Finite Group Databasebeta

← #37543988

Subgroups — #37543988

Order 23168.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041903C211yesmaximal, characteristic, complemented
2#26041758C211yesmaximal, characteristic, complemented
3#26041616C211yesmaximal, characteristic, complemented
4#26041594C211yesmaximal, characteristic, complemented
5#26041571C211yesmaximal, characteristic, complemented
6#26041502C211yesmaximal, characteristic, complemented
7#26041494C211yesmaximal, characteristic, complemented
8#26041442C211yesmaximal, characteristic, complemented
9#26041425C211yesmaximal, characteristic
10#26041378C211yesmaximal, characteristic, complemented
11#26041376C211yesmaximal, characteristic, complemented
12#26041373C211yesmaximal, characteristic, complemented
13#26041359C211yesmaximal, characteristic, complemented
14#26041339C211yesmaximal, characteristic, complemented
15#474×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21#19153811—21no—
22#19153805—21no—
23#19153804C2211yescharacteristic
24#19153801—21no—
25#19153796C2211yescharacteristic
26#19153792—21no—
27#19153791C2211yescharacteristic
28C4×Dic362C2211yescharacteristic
29#19153781C2211yescharacteristic
30#19153781C2211yescharacteristic
31D4×Dic181C2211yescharacteristic
32#19153778C2211yescharacteristic
33C4×C22⋊D181—21no—
34#19153776—21no—
35#19153773C2211yescharacteristic
36#19153772—21no—
37C2×#15668428—21no—
38C4⋊C4×D181C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—22no—
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C22×Dic181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71Dic724—22no—
72#15668438—22no—
73#15668437—22no—
74#15668434—22no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C4⋊Dic181—21no—
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92#15668426D411yescharacteristic
93C4×Dic181—21no—
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#4112yes—
114D724—21no—
115D724—21no—
116D724—81no—
117C22⋊D181—24no—
118C2×Dic181—24no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—81no—
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—81no—
129C4×D181—81no—
130#13089678—21no—
131#13089678—21no—
132C23×C181—21no—
133Q8×C181—81no—
134D4×C181—21no—
135D4×C181#4112yes—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—81no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C22×C181—22no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181C22×D411yescharacteristic
149C2×D181—21no—
150C2×D181—21no—
151C2×D181—21no—
152C2×D181—41no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—21no—
156C4×C181—21no—
157C4×C181—41no—
158C4×C181—41no—
159C4×C181—41no—
160C4×C181C2×#4111yescharacteristic
161C4×C181C2×#4111yescharacteristic
162Dic181—21no—
163Dic181—22no—
164Dic181—21no—
165Dic181—21no—
166Dic181—41no—
167Dic181—41no—
168C2×C181—42no—
169C2×C181#52511yescharacteristic
170C2×C181#57611yescharacteristic
171C2×C181#57811yescharacteristic
172D181—41no—
173D181—81no—
174C181#312411yescharacteristic, complemented, Sylow
175#3124—1811nomaximal, Sylow
176#542—1811no—
177#520—1811no—
178#484—1811no—
179#480—1811no—
180#477—1811no—
181#474D18111yescharacteristic, complemented
182#464—1811no—
183#463—1811no—
184#452—1811no—
185#449—1811no—
186#440—1811no—
187#440—1811no—
188C4×Q16—1811no—
189C4×D8—1811no—
190#433—1811no—
191C2×#41—1811no—
192C2×Q16—1811no—
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×D8—1811no—
196C4⋊Q8C2×D18111yescharacteristic
197#126—3621no—
198#124—3621no—
199#124—1811no—
200#123—3621no—
201C22⋊Q8—3621no—
202C22⋊Q8—1811no—
203#121—1811no—
204C4×Q8—1811no—
205C4×Q8—1811no—
206C4×Q8—1811no—
207C4×D4—3621no—
208C4×D4—3621no—
209C4×D4—1811no—
210C4×D4—1811no—
211C4×D4C2×D18111yescharacteristic
212#117—3621no—
213#117—1811no—
214C2×C4⋊C4—3621no—
215C2×C4⋊C4—1811no—
216#107—1811no—
217#107—1811no—
218#107C2×D18111yescharacteristic
219#107C2×D18111yescharacteristic
220C4⋊C8—1811no—
221C4⋊C8C2×D18111yescharacteristic
222#103—1811no—
223#103—1811no—
224#103—1811no—
225#103—1811no—
226#102—1811no—
227#102—1811no—
228#102C2×D18111yescharacteristic
229#102C2×D18111yescharacteristic
230C22⋊C8—1811no—
231C22⋊C8—1811no—
232#97—1811no—
233C4×C8—1811no—
234#41—3622no—
235#41—3622no—
236C2×Q8—21no—
237C2×Q8—1811no—
238C2×Q8—1811no—
239C2×D4—3621no—
240C2×D4—3621no—
241C2×D4—1811no—
242C2×D4C22×D18111yescharacteristic
243C22×C4—21no—
244C22×C4—3621no—
245C22×C4—3621no—
246C22×C4—3621no—
247C22×C4—3621no—
248C22×C4—1811no—
249Q16—3622no—
250SD16—3622no—
251SD16—3622no—
252D8—3622no—
253C2×C8—1811no—
254C2×C8—1811no—
255C2×C8C22×D18111yescharacteristic
256C2×C8C22×D18111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4C22×D18111yescharacteristic
267C4⋊C4C22×D18111yescharacteristic
268C4⋊C4C22×D18111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4—1811no—
277C22⋊C4—1811no—
278C42—3621no—
279C42—3621no—
280C42—3621no—
281C42—1811no—
282C42C22×D18111yescharacteristic
283C23—21no—
284C23—3621no—
285C23—1811no—
286Q8—81no—
287Q8—3621no—
288Q8—3621no—
289Q8—3621no—
290Q8—1812no—
291D4—21no—
292D4—3624no—
293D4—3621no—
294D4—3621no—
295D4—14481no—
296D4#1566845012yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—3624no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—3621no—
306C2×C4—3621no—
307C2×C4—14481no—
308C2×C4—14481no—
309C2×C4—14481no—
310C2×C4—1811no—
311C2×C4—1811no—
312C2×C4—1811no—
313C2×C4D4×D18111yescharacteristic
314C2×C4D4×D18111yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3621no—
319C8—3621no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—3621no—
324C22—3621no—
325C22—3621no—
326C22—7241no—
327C22—7241no—
328C22—7241no—
329C22C2×D4×D18111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3621no—
336C4—3622no—
337C4—3621no—
338C4—3621no—
339C4—7241no—
340C4—7241no—
341C4#41×D18111yescharacteristic
342C4C2×#1566845011yescharacteristic
343C2—42no—
344C2—14481no—
345C2—7241no—
346C2#2604179211yescharacteristic
347C2#2604208011yescharacteristic
348C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#474×C181C2
socleC22×C181C22×D4
prime radical#26041425C2
hypercenter#474D181
hypocenterC181#3124
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. #26041758C2semidirect
3. #26041616C2semidirect
4. #26041594C2semidirect
5. #26041571C2semidirect
6. #26041502C2semidirect
7. #26041494C2semidirect
8. #26041442C2semidirect
10. #26041378C2semidirect
11. #26041376C2semidirect
12. #26041373C2semidirect
13. #26041359C2semidirect
14. #26041339C2semidirect
15. #474×C181C2semidirect
174. C181#3124semidirect
181. #474D181semidirect

Maximal subgroups

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

subgroupindex
#260419032
#260417582
#260416162
#260415942
#260415712
#260415022
#260414942
#260414422
#260414252
#260413782
#260413762
#260413732
#260413592
#260413392
#474×C1812
#3124181