Finite Group Databasebeta

← C2×#31826387 #49124481

Subgroups — C2×#31826387 #49124481

Order 36224.

908 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Dic283C211yesmaximal, characteristic, complemented
2C22×Dic283⋊C4C211yesmaximal, characteristic, complemented
3C22×(C2×D283)⋊C4C211yesmaximal, characteristic
4C22×(C2×D283)⋊C4C211yesmaximal, characteristic
5C22×(C2×D283)⋊C4C211yesmaximal, characteristic
6#31826387C218yesmaximal, direct product factor
7C2×C283⋊#95C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C283C211yesmaximal, characteristic, complemented
9C24×D283C2211yescharacteristic
10C23×Dic283C2211yescharacteristic
11C23×Dic283C2211yescharacteristic
12C23×Dic283C2211yescharacteristic
13C2×C4⋊Dic283—24no—
14C2×C4⋊Dic283C2214yescomplemented
15C2×Dic283⋊C4—24no—
16C2×Dic283⋊C4C2214yescomplemented
17C2×(C2×D283)⋊C4—24no—
18C2×(C2×D283)⋊C4—24no—
19C2×(C2×D283)⋊C4—24no—
20C2×(C2×D283)⋊C4C2214yes—
21C2×(C2×D283)⋊C4C2214yes—
22C2×(C2×D283)⋊C4C2214yes—
23C283⋊#95C2214yescomplemented
24C23×C4×C283C2211yescharacteristic
25C23×C4×C283C2211yescharacteristic
26C23×C4×C283C2211yescharacteristic
27C2×C4⋊C4×C283—24no—
28C2×C4⋊C4×C283C2214yescomplemented
29C23×D283—22no—
30C23×D283—22no—
31C23×D283—22no—
32C23×D283—22no—
33C23×D283—22no—
34C23×D283—22no—
35C23×D283Q814yes—
36C23×D283C2312yes—
37C22×Dic283—22no—
38C22×Dic283—22no—
39C22×Dic283—22no—
40C22×Dic283—22no—
41C22×Dic283—22no—
42C22×Dic283—22no—
43C22×Dic283—22no—
44C22×Dic283—22no—
45C22×Dic283D414yes—
46C22×Dic283C2312yes—
47C22×Dic283C2312yes—
48C22×Dic283C2312yes—
49C4⋊Dic283—28no—
50Dic283⋊C4—28no—
51(C2×D283)⋊C4—28no—
52(C2×D283)⋊C4—28no—
53(C2×D283)⋊C4—28no—
54C24×C283C2311yescharacteristic
55C22×C4×C283—22no—
56C22×C4×C283—22no—
57C22×C4×C283—22no—
58C22×C4×C283—22no—
59C22×C4×C283—22no—
60C22×C4×C283—22no—
61C22×C4×C283—22no—
62C22×C4×C283D414yes—
63C22×C4×C283D414yes—
64C22×C4×C283C2312yes—
65C22×C4×C283C2312yes—
66C22×C4×C283C2312yes—
67C4⋊C4×C283—28no—
68C22×D283—28no—
69C22×D283—28no—
70C22×D283—28no—
71C22×D283—22no—
72C22×D283—22no—
73C22×D283—22no—
74C22×D283—22no—
75C22×D283—22no—
76C22×D283—22no—
77C22×D283—44no—
78C22×D283—44no—
79C22×D283—44no—
80C22×D283—44no—
81C22×D283C2×Q814yes—
82C2×Dic283—28no—
83C2×Dic283—22no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—22no—
91C2×Dic283—44no—
92C2×Dic283—44no—
93C2×Dic283C2×D414yes—
94C23×C283C2×D412yes—
95C23×C283C2×D412yes—
96C23×C283C2×D412yes—
97C23×C283C2×Q812yes—
98C23×C283#4112yes—
99C23×C283#4112yes—
100C23×C283#4112yes—
101C23×C283C2411yescharacteristic
102C2×C4×C283—28no—
103C2×C4×C283—28no—
104C2×C4×C283—22no—
105C2×C4×C283—22no—
106C2×C4×C283—22no—
107C2×C4×C283—22no—
108C2×C4×C283—22no—
109C2×C4×C283—22no—
110C2×C4×C283—22no—
111C2×C4×C283—44no—
112C2×C4×C283C2×D414yes—
113C2×C4×C283C2×D414yes—
114C22×C283#12114yes—
115C22×C283#12114yes—
116C22×C283#12114yes—
117C22×C283C22⋊Q814yes—
118C22×C283C22⋊Q814yes—
119C22×C283C22⋊Q814yes—
120C22×C283#12614yes—
121C22×C283C22×D411yescharacteristic
122C22×C283C22×D411yescharacteristic
123C22×C283C22×D411yescharacteristic
124C22×C283C22×Q811yescharacteristic
125C22×C283C2×#4111yescharacteristic
126C22×C283C2×#4111yescharacteristic
127C22×C283C2×#4111yescharacteristic
128C2×D283—24no—
129C2×D283—24no—
130C2×D283—24no—
131C2×D283—42no—
132C2×D283—42no—
133C2×D283—42no—
134C2×D283—42no—
135C2×D283—416no—
136C4×C283—24no—
137C4×C283—24no—
138C4×C283—42no—
139Dic283—24no—
140Dic283—42no—
141Dic283—42no—
142C2×C283#39618yescomplemented
143C2×C283C2×#12111yescharacteristic
144C2×C283C2×#12111yescharacteristic
145C2×C283C2×#12111yescharacteristic
146C2×C283C2×C22⋊Q811yescharacteristic
147C2×C283C2×C22⋊Q811yescharacteristic
148C2×C283C2×C22⋊Q811yescharacteristic
149C2×C283C2×#12611yescharacteristic
150D283—44no—
151C283C2×#39611yescharacteristic, complemented, Sylow
152C2×#396—2831nomaximal, Sylow
153C22×C4⋊C4—2831no—
154C22×C4⋊C4—2831no—
155C22×C4⋊C4D28311yescharacteristic, complemented
156C22×C22⋊C4—2831no—
157C22×C22⋊C4—2831no—
158C22×C22⋊C4—2831no—
159#396—2838no—
160C2×#95—2831no—
161C25—2831no—
162C23×C4—2831no—
163C23×C4—2831no—
164C23×C4—2831no—
165C23×C4C2×D28311yescharacteristic
166C23×C4C2×D28311yescharacteristic
167C23×C4C2×D28311yescharacteristic
168C2×C4⋊C4—24no—
169C2×C4⋊C4—2834no—
170C2×C4⋊C4—2834no—
171C2×C4⋊C4—5664no—
172C2×C4⋊C4—5664no—
173C2×C4⋊C4C2×D28314yescomplemented
174C2×C22⋊C4—2834no—
175C2×C22⋊C4—2834no—
176C2×C22⋊C4—2834no—
177C2×C22⋊C4—5664no—
178C2×C22⋊C4—5664no—
179C2×C22⋊C4—5664no—
180#95—2834no—
181C24—2834no—
182C24—2832no—
183C24—5662no—
184C24—5662no—
185C24—5662no—
186C24—5662no—
187C24—5662no—
188C24—5662no—
189C24C22×D28311yescharacteristic
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—2834no—
198C22×C4—2832no—
199C22×C4—2832no—
200C22×C4—2832no—
201C22×C4—5662no—
202C22×C4—5662no—
203C22×C4—5662no—
204C22×C4—5662no—
205C22×C4—5662no—
206C22×C4—5662no—
207C22×C4—5662no—
208C22×C4—5662no—
209C22×C4C22⋊D28314yes—
210C22×C4D113214yes—
211C22×C4C22×D28312yes—
212C22×C4C22×D28312yes—
213C22×C4C22×D28312yes—
214C4⋊C4—28no—
215C4⋊C4—5668no—
216C4⋊C4—5668no—
217C22⋊C4—5668no—
218C22⋊C4—5668no—
219C22⋊C4—5668no—
220C23—2834no—
221C23—5668no—
222C23—5668no—
223C23—5668no—
224C23—5662no—
225C23—5662no—
226C23—5662no—
227C23—5662no—
228C23—5662no—
229C23—5662no—
230C23—11324no—
231C23—11324no—
232C23—11324no—
233C23—11324no—
234C23D4×D28312yes—
235C23C2×C22⋊D28312yes—
236C23C2×D113212yes—
237C23Q8×D28312yes—
238C23#1798539112yes—
239C23#1798539212yes—
240C23#1798539312yes—
241C23C23×D28311yescharacteristic
242C2×C4—28no—
243C2×C4—28no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—44no—
252C2×C4—2834no—
253C2×C4—5668no—
254C2×C4—5662no—
255C2×C4—5662no—
256C2×C4—5662no—
257C2×C4—5662no—
258C2×C4—5662no—
259C2×C4—5662no—
260C2×C4—5662no—
261C2×C4—5662no—
262C2×C4—11324no—
263C2×C4—11324no—
264C2×C4C2×C22⋊D28314yes—
265C2×C4C2×D113214yes—
266C22—5664no—
267C22—5664no—
268C22—5664no—
269C22—11322no—
270C22—11322no—
271C22—11322no—
272C22—11322no—
273C22—113216no—
274C22#2258358214yes—
275C22#2258358414yes—
276C22#2258358514yes—
277C22#2258358614yes—
278C22#2258358814yes—
279C22#2258359014yes—
280C22#2258360514yes—
281C22C2×D4×D28311yescharacteristic
282C22C22×C22⋊D28311yescharacteristic
283C22C22×D113211yescharacteristic
284C22C2×Q8×D28311yescharacteristic
285C22C2×#1798539111yescharacteristic
286C22C2×#1798539211yescharacteristic
287C22C2×#1798539311yescharacteristic
288C4—24no—
289C4—24no—
290C4—42no—
291C4—5664no—
292C4—11322no—
293C4—11322no—
294C2—11324no—
295C2#3182638718yesdirect product factor
296C2C2×#2258358211yescharacteristic
297C2C2×#2258358411yescharacteristic
298C2C2×#2258358511yescharacteristic
299C2C2×#2258358611yescharacteristic
300C2C2×#2258358811yescharacteristic
301C2C2×#2258359011yescharacteristic
302C2C2×#2258360511yescharacteristic
subgroupG/H
centerC24C22×D283
commutator, cosocleC23×C283C24
FrattiniC23C23×D283
FittingC22×C4⋊C4×C283C2
socleC24×C283C23
prime radicalC24×D283C22
hypercenterC22×C4⋊C4D283
hypocenterC283C2×#396
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic283C2semidirect
2. C22×Dic283⋊C4C2semidirect
6. #31826387C2direct (N × H)
7. C2×C283⋊#95C2semidirect
8. C22×C4⋊C4×C283C2semidirect
14. C2×C4⋊Dic283C22semidirect
16. C2×Dic283⋊C4C22semidirect
23. C283⋊#95C22semidirect
28. C2×C4⋊C4×C283C22semidirect
142. C2×C283#396semidirect
151. C283C2×#396semidirect
155. C22×C4⋊C4D283semidirect
173. C2×C4⋊C4C2×D283semidirect
295. C2#31826387direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic2832
C22×Dic283⋊C42
C22×(C2×D283)⋊C42
#318263872
C2×C283⋊#952
C22×C4⋊C4×C2832
C2×#396283