Finite Group Databasebeta

← #37544008

Subgroups — #37544008

Order 23168.

382 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#26041882C211yesmaximal, characteristic
2#26041756C211yesmaximal, characteristic, complemented
3#26041603C211yesmaximal, characteristic, complemented
4#26041589C211yesmaximal, characteristic, complemented
5#26041585C211yesmaximal, characteristic, complemented
6#26041478C211yesmaximal, characteristic, complemented
7#26041478C211yesmaximal, characteristic, complemented
8#26041420C211yesmaximal, characteristic, complemented
9#26041417C211yesmaximal, characteristic, complemented
10#26041378C211yesmaximal, characteristic, complemented
11#26041376C211yesmaximal, characteristic, complemented
12#26041370C211yesmaximal, characteristic, complemented
13#26041366C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C22×Dic362C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21#19153812C2211yescharacteristic
22#19153807C2211yescharacteristic
23#19153800—21no—
24#19153798—21no—
25#19153790C2211yescharacteristic
26#19153788—21no—
27#19153787—21no—
28C4×Dic362—21no—
29C4×Dic362—21no—
30#19153781C2211yescharacteristic
31#19153781C2211yescharacteristic
32#19153781C2211yescharacteristic
33#19153781C2211yescharacteristic
34D4×Dic181C2211yescharacteristic
35#19153778C2211yescharacteristic
36#19153775C2211yescharacteristic
37#19153772—21no—
38#19153772—21no—
39#19153749C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—22no—
60C2×Dic362—22no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71#15668438—22no—
72#15668438—22no—
73#15668437—22no—
74#15668437—22no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C4⋊Dic181—21no—
78C4⋊Dic181D411yescharacteristic
79C4⋊Dic181D411yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181D411yescharacteristic
88C22⋊Dic181D411yescharacteristic
89#15668426—21no—
90#15668426—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C4×Dic181C2311yescharacteristic
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181—21no—
108C22×D181—21no—
109Dic362—24no—
110Dic362—21no—
111Dic362—21no—
112Dic362#4112yes—
113Dic362#4112yes—
114D724—21no—
115D724—21no—
116C22⋊D181—81no—
117C22⋊D181—81no—
118C22⋊D181—81no—
119C2×Dic181—24no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—81no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—81no—
129#13089678—21no—
130#13089678—21no—
131C23×C181—21no—
132C23×C181C2×D411yescharacteristic
133D4×C181—21no—
134D4×C181—21no—
135D4×C181—81no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C22×C181—21no—
146C22×C181—21no—
147C22×C181—21no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181C22×D411yescharacteristic
152C2×D181—41no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—21no—
156C4×C181—41no—
157C4×C181—41no—
158C4×C181—41no—
159C4×C181C2×#4111yescharacteristic
160C4×C181C2×#4111yescharacteristic
161Dic181—22no—
162Dic181—22no—
163Dic181—21no—
164Dic181—21no—
165Dic181—21no—
166Dic181—21no—
167Dic181—41no—
168C2×C181—41no—
169C2×C181—81no—
170C2×C181#52511yescharacteristic
171C2×C181#57711yescharacteristic
172C2×C181#57711yescharacteristic
173D181—81no—
174C181#312611yescharacteristic, complemented, Sylow
175#3126—1811nomaximal, Sylow
176#540—1811no—
177#519—1811no—
178#482—1811no—
179#482D18111yescharacteristic, complemented
180#479—1811no—
181#479—1811no—
182#460—1811no—
183#460—1811no—
184#448—1811no—
185#448—1811no—
186#440—1811no—
187#440—1811no—
188C4×SD16—1811no—
189C4×SD16—1811no—
190#433—1811no—
191C22×Q8—1811no—
192C2×SD16—1811no—
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×SD16—1811no—
196#127—1811no—
197#125—1811no—
198#123—3621no—
199#123—3621no—
200#121—3621no—
201#121—3621no—
202#121—1811no—
203#121C2×D18111yescharacteristic
204C4×Q8—3621no—
205C4×Q8—3621no—
206C4×Q8—1811no—
207C4×Q8—1811no—
208C4×Q8—1811no—
209C4×Q8—1811no—
210C4×D4—1811no—
211C4×D4—1811no—
212#117—3621no—
213#117—3621no—
214#117—1811no—
215#117C2×D18111yescharacteristic
216#107—1811no—
217#107C2×D18111yescharacteristic
218#106—1811no—
219#106C2×D18111yescharacteristic
220C4⋊C8—1811no—
221C4⋊C8—1811no—
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⋊C8C2×D18111yescharacteristic
232#97—1811no—
233C4×C8—1811no—
234C2×Q8—3622no—
235C2×Q8—3622no—
236C2×Q8—3621no—
237C2×Q8—1811no—
238C2×Q8—1811no—
239C2×D4—21no—
240C2×D4—3621no—
241C2×D4—3621no—
242C2×D4—3621no—
243C2×D4—1811no—
244C2×D4C22×D18111yescharacteristic
245C22×C4—3621no—
246C22×C4—3621no—
247C22×C4—3621no—
248C22×C4C22×D18111yescharacteristic
249SD16—3622no—
250SD16—3622no—
251SD16—3622no—
252SD16—3622no—
253C2×C8—1811no—
254C2×C8—1811no—
255C2×C8C22×D18111yescharacteristic
256C2×C8C22×D18111yescharacteristic
257C4⋊C4—3621no—
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—21no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—1811no—
275C22⋊C4—1811no—
276C42—21no—
277C42—3621no—
278C42—3621no—
279C42—3621no—
280C42—3621no—
281C42—1811no—
282C42—1811no—
283C23—21no—
284C23—3621no—
285C23D4×D18111yescharacteristic
286Q8—3624no—
287Q8—3621no—
288Q8—3621no—
289Q8—1812no—
290Q8—1812no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—3621no—
295D4—3621no—
296D4—14481no—
297D4—14481no—
298D4—14481no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—3624no—
305C2×C4—3621no—
306C2×C4—3621no—
307C2×C4—3621no—
308C2×C4—14481no—
309C2×C4—14481no—
310C2×C4—1811no—
311C2×C4—1811no—
312C2×C4—1811no—
313C2×C4—1811no—
314C2×C4D4×D18111yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3621no—
319C8—3621no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—7241no—
327C22—7241no—
328C22—7241no—
329C22C2×D4×D18111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—3622no—
335C4—3622no—
336C4—3621no—
337C4—3621no—
338C4—3621no—
339C4—3621no—
340C4—7241no—
341C4#41×D18111yescharacteristic
342C4#41×D18111yescharacteristic
343C2—41no—
344C2—81no—
345C2—14481no—
346C2#2604178711yescharacteristic
347C2#2604208611yescharacteristic
348C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
prime radical#26041882C2
hypercenter#482D181
hypocenterC181#3126
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #26041756C2semidirect
3. #26041603C2semidirect
4. #26041589C2semidirect
5. #26041585C2semidirect
6. #26041478C2semidirect
7. #26041478C2semidirect
8. #26041420C2semidirect
9. #26041417C2semidirect
10. #26041378C2semidirect
11. #26041376C2semidirect
12. #26041370C2semidirect
13. #26041366C2semidirect
14. #26041337C2semidirect
15. #482×C181C2semidirect
174. C181#3126semidirect
179. #482D181semidirect

Maximal subgroups

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

subgroupindex
#260418822
#260417562
#260416032
#260415892
#260415852
#260414782
#260414202
#260414172
#260413782
#260413762
#260413702
#260413662
#260413372
#482×C1812
#3126181