Finite Group Databasebeta

← #37546182

Subgroups — #37546182

Order 23168.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041987C211yesmaximal, characteristic
2#26041971C211yesmaximal, characteristic
3#26041687C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041612C211yesmaximal, characteristic, complemented
6#26041608C211yesmaximal, characteristic, complemented
7#26041607C211yesmaximal, characteristic, complemented
8#26041584C211yesmaximal, characteristic, complemented
9#26041562C211yesmaximal, characteristic, complemented
10#26041534C211yesmaximal, characteristic, complemented
11#26041386C211yesmaximal, characteristic, complemented
12#26041350C211yesmaximal, characteristic
13#26041320C211yesmaximal, characteristic, complemented
14C2×#19153748C211yesmaximal, characteristic, complemented
15#467×C181C211yesmaximal, characteristic, complemented
16C2×#15668432C2211yescharacteristic
17#19153815C2211yescharacteristic
18#19153811—21no—
19#19153807—21no—
20#19153807C2211yescharacteristic
21#19153806—21no—
22#19153800—21no—
23#19153796—21no—
24#19153793—21no—
25#19153792C2211yescharacteristic
26#19153792C2211yescharacteristic
27Q8×Dic181C2211yescharacteristic
28Q8×Dic181C2211yescharacteristic
29C4×C22⋊D181C2211yescharacteristic
30#19153776—21no—
31#19153774C2211yescharacteristic
32#19153772—21no—
33C2×C4⋊Dic181C2211yescharacteristic
34C2×C4⋊Dic181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36#19153749C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153740C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×C22⋊D181D411yescharacteristic
61C22×Dic181—21no—
62C22×Dic181—21no—
63C2×C4×D181—21no—
64C2×C4×D181C2311yescharacteristic
65#15668432—22no—
66C2×#13089678C2311yescharacteristic
67C2×#13089678C2311yescharacteristic
68C4⋊Dic181—21no—
69C4⋊Dic181—21no—
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⋊Dic181D411yescharacteristic
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426D411yescharacteristic
88C4×Dic181—21no—
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181C2311yescharacteristic
92C2×Q8×C181C2311yescharacteristic
93C2×Q8×C181C2311yescharacteristic
94C22×C4×C181C2311yescharacteristic
95Q16×C181—22no—
96C2×C8×C181—22no—
97C2×C8×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
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—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—42no—
113C2×Dic181—81no—
114C2×Dic181C2×D411yescharacteristic
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C4×D181—21no—
118C4×D181—21no—
119C4×D181—81no—
120#13089678—21no—
121#13089678—21no—
122C23×C181C2×D411yescharacteristic
123Q8×C181—21no—
124Q8×C181—21no—
125Q8×C181—21no—
126Q8×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2411yescharacteristic
135C8×C181—21no—
136C8×C181#4112yes—
137C22×C181—21no—
138C22×C181—21no—
139C22×C181#13712yes—
140C22×C181C22×D411yescharacteristic
141C2×D181—21no—
142C2×D181—21no—
143C2×D181—21no—
144C4×C181—21no—
145C4×C181—41no—
146C4×C181—41no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181C2×#4111yescharacteristic
150C4×C1812−1+411yescharacteristic
151Dic181—21no—
152Dic181—21no—
153Dic181—21no—
154Dic181—41no—
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158C2×C181—22no—
159C2×C181#54711yescharacteristic
160C2×C181C2×#13711yescharacteristic
161C2×C181#57711yescharacteristic
162D181—41no—
163C181#334411yescharacteristic, complemented, Sylow
164#3344—1811nomaximal, Sylow
165#554—1811no—
166#552—1811no—
167#501—1811no—
168#485—1811no—
169#484—1811no—
170#483—1811no—
171#483—1811no—
172#479—1811no—
173#475—1811no—
174#470—1811no—
175#467D18111yescharacteristic, complemented
176#441—1811no—
177#435—1811no—
178#428—1811no—
179C2×#106—1811no—
180C2×Q16C2×D18111yescharacteristic
181C2×M16—1811no—
182C22×C8C2×D18111yescharacteristic
183C4⋊Q8—1811no—
184#126—3621no—
185#125—3621no—
186#125—3621no—
187#125—1811no—
188#123—3621no—
189C22⋊Q8—3621no—
190C22⋊Q8—3621no—
191C22⋊Q8—1811no—
192C22⋊Q8—1811no—
193C22⋊Q8C2×D18111yescharacteristic
194C22⋊Q8C2×D18111yescharacteristic
195C4×Q8—1811no—
196C4×Q8—1811no—
197C4×D4—3621no—
198C4×D4—1811no—
199#117—3621no—
200#117—1811no—
201C2×C4⋊C4—1811no—
202C2×C4⋊C4—1811no—
203C2×C4⋊C4—1811no—
204#107—1811no—
205#107—1811no—
206#107C2×D18111yescharacteristic
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211#106—1811no—
212#106—1811no—
213C4⋊C8—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#103—1811no—
218#103C2×D18111yescharacteristic
219#103C2×D18111yescharacteristic
220C22⋊C8—1811no—
221C22⋊C8—1811no—
222#97—1811no—
223C2×Q8—3621no—
224C2×Q8C22×D18111yescharacteristic
225C2×Q8C22×D18111yescharacteristic
226C2×D4—1811no—
227C22×C4—3621no—
228C22×C4—3621no—
229C22×C4—3621no—
230C22×C4—1811no—
231C22×C4C22×D18111yescharacteristic
232Q16—22no—
233M16—3622no—
234C2×C8—22no—
235C2×C8—1811no—
236C2×C8—1811no—
237C2×C8C22×D18111yescharacteristic
238C2×C8C22×D18111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4—1811no—
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—1811no—
264C22⋊C4—1811no—
265C42—3621no—
266C42—3621no—
267C42—3621no—
268C42—1811no—
269C23—1811no—
270C23D4×D18111yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—14481no—
276D4—3622no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
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—7242no—
295C2×C4D4×D18111yescharacteristic
296C2×C4C23×D18111yescharacteristic
297C8—21no—
298C8—3621no—
299C8—3621no—
300C8#1566844812yes—
301C22—21no—
302C22—21no—
303C22—3621no—
304C22—3621no—
305C22—3621no—
306C22#1915384812yes—
307C22C2×D4×D18111yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3621no—
314C4—3621no—
315C4—3621no—
316C4—7241no—
317C4—7241no—
318C4—7241no—
319C4—7241no—
320C4C2×#1566844811yescharacteristic
321C4#1915386311yescharacteristic
322C2—22no—
323C2—7241no—
324C2#2604192911yescharacteristic
325C2C2×#1915384811yescharacteristic
326C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#467×C181C2
socleC22×C181C22×D4
prime radicalC2×C22⋊D181D4
hypercenter#467D181
hypocenterC181#3344
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #26041687C2semidirect
4. #26041618C2semidirect
5. #26041612C2semidirect
6. #26041608C2semidirect
7. #26041607C2semidirect
8. #26041584C2semidirect
9. #26041562C2semidirect
10. #26041534C2semidirect
11. #26041386C2semidirect
13. #26041320C2semidirect
14. C2×#19153748C2semidirect
15. #467×C181C2semidirect
163. C181#3344semidirect
175. #467D181semidirect

Maximal subgroups

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

subgroupindex
#260419872
#260419712
#260416872
#260416182
#260416122
#260416082
#260416072
#260415842
#260415622
#260415342
#260413862
#260413502
#260413202
C2×#191537482
#467×C1812
#3344181