Finite Group Databasebeta

← #37546174

Subgroups — #37546174

Order 23168.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041984C211yesmaximal, characteristic
2#26041971C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041610C211yesmaximal, characteristic, complemented
6#26041608C211yesmaximal, characteristic, complemented
7#26041585C211yesmaximal, characteristic, complemented
8#26041562C211yesmaximal, characteristic, complemented
9#26041536C211yesmaximal, characteristic, complemented
10#26041518C211yesmaximal, characteristic, complemented
11#26041383C211yesmaximal, characteristic, complemented
12#26041347C211yesmaximal, characteristic
13#26041320C211yesmaximal, characteristic, complemented
14C2×#19153747C211yesmaximal, characteristic, complemented
15#484×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668432C2211yescharacteristic
18C22×#13089678C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153811—21no—
21#19153807—21no—
22#19153807C2211yescharacteristic
23#19153806—21no—
24#19153800—21no—
25#19153796C2211yescharacteristic
26#19153795—21no—
27#19153795C2211yescharacteristic
28#19153794—21no—
29#19153792C2211yescharacteristic
30Q8×Dic181C2211yescharacteristic
31#19153781C2211yescharacteristic
32C4×C22⋊D181—21no—
33C4×C22⋊D181C2211yescharacteristic
34#19153774C2211yescharacteristic
35#19153772—21no—
36C2×C4⋊Dic181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153740C2211yescharacteristic
49#19153739C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C22⋊Q8×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×C22⋊D181D411yescharacteristic
62C22×Dic181—21no—
63C2×C4×D181—21no—
64C2×C4×D181C2311yescharacteristic
65#15668439—22no—
66#15668432—22no—
67C2×#13089678—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84C22⋊Dic181—21no—
85C22⋊Dic181D411yescharacteristic
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C2×Q8×C181C2311yescharacteristic
95C22×C4×C181—21no—
96C22×C4×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22×D181C2×D411yescharacteristic
106Dic362—21no—
107Dic362—21no—
108Dic362—81no—
109C22⋊D181—22no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—42no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—81no—
121#13089678—21no—
122#13089678#4112yes—
123C23×C181C2×D411yescharacteristic
124Q8×C181—21no—
125Q8×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—81no—
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2411yescharacteristic
135C8×C181—21no—
136C8×C181—21no—
137C22×C181—21no—
138C22×C181—21no—
139C22×C181#13712yes—
140C22×C181C22×D411yescharacteristic
141C2×D181—21no—
142C2×D181—21no—
143C2×D181—21no—
144C4×C181—21no—
145C4×C181—41no—
146C4×C181—41no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181C2×#4111yescharacteristic
150C4×C1812−1+411yescharacteristic
151Dic181—21no—
152Dic181—21no—
153Dic181—21no—
154Dic181—41no—
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158C2×C181—22no—
159C2×C181#54711yescharacteristic
160C2×C181C2×#13711yescharacteristic
161C2×C181#57711yescharacteristic
162D181—41no—
163C181#334411yescharacteristic, complemented, Sylow
164#3344—1811nomaximal, Sylow
165#554—1811no—
166#552—1811no—
167#501—1811no—
168#485—1811no—
169#484D18111yescharacteristic, complemented
170#483—1811no—
171#483—1811no—
172#479—1811no—
173#475—1811no—
174#470—1811no—
175#467—1811no—
176#441—1811no—
177#435—1811no—
178#428—1811no—
179C2×#106—1811no—
180C2×Q16—1811no—
181C2×M16—1811no—
182C22×C8—1811no—
183C4⋊Q8—1811no—
184#126—3621no—
185#125—3621no—
186#125—3621no—
187#125—1811no—
188#123—3621no—
189C22⋊Q8—3621no—
190C22⋊Q8—3621no—
191C22⋊Q8—1811no—
192C22⋊Q8—1811no—
193C22⋊Q8—1811no—
194C22⋊Q8C2×D18111yescharacteristic
195C4×Q8—1811no—
196C4×Q8—1811no—
197C4×D4—3621no—
198C4×D4—1811no—
199#117—3621no—
200#117—1811no—
201C2×C4⋊C4—1811no—
202C2×C4⋊C4—1811no—
203C2×C4⋊C4C2×D18111yescharacteristic
204#107—1811no—
205#107C2×D18111yescharacteristic
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211#106—1811no—
212#106—1811no—
213C4⋊C8—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#103—1811no—
218#103C2×D18111yescharacteristic
219#103C2×D18111yescharacteristic
220C22⋊C8—1811no—
221C22⋊C8C2×D18111yescharacteristic
222#97—1811no—
223C2×Q8—3621no—
224C2×Q8—1811no—
225C2×Q8C22×D18111yescharacteristic
226C2×D4—1811no—
227C22×C4—21no—
228C22×C4—3621no—
229C22×C4—3621no—
230C22×C4—1811no—
231C22×C4C22×D18111yescharacteristic
232Q16—3622no—
233M16—3622no—
234C2×C8—3622no—
235C2×C8—1811no—
236C2×C8—1811no—
237C2×C8C22×D18111yescharacteristic
238C2×C8C22×D18111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—1811no—
264C22⋊C4—1811no—
265C42—3621no—
266C42—3621no—
267C42—3621no—
268C42—1811no—
269C23—1811no—
270C23D4×D18111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—3621no—
274Q8—3621no—
275Q8—14481no—
276D4—3622no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—81no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—14481no—
291C2×C4—1811no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—7242no—
295C2×C4D4×D18111yescharacteristic
296C2×C4C23×D18111yescharacteristic
297C8—21no—
298C8—21no—
299C8—3621no—
300C8—1812no—
301C22—21no—
302C22—21no—
303C22—3621no—
304C22—3621no—
305C22—3621no—
306C22#1915384812yes—
307C22C2×D4×D18111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3621no—
314C4—3621no—
315C4—3621no—
316C4—7241no—
317C4—7241no—
318C4—7241no—
319C4—7241no—
320C4#41×D18111yescharacteristic
321C4#1915386311yescharacteristic
322C2—22no—
323C2—7241no—
324C2#2604192711yescharacteristic
325C2C2×#1915384811yescharacteristic
326C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#484×C181C2
socleC22×C181C22×D4
prime radicalC2×C22⋊D181D4
hypercenter#484D181
hypocenterC181#3344
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #26041687C2semidirect
4. #26041622C2semidirect
5. #26041610C2semidirect
6. #26041608C2semidirect
7. #26041585C2semidirect
8. #26041562C2semidirect
9. #26041536C2semidirect
10. #26041518C2semidirect
11. #26041383C2semidirect
13. #26041320C2semidirect
14. C2×#19153747C2semidirect
15. #484×C181C2semidirect
163. C181#3344semidirect
169. #484D181semidirect

Maximal subgroups

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

subgroupindex
#260419842
#260419712
#260416872
#260416222
#260416102
#260416082
#260415852
#260415622
#260415362
#260415182
#260413832
#260413472
#260413202
C2×#191537472
#484×C1812
#3344181