Finite Group Databasebeta

← #37543935

Subgroups — #37543935

Order 23168.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041891C211yesmaximal, characteristic, complemented
2#26041614C211yesmaximal, characteristic, complemented
3#26041609C211yesmaximal, characteristic, complemented
4#26041586C211yesmaximal, characteristic, complemented
5#26041579C211yesmaximal, characteristic, complemented
6#26041489C211yesmaximal, characteristic, complemented
7#26041484C211yesmaximal, characteristic, complemented
8#26041441C211yesmaximal, characteristic
9#26041441C211yesmaximal, characteristic
10#26041384C211yesmaximal, characteristic, complemented
11#26041379C211yesmaximal, characteristic, complemented
12C4×#15668439C211yesmaximal, characteristic, complemented
13C4×#15668437C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#520×C181C211yesmaximal, characteristic
16C2×#15668439C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20#19153816C2211yescharacteristic
21#19153809—21no—
22#19153809—21no—
23#19153808C2211yescharacteristic
24#19153806—21no—
25#19153806—21no—
26#19153795C2211yescharacteristic
27#19153795C2211yescharacteristic
28C4×Dic362C2211yescharacteristic
29C4×Dic362C2211yescharacteristic
30#19153749C2211yescharacteristic
31#19153749C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153739C2211yescharacteristic
39#19153739C2211yescharacteristic
40#19153739C2211yescharacteristic
41#19153739C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48C2×#41×C181C2211yescharacteristic
49C4×Q8×C181C2211yescharacteristic
50C4×Q8×C181C2211yescharacteristic
51C4×D4×C181—21no—
52C4×D4×C181—21no—
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#117×C181—21no—
56#117×C181C2211yescharacteristic
57C2×C4⋊C4×C181—21no—
58C2×C4⋊C4×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×Dic362C2311yescharacteristic
61#15668439—22no—
62#15668439—22no—
63#15668437—22no—
64#15668437—22no—
65C2×#13089678C2311yescharacteristic
66C2×#13089678C2311yescharacteristic
67C2×#13089678C2311yescharacteristic
68C2×#13089678C2311yescharacteristic
69C4⋊Dic181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181C2311yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73#15668428—21no—
74#15668428—21no—
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79C22⋊Dic181—21no—
80C22⋊Dic181—21no—
81C4×Dic181—21no—
82C4×Dic181—21no—
83#41×C181—22no—
84#41×C181—22no—
85C2×Q8×C181C2311yescharacteristic
86C2×D4×C181—21no—
87C2×D4×C181C2311yescharacteristic
88C22×C4×C181—21no—
89C22×C4×C181—21no—
90C22×C4×C181—21no—
91C22×C4×C181—21no—
92C22×C4×C181C2311yescharacteristic
93C4⋊C4×C181—21no—
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181D411yescharacteristic
97C4⋊C4×C181D411yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C22⋊C4×C181D411yescharacteristic
103C22⋊C4×C181D411yescharacteristic
104C42×C181—21no—
105C42×C181—21no—
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108Dic362—21no—
109Dic362—21no—
110Dic362—21no—
111Dic362—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116#13089678—21no—
117#13089678—21no—
118#13089678—21no—
119#13089678—21no—
120C23×C181—21no—
121C23×C181C2×D411yescharacteristic
122Q8×C181—21no—
123Q8×C181#4112yes—
124D4×C181—24no—
125D4×C181—21no—
126D4×C181#4112yes—
127C2×C4×C181—24no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—81no—
134C2×C4×C181—81no—
135C2×C4×C181—81no—
136C2×C4×C181C2×D411yescharacteristic
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2411yescharacteristic
142C22×C181—21no—
143C22×C181—22no—
144C22×C181—21no—
145C22×C181—21no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181C22×D411yescharacteristic
149C4×C181—21no—
150C4×C181—22no—
151C4×C181—21no—
152C4×C181—21no—
153C4×C181—21no—
154C4×C181—21no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181C2×#4111yescharacteristic
158C4×C181C2×#4111yescharacteristic
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163C2×C181—41no—
164C2×C181—42no—
165C2×C181#52511yescharacteristic
166C2×C181#57711yescharacteristic
167C2×C181#57811yescharacteristic
168C181#312011yescharacteristic, complemented, Sylow
169#3120—1811nomaximal, Sylow
170#541—1811no—
171#520D18111yescharacteristic
172#484—1811no—
173#483—1811no—
174#479—1811no—
175#478—1811no—
176#462—1811no—
177#461—1811no—
178#452—1811no—
179#452—1811no—
180#441—1811no—
181#440—1811no—
182C4×Q16—1811no—
183C4×SD16—1811no—
184#433—1811no—
185C2×#41C2×D18111yescharacteristic
186C2×Q16—1811no—
187C2×Q16—1811no—
188C2×SD16—1811no—
189C2×SD16—1811no—
190C4⋊Q8—1811no—
191#126—3621no—
192#126—3621no—
193#125—3621no—
194#125—3621no—
195#125—1811no—
196C22⋊Q8—1811no—
197C22⋊Q8—1811no—
198C4×Q8—1811no—
199C4×Q8—1811no—
200C4×Q8C2×D18111yescharacteristic
201C4×Q8C2×D18111yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D18111yescharacteristic
205C4×D4C2×D18111yescharacteristic
206#117—21no—
207#117C2×D18111yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×D18111yescharacteristic
210#107—1811no—
211#107—1811no—
212#106—1811no—
213#106—1811no—
214C4⋊C8—1811no—
215C4⋊C8—1811no—
216#103—1811no—
217#103—1811no—
218#103—1811no—
219#103—1811no—
220#103—1811no—
221#103—1811no—
222#102—1811no—
223#102—1811no—
224C22⋊C8—1811no—
225C22⋊C8—1811no—
226#97—1811no—
227C4×C8—1811no—
228#41—22no—
229#41—22no—
230C2×Q8—1811no—
231C2×Q8—1811no—
232C2×Q8C22×D18111yescharacteristic
233C2×D4—21no—
234C2×D4C22×D18111yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22×D18111yescharacteristic
240Q16—3622no—
241Q16—3622no—
242SD16—3622no—
243SD16—3622no—
244C2×C8—1811no—
245C2×C8—1811no—
246C2×C8—1811no—
247C2×C8—1811no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4C22⋊D18111yescharacteristic
262C4⋊C4C22⋊D18111yescharacteristic
263C4⋊C4C22×D18111yescharacteristic
264C4⋊C4C22×D18111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4C22⋊D18111yescharacteristic
270C22⋊C4C22⋊D18111yescharacteristic
271C42—21no—
272C42—21no—
273C42—3621no—
274C42—3621no—
275C42C22×D18111yescharacteristic
276C42C22×D18111yescharacteristic
277C23—21no—
278C23C2×C22⋊D18111yescharacteristic
279Q8—21no—
280Q8—3621no—
281Q8—3621no—
282Q8—3621no—
283Q8—3621no—
284Q8#1566844912yes—
285D4—24no—
286D4—21no—
287D4#1566844912yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4C2×C22⋊D18111yescharacteristic
302C2×C4C2×C22⋊D18111yescharacteristic
303C2×C4C2×C22⋊D18111yescharacteristic
304C2×C4C2×C22⋊D18111yescharacteristic
305C2×C4C2×C22⋊D18111yescharacteristic
306C2×C4C23×D18111yescharacteristic
307C8—3621no—
308C8—3621no—
309C8—3621no—
310C8—3621no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D18111yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—7241no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4C2×#1566844911yescharacteristic
331C4C2×#1566844911yescharacteristic
332C2—41no—
333C2—42no—
334C2#2604179011yescharacteristic
335C2#2604209011yescharacteristic
336C2#2604209411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#520×C181C2
socleC22×C181C22×D4
prime radicalC2×#41×C181C22
hypercenter#520D181
hypocenterC181#3120
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #26041891C2semidirect
2. #26041614C2semidirect
3. #26041609C2semidirect
4. #26041586C2semidirect
5. #26041579C2semidirect
6. #26041489C2semidirect
7. #26041484C2semidirect
10. #26041384C2semidirect
11. #26041379C2semidirect
12. C4×#15668439C2semidirect
13. C4×#15668437C2semidirect
14. #26041340C2semidirect
168. C181#3120semidirect

Maximal subgroups

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

subgroupindex
#260418912
#260416142
#260416092
#260415862
#260415792
#260414892
#260414842
#260414412
#260413842
#260413792
C4×#156684392
C4×#156684372
#260413402
#520×C1812
#3120181