Finite Group Databasebeta

← #37545119

Subgroups — #37545119

Order 23168.

354 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041811C211yesmaximal, characteristic, complemented
2#26041808C211yesmaximal, characteristic, complemented
3#26041587C211yesmaximal, characteristic, complemented
4#26041584C211yesmaximal, characteristic, complemented
5#26041579C211yesmaximal, characteristic, complemented
6#26041577C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic, complemented
8#26041529C211yesmaximal, characteristic
9#26041524C211yesmaximal, characteristic, complemented
10#26041522C211yesmaximal, characteristic, complemented
11#26041499C211yesmaximal, characteristic, complemented
12#26041498C211yesmaximal, characteristic, complemented
13#26041492C211yesmaximal, characteristic, complemented
14#26041301C211yesmaximal, characteristic, complemented
15#463×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×#15668432C2211yescharacteristic
20#19153809—21no—
21#19153809—21no—
22#19153808C2211yescharacteristic
23#19153807C2211yescharacteristic
24#19153803C2211yescharacteristic
25#19153798—21no—
26#19153798—21no—
27#19153796C2211yescharacteristic
28#19153792C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32C4×Dic362C2211yescharacteristic
33D4×Dic181C2211yescharacteristic
34C4×C22⋊D181—21no—
35#19153776—21no—
36#19153775—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#19153737C2211yescharacteristic
50#19153737C2211yescharacteristic
51#19153737C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×C22⋊D181—21no—
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⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88#15668426—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181D411yescharacteristic
93C4×Dic181D411yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×D4×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99SD16×C181—41no—
100D8×C181—41no—
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181C2×D411yescharacteristic
109Dic362—21no—
110Dic362—21no—
111C22⋊D181—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—41no—
124C4×D181—41no—
125#13089678—21no—
126#13089678—21no—
127C23×C181—21no—
128C23×C181—21no—
129Q8×C181—21no—
130Q8×C181—21no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134D4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—42no—
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2411yescharacteristic
141C8×C181—21no—
142C8×C181—21no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181—41no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181C22×D411yescharacteristic
150C2×D181—21no—
151C2×D181—21no—
152C2×D181—21no—
153C4×C181—21no—
154C4×C181—21no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181H(5,𝔽2)11yescharacteristic
158C4×C1812−1+411yescharacteristic
159Dic181—21no—
160Dic181—21no—
161Dic181—21no—
162Dic181—41no—
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—81no—
167C2×C181—81no—
168C2×C181#53711yescharacteristic
169C2×C181#57511yescharacteristic
170C2×C181#57511yescharacteristic
171D181—41no—
172C181#325611yescharacteristic, complemented, Sylow
173#3256—1811nomaximal, Sylow
174#529—1811no—
175#529—1811no—
176#479—1811no—
177#479—1811no—
178#478—1811no—
179#478—1811no—
180#470—1811no—
181#469—1811no—
182#468—1811no—
183#468—1811no—
184#464—1811no—
185#464—1811no—
186#463—1811no—
187#463D18111yescharacteristic, complemented
188#423—1811no—
189C2×Q16—1811no—
190C2×SD16—1811no—
191C2×SD16C2×D18111yescharacteristic
192C2×D8C2×D18111yescharacteristic
193C2×M16—1811no—
194C2×M16—1811no—
195#126—3621no—
196#126—3621no—
197#125—1811no—
198#125—1811no—
199#124—1811no—
200#124C2×D18111yescharacteristic
201#123—3621no—
202#123—3621no—
203C22⋊Q8—1811no—
204C22⋊Q8—1811no—
205#121—1811no—
206#121—1811no—
207C4×Q8—1811no—
208C4×Q8—1811no—
209C4×D4—3621no—
210C4×D4—3621no—
211C4×D4—1811no—
212C4×D4C2×D18111yescharacteristic
213#117—3621no—
214#117—3621no—
215C2×C42—1811no—
216#107—1811no—
217#107—1811no—
218#106—1811no—
219#106—1811no—
220C4⋊C8—1811no—
221C4⋊C8—1811no—
222C4⋊C8—1811no—
223C4⋊C8C2×D18111yescharacteristic
224#103—1811no—
225#103—1811no—
226#103—1811no—
227#103C2×D18111yescharacteristic
228#102—1811no—
229#102—1811no—
230#102—1811no—
231#102C2×D18111yescharacteristic
232C2×Q8—1811no—
233C2×Q8C22×D18111yescharacteristic
234C2×D4—3621no—
235C2×D4—3621no—
236C2×D4C22×D18111yescharacteristic
237C2×D4C22×D18111yescharacteristic
238C22×C4—21no—
239C22×C4—3621no—
240C22×C4—1811no—
241C22×C4—1811no—
242C22×C4—1811no—
243Q16—7241no—
244SD16—41no—
245SD16—7241no—
246D8—41no—
247M16—7241no—
248M16—7241no—
249C2×C8—1811no—
250C2×C8—1811no—
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—1811no—
262C4⋊C4—1811no—
263C4⋊C4—1811no—
264C4⋊C4C22×D18111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C42—3621no—
276C42—3621no—
277C42—1811no—
278C42—1811no—
279C42—1811no—
280C42C22×D18111yescharacteristic
281C23—21no—
282C23—21no—
283C23—1811no—
284Q8—21no—
285Q8—21no—
286Q8—3621no—
287Q8—3621no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—7242no—
293D4—7242no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—1811no—
304C2×C4—1811no—
305C2×C4—1811no—
306C2×C4—7241no—
307C2×C4—7241no—
308C2×C4—7242no—
309C2×C4D4×D18111yescharacteristic
310C2×C4D4×D18111yescharacteristic
311C2×C4C23×D18111yescharacteristic
312C8—21no—
313C8—21no—
314C8—3621no—
315C8—3621no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—3621no—
323C22—3621no—
324C22—3621no—
325C22C2×D4×D18111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—3621no—
331C4—3621no—
332C4—3621no—
333C4—7241no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4#1915386111yescharacteristic
338C4#1915386311yescharacteristic
339C2—81no—
340C2—81no—
341C2—7241no—
342C2#2604185811yescharacteristic
343C2#2604207511yescharacteristic
344C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#463×C181C2
socleC22×C181C22×D4
prime radical#26041529C2
hypercenter#463D181
hypocenterC181#3256
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #26041811C2semidirect
2. #26041808C2semidirect
3. #26041587C2semidirect
4. #26041584C2semidirect
5. #26041579C2semidirect
6. #26041577C2semidirect
7. #26041536C2semidirect
9. #26041524C2semidirect
10. #26041522C2semidirect
11. #26041499C2semidirect
12. #26041498C2semidirect
13. #26041492C2semidirect
14. #26041301C2semidirect
15. #463×C181C2semidirect
172. C181#3256semidirect
187. #463D181semidirect

Maximal subgroups

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

subgroupindex
#260418112
#260418082
#260415872
#260415842
#260415792
#260415772
#260415362
#260415292
#260415242
#260415222
#260414992
#260414982
#260414922
#260413012
#463×C1812
#3256181