Finite Group Databasebeta

← #37545091

Subgroups — #37545091

Order 23168.

348 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#26041833C211yesmaximal, characteristic, complemented
2#26041808C211yesmaximal, characteristic
3#26041587C211yesmaximal, characteristic, complemented
4#26041586C211yesmaximal, characteristic, complemented
5#26041572C211yesmaximal, characteristic, complemented
6#26041567C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic, complemented
8#26041534C211yesmaximal, characteristic, complemented
9#26041524C211yesmaximal, characteristic
10#26041522C211yesmaximal, characteristic
11#26041498C211yesmaximal, characteristic, complemented
12#26041487C211yesmaximal, characteristic, complemented
13#26041482C211yesmaximal, characteristic, complemented
14#26041301C211yesmaximal, characteristic, complemented
15#464×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×#15668432C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153814C2211yescharacteristic
22#19153809—21no—
23#19153808C2211yescharacteristic
24#19153806—21no—
25#19153798—21no—
26#19153796C2211yescharacteristic
27#19153794—21no—
28#19153792C2211yescharacteristic
29#19153792C2211yescharacteristic
30#19153787C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32C4×Dic362—21no—
33C4×Dic362C2211yescharacteristic
34D4×Dic181C2211yescharacteristic
35#19153776—21no—
36#19153773—21no—
37#19153772—21no—
38C42×D181C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153740C2211yescharacteristic
49#19153740C2211yescharacteristic
50#19153740C2211yescharacteristic
51#19153737C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×C22⋊D181—21no—
62C22×Dic181—21no—
63C2×C4×D181D411yescharacteristic
64C2×C4×D181D411yescharacteristic
65C2×C4×D181C2311yescharacteristic
66#15668439—41no—
67#15668437—41no—
68#15668432—41no—
69#15668432—41no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
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#15668428—21no—
84#15668428—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181D411yescharacteristic
93C4×Dic181D411yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98Q16×C181—41no—
99SD16×C181—41no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181C2×D411yescharacteristic
109Dic362—21no—
110Dic362—21no—
111Dic362—42no—
112C22⋊D181—42no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—42no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—21no—
122C4×D181—21no—
123C4×D181—22no—
124C4×D181—41no—
125#13089678—21no—
126#13089678—21no—
127C23×C181—21no—
128Q8×C181—21no—
129Q8×C181—21no—
130Q8×C181—21no—
131Q8×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2411yescharacteristic
140C8×C181—21no—
141C8×C181—21no—
142C22×C181—41no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181C22×D411yescharacteristic
146C2×D181—21no—
147C2×D181—21no—
148C2×D181—21no—
149C4×C181—21no—
150C4×C181—21no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181H(5,𝔽2)11yescharacteristic
155C4×C1812−1+411yescharacteristic
156Dic181—21no—
157Dic181—21no—
158Dic181—41no—
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181#13712yes—
163C2×C181—81no—
164C2×C181#53711yescharacteristic
165C2×C181C2×#13711yescharacteristic
166C2×C181#57511yescharacteristic
167D181—41no—
168C181#325211yescharacteristic, complemented, Sylow
169#3252—1811nomaximal, Sylow
170#533—1811no—
171#529—1811no—
172#479—1811no—
173#479—1811no—
174#477—1811no—
175#476—1811no—
176#470—1811no—
177#470—1811no—
178#468—1811no—
179#468—1811no—
180#464—1811no—
181#464D18111yescharacteristic, complemented
182#462—1811no—
183#461—1811no—
184#423—1811no—
185C2×Q16—1811no—
186C2×Q16C2×D18111yescharacteristic
187C2×SD16—1811no—
188C2×SD16C2×D18111yescharacteristic
189C2×M16—1811no—
190C2×M16—1811no—
191C4⋊Q8—1811no—
192C4⋊Q8—1811no—
193#126—3621no—
194#125—3621no—
195#125—1811no—
196#124C2×D18111yescharacteristic
197#123—3621no—
198C22⋊Q8—3621no—
199C22⋊Q8—1811no—
200C22⋊Q8—1811no—
201C22⋊Q8—1811no—
202#121—1811no—
203C4×Q8—3621no—
204C4×Q8—1811no—
205C4×Q8—1811no—
206C4×Q8C2×D18111yescharacteristic
207C4×D4—3621no—
208C4×D4—1811no—
209#117—3621no—
210#117—3621no—
211C2×C42—1811no—
212#107—1811no—
213#107—1811no—
214#106—1811no—
215#106—1811no—
216C4⋊C8—1811no—
217C4⋊C8—1811no—
218C4⋊C8—1811no—
219C4⋊C8C2×D18111yescharacteristic
220#103—1811no—
221#103—1811no—
222#103—1811no—
223#103—1811no—
224#103—1811no—
225#103C2×D18111yescharacteristic
226#102—1811no—
227#102C2×D18111yescharacteristic
228C2×Q8—3621no—
229C2×Q8—1811no—
230C2×Q8C22×D18111yescharacteristic
231C2×Q8C22×D18111yescharacteristic
232C2×D4—3621no—
233C2×D4C22×D18111yescharacteristic
234C22×C4—3621no—
235C22×C4—1811no—
236C22×C4—1811no—
237C22×C4—1811no—
238Q16—41no—
239Q16—7241no—
240SD16—41no—
241SD16—7241no—
242M16—7241no—
243M16—7241no—
244C2×C8—1811no—
245C2×C8—1811no—
246C2×C8C22×D18111yescharacteristic
247C2×C8C22×D18111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4—1811no—
262C4⋊C4C22×D18111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C42—21no—
271C42—3621no—
272C42—3621no—
273C42—1811no—
274C42—1811no—
275C42—1811no—
276C42C22×D18111yescharacteristic
277C23—21no—
278C23—1811no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—3621no—
284Q8—3621no—
285Q8—7242no—
286D4—21no—
287D4—21no—
288D4—7242no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3622no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—1811no—
300C2×C4—1811no—
301C2×C4—1811no—
302C2×C4—7241no—
303C2×C4—7242no—
304C2×C4D4×D18111yescharacteristic
305C2×C4D4×D18111yescharacteristic
306C2×C4C23×D18111yescharacteristic
307C8—21no—
308C8—21no—
309C8—3621no—
310C8—3621no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—3621no—
315C22—3621no—
316C22—3621no—
317C22C2×D4×D18111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—3621no—
324C4—3621no—
325C4—1812no—
326C4—7241no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4#1915386111yescharacteristic
331C4#1915386311yescharacteristic
332C2—81no—
333C2—7241no—
334C2#2604185811yescharacteristic
335C2#137×D18111yescharacteristic
336C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#464×C181C2
socleC22×C181C22×D4
prime radical#19153787C22
hypercenter#464D181
hypocenterC181#3252
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #26041833C2semidirect
3. #26041587C2semidirect
4. #26041586C2semidirect
5. #26041572C2semidirect
6. #26041567C2semidirect
7. #26041536C2semidirect
8. #26041534C2semidirect
11. #26041498C2semidirect
12. #26041487C2semidirect
13. #26041482C2semidirect
14. #26041301C2semidirect
15. #464×C181C2semidirect
168. C181#3252semidirect
181. #464D181semidirect

Maximal subgroups

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

subgroupindex
#260418332
#260418082
#260415872
#260415862
#260415722
#260415672
#260415362
#260415342
#260415242
#260415222
#260414982
#260414872
#260414822
#260413012
#464×C1812
#3252181