Finite Group Databasebeta

← #37545023

Subgroups — #37545023

Order 23168.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041910C211yesmaximal, characteristic, complemented
2#26041902C211yesmaximal, characteristic
3#26041686C211yesmaximal, characteristic, complemented
4#26041676C211yesmaximal, characteristic, complemented
5#26041640C211yesmaximal, characteristic, complemented
6#26041635C211yesmaximal, characteristic, complemented
7#26041617C211yesmaximal, characteristic, complemented
8#26041604C211yesmaximal, characteristic
9#26041597C211yesmaximal, characteristic
10#26041588C211yesmaximal, characteristic, complemented
11#26041578C211yesmaximal, characteristic, complemented
12#26041568C211yesmaximal, characteristic, complemented
13#26041562C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#483×C181C211yesmaximal, characteristic, complemented
16#19153815—21no—
17#19153815C2211yescharacteristic
18#19153815C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153811—21no—
21#19153807—21no—
22#19153807C2211yescharacteristic
23#19153807C2211yescharacteristic
24#19153805C2211yescharacteristic
25#19153802—21no—
26#19153798—21no—
27#19153796—21no—
28#19153795—21no—
29#19153795—21no—
30#19153790C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32#19153778C2211yescharacteristic
33#19153775C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153750C2211yescharacteristic
36#19153749C2211yescharacteristic
37#19153748C2211yescharacteristic
38#19153747C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C22⋊Q8×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#106×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362—21no—
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C4×D181—21no—
65C2×#13089678C2311yescharacteristic
66C2×#13089678C2311yescharacteristic
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181—21no—
70C4⋊Dic181D411yescharacteristic
71C4⋊Dic181D411yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80C22⋊Dic181—21no—
81C22⋊Dic181D411yescharacteristic
82C22⋊Dic181D411yescharacteristic
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87C4×Dic181—21no—
88C4×Dic181—21no—
89C4×Dic181C2311yescharacteristic
90C4×Dic181C2311yescharacteristic
91C2×Q8×C181C2311yescharacteristic
92C22×C4×C181—21no—
93C22×C4×C181C2311yescharacteristic
94C2×C8×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C4⋊C4×C181—21no—
97C4⋊C4×C181—21no—
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C22⋊C4×C181—21no—
102C22×D181—21no—
103Dic362—81no—
104Dic362—81no—
105Dic362—81no—
106D724—21no—
107D724—21no—
108C22⋊D181—81no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181C2×D411yescharacteristic
113C2×Dic181C2×D411yescharacteristic
114C2×Dic181C2×D411yescharacteristic
115C2×Dic181C2×D411yescharacteristic
116C4×D181—81no—
117#13089678—21no—
118#13089678—21no—
119C23×C181C2×D411yescharacteristic
120Q8×C181—21no—
121Q8×C181—21no—
122C2×C4×C181—21no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—81no—
129C2×C4×C181C2×D411yescharacteristic
130C2×C4×C181C2411yescharacteristic
131C8×C181—21no—
132C8×C181—21no—
133C22×C181—21no—
134C22×C181—21no—
135C22×C181—21no—
136C22×C181C22×D411yescharacteristic
137C2×D181—41no—
138C2×D181—41no—
139C2×D181—41no—
140C4×C181—21no—
141C4×C181—41no—
142C4×C181—41no—
143C4×C181—41no—
144C4×C181—41no—
145C4×C1812−1+411yescharacteristic
146C4×C1812−1+411yescharacteristic
147Dic181—21no—
148Dic181—21no—
149Dic181—21no—
150Dic181—21no—
151Dic181—41no—
152Dic181—41no—
153Dic181—41no—
154C2×C181—41no—
155C2×C181#53611yescharacteristic
156C2×C181#57711yescharacteristic
157C2×C181#57711yescharacteristic
158D181—81no—
159C181#324411yescharacteristic, complemented, Sylow
160#3244—1811nomaximal, Sylow
161#544—1811no—
162#542—1811no—
163#501—1811no—
164#498—1811no—
165#489—1811no—
166#488—1811no—
167#485—1811no—
168#483D18111yescharacteristic, complemented
169#482—1811no—
170#481—1811no—
171#479—1811no—
172#478—1811no—
173#476—1811no—
174#475—1811no—
175#433—1811no—
176C4⋊Q8—3621no—
177C4⋊Q8—1811no—
178C4⋊Q8—1811no—
179C4⋊Q8—1811no—
180#126—3621no—
181#125—3621no—
182#125—1811no—
183#125—1811no—
184#124—3621no—
185#124—1811no—
186#123—3621no—
187C22⋊Q8—3621no—
188C22⋊Q8—3621no—
189C22⋊Q8—3621no—
190C22⋊Q8C2×D18111yescharacteristic
191#121—1811no—
192C4×Q8—1811no—
193C4×D4—1811no—
194#117—1811no—
195#117—1811no—
196C2×C4⋊C4C2×D18111yescharacteristic
197#107—1811no—
198#107—1811no—
199#106—1811no—
200#106—1811no—
201#106—1811no—
202#106—1811no—
203#106C2×D18111yescharacteristic
204#106C2×D18111yescharacteristic
205C4⋊C8—1811no—
206C4⋊C8—1811no—
207#103—1811no—
208#103—1811no—
209#103C2×D18111yescharacteristic
210#103C2×D18111yescharacteristic
211#102—1811no—
212#102—1811no—
213#102—1811no—
214#102—1811no—
215C22⋊C8—1811no—
216C22⋊C8C2×D18111yescharacteristic
217#97—1811no—
218C4×C8—1811no—
219C2×Q8—3621no—
220C2×Q8—3621no—
221C2×Q8—3621no—
222C2×Q8C22×D18111yescharacteristic
223C2×D4—3621no—
224C2×D4—1811no—
225C22×C4—21no—
226C22×C4—3621no—
227C22×C4C22×D18111yescharacteristic
228C2×C8—1811no—
229C2×C8—1811no—
230C2×C8C22×D18111yescharacteristic
231C2×C8C22×D18111yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—3621no—
235C4⋊C4—3621no—
236C4⋊C4—3621no—
237C4⋊C4—3621no—
238C4⋊C4—3621no—
239C4⋊C4—3621no—
240C4⋊C4—3621no—
241C4⋊C4—3621no—
242C4⋊C4—1811no—
243C4⋊C4—1811no—
244C4⋊C4—1811no—
245C4⋊C4—1811no—
246C4⋊C4—1811no—
247C4⋊C4C22×D18111yescharacteristic
248C4⋊C4C22×D18111yescharacteristic
249C4⋊C4C22×D18111yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—3621no—
252C22⋊C4—3621no—
253C22⋊C4—3621no—
254C22⋊C4—3621no—
255C22⋊C4—3621no—
256C22⋊C4—1811no—
257C22⋊C4—1811no—
258C42—3621no—
259C42—3621no—
260C42—1811no—
261C42—1811no—
262C23—3621no—
263C23D4×D18111yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—14481no—
267Q8—14481no—
268Q8—14481no—
269D4—3621no—
270D4—3621no—
271D4—14481no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—81no—
279C2×C4—3621no—
280C2×C4—3621no—
281C2×C4—3621no—
282C2×C4—14481no—
283C2×C4—1811no—
284C2×C4—1811no—
285C2×C4—1811no—
286C2×C4—1811no—
287C2×C4D4×D18111yescharacteristic
288C2×C4C23×D18111yescharacteristic
289C8—21no—
290C8—21no—
291C8—3621no—
292C8—3621no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—7241no—
297C22—7241no—
298C22—7241no—
299C22C2×D4×D18111yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—3621no—
306C4—3621no—
307C4—3621no—
308C4—3621no—
309C4—7241no—
310C4—7241no—
311C4—7241no—
312C4#1915386311yescharacteristic
313C4#1915386311yescharacteristic
314C2—41no—
315C2—14481no—
316C2#2604185111yescharacteristic
317C2#2604208511yescharacteristic
318C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#483×C181C2
socleC22×C181C22×D4
prime radical#19153790C22
hypercenter#483D181
hypocenterC181#3244
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #26041910C2semidirect
3. #26041686C2semidirect
4. #26041676C2semidirect
5. #26041640C2semidirect
6. #26041635C2semidirect
7. #26041617C2semidirect
10. #26041588C2semidirect
11. #26041578C2semidirect
12. #26041568C2semidirect
13. #26041562C2semidirect
14. #26041337C2semidirect
15. #483×C181C2semidirect
159. C181#3244semidirect
168. #483D181semidirect

Maximal subgroups

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

subgroupindex
#260419102
#260419022
#260416862
#260416762
#260416402
#260416352
#260416172
#260416042
#260415972
#260415882
#260415782
#260415682
#260415622
#260413372
#483×C1812
#3244181