Finite Group Databasebeta

← #37545667

Subgroups — #37545667

Order 23168.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041992C211yesmaximal, characteristic, complemented
2#26041948C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041603C211yesmaximal, characteristic, complemented
5#26041601C211yesmaximal, characteristic, complemented
6#26041572C211yesmaximal, characteristic, complemented
7#26041515C211yesmaximal, characteristic, complemented
8#26041514C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041427C211yesmaximal, characteristic, complemented
11#26041424C211yesmaximal, characteristic, complemented
12#26041364C211yesmaximal, characteristic, complemented
13C8×C22⋊D181C211yesmaximal, characteristic, complemented
14#26041274C211yesmaximal, characteristic, complemented
15#416×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153812—21no—
23#19153812C2211yescharacteristic
24#19153804—21no—
25#19153802—21no—
26#19153791C2211yescharacteristic
27#19153790—21no—
28#19153790C2211yescharacteristic
29#19153790C2211yescharacteristic
30#19153789—21no—
31#19153787—21no—
32#19153787C2211yescharacteristic
33Q8×Dic181C2211yescharacteristic
34#19153778C2211yescharacteristic
35C4×C22⋊D181—21no—
36C4×C22⋊D181C2211yescharacteristic
37#19153774C2211yescharacteristic
38#19153773—21no—
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54#117×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—41no—
61C2×Dic362—21no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668436—22no—
76D1448—41no—
77#15668434—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—41no—
81C4⋊Dic181—21no—
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428D411yescharacteristic
86C22⋊Dic181—21no—
87C22⋊Dic181D411yescharacteristic
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97#41×C181—22no—
98#41×C181—41no—
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104C2×C8×C181—41no—
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C42×C181—21no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181C2×D411yescharacteristic
114Dic362—81no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—42no—
120D724—81no—
121C22⋊D181—22no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C22⋊D181—81no—
126C22⋊D181—81no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135C4×D181—42no—
136#13089678—21no—
137#13089678—21no—
138C23×C181—21no—
139C23×C181C2×D411yescharacteristic
140Q8×C181—21no—
141Q8×C181#4112yes—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—42no—
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×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—21no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—22no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181C2×#4111yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—41no—
180Dic181—41no—
181Dic181#13512yes—
182C2×C181—41no—
183C2×C181—81no—
184C2×C181#54611yescharacteristic
185C2×C181C2×#13511yescharacteristic
186C2×C181#57611yescharacteristic
187D181—41no—
188D181—81no—
189D181—81no—
190C181#330511yescharacteristic, complemented, Sylow
191#3305—1811nomaximal, Sylow
192#555—1811no—
193#550—1811no—
194#486—1811no—
195#482—1811no—
196#482—1811no—
197#477—1811no—
198#466—1811no—
199#466—1811no—
200#459—1811no—
201#449—1811no—
202#449—1811no—
203C4×SD16—1811no—
204C8×D4—1811no—
205#416—1811no—
206#416D18111yescharacteristic, complemented
207C2×#41—1811no—
208C2×#41C2×D18111yescharacteristic
209C2×SD16—1811no—
210C2×D8—1811no—
211C2×D8—1811no—
212C22×C8—1811no—
213C22×C8C2×D18111yescharacteristic
214C4⋊Q8—1811no—
215#127—3621no—
216#127—1811no—
217#124—3621no—
218#124—3621no—
219#121—3621no—
220#121—3621no—
221#121—3621no—
222#121—1811no—
223#121—1811no—
224#121—1811no—
225#121—1811no—
226C4×Q8—1811no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230#117—3621no—
231#117—1811no—
232#117C2×D18111yescharacteristic
233#107—1811no—
234#107—1811no—
235#106—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103C2×D18111yescharacteristic
239#103C2×D18111yescharacteristic
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102C2×D18111yescharacteristic
246#102C2×D18111yescharacteristic
247C22⋊C8—1811no—
248C22⋊C8—1811no—
249C4×C8—1811no—
250#41—22no—
251#41—41no—
252#41—3622no—
253#41—7241no—
254C2×Q8—3621no—
255C2×Q8C22×D18111yescharacteristic
256C2×D4—21no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—1811no—
265C2×D4—1811no—
266C2×D4—1811no—
267C2×D4C22×D18111yescharacteristic
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—1811no—
272C22×C4C22×D18111yescharacteristic
273SD16—3622no—
274D8—7241no—
275D8—7241no—
276C2×C8—41no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8—7241no—
280C2×C8C22×D18111yescharacteristic
281C2×C8C22×D18111yescharacteristic
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4C22×D18111yescharacteristic
288C4⋊C4C22×D18111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—1811no—
297C22⋊C4—1811no—
298C42—21no—
299C42—3621no—
300C42—3621no—
301C42—1811no—
302C23—21no—
303C23—3621no—
304C23—3621no—
305C23—1811no—
306C23D4×D18111yescharacteristic
307Q8—21no—
308Q8—14481no—
309Q8#1566844912yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—3622no—
314D4—3621no—
315D4—3621no—
316D4—3621no—
317D4—3621no—
318D4—14481no—
319D4—14481no—
320D4—14481no—
321D4—14481no—
322D4—14481no—
323D4—7242no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—1811no—
336C2×C4—1811no—
337C2×C4—1811no—
338C2×C4—7242no—
339C2×C4—7242no—
340C2×C4D4×D18111yescharacteristic
341C2×C4C23×D18111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3621no—
345C8—3621no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3621no—
353C22—3621no—
354C22—3621no—
355C22—7241no—
356C22—7241no—
357C22—7241no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C2×D4×D18111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—3621no—
367C4—3621no—
368C4—1812no—
369C4—7241no—
370C4—7241no—
371C4C2×#1566844911yescharacteristic
372C4#1915386111yescharacteristic
373C2—41no—
374C2—81no—
375C2—14481no—
376C2—14481no—
377C2—7241no—
378C2#2604191911yescharacteristic
379C2#135×D18111yescharacteristic
380C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#416×C181C2
socleC22×C181C22×D4
hypercenter#416D181
hypocenterC181#3305
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #26041992C2semidirect
2. #26041948C2semidirect
3. #26041624C2semidirect
4. #26041603C2semidirect
5. #26041601C2semidirect
6. #26041572C2semidirect
7. #26041515C2semidirect
8. #26041514C2semidirect
9. #26041473C2semidirect
10. #26041427C2semidirect
11. #26041424C2semidirect
12. #26041364C2semidirect
13. C8×C22⋊D181C2semidirect
14. #26041274C2semidirect
15. #416×C181C2semidirect
190. C181#3305semidirect
206. #416D181semidirect

Maximal subgroups

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

subgroupindex
#260419922
#260419482
#260416242
#260416032
#260416012
#260415722
#260415152
#260415142
#260414732
#260414272
#260414242
#260413642
C8×C22⋊D1812
#260412742
#416×C1812
#3305181