Finite Group Databasebeta

← #37545574

Subgroups — #37545574

Order 23168.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041973C211yesmaximal, characteristic, complemented
2#26041926C211yesmaximal, characteristic, complemented
3#26041632C211yesmaximal, characteristic, complemented
4#26041616C211yesmaximal, characteristic, complemented
5#26041578C211yesmaximal, characteristic, complemented
6#26041513C211yesmaximal, characteristic, complemented
7#26041509C211yesmaximal, characteristic, complemented
8#26041493C211yesmaximal, characteristic, complemented
9#26041426C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041361C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13#26041273C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668438C2211yescharacteristic, complemented
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C22×#13089678C2211yescharacteristic, complemented
22C2×C8×D181C2211yescharacteristic
23#19153810—21no—
24#19153807C2211yescharacteristic, complemented
25#19153803C2211yescharacteristic
26#19153798—21no—
27#19153798—21no—
28#19153796C2211yescharacteristic
29#19153791C2211yescharacteristic
30#19153790C2211yescharacteristic, complemented
31#19153789—21no—
32#19153787—21no—
33#19153784—21no—
34C4×D724—21no—
35#19153778C2211yescharacteristic
36#19153778C2211yescharacteristic, complemented
37C4×C22⋊D181C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39C22⋊C4×D181—21no—
40#19153749C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—22no—
61#15668449—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70D4×D181—22no—
71D4×D181—41no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77#15668438—41no—
78D1448—22no—
79#15668434—41no—
80C2×#13089678—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181—21no—
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181D411yescharacteristic
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426D411yescharacteristic
99C4×Dic181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117Dic362—21no—
118Dic362—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—42no—
123D724#4112yes—
124C22⋊D181—22no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—81no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—42no—
136C4×D181—81no—
137C4×D181—81no—
138C4×D181—81no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181C2×D411yescharacteristic
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—81no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—22no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—84no—
171C2×D181#13512yes—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181—41no—
176C4×C181C2×#4111yescharacteristic
177C4×C181H(5,𝔽2)11yescharacteristic
178Dic181—21no—
179Dic181—21no—
180Dic181—21no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—41no—
184C2×C181—81no—
185C2×C181#54611yescharacteristic
186C2×C181C2×#13511yescharacteristic
187C2×C181#57611yescharacteristic
188D181—22no—
189D181—42no—
190D181—81no—
191C181#329711yescharacteristic, complemented, Sylow
192#3297—1811nomaximal, Sylow
193#553—1811no—
194#546—1811no—
195#488—1811no—
196#484—1811no—
197#482D18111yescharacteristic, complemented
198#478—1811no—
199#466—1811no—
200#465—1811no—
201#463—1811no—
202#449—1811no—
203#447—1811no—
204C4×D8—1811no—
205C8×D4—1811no—
206#416—1811no—
207C2×#102—1811no—
208C2×#41—1811no—
209C22×D4—1811no—
210C2×SD16—1811no—
211C2×D8—1811no—
212C2×D8—1811no—
213C22×C8—1811no—
214C22×C8—1811no—
215#126—3621no—
216#125—1811no—
217#124—1811no—
218#123—3621no—
219#123—3621no—
220C22⋊Q8—1811no—
221#121—3621no—
222#121—3621no—
223#121—1811no—
224#121—1811no—
225#121C2×D18111yescharacteristic
226#120—3621no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4—1811no—
231#117C2×D18111yescharacteristic, complemented
232C2×C4⋊C4—1811no—
233C2×C22⋊C4—3621no—
234#107—1811no—
235#107C2×D18111yescharacteristic, complemented
236#106C2×D18111yescharacteristic, complemented
237C4⋊C8—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102C2×D18111yescharacteristic
247#102C2×D18111yescharacteristic
248C22⋊C8—1811no—
249C22⋊C8C2×D18111yescharacteristic, complemented
250C4×C8—1811no—
251C24—3621no—
252#41—3622no—
253#41—7241no—
254C2×Q8—1811no—
255C2×D4—21no—
256C2×D4—3621no—
257C2×D4—3622no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—1811no—
262C2×D4—1811no—
263C2×D4—1811no—
264C2×D4—7241no—
265C2×D4C22×D18111yescharacteristic
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4C22×D18111yescharacteristic
272SD16—7241no—
273D8—3622no—
274D8—7241no—
275C2×C8—1811no—
276C2×C8—1811no—
277C2×C8—7241no—
278C2×C8—7241no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4C22×D18111yescharacteristic
288C4⋊C4C22×D18111yescharacteristic
289C4⋊C4C22×D18111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—1811no—
300C22⋊C4—1811no—
301C42—21no—
302C42—1811no—
303C23—21no—
304C23—3621no—
305C23—3621no—
306C23—14481no—
307C23—1811no—
308C23—7242no—
309C23—7242no—
310C23D4×D18111yescharacteristic
311Q8—3621no—
312Q8—3621no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—3622no—
317D4—3621no—
318D4—3621no—
319D4—3621no—
320D4—14481no—
321D4—1812no—
322D4—7242no—
323D4—7242no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—14481no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—7242no—
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3621no—
354C22—3621no—
355C22—3622no—
356C22—14484no—
357C22—1812no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22—7241no—
362C22—7241no—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3621no—
369C4—3621no—
370C4—3621no—
371C4—7241no—
372C4—7241no—
373C4#41×D18111yescharacteristic
374C4#1915386211yescharacteristic
375C2—41no—
376C2—81no—
377C2—3622no—
378C2—14481no—
379C2—7242no—
380C2#2604192111yescharacteristic
381C2#135×D18111yescharacteristic
382C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
hypercenter#482D181
hypocenterC181#3297
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26041973C2semidirect
2. #26041926C2semidirect
3. #26041632C2semidirect
4. #26041616C2semidirect
5. #26041578C2semidirect
6. #26041513C2semidirect
7. #26041509C2semidirect
8. #26041493C2semidirect
9. #26041426C2semidirect
10. #26041414C2semidirect
11. #26041361C2semidirect
12. #26041342C2semidirect
13. #26041273C2semidirect
14. #102×D181C2semidirect
15. #482×C181C2semidirect
18. C2×#15668438C22semidirect
21. C22×#13089678C22semidirect
24. #19153807C22semidirect
30. #19153790C22semidirect
36. #19153778C22semidirect
40. #19153749C22semidirect
41. #19153745C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
44. #19153739C22semidirect
49. #19153736C22semidirect
51. C8×Dic181C22semidirect
53. #117×C181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
58. C22⋊C8×C181C22semidirect
191. C181#3297semidirect
197. #482D181semidirect
231. #117C2×D181semidirect
235. #107C2×D181semidirect
236. #106C2×D181semidirect
249. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419732
#260419262
#260416322
#260416162
#260415782
#260415132
#260415092
#260414932
#260414262
#260414142
#260413612
#260413422
#260412732
#102×D1812
#482×C1812
#3297181