Finite Group Databasebeta

← #37546322

Subgroups — #37546322

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#26041981C211yesmaximal, characteristic, complemented
2#26041976C211yesmaximal, characteristic, complemented
3#26041679C211yesmaximal, characteristic, complemented
4#26041602C211yesmaximal, characteristic, complemented
5#26041600C211yesmaximal, characteristic, complemented
6#26041591C211yesmaximal, characteristic, complemented
7#26041590C211yesmaximal, characteristic, complemented
8#26041581C211yesmaximal, characteristic, complemented
9#26041577C211yesmaximal, characteristic, complemented
10#26041529C211yesmaximal, characteristic, complemented
11D8×Dic181C211yesmaximal, characteristic, complemented
12#26041355C211yesmaximal, characteristic, complemented
13#26041321C211yesmaximal, characteristic, complemented
14#26041318C211yesmaximal, characteristic, complemented
15#469×C181C211yesmaximal, characteristic, complemented
16C2×#15668432C2211yescharacteristic
17#19153809—21no—
18#19153809—21no—
19#19153807C2211yescharacteristic
20#19153807C2211yescharacteristic
21#19153800—21no—
22#19153797—21no—
23#19153788—21no—
24#19153787—21no—
25#19153787C2211yescharacteristic
26#19153787C2211yescharacteristic
27D4×Dic181—21no—
28D4×Dic181C2211yescharacteristic
29D4×Dic181C2211yescharacteristic
30C4×C22⋊D181C2211yescharacteristic
31#19153776—21no—
32#19153775C2211yescharacteristic
33#19153774C2211yescharacteristic
34C2×C4⋊Dic181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36#19153750C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×D8×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×C22⋊D181—21no—
60C2×C22⋊D181—21no—
61C2×C22⋊D181D411yescharacteristic
62C22×Dic181—21no—
63C22×Dic181—21no—
64C22×Dic181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67#15668432—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428D411yescharacteristic
81C22⋊Dic181—21no—
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426D411yescharacteristic
89C4×Dic181—21no—
90C4×Dic181—21no—
91C4×Dic181C2311yescharacteristic
92C2×D4×C181—21no—
93C2×D4×C181—21no—
94C2×D4×C181C2311yescharacteristic
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181C2311yescharacteristic
97D8×C181—22no—
98M16×C181—22no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C22×D181C2×D411yescharacteristic
106C22⋊D181—41no—
107C22⋊D181—42no—
108C22⋊D181—81no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—81no—
114C2×Dic181—81no—
115C2×Dic181—81no—
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C4×D181—21no—
120C4×D181—21no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124C23×C181—21no—
125C23×C181—21no—
126C23×C181C2×D411yescharacteristic
127D4×C181—21no—
128D4×C181—21no—
129D4×C181—21no—
130D4×C181—21no—
131D4×C181—42no—
132D4×C181—81no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181C2×D411yescharacteristic
138C2×C4×C181C2411yescharacteristic
139C8×C181—21no—
140C8×C181#4112yes—
141C22×C181—21no—
142C22×C181—21no—
143C22×C181—21no—
144C22×C181—41no—
145C22×C181—41no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181C22×D411yescharacteristic
151C2×D181—21no—
152C2×D181—21no—
153C2×D181—21no—
154C4×C181—21no—
155C4×C181—41no—
156C4×C181—41no—
157C4×C181C2×#4111yescharacteristic
158C4×C1812−1+411yescharacteristic
159Dic181—21no—
160Dic181—21no—
161Dic181—21no—
162Dic181—41no—
163Dic181—41no—
164Dic181—41no—
165Dic181—41no—
166C2×C181—41no—
167C2×C181—81no—
168C2×C181—81no—
169C2×C181#54711yescharacteristic
170C2×C181#57511yescharacteristic
171C2×C181#57611yescharacteristic
172D181—41no—
173C181#335511yescharacteristic, complemented, Sylow
174#3355—1811nomaximal, Sylow
175#553—1811no—
176#553—1811no—
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#469D18111yescharacteristic, complemented
186C4×D8—1811no—
187#436—1811no—
188#428—1811no—
189#428—1811no—
190C2×D8C2×D18111yescharacteristic
191C2×M16—1811no—
192C2×M16C2×D18111yescharacteristic
193#126—3621no—
194#126—3621no—
195#125—1811no—
196#125—1811no—
197#123—3621no—
198#123—3621no—
199#121—3621no—
200#121—3621no—
201#121—1811no—
202#121—1811no—
203#121C2×D18111yescharacteristic
204#121C2×D18111yescharacteristic
205C4×D4—3621no—
206C4×D4—3621no—
207C4×D4—1811no—
208C4×D4—1811no—
209C4×D4—1811no—
210#117—1811no—
211#117—1811no—
212C2×C4⋊C4—1811no—
213C2×C4⋊C4—1811no—
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#106C2×D18111yescharacteristic
223C4⋊C8—1811no—
224#102—1811no—
225#102—1811no—
226#102—1811no—
227#102—1811no—
228#102C2×D18111yescharacteristic
229#102C2×D18111yescharacteristic
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—3621no—
241C22×C4—3621no—
242C22×C4—3621no—
243C22×C4—3621no—
244C22×C4—1811no—
245C22×C4C22×D18111yescharacteristic
246D8—22no—
247M16—22no—
248M16—3622no—
249C2×C8—1811no—
250C2×C8—1811no—
251C2×C8C22×D18111yescharacteristic
252C2×C8C22×D18111yescharacteristic
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—3621no—
256C4⋊C4—3621no—
257C4⋊C4—3621no—
258C4⋊C4—3621no—
259C4⋊C4—1811no—
260C4⋊C4—1811no—
261C4⋊C4—1811no—
262C4⋊C4—1811no—
263C4⋊C4—1811no—
264C4⋊C4C22×D18111yescharacteristic
265C4⋊C4C22×D18111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—3621no—
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—1811no—
275C22⋊C4—1811no—
276C42—3621no—
277C42—3621no—
278C42—1811no—
279C23—21no—
280C23—21no—
281C23—1811no—
282C23D4×D18111yescharacteristic
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—14481no—
290D4—7241no—
291D4—7242no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—3621no—
300C2×C4—3621no—
301C2×C4—3621no—
302C2×C4—14481no—
303C2×C4—14481no—
304C2×C4—14481no—
305C2×C4—14481no—
306C2×C4—1811no—
307C2×C4—1811no—
308C2×C4—1811no—
309C2×C4D4×D18111yescharacteristic
310C2×C4C23×D18111yescharacteristic
311C8—21no—
312C8—3621no—
313C8—3621no—
314C8#1566844812yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—3621no—
325C22—3621no—
326C22—3621no—
327C22C2×D4×D18111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—3621no—
332C4—3621no—
333C4—3621no—
334C4—7241no—
335C4—7241no—
336C4—7241no—
337C4—7241no—
338C4C2×#1566844811yescharacteristic
339C4#1915386311yescharacteristic
340C2—41no—
341C2—81no—
342C2—81no—
343C2—7241no—
344C2#2604192911yescharacteristic
345C2#2604207511yescharacteristic
346C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#469×C181C2
socleC22×C181C22×D4
hypercenter#469D181
hypocenterC181#3355
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #26041981C2semidirect
2. #26041976C2semidirect
3. #26041679C2semidirect
4. #26041602C2semidirect
5. #26041600C2semidirect
6. #26041591C2semidirect
7. #26041590C2semidirect
8. #26041581C2semidirect
9. #26041577C2semidirect
10. #26041529C2semidirect
11. D8×Dic181C2semidirect
12. #26041355C2semidirect
13. #26041321C2semidirect
14. #26041318C2semidirect
15. #469×C181C2semidirect
173. C181#3355semidirect
185. #469D181semidirect

Maximal subgroups

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

subgroupindex
#260419812
#260419762
#260416792
#260416022
#260416002
#260415912
#260415902
#260415812
#260415772
#260415292
D8×Dic1812
#260413552
#260413212
#260413182
#469×C1812
#3355181