Finite Group Databasebeta

← C2×#10590431 #11868416

Subgroups — C2×#10590431 #11868416

Order 1152.

981 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 981 conjugacy classes of subgroups — too many to draw. Only its 228 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
1C2×#64096C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic
3C2×C3×#808C212yesmaximal
4C2×#63572C211yesmaximal, characteristic
5C2×#63567C212yesmaximal
6#10590431C218yesmaximal, direct product factor
7C2×#4854—32nomaximal
8C22×#634C2211yescharacteristic
9C22×#627—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3750—21no—
12C2×C4×C3⋊Dic3—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64096—22no—
15#64096C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yes—
21C3×#808C2218yes—
22#63572C2214yes—
23#63567C2218yes—
24C2×#888—32no—
25C2×#887—32no—
26C2×#887—61no—
27C2×C3×#106—32no—
28C2×#816—32no—
29C2×Dic3⋊C8—32no—
30C2×#810—32no—
31C2×#808D312yes—
32#4854—316no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×#634—21no—
39C2×#634—22no—
40C2×#634Q814yescomplemented
41C2×#634C2312yes—
42C22×C3×Dic3—22no—
43C2×#627—24no—
44C2×#627—44no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2312yes—
47#3750—24no—
48C4×C3⋊Dic3—24no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C2×C3×C3⋊C8—24no—
54C2×C3×C3⋊C8C2314yes—
55#3724—24no—
56C2×#475—91noSylow
57C22×Dic6—32no—
58C22×Dic6—61no—
59C22×Dic6—62no—
60C22×C3×C8—32no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4C2×D312yes—
64C2×C4⋊Dic3C2×D312yes—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—62no—
71C2×C4×Dic3—62no—
72C22×C3⋊C8C2×D312yes—
73#888—38no—
74#888—64no—
75#887—38no—
76#887—64no—
77#887—64no—
78#887—64no—
79C3×#106—38no—
80#816—38no—
81Dic3⋊C8—38no—
82#810—38no—
83#808C2×D318yes—
84C23×C32C2×D411yescharacteristic
85C2×C32×C4—22no—
86C2×C32×C4—42no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×Q812yes—
89C2×C32×C4#4112yes—
90C2×C32×C4C2411yescharacteristic
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3SD1614yes—
95C2×C3⋊Dic3C2×D412yes—
96C2×C3⋊Dic3C2×D412yes—
97#634—24no—
98#634—22no—
99#634C2×Q814yescomplemented
100C2×C3×Dic3—24no—
101C2×C3×Dic3—44no—
102#627—48no—
103C3×C3⋊C8—24no—
104C2×C4⋊Q8—91no—
105C2×C4×Q8—91no—
106#475—98no—
107C2×#106—32no—
108C2×C4⋊C8—91no—
109C2×#103—92no—
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4—21no—
113C22×C3×C4—62no—
114C22×C3×C4C22×D312yes—
115C22×Dic3—22no—
116C22×Dic3—32no—
117C22×Dic3—32no—
118C22×Dic3—61no—
119C22×Dic3—61no—
120C22×Dic3—62no—
121C22×Dic3—62no—
122C2×Dic6—38no—
123C2×Dic6—34no—
124C2×Dic6—62no—
125C2×Dic6—64no—
126C2×Dic6—62no—
127C2×Dic6—64no—
128C2×Dic6—64no—
129C2×Dic6—62no—
130C2×Dic6—68no—
131C2×Dic6—128no—
132C2×C3×C8—34no—
133C2×C3×C8—64no—
134C3×C4⋊C4—22no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4C22×D314yes—
140C4⋊Dic3—22no—
141C4⋊Dic3C22×D314yes—
142Dic3⋊C4—68no—
143Dic3⋊C4—68no—
144Dic3⋊C4—68no—
145C4×Dic3—34no—
146C4×Dic3—34no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149C4×Dic3—68no—
150C4×Dic3—68no—
151C2×C3⋊C8—24no—
152C2×C3⋊C8C22×D314yes—
153C22×C32C22⋊Q812yes—
154C22×C32C2×SD1612yes—
155C22×C32#13712yes—
156C22×C32C22×D411yescharacteristic
157C32×C4—42no—
158C32×C4C22⋊Q812yes—
159C32×C4C22×Q811yescharacteristic
160C32×C4C2×#4111yescharacteristic
161C3⋊Dic3—24no—
162C3⋊Dic3—22no—
163C3⋊Dic3C2×SD1614yes—
164C3×Dic3—44no—
165C22×Q8—91no—
166C22×Q8—181no—
167C22×C8—32no—
168C4⋊Q8—94no—
169C4⋊Q8—182no—
170C4×Q8—94no—
171C4×Q8—182no—
172C2×C4⋊C4—32no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4D3211yescharacteristic
176C2×C42—91no—
177C2×C42—181no—
178#106—38no—
179C4⋊C8—94no—
180#103—98no—
181C23×C3—21no—
182C23×C3D3×D412yes—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—44no—
190C2×C3×C4—44no—
191C2×C3×C4—64no—
192C2×C3×C4—124no—
193C2×C3×C4#23514yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4D3×Q814yes—
196C2×C3×C4C23×D312yes—
197C2×Dic3—24no—
198C2×Dic3—38no—
199C2×Dic3—34no—
200C2×Dic3—34no—
201C2×Dic3—44no—
202C2×Dic3—64no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—64no—
206C2×Dic3—68no—
207C2×Dic3—68no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—122no—
211Dic6—38no—
212Dic6—64no—
213Dic6—64no—
214Dic6—68no—
215Dic6—68no—
216Dic6—64no—
217Dic6—1216no—
218C3×C8—64no—
219C3⋊C8—24no—
220C2×C32#47514yescomplemented
221C2×C32C2×C22⋊Q811yescharacteristic
222C2×C32C22×SD1611yescharacteristic
223C2×C32C2×#13711yescharacteristic
224C2×Q8—92no—
225C2×Q8—94no—
226C2×Q8—184no—
227C2×Q8—182no—
228C2×Q8—181no—
229C2×Q8—364no—
230C22×C4—21no—
231C22×C4—62no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—181no—
235C22×C4C2×D3211yescharacteristic
236C2×C8—34no—
237C2×C8—64no—
238C4⋊C4—21no—
239C4⋊C4—34no—
240C4⋊C4—62no—
241C4⋊C4—184no—
242C4⋊C4—184no—
243C4⋊C4C2×D3212yes—
244C42—92no—
245C42—92no—
246C42—184no—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3#89614yes—
252C22×C3D3×SD1614yes—
253C22×C3#91514yes—
254C22×C3C2×D3×D412yes—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—22no—
258C3×C4—44no—
259C3×C4—44no—
260C3×C4—124no—
261C3×C4#89614yes—
262C3×C4C2×#23512yes—
263C3×C4C2×D3×Q812yes—
264Dic3—38no—
265Dic3—44no—
266Dic3—64no—
267Dic3—68no—
268Dic3—64no—
269Dic3—68no—
270Dic3—122no—
271C32C2×#47511yescharacteristic, complemented, Sylow
272C23#381111yescharacteristic
273Q8—94no—
274Q8—182no—
275Q8—184no—
276Q8—368no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—64no—
280C2×C4—92no—
281C2×C4—94no—
282C2×C4—92no—
283C2×C4—124no—
284C2×C4—182no—
285C2×C4—184no—
286C2×C4—182no—
287C2×C4#379712yes—
288C2×C4#379812yes—
289C2×C4#381111yescharacteristic
290C2×C4C22×D3211yescharacteristic
291C8—64no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—24no—
295C2×C3—21no—
296C2×C3#485418yescomplemented
297C2×C3C2×#89612yes—
298C2×C3C2×D3×SD1612yes—
299C2×C3C2×#91512yes—
300C22#6386512yes—
301C22#6393112yes—
302C22#6394012yes—
303C22C2×#381111yescharacteristic
304C4—42no—
305C4—94no—
306C4—124no—
307C4—182no—
308C4—184no—
309C4#6386512yes—
310C4C2×#379711yescharacteristic
311C4C2×#379811yescharacteristic
312C3—21no—
313C3C2×#485412yescomplemented
314C2#1059043114yesdirect product factor
315C2C2×#6386511yescharacteristic
316C2C2×#6393111yescharacteristic
317C2C2×#6394011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#475
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10590431C2direct (N × H)
40. C2×#634Q8semidirect
99. #634C2×Q8semidirect
220. C2×C32#475semidirect
271. C32C2×#475semidirect
296. C2×C3#4854semidirect
313. C3C2×#4854semidirect
314. C2#10590431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#639192
C2×C3×#8082
C2×#635722
C2×#635672
#105904312
C2×#48543