Finite Group Databasebeta

← C2×#10590564 #11875045

Subgroups — C2×#10590564 #11875045

Order 1152.

881 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 881 conjugacy classes of subgroups — too many to draw. Only its 244 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×#64099C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic
3C2×C3×#808C212yesmaximal
4C2×#63575C212yesmaximal
5C2×#63555C211yesmaximal, characteristic
6#10590564C218yesmaximal, direct product factor
7C2×#4856—32nomaximal
8C22×#627—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64099—22no—
15#64099C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63919—22no—
20#63919C2214yes—
21C3×#808C2218yes—
22#63575C2218yes—
23#63555C2214yes—
24C2×#890—32no—
25C2×#890—61no—
26C2×#888—32no—
27C2×C3×#106—32no—
28C2×#818—32no—
29C2×#815—32no—
30C2×#808D312yes—
31C2×#807—32no—
32#4856—316no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3×Dic3—22no—
39C2×#627—24no—
40C2×#627—44no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4C2312yes—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—24no—
45C4⋊(C3⋊Dic3)C2312yes—
46#3750—24no—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3C2312yes—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3C2314yes—
51C2×C3×C3⋊C8Q818yescomplemented
52C2×C3×C3⋊C8C2314yes—
53#3724—24no—
54C2×#501—91noSylow
55C22×Dic6—62no—
56C22×C3×C8—32no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C4⋊C4C2×D312yes—
60C2×C4⋊Dic3—32no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3—62no—
63C2×C4⋊Dic3—62no—
64C2×C4⋊Dic3C2×D312yes—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8C2×D312yes—
71#890—38no—
72#890—64no—
73#890—64no—
74#890—64no—
75#888—38no—
76#888—64no—
77C3×#106—38no—
78#818—38no—
79#815—38no—
80#808C2×D318yes—
81#807—38no—
82C23×C32C2×D411yescharacteristic
83C2×C32×C4—22no—
84C2×C32×C4—42no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q814yes—
87C2×C32×C4C2411yescharacteristic
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3C2×D412yes—
93C2×C3⋊Dic3C2×D412yes—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—44no—
96#627—48no—
97C3×C3⋊C8C2×Q818yescomplemented
98C2×C4⋊Q8—91no—
99C2×#125—91no—
100#501—98no—
101C2×#107—92no—
102C2×#106—32no—
103C2×#97—91no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×Dic6—68no—
117C2×Dic6—128no—
118C2×C3×C8—38no—
119C2×C3×C8—34no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—22no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—34no—
124C3×C4⋊C4—62no—
125C3×C4⋊C4C22×D314yes—
126C4⋊Dic3—22no—
127C4⋊Dic3—34no—
128C4⋊Dic3—62no—
129C4⋊Dic3—68no—
130C4⋊Dic3—68no—
131C4⋊Dic3—62no—
132C4⋊Dic3—62no—
133C4⋊Dic3C22×D314yes—
134Dic3⋊C4—68no—
135Dic3⋊C4—68no—
136Dic3⋊C4—68no—
137C4×Dic3—34no—
138C4×Dic3—34no—
139C4×Dic3—62no—
140C4×Dic3—62no—
141C2×C3⋊C8Dic618yescomplemented
142C2×C3⋊C8C22×D314yes—
143C22×C32C4⋊Q812yes—
144C22×C32AGL(1,ℤ/8)12yes—
145C22×C32#13712yes—
146C22×C32C22×D411yescharacteristic
147C32×C4—42no—
148C32×C4C4⋊Q812yes—
149C32×C4C22×Q812yes—
150C3⋊Dic3—22no—
151C3⋊Dic3—22no—
152C3⋊Dic3—42no—
153C3×Dic3—44no—
154C22×Q8—181no—
155C22×C8—32no—
156C4⋊Q8—94no—
157C4⋊Q8—182no—
158#125—94no—
159#125—182no—
160C2×C4⋊C4—32no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—181no—
163C2×C4⋊C4—181no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4D3211yescharacteristic
166C2×C42—91no—
167#107—98no—
168#106—38no—
169#97—94no—
170C23×C3—21no—
171C23×C3D3×D412yes—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—21no—
175C2×C3×C4—24no—
176C2×C3×C4—21no—
177C2×C3×C4—44no—
178C2×C3×C4—44no—
179C2×C3×C4—64no—
180C2×C3×C4—124no—
181C2×C3×C4C2×Dic614yes—
182C2×C3×C4D3×D412yes—
183C2×C3×C4D3×Q814yes—
184C2×C3×C4C23×D312yes—
185C2×Dic3—24no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—44no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C2×Dic3—124no—
198C2×Dic3—124no—
199Dic6—1216no—
200C3×C8—38no—
201C3⋊C8C2×Dic618yescomplemented
202C2×C32#50114yescomplemented
203C2×C32C2×C4⋊Q811yescharacteristic
204C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C32C2×#13711yescharacteristic
206C2×Q8—184no—
207C2×Q8—364no—
208C22×C4—21no—
209C22×C4—62no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—181no—
213C22×C4C2×D3211yescharacteristic
214C2×C8—34no—
215C2×C8—38no—
216C4⋊C4—21no—
217C4⋊C4—34no—
218C4⋊C4—62no—
219C4⋊C4—92no—
220C4⋊C4—184no—
221C4⋊C4—184no—
222C4⋊C4—184no—
223C4⋊C4—181no—
224C4⋊C4C2×D3212yes—
225C42—92no—
226C42—92no—
227C22×C3—21no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C22×C3#88814yes—
232C22×C3#91414yes—
233C22×C3#91514yes—
234C22×C3C2×D3×D412yes—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—44no—
238C3×C4—44no—
239C3×C4—124no—
240C3×C4#88814yes—
241C3×C4C22×Dic612yes—
242C3×C4C2×D3×Q812yes—
243Dic3—44no—
244Dic3—64no—
245Dic3—64no—
246Dic3—122no—
247Dic3—122no—
248Dic3—124no—
249Dic3—124no—
250C32C2×#50111yescharacteristic, complemented, Sylow
251C23#381111yescharacteristic
252Q8—368no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—64no—
256C2×C4—92no—
257C2×C4—92no—
258C2×C4—124no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4—182no—
262C2×C4—362no—
263C2×C4D3×Dic614yes—
264C2×C4#381111yescharacteristic
265C2×C4C22×D3211yescharacteristic
266C8—38no—
267C2×C3—21no—
268C2×C3—24no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3#485618yescomplemented
272C2×C3C2×#88812yes—
273C2×C3C2×#91412yes—
274C2×C3C2×#91512yes—
275C22#6384012yes—
276C22#6393112yes—
277C22#6394112yes—
278C22C2×#381111yescharacteristic
279C4—42no—
280C4—124no—
281C4—182no—
282C4—182no—
283C4—362no—
284C4#6384012yes—
285C4C2×D3×Dic612yes—
286C3—21no—
287C3C2×#485612yescomplemented
288C2#1059056414yesdirect product factor
289C2C2×#6384011yescharacteristic
290C2C2×#6393111yescharacteristic
291C2C2×#6394111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#501
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. #10590564C2direct (N × H)
51. C2×C3×C3⋊C8Q8semidirect
97. C3×C3⋊C8C2×Q8semidirect
141. C2×C3⋊C8Dic6semidirect
201. C3⋊C8C2×Dic6semidirect
202. C2×C32#501semidirect
250. C32C2×#501semidirect
271. C2×C3#4856semidirect
287. C3C2×#4856semidirect
288. C2#10590564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#639192
C2×C3×#8082
C2×#635752
C2×#635552
#105905642
C2×#48563