Finite Group Databasebeta

← #37542377

Subgroups — #37542377

Order 23168.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#117×D181C211yesmaximal, characteristic
2#26041340C211yesmaximal, characteristic, complemented
3#26041337C211yesmaximal, characteristic, complemented
4#26041337C211yesmaximal, characteristic, complemented
5#26041335C211yesmaximal, characteristic, complemented
6#26041334C211yesmaximal, characteristic, complemented
7#26041331C211yesmaximal, characteristic, complemented
8#26041330C211yesmaximal, characteristic, complemented
9#26041304C211yesmaximal, characteristic, complemented
10#26041304C211yesmaximal, characteristic, complemented
11#26041241C211yesmaximal, characteristic
12C22⋊C8×D181C211yesmaximal, characteristic
13#26041236C211yesmaximal, characteristic, complemented
14#26041233C211yesmaximal, characteristic, complemented
15#433×C181C211yesmaximal, characteristic, complemented
16C22×C4×D181C2211yescharacteristic
17C2×#15668432C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153775C2211yescharacteristic
22#19153774C411yescharacteristic
23#19153774C411yescharacteristic
24#19153773C2211yescharacteristic
25#19153773C2211yescharacteristic
26#19153772C411yescharacteristic
27#19153772C411yescharacteristic
28C4⋊C4×D181C411yescharacteristic
29C4⋊C4×D181C411yescharacteristic
30C22⋊C4×D181C411yescharacteristic
31C22⋊C4×D181C411yescharacteristic
32C42×D181C2211yescharacteristic
33C42×D181C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic, complemented
35C4⋊#13089678C2211yescharacteristic, complemented
36#19153745C2211yescharacteristic, complemented
37#19153745C2211yescharacteristic, complemented
38#19153745C2211yescharacteristic, complemented
39#19153745C2211yescharacteristic, complemented
40C22⋊#13089678C2211yescharacteristic
41C22⋊#13089678C2211yescharacteristic
42#19153728C2211yescharacteristic
43#19153728C2211yescharacteristic
44#19153728C2211yescharacteristic
45#19153728C2211yescharacteristic
46#19153727C2211yescharacteristic, complemented
47#19153726C2211yescharacteristic, complemented
48#19153726C2211yescharacteristic, complemented
49C4×#13089678C2211yescharacteristic, complemented
50C8×Dic181C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52#117×C181C2211yescharacteristic
53C4⋊C8×C181C2211yescharacteristic, complemented
54C4⋊C8×C181C2211yescharacteristic, complemented
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57#97×C181C2211yescharacteristic, complemented
58C4×C8×C181C2211yescharacteristic, complemented
59C23×D181C2×C411yescharacteristic
60C22×Dic181C2×C411yescharacteristic
61C2×C4×D181—22no—
62C2×C4×D181—22no—
63C2×C4×D181C2×C411yescharacteristic
64C2×C4×D181C2×C411yescharacteristic
65C2×C4×D181C2×C411yescharacteristic
66C2×C4×D181C2×C411yescharacteristic
67C2×C4×D181C2×C411yescharacteristic
68C2×C4×D181C2×C411yescharacteristic
69C2×C4×D181C2311yescharacteristic
70C2×C4×D181C2311yescharacteristic
71#15668432—22no—
72#15668432—22no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—22no—
78C8×D181—22no—
79C4⋊Dic181C2×C411yescharacteristic
80C4⋊Dic181C2×C411yescharacteristic
81#15668428C2×C411yescharacteristic
82#15668428C2×C411yescharacteristic
83#15668428C2×C411yescharacteristic
84#15668428C2×C411yescharacteristic
85C22⋊Dic181C2×C411yescharacteristic
86C22⋊Dic181C2×C411yescharacteristic
87#15668426C2×C411yescharacteristic
88#15668426C2×C411yescharacteristic
89#15668426C2×C411yescharacteristic
90#15668426C2×C411yescharacteristic
91C4×Dic181C2×C411yescharacteristic
92C4×Dic181C2×C411yescharacteristic
93C4×Dic181C2×C411yescharacteristic
94C4×Dic181C2×C411yescharacteristic
95C4×Dic181C2311yescharacteristic
96C4×Dic181C2311yescharacteristic
97C22×C4×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181C2×C411yescharacteristic
103C4⋊C4×C181C2×C411yescharacteristic
104C22⋊C4×C181C2×C411yescharacteristic
105C22⋊C4×C181C2×C411yescharacteristic
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—22no—
109C22×D181—22no—
110C22×D181—41no—
111C22×D181C22×C411yescharacteristic
112C22×D181C22×C411yescharacteristic
113C2×Dic181—22no—
114C2×Dic181C22×C411yescharacteristic
115C2×Dic181C22×C411yescharacteristic
116C2×Dic181C22×C411yescharacteristic
117C2×Dic181C22×C411yescharacteristic
118C2×Dic181C22×C411yescharacteristic
119C2×Dic181C22×C411yescharacteristic
120C4×D181—22no—
121C4×D181—22no—
122C4×D181—22no—
123C4×D181—21no—
124C4×D181—21no—
125C4×D181—22no—
126C4×D181—41no—
127C4×D181—41no—
128C4×D181#4112yes—
129C4×D181#4112yes—
130#13089678—21no—
131#13089678—21no—
132#13089678—21no—
133#13089678—21no—
134C23×C181C22×C411yescharacteristic
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181C22×C411yescharacteristic
138C2×C4×C181C22×C411yescharacteristic
139C2×C4×C181C22×C411yescharacteristic
140C2×C4×C181C22×C411yescharacteristic
141C2×C4×C181C22×C411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C8×C181—21no—
146C8×C181—21no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—21no—
150C22×C181C23×C411yescharacteristic
151C2×D181—21no—
152C2×D181—21no—
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—44no—
156C2×D181#11712yes—
157C2×D181#13112yes—
158C4×C181—21no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—21no—
162C4×C181—21no—
163C4×C181C2×#4111yescharacteristic
164C4×C181C2×#4111yescharacteristic
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—21no—
169Dic181—21no—
170Dic181#11712yes—
171C2×C181—41no—
172C2×C181C2×#11711yescharacteristic
173C2×C181C2×#13111yescharacteristic
174C2×C181#56811yescharacteristic
175D181—22no—
176D181—22no—
177C181#292411yescharacteristic, complemented, Sylow
178#2924—1811nomaximal, Sylow
179C2×#117—1811no—
180#433—1811no—
181#433—1811no—
182#433—1811no—
183#433D18111yescharacteristic, complemented
184#432—1811no—
185#432—1811no—
186#431—1811no—
187#431—1811no—
188#424—1811no—
189#424—1811no—
190#407—1811no—
191C2×C22⋊C8—1811no—
192#405—1811no—
193#405—1811no—
194C23×C4—1811no—
195C2×M16—1811no—
196C2×M16—1811no—
197C22×C8—1811no—
198C22×C8—1811no—
199#117—1811no—
200#117—1811no—
201#117—1811no—
202#117—1811no—
203#117—1811no—
204#117—1811no—
205#117—1811no—
206#117C2×D18111yescharacteristic
207C2×C4⋊C4—1811no—
208C2×C4⋊C4—1811no—
209C2×C22⋊C4—1811no—
210C2×C22⋊C4—1811no—
211C2×C42—1811no—
212C2×C42—1811no—
213C4⋊C8—1811no—
214C4⋊C8—1811no—
215C4⋊C8—1811no—
216C4⋊C8—1811no—
217C4⋊C8—1811no—
218C4⋊C8—1811no—
219C4⋊C8C2×D18111yescharacteristic, complemented
220C4⋊C8C2×D18111yescharacteristic, complemented
221C22⋊C8—1811no—
222C22⋊C8—1811no—
223C22⋊C8—1811no—
224C22⋊C8—1811no—
225C22⋊C8—1811no—
226C22⋊C8—1811no—
227C22⋊C8C2×D18111yescharacteristic
228C22⋊C8C2×D18111yescharacteristic
229#97—1811no—
230#97—1811no—
231#97—1811no—
232#97C2×D18111yescharacteristic, complemented
233C4×C8—1811no—
234C4×C8—1811no—
235C4×C8—1811no—
236C4×C8C2×D18111yescharacteristic, complemented
237C24—1811no—
238C22×C4—3622no—
239C22×C4—3622no—
240C22×C4—1811no—
241C22×C4—1811no—
242C22×C4—1811no—
243C22×C4—1811no—
244C22×C4—1811no—
245C22×C4—1811no—
246C22×C4—1811no—
247C22×C4—1811no—
248C22×C4—1811no—
249C22×C4C22×D18111yescharacteristic
250M16—3622no—
251M16—3622no—
252C2×C8—3622no—
253C2×C8—3622no—
254C2×C8—1811no—
255C2×C8—1811no—
256C2×C8—1811no—
257C2×C8—1811no—
258C2×C8C22×D18111yescharacteristic
259C2×C8C22×D18111yescharacteristic
260C2×C8C22×D18111yescharacteristic
261C2×C8C22×D18111yescharacteristic
262C4⋊C4—1811no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4—1811no—
268C4⋊C4C4×D18111yescharacteristic
269C4⋊C4C4×D18111yescharacteristic
270C22⋊C4—1811no—
271C22⋊C4—1811no—
272C22⋊C4—1811no—
273C22⋊C4—1811no—
274C22⋊C4—1811no—
275C22⋊C4—1811no—
276C22⋊C4C4×D18111yescharacteristic
277C22⋊C4C4×D18111yescharacteristic
278C42—1811no—
279C42—1811no—
280C42—1811no—
281C42—1811no—
282C42—1811no—
283C42—1811no—
284C42C22×D18111yescharacteristic
285C42C22×D18111yescharacteristic
286C23—3622no—
287C23—3622no—
288C23—1811no—
289C23—1811no—
290C23—7241no—
291C23C2×C4×D18111yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—3622no—
295C2×C4—3622no—
296C2×C4—3622no—
297C2×C4—3622no—
298C2×C4—3622no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—1811no—
304C2×C4—1811no—
305C2×C4—1811no—
306C2×C4—1811no—
307C2×C4—1812no—
308C2×C4—1812no—
309C2×C4—7241no—
310C2×C4—7241no—
311C2×C4C2×C4×D18111yescharacteristic
312C2×C4C2×C4×D18111yescharacteristic
313C2×C4C2×C4×D18111yescharacteristic
314C2×C4C2×C4×D18111yescharacteristic
315C2×C4C2×C4×D18111yescharacteristic
316C2×C4C23×D18111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C8—3621no—
322C8—3621no—
323C8—3621no—
324C8—3621no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—3621no—
329C22—3621no—
330C22—3621no—
331C22—3621no—
332C22—1812no—
333C22—1812no—
334C22—7244no—
335C22C22×C4×D18111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—3621no—
342C4—3621no—
343C4—3621no—
344C4—3621no—
345C4—3621no—
346C4—1812no—
347C4#41×D18111yescharacteristic
348C4#41×D18111yescharacteristic
349C2—41no—
350C2—3622no—
351C2—3622no—
352C2#117×D18111yescharacteristic
353C2#131×D18111yescharacteristic
354C2#2604204411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D181
commutator, socleC22×C181C23×C4
Fitting#433×C181C2
prime radicalC23×D181C2×C4
cosocleC2×C4×C181C24
hypercenter#433D181
hypocenterC181#2924
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #26041340C2semidirect
3. #26041337C2semidirect
4. #26041337C2semidirect
5. #26041335C2semidirect
6. #26041334C2semidirect
7. #26041331C2semidirect
8. #26041330C2semidirect
9. #26041304C2semidirect
10. #26041304C2semidirect
13. #26041236C2semidirect
14. #26041233C2semidirect
15. #433×C181C2semidirect
34. C4⋊#13089678C22semidirect
35. C4⋊#13089678C22semidirect
36. #19153745C22semidirect
37. #19153745C22semidirect
38. #19153745C22semidirect
39. #19153745C22semidirect
46. #19153727C22semidirect
47. #19153726C22semidirect
48. #19153726C22semidirect
49. C4×#13089678C22semidirect
50. C8×Dic181C22semidirect
51. C8×Dic181C22semidirect
53. C4⋊C8×C181C22semidirect
54. C4⋊C8×C181C22semidirect
57. #97×C181C22semidirect
58. C4×C8×C181C22semidirect
177. C181#2924semidirect
183. #433D181semidirect
219. C4⋊C8C2×D181semidirect
220. C4⋊C8C2×D181semidirect
232. #97C2×D181semidirect
236. C4×C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#117×D1812
#260413402
#260413372
#260413352
#260413342
#260413312
#260413302
#260413042
#260412412
C22⋊C8×D1812
#260412362
#260412332
#433×C1812
#2924181