Finite Group Databasebeta

← #37545721

Subgroups — #37545721

Order 23168.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041950C211yesmaximal, characteristic, complemented
2#26041645C211yesmaximal, characteristic, complemented
3#26041603C211yesmaximal, characteristic, complemented
4#26041592C211yesmaximal, characteristic, complemented
5#26041583C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041513C211yesmaximal, characteristic, complemented
8#26041474C211yesmaximal, characteristic, complemented
9#26041422C211yesmaximal, characteristic, complemented
10#26041422C211yesmaximal, characteristic, complemented
11#26041379C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041278C211yesmaximal, characteristic, complemented
14#26041273C211yesmaximal, characteristic, complemented
15#553×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
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#19153749C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35#19153739C2211yescharacteristic
36#19153739C2211yescharacteristic
37#19153739C2211yescharacteristic
38#19153737C2211yescharacteristic
39#19153736C2211yescharacteristic
40#19153736C2211yescharacteristic
41#19153736C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44#19153736C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic
47#19153727C2211yescharacteristic
48#126×C181—21no—
49#125×C181C2211yescharacteristic
50#123×C181—21no—
51#121×C181—21no—
52#121×C181C2211yescharacteristic
53#121×C181C2211yescharacteristic
54C4×D4×C181—21no—
55C4×D4×C181C2211yescharacteristic
56C4×D4×C181C2211yescharacteristic
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#15668437—22no—
75#15668434—41no—
76#15668434—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×D4×C181—21no—
89C2×D4×C181—21no—
90C2×D4×C181D411yescharacteristic
91C2×D4×C181C2311yescharacteristic
92C22×C4×C181—21no—
93C22×C4×C181—21no—
94C22×C4×C181C2311yescharacteristic
95C22×C4×C181C2311yescharacteristic
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×C181—21no—
107C22⋊C4×C181D411yescharacteristic
108C22⋊C4×C181D411yescharacteristic
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×C181—21no—
134C23×C181C2×D411yescharacteristic
135C23×C181C2×D411yescharacteristic
136D4×C181—21no—
137D4×C181—21no—
138D4×C181—41no—
139D4×C181—42no—
140D4×C181—81no—
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—21no—
148C2×C4×C181—81no—
149C2×C4×C181—81no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181C22×D411yescharacteristic
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—21no—
173C4×C181—21no—
174C4×C181—21no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181—41no—
178C4×C181C2×#4111yescharacteristic
179C4×C181H(5,𝔽2)11yescharacteristic
180Dic181—22no—
181Dic181—41no—
182C2×C181—41no—
183C2×C181—41no—
184C2×C181—81no—
185C2×C181#54611yescharacteristic
186C2×C181#57511yescharacteristic
187C2×C181#57611yescharacteristic
188D181—81no—
189D181—81no—
190C181#330911yescharacteristic, complemented, Sylow
191#3309—1811nomaximal, Sylow
192#553D18111yescharacteristic, complemented
193#550—1811no—
194#490—1811no—
195#482—1811no—
196#480—1811no—
197#479—1811no—
198#469—1811no—
199#466—1811no—
200#459—1811no—
201#449—1811no—
202#449—1811no—
203#440—1811no—
204#435—1811no—
205#417—1811no—
206#416—1811no—
207C2×#41—1811no—
208C2×#41—1811no—
209C2×SD16—1811no—
210C2×D8—1811no—
211C2×D8—1811no—
212C2×M16—1811no—
213C22×C8—1811no—
214#127—3621no—
215#127—1811no—
216#126—21no—
217#125C2×D18111yescharacteristic
218#123—21no—
219#121—21no—
220#121—3621no—
221#121—3621no—
222#121—1811no—
223#121—1811no—
224#121C2×D18111yescharacteristic
225#121C2×D18111yescharacteristic
226C4×Q8—1811no—
227C4×D4—21no—
228C4×D4—3621no—
229C4×D4C2×D18111yescharacteristic
230C4×D4C2×D18111yescharacteristic
231#117C2×D18111yescharacteristic
232C2×C4⋊C4C2×D18111yescharacteristic
233#107—1811no—
234#107—1811no—
235#106—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103—1811no—
239#103—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247C22⋊C8—1811no—
248C22⋊C8—1811no—
249#97—1811no—
250#41—3622no—
251#41—3622no—
252#41—7241no—
253#41—7241no—
254C2×Q8—1811no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4C22⋊D18111yescharacteristic
266C2×D4C22×D18111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4C22×D18111yescharacteristic
272C22×C4C22×D18111yescharacteristic
273SD16—3622no—
274D8—7241no—
275D8—7241no—
276M16—7241no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8—1811no—
280C2×C8—1811no—
281C2×C8—7241no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—3621no—
286C4⋊C4—1811no—
287C4⋊C4C22⋊D18111yescharacteristic
288C4⋊C4C22×D18111yescharacteristic
289C4⋊C4C22×D18111yescharacteristic
290C4⋊C4C22×D18111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4C22⋊D18111yescharacteristic
298C22⋊C4C22⋊D18111yescharacteristic
299C42—21no—
300C42—3621no—
301C42C22×D18111yescharacteristic
302C23—21no—
303C23—3621no—
304C23—3621no—
305C23C2×C22⋊D18111yescharacteristic
306C23C2×C22⋊D18111yescharacteristic
307Q8—3621no—
308Q8—1812no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—3621no—
315D4—3621no—
316D4—3621no—
317D4—3621no—
318D4—14481no—
319D4—14481no—
320D4—14481no—
321D4—7242no—
322D4—7242no—
323D4—7242no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—7242no—
336C2×C4—7242no—
337C2×C4C2×C22⋊D18111yescharacteristic
338C2×C4C2×C22⋊D18111yescharacteristic
339C2×C4C2×C22⋊D18111yescharacteristic
340C2×C4C2×C22⋊D18111yescharacteristic
341C2×C4C23×D18111yescharacteristic
342C8—3621no—
343C8—3621no—
344C8—3621no—
345C8—3621no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—7241no—
356C22—7241no—
357C22—7241no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C22×C22⋊D18111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3622no—
370C4—7241no—
371C4#41×D18111yescharacteristic
372C4#1915386211yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—14481no—
377C2—14481no—
378C2#2604191711yescharacteristic
379C2#2604207711yescharacteristic
380C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#553×C181C2
socleC22×C181C22×D4
hypercenter#553D181
hypocenterC181#3309
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #26041950C2semidirect
2. #26041645C2semidirect
3. #26041603C2semidirect
4. #26041592C2semidirect
5. #26041583C2semidirect
6. #26041530C2semidirect
7. #26041513C2semidirect
8. #26041474C2semidirect
9. #26041422C2semidirect
10. #26041422C2semidirect
11. #26041379C2semidirect
12. #26041351C2semidirect
13. #26041278C2semidirect
14. #26041273C2semidirect
15. #553×C181C2semidirect
190. C181#3309semidirect
192. #553D181semidirect

Maximal subgroups

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

subgroupindex
#260419502
#260416452
#260416032
#260415922
#260415832
#260415302
#260415132
#260414742
#260414222
#260413792
#260413512
#260412782
#260412732
#553×C1812
#3309181