Finite Group Databasebeta

← #37546157

Subgroups — #37546157

Order 23168.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041964C211yesmaximal, characteristic, complemented
2#26041930C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041616C211yesmaximal, characteristic, complemented
5#26041609C211yesmaximal, characteristic, complemented
6#26041606C211yesmaximal, characteristic, complemented
7#26041592C211yesmaximal, characteristic, complemented
8#26041582C211yesmaximal, characteristic, complemented
9#26041573C211yesmaximal, characteristic, complemented
10#26041526C211yesmaximal, characteristic, complemented
11#26041508C211yesmaximal, characteristic, complemented
12#26041378C211yesmaximal, characteristic, complemented
13#26041350C211yesmaximal, characteristic, complemented
14#26041320C211yesmaximal, characteristic, complemented
15C2×#107×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668438C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153811—21no—
21#19153807C2211yescharacteristic
22#19153806—21no—
23#19153801—21no—
24#19153799—21no—
25#19153799—21no—
26#19153796C2211yescharacteristic
27#19153795C2211yescharacteristic
28#19153794—21no—
29#19153791C2211yescharacteristic
30#19153790C2211yescharacteristic
31#19153781C2211yescharacteristic
32#19153778C2211yescharacteristic
33C4×C22⋊D181C2211yescharacteristic
34#19153775—21no—
35#19153774C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C22×C8×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#107×C181C2211yescharacteristic
58#107×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181D411yescharacteristic
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181C2311yescharacteristic
69#15668438—22no—
70#15668432—22no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84C22⋊Dic181D411yescharacteristic
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426D411yescharacteristic
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C22×C4×C181—21no—
95C22×C4×C181—21no—
96C22×C4×C181C2311yescharacteristic
97C2×C8×C181—22no—
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C4⋊C4×C181—21no—
101C4⋊C4×C181—21no—
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22×D181—21no—
107C22×D181C2×D411yescharacteristic
108Dic362—21no—
109Dic362—21no—
110Dic362—42no—
111D724—21no—
112D724—21no—
113D724—42no—
114C22⋊D181—22no—
115C22⋊D181—42no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C4×D181—21no—
123C4×D181—21no—
124C4×D181—42no—
125C4×D181—42no—
126#13089678—21no—
127#13089678—21no—
128C23×C181C2×D411yescharacteristic
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—42no—
136C2×C4×C181—42no—
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2411yescharacteristic
139C8×C181—21no—
140C8×C181#4112yescomplemented
141C22×C181—21no—
142C22×C181—21no—
143C22×C181AGL(1,ℤ/8)12yes—
144C22×C181C22×D411yescharacteristic
145C2×D181—21no—
146C2×D181—21no—
147C2×D181—21no—
148C2×D181—41no—
149C2×D181—41no—
150C2×D181—41no—
151C4×C181—21no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181—41no—
155C4×C181—41no—
156C4×C181C2×#4111yescharacteristic
157C4×C1812−1+411yescharacteristic
158Dic181—21no—
159Dic181—21no—
160Dic181—21no—
161Dic181—41no—
162Dic181—41no—
163Dic181—41no—
164C2×C181—22no—
165C2×C181#54711yescharacteristic
166C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C181#57811yescharacteristic
168D181—41no—
169D181—81no—
170C181#334311yescharacteristic, complemented, Sylow
171#3343—1811nomaximal, Sylow
172#552—1811no—
173#547—1811no—
174#501—1811no—
175#484—1811no—
176#483—1811no—
177#482—1811no—
178#480—1811no—
179#478—1811no—
180#477—1811no—
181#468—1811no—
182#465—1811no—
183#440—1811no—
184#435—1811no—
185#428—1811no—
186C2×#107D18111yescharacteristic, complemented
187C2×#41—3621no—
188C2×SD16—1811no—
189C2×M16—1811no—
190C22×C8C2×D18111yescharacteristic
191C4⋊Q8—1811no—
192#126—3621no—
193#125—3621no—
194#125—1811no—
195#123—3621no—
196#123—3621no—
197#123—3621no—
198C22⋊Q8—3621no—
199C22⋊Q8—1811no—
200C22⋊Q8—1811no—
201#121—1811no—
202#121—1811no—
203C4×Q8—1811no—
204C4×D4—1811no—
205C4×D4—1811no—
206#117—3621no—
207#117—1811no—
208C2×C4⋊C4—1811no—
209C2×C4⋊C4C2×D18111yescharacteristic
210C2×C4⋊C4C2×D18111yescharacteristic
211#107—1811no—
212#107—1811no—
213#107C2×D18111yescharacteristic
214#107C2×D18111yescharacteristic
215#107C2×D18111yescharacteristic
216#107C2×D18111yescharacteristic
217#106—1811no—
218#106—1811no—
219#106—1811no—
220C4⋊C8—1811no—
221#103—1811no—
222#103—1811no—
223#103—1811no—
224#102—1811no—
225#102—1811no—
226#102—1811no—
227C22⋊C8—1811no—
228C22⋊C8—1811no—
229#97—1811no—
230#41—7244no—
231C2×Q8—3621no—
232C2×Q8—1811no—
233C2×D4—3621no—
234C2×D4—3621no—
235C2×D4—1811no—
236C2×D4—1811no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—3621no—
240C22×C4—3621no—
241C22×C4—1811no—
242C22×C4C22×D18111yescharacteristic
243SD16—3622no—
244M16—3622no—
245C2×C8—22no—
246C2×C8—1811no—
247C2×C8—1811no—
248C2×C8C22×D18111yescharacteristic
249C2×C8C22×D18111yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
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⋊C4—1811no—
262C4⋊C4C22×D18111yescharacteristic
263C4⋊C4C22×D18111yescharacteristic
264C4⋊C4C22×D18111yescharacteristic
265C4⋊C4C22×D18111yescharacteristic
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—1811no—
273C22⋊C4—1811no—
274C42—3621no—
275C42—3621no—
276C42—1811no—
277C23—3621no—
278C23—1811no—
279C23D4×D18111yescharacteristic
280Q8—3621no—
281Q8—3621no—
282Q8—7242no—
283D4—3622no—
284D4—3621no—
285D4—3621no—
286D4—7242no—
287D4—7242no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—1811no—
304C2×C4—7242no—
305C2×C4—7242no—
306C2×C4D4×D18111yescharacteristic
307C2×C4C23×D18111yescharacteristic
308C8—21no—
309C8—3621no—
310C8—3621no—
311C8#1566844912yescomplemented
312C22—21no—
313C22—21no—
314C22—3621no—
315C22—3621no—
316C22—3621no—
317C22—7241no—
318C22—7241no—
319C22—7241no—
320C22#1915384012yes—
321C22C2×D4×D18111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—3621no—
328C4—3621no—
329C4—3621no—
330C4—7241no—
331C4—7241no—
332C4—7241no—
333C4C2×#1566844911yescharacteristic
334C4#1915386411yescharacteristic
335C2—22no—
336C2—14481no—
337C2—7241no—
338C2#2604193011yescharacteristic
339C2C2×#1915384011yescharacteristic
340C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#107×C181C2
socleC22×C181C22×D4
prime radical#26041930C2
hypercenterC2×#107D181
hypocenterC181#3343
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #26041964C2semidirect
3. #26041687C2semidirect
4. #26041616C2semidirect
5. #26041609C2semidirect
6. #26041606C2semidirect
7. #26041592C2semidirect
8. #26041582C2semidirect
9. #26041573C2semidirect
10. #26041526C2semidirect
11. #26041508C2semidirect
12. #26041378C2semidirect
13. #26041350C2semidirect
14. #26041320C2semidirect
15. C2×#107×C181C2semidirect
140. C8×C181#41semidirect
170. C181#3343semidirect
186. C2×#107D181semidirect
311. C8#15668449semidirect

Maximal subgroups

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

subgroupindex
#260419642
#260419302
#260416872
#260416162
#260416092
#260416062
#260415922
#260415822
#260415732
#260415262
#260415082
#260413782
#260413502
#260413202
C2×#107×C1812
#3343181