Finite Group Databasebeta

← #37546795

Subgroups — #37546795

Order 23168.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042003C211yesmaximal, characteristic, complemented
2#26042001C211yesmaximal, characteristic, complemented
3#26041672C211yesmaximal, characteristic, complemented
4#26041671C211yesmaximal, characteristic, complemented
5#26041664C211yesmaximal, characteristic
6#26041504C211yesmaximal, characteristic, complemented
7#26041503C211yesmaximal, characteristic, complemented
8#26041497C211yesmaximal, characteristic
9#26041495C211yesmaximal, characteristic
10#26041487C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041382C211yesmaximal, characteristic, complemented
13#26041377C211yesmaximal, characteristic, complemented
14#26041371C211yesmaximal, characteristic, complemented
15#462×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×D1448C2211yescharacteristic
23#19153814C2211yescharacteristic
24#19153811—21no—
25#19153811—21no—
26#19153811—21no—
27#19153810—21no—
28#19153805C2211yescharacteristic
29#19153805C2211yescharacteristic
30#19153805C2211yescharacteristic
31#19153804C2211yescharacteristic
32#19153796—21no—
33#19153794—21no—
34Q8×Dic181C2211yescharacteristic
35Q8×Dic181C2211yescharacteristic
36C4×Dic362C2211yescharacteristic
37#19153781C2211yescharacteristic
38C4×D724C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153774—21no—
41#19153773—21no—
42#19153749C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C4⋊Q8×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362D411yescharacteristic
60C2×Dic362C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C4×D181—21no—
64C2×C4×D181—21no—
65#15668439—22no—
66#15668439—41no—
67#15668438—41no—
68#15668436—22no—
69#15668436—22no—
70#15668436—41no—
71D1448—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C4⋊Dic181—21no—
75C4⋊Dic181—21no—
76C4⋊Dic181D411yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82#15668428D411yescharacteristic
83#15668426—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C4×Dic181C2311yescharacteristic
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×Q8×C181C2311yescharacteristic
101Q16×C181—41no—
102Q16×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181—21no—
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—21no—
113Dic362—21no—
114Dic362—21no—
115Dic362—41no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—42no—
127C4×D181—42no—
128#13089678—21no—
129#13089678#4112yes—
130Q8×C181—21no—
131Q8×C181—21no—
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181—21no—
135Q8×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C22×C181C22×D411yescharacteristic
146C2×D181—41no—
147C2×D181—41no—
148C2×D181—41no—
149C2×D181—41no—
150C2×D181—41no—
151C2×D181—41no—
152C4×C181—21no—
153C4×C181—21no—
154C4×C181—41no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181—41no—
158C4×C181C2×#4111yescharacteristic
159C4×C181H(5,𝔽2)11yescharacteristic
160Dic181—21no—
161Dic181—21no—
162Dic181—21no—
163Dic181—21no—
164Dic181—41no—
165Dic181—41no—
166C2×C181#55011yescharacteristic
167C2×C181#57511yescharacteristic
168C2×C181#57811yescharacteristic
169D181—81no—
170D181—81no—
171C181#340211yescharacteristic, complemented, Sylow
172#3402—1811nomaximal, Sylow
173#556—1811no—
174#556—1811no—
175#497—1811no—
176#497—1811no—
177#495—1811no—
178#464—1811no—
179#464—1811no—
180#463—1811no—
181#463—1811no—
182#462—1811no—
183#462D18111yescharacteristic, complemented
184#446—1811no—
185#440—1811no—
186#440—1811no—
187C4×Q16—1811no—
188C2×Q16—1811no—
189C2×Q16—1811no—
190C2×Q16C2×D18111yescharacteristic
191C2×Q16C2×D18111yescharacteristic
192C2×SD16—1811no—
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×SD16—1811no—
196C2×D8—1811no—
197C4⋊Q8—1811no—
198C4⋊Q8C2×D18111yescharacteristic
199#126—3621no—
200#126—3621no—
201#126—3621no—
202#126—3621no—
203#124—1811no—
204#124—1811no—
205#124—1811no—
206#124—1811no—
207C22⋊Q8—3621no—
208C22⋊Q8—3621no—
209C4×Q8—1811no—
210C4×Q8—1811no—
211C4×Q8—1811no—
212C4×Q8—1811no—
213C4×Q8C2×D18111yescharacteristic
214C4×D4—1811no—
215C4×D4—1811no—
216#117—3621no—
217#117—3621no—
218#107—1811no—
219C4⋊C8—1811no—
220C4⋊C8—1811no—
221C4⋊C8C2×D18111yescharacteristic
222#103—1811no—
223#103—1811no—
224#103C2×D18111yescharacteristic
225#103C2×D18111yescharacteristic
226#102—1811no—
227#102—1811no—
228#97—1811no—
229#97—1811no—
230C4×C8—1811no—
231C2×Q8—1811no—
232C2×Q8—1811no—
233C2×Q8C22×D18111yescharacteristic
234C2×Q8C22×D18111yescharacteristic
235C2×Q8C22×D18111yescharacteristic
236C2×D4—1811no—
237C2×D4—1811no—
238C22×C4—3621no—
239C22×C4—3621no—
240Q16—41no—
241Q16—41no—
242Q16—3622no—
243Q16—7241no—
244SD16—3622no—
245SD16—3622no—
246SD16—7241no—
247SD16—7241no—
248D8—7241no—
249C2×C8—1811no—
250C2×C8—1811no—
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—1811no—
262C4⋊C4—1811no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4C22×D18111yescharacteristic
266C22⋊C4—3621no—
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—3621no—
276C42—21no—
277C42—3621no—
278C42—3621no—
279C42—3621no—
280C42—1811no—
281C42—1811no—
282C42C22×D18111yescharacteristic
283C23—3621no—
284C23—3621no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—3621no—
292Q8—3621no—
293Q8—7241no—
294D4—3621no—
295D4—3621no—
296D4—3621no—
297D4—3621no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—1811no—
305C2×C4—1811no—
306C2×C4—1811no—
307C2×C4—1811no—
308C2×C4—7242no—
309C2×C4—7242no—
310C2×C4D4×D18111yescharacteristic
311C2×C4D4×D18111yescharacteristic
312C2×C4C23×D18111yescharacteristic
313C8—21no—
314C8—21no—
315C8—3621no—
316C8—1812no—
317C22—7241no—
318C22—7241no—
319C22—7241no—
320C22—7241no—
321C22—7241no—
322C22—7241no—
323C22C2×D4×D18111yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3621no—
331C4—3621no—
332C4—3621no—
333C4—3621no—
334C4—7241no—
335C4—7241no—
336C4#41×D18111yescharacteristic
337C4#1915386111yescharacteristic
338C2—14481no—
339C2—14481no—
340C2#2604194711yescharacteristic
341C2#2604207811yescharacteristic
342C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#462×C181C2
socleC22×C181C22×D4
prime radicalC2×D1448C22
hypercenter#462D181
hypocenterC181#3402
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #26042003C2semidirect
2. #26042001C2semidirect
3. #26041672C2semidirect
4. #26041671C2semidirect
6. #26041504C2semidirect
7. #26041503C2semidirect
10. #26041487C2semidirect
11. #26041408C2semidirect
12. #26041382C2semidirect
13. #26041377C2semidirect
14. #26041371C2semidirect
15. #462×C181C2semidirect
171. C181#3402semidirect
183. #462D181semidirect

Maximal subgroups

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

subgroupindex
#260420032
#260420012
#260416722
#260416712
#260416642
#260415042
#260415032
#260414972
#260414952
#260414872
#260414082
#260413822
#260413772
#260413712
#462×C1812
#3402181