Finite Group Databasebeta

← #37544976

Subgroups — #37544976

Order 23168.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041907C211yesmaximal, characteristic, complemented
2#26041884C211yesmaximal, characteristic
3#26041688C211yesmaximal, characteristic, complemented
4#26041681C211yesmaximal, characteristic, complemented
5#26041644C211yesmaximal, characteristic, complemented
6#26041626C211yesmaximal, characteristic, complemented
7#26041604C211yesmaximal, characteristic, complemented
8#26041604C211yesmaximal, characteristic, complemented
9#26041598C211yesmaximal, characteristic, complemented
10#26041593C211yesmaximal, characteristic, complemented
11#26041580C211yesmaximal, characteristic, complemented
12#26041580C211yesmaximal, characteristic, complemented
13#26041570C211yesmaximal, characteristic, complemented
14#26041560C211yesmaximal, characteristic, complemented
15#433×C181C211yesmaximal, characteristic, complemented
16#19153816C2211yescharacteristic
17#19153816C2211yescharacteristic
18#19153815—21no—
19#19153813C2211yescharacteristic
20#19153808C2211yescharacteristic
21#19153808C2211yescharacteristic
22#19153808C2211yescharacteristic
23#19153807—21no—
24#19153801—21no—
25#19153801—21no—
26#19153793—21no—
27#19153793—21no—
28#19153790C2211yescharacteristic
29#19153790C2211yescharacteristic
30#19153789—21no—
31#19153789—21no—
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34#19153775C2211yescharacteristic
35C2×C4⋊Dic181C2211yescharacteristic
36#19153750C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153748C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153738C2211yescharacteristic
52#117×C181C2211yescharacteristic
53C4⋊C8×C181C2211yescharacteristic
54C4⋊C8×C181C2211yescharacteristic
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57#97×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C22×C4×C181C2311yescharacteristic
92C2×C8×C181C2311yescharacteristic
93C2×C8×C181C2311yescharacteristic
94C2×C8×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C4⋊C4×C181D411yescharacteristic
97C4⋊C4×C181D411yescharacteristic
98C22⋊C4×C181D411yescharacteristic
99C22⋊C4×C181D411yescharacteristic
100C42×C181C2311yescharacteristic
101C42×C181C2311yescharacteristic
102C22×D181—21no—
103C22×D181—21no—
104Dic362—81no—
105Dic362—81no—
106D724—21no—
107D724—21no—
108D724—21no—
109D724—21no—
110D724—81no—
111D724—81no—
112C22⋊D181—81no—
113C22⋊D181—81no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—81no—
121C4×D181—81no—
122C4×D181—81no—
123C23×C181C2×D411yescharacteristic
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181C2×D411yescharacteristic
127C2×C4×C181C2×D411yescharacteristic
128C2×C4×C181C2×D411yescharacteristic
129C2×C4×C181C2×D411yescharacteristic
130C2×C4×C181C2×D411yescharacteristic
131C2×C4×C181C2411yescharacteristic
132C8×C181—21no—
133C8×C181—21no—
134C8×C181—21no—
135C8×C181—21no—
136C22×C181—21no—
137C22×C181—21no—
138C22×C181—21no—
139C22×C181C22×D411yescharacteristic
140C2×D181—41no—
141C2×D181—41no—
142C2×D181—41no—
143C2×D181—41no—
144C2×D181—41no—
145C2×D181—41no—
146C4×C181—21no—
147C4×C181—21no—
148C4×C181—21no—
149C4×C181—21no—
150C4×C181—21no—
151C4×C1812−1+411yescharacteristic
152C4×C1812−1+411yescharacteristic
153Dic181—41no—
154Dic181—41no—
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159C2×C181—41no—
160C2×C181#53611yescharacteristic
161C2×C181#57611yescharacteristic
162C2×C181#57711yescharacteristic
163D181—81no—
164D181—81no—
165C181#324111yescharacteristic, complemented, Sylow
166#3241—1811nomaximal, Sylow
167#544—1811no—
168#540—1811no—
169#501—1811no—
170#499—1811no—
171#490—1811no—
172#486—1811no—
173#482—1811no—
174#482—1811no—
175#481—1811no—
176#480—1811no—
177#478—1811no—
178#478—1811no—
179#476—1811no—
180#474—1811no—
181#433D18111yescharacteristic, complemented
182C4⋊Q8—3621no—
183C4⋊Q8—1811no—
184C4⋊Q8—1811no—
185#127—1811no—
186#125—3621no—
187#125—1811no—
188#125—1811no—
189#125—1811no—
190#123—3621no—
191#123—3621no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194#121—3621no—
195#121—3621no—
196#121—1811no—
197#121—1811no—
198C4×D4—1811no—
199C4×D4—1811no—
200#117—1811no—
201#117C2×D18111yescharacteristic
202C2×C4⋊C4—1811no—
203#107—1811no—
204#107—1811no—
205#107—1811no—
206#107—1811no—
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211C4⋊C8C2×D18111yescharacteristic
212C4⋊C8C2×D18111yescharacteristic
213#102—1811no—
214#102—1811no—
215#102—1811no—
216#102—1811no—
217#102—1811no—
218#102—1811no—
219#102—1811no—
220#102—1811no—
221C22⋊C8C2×D18111yescharacteristic
222C22⋊C8C2×D18111yescharacteristic
223#97C2×D18111yescharacteristic
224C4×C8C2×D18111yescharacteristic
225C2×Q8—3621no—
226C2×Q8—3621no—
227C2×D4—3621no—
228C2×D4—3621no—
229C2×D4—3621no—
230C2×D4—3621no—
231C2×D4—1811no—
232C2×D4—1811no—
233C22×C4—3621no—
234C22×C4—3621no—
235C22×C4—3621no—
236C22×C4C22×D18111yescharacteristic
237C2×C8C22×D18111yescharacteristic
238C2×C8C22×D18111yescharacteristic
239C2×C8C22×D18111yescharacteristic
240C2×C8C22×D18111yescharacteristic
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4—1811no—
256C4⋊C4D72411yescharacteristic
257C4⋊C4D72411yescharacteristic
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4D72411yescharacteristic
264C22⋊C4D72411yescharacteristic
265C42—3621no—
266C42C22×D18111yescharacteristic
267C42C22×D18111yescharacteristic
268C23—3621no—
269C23—3621no—
270C23C2×D72411yescharacteristic
271Q8—14481no—
272Q8—14481no—
273D4—3621no—
274D4—3621no—
275D4—3621no—
276D4—3621no—
277D4—14481no—
278D4—14481no—
279D4—14481no—
280D4—14481no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—14481no—
290C2×C4—14481no—
291C2×C4—14481no—
292C2×C4C2×D72411yescharacteristic
293C2×C4C2×D72411yescharacteristic
294C2×C4C2×D72411yescharacteristic
295C2×C4C2×D72411yescharacteristic
296C2×C4C2×D72411yescharacteristic
297C2×C4C23×D18111yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—7241no—
306C22—7241no—
307C22—7241no—
308C22—7241no—
309C22—7241no—
310C22—7241no—
311C22C22×D72411yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—7241no—
318C4—7241no—
319C4—7241no—
320C4—7241no—
321C4—7241no—
322C4—7241no—
323C4#1915386311yescharacteristic
324C4#1915386311yescharacteristic
325C2—41no—
326C2—14481no—
327C2—14481no—
328C2#2604185511yescharacteristic
329C2#2604208411yescharacteristic
330C2#2604209111yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#433×C181C2
socleC22×C181C22×D4
prime radical#26041884C2
hypercenter#433D181
hypocenterC181#3241
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #26041907C2semidirect
3. #26041688C2semidirect
4. #26041681C2semidirect
5. #26041644C2semidirect
6. #26041626C2semidirect
7. #26041604C2semidirect
8. #26041604C2semidirect
9. #26041598C2semidirect
10. #26041593C2semidirect
11. #26041580C2semidirect
12. #26041580C2semidirect
13. #26041570C2semidirect
14. #26041560C2semidirect
15. #433×C181C2semidirect
165. C181#3241semidirect
181. #433D181semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260418842
#260416882
#260416812
#260416442
#260416262
#260416042
#260415982
#260415932
#260415802
#260415702
#260415602
#433×C1812
#3241181