Finite Group Databasebeta

← C2×D181⋊#99 #37550314

Subgroups — C2×D181⋊#99 #37550314

Order 23168.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#10624382C212yesmaximal, complemented
2C2×#19153875C212yesmaximal, complemented
3D181⋊#99C218yesmaximal, direct product factor
4C2×#19153874C212yesmaximal, complemented
5C22×D4×D181C211yesmaximal, characteristic
6C23×#10624382—22no—
7C2×C22⋊#10624382—22no—
8C2×C22⋊#10624382—24no—
9C2×C22⋊#10624382C2214yescomplemented
10C2×C22⋊#10624382C2218yescomplemented
11#19153875C2218yescomplemented
12#19153874C2218yescomplemented
13C24×D181C411yescharacteristic, complemented
14C24×D181C2211yescharacteristic
15C22×D724C2211yescharacteristic
16C22×C22⋊D181C411yescharacteristic, complemented
17C22×C22⋊D181C2211yescharacteristic
18C2×D4×D181—22no—
19C2×D4×D181—22no—
20C2×D4×D181—24no—
21C2×D4×D181C414yescomplemented
22C2×D4×D181C2214yes—
23C22×C4×D181C411yescharacteristic, complemented
24C22×D4×C181C411yescharacteristic, complemented
25C22×#10624382—28no—
26C22×#10624382—24no—
27C22×#10624382—48no—
28C22⋊#10624382—28no—
29C22⋊#10624382—24no—
30C22⋊#10624382C2318yescomplemented
31C23×D181—22no—
32C23×D181—21no—
33C23×D181—21no—
34C23×D181—44no—
35C23×D181—44no—
36C23×D181C2×C411yescharacteristic
37C23×D181C2×C412yes—
38C23×D181C2×C411yescharacteristic, complemented
39C23×D181C2×C414yescomplemented
40C23×D181D412yes—
41C23×D181D412yes—
42C23×D181D414yes—
43C23×D181C2312yes—
44C23×D181C2311yescharacteristic
45C2×D724—22no—
46C2×D724—22no—
47C2×D724C2×C412yescomplemented
48C2×D724C2312yes—
49C2×C22⋊D181—22no—
50C2×C22⋊D181—22no—
51C2×C22⋊D181—22no—
52C2×C22⋊D181—22no—
53C2×C22⋊D181C2×C414yescomplemented
54C2×C22⋊D181C2×C412yescomplemented
55C2×C22⋊D181C2312yes—
56D4×D181—28no—
57D4×D181—28no—
58D4×D181—28no—
59D4×D181—28no—
60C22×Dic181C2×C411yescharacteristic, complemented
61C2×C4×D181—22no—
62C2×C4×D181—21no—
63C2×C4×D181—21no—
64C2×C4×D181C2×C414yescomplemented
65C24×C181C2×C411yescharacteristic
66C24×C181C2×C411yescharacteristic, complemented
67C2×D4×C181—22no—
68C2×D4×C181—22no—
69C2×D4×C181C2×C414yescomplemented
70C22×C4×C181C2×C411yescharacteristic, complemented
71C2×#10624382—28no—
72C2×#10624382—48no—
73C2×#10624382—416no—
74C22×D181—24no—
75C22×D181—28no—
76C22×D181—21no—
77C22×D181—21no—
78C22×D181—24no—
79C22×D181—24no—
80C22×D181—44no—
81C22×D181—48no—
82C22×D181—44no—
83C22×D181—44no—
84C22×D181—42no—
85C22×D181—44no—
86C22×D181—48no—
87C22×D181—48no—
88C22×D181—44no—
89C22×D181—42no—
90C22×D181C22⋊C412yes—
91C22×D181C22⋊C411yescharacteristic
92C22×D181C22⋊C414yes—
93C22×D181C22⋊C414yes—
94C22×D181C22⋊C411yescharacteristic
95C22×D181C22×C412yes—
96C22×D181C22×C411yescharacteristic
97C22×D181C22×C412yescomplemented
98C22×D181C2×D414yes—
99C22×D181C2×D412yes—
100C22×D181C2×D414yes—
101C22×D181C2×D412yes—
102C22×D181C2411yescharacteristic
103D724—24no—
104D724—24no—
105C22⋊D181—28no—
106C22⋊D181—24no—
107C22⋊D181—24no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181C22×C412yescomplemented
111C4×D181—24no—
112C4×D181—24no—
113C23×C181—21no—
114C23×C181—21no—
115C23×C181—42no—
116C23×C181—42no—
117C23×C181C22⋊C412yes—
118C23×C181C22⋊C412yes—
119C23×C181C22×C411yescharacteristic
120C23×C181C22×C412yes—
121C23×C181C22×C412yescomplemented
122D4×C181—28no—
123C2×C4×C181—21no—
124C2×C4×C181—21no—
125C2×C4×C181C22×C412yescomplemented
126C22×C181—22no—
127C22×C181—24no—
128C22×C181—22no—
129C22×C181—42no—
130C22×C181—42no—
131C22×C181—42no—
132C22×C181—42no—
133C22×C181—42no—
134C22×C181C2×C22⋊C411yescharacteristic
135C22×C181C2×C22⋊C414yes—
136C22×C181C2×C22⋊C411yescharacteristic
137C22×C181C23×C411yescharacteristic
138C2×D181—22no—
139C2×D181—24no—
140C2×D181—24no—
141C2×D181—24no—
142C2×D181—28no—
143C2×D181—28no—
144C2×D181—22no—
145C2×D181—44no—
146C2×D181—41no—
147C2×D181—44no—
148C2×D181—42no—
149C2×D181—41no—
150C2×D181—48no—
151C2×D181—42no—
152C2×D181—42no—
153C2×D181—48no—
154C2×D181—42no—
155C2×D181#9914yescomplemented
156C2×D181C2×C22⋊C412yes—
157C2×D181C2×C22⋊C412yes—
158C2×D181C2×C22⋊C412yes—
159C2×D181C22×D412yes—
160#10624382—48no—
161C4×C181—22no—
162Dic181—22no—
163C2×C181—21no—
164C2×C181—21no—
165C2×C181—24no—
166C2×C181—42no—
167C2×C181C2×#9912yescomplemented
168C2×C181C22×C22⋊C411yescharacteristic
169D181—22no—
170D181—22no—
171D181—22no—
172D181—42no—
173D181C2×#9914yescomplemented
174C181C22×#9911yescharacteristic, complemented, Sylow
175C22×#99—1811nomaximal, Sylow
176C23×D4—1811no—
177C22×C22⋊C4—1812no—
178C2×#99—1812no—
179C2×#99—1818no—
180C2×#99—1812no—
181C25—1811no—
182C25—1811no—
183C22×D4—3622no—
184C22×D4—3624no—
185C22×D4—3622no—
186C22×D4—1811no—
187C22×D4—1811no—
188C22×D4—1814no—
189C22×D4—1814no—
190C22×D4—1811no—
191C22×D4#1062438211yescharacteristic, complemented
192C23×C4—3622no—
193C23×C4—1811no—
194C2×C22⋊C4—3624no—
195C2×C22⋊C4—3622no—
196C2×C22⋊C4—1814no—
197C2×C22⋊C4—1818no—
198#99—1818no—
199#99—1818no—
200C24—3622no—
201C24—3621no—
202C24—3621no—
203C24—1812no—
204C24—1811no—
205C24—1811no—
206C24—1814no—
207C24—1814no—
208C24—1812no—
209C24—1812no—
210C24—1811no—
211C24—1812no—
212C24—7244no—
213C24—7244no—
214C24C2×#1062438211yescharacteristic
215C24C2×#1062438211yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—3622no—
219C2×D4—3622no—
220C2×D4—3628no—
221C2×D4—3628no—
222C2×D4—3628no—
223C2×D4—3628no—
224C2×D4—3622no—
225C2×D4—3622no—
226C2×D4—3622no—
227C2×D4—3622no—
228C2×D4—1814no—
229C2×D4—1812no—
230C2×D4—1812no—
231C2×D4—1812no—
232C2×D4—1812no—
233C2×D4C2×#1062438214yescomplemented
234C22×C4—3622no—
235C22×C4—3621no—
236C22×C4—3621no—
237C22×C4—3628no—
238C22×C4—3624no—
239C22×C4—1811no—
240C22×C4—1814no—
241C22×C4—7248no—
242C22×C4C2×#1062438211yescharacteristic, complemented
243C22⋊C4—3628no—
244C22⋊C4—3624no—
245C22⋊C4—1818no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—3628no—
251C23—3624no—
252C23—3624no—
253C23—3624no—
254C23—3621no—
255C23—3621no—
256C23—1814no—
257C23—1812no—
258C23—1814no—
259C23—1812no—
260C23—1811no—
261C23—1812no—
262C23—1812no—
263C23—1811no—
264C23—1814no—
265C23—1812no—
266C23—1814no—
267C23—1811no—
268C23—1811no—
269C23—7242no—
270C23—7244no—
271C23—7242no—
272C23—7248no—
273C23—7244no—
274C23—7244no—
275C23—7248no—
276C23—7248no—
277C23—7244no—
278C23—7244no—
279C23C22⋊#1062438212yes—
280C23C22⋊#1062438212yes—
281C23C22×#1062438211yescharacteristic
282C23C22×#1062438212yes—
283C23C22×#1062438212yescomplemented
284D4—28no—
285D4—3624no—
286D4—3624no—
287D4—3624no—
288D4—3624no—
289D4—3628no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—3624no—
293C2×C4—3624no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3628no—
297C2×C4—1812no—
298C2×C4—72416no—
299C2×C4—7248no—
300C2×C4C22×#1062438212yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—3628no—
310C22—3624no—
311C22—3624no—
312C22—3628no—
313C22—3624no—
314C22—3622no—
315C22—3622no—
316C22—1812no—
317C22—1812no—
318C22—1812no—
319C22—1814no—
320C22—1812no—
321C22—7242no—
322C22—7241no—
323C22—7241no—
324C22—7244no—
325C22—7244no—
326C22—7242no—
327C22—7242no—
328C22—7248no—
329C22—7248no—
330C22—7242no—
331C22C2×C22⋊#1062438211yescharacteristic
332C22C2×C22⋊#1062438214yes—
333C22C2×C22⋊#1062438211yescharacteristic
334C22C23×#1062438211yescharacteristic
335C4—22no—
336C4—3622no—
337C4—7248no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—3622no—
343C2—3622no—
344C2—3622no—
345C2—1814no—
346C2—7242no—
347C2D181⋊#9912yesdirect product factor
348C2C22×C22⋊#1062438211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC22×C181C23×C4
FrattiniC22C23×#10624382
FittingC22×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D4×D181C2
cosocleC22×D181C24
hypercenterC22×D4#10624382
hypocenterC181C22×#99
LCSG ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#10624382C2semidirect
2. C2×#19153875C2semidirect
3. D181⋊#99C2direct (N × H)
4. C2×#19153874C2semidirect
9. C2×C22⋊#10624382C22semidirect
10. C2×C22⋊#10624382C22semidirect
11. #19153875C22semidirect
12. #19153874C22semidirect
13. C24×D181C4semidirect
16. C22×C22⋊D181C4semidirect
21. C2×D4×D181C4semidirect
23. C22×C4×D181C4semidirect
24. C22×D4×C181C4semidirect
30. C22⋊#10624382C23semidirect
38. C23×D181C2×C4semidirect
39. C23×D181C2×C4semidirect
47. C2×D724C2×C4semidirect
53. C2×C22⋊D181C2×C4semidirect
54. C2×C22⋊D181C2×C4semidirect
60. C22×Dic181C2×C4semidirect
64. C2×C4×D181C2×C4semidirect
66. C24×C181C2×C4semidirect
69. C2×D4×C181C2×C4semidirect
70. C22×C4×C181C2×C4semidirect
97. C22×D181C22×C4semidirect
110. C2×Dic181C22×C4semidirect
121. C23×C181C22×C4semidirect
125. C2×C4×C181C22×C4semidirect
155. C2×D181#99semidirect
167. C2×C181C2×#99semidirect
173. D181C2×#99semidirect
174. C181C22×#99semidirect
191. C22×D4#10624382semidirect
215. C24C2×#10624382semidirect
233. C2×D4C2×#10624382semidirect
242. C22×C4C2×#10624382semidirect
283. C23C22×#10624382semidirect
300. C2×C4C22×#10624382semidirect
347. C2D181⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#106243822
C2×#191538752
D181⋊#992
C2×#191538742
C22×D4×D1812
C22×#99181