Finite Group Databasebeta

← #37545846

Subgroups — #37545846

Order 23168.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041967C211yesmaximal, characteristic, complemented
2#26041949C211yesmaximal, characteristic
3#26041602C211yesmaximal, characteristic, complemented
4#26041596C211yesmaximal, characteristic, complemented
5#26041583C211yesmaximal, characteristic, complemented
6#26041524C211yesmaximal, characteristic, complemented
7#26041507C211yesmaximal, characteristic, complemented
8#26041476C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041442C211yesmaximal, characteristic, complemented
11#26041387C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041277C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#490×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic
23#19153812—21no—
24#19153811—21no—
25#19153807—21no—
26#19153801—21no—
27#19153796C2211yescharacteristic
28#19153796C2211yescharacteristic
29#19153788—21no—
30#19153788—21no—
31#19153787C2211yescharacteristic
32#19153787C2211yescharacteristic
33C4×Dic362C2211yescharacteristic
34C4×Dic362C2211yescharacteristic
35C4×D724C2211yescharacteristic
36D4×Dic181—21no—
37#19153774—21no—
38#19153774C2211yescharacteristic
39C4⋊C4×D181C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52#127×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#102×C181C2211yescharacteristic
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—22no—
61#15668448—41no—
62#15668448—41no—
63C2×Dic362C2311yescharacteristic
64C2×Dic362C2311yescharacteristic
65C2×D724D411yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C22×Dic181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74C2×C4×D181C2311yescharacteristic
75Dic724—22no—
76#15668437—41no—
77#15668437—41no—
78#15668432—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C8×D181—41no—
82C4⋊Dic181—21no—
83C4⋊Dic181—21no—
84C4⋊Dic181D411yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C42×C181C2311yescharacteristic
111C22×D181C2×D411yescharacteristic
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362#4112yes—
117D724—41no—
118C22⋊D181—42no—
119C22⋊D181—42no—
120C22⋊D181—81no—
121C22⋊D181—81no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—42no—
127C2×Dic181—42no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138C23×C181—21no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—42no—
144D4×C181—81no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181C2×#4111yescharacteristic
170C4×C181H(5,𝔽2)11yescharacteristic
171Dic181—21no—
172Dic181—21no—
173Dic181—22no—
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—81no—
178C2×C181—81no—
179C2×C181#54611yescharacteristic
180C2×C181#57511yescharacteristic
181C2×C181#57711yescharacteristic
182D181—41no—
183D181—41no—
184C181#331711yescharacteristic, complemented, Sylow
185#3317—1811nomaximal, Sylow
186#552—1811no—
187#550—1811no—
188#490D18111yescharacteristic, complemented
189#482—1811no—
190#481—1811no—
191#479—1811no—
192#468—1811no—
193#465—1811no—
194#460—1811no—
195#452—1811no—
196#452—1811no—
197#441—1811no—
198#435—1811no—
199#417—1811no—
200#416—1811no—
201C2×#41—1811no—
202C2×#41—1811no—
203C2×Q16—1811no—
204C2×SD16—1811no—
205C2×SD16—1811no—
206C2×M16—1811no—
207C22×C8—1811no—
208#127—3621no—
209#127C2×D18111yescharacteristic
210#126—3621no—
211#125—3621no—
212#125C2×D18111yescharacteristic
213#123—3621no—
214C22⋊Q8—1811no—
215C22⋊Q8—1811no—
216#121—3621no—
217#121—3621no—
218#121—1811no—
219#121—1811no—
220C4×Q8—1811no—
221C4×Q8—1811no—
222C4×D4—3621no—
223C4×D4—1811no—
224#117—3621no—
225#117—1811no—
226C2×C4⋊C4—1811no—
227#107—1811no—
228#106—1811no—
229#106—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#102—1811no—
236#102—1811no—
237#102C2×D18111yescharacteristic
238#102C2×D18111yescharacteristic
239#102C2×D18111yescharacteristic
240#102C2×D18111yescharacteristic
241C22⋊C8—1811no—
242C22⋊C8—1811no—
243#97C2×D18111yescharacteristic
244#41—3622no—
245#41—3622no—
246#41—7241no—
247#41—7241no—
248C2×Q8—1811no—
249C2×Q8—1811no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—1811no—
257C2×D4C22×D18111yescharacteristic
258C2×D4C22×D18111yescharacteristic
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4—1811no—
264Q16—3622no—
265SD16—7241no—
266SD16—7241no—
267M16—7241no—
268C2×C8—1811no—
269C2×C8—1811no—
270C2×C8—7241no—
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4—1811no—
283C4⋊C4C22×D18111yescharacteristic
284C4⋊C4C22×D18111yescharacteristic
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—1811no—
291C22⋊C4—1811no—
292C42—3621no—
293C42—3621no—
294C42—3621no—
295C42C22×D18111yescharacteristic
296C23—21no—
297C23—21no—
298C23—1811no—
299C23—1811no—
300Q8—3621no—
301Q8—3621no—
302Q8—3621no—
303Q8—1812no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—14481no—
311D4—14481no—
312D4—7241no—
313D4—7242no—
314D4—7242no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—3621no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—1811no—
326C2×C4—1811no—
327C2×C4—7242no—
328C2×C4—7242no—
329C2×C4—7242no—
330C2×C4D4×D18111yescharacteristic
331C2×C4D4×D18111yescharacteristic
332C2×C4C23×D18111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3621no—
336C8—3621no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3621no—
344C22—3621no—
345C22—3621no—
346C22—3621no—
347C22—3621no—
348C22—3621no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—3621no—
355C4—3621no—
356C4—3622no—
357C4—7241no—
358C4—7241no—
359C4—7241no—
360C4#41×D18111yescharacteristic
361C4#1915386211yescharacteristic
362C2—81no—
363C2—81no—
364C2—7241no—
365C2—7241no—
366C2#2604192211yescharacteristic
367C2#2604207511yescharacteristic
368C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
prime radical#26041949C2
hypercenter#490D181
hypocenterC181#3317
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #26041967C2semidirect
3. #26041602C2semidirect
4. #26041596C2semidirect
5. #26041583C2semidirect
6. #26041524C2semidirect
7. #26041507C2semidirect
8. #26041476C2semidirect
9. #26041442C2semidirect
10. #26041442C2semidirect
11. #26041387C2semidirect
12. #26041352C2semidirect
13. #26041277C2semidirect
14. #26041272C2semidirect
15. #490×C181C2semidirect
184. C181#3317semidirect
188. #490D181semidirect

Maximal subgroups

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

subgroupindex
#260419672
#260419492
#260416022
#260415962
#260415832
#260415242
#260415072
#260414762
#260414422
#260413872
#260413522
#260412772
#260412722
#490×C1812
#3317181