Finite Group Databasebeta

← #37545802

Subgroups — #37545802

Order 23168.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041986C211yesmaximal, characteristic, complemented
2#26041638C211yesmaximal, characteristic, complemented
3#26041612C211yesmaximal, characteristic, complemented
4#26041590C211yesmaximal, characteristic, complemented
5#26041559C211yesmaximal, characteristic, complemented
6#26041523C211yesmaximal, characteristic, complemented
7#26041518C211yesmaximal, characteristic, complemented
8#26041498C211yesmaximal, characteristic, complemented
9#26041441C211yesmaximal, characteristic, complemented
10#26041430C211yesmaximal, characteristic, complemented
11#26041379C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041280C211yesmaximal, characteristic, complemented
14C2×#19153737C211yesmaximal, characteristic, complemented
15#546×C181C211yesmaximal, characteristic
16C2×#15668439C2211yescharacteristic, complemented
17C2×#15668437C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668433C2211yescharacteristic, complemented
20C22×#13089678C2211yescharacteristic
21#19153816C2211yescharacteristic, complemented
22#19153807—21no—
23#19153795C2211yescharacteristic
24#19153795C2211yescharacteristic, complemented
25#19153793—21no—
26#19153793—21no—
27C4×Dic362C2211yescharacteristic, complemented
28D4×Dic181—21no—
29C2×C4⋊Dic181C2211yescharacteristic
30C2×C4⋊Dic181C2211yescharacteristic, complemented
31#19153749C2211yescharacteristic, complemented
32#19153749C2211yescharacteristic, complemented
33#19153749C2211yescharacteristic, complemented
34C4⋊#13089678C2211yescharacteristic, complemented
35#19153740C2211yescharacteristic, complemented
36#19153740C2211yescharacteristic, complemented
37#19153740C2211yescharacteristic, complemented
38#19153739C2211yescharacteristic, complemented
39#19153737C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44#19153737C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic, complemented
47#19153727C2211yescharacteristic, complemented
48C2×#41×C181C2211yescharacteristic
49C22×D4×C181C2211yescharacteristic
50#124×C181C2211yescharacteristic
51#123×C181—21no—
52C22⋊Q8×C181C2211yescharacteristic
53#121×C181—21no—
54#121×C181C2211yescharacteristic
55#120×C181—21no—
56C4×D4×C181C2211yescharacteristic
57C4×D4×C181C2211yescharacteristic
58C2×C22⋊C4×C181—21no—
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C22×Dic181—21no—
62C22×Dic181—21no—
63#15668439—41no—
64#15668437—22no—
65#15668437—41no—
66#15668433—41no—
67C2×#13089678—41no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181—21no—
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81C22⋊Dic181—21no—
82C22⋊Dic181—21no—
83C4×Dic181—21no—
84C24×C181—21no—
85#41×C181—22no—
86#41×C181—41no—
87C2×Q8×C181C2311yescharacteristic
88C2×D4×C181—22no—
89C2×D4×C181—21no—
90C2×D4×C181—21no—
91C2×D4×C181—21no—
92C2×D4×C181—41no—
93C2×D4×C181D411yescharacteristic
94C2×D4×C181C2311yescharacteristic
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181—21no—
97C22×C4×C181—21no—
98C22×C4×C181C2311yescharacteristic
99C22×C4×C181C2311yescharacteristic
100C4⋊C4×C181—21no—
101C4⋊C4×C181D411yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181D411yescharacteristic
109C22⋊C4×C181D411yescharacteristic
110C42×C181C2311yescharacteristic
111Dic362—21no—
112Dic362—21no—
113Dic362—81no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—81no—
119C2×Dic181—81no—
120#13089678—21no—
121#13089678—21no—
122#13089678—21no—
123#13089678—21no—
124C23×C181—21no—
125C23×C181—21no—
126C23×C181—42no—
127C23×C181—42no—
128C23×C181—81no—
129C23×C181C2×D411yescharacteristic
130C23×C181C2×D411yescharacteristic
131Q8×C181—21no—
132Q8×C181—21no—
133D4×C181—22no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—42no—
138D4×C181—42no—
139D4×C181—81no—
140D4×C181#4112yes—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—42no—
148C2×C4×C181—81no—
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2411yescharacteristic
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—22no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—84no—
166C22×C181#13712yes—
167C22×C181C22×D411yescharacteristic
168C4×C181—21no—
169C4×C181—21no—
170C4×C181—21no—
171C4×C181—21no—
172C4×C181—41no—
173C4×C181—41no—
174C4×C181C2×#4111yescharacteristic
175C4×C181H(5,𝔽2)11yescharacteristic
176Dic181—41no—
177Dic181—41no—
178Dic181—41no—
179Dic181—41no—
180C2×C181—22no—
181C2×C181—41no—
182C2×C181—42no—
183C2×C181—81no—
184C2×C181#54611yescharacteristic
185C2×C181C2×#13711yescharacteristic
186C2×C181#57611yescharacteristic
187C181#331411yescharacteristic, complemented, Sylow
188#3314—1811nomaximal, Sylow
189#554—1811no—
190#546D18111yescharacteristic
191#489—1811no—
192#484—1811no—
193#480—1811no—
194#474—1811no—
195#468—1811no—
196#467—1811no—
197#464—1811no—
198#452—1811no—
199#450—1811no—
200#440—1811no—
201#435—1811no—
202#417—1811no—
203C2×#102—1811no—
204C2×#41C2×D18111yescharacteristic
205C22×D4C2×D18111yescharacteristic
206C2×Q16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×M16—1811no—
210C22×C8—1811no—
211C4⋊Q8—1811no—
212#125—3621no—
213#124C2×D18111yescharacteristic
214#123—21no—
215C22⋊Q8—3621no—
216C22⋊Q8—3621no—
217C22⋊Q8—1811no—
218C22⋊Q8—1811no—
219C22⋊Q8C2×D18111yescharacteristic
220#121—21no—
221#121C2×D18111yescharacteristic
222#120—21no—
223C4×Q8—1811no—
224C4×D4—3621no—
225C4×D4C2×D18111yescharacteristic
226C4×D4C2×D18111yescharacteristic
227C2×C4⋊C4—1811no—
228C2×C4⋊C4—1811no—
229C2×C22⋊C4—21no—
230#107—1811no—
231#107—1811no—
232#107—1811no—
233C4⋊C8—1811no—
234#103—1811no—
235#103—1811no—
236#103—1811no—
237#103—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244C22⋊C8—1811no—
245C22⋊C8—1811no—
246#97—1811no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—3621no—
251C2×Q8—1811no—
252C2×Q8C22×D18111yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D18111yescharacteristic
259C2×D4C22×D18111yescharacteristic
260C2×D4C22×D18111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—3621no—
264C22×C4—3621no—
265C22×C4C22×D18111yescharacteristic
266C22×C4C22×D18111yescharacteristic
267Q16—7241no—
268SD16—3622no—
269SD16—7241no—
270M16—7241no—
271C2×C8—1811no—
272C2×C8—1811no—
273C2×C8—1811no—
274C2×C8—1811no—
275C2×C8—7241no—
276C4⋊C4—21no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4C22⋊D18111yescharacteristic
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4C22⋊D18111yescharacteristic
296C22⋊C4C22⋊D18111yescharacteristic
297C42—3621no—
298C42C22×D18111yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D18111yescharacteristic
305C23C2×C22⋊D18111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—3621no—
309Q8—3621no—
310Q8—14481no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1566844812yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—14481no—
332C2×C4—14481no—
333C2×C4C2×C22⋊D18111yescharacteristic
334C2×C4C2×C22⋊D18111yescharacteristic
335C2×C4C2×C22⋊D18111yescharacteristic
336C2×C4C2×C22⋊D18111yescharacteristic
337C2×C4C23×D18111yescharacteristic
338C8—3621no—
339C8—3621no—
340C8—3621no—
341C8—3621no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1915384612yes—
355C22C22×C22⋊D18111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—7241no—
363C4—7241no—
364C4—7241no—
365C4—7241no—
366C4C2×#1566844811yescharacteristic
367C4#1915386111yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#2604192311yescharacteristic
373C2C2×#1915384611yescharacteristic
374C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radical#546×C181C2
socleC22×C181C22×D4
hypercenter#546D181
hypocenterC181#3314
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #26041986C2semidirect
2. #26041638C2semidirect
3. #26041612C2semidirect
4. #26041590C2semidirect
5. #26041559C2semidirect
6. #26041523C2semidirect
7. #26041518C2semidirect
8. #26041498C2semidirect
9. #26041441C2semidirect
10. #26041430C2semidirect
11. #26041379C2semidirect
12. #26041351C2semidirect
13. #26041280C2semidirect
14. C2×#19153737C2semidirect
16. C2×#15668439C22semidirect
19. C2×#15668433C22semidirect
21. #19153816C22semidirect
24. #19153795C22semidirect
27. C4×Dic362C22semidirect
30. C2×C4⋊Dic181C22semidirect
31. #19153749C22semidirect
32. #19153749C22semidirect
33. #19153749C22semidirect
34. C4⋊#13089678C22semidirect
35. #19153740C22semidirect
36. #19153740C22semidirect
37. #19153740C22semidirect
38. #19153739C22semidirect
46. C22⋊#13089678C22semidirect
47. #19153727C22semidirect
187. C181#3314semidirect

Maximal subgroups

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

subgroupindex
#260419862
#260416382
#260416122
#260415902
#260415592
#260415232
#260415182
#260414982
#260414412
#260414302
#260413792
#260413512
#260412802
C2×#191537372
#546×C1812
#3314181