Finite Group Databasebeta

← #37545841

Subgroups — #37545841

Order 23168.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041950C211yesmaximal, characteristic
2#26041645C211yesmaximal, characteristic, complemented
3#26041603C211yesmaximal, characteristic, complemented
4#26041597C211yesmaximal, characteristic, complemented
5#26041583C211yesmaximal, characteristic, complemented
6#26041527C211yesmaximal, characteristic, complemented
7#26041510C211yesmaximal, characteristic, complemented
8#26041479C211yesmaximal, characteristic, complemented
9#26041439C211yesmaximal, characteristic, complemented
10#26041439C211yesmaximal, characteristic, complemented
11#26041384C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041278C211yesmaximal, characteristic, complemented
14#26041273C211yesmaximal, characteristic, complemented
15#552×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668433C2211yescharacteristic
22C22×#13089678C2211yescharacteristic
23#19153813C2211yescharacteristic
24#19153812—21no—
25#19153790C2211yescharacteristic
26#19153790C2211yescharacteristic
27#19153789—21no—
28#19153789—21no—
29C4×Dic362C2211yescharacteristic
30#19153778—21no—
31#19153749C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35#19153740C2211yescharacteristic
36#19153739C2211yescharacteristic
37#19153739C2211yescharacteristic
38#19153739C2211yescharacteristic
39#19153736C2211yescharacteristic
40#19153736C2211yescharacteristic
41#19153736C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44#19153736C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic
47#19153727C2211yescharacteristic
48#126×C181—21no—
49#125×C181—21no—
50#125×C181C2211yescharacteristic
51#123×C181—21no—
52C22⋊Q8×C181C2211yescharacteristic
53C22⋊Q8×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56#117×C181—21no—
57#117×C181C2211yescharacteristic
58C2×C4⋊C4×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—22no—
61#15668449—41no—
62#15668449—41no—
63C2×Dic362C2311yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74#15668439—22no—
75#15668436—41no—
76#15668436—41no—
77#15668433—41no—
78C2×#13089678—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668426—21no—
86#15668426—21no—
87C4×Dic181—21no—
88C2×Q8×C181C2311yescharacteristic
89C2×D4×C181D411yescharacteristic
90C22×C4×C181—21no—
91C22×C4×C181C2311yescharacteristic
92C22×C4×C181C2311yescharacteristic
93C4⋊C4×C181—21no—
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181—21no—
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181D411yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C22⋊C4×C181—21no—
106C22⋊C4×C181D411yescharacteristic
107C22⋊C4×C181D411yescharacteristic
108C42×C181—21no—
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—21no—
113Dic362—21no—
114Dic362#4112yes—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—42no—
120D724—81no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C4×D181—42no—
128C4×D181—42no—
129#13089678—21no—
130#13089678—21no—
131#13089678—21no—
132#13089678—21no—
133C23×C181C2×D411yescharacteristic
134C23×C181C2×D411yescharacteristic
135Q8×C181—21no—
136Q8×C181—21no—
137D4×C181—41no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—42no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181C22×D411yescharacteristic
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181C2×#4111yescharacteristic
174C4×C181H(5,𝔽2)11yescharacteristic
175Dic181—22no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181—41no—
179C2×C181#54611yescharacteristic
180C2×C181#57511yescharacteristic
181C2×C181#57711yescharacteristic
182D181—81no—
183D181—81no—
184C181#331711yescharacteristic, complemented, Sylow
185#3317—1811nomaximal, Sylow
186#552D18111yescharacteristic, complemented
187#550—1811no—
188#490—1811no—
189#482—1811no—
190#481—1811no—
191#479—1811no—
192#468—1811no—
193#465—1811no—
194#460—1811no—
195#452—1811no—
196#452—1811no—
197#441—1811no—
198#435—1811no—
199#417—1811no—
200#416—1811no—
201C2×#41—1811no—
202C2×#41—1811no—
203C2×Q16—1811no—
204C2×SD16—1811no—
205C2×SD16—1811no—
206C2×M16—1811no—
207C22×C8—1811no—
208#127—3621no—
209#127—1811no—
210#126—21no—
211#125—21no—
212#125C2×D18111yescharacteristic
213#123—21no—
214C22⋊Q8C2×D18111yescharacteristic
215C22⋊Q8C2×D18111yescharacteristic
216#121—3621no—
217#121—3621no—
218#121—1811no—
219#121—1811no—
220C4×Q8—1811no—
221C4×Q8C2×D18111yescharacteristic
222C4×D4—3621no—
223C4×D4C2×D18111yescharacteristic
224#117—21no—
225#117C2×D18111yescharacteristic
226C2×C4⋊C4C2×D18111yescharacteristic
227#107—1811no—
228#106—1811no—
229#106—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#102—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241C22⋊C8—1811no—
242C22⋊C8—1811no—
243#97—1811no—
244#41—3622no—
245#41—3622no—
246#41—7241no—
247#41—7241no—
248C2×Q8—1811no—
249C2×Q8C22×D18111yescharacteristic
250C2×D4—3621no—
251C2×D4—3621no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—1811no—
257C2×D4—1811no—
258C2×D4C22⋊D18111yescharacteristic
259C22×C4—21no—
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4C22×D18111yescharacteristic
263C22×C4C22×D18111yescharacteristic
264Q16—3622no—
265SD16—7241no—
266SD16—7241no—
267M16—7241no—
268C2×C8—1811no—
269C2×C8—1811no—
270C2×C8—1811no—
271C2×C8—1811no—
272C2×C8—7241no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4C22⋊D18111yescharacteristic
282C4⋊C4C22×D18111yescharacteristic
283C4⋊C4C22×D18111yescharacteristic
284C4⋊C4C22×D18111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4C22⋊D18111yescharacteristic
291C22⋊C4C22⋊D18111yescharacteristic
292C42—21no—
293C42—21no—
294C42—3621no—
295C42C22×D18111yescharacteristic
296C23—3621no—
297C23—3621no—
298C23C2×C22⋊D18111yescharacteristic
299C23C2×C22⋊D18111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—3621no—
303Q8—1812no—
304D4—41no—
305D4—3621no—
306D4—3621no—
307D4—3621no—
308D4—3621no—
309D4—14481no—
310D4—14481no—
311D4—14481no—
312D4—7242no—
313D4—7242no—
314D4—7242no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—7242no—
327C2×C4—7242no—
328C2×C4C2×C22⋊D18111yescharacteristic
329C2×C4C2×C22⋊D18111yescharacteristic
330C2×C4C2×C22⋊D18111yescharacteristic
331C2×C4C2×C22⋊D18111yescharacteristic
332C2×C4C23×D18111yescharacteristic
333C8—3621no—
334C8—3621no—
335C8—3621no—
336C8—3621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22C22×C22⋊D18111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—3622no—
359C4—7241no—
360C4#41×D18111yescharacteristic
361C4#1915386211yescharacteristic
362C2—41no—
363C2—41no—
364C2—14481no—
365C2—14481no—
366C2#2604191711yescharacteristic
367C2#2604207711yescharacteristic
368C2#2604208711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#552×C181C2
socleC22×C181C22×D4
prime radical#26041950C2
hypercenter#552D181
hypocenterC181#3317
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #26041645C2semidirect
3. #26041603C2semidirect
4. #26041597C2semidirect
5. #26041583C2semidirect
6. #26041527C2semidirect
7. #26041510C2semidirect
8. #26041479C2semidirect
9. #26041439C2semidirect
10. #26041439C2semidirect
11. #26041384C2semidirect
12. #26041351C2semidirect
13. #26041278C2semidirect
14. #26041273C2semidirect
15. #552×C181C2semidirect
184. C181#3317semidirect
186. #552D181semidirect

Maximal subgroups

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

subgroupindex
#260419502
#260416452
#260416032
#260415972
#260415832
#260415272
#260415102
#260414792
#260414392
#260413842
#260413512
#260412782
#260412732
#552×C1812
#3317181