Finite Group Databasebeta

← #37546551

Subgroups — #37546551

Order 23168.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041999C211yesmaximal, characteristic, complemented
2#26041985C211yesmaximal, characteristic, complemented
3#26041649C211yesmaximal, characteristic, complemented
4#26041637C211yesmaximal, characteristic, complemented
5#26041632C211yesmaximal, characteristic, complemented
6#26041585C211yesmaximal, characteristic, complemented
7#26041563C211yesmaximal, characteristic, complemented
8#26041493C211yesmaximal, characteristic
9#26041493C211yesmaximal, characteristic
10#26041485C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041389C211yesmaximal, characteristic
13#26041378C211yesmaximal, characteristic, complemented
14#26041366C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C2×#15668438C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19#19153816C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153809—21no—
22#19153809—21no—
23#19153807C2211yescharacteristic
24#19153803C2211yescharacteristic
25#19153803C2211yescharacteristic
26#19153796—21no—
27#19153795—21no—
28#19153794—21no—
29#19153794—21no—
30C4×Dic362C2211yescharacteristic
31#19153781C2211yescharacteristic
32#19153781C2211yescharacteristic
33C4×D724C2211yescharacteristic
34#19153778C2211yescharacteristic
35#19153778C2211yescharacteristic
36#19153775—21no—
37C4⋊C4×D181—21no—
38#19153747C2211yescharacteristic
39#19153745C2211yescharacteristic
40#19153745C2211yescharacteristic
41#19153741C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362D411yescharacteristic
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67#15668438—22no—
68#15668438—22no—
69#15668434—22no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181D411yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181C2311yescharacteristic
93C4×Dic181C2311yescharacteristic
94C2×D4×C181C2311yescharacteristic
95C22×C4×C181—21no—
96C2×C8×C181C2311yescharacteristic
97C2×C8×C181C2311yescharacteristic
98C4⋊C4×C181—21no—
99C4⋊C4×C181—21no—
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C42×C181C2311yescharacteristic
105C22×D181—21no—
106Dic362—21no—
107Dic362—21no—
108Dic362—21no—
109Dic362—21no—
110Dic362—41no—
111Dic362—81no—
112D724—21no—
113D724#4112yes—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—42no—
122C4×D181—81no—
123C4×D181—81no—
124#13089678—21no—
125#13089678—21no—
126C23×C181—21no—
127D4×C181—21no—
128D4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—42no—
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2411yescharacteristic
136C8×C181—21no—
137C8×C181—21no—
138C22×C181—41no—
139C22×C181—41no—
140C22×C181—41no—
141C22×C181C22×D411yescharacteristic
142C2×D181—22no—
143C2×D181—41no—
144C2×D181—41no—
145C4×C181—21no—
146C4×C181—21no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181—41no—
150C4×C181C2×#4111yescharacteristic
151C4×C1812−1+411yescharacteristic
152Dic181—21no—
153Dic181—21no—
154Dic181—21no—
155Dic181—21no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159C2×C181—81no—
160C2×C181#54811yescharacteristic
161C2×C181#57511yescharacteristic
162C2×C181#57711yescharacteristic
163D181—42no—
164C181#337611yescharacteristic, complemented, Sylow
165#3376—1811nomaximal, Sylow
166#556—1811no—
167#554—1811no—
168#491—1811no—
169#489—1811no—
170#488—1811no—
171#479—1811no—
172#478D18111yescharacteristic, complemented
173#475—1811no—
174#463—1811no—
175#463—1811no—
176#461—1811no—
177#446—1811no—
178#442—1811no—
179#440—1811no—
180C4×SD16—1811no—
181C2×SD16—1811no—
182C2×SD16—1811no—
183C2×D8—1811no—
184C4⋊Q8—1811no—
185C4⋊Q8—1811no—
186#126—3621no—
187#126—3621no—
188#125—1811no—
189#125C2×D18111yescharacteristic
190#124—1811no—
191#124—1811no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194C22⋊Q8—3621no—
195C22⋊Q8—3621no—
196C4×Q8—1811no—
197C4×Q8—1811no—
198C4×Q8—1811no—
199C4×D4—1811no—
200C4×D4—1811no—
201C4×D4—1811no—
202C4×D4C2×D18111yescharacteristic
203#117—3621no—
204C2×C4⋊C4—3621no—
205#107C2×D18111yescharacteristic
206#106—1811no—
207#106C2×D18111yescharacteristic
208C4⋊C8—1811no—
209C4⋊C8—1811no—
210C4⋊C8C2×D18111yescharacteristic
211#103—1811no—
212#103—1811no—
213#103—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#102—1811no—
218#102—1811no—
219#102C2×D18111yescharacteristic
220#102C2×D18111yescharacteristic
221#97—1811no—
222#97—1811no—
223C4×C8—1811no—
224C2×Q8—3621no—
225C2×Q8—1811no—
226C2×Q8—1811no—
227C2×Q8—1811no—
228C2×D4—1811no—
229C2×D4C22×D18111yescharacteristic
230C22×C4—21no—
231C22×C4—3621no—
232C22×C4—3621no—
233C22×C4—3621no—
234SD16—3622no—
235SD16—3622no—
236D8—3622no—
237C2×C8—1811no—
238C2×C8—1811no—
239C2×C8C22×D18111yescharacteristic
240C2×C8C22×D18111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4C22×D18111yescharacteristic
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C42—3621no—
266C42—3621no—
267C42—1811no—
268C42—1811no—
269C42C22×D18111yescharacteristic
270C23—21no—
271C23—3621no—
272Q8—3621no—
273Q8—3621no—
274Q8—3621no—
275Q8—3621no—
276Q8—14481no—
277Q8—7241no—
278D4—21no—
279D4—21no—
280D4—3621no—
281D4—1812no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—14481no—
290C2×C4—14481no—
291C2×C4—1811no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—1811no—
295C2×C4—7242no—
296C2×C4D4×D18111yescharacteristic
297C2×C4D4×D18111yescharacteristic
298C2×C4C23×D18111yescharacteristic
299C8—21no—
300C8—21no—
301C8—3621no—
302C8—3621no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—3622no—
307C22—7241no—
308C22—7241no—
309C22C2×D4×D18111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—3621no—
316C4—3621no—
317C4—3621no—
318C4—3621no—
319C4—7241no—
320C4—7241no—
321C4—7241no—
322C4#41×D18111yescharacteristic
323C4#1915386411yescharacteristic
324C2—81no—
325C2—7242no—
326C2#2604193911yescharacteristic
327C2#2604207511yescharacteristic
328C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
prime radicalC2×#15668434C22
hypercenter#478D181
hypocenterC181#3376
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041999C2semidirect
2. #26041985C2semidirect
3. #26041649C2semidirect
4. #26041637C2semidirect
5. #26041632C2semidirect
6. #26041585C2semidirect
7. #26041563C2semidirect
10. #26041485C2semidirect
11. #26041408C2semidirect
13. #26041378C2semidirect
14. #26041366C2semidirect
15. #478×C181C2semidirect
164. C181#3376semidirect
172. #478D181semidirect

Maximal subgroups

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

subgroupindex
#260419992
#260419852
#260416492
#260416372
#260416322
#260415852
#260415632
#260414932
#260414852
#260414082
#260413892
#260413782
#260413662
#478×C1812
#3376181