Finite Group Databasebeta

← #37545181

Subgroups — #37545181

Order 23168.

346 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#26041903C211yesmaximal, characteristic, complemented
2#26041894C211yesmaximal, characteristic, complemented
3#26041573C211yesmaximal, characteristic, complemented
4#26041571C211yesmaximal, characteristic, complemented
5#26041558C211yesmaximal, characteristic, complemented
6#26041526C211yesmaximal, characteristic, complemented
7#26041524C211yesmaximal, characteristic, complemented
8#26041521C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic
10#26041502C211yesmaximal, characteristic, complemented
11#26041500C211yesmaximal, characteristic, complemented
12#26041494C211yesmaximal, characteristic, complemented
13#26041493C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#474×C181C211yesmaximal, characteristic, complemented
16C2×Dic724C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153815C2211yescharacteristic
23#19153811—21no—
24#19153809—21no—
25#19153805—21no—
26#19153804C2211yescharacteristic
27#19153803C2211yescharacteristic
28#19153802—21no—
29#19153801—21no—
30#19153799—21no—
31#19153796C2211yescharacteristic
32#19153796C2211yescharacteristic
33#19153795—21no—
34#19153792—21no—
35#19153791C2211yescharacteristic
36#19153787C2211yescharacteristic
37C4×Dic362C2211yescharacteristic
38#19153781C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153773C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153749C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153739C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153736C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67Dic724—41no—
68#15668438—41no—
69#15668437—41no—
70#15668434—41no—
71#15668432—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C8×D181—41no—
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181—21no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110Dic362—21no—
111Dic362—21no—
112Dic362—21no—
113Dic362—21no—
114Dic362—81no—
115D724—21no—
116D724—21no—
117D724—81no—
118C22⋊D181—81no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—21no—
126C4×D181—21no—
127C4×D181—81no—
128#13089678—21no—
129#13089678—21no—
130C23×C181—21no—
131Q8×C181—81no—
132D4×C181—21no—
133D4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—81no—
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×C181C22×D411yescharacteristic
147C2×D181—21no—
148C2×D181—21no—
149C2×D181—21no—
150C2×D181—41no—
151C2×D181—41no—
152C2×D181—41no—
153C4×C181—21no—
154C4×C181—21no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181—41no—
158C4×C181H(5,𝔽2)11yescharacteristic
159C4×C1812−1+411yescharacteristic
160Dic181—21no—
161Dic181—21no—
162Dic181—21no—
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—81no—
167C2×C181#53711yescharacteristic
168C2×C181#57611yescharacteristic
169C2×C181#57811yescharacteristic
170D181—41no—
171D181—81no—
172C181#326211yescharacteristic, complemented, Sylow
173#3262—1811nomaximal, Sylow
174#542—1811no—
175#542—1811no—
176#477—1811no—
177#477—1811no—
178#474—1811no—
179#474D18111yescharacteristic, complemented
180#468—1811no—
181#468—1811no—
182#467—1811no—
183#466—1811no—
184#464—1811no—
185#464—1811no—
186#463—1811no—
187#463—1811no—
188#424—1811no—
189C2×Q16—1811no—
190C2×SD16—1811no—
191C2×SD16—1811no—
192C2×D8—1811no—
193C2×M16—1811no—
194C22×C8—1811no—
195C4⋊Q8—1811no—
196C4⋊Q8C2×D18111yescharacteristic
197#126—3621no—
198#126—3621no—
199#124—3621no—
200#124—3621no—
201#124—1811no—
202#124—1811no—
203#123—3621no—
204#123—3621no—
205C22⋊Q8—3621no—
206C22⋊Q8—3621no—
207C22⋊Q8—1811no—
208C22⋊Q8—1811no—
209#121—1811no—
210#121—1811no—
211C4×Q8—1811no—
212C4×Q8—1811no—
213C4×D4—1811no—
214C4×D4C2×D18111yescharacteristic
215#117—1811no—
216#107—1811no—
217#107—1811no—
218#107C2×D18111yescharacteristic
219#107C2×D18111yescharacteristic
220C4⋊C8—1811no—
221C4⋊C8—1811no—
222C4⋊C8—1811no—
223C4⋊C8C2×D18111yescharacteristic
224#103—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#102—1811no—
229#102—1811no—
230#102C2×D18111yescharacteristic
231#102C2×D18111yescharacteristic
232C2×Q8—21no—
233C2×Q8—3621no—
234C2×Q8—1811no—
235C2×Q8—1811no—
236C2×D4—3621no—
237C2×D4—3621no—
238C2×D4—1811no—
239C2×D4C22×D18111yescharacteristic
240C22×C4—21no—
241C22×C4—3621no—
242C22×C4—1811no—
243Q16—7241no—
244SD16—7241no—
245SD16—7241no—
246D8—7241no—
247M16—7241no—
248C2×C8—1811no—
249C2×C8—1811no—
250C2×C8—7241no—
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—21no—
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
263C4⋊C4C22×D18111yescharacteristic
264C4⋊C4C22×D18111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—1811no—
276C22⋊C4—1811no—
277C42—3621no—
278C42—3621no—
279C42—1811no—
280C42C22×D18111yescharacteristic
281C23—21no—
282C23—3621no—
283C23—1811no—
284Q8—81no—
285Q8—3621no—
286Q8—3621no—
287Q8—3621no—
288Q8—3621no—
289Q8—14481no—
290D4—21no—
291D4—21no—
292D4—3621no—
293D4—3621no—
294D4—14481no—
295D4—14481no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—3621no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—14481no—
306C2×C4—1811no—
307C2×C4—1811no—
308C2×C4—1811no—
309C2×C4D4×D18111yescharacteristic
310C2×C4D4×D18111yescharacteristic
311C2×C4C23×D18111yescharacteristic
312C8—21no—
313C8—21no—
314C8—3621no—
315C8—3621no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—3621no—
320C22—3621no—
321C22—3621no—
322C22—7241no—
323C22—7241no—
324C22—7241no—
325C22C2×D4×D18111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3621no—
332C4—3621no—
333C4—3621no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4#1915386211yescharacteristic
338C4#1915386411yescharacteristic
339C2—81no—
340C2—14481no—
341C2—7241no—
342C2#2604185911yescharacteristic
343C2#2604208011yescharacteristic
344C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#474×C181C2
socleC22×C181C22×D4
prime radical#26041514C2
hypercenter#474D181
hypocenterC181#3262
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #26041903C2semidirect
2. #26041894C2semidirect
3. #26041573C2semidirect
4. #26041571C2semidirect
5. #26041558C2semidirect
6. #26041526C2semidirect
7. #26041524C2semidirect
8. #26041521C2semidirect
10. #26041502C2semidirect
11. #26041500C2semidirect
12. #26041494C2semidirect
13. #26041493C2semidirect
14. #26041304C2semidirect
15. #474×C181C2semidirect
172. C181#3262semidirect
179. #474D181semidirect

Maximal subgroups

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

subgroupindex
#260419032
#260418942
#260415732
#260415712
#260415582
#260415262
#260415242
#260415212
#260415142
#260415022
#260415002
#260414942
#260414932
#260413042
#474×C1812
#3262181