Finite Group Databasebeta

← #37545664

Subgroups — #37545664

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#26041993C211yesmaximal, characteristic, complemented
2#26041948C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041572C211yesmaximal, characteristic, complemented
7#26041513C211yesmaximal, characteristic, complemented
8#26041512C211yesmaximal, characteristic, complemented
9#26041472C211yesmaximal, characteristic, complemented
10#26041423C211yesmaximal, characteristic, complemented
11SD16×Dic181C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13#26041275C211yesmaximal, characteristic, complemented
14#26041274C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668434C2211yescharacteristic
18C22×#13089678C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153812—21no—
22#19153812C2211yescharacteristic
23#19153803—21no—
24#19153802—21no—
25#19153790—21no—
26#19153790C2211yescharacteristic
27#19153788—21no—
28#19153787—21no—
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31Q8×Dic181C2211yescharacteristic
32D4×Dic181C2211yescharacteristic
33C4×C22⋊D181—21no—
34C4×C22⋊D181C2211yescharacteristic
35#19153775C2211yescharacteristic
36#19153774C2211yescharacteristic
37#19153772—21no—
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—41no—
61C2×Dic362—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C22×Dic181—21no—
71C2×C4×D181—21no—
72C2×C4×D181C2311yescharacteristic
73#15668434—41no—
74C2×#13089678—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—41no—
78C4⋊Dic181—21no—
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428D411yescharacteristic
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181D411yescharacteristic
89#15668426—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96#41×C181—22no—
97#41×C181—41no—
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105SD16×C181—22no—
106D8×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181—21no—
112C22×D181C2×D411yescharacteristic
113Dic362—81no—
114D724—21no—
115D724—21no—
116D724—42no—
117C22⋊D181—22no—
118C22⋊D181—42no—
119C22⋊D181—81no—
120C22⋊D181—81no—
121C22⋊D181—81no—
122C22⋊D181—81no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—42no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—42no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136C23×C181—21no—
137C23×C181C2×D411yescharacteristic
138Q8×C181—21no—
139Q8×C181#4112yes—
140D4×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—42no—
145D4×C181—81no—
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×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181C22×D411yescharacteristic
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—22no—
173C4×C181—41no—
174C4×C181C2×#4111yescharacteristic
175C4×C181H(5,𝔽2)11yescharacteristic
176Dic181—21no—
177Dic181—21no—
178Dic181—41no—
179Dic181—41no—
180Dic181—41no—
181Dic181#13512yes—
182C2×C181—41no—
183C2×C181—81no—
184C2×C181—81no—
185C2×C181#54611yescharacteristic
186C2×C181C2×#13511yescharacteristic
187C2×C181#57611yescharacteristic
188D181—41no—
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#449D18111yescharacteristic, complemented
203C4×SD16—1811no—
204C8×D4—1811no—
205#416—1811no—
206#416—1811no—
207C2×#41—1811no—
208C2×#41C2×D18111yescharacteristic
209C2×SD16C2×D18111yescharacteristic
210C2×D8—1811no—
211C2×D8C2×D18111yescharacteristic
212C22×C8—1811no—
213C22×C8—1811no—
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#121C2×D18111yescharacteristic
226C4×Q8—1811no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230#117—3621no—
231#117—1811no—
232#117—1811no—
233#107—1811no—
234#107—1811no—
235#106—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103—1811no—
239#103C2×D18111yescharacteristic
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102C2×D18111yescharacteristic
247C22⋊C8—1811no—
248C22⋊C8C2×D18111yescharacteristic
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—21no—
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×D4C22×D18111yescharacteristic
267C2×D4C22×D18111yescharacteristic
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—1811no—
272C22×C4C22×D18111yescharacteristic
273SD16—22no—
274D8—41no—
275D8—7241no—
276C2×C8—1811no—
277C2×C8—1811no—
278C2×C8—7241no—
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⋊C4—1811no—
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—3621no—
299C42—3621no—
300C42—3621no—
301C42—1811no—
302C23—21no—
303C23—21no—
304C23—3621no—
305C23—1811no—
306C23D4×D18111yescharacteristic
307Q8—21no—
308Q8—14481no—
309Q8#1566844812yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—3622no—
317D4—3621no—
318D4—3621no—
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—42no—
330C2×C4—3621no—
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—41no—
353C22—41no—
354C22—41no—
355C22—3621no—
356C22—3621no—
357C22—3621no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C2×D4×D18111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—3621no—
366C4—3621no—
367C4—1812no—
368C4—7241no—
369C4—7241no—
370C4—7241no—
371C4C2×#1566844811yescharacteristic
372C4#1915386111yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—14481no—
377C2—7241no—
378C2#2604191611yescharacteristic
379C2#135×D18111yescharacteristic
380C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3305
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041993C2semidirect
2. #26041948C2semidirect
3. #26041624C2semidirect
4. #26041604C2semidirect
5. #26041602C2semidirect
6. #26041572C2semidirect
7. #26041513C2semidirect
8. #26041512C2semidirect
9. #26041472C2semidirect
10. #26041423C2semidirect
11. SD16×Dic181C2semidirect
12. #26041342C2semidirect
13. #26041275C2semidirect
14. #26041274C2semidirect
15. #449×C181C2semidirect
190. C181#3305semidirect
202. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260419932
#260419482
#260416242
#260416042
#260416022
#260415722
#260415132
#260415122
#260414722
#260414232
SD16×Dic1812
#260413422
#260412752
#260412742
#449×C1812
#3305181