Finite Group Databasebeta

← #37546196

Subgroups — #37546196

Order 23168.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041979C211yesmaximal, characteristic, complemented
2#26041934C211yesmaximal, characteristic, complemented
3#26041688C211yesmaximal, characteristic, complemented
4#26041601C211yesmaximal, characteristic, complemented
5#26041596C211yesmaximal, characteristic, complemented
6#26041596C211yesmaximal, characteristic, complemented
7#26041591C211yesmaximal, characteristic, complemented
8#26041579C211yesmaximal, characteristic, complemented
9#26041569C211yesmaximal, characteristic, complemented
10#26041529C211yesmaximal, characteristic, complemented
11#26041512C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041318C211yesmaximal, characteristic, complemented
14#106×D181C211yesmaximal, characteristic, complemented
15#442×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668432C2211yescharacteristic
18C2×C8×D181C2211yescharacteristic
19#19153816C2211yescharacteristic
20#19153809—21no—
21#19153808C2211yescharacteristic
22#19153799—21no—
23#19153798—21no—
24#19153798—21no—
25#19153795—21no—
26#19153789—21no—
27#19153787C2211yescharacteristic
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31C4×D724C2211yescharacteristic
32C4×C22⋊D181—21no—
33#19153774C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45C4⋊#13089678C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×D8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362—21no—
61C2×D724D411yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181C2311yescharacteristic
70C2×C4×D181C2311yescharacteristic
71#15668432—22no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C8×D181—22no—
75C4⋊Dic181—21no—
76C4⋊Dic181D411yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90#15668426—21no—
91#15668426D411yescharacteristic
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C2×D4×C181C2311yescharacteristic
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181—21no—
97C22×C4×C181—21no—
98D8×C181—22no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C22⋊C4×C181—21no—
104C22⋊C4×C181—21no—
105C42×C181C2311yescharacteristic
106C22×D181C2×D411yescharacteristic
107C22×D181C2×D411yescharacteristic
108Dic362—42no—
109D724—22no—
110C22⋊D181—42no—
111C22⋊D181—42no—
112C22⋊D181—42no—
113C22⋊D181—81no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C4×D181—21no—
121C4×D181—21no—
122C4×D181—21no—
123C4×D181—21no—
124C4×D181—42no—
125C4×D181—42no—
126C4×D181—81no—
127#13089678—21no—
128#13089678—21no—
129C23×C181—21no—
130C23×C181—21no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134D4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—42no—
138C2×C4×C181—81no—
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2411yescharacteristic
142C8×C181—21no—
143C8×C181#4112yescomplemented
144C22×C181—41no—
145C22×C181—41no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181C22×D411yescharacteristic
151C2×D181—21no—
152C2×D181—21no—
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181AGL(1,ℤ/8)12yes—
157C4×C181—21no—
158C4×C181—21no—
159C4×C181—41no—
160C4×C181—41no—
161C4×C181C2×#4111yescharacteristic
162C4×C1812−1+411yescharacteristic
163Dic181—21no—
164Dic181—21no—
165Dic181—41no—
166Dic181—41no—
167Dic181—41no—
168Dic181—41no—
169C2×C181—81no—
170C2×C181—81no—
171C2×C181#54711yescharacteristic
172C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C181#57711yescharacteristic
174D181—22no—
175D181—41no—
176C181#334511yescharacteristic, complemented, Sylow
177#3345—1811nomaximal, Sylow
178#553—1811no—
179#547—1811no—
180#501—1811no—
181#482—1811no—
182#481—1811no—
183#481—1811no—
184#480—1811no—
185#478—1811no—
186#476—1811no—
187#469—1811no—
188#466—1811no—
189#442D18111yescharacteristic, complemented
190#435—1811no—
191#428—1811no—
192C2×#106—1811no—
193C2×#41—3621no—
194C2×D8C2×D18111yescharacteristic
195C2×M16—1811no—
196C22×C8—1811no—
197C4⋊Q8—1811no—
198#126—3621no—
199#125—1811no—
200#123—3621no—
201#123—3621no—
202#123—3621no—
203C22⋊Q8—3621no—
204#121—3621no—
205#121—1811no—
206#121—1811no—
207#121—1811no—
208#121—1811no—
209C4×D4—3621no—
210C4×D4—1811no—
211C4×D4C2×D18111yescharacteristic
212C4×D4C2×D18111yescharacteristic
213#117—1811no—
214C2×C4⋊C4—1811no—
215C2×C4⋊C4—1811no—
216C2×C4⋊C4—1811no—
217#107—1811no—
218#107—1811no—
219#107—1811no—
220#106—1811no—
221#106—1811no—
222#106—1811no—
223#106—1811no—
224#106—1811no—
225#106C2×D18111yescharacteristic
226C4⋊C8—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230#102—1811no—
231#102C2×D18111yescharacteristic
232#102C2×D18111yescharacteristic
233C22⋊C8—1811no—
234C22⋊C8—1811no—
235#97C2×D18111yescharacteristic
236#41—7244no—
237C2×Q8—3621no—
238C2×D4—3621no—
239C2×D4—3621no—
240C2×D4—3621no—
241C2×D4—3621no—
242C2×D4—1811no—
243C2×D4C22×D18111yescharacteristic
244C2×D4C22×D18111yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—3621no—
248C22×C4—3621no—
249C22×C4—3621no—
250C22×C4—1811no—
251C22×C4—1811no—
252D8—22no—
253M16—3622no—
254C2×C8—3622no—
255C2×C8—1811no—
256C2×C8—1811no—
257C2×C8C22×D18111yescharacteristic
258C2×C8C22×D18111yescharacteristic
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—3621no—
264C4⋊C4—3621no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4—1811no—
268C4⋊C4—1811no—
269C4⋊C4—1811no—
270C4⋊C4C22×D18111yescharacteristic
271C4⋊C4C22×D18111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4—3621no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—1811no—
280C22⋊C4—1811no—
281C42—3621no—
282C42C22×D18111yescharacteristic
283C23—21no—
284C23—21no—
285C23—1811no—
286C23—1811no—
287Q8—7242no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—3622no—
293D4—14481no—
294D4—7242no—
295D4—7242no—
296D4—7242no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—3621no—
306C2×C4—3621no—
307C2×C4—3621no—
308C2×C4—3621no—
309C2×C4—14481no—
310C2×C4—1811no—
311C2×C4—1811no—
312C2×C4—7242no—
313C2×C4—7242no—
314C2×C4D4×D18111yescharacteristic
315C2×C4D4×D18111yescharacteristic
316C2×C4C23×D18111yescharacteristic
317C8—21no—
318C8—3621no—
319C8—3621no—
320C8#1566844912yescomplemented
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—3621no—
328C22—3621no—
329C22—3621no—
330C22—3621no—
331C22—3621no—
332C22—1812no—
333C22C2×D4×D18111yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—3621no—
339C4—3621no—
340C4—7241no—
341C4—7241no—
342C4—7241no—
343C4—7241no—
344C4C2×#1566844911yescharacteristic
345C4#1915386311yescharacteristic
346C2—81no—
347C2—81no—
348C2—3622no—
349C2—7241no—
350C2#2604193411yescharacteristic
351C2AGL(1,ℤ/8)×D18111yescharacteristic
352C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#442×C181C2
socleC22×C181C22×D4
hypercenter#442D181
hypocenterC181#3345
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #26041979C2semidirect
2. #26041934C2semidirect
3. #26041688C2semidirect
4. #26041601C2semidirect
5. #26041596C2semidirect
6. #26041596C2semidirect
7. #26041591C2semidirect
8. #26041579C2semidirect
9. #26041569C2semidirect
10. #26041529C2semidirect
11. #26041512C2semidirect
12. #26041352C2semidirect
13. #26041318C2semidirect
14. #106×D181C2semidirect
15. #442×C181C2semidirect
143. C8×C181#41semidirect
176. C181#3345semidirect
189. #442D181semidirect
320. C8#15668449semidirect

Maximal subgroups

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

subgroupindex
#260419792
#260419342
#260416882
#260416012
#260415962
#260415912
#260415792
#260415692
#260415292
#260415122
#260413522
#260413182
#106×D1812
#442×C1812
#3345181