Finite Group Databasebeta

← #37545185

Subgroups — #37545185

Order 23168.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041902C211yesmaximal, characteristic, complemented
2#26041896C211yesmaximal, characteristic, complemented
3#26041568C211yesmaximal, characteristic, complemented
4#26041567C211yesmaximal, characteristic, complemented
5#26041563C211yesmaximal, characteristic, complemented
6#26041562C211yesmaximal, characteristic, complemented
7#26041535C211yesmaximal, characteristic, complemented
8#26041530C211yesmaximal, characteristic
9#26041508C211yesmaximal, characteristic, complemented
10#26041504C211yesmaximal, characteristic, complemented
11#26041499C211yesmaximal, characteristic, complemented
12#26041496C211yesmaximal, characteristic, complemented
13#26041493C211yesmaximal, characteristic, complemented
14#26041305C211yesmaximal, characteristic, complemented
15#465×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668433C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153811—21no—
23#19153809—21no—
24#19153805C2211yescharacteristic
25#19153803—21no—
26#19153803C2211yescharacteristic
27#19153802—21no—
28#19153798—21no—
29#19153797—21no—
30#19153796—21no—
31#19153795C2211yescharacteristic
32#19153793—21no—
33#19153790C2211yescharacteristic
34Q8×Dic181C2211yescharacteristic
35#19153781C2211yescharacteristic
36D4×Dic181C2211yescharacteristic
37#19153778C2211yescharacteristic
38#19153775C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153737C2211yescharacteristic
51#19153736C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C22×Dic181—21no—
65C2×C4×D181—21no—
66#15668439—41no—
67#15668438—41no—
68#15668434—41no—
69#15668433—41no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181D411yescharacteristic
74C4⋊Dic181D411yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81C22⋊Dic181—21no—
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181D411yescharacteristic
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181C2311yescharacteristic
99SD16×C181—41no—
100C2×C8×C181—41no—
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181—21no—
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22×D181—21no—
109Dic362—21no—
110Dic362—21no—
111Dic362—81no—
112Dic362—81no—
113D724—21no—
114D724—21no—
115C22⋊D181—81no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—81no—
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C4×D181—81no—
125#13089678—21no—
126#13089678—21no—
127C23×C181—21no—
128C23×C181C2×D411yescharacteristic
129Q8×C181—21no—
130Q8×C181—21no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—81no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2411yescharacteristic
141C8×C181—21no—
142C8×C181—21no—
143C22×C181—21no—
144C22×C181—21no—
145C22×C181—21no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181C22×D411yescharacteristic
150C2×D181—41no—
151C2×D181—41no—
152C2×D181—41no—
153C4×C181—21no—
154C4×C181—41no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181H(5,𝔽2)11yescharacteristic
158C4×C1812−1+411yescharacteristic
159Dic181—21no—
160Dic181—21no—
161Dic181—21no—
162Dic181—21no—
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—41no—
167C2×C181—81no—
168C2×C181#53711yescharacteristic
169C2×C181#57711yescharacteristic
170C2×C181#57711yescharacteristic
171D181—81no—
172C181#326311yescharacteristic, complemented, Sylow
173#3263—1811nomaximal, Sylow
174#542—1811no—
175#542—1811no—
176#476—1811no—
177#476—1811no—
178#475—1811no—
179#475—1811no—
180#470—1811no—
181#469—1811no—
182#465—1811no—
183#465D18111yescharacteristic, complemented
184#464—1811no—
185#464—1811no—
186#463—1811no—
187#463—1811no—
188#424—1811no—
189C2×Q16—1811no—
190C2×SD16—1811no—
191C2×SD16C2×D18111yescharacteristic
192C2×D8—1811no—
193C2×M16—1811no—
194C22×C8C2×D18111yescharacteristic
195C4⋊Q8—1811no—
196C4⋊Q8—1811no—
197#126—3621no—
198#126—3621no—
199#124—3621no—
200#124—3621no—
201#124—1811no—
202#124—1811no—
203#123—3621no—
204#123—3621no—
205C22⋊Q8—3621no—
206C22⋊Q8—3621no—
207C22⋊Q8—1811no—
208C22⋊Q8C2×D18111yescharacteristic
209#121—1811no—
210#121C2×D18111yescharacteristic
211C4×Q8—1811no—
212C4×Q8—1811no—
213C4×D4—1811no—
214C4×D4—1811no—
215#117—1811no—
216#106—1811no—
217#106—1811no—
218#106—1811no—
219#106C2×D18111yescharacteristic
220C4⋊C8—1811no—
221C4⋊C8—1811no—
222C4⋊C8—1811no—
223C4⋊C8—1811no—
224#103—1811no—
225#103—1811no—
226#103—1811no—
227#103C2×D18111yescharacteristic
228#102—1811no—
229#102—1811no—
230#102—1811no—
231#102C2×D18111yescharacteristic
232C2×Q8—3621no—
233C2×Q8—3621no—
234C2×Q8—1811no—
235C2×Q8C22×D18111yescharacteristic
236C2×D4—21no—
237C2×D4—3621no—
238C2×D4—1811no—
239C2×D4C22×D18111yescharacteristic
240C22×C4—3621no—
241C22×C4—3621no—
242C22×C4C22×D18111yescharacteristic
243Q16—7241no—
244SD16—41no—
245SD16—7241no—
246D8—7241no—
247M16—7241no—
248C2×C8—41no—
249C2×C8—1811no—
250C2×C8—1811no—
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—21no—
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—21no—
266C22⋊C4—21no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—1811no—
276C22⋊C4—1811no—
277C42—3621no—
278C42—3621no—
279C42—1811no—
280C42—1811no—
281C23—21no—
282C23—3621no—
283C23D4×D18111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3621no—
287Q8—3621no—
288Q8—14481no—
289Q8—14481no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—3621no—
294D4—3621no—
295D4—14481no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—14481no—
305C2×C4—14481no—
306C2×C4—1811no—
307C2×C4—1811no—
308C2×C4—1811no—
309C2×C4—1811no—
310C2×C4D4×D18111yescharacteristic
311C2×C4C23×D18111yescharacteristic
312C8—21no—
313C8—21no—
314C8—3621no—
315C8—3621no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—7241no—
323C22—7241no—
324C22—7241no—
325C22C2×D4×D18111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3621no—
331C4—3621no—
332C4—3621no—
333C4—3621no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4#1915386111yescharacteristic
338C4#1915386311yescharacteristic
339C2—41no—
340C2—81no—
341C2—14481no—
342C2#2604185611yescharacteristic
343C2#2604208511yescharacteristic
344C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#465×C181C2
socleC22×C181C22×D4
prime radical#26041530C2
hypercenter#465D181
hypocenterC181#3263
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #26041902C2semidirect
2. #26041896C2semidirect
3. #26041568C2semidirect
4. #26041567C2semidirect
5. #26041563C2semidirect
6. #26041562C2semidirect
7. #26041535C2semidirect
9. #26041508C2semidirect
10. #26041504C2semidirect
11. #26041499C2semidirect
12. #26041496C2semidirect
13. #26041493C2semidirect
14. #26041305C2semidirect
15. #465×C181C2semidirect
172. C181#3263semidirect
183. #465D181semidirect

Maximal subgroups

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

subgroupindex
#260419022
#260418962
#260415682
#260415672
#260415632
#260415622
#260415352
#260415302
#260415082
#260415042
#260414992
#260414962
#260414932
#260413052
#465×C1812
#3263181