Finite Group Databasebeta

← C2×#10591616 #11873614

Subgroups — C2×#10591616 #11873614

Order 1152.

913 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 913 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64153C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic
3C2×C3×#835C212yesmaximal
4#10591616C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal
6C2×#63555C211yesmaximal, characteristic
7C2×#4797—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10#64153—22no—
11#64153C2214yes—
12C2×#3750—22no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic3⋊Dic3—22no—
17#63872—22no—
18#63872C2214yes—
19C3×#835C2218yes—
20#63567C2218yes—
21#63555C2214yes—
22C2×#944—32no—
23C2×#944—61no—
24C2×#890—32no—
25C2×C3×#103—32no—
26C2×#835D312yes—
27C2×#816—32no—
28C2×#815—32no—
29C2×#810—32no—
30#4797—316no—
31C2×C32×Q8—21no—
32C2×C32×Q8—24no—
33C2×C32×Q8C2312yes—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D412yes—
38C2×#634—24no—
39C2×#634—21no—
40C2×#634C2312yes—
41C22×C3×Dic3—22no—
42#3750—28no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3C2312yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2314yes—
47C2×C3×C3⋊C8—24no—
48C2×C3×C3⋊C8C2314yes—
49Dic3⋊Dic3—28no—
50C2×#491—91noSylow
51C22×C3×Q8—21no—
52C22×C3×Q8C2×D312yes—
53C22×Dic6—32no—
54C22×Dic6—61no—
55C22×C3×C8—32no—
56C2×C3×C4⋊C4—32no—
57#944—38no—
58#944—64no—
59#944—64no—
60#944—64no—
61C2×C4⋊Dic3—62no—
62C2×C4⋊Dic3C2×D312yes—
63C2×Dic3⋊C4—62no—
64C2×Dic3⋊C4—62no—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—64no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C22×C3⋊C8C2×D312yes—
70#890—38no—
71#890—64no—
72C3×#103—38no—
73#835C2×D318yes—
74#816—38no—
75#815—38no—
76#810—38no—
77C23×C32C2×D411yescharacteristic
78C32×Q8—24no—
79C32×Q8—42no—
80C2×C32×C4—22no—
81C2×C32×C4—42no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4#4114yes—
84C2×C32×C4C2411yescharacteristic
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3C2×D414yes—
89#634—24no—
90#634—42no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—44no—
93C3×C3⋊C8—24no—
94C2×C4⋊Q8—91no—
95C2×#125—91no—
96#491—98no—
97C2×#103—32no—
98C2×#103—92no—
99C2×#97—91no—
100C2×C3×Q8—22no—
101C2×C3×Q8—22no—
102C2×C3×Q8—24no—
103C2×C3×Q8—24no—
104C2×C3×Q8—22no—
105C2×C3×Q8—44no—
106C2×C3×Q8C22×D314yes—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—21no—
110C22×C3×C4—62no—
111C22×C3×C4C22×D312yes—
112C22×Dic3—22no—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C2×Dic6—34no—
119C2×Dic6—62no—
120C2×Dic6—64no—
121C2×Dic6—64no—
122C2×Dic6—62no—
123C2×Dic6—62no—
124C2×Dic6—124no—
125C2×C3×C8—34no—
126C2×C3×C8—64no—
127C3×C4⋊C4—34no—
128C3×C4⋊C4—62no—
129C4⋊Dic3—22no—
130C4⋊Dic3—68no—
131C4⋊Dic3C22×D314yes—
132Dic3⋊C4—68no—
133Dic3⋊C4—68no—
134Dic3⋊C4—68no—
135Dic3⋊C4—616no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C2×C3⋊C8—24no—
141C2×C3⋊C8C22×D314yes—
142C22×C32#12412yes—
143C22×C32#13714yes—
144C22×C32C22×D411yescharacteristic
145C32×C4—42no—
146C32×C4#12412yes—
147C32×C4C2×#4112yes—
148C3⋊Dic3—24no—
149C3⋊Dic3—42no—
150C3×Dic3—44no—
151C22×Q8—91no—
152C22×Q8D3211yescharacteristic
153C22×C8—32no—
154C4⋊Q8—94no—
155C4⋊Q8—182no—
156#125—94no—
157#125—182no—
158C2×C4⋊C4—32no—
159C2×C4⋊C4—182no—
160C2×C4⋊C4—182no—
161C2×C42—91no—
162#103—38no—
163#103—98no—
164#97—94no—
165C23×C3—21no—
166C23×C3D3×D412yes—
167C3×Q8—24no—
168C3×Q8—24no—
169C3×Q8—44no—
170C3×Q8—44no—
171C3×Q8—44no—
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×C4#23514yes—
182C2×C3×C4D3×D412yes—
183C2×C3×C4#23714yes—
184C2×C3×C4C23×D312yes—
185C2×Dic3—24no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—44no—
189C2×Dic3—64no—
190C2×Dic3—68no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—124no—
196C2×Dic3—124no—
197Dic6—64no—
198Dic6—64no—
199Dic6—124no—
200Dic6—124no—
201Dic6—124no—
202C3×C8—64no—
203C3⋊C8—24no—
204C2×C32#49114yescomplemented
205C2×C32C2×#12411yescharacteristic
206C2×C32C2×#13712yes—
207C2×Q8—21no—
208C2×Q8—24no—
209C2×Q8—92no—
210C2×Q8—181no—
211C2×Q8—184no—
212C2×Q8C2×D3212yes—
213C22×C4—21no—
214C22×C4—62no—
215C22×C4—92no—
216C22×C4—181no—
217C22×C4C2×D3211yescharacteristic
218C2×C8—34no—
219C2×C8—64no—
220C4⋊C4—34no—
221C4⋊C4—62no—
222C4⋊C4—188no—
223C4⋊C4—188no—
224C42—92no—
225C42—92no—
226C22×C3—21no—
227C22×C3—24no—
228C22×C3—22no—
229C22×C3#88514yes—
230C22×C3#91514yes—
231C22×C3#91814yes—
232C22×C3C2×D3×D412yes—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—44no—
236C3×C4—44no—
237C3×C4—124no—
238C3×C4#88514yes—
239C3×C4C2×#23512yes—
240C3×C4C2×#23712yes—
241Dic3—44no—
242Dic3—68no—
243Dic3—64no—
244Dic3—64no—
245Dic3—124no—
246Dic3—124no—
247C32C2×#49111yescharacteristic, complemented, Sylow
248C23#381111yescharacteristic
249Q8—24no—
250Q8—42no—
251Q8—184no—
252Q8—362no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—64no—
256C2×C4—94no—
257C2×C4—124no—
258C2×C4—184no—
259C2×C4—182no—
260C2×C4—362no—
261C2×C4#380414yes—
262C2×C4#381111yescharacteristic
263C2×C4C22×D3211yescharacteristic
264C8—64no—
265C2×C3—22no—
266C2×C3—24no—
267C2×C3—21no—
268C2×C3#479718yescomplemented
269C2×C3C2×#88512yes—
270C2×C3C2×#91512yes—
271C2×C3C2×#91812yes—
272C22#6395114yes—
273C22#6395312yes—
274C22C2×#381111yescharacteristic
275C4—42no—
276C4—124no—
277C4—184no—
278C4—362no—
279C4#6395312yes—
280C4C2×#380412yes—
281C3—21no—
282C3C2×#479712yescomplemented
283C2#1059161614yesdirect product factor
284C2C2×#6395112yes—
285C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591616C2direct (N × H)
204. C2×C32#491semidirect
247. C32C2×#491semidirect
268. C2×C3#4797semidirect
282. C3C2×#4797semidirect
283. C2#10591616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×#638722
C2×C3×#8352
#105916162
C2×#635672
C2×#635552
C2×#47973