Finite Group Databasebeta

← #37544081

Subgroups — #37544081

Order 23168.

372 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#26041906C211yesmaximal, characteristic, complemented
2#26041854C211yesmaximal, characteristic
3#26041647C211yesmaximal, characteristic, complemented
4#26041646C211yesmaximal, characteristic, complemented
5#26041641C211yesmaximal, characteristic, complemented
6#26041640C211yesmaximal, characteristic, complemented
7#26041635C211yesmaximal, characteristic, complemented
8#26041634C211yesmaximal, characteristic, complemented
9#26041628C211yesmaximal, characteristic, complemented
10#26041286C211yesmaximal, characteristic, complemented
11#26041279C211yesmaximal, characteristic
12#26041274C211yesmaximal, characteristic
13#103×D181C211yesmaximal, characteristic, complemented
14#26041233C211yesmaximal, characteristic, complemented
15#487×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153814—21no—
22#19153814C2211yescharacteristic
23#19153808C2211yescharacteristic
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153805C2211yescharacteristic
27#19153804C2211yescharacteristic
28#19153801—21no—
29#19153801—21no—
30#19153794—21no—
31#19153794—21no—
32#19153794—21no—
33#19153792—21no—
34#19153774C2211yescharacteristic
35#19153773C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153741C2211yescharacteristic
38#19153741C2211yescharacteristic
39#19153740C2211yescharacteristic
40#19153740C2211yescharacteristic
41#19153740C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4⋊Q8×C181C2211yescharacteristic
54#103×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×Dic362C2311yescharacteristic
64Q8×D181—22no—
65Q8×D181—22no—
66C2×D724—21no—
67C2×D724C2311yescharacteristic
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72#15668432—22no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C8×D181—22no—
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#15668428—21no—
86#15668428D411yescharacteristic
87#15668428D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181—21no—
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181—21no—
104C4⋊C4×C181—21no—
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110Dic362—21no—
111Dic362—21no—
112Dic362—42no—
113Dic362—81no—
114D724—21no—
115D724—21no—
116D724—42no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C2×Dic181C2×D411yescharacteristic
123C4×D181—42no—
124C4×D181—42no—
125C4×D181—81no—
126C4×D181#4112yes—
127C4×D181#4112yes—
128#13089678—21no—
129#13089678—21no—
130Q8×C181—21no—
131Q8×C181—21no—
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181—81no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2411yescharacteristic
142C8×C181—21no—
143C8×C181—21no—
144C22×C181C22×D411yescharacteristic
145C2×D181—21no—
146C2×D181—21no—
147C2×D181—41no—
148C2×D181—41no—
149C2×D181—41no—
150C2×D181#12412yes—
151C4×C181—21no—
152C4×C181—21no—
153C4×C181—41no—
154C4×C181—41no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181C2×#4111yescharacteristic
158C4×C181C2×#4111yescharacteristic
159Dic181—21no—
160Dic181—21no—
161Dic181—41no—
162Dic181—41no—
163Dic181—41no—
164Dic181#12412yes—
165C2×C181C2×#12411yescharacteristic
166C2×C181#57711yescharacteristic
167C2×C181#57811yescharacteristic
168D181—22no—
169D181—81no—
170C181#313711yescharacteristic, complemented, Sylow
171#3137—1811nomaximal, Sylow
172#544—1811no—
173#536—1811no—
174#491—1811no—
175#491—1811no—
176#489—1811no—
177#489—1811no—
178#488—1811no—
179#488—1811no—
180#487—1811no—
181#487D18111yescharacteristic, complemented
182#419—1811no—
183#417—1811no—
184#416—1811no—
185C2×#103—1811no—
186#405—1811no—
187C2×#41—1811no—
188C22×Q8—1811no—
189C2×M16—1811no—
190C22×C8—1811no—
191C4⋊Q8—3621no—
192C4⋊Q8—1811no—
193C4⋊Q8—1811no—
194C4⋊Q8C2×D18111yescharacteristic
195C4⋊Q8C2×D18111yescharacteristic
196#125—3621no—
197#125—1811no—
198#125—1811no—
199#124—1811no—
200#124—1811no—
201#123—3621no—
202#123—3621no—
203C22⋊Q8—3621no—
204C22⋊Q8—3621no—
205C22⋊Q8—3621no—
206C22⋊Q8—3621no—
207#117—1811no—
208#117—1811no—
209C2×C4⋊C4—1811no—
210#103—1811no—
211#103—1811no—
212#103—1811no—
213#103—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#103—1811no—
218#103C2×D18111yescharacteristic
219#103C2×D18111yescharacteristic
220#103C2×D18111yescharacteristic
221#103C2×D18111yescharacteristic
222#102—1811no—
223#102—1811no—
224#102—1811no—
225#102—1811no—
226#97—1811no—
227#97—1811no—
228C4×C8—1811no—
229C4×C8C2×D18111yescharacteristic
230#41—3622no—
231#41—3622no—
232C2×Q8—21no—
233C2×Q8—3621no—
234C2×Q8—3621no—
235C2×Q8—3622no—
236C2×Q8—3622no—
237C2×Q8—1811no—
238C2×Q8C22×D18111yescharacteristic
239C2×Q8C22×D18111yescharacteristic
240C2×D4—3621no—
241C2×D4—1811no—
242C22×C4—3621no—
243C22×C4—3621no—
244C22×C4—3621no—
245C22×C4—1811no—
246M16—3622no—
247C2×C8—3622no—
248C2×C8—1811no—
249C2×C8—1811no—
250C2×C8C22×D18111yescharacteristic
251C2×C8C22×D18111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4C22×D18111yescharacteristic
268C4⋊C4C22×D18111yescharacteristic
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—1811no—
275C22⋊C4—1811no—
276C42—3621no—
277C42—1811no—
278C42C22×D18111yescharacteristic
279C23—3621no—
280C23—1811no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—81no—
286Q8—3621no—
287Q8—3621no—
288Q8—14481no—
289Q8—7242no—
290D4—3621no—
291D4—3621no—
292D4—7242no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—14481no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—1811no—
304C2×C4—1812no—
305C2×C4—1812no—
306C2×C4—7242no—
307C2×C4—7242no—
308C2×C4D4×D18111yescharacteristic
309C2×C4D4×D18111yescharacteristic
310C2×C4C23×D18111yescharacteristic
311C8—21no—
312C8—21no—
313C8—3621no—
314C8—3621no—
315C22—3621no—
316C22—3621no—
317C22—1812no—
318C22—7241no—
319C22—7241no—
320C22—7241no—
321C22C2×D4×D18111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—3621no—
329C4—3621no—
330C4—1812no—
331C4—7241no—
332C4—7241no—
333C4—7241no—
334C4#41×D18111yescharacteristic
335C4#41×D18111yescharacteristic
336C2—3622no—
337C2—14481no—
338C2#124×D18111yescharacteristic
339C2#2604208511yescharacteristic
340C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#487×C181C2
socleC22×C181C22×D4
prime radicalC2×#15668450C22
hypercenter#487D181
hypocenterC181#3137
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #26041906C2semidirect
3. #26041647C2semidirect
4. #26041646C2semidirect
5. #26041641C2semidirect
6. #26041640C2semidirect
7. #26041635C2semidirect
8. #26041634C2semidirect
9. #26041628C2semidirect
10. #26041286C2semidirect
13. #103×D181C2semidirect
14. #26041233C2semidirect
15. #487×C181C2semidirect
170. C181#3137semidirect
181. #487D181semidirect

Maximal subgroups

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

subgroupindex
#260419062
#260418542
#260416472
#260416462
#260416412
#260416402
#260416352
#260416342
#260416282
#260412862
#260412792
#260412742
#103×D1812
#260412332
#487×C1812
#3137181