Finite Group Databasebeta

← #37545822

Subgroups — #37545822

Order 23168.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041970C211yesmaximal, characteristic, complemented
2#26041933C211yesmaximal, characteristic
3#26041648C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041616C211yesmaximal, characteristic, complemented
6#26041579C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic, complemented
8#26041519C211yesmaximal, characteristic, complemented
9#26041489C211yesmaximal, characteristic, complemented
10#26041438C211yesmaximal, characteristic, complemented
11#26041438C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041277C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#440×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153816C2211yescharacteristic
23#19153810—21no—
24#19153808C2211yescharacteristic
25#19153806—21no—
26#19153801—21no—
27#19153800—21no—
28#19153800—21no—
29#19153796C2211yescharacteristic
30#19153796C2211yescharacteristic
31#19153792C2211yescharacteristic
32#19153792C2211yescharacteristic
33#19153790—21no—
34C4×D724C2211yescharacteristic
35#19153774C2211yescharacteristic
36#19153773—21no—
37C2×C4⋊Dic181—21no—
38C4⋊C4×D181C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153747C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—22no—
61#15668448—41no—
62#15668448—41no—
63C2×Dic362C2311yescharacteristic
64C2×Dic362C2311yescharacteristic
65C2×D724D411yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72C2×C4×D181C2311yescharacteristic
73#15668439—41no—
74#15668439—41no—
75#15668432—41no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C8×D181—41no—
79C4⋊Dic181—21no—
80C4⋊Dic181—21no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181D411yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101C22×C4×C181—21no—
102SD16×C181—22no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181C2×D411yescharacteristic
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362—21no—
117D724—41no—
118C22⋊D181—42no—
119C22⋊D181—42no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—42no—
125C2×Dic181—42no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—21no—
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—42no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136Q8×C181—21no—
137Q8×C181—21no—
138D4×C181—21no—
139D4×C181#4112yes—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—42no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—22no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181C22×D411yescharacteristic
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181C2×#4111yescharacteristic
165C4×C181H(5,𝔽2)11yescharacteristic
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—42no—
173C2×C181#54611yescharacteristic
174C2×C181#57511yescharacteristic
175C2×C181#57811yescharacteristic
176D181—41no—
177D181—41no—
178C181#331511yescharacteristic, complemented, Sylow
179#3315—1811nomaximal, Sylow
180#552—1811no—
181#547—1811no—
182#491—1811no—
183#485—1811no—
184#484—1811no—
185#478—1811no—
186#470—1811no—
187#467—1811no—
188#462—1811no—
189#452—1811no—
190#452—1811no—
191#440D18111yescharacteristic, complemented
192#435—1811no—
193#417—1811no—
194#416—1811no—
195C2×#41—1811no—
196C2×#41—1811no—
197C2×Q16—1811no—
198C2×Q16—1811no—
199C2×SD16C2×D18111yescharacteristic
200C2×M16—1811no—
201C22×C8—1811no—
202C4⋊Q8—1811no—
203#126—3621no—
204#125—3621no—
205#125—1811no—
206#123—3621no—
207#123—3621no—
208#123—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212C22⋊Q8—1811no—
213#121—3621no—
214C4×Q8C2×D18111yescharacteristic
215C4×D4—1811no—
216C4×D4C2×D18111yescharacteristic
217#117—3621no—
218#117—1811no—
219C2×C4⋊C4—3621no—
220C2×C4⋊C4—1811no—
221#107—1811no—
222#107C2×D18111yescharacteristic
223#106—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102—1811no—
234#102C2×D18111yescharacteristic
235C22⋊C8—1811no—
236C22⋊C8—1811no—
237#97C2×D18111yescharacteristic
238#41—3622no—
239#41—3622no—
240#41—7241no—
241#41—7241no—
242C2×Q8—1811no—
243C2×Q8—1811no—
244C2×Q8C22×D18111yescharacteristic
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—1811no—
248C2×D4C22×D18111yescharacteristic
249C22×C4—21no—
250C22×C4—3621no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4—1811no—
255Q16—7241no—
256Q16—7241no—
257SD16—22no—
258M16—7241no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—1811no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C4⋊C4C22×D18111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—1811no—
286C22⋊C4—1811no—
287C42—21no—
288C42—3621no—
289C42C22×D18111yescharacteristic
290C23—21no—
291C23—1811no—
292C23—1811no—
293Q8—21no—
294Q8—21no—
295Q8—3621no—
296Q8—3621no—
297Q8—3621no—
298Q8—3621no—
299D4—21no—
300D4—7241no—
301D4—7242no—
302D4—7242no—
303D4#1566844912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—1811no—
317C2×C4—1811no—
318C2×C4—7242no—
319C2×C4—7242no—
320C2×C4—7242no—
321C2×C4D4×D18111yescharacteristic
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—3621no—
332C22—3621no—
333C22—3621no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3621no—
344C4—3621no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4C2×#1566844911yescharacteristic
350C4#1915386211yescharacteristic
351C2—42no—
352C2—7241no—
353C2—7241no—
354C2#2604192511yescharacteristic
355C2#2604207511yescharacteristic
356C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#440×C181C2
socleC22×C181C22×D4
prime radical#26041933C2
hypercenter#440D181
hypocenterC181#3315
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #26041970C2semidirect
3. #26041648C2semidirect
4. #26041622C2semidirect
5. #26041616C2semidirect
6. #26041579C2semidirect
7. #26041536C2semidirect
8. #26041519C2semidirect
9. #26041489C2semidirect
10. #26041438C2semidirect
11. #26041438C2semidirect
12. #26041352C2semidirect
13. #26041277C2semidirect
14. #26041272C2semidirect
15. #440×C181C2semidirect
178. C181#3315semidirect
191. #440D181semidirect

Maximal subgroups

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

subgroupindex
#260419702
#260419332
#260416482
#260416222
#260416162
#260415792
#260415362
#260415192
#260414892
#260414382
#260413522
#260412772
#260412722
#440×C1812
#3315181