
323C4—3621no—
324C4—3621no—
325C4—1812no—
326C4—7241no—
327C4—7241no—
328C4—7241no—
329C4#1915386311yescharacteristic
330C4#1915386311yescharacteristic
331C2—41no—
332C2—81no—
333C2—14481no—
334C2#2604185111yescharacteristic
335C2AGL(1,ℤ/8)×D18111yescharacteristic
336C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
prime radical#26041824C2
hypercenter#482D181
hypocenterC181#3235
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26041832C2semidirect
3. #26041687C2semidirect
4. #26041686C2semidirect
5. #26041642C2semidirect
6. #26041642C2semidirect
7. #26041604C2semidirect
8. #26041603C2semidirect
9. #26041600C2semidirect
10. #26041568C2semidirect
11. #26041567C2semidirect
12. #26041558C2semidirect
13. #26041557C2semidirect
14. #26041333C2semidirect
15. #482×C181C2semidirect
168. C181#3235semidirect
179. #482D181semidirect

Maximal subgroups

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

subgroupindex
#260418322
#260418242
#260416872
#260416862
#260416422
#260416042
#260416032
#260416002
#260415682
#260415672
#260415582
#260415572
#260413332
#482×C1812
#3235181