Finite Group Databasebeta

← #37546203

Subgroups — #37546203

Order 23168.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041990C211yesmaximal, characteristic, complemented
2#26041979C211yesmaximal, characteristic
3#26041685C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041616C211yesmaximal, characteristic, complemented
6#26041596C211yesmaximal, characteristic, complemented
7#26041591C211yesmaximal, characteristic, complemented
8#26041587C211yesmaximal, characteristic, complemented
9#26041524C211yesmaximal, characteristic, complemented
10#26041507C211yesmaximal, characteristic, complemented
11#26041379C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041320C211yesmaximal, characteristic, complemented
14#107×D181C211yesmaximal, characteristic, complemented
15#474×C181C211yesmaximal, characteristic, complemented
16C2×#15668437C2211yescharacteristic
17C2×#15668432C2211yescharacteristic
18C2×C8×D181C2211yescharacteristic
19#19153809—21no—
20#19153808C2211yescharacteristic
21#19153807—21no—
22#19153799—21no—
23#19153796C2211yescharacteristic
24#19153796C2211yescharacteristic
25#19153792—21no—
26#19153792—21no—
27#19153789—21no—
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30C4×Dic362C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153778—21no—
33C4×C22⋊D181—21no—
34#19153774C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153727C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×D724D411yescharacteristic
61C2×C22⋊D181—21no—
62C2×C22⋊D181—21no—
63C2×C4×D181—21no—
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67C2×C4×D181C2311yescharacteristic
68#15668437—22no—
69#15668432—22no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C8×D181—22no—
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181D411yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426D411yescharacteristic
91#15668426D411yescharacteristic
92C4×Dic181—21no—
93C4×Dic181—21no—
94C2×Q8×C181—21no—
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181—21no—
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C42×C181C2311yescharacteristic
105C22×D181C2×D411yescharacteristic
106C22×D181C2×D411yescharacteristic
107Dic362—21no—
108Dic362—21no—
109D724—22no—
110C22⋊D181—42no—
111C22⋊D181—81no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—21no—
121C4×D181—21no—
122C4×D181—81no—
123C4×D181—81no—
124C4×D181—81no—
125#13089678—21no—
126#13089678#4112yes—
127C23×C181—21no—
128Q8×C181—81no—
129D4×C181—21no—
130D4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—81no—
135C2×C4×C181C2×D411yescharacteristic
136C2×C4×C181C2×D411yescharacteristic
137C2×C4×C181C2411yescharacteristic
138C8×C181—21no—
139C8×C181—21no—
140C22×C181—41no—
141C22×C181—41no—
142C22×C181—41no—
143C22×C181C22×D411yescharacteristic
144C2×D181—21no—
145C2×D181—21no—
146C2×D181—21no—
147C2×D181—21no—
148C2×D181—21no—
149C2×D181#13712yes—
150C4×C181—21no—
151C4×C181—21no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181—41no—
155C4×C181C2×#4111yescharacteristic
156C4×C1812−1+411yescharacteristic
157Dic181—21no—
158Dic181—21no—
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163C2×C181—81no—
164C2×C181#54711yescharacteristic
165C2×C181C2×#13711yescharacteristic
166C2×C181#57611yescharacteristic
167D181—22no—
168D181—41no—
169C181#334611yescharacteristic, complemented, Sylow
170#3346—1811nomaximal, Sylow
171#554—1811no—
172#553—1811no—
173#501—1811no—
174#485—1811no—
175#484—1811no—
176#481—1811no—
177#480—1811no—
178#479—1811no—
179#474D18111yescharacteristic, complemented
180#468—1811no—
181#465—1811no—
182#440—1811no—
183#435—1811no—
184#428—1811no—
185C2×#107—1811no—
186C2×SD16—1811no—
187C2×M16—1811no—
188C22×C8—1811no—
189C4⋊Q8C2×D18111yescharacteristic
190#126—3621no—
191#125—3621no—
192#125—1811no—
193#123—3621no—
194C22⋊Q8—3621no—
195C22⋊Q8—3621no—
196C22⋊Q8—1811no—
197C22⋊Q8—1811no—
198#121—3621no—
199#121—1811no—
200#121—1811no—
201C4×Q8—1811no—
202C4×D4—3621no—
203C4×D4—3621no—
204C4×D4—1811no—
205C4×D4C2×D18111yescharacteristic
206#117—1811no—
207C2×C4⋊C4—1811no—
208C2×C4⋊C4—1811no—
209C2×C4⋊C4—1811no—
210#107—1811no—
211#107—1811no—
212#107—1811no—
213#107—1811no—
214#107C2×D18111yescharacteristic
215#107C2×D18111yescharacteristic
216#106—1811no—
217#106—1811no—
218#106—1811no—
219C4⋊C8C2×D18111yescharacteristic
220#103—1811no—
221#103—1811no—
222#103—1811no—
223#102—1811no—
224#102C2×D18111yescharacteristic
225#102C2×D18111yescharacteristic
226C22⋊C8—1811no—
227C22⋊C8—1811no—
228#97—1811no—
229C2×Q8—21no—
230C2×Q8—1811no—
231C2×D4—3621no—
232C2×D4—3621no—
233C2×D4—1811no—
234C2×D4C22×D18111yescharacteristic
235C22×C4—21no—
236C22×C4—3621no—
237C22×C4—3621no—
238C22×C4—3621no—
239C22×C4—1811no—
240C22×C4—1811no—
241SD16—3622no—
242M16—3622no—
243C2×C8—3622no—
244C2×C8—1811no—
245C2×C8—1811no—
246C2×C8C22×D18111yescharacteristic
247C2×C8C22×D18111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—1811no—
258C4⋊C4—1811no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4C22×D18111yescharacteristic
262C4⋊C4C22×D18111yescharacteristic
263C4⋊C4C22×D18111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—1811no—
271C22⋊C4—1811no—
272C42—3621no—
273C42—3621no—
274C42C22×D18111yescharacteristic
275C23—21no—
276C23—1811no—
277C23—1811no—
278Q8—81no—
279Q8—3621no—
280Q8—3621no—
281D4—21no—
282D4—21no—
283D4—3622no—
284D4—14481no—
285D4—7242no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
290C2×C4—3621no—
291C2×C4—3621no—
292C2×C4—3621no—
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×C4D4×D18111yescharacteristic
304C2×C4D4×D18111yescharacteristic
305C2×C4C23×D18111yescharacteristic
306C8—21no—
307C8—21no—
308C8—3621no—
309C8—1812no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—3621no—
314C22—3621no—
315C22—3621no—
316C22—3621no—
317C22—3621no—
318C22—1812no—
319C22C2×D4×D18111yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—3621no—
326C4—3621no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4—7241no—
331C4#41×D18111yescharacteristic
332C4#1915386411yescharacteristic
333C2—81no—
334C2—3622no—
335C2—7241no—
336C2#2604193111yescharacteristic
337C2#137×D18111yescharacteristic
338C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#474×C181C2
socleC22×C181C22×D4
prime radical#26041979C2
hypercenter#474D181
hypocenterC181#3346
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #26041990C2semidirect
3. #26041685C2semidirect
4. #26041622C2semidirect
5. #26041616C2semidirect
6. #26041596C2semidirect
7. #26041591C2semidirect
8. #26041587C2semidirect
9. #26041524C2semidirect
10. #26041507C2semidirect
11. #26041379C2semidirect
12. #26041349C2semidirect
13. #26041320C2semidirect
14. #107×D181C2semidirect
15. #474×C181C2semidirect
169. C181#3346semidirect
179. #474D181semidirect

Maximal subgroups

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

subgroupindex
#260419902
#260419792
#260416852
#260416222
#260416162
#260415962
#260415912
#260415872
#260415242
#260415072
#260413792
#260413492
#260413202
#107×D1812
#474×C1812
#3346181