Finite Group Databasebeta

← #37545642

Subgroups — #37545642

Order 23168.

398 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#26041993C211yesmaximal, characteristic, complemented
2#26041928C211yesmaximal, characteristic, complemented
3#26041628C211yesmaximal, characteristic, complemented
4#26041621C211yesmaximal, characteristic, complemented
5#26041619C211yesmaximal, characteristic, complemented
6#26041567C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041505C211yesmaximal, characteristic, complemented
9#26041482C211yesmaximal, characteristic, complemented
10#26041421C211yesmaximal, characteristic, complemented
11D8×Dic181C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13#26041275C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C22×#13089678C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153814C2211yescharacteristic
22#19153803—21no—
23#19153802—21no—
24#19153799—21no—
25#19153797—21no—
26#19153795C2211yescharacteristic
27#19153792C2211yescharacteristic
28#19153788—21no—
29#19153788—21no—
30#19153787C2211yescharacteristic
31D4×Dic181C2211yescharacteristic
32D4×Dic181C2211yescharacteristic
33C4×C22⋊D181C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153774C2211yescharacteristic
36#19153772—21no—
37C2×#15668428—21no—
38#19153750C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181D411yescharacteristic
66C22×Dic181—21no—
67C22×Dic181—21no—
68C22×Dic181—21no—
69C2×C4×D181C2311yescharacteristic
70#15668437—41no—
71C2×#13089678—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C8×D181—41no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96#41×C181—22no—
97#41×C181—41no—
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105SD16×C181—41no—
106D8×C181—22no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—81no—
115C22⋊D181—22no—
116C22⋊D181—42no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—42no—
123C2×Dic181—42no—
124C2×Dic181—42no—
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—21no—
129C4×D181—21no—
130#13089678—21no—
131#13089678—21no—
132C23×C181—21no—
133C23×C181—21no—
134C23×C181C2×D411yescharacteristic
135Q8×C181—21no—
136Q8×C181—21no—
137D4×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—42no—
141D4×C181—81no—
142D4×C181#4112yes—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—42no—
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C22×C181—21no—
153C22×C181—22no—
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C4×C181—21no—
166C4×C181—41no—
167C4×C181—41no—
168C4×C181C2×#4111yescharacteristic
169C4×C181H(5,𝔽2)11yescharacteristic
170Dic181—21no—
171Dic181—21no—
172Dic181—41no—
173Dic181—41no—
174Dic181—41no—
175Dic181—41no—
176Dic181#13512yes—
177C2×C181—41no—
178C2×C181—42no—
179C2×C181—81no—
180C2×C181#54611yescharacteristic
181C2×C181C2×#13511yescharacteristic
182C2×C181#57711yescharacteristic
183D181—41no—
184C181#330311yescharacteristic, complemented, Sylow
185#3303—1811nomaximal, Sylow
186#555—1811no—
187#547—1811no—
188#487—1811no—
189#485—1811no—
190#485—1811no—
191#476—1811no—
192#465—1811no—
193#465—1811no—
194#461—1811no—
195#449—1811no—
196#449D18111yescharacteristic, complemented
197C4×D8—1811no—
198C8×D4—1811no—
199#416—1811no—
200#416—1811no—
201C2×#41—1811no—
202C2×#41C2×D18111yescharacteristic
203C2×SD16—1811no—
204C2×SD16C2×D18111yescharacteristic
205C2×D8C2×D18111yescharacteristic
206C22×C8—1811no—
207C22×C8—1811no—
208C4⋊Q8—1811no—
209C4⋊Q8—1811no—
210#124—3621no—
211#124—3621no—
212#123—3621no—
213#123—3621no—
214C22⋊Q8—1811no—
215C22⋊Q8—1811no—
216#121—3621no—
217#121—3621no—
218#121—1811no—
219#121C2×D18111yescharacteristic
220C4×D4—1811no—
221C4×D4—1811no—
222C4×D4—1811no—
223#117—3621no—
224#117—1811no—
225#117—1811no—
226C2×C4⋊C4—3621no—
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#103—1811no—
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241C22⋊C8—1811no—
242C22⋊C8C2×D18111yescharacteristic
243C4×C8—1811no—
244#41—22no—
245#41—41no—
246#41—3622no—
247#41—7241no—
248C2×Q8—3621no—
249C2×Q8—1811no—
250C2×Q8C22×D18111yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4C22×D18111yescharacteristic
257C2×D4C22×D18111yescharacteristic
258C22×C4—21no—
259C22×C4—3621no—
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4C22×D18111yescharacteristic
264SD16—41no—
265SD16—7241no—
266D8—22no—
267C2×C8—1811no—
268C2×C8—1811no—
269C2×C8—7241no—
270C2×C8—7241no—
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22×D18111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—1811no—
292C22⋊C4—1811no—
293C42—3621no—
294C42—3621no—
295C42—1811no—
296C23—21no—
297C23—21no—
298C23—1811no—
299C23D4×D18111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—3621no—
303Q8—3621no—
304Q8—14481no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3622no—
311D4—14481no—
312D4—7242no—
313D4#1566844812yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
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—1811no—
328C2×C4—7242no—
329C2×C4—7242no—
330C2×C4—7242no—
331C2×C4D4×D18111yescharacteristic
332C2×C4C23×D18111yescharacteristic
333C8—21no—
334C8—21no—
335C8—3621no—
336C8—3621no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3621no—
347C22—3621no—
348C22—3621no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—3621no—
354C4—3621no—
355C4—1812no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4—7241no—
360C4C2×#1566844811yescharacteristic
361C4#1915386111yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—7241no—
366C2#2604191611yescharacteristic
367C2#135×D18111yescharacteristic
368C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3303
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041993C2semidirect
2. #26041928C2semidirect
3. #26041628C2semidirect
4. #26041621C2semidirect
5. #26041619C2semidirect
6. #26041567C2semidirect
7. #26041506C2semidirect
8. #26041505C2semidirect
9. #26041482C2semidirect
10. #26041421C2semidirect
11. D8×Dic181C2semidirect
12. #26041342C2semidirect
13. #26041275C2semidirect
14. #26041272C2semidirect
15. #449×C181C2semidirect
184. C181#3303semidirect
196. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260419932
#260419282
#260416282
#260416212
#260416192
#260415672
#260415062
#260415052
#260414822
#260414212
D8×Dic1812
#260413422
#260412752
#260412722
#449×C1812
#3303181