Finite Group Databasebeta

← #37544248

Subgroups — #37544248

Order 23168.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041909C211yesmaximal, characteristic
2#26041906C211yesmaximal, characteristic
3#26041688C211yesmaximal, characteristic, complemented
4#26041687C211yesmaximal, characteristic, complemented
5#26041686C211yesmaximal, characteristic, complemented
6#26041680C211yesmaximal, characteristic, complemented
7#26041678C211yesmaximal, characteristic, complemented
8#26041676C211yesmaximal, characteristic, complemented
9#26041675C211yesmaximal, characteristic, complemented
10#26041320C211yesmaximal, characteristic
11#26041318C211yesmaximal, characteristic
12#26041316C211yesmaximal, characteristic
13#106×D181C211yesmaximal, characteristic
14#26041236C211yesmaximal, characteristic
15#501×C181C211yesmaximal, characteristic, complemented
16C2×#15668432C2211yescharacteristic
17C2×C8×D181C2211yescharacteristic
18#19153816C2211yescharacteristic
19#19153815—21no—
20#19153815C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153814—21no—
23#19153808C2211yescharacteristic
24#19153807C2211yescharacteristic
25#19153807C2211yescharacteristic
26#19153806—21no—
27#19153806—21no—
28#19153796—21no—
29#19153794—21no—
30#19153794—21no—
31#19153792—21no—
32#19153774C2211yescharacteristic
33#19153774C2211yescharacteristic
34#19153773C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153747C2211yescharacteristic
46#19153747C2211yescharacteristic
47#19153747C2211yescharacteristic
48#19153747C2211yescharacteristic
49#19153726C2211yescharacteristic
50C4×#13089678C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#106×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362—21no—
62C2×C4×D181—21no—
63C2×C4×D181—21no—
64C2×C4×D181C2311yescharacteristic
65#15668432Q814yescomplemented
66C2×#13089678C2311yescharacteristic
67C2×#13089678C2311yescharacteristic
68C8×D181Q814yescomplemented
69C4⋊Dic181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428D411yescharacteristic
85#15668428D411yescharacteristic
86#15668426—21no—
87#15668426—21no—
88#15668426D411yescharacteristic
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181C2311yescharacteristic
93C2×Q8×C181—21no—
94C2×C8×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C4⋊C4×C181—21no—
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C42×C181C2311yescharacteristic
104C22×D181C2×D411yescharacteristic
105Dic362—81no—
106Dic362—81no—
107Dic362—81no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181C2×D411yescharacteristic
113C2×Dic181C2×D411yescharacteristic
114C2×Dic181C2×D411yescharacteristic
115C4×D181—81no—
116C4×D181—81no—
117C4×D181C2×Q812yes—
118C4×D181C2×Q812yes—
119#13089678C2×Q812yes—
120#13089678C2×Q812yes—
121Q8×C181—81no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181C2×D411yescharacteristic
127C2×C4×C181C2×D411yescharacteristic
128C2×C4×C181C2411yescharacteristic
129C8×C181C2×Q812yes—
130C8×C181C2×Q812yes—
131C22×C181C22×D411yescharacteristic
132C2×D181—21no—
133C2×D181—21no—
134C2×D181C4⋊Q812yes—
135C4×C181—21no—
136C4×C181—21no—
137C4×C181—41no—
138C4×C181—41no—
139C4×C181—41no—
140C4×C181—41no—
141C4×C181C22×Q811yescharacteristic
142C4×C181C22×Q811yescharacteristic
143Dic181—21no—
144Dic181—21no—
145Dic181—41no—
146Dic181—41no—
147Dic181—41no—
148Dic181—41no—
149Dic181C4⋊Q812yes—
150C2×C181C2×C4⋊Q811yescharacteristic
151C2×C181#57711yescharacteristic
152C2×C181#57711yescharacteristic
153D181—22no—
154C181#316311yescharacteristic, complemented, Sylow
155#3163—1811nomaximal, Sylow
156#544—1811no—
157#544—1811no—
158#501—1811no—
159#501—1811no—
160#501—1811no—
161#501D18111yescharacteristic, complemented
162#499—1811no—
163#499—1811no—
164#498—1811no—
165#498—1811no—
166#428—1811no—
167#428—1811no—
168#427—1811no—
169C2×#106—1811no—
170#405—1811no—
171C2×M16—1811no—
172C22×C8—1811no—
173C4⋊Q8—3621no—
174C4⋊Q8—3621no—
175C4⋊Q8—1811no—
176C4⋊Q8—1811no—
177C4⋊Q8—1811no—
178C4⋊Q8C2×D18111yescharacteristic
179#125—3621no—
180#125—3621no—
181#125—1811no—
182#125—1811no—
183#125—1811no—
184#125C2×D18111yescharacteristic
185C22⋊Q8—3621no—
186C22⋊Q8—3621no—
187C22⋊Q8—3621no—
188C22⋊Q8—3621no—
189#117—1811no—
190#117—1811no—
191#117—1811no—
192C2×C4⋊C4—1811no—
193C2×C4⋊C4—1811no—
194#107—1811no—
195#107—1811no—
196#107—1811no—
197#107—1811no—
198#107C2×D18111yescharacteristic
199#107C2×D18111yescharacteristic
200#106—1811no—
201#106—1811no—
202#106—1811no—
203#106—1811no—
204#106—1811no—
205#106—1811no—
206#106—1811no—
207#106—1811no—
208#106C2×D18111yescharacteristic
209#106C2×D18111yescharacteristic
210#97—1811no—
211#97C2×D18111yescharacteristic
212C4×C8—1811no—
213C4×C8—1811no—
214C2×Q8—21no—
215C2×Q8—3621no—
216C2×Q8—3621no—
217C2×Q8—3621no—
218C22×C4—3621no—
219C22×C4—3621no—
220C22×C4—1811no—
221M16—1814no—
222C2×C8—1811no—
223C2×C8—1811no—
224C2×C8—1814no—
225C2×C8C22×D18111yescharacteristic
226C2×C8C22×D18111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—3621no—
231C4⋊C4—3621no—
232C4⋊C4—3621no—
233C4⋊C4—3621no—
234C4⋊C4—3621no—
235C4⋊C4—3621no—
236C4⋊C4—3621no—
237C4⋊C4—3621no—
238C4⋊C4—3621no—
239C4⋊C4—3621no—
240C4⋊C4—3621no—
241C4⋊C4—1811no—
242C4⋊C4—1811no—
243C4⋊C4—1811no—
244C4⋊C4—1811no—
245C4⋊C4—1811no—
246C4⋊C4—1811no—
247C4⋊C4C22×D18111yescharacteristic
248C4⋊C4C22×D18111yescharacteristic
249C4⋊C4C22×D18111yescharacteristic
250C4⋊C4C22×D18111yescharacteristic
251C22⋊C4—3621no—
252C22⋊C4—3621no—
253C22⋊C4—1811no—
254C22⋊C4—1811no—
255C42—3621no—
256C42—3621no—
257C42—1811no—
258C42C22×D18111yescharacteristic
259C23—1811no—
260Q8—81no—
261Q8—14481no—
262Q8—14481no—
263Q8—14481no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—3621no—
269C2×C4—3621no—
270C2×C4—3621no—
271C2×C4—3621no—
272C2×C4—14481no—
273C2×C4—14481no—
274C2×C4—1811no—
275C2×C4—1811no—
276C2×C4—1811no—
277C2×C4—1812no—
278C2×C4—1812no—
279C2×C4D4×D18111yescharacteristic
280C2×C4D4×D18111yescharacteristic
281C2×C4C23×D18111yescharacteristic
282C8—1812no—
283C8—1812no—
284C8Q8×D18112yes—
285C8Q8×D18112yes—
286C22—3621no—
287C22—3621no—
288C22—1812no—
289C22C2×D4×D18111yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3621no—
297C4—3621no—
298C4—1812no—
299C4—7241no—
300C4—7241no—
301C4—7241no—
302C4—7241no—
303C4C2×Q8×D18111yescharacteristic
304C4C2×Q8×D18111yescharacteristic
305C2—3622no—
306C2C4⋊Q8×D18111yescharacteristic
307C2#2604208811yescharacteristic
308C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#501×C181C2
socleC22×C181C22×D4
prime radicalC22×D181C2×D4
hypercenter#501D181
hypocenterC181#3163
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #26041688C2semidirect
4. #26041687C2semidirect
5. #26041686C2semidirect
6. #26041680C2semidirect
7. #26041678C2semidirect
8. #26041676C2semidirect
9. #26041675C2semidirect
15. #501×C181C2semidirect
65. #15668432Q8semidirect
68. C8×D181Q8semidirect
154. C181#3163semidirect
161. #501D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260419062
#260416882
#260416872
#260416862
#260416802
#260416782
#260416762
#260416752
#260413202
#260413182
#260413162
#106×D1812
#260412362
#501×C1812
#3163181