Finite Group Databasebeta

← #37543586

Subgroups — #37543586

Order 23168.

376 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#26041761C211yesmaximal, characteristic
3#26041584C211yesmaximal, characteristic, complemented
4#26041582C211yesmaximal, characteristic, complemented
5#26041576C211yesmaximal, characteristic, complemented
6#26041570C211yesmaximal, characteristic, complemented
7#26041568C211yesmaximal, characteristic, complemented
8#26041564C211yesmaximal, characteristic, complemented
9#26041562C211yesmaximal, characteristic, complemented
10#26041320C211yesmaximal, characteristic, complemented
11#106×D181C211yesmaximal, characteristic, complemented
12#26041304C211yesmaximal, characteristic, complemented
13#26041279C211yesmaximal, characteristic
14#26041274C211yesmaximal, characteristic
15#479×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668432C2211yescharacteristic
18C2×C8×D181C2211yescharacteristic
19#19153816C2211yescharacteristic
20#19153815—21no—
21#19153815C2211yescharacteristic
22#19153807C2211yescharacteristic
23#19153806—21no—
24#19153796—21no—
25#19153794—21no—
26Q8×Dic181C2211yescharacteristic
27C4×D724—21no—
28C4×D724C2211yescharacteristic
29#19153778—21no—
30#19153778C2211yescharacteristic
31#19153774C2211yescharacteristic
32#19153773—21no—
33#19153773C2211yescharacteristic
34C4⋊C4×D181—21no—
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153736C2211yescharacteristic
51#19153736C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#15668450—22no—
60#15668450Q814yescomplemented
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71#15668432—22no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C8×D181—22no—
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181—21no—
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86#15668428D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426D411yescharacteristic
91#15668426D411yescharacteristic
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C42×C181—21no—
105C42×C181C2311yescharacteristic
106C22×D181—21no—
107C22×D181C2×D411yescharacteristic
108Dic362—81no—
109Dic362—81no—
110D724—24no—
111D724—21no—
112D724C2×Q812yes—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C4×D181—24no—
120C4×D181—81no—
121C4×D181—81no—
122C4×D181—81no—
123C4×D181—81no—
124C4×D181C2×Q812yes—
125C4×D181#4112yes—
126#13089678—21no—
127#13089678—21no—
128Q8×C181—21no—
129Q8×C181C2×Q812yes—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2×D411yescharacteristic
136C2×C4×C181C2411yescharacteristic
137C8×C181—21no—
138C8×C181—21no—
139C22×C181C22×D411yescharacteristic
140C2×D181—21no—
141C2×D181—21no—
142C2×D181—22no—
143C2×D181—41no—
144C2×D181—41no—
145C2×D181C22⋊Q812yes—
146C4×C181—22no—
147C4×C181—21no—
148C4×C181—21no—
149C4×C181—41no—
150C4×C181—41no—
151C4×C181—41no—
152C4×C181C22×Q811yescharacteristic
153C4×C181C2×#4111yescharacteristic
154Dic181—21no—
155Dic181—21no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159Dic181C22⋊Q812yes—
160C2×C181C2×C22⋊Q811yescharacteristic
161C2×C181#57711yescharacteristic
162C2×C181#57711yescharacteristic
163D181—22no—
164D181—42no—
165C181#308411yescharacteristic, complemented, Sylow
166#3084—1811nomaximal, Sylow
167#544—1811no—
168#520—1811no—
169#479—1811no—
170#479D18111yescharacteristic, complemented
171#478—1811no—
172#478—1811no—
173#476—1811no—
174#476—1811no—
175#475—1811no—
176#475—1811no—
177#428—1811no—
178C2×#106—1811no—
179#424—1811no—
180#417—1811no—
181#416—1811no—
182C2×#41—1811no—
183C2×M16—1811no—
184C22×C8—1811no—
185C4⋊Q8—3621no—
186C4⋊Q8—1811no—
187C4⋊Q8—1811no—
188#125—3621no—
189#125—1811no—
190#125C2×D18111yescharacteristic
191C22⋊Q8—3621no—
192C22⋊Q8—3621no—
193C4×Q8—1811no—
194C4×Q8C2×D18111yescharacteristic
195C4×D4—3621no—
196C4×D4—3621no—
197C4×D4—1811no—
198C4×D4—1811no—
199#117—3621no—
200#117—1811no—
201#117—1811no—
202C2×C4⋊C4—3621no—
203C2×C4⋊C4—1811no—
204C2×C4⋊C4—1811no—
205#107—1811no—
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211#106—1811no—
212#106C2×D18111yescharacteristic
213C4⋊C8—1811no—
214C4⋊C8—1811no—
215C4⋊C8—1811no—
216C4⋊C8C2×D18111yescharacteristic
217#103—1811no—
218#103—1811no—
219#103C2×D18111yescharacteristic
220#103C2×D18111yescharacteristic
221#102—1811no—
222#102—1811no—
223#102—1811no—
224#102—1811no—
225#41—3622no—
226#41—1814no—
227C2×Q8—3621no—
228C2×Q8—3621no—
229C2×Q8C22×D18111yescharacteristic
230C2×D4—3621no—
231C2×D4—1811no—
232C22×C4—3621no—
233C22×C4—3621no—
234C22×C4—3621no—
235C22×C4—3621no—
236C22×C4—3621no—
237C22×C4—1811no—
238M16—3622no—
239C2×C8—3622no—
240C2×C8—1811no—
241C2×C8—1811no—
242C2×C8C22×D18111yescharacteristic
243C2×C8C22×D18111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
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⋊C4—1811no—
258C4⋊C4—1811no—
259C4⋊C4C22×D18111yescharacteristic
260C4⋊C4C22×D18111yescharacteristic
261C4⋊C4C22×D18111yescharacteristic
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C22⋊C4—1811no—
266C22⋊C4—1811no—
267C42—21no—
268C42—3621no—
269C42—3621no—
270C42—1811no—
271C42C22×D18111yescharacteristic
272C23—3621no—
273C23—1811no—
274Q8—21no—
275Q8—14481no—
276Q8—14481no—
277Q8Q8×D18112yes—
278D4—3624no—
279D4—3621no—
280D4—1812no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—3624no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—14481no—
290C2×C4—14481no—
291C2×C4—14481no—
292C2×C4—14481no—
293C2×C4—1811no—
294C2×C4—1811no—
295C2×C4—1811no—
296C2×C4—1812no—
297C2×C4—1812no—
298C2×C4D4×D18111yescharacteristic
299C2×C4D4×D18111yescharacteristic
300C2×C4C23×D18111yescharacteristic
301C8—21no—
302C8—21no—
303C8—3621no—
304C8—3621no—
305C22—3621no—
306C22—3621no—
307C22—3622no—
308C22—1812no—
309C22—7241no—
310C22—7241no—
311C22C2×D4×D18111yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—3621no—
319C4—3621no—
320C4—1812no—
321C4—7241no—
322C4—7241no—
323C4—7241no—
324C4C2×Q8×D18111yescharacteristic
325C4#41×D18111yescharacteristic
326C2—3622no—
327C2—7242no—
328C2C22⋊Q8×D18111yescharacteristic
329C2#2604208611yescharacteristic
330C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#479×C181C2
socleC22×C181C22×D4
prime radicalC2×#15668450C22
hypercenter#479D181
hypocenterC181#3084
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. #26041909C2semidirect
3. #26041584C2semidirect
4. #26041582C2semidirect
5. #26041576C2semidirect
6. #26041570C2semidirect
7. #26041568C2semidirect
8. #26041564C2semidirect
9. #26041562C2semidirect
10. #26041320C2semidirect
11. #106×D181C2semidirect
12. #26041304C2semidirect
15. #479×C181C2semidirect
60. #15668450Q8semidirect
165. C181#3084semidirect
170. #479D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260417612
#260415842
#260415822
#260415762
#260415702
#260415682
#260415642
#260415622
#260413202
#106×D1812
#260413042
#260412792
#260412742
#479×C1812
#3084181