Finite Group Databasebeta

← #37546321

Subgroups — #37546321

Order 23168.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041975C211yesmaximal, characteristic, complemented
2#26041678C211yesmaximal, characteristic, complemented
3#26041603C211yesmaximal, characteristic, complemented
4#26041600C211yesmaximal, characteristic, complemented
5#26041592C211yesmaximal, characteristic, complemented
6#26041590C211yesmaximal, characteristic, complemented
7#26041579C211yesmaximal, characteristic, complemented
8#26041576C211yesmaximal, characteristic, complemented
9#26041530C211yesmaximal, characteristic, complemented
10#26041530C211yesmaximal, characteristic, complemented
11C4×#15668434C211yesmaximal, characteristic, complemented
12#26041357C211yesmaximal, characteristic, complemented
13#26041322C211yesmaximal, characteristic, complemented
14#26041319C211yesmaximal, characteristic, complemented
15#553×C181C211yesmaximal, characteristic, complemented
16C2×#15668434C2211yescharacteristic
17C2×#15668433C2211yescharacteristic
18C2×#15668433C2211yescharacteristic
19#19153811—21no—
20#19153808C2211yescharacteristic
21#19153798—21no—
22#19153790C2211yescharacteristic
23#19153790C2211yescharacteristic
24#19153788—21no—
25C4×D724C2211yescharacteristic
26#19153776—21no—
27#19153775C2211yescharacteristic
28C2×C4⋊Dic181C2211yescharacteristic
29#19153749C2211yescharacteristic
30#19153749C2211yescharacteristic
31#19153749C2211yescharacteristic
32#19153749C2211yescharacteristic
33#19153749C2211yescharacteristic
34#19153747C2211yescharacteristic
35#19153747C2211yescharacteristic
36#19153747C2211yescharacteristic
37#19153747C2211yescharacteristic
38C4⋊#13089678C2211yescharacteristic
39#19153737C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44#19153736C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
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
59C2×D724C2311yescharacteristic
60C2×C22⋊D181—21no—
61C2×C22⋊D181—21no—
62C22×Dic181—21no—
63C2×C4×D181—21no—
64#15668434—22no—
65#15668433—22no—
66#15668433—22no—
67C2×#13089678C2311yescharacteristic
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C4⋊Dic181—21no—
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77C22⋊Dic181—21no—
78#15668426—21no—
79#15668426—21no—
80#15668426—21no—
81C4×Dic181—21no—
82C2×D4×C181—21no—
83C2×D4×C181—21no—
84C2×D4×C181D411yescharacteristic
85C2×D4×C181C2311yescharacteristic
86C22×C4×C181—21no—
87C22×C4×C181—21no—
88C22×C4×C181C2311yescharacteristic
89C22×C4×C181C2311yescharacteristic
90C4⋊C4×C181—21no—
91C4⋊C4×C181—21no—
92C4⋊C4×C181—21no—
93C4⋊C4×C181D411yescharacteristic
94C4⋊C4×C181C2311yescharacteristic
95C4⋊C4×C181C2311yescharacteristic
96C4⋊C4×C181C2311yescharacteristic
97C22⋊C4×C181—21no—
98C22⋊C4×C181—21no—
99C22⋊C4×C181—21no—
100C22⋊C4×C181—21no—
101C22⋊C4×C181D411yescharacteristic
102C22⋊C4×C181D411yescharacteristic
103C42×C181—21no—
104C42×C181C2311yescharacteristic
105C22×D181—21no—
106D724—21no—
107D724—21no—
108C22⋊D181—42no—
109C22⋊D181—81no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—81no—
114C4×D181—81no—
115#13089678—21no—
116#13089678—21no—
117#13089678—21no—
118#13089678#4112yes—
119C23×C181—21no—
120C23×C181C2×D411yescharacteristic
121C23×C181C2×D411yescharacteristic
122D4×C181—21no—
123D4×C181—21no—
124D4×C181—41no—
125D4×C181—42no—
126D4×C181—81no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—81no—
135C2×C4×C181—81no—
136C2×C4×C181C2×D411yescharacteristic
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2×D411yescharacteristic
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2411yescharacteristic
141C22×C181—21no—
142C22×C181—21no—
143C22×C181—21no—
144C22×C181—21no—
145C22×C181—21no—
146C22×C181—21no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181C22×D411yescharacteristic
151C2×D181—41no—
152C2×D181—41no—
153C2×D181—41no—
154C4×C181—21no—
155C4×C181—21no—
156C4×C181—21no—
157C4×C181—21no—
158C4×C181—41no—
159C4×C181—41no—
160C4×C181—41no—
161C4×C181C2×#4111yescharacteristic
162C4×C1812−1+411yescharacteristic
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—41no—
167C2×C181—41no—
168C2×C181—81no—
169C2×C181#54711yescharacteristic
170C2×C181#57511yescharacteristic
171C2×C181#57611yescharacteristic
172D181—81no—
173C181#335511yescharacteristic, complemented, Sylow
174#3355—1811nomaximal, Sylow
175#553—1811no—
176#553D18111yescharacteristic, complemented
177#499—1811no—
178#482—1811no—
179#482—1811no—
180#480—1811no—
181#480—1811no—
182#478—1811no—
183#478—1811no—
184#469—1811no—
185#469—1811no—
186C4×D8—1811no—
187#436—1811no—
188#428—1811no—
189#428—1811no—
190C2×D8—1811no—
191C2×M16—1811no—
192C2×M16—1811no—
193#126—21no—
194#126—3621no—
195#125—1811no—
196#125C2×D18111yescharacteristic
197#123—21no—
198#123—3621no—
199#121—21no—
200#121—3621no—
201#121—1811no—
202#121—1811no—
203#121C2×D18111yescharacteristic
204#121C2×D18111yescharacteristic
205C4×D4—21no—
206C4×D4—3621no—
207C4×D4—1811no—
208C4×D4C2×D18111yescharacteristic
209C4×D4C2×D18111yescharacteristic
210#117—1811no—
211#117C2×D18111yescharacteristic
212C2×C4⋊C4—1811no—
213C2×C4⋊C4C2×D18111yescharacteristic
214#107—1811no—
215#107—1811no—
216#107—1811no—
217#107—1811no—
218#107—1811no—
219#106—1811no—
220#106—1811no—
221#106—1811no—
222#106—1811no—
223C4⋊C8—1811no—
224#102—1811no—
225#102—1811no—
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230C22⋊C8—1811no—
231C22⋊C8—1811no—
232C4×C8—1811no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—3621no—
236C2×D4—3621no—
237C2×D4—1811no—
238C2×D4C22⋊D18111yescharacteristic
239C2×D4C22×D18111yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—3621no—
243C22×C4—3621no—
244C22×C4C22×D18111yescharacteristic
245C22×C4C22×D18111yescharacteristic
246D8—3622no—
247M16—3622no—
248M16—3622no—
249C2×C8—1811no—
250C2×C8—1811no—
251C2×C8—1811no—
252C2×C8—1811no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4—1811no—
262C4⋊C4C22⋊D18111yescharacteristic
263C4⋊C4C22×D18111yescharacteristic
264C4⋊C4C22×D18111yescharacteristic
265C4⋊C4C22×D18111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4C22⋊D18111yescharacteristic
275C22⋊C4C22⋊D18111yescharacteristic
276C42—21no—
277C42—3621no—
278C42C22×D18111yescharacteristic
279C23—21no—
280C23—3621no—
281C23C2×C22⋊D18111yescharacteristic
282C23C2×C22⋊D18111yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—3621no—
289D4—3621no—
290D4—14481no—
291D4—7242no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—14481no—
305C2×C4—14481no—
306C2×C4C2×C22⋊D18111yescharacteristic
307C2×C4C2×C22⋊D18111yescharacteristic
308C2×C4C2×C22⋊D18111yescharacteristic
309C2×C4C2×C22⋊D18111yescharacteristic
310C2×C4C23×D18111yescharacteristic
311C8—3621no—
312C8—3621no—
313C8—3621no—
314C8—1812no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—7241no—
325C22—7241no—
326C22—7241no—
327C22C22×C22⋊D18111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—7241no—
336C4—7241no—
337C4—7241no—
338C4#41×D18111yescharacteristic
339C4#1915386311yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—14481no—
344C2#2604192811yescharacteristic
345C2#2604207711yescharacteristic
346C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#553×C181C2
socleC22×C181C22×D4
hypercenter#553D181
hypocenterC181#3355
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. #26041975C2semidirect
2. #26041678C2semidirect
3. #26041603C2semidirect
4. #26041600C2semidirect
5. #26041592C2semidirect
6. #26041590C2semidirect
7. #26041579C2semidirect
8. #26041576C2semidirect
9. #26041530C2semidirect
10. #26041530C2semidirect
11. C4×#15668434C2semidirect
12. #26041357C2semidirect
13. #26041322C2semidirect
14. #26041319C2semidirect
15. #553×C181C2semidirect
173. C181#3355semidirect
176. #553D181semidirect

Maximal subgroups

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

subgroupindex
#260419752
#260416782
#260416032
#260416002
#260415922
#260415902
#260415792
#260415762
#260415302
C4×#156684342
#260413572
#260413222
#260413192
#553×C1812
#3355181