Finite Group Databasebeta

← #37543933

Subgroups — #37543933

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#26041887C211yesmaximal, characteristic, complemented
2#26041761C211yesmaximal, characteristic
3#26041613C211yesmaximal, characteristic, complemented
4#26041611C211yesmaximal, characteristic, complemented
5#26041588C211yesmaximal, characteristic, complemented
6#26041578C211yesmaximal, characteristic, complemented
7#26041487C211yesmaximal, characteristic, complemented
8#26041483C211yesmaximal, characteristic, complemented
9#26041444C211yesmaximal, characteristic
10#26041440C211yesmaximal, characteristic
11#26041381C211yesmaximal, characteristic, complemented
12C4×#15668439C211yesmaximal, characteristic, complemented
13C4×#15668436C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic, complemented
15#441×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20#19153814C2211yescharacteristic
21#19153811—21no—
22#19153810—21no—
23#19153808—21no—
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153796C2211yescharacteristic
27#19153792C2211yescharacteristic
28Q8×Dic181C2211yescharacteristic
29C4×Dic362C2211yescharacteristic
30C4×D724—21no—
31C4×D724C2211yescharacteristic
32#19153778—21no—
33#19153778C2211yescharacteristic
34#19153773—21no—
35#19153773C2211yescharacteristic
36C4⋊C4×D181—21no—
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181C2311yescharacteristic
69#15668439—22no—
70#15668438—22no—
71#15668436—22no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C4⋊Dic181—21no—
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86#15668428D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98Q16×C181—22no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C42×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110Dic362—21no—
111Dic362—21no—
112D724—24no—
113D724—21no—
114D724#4112yes—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—24no—
122C4×D181—21no—
123C4×D181—21no—
124C4×D181—81no—
125C4×D181—81no—
126C4×D181—81no—
127#13089678—21no—
128#13089678—21no—
129Q8×C181—21no—
130Q8×C181—21no—
131Q8×C181—21no—
132Q8×C181#4112yes—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2411yescharacteristic
140C8×C181—21no—
141C8×C181—21no—
142C22×C181C22×D411yescharacteristic
143C2×D181—21no—
144C2×D181—22no—
145C2×D181—21no—
146C2×D181—21no—
147C2×D181—41no—
148C2×D181—41no—
149C4×C181—22no—
150C4×C181—21no—
151C4×C181—21no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181—41no—
155C4×C181C2×#4111yescharacteristic
156C4×C181C2×#4111yescharacteristic
157Dic181—21no—
158Dic181—21no—
159Dic181—21no—
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163C2×C181#52511yescharacteristic
164C2×C181#57711yescharacteristic
165C2×C181#57811yescharacteristic
166D181—41no—
167D181—42no—
168C181#312011yescharacteristic, complemented, Sylow
169#3120—1811nomaximal, Sylow
170#541—1811no—
171#520—1811no—
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#441D18111yescharacteristic, complemented
181#440—1811no—
182C4×Q16—1811no—
183C4×SD16—1811no—
184#433—1811no—
185C2×#41—1811no—
186C2×Q16—1811no—
187C2×Q16C2×D18111yescharacteristic
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—3621no—
203C4×D4—3621no—
204C4×D4—1811no—
205C4×D4—1811no—
206#117—3621no—
207#117—1811no—
208C2×C4⋊C4—3621no—
209C2×C4⋊C4—1811no—
210#107—1811no—
211#107—1811no—
212#106—1811no—
213#106C2×D18111yescharacteristic
214C4⋊C8—1811no—
215C4⋊C8—1811no—
216#103—1811no—
217#103—1811no—
218#103—1811no—
219#103—1811no—
220#103C2×D18111yescharacteristic
221#103C2×D18111yescharacteristic
222#102—1811no—
223#102—1811no—
224C22⋊C8—1811no—
225C22⋊C8—1811no—
226#97C2×D18111yescharacteristic
227C4×C8—1811no—
228#41—3622no—
229#41—3622no—
230C2×Q8—1811no—
231C2×Q8C22×D18111yescharacteristic
232C2×Q8C22×D18111yescharacteristic
233C2×D4—3621no—
234C2×D4—1811no—
235C22×C4—3621no—
236C22×C4—3621no—
237C22×C4—3621no—
238C22×C4—3621no—
239C22×C4—1811no—
240Q16—22no—
241Q16—3622no—
242SD16—3622no—
243SD16—3622no—
244C2×C8—1811no—
245C2×C8—1811no—
246C2×C8C22×D18111yescharacteristic
247C2×C8C22×D18111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—3621no—
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⋊C4—1811no—
262C4⋊C4—1811no—
263C4⋊C4C22×D18111yescharacteristic
264C4⋊C4C22×D18111yescharacteristic
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—1811no—
270C22⋊C4—1811no—
271C42—21no—
272C42—21no—
273C42—3621no—
274C42—3621no—
275C42—1811no—
276C42C22×D18111yescharacteristic
277C23—3621no—
278C23—1811no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—3621no—
283Q8—3621no—
284Q8#1566844912yes—
285D4—3624no—
286D4—3621no—
287D4—1812no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3624no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—14481no—
299C2×C4—14481no—
300C2×C4—14481no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—1811no—
304C2×C4D4×D18111yescharacteristic
305C2×C4D4×D18111yescharacteristic
306C2×C4C23×D18111yescharacteristic
307C8—21no—
308C8—21no—
309C8—3621no—
310C8—3621no—
311C22—3621no—
312C22—3622no—
313C22—3621no—
314C22—3621no—
315C22—7241no—
316C22—7241no—
317C22C2×D4×D18111yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3621no—
325C4—3621no—
326C4—3621no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4#41×D18111yescharacteristic
331C4C2×#1566844911yescharacteristic
332C2—7241no—
333C2—7242no—
334C2#2604178811yescharacteristic
335C2#2604208811yescharacteristic
336C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#441×C181C2
socleC22×C181C22×D4
prime radicalC2×#15668450C22
hypercenter#441D181
hypocenterC181#3120
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #26041887C2semidirect
3. #26041613C2semidirect
4. #26041611C2semidirect
5. #26041588C2semidirect
6. #26041578C2semidirect
7. #26041487C2semidirect
8. #26041483C2semidirect
11. #26041381C2semidirect
12. C4×#15668439C2semidirect
13. C4×#15668436C2semidirect
14. #26041341C2semidirect
15. #441×C181C2semidirect
168. C181#3120semidirect
180. #441D181semidirect

Maximal subgroups

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

subgroupindex
#260418872
#260417612
#260416132
#260416112
#260415882
#260415782
#260414872
#260414832
#260414442
#260414402
#260413812
C4×#156684392
C4×#156684362
#260413412
#441×C1812
#3120181