Finite Group Databasebeta

← #37545676

Subgroups — #37545676

Order 23168.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041925C211yesmaximal, characteristic, complemented
2#26041641C211yesmaximal, characteristic, complemented
3#26041609C211yesmaximal, characteristic, complemented
4#26041597C211yesmaximal, characteristic, complemented
5#26041566C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041494C211yesmaximal, characteristic, complemented
9#26041422C211yesmaximal, characteristic, complemented
10#26041412C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041278C211yesmaximal, characteristic, complemented
14C2×#19153736C211yesmaximal, characteristic, complemented
15#547×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×#15668437C2211yescharacteristic, complemented
19C2×#15668434C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668433C2211yescharacteristic, complemented
22C22×#13089678C2211yescharacteristic
23#19153804C2211yescharacteristic
24#19153801—21no—
25#19153795C2211yescharacteristic
26#19153790C2211yescharacteristic
27#19153789—21no—
28#19153784—21no—
29C4×D724C2211yescharacteristic
30C22⋊C4×D181—21no—
31#19153747C2211yescharacteristic, complemented
32#19153747C2211yescharacteristic, complemented
33#19153747C2211yescharacteristic, complemented
34C4⋊#13089678C2211yescharacteristic, complemented
35#19153739C2211yescharacteristic, complemented
36#19153739C2211yescharacteristic, complemented
37#19153739C2211yescharacteristic, complemented
38#19153737C2211yescharacteristic, complemented
39#19153736C2211yescharacteristic
40#19153736C2211yescharacteristic
41#19153736C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44#19153736C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46C22⋊#13089678C2211yescharacteristic, complemented
47#19153727C2211yescharacteristic, complemented
48C2×#41×C181—21no—
49C4⋊Q8×C181C2211yescharacteristic, complemented
50#123×C181—21no—
51#123×C181—21no—
52C22⋊Q8×C181—21no—
53#121×C181C2211yescharacteristic
54#121×C181C2211yescharacteristic, complemented
55C4×D4×C181C2211yescharacteristic
56C4×D4×C181C2211yescharacteristic, complemented
57C2×C4⋊C4×C181C2211yescharacteristic
58C2×C4⋊C4×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—22no—
61#15668449—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724—22no—
64C2×D724—21no—
65C2×D724—41no—
66C2×D724C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72#15668437—41no—
73#15668434—22no—
74#15668434—41no—
75#15668433—41no—
76C2×#13089678—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83C22⋊Dic181—21no—
84#15668426—21no—
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#41×C181—44no—
89C2×Q8×C181—21no—
90C2×D4×C181—21no—
91C2×D4×C181—21no—
92C2×D4×C181D411yescharacteristic
93C2×D4×C181C2311yescharacteristic
94C22×C4×C181—21no—
95C22×C4×C181—21no—
96C22×C4×C181—21no—
97C22×C4×C181C2311yescharacteristic
98C22×C4×C181C2311yescharacteristic
99C4⋊C4×C181—21no—
100C4⋊C4×C181—21no—
101C4⋊C4×C181—21no—
102C4⋊C4×C181D411yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181D411yescharacteristic
110C22⋊C4×C181D411yescharacteristic
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—42no—
115C22×D181—42no—
116C22×D181—81no—
117Dic362—21no—
118Dic362—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—42no—
123D724#4112yescomplemented
124C22⋊D181—42no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C4×D181—42no—
129C4×D181—81no—
130#13089678—21no—
131#13089678—21no—
132#13089678—21no—
133#13089678—21no—
134C23×C181—21no—
135C23×C181C2×D411yescharacteristic
136C23×C181C2×D411yescharacteristic
137Q8×C181—42no—
138D4×C181—22no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—42no—
142D4×C181—42no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—42no—
151C2×C4×C181—42no—
152C2×C4×C181—42no—
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2×D411yescharacteristic
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2411yescharacteristic
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181AGL(1,ℤ/8)12yes—
167C22×C181C22×D411yescharacteristic
168C2×D181—22no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—84no—
175C4×C181—21no—
176C4×C181—21no—
177C4×C181—21no—
178C4×C181—21no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181—41no—
182C4×C181C2×#4111yescharacteristic
183C4×C181H(5,𝔽2)11yescharacteristic
184Dic181—41no—
185Dic181—41no—
186C2×C181—22no—
187C2×C181—41no—
188C2×C181—81no—
189C2×C181#54611yescharacteristic
190C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C181#57711yescharacteristic
192D181—42no—
193D181—81no—
194C181#330611yescharacteristic, complemented, Sylow
195#3306—1811nomaximal, Sylow
196#547D18111yescharacteristic, complemented
197#546—1811no—
198#489—1811no—
199#483—1811no—
200#481—1811no—
201#476—1811no—
202#469—1811no—
203#465—1811no—
204#463—1811no—
205#449—1811no—
206#447—1811no—
207#442—1811no—
208#435—1811no—
209#417—1811no—
210C2×#102—1811no—
211C2×#41—21no—
212C2×#41—1811no—
213C22×D4—1811no—
214C2×SD16—1811no—
215C2×D8—1811no—
216C2×D8—1811no—
217C2×M16—1811no—
218C22×C8—1811no—
219C4⋊Q8C2×D18111yescharacteristic, complemented
220#124—1811no—
221#123—21no—
222#123—21no—
223#123—3621no—
224C22⋊Q8—21no—
225C22⋊Q8—1811no—
226#121—3621no—
227#121—1811no—
228#121C2×D18111yescharacteristic
229#121C2×D18111yescharacteristic, complemented
230#120—3621no—
231C4×D4—1811no—
232C4×D4C2×D18111yescharacteristic
233C4×D4C2×D18111yescharacteristic, complemented
234C2×C4⋊C4C2×D18111yescharacteristic
235C2×C4⋊C4C2×D18111yescharacteristic, complemented
236C2×C22⋊C4—3621no—
237#106—1811no—
238#106—1811no—
239#106—1811no—
240C4⋊C8—1811no—
241#103—1811no—
242#103—1811no—
243#103—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251C22⋊C8—1811no—
252C22⋊C8—1811no—
253#97—1811no—
254C24—3621no—
255#41—44no—
256#41—3622no—
257#41—7241no—
258C2×Q8—21no—
259C2×Q8—1811no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—3622no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—1811no—
267C2×D4—1811no—
268C2×D4—7241no—
269C2×D4C22⋊D18111yescharacteristic
270C2×D4C22×D18111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—3621no—
275C22×C4—3621no—
276C22×C4C22×D18111yescharacteristic
277C22×C4C22×D18111yescharacteristic
278SD16—7241no—
279D8—3622no—
280D8—7241no—
281M16—7241no—
282C2×C8—1811no—
283C2×C8—1811no—
284C2×C8—1811no—
285C2×C8—1811no—
286C2×C8—7241no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—3621no—
291C4⋊C4—1811no—
292C4⋊C4C22⋊D18111yescharacteristic
293C4⋊C4C22×D18111yescharacteristic
294C4⋊C4C22×D18111yescharacteristic
295C4⋊C4C22×D18111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4C22⋊D18111yescharacteristic
305C22⋊C4C22⋊D18111yescharacteristic
306C42C22×D18111yescharacteristic
307C23—21no—
308C23—3621no—
309C23—3621no—
310C23—14481no—
311C23—7242no—
312C23—7242no—
313C23C2×C22⋊D18111yescharacteristic
314C23C2×C22⋊D18111yescharacteristic
315Q8—42no—
316Q8—3621no—
317Q8—3621no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—3621no—
324D4—3621no—
325D4—3621no—
326D4—14481no—
327D4—1812no—
328D4—7242no—
329D4—7242no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—14481no—
343C2×C4—7242no—
344C2×C4C2×C22⋊D18111yescharacteristic
345C2×C4C2×C22⋊D18111yescharacteristic
346C2×C4C2×C22⋊D18111yescharacteristic
347C2×C4C2×C22⋊D18111yescharacteristic
348C2×C4C23×D18111yescharacteristic
349C8—3621no—
350C8—3621no—
351C8—3621no—
352C8—3621no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3622no—
362C22—14484no—
363C22—7241no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22#1915384212yes—
369C22C22×C22⋊D18111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—7241no—
378C4—7241no—
379C4#41×D18111yescharacteristic
380C4#1915386211yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—14481no—
385C2—7242no—
386C2#2604191711yescharacteristic
387C2C2×#1915384211yescharacteristic
388C2#2604208711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#547×C181C2
socleC22×C181C22×D4
hypercenter#547D181
hypocenterC181#3306
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #26041925C2semidirect
2. #26041641C2semidirect
3. #26041609C2semidirect
4. #26041597C2semidirect
5. #26041566C2semidirect
6. #26041530C2semidirect
7. #26041506C2semidirect
8. #26041494C2semidirect
9. #26041422C2semidirect
10. #26041412C2semidirect
11. #26041389C2semidirect
12. #26041351C2semidirect
13. #26041278C2semidirect
14. C2×#19153736C2semidirect
15. #547×C181C2semidirect
18. C2×#15668437C22semidirect
21. C2×#15668433C22semidirect
31. #19153747C22semidirect
32. #19153747C22semidirect
33. #19153747C22semidirect
34. C4⋊#13089678C22semidirect
35. #19153739C22semidirect
36. #19153739C22semidirect
37. #19153739C22semidirect
38. #19153737C22semidirect
46. C22⋊#13089678C22semidirect
47. #19153727C22semidirect
49. C4⋊Q8×C181C22semidirect
54. #121×C181C22semidirect
56. C4×D4×C181C22semidirect
58. C2×C4⋊C4×C181C22semidirect
123. D724#41semidirect
194. C181#3306semidirect
196. #547D181semidirect
219. C4⋊Q8C2×D181semidirect
229. #121C2×D181semidirect
233. C4×D4C2×D181semidirect
235. C2×C4⋊C4C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419252
#260416412
#260416092
#260415972
#260415662
#260415302
#260415062
#260414942
#260414222
#260414122
#260413892
#260413512
#260412782
C2×#191537362
#547×C1812
#3306181