Finite Group Databasebeta

← #37545818

Subgroups — #37545818

Order 23168.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041964C211yesmaximal, characteristic, complemented
2#26041928C211yesmaximal, characteristic
3#26041646C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041614C211yesmaximal, characteristic, complemented
6#26041581C211yesmaximal, characteristic, complemented
7#26041537C211yesmaximal, characteristic, complemented
8#26041519C211yesmaximal, characteristic, complemented
9#26041488C211yesmaximal, characteristic, complemented
10#26041442C211yesmaximal, characteristic, complemented
11#26041441C211yesmaximal, characteristic, complemented
12#26041376C211yesmaximal, characteristic, complemented
13#26041348C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#417×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153814C2211yescharacteristic
22#19153811—21no—
23#19153807C2211yescharacteristic
24#19153806—21no—
25#19153799—21no—
26#19153799—21no—
27#19153797—21no—
28#19153796C2211yescharacteristic
29#19153795C2211yescharacteristic
30#19153795C2211yescharacteristic
31#19153792C2211yescharacteristic
32#19153788—21no—
33#19153781C2211yescharacteristic
34D4×Dic181C2211yescharacteristic
35C4×C22⋊D181C2211yescharacteristic
36#19153775—21no—
37#19153774C2211yescharacteristic
38C2×#15668428—21no—
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181D411yescharacteristic
65C22×Dic181—21no—
66C22×Dic181—21no—
67C2×C4×D181C2311yescharacteristic
68Dic724—41no—
69#15668439—41no—
70#15668437—22no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C8×D181—41no—
74C4⋊Dic181—21no—
75C4⋊Dic181—21no—
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97#41×C181—22no—
98#41×C181—41no—
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105M16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116C22⋊D181—41no—
117C22⋊D181—42no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—42no—
123C2×Dic181—42no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C4×D181—21no—
128C4×D181—21no—
129#13089678—21no—
130#13089678—21no—
131C23×C181—21no—
132C23×C181C2×D411yescharacteristic
133Q8×C181—21no—
134Q8×C181—21no—
135D4×C181—21no—
136D4×C181—42no—
137D4×C181#4112yes—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—42no—
144C2×C4×C181—42no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—21no—
150C22×C181—22no—
151C22×C181—21no—
152C22×C181—21no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181C2×#4111yescharacteristic
164C4×C181H(5,𝔽2)11yescharacteristic
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—41no—
173C2×C181—42no—
174C2×C181#54611yescharacteristic
175C2×C181#57511yescharacteristic
176C2×C181#57811yescharacteristic
177D181—41no—
178C181#331511yescharacteristic, complemented, Sylow
179#3315—1811nomaximal, Sylow
180#552—1811no—
181#547—1811no—
182#491—1811no—
183#485—1811no—
184#484—1811no—
185#478—1811no—
186#470—1811no—
187#467—1811no—
188#462—1811no—
189#452—1811no—
190#452—1811no—
191#440—1811no—
192#435—1811no—
193#417D18111yescharacteristic, complemented
194#416—1811no—
195C2×#41—1811no—
196C2×#41C2×D18111yescharacteristic
197C2×Q16—1811no—
198C2×Q16—1811no—
199C2×SD16—1811no—
200C2×M16C2×D18111yescharacteristic
201C22×C8—1811no—
202C4⋊Q8—1811no—
203#126—3621no—
204#125—3621no—
205#125—1811no—
206#123—3621no—
207#123—3621no—
208#123—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212C22⋊Q8—1811no—
213#121—3621no—
214C4×Q8—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217#117—3621no—
218#117—1811no—
219C2×C4⋊C4—3621no—
220C2×C4⋊C4C2×D18111yescharacteristic
221#107—1811no—
222#107—1811no—
223#106—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103C2×D18111yescharacteristic
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102C2×D18111yescharacteristic
234#102C2×D18111yescharacteristic
235C22⋊C8—1811no—
236C22⋊C8—1811no—
237#97—1811no—
238#41—22no—
239#41—41no—
240#41—3622no—
241#41—7241no—
242C2×Q8—1811no—
243C2×Q8—1811no—
244C2×Q8C22×D18111yescharacteristic
245C2×D4—21no—
246C2×D4—3621no—
247C2×D4—1811no—
248C2×D4C22×D18111yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4C22×D18111yescharacteristic
255Q16—7241no—
256Q16—7241no—
257SD16—3622no—
258M16—41no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—1811no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C4⋊C4C22×D18111yescharacteristic
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—1811no—
286C22⋊C4—1811no—
287C42—3621no—
288C42—3621no—
289C42—1811no—
290C23—21no—
291C23—1811no—
292C23D4×D18111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3621no—
296Q8—3621no—
297Q8—3621no—
298Q8—3621no—
299D4—21no—
300D4—42no—
301D4—7241no—
302D4—7242no—
303D4#1566844912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—1811no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—7242no—
321C2×C4—7242no—
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—21no—
329C22—22no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3621no—
343C4—3621no—
344C4—3621no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4C2×#1566844911yescharacteristic
350C4#1915386111yescharacteristic
351C2—41no—
352C2—42no—
353C2—7241no—
354C2#2604191911yescharacteristic
355C2#2604207511yescharacteristic
356C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#417×C181C2
socleC22×C181C22×D4
prime radical#26041928C2
hypercenter#417D181
hypocenterC181#3315
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #26041964C2semidirect
3. #26041646C2semidirect
4. #26041618C2semidirect
5. #26041614C2semidirect
6. #26041581C2semidirect
7. #26041537C2semidirect
8. #26041519C2semidirect
9. #26041488C2semidirect
10. #26041442C2semidirect
11. #26041441C2semidirect
12. #26041376C2semidirect
13. #26041348C2semidirect
14. #26041272C2semidirect
15. #417×C181C2semidirect
178. C181#3315semidirect
193. #417D181semidirect

Maximal subgroups

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

subgroupindex
#260419642
#260419282
#260416462
#260416182
#260416142
#260415812
#260415372
#260415192
#260414882
#260414422
#260414412
#260413762
#260413482
#260412722
#417×C1812
#3315181