Finite Group Databasebeta

← #37546201

Subgroups — #37546201

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#26041987C211yesmaximal, characteristic, complemented
2#26041976C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041617C211yesmaximal, characteristic, complemented
5#26041613C211yesmaximal, characteristic, complemented
6#26041596C211yesmaximal, characteristic, complemented
7#26041590C211yesmaximal, characteristic, complemented
8#26041584C211yesmaximal, characteristic, complemented
9#26041557C211yesmaximal, characteristic, complemented
10#26041505C211yesmaximal, characteristic, complemented
11#26041380C211yesmaximal, characteristic, complemented
12#26041348C211yesmaximal, characteristic, complemented
13#26041321C211yesmaximal, characteristic, complemented
14#107×D181C211yesmaximal, characteristic, complemented
15#468×C181C211yesmaximal, characteristic, complemented
16C2×C8×D181C2211yescharacteristic
17#19153815C2211yescharacteristic
18#19153809—21no—
19#19153807C2211yescharacteristic
20#19153806—21no—
21#19153797—21no—
22#19153796—21no—
23#19153793—21no—
24#19153792C2211yescharacteristic
25#19153787—21no—
26#19153787C2211yescharacteristic
27Q8×Dic181C2211yescharacteristic
28D4×Dic181C2211yescharacteristic
29C4×C22⋊D181C2211yescharacteristic
30#19153776—21no—
31#19153776—21no—
32#19153775C2211yescharacteristic
33C2×C4⋊Dic181C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36#19153750C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×C22⋊D181—21no—
61C2×C22⋊D181D411yescharacteristic
62C22×Dic181—21no—
63C22×Dic181—21no—
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67C2×#13089678C2311yescharacteristic
68C2×#13089678C2311yescharacteristic
69C8×D181—22no—
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
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⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426D411yescharacteristic
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181C2311yescharacteristic
92C2×Q8×C181C2311yescharacteristic
93C2×D4×C181—21no—
94C2×D4×C181C2311yescharacteristic
95C22×C4×C181C2311yescharacteristic
96SD16×C181—22no—
97M16×C181—22no—
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C22×D181C2×D411yescharacteristic
106Dic362—81no—
107C22⋊D181—22no—
108C22⋊D181—42no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—81no—
114C2×Dic181—81no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120C4×D181—81no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124C23×C181—21no—
125C23×C181C2×D411yescharacteristic
126Q8×C181—21no—
127Q8×C181—21no—
128D4×C181—21no—
129D4×C181—21no—
130D4×C181—81no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181C2×D411yescharacteristic
137C2×C4×C181C2411yescharacteristic
138C8×C181—21no—
139C8×C181#4112yes—
140C22×C181—21no—
141C22×C181—21no—
142C22×C181—21no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181—41no—
146C22×C181C22×D411yescharacteristic
147C2×D181—21no—
148C2×D181—21no—
149C2×D181#13712yes—
150C4×C181—21no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181C2×#4111yescharacteristic
155C4×C1812−1+411yescharacteristic
156Dic181—21no—
157Dic181—21no—
158Dic181—21no—
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181—41no—
163C2×C181—41no—
164C2×C181—81no—
165C2×C181#54711yescharacteristic
166C2×C181C2×#13711yescharacteristic
167C2×C181#57611yescharacteristic
168D181—22no—
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#474—1811no—
180#468D18111yescharacteristic, complemented
181#465—1811no—
182#440—1811no—
183#435—1811no—
184#428—1811no—
185C2×#107—1811no—
186C2×SD16C2×D18111yescharacteristic
187C2×M16C2×D18111yescharacteristic
188C22×C8—1811no—
189C4⋊Q8—1811no—
190#126—3621no—
191#125—3621no—
192#125—1811no—
193#123—3621no—
194C22⋊Q8—3621no—
195C22⋊Q8—3621no—
196C22⋊Q8—1811no—
197C22⋊Q8C2×D18111yescharacteristic
198#121—3621no—
199#121—1811no—
200#121C2×D18111yescharacteristic
201C4×Q8—1811no—
202C4×D4—3621no—
203C4×D4—3621no—
204C4×D4—1811no—
205C4×D4—1811no—
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#107—1811no—
215#107C2×D18111yescharacteristic
216#106—1811no—
217#106—1811no—
218#106—1811no—
219C4⋊C8—1811no—
220#103—1811no—
221#103—1811no—
222#103C2×D18111yescharacteristic
223#102—1811no—
224#102—1811no—
225#102C2×D18111yescharacteristic
226C22⋊C8—1811no—
227C22⋊C8—1811no—
228#97—1811no—
229C2×Q8—3621no—
230C2×Q8C22×D18111yescharacteristic
231C2×D4—21no—
232C2×D4—3621no—
233C2×D4—1811no—
234C2×D4C22×D18111yescharacteristic
235C22×C4—3621no—
236C22×C4—3621no—
237C22×C4—3621no—
238C22×C4—3621no—
239C22×C4—1811no—
240C22×C4C22×D18111yescharacteristic
241SD16—22no—
242M16—22no—
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⋊C4—1811no—
262C4⋊C4C22×D18111yescharacteristic
263C4⋊C4C22×D18111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—1811no—
271C22⋊C4—1811no—
272C42—3621no—
273C42—3621no—
274C42—1811no—
275C23—21no—
276C23—1811no—
277C23D4×D18111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—14481no—
281D4—21no—
282D4—21no—
283D4—81no—
284D4—3622no—
285D4—7242no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—3621no—
292C2×C4—3621no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—14481no—
298C2×C4—14481no—
299C2×C4—14481no—
300C2×C4—14481no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—1811no—
304C2×C4D4×D18111yescharacteristic
305C2×C4C23×D18111yescharacteristic
306C8—21no—
307C8—3621no—
308C8—3621no—
309C8#1566844812yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—3621no—
317C22—3621no—
318C22—1812no—
319C22C2×D4×D18111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3621no—
325C4—3621no—
326C4—3621no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4—7241no—
331C4C2×#1566844811yescharacteristic
332C4#1915386311yescharacteristic
333C2—41no—
334C2—81no—
335C2—3622no—
336C2#2604192911yescharacteristic
337C2#137×D18111yescharacteristic
338C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#468×C181C2
socleC22×C181C22×D4
prime radical#26041976C2
hypercenter#468D181
hypocenterC181#3346
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #26041987C2semidirect
3. #26041687C2semidirect
4. #26041617C2semidirect
5. #26041613C2semidirect
6. #26041596C2semidirect
7. #26041590C2semidirect
8. #26041584C2semidirect
9. #26041557C2semidirect
10. #26041505C2semidirect
11. #26041380C2semidirect
12. #26041348C2semidirect
13. #26041321C2semidirect
14. #107×D181C2semidirect
15. #468×C181C2semidirect
169. C181#3346semidirect
180. #468D181semidirect

Maximal subgroups

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

subgroupindex
#260419872
#260419762
#260416872
#260416172
#260416132
#260415962
#260415902
#260415842
#260415572
#260415052
#260413802
#260413482
#260413212
#107×D1812
#468×C1812
#3346181