Finite Group Databasebeta

← C2×#10591539 #11873455

Subgroups — C2×#10591539 #11873455

Order 1152.

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

normal subgroups only

This group has 989 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×#64156C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×C3×#835C212yesmaximal, complemented
4#10591539C218yesmaximal, direct product factor
5C2×#63564C212yesmaximal
6C2×#63553C211yesmaximal, characteristic, complemented
7C2×#4800—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10#64156—22no—
11#64156C2214yes—
12C2×#3752—22no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic3⋊Dic3—22no—
17#63872—22no—
18#63872C2214yescomplemented
19C3×#835C2218yescomplemented
20#63564C2218yes—
21#63553C2214yescomplemented
22C2×#947—32no—
23C2×#947—61no—
24C2×#890—32no—
25C2×C3×#103—32no—
26C2×#835D312yescomplemented
27C2×#821—32no—
28C2×C8×Dic3—32no—
29C2×#809—32no—
30#4800—316no—
31C23×C3⋊D3—21no—
32C2×C32×Q8—21no—
33C2×C32×Q8—24no—
34C2×C32×Q8C2312yes—
35C22×C32×C4—21no—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3D412yes—
38C2×C4⋊(C3⋊D3)—24no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)C2312yes—
41C22×C3×Dic3—22no—
42#3752—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×#488—91noSylow
51C22×C3×Q8—21no—
52C22×C3×Q8C2×D312yes—
53C22×D12—32no—
54C22×D12—61no—
55C22×C3×C8—32no—
56C2×C3×C4⋊C4—32no—
57#947—38no—
58#947—64no—
59#947—64no—
60#947—64no—
61C2×(C2×D3)⋊C4—62no—
62C2×(C2×D3)⋊C4—62no—
63C2×(C2×D3)⋊C4—64no—
64C2×C4⋊Dic3—62no—
65C2×C4⋊Dic3C2×D312yes—
66C2×Dic3⋊C4—62no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C22×C3⋊C8C2×D312yes—
70#890—38no—
71#890—64no—
72C3×#103—38no—
73#835C2×D318yescomplemented
74#821—38no—
75C8×Dic3—38no—
76#809—38no—
77C23×C32C2×D411yescharacteristic
78C22×C3⋊D3—22no—
79C22×C3⋊D3—42no—
80C22×C3⋊D3—44no—
81C32×Q8—24no—
82C32×Q8—42no—
83C2×C32×C4—22no—
84C2×C32×C4—42no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4#4114yes—
87C2×C32×C4C2411yescharacteristic
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3C2×D414yes—
90C4⋊(C3⋊D3)—24no—
91C4⋊(C3⋊D3)—42no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—44no—
94C3×C3⋊C8—24no—
95C2×#125—91no—
96C2×#124—91no—
97#488—98no—
98C2×#103—32no—
99C2×#102—92no—
100C2×C4×C8—91no—
101C23×D3—62no—
102C23×D3—62no—
103C2×C3×Q8—22no—
104C2×C3×Q8—22no—
105C2×C3×Q8—24no—
106C2×C3×Q8—24no—
107C2×C3×Q8—22no—
108C2×C3×Q8—44no—
109C2×C3×Q8C22×D314yes—
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—62no—
119C2×D12—34no—
120C2×D12—62no—
121C2×D12—64no—
122C2×D12—64no—
123C2×D12—62no—
124C2×D12—62no—
125C2×D12—124no—
126C2×C3×C8—34no—
127C2×C3×C8—64no—
128C3×C4⋊C4—34no—
129C3×C4⋊C4—62no—
130(C2×D3)⋊C4—68no—
131(C2×D3)⋊C4—68no—
132(C2×D3)⋊C4—616no—
133C4⋊Dic3—22no—
134C4⋊Dic3—68no—
135C4⋊Dic3C22×D314yes—
136Dic3⋊C4—68no—
137C4×Dic3—34no—
138C4×Dic3—34no—
139C4×Dic3—62no—
140C4×Dic3—62no—
141C2×C3⋊C8—24no—
142C2×C3⋊C8C22×D314yes—
143C22×C32#12412yes—
144C22×C32#13514yes—
145C22×C32C22×D411yescharacteristic
146C2×C3⋊D3—42no—
147C2×C3⋊D3—44no—
148C2×C3⋊D3—84no—
149C32×C4—42no—
150C32×C4#12412yes—
151C32×C4C2×#4112yes—
152C3⋊Dic3—24no—
153C3×Dic3—44no—
154C22×Q8D3211yescharacteristic
155C22×D4—91no—
156C22×C8—32no—
157#125—94no—
158#125—182no—
159#124—94no—
160#124—182no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—182no—
163C2×C22⋊C4—182no—
164C2×C42—91no—
165#103—38no—
166#102—98no—
167C4×C8—94no—
168C23×C3—21no—
169C23×C3D3×D412yes—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—124no—
173C22×D3—128no—
174C22×D3—124no—
175C22×D3—124no—
176C22×D3—124no—
177C3×Q8—24no—
178C3×Q8—24no—
179C3×Q8—44no—
180C3×Q8—44no—
181C3×Q8—44no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—21no—
185C2×C3×C4—24no—
186C2×C3×C4—21no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4—64no—
190C2×C3×C4—124no—
191C2×C3×C4#23514yes—
192C2×C3×C4D3×D412yes—
193C2×C3×C4#23714yes—
194C2×C3×C4C23×D312yes—
195C2×Dic3—24no—
196C2×Dic3—34no—
197C2×Dic3—34no—
198C2×Dic3—44no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—124no—
203D12—64no—
204D12—64no—
205D12—124no—
206D12—124no—
207D12—124no—
208C3×C8—64no—
209C3⋊C8—24no—
210C2×C32#48814yescomplemented
211C2×C32C2×#12411yescharacteristic
212C2×C32C2×#13512yes—
213C3⋊D3—82no—
214C24—181no—
215C2×Q8—21no—
216C2×Q8—24no—
217C2×Q8C2×D3212yes—
218C2×D4—92no—
219C2×D4—184no—
220C2×D4—181no—
221C22×C4—21no—
222C22×C4—62no—
223C22×C4—92no—
224C22×C4C2×D3211yescharacteristic
225C2×C8—34no—
226C2×C8—64no—
227C4⋊C4—34no—
228C4⋊C4—62no—
229C4⋊C4—188no—
230C22⋊C4—188no—
231C42—92no—
232C42—92no—
233C22×C3—21no—
234C22×C3—24no—
235C22×C3—22no—
236C22×C3#88514yes—
237C22×C3#91614yes—
238C22×C3#91914yes—
239C22×C3C2×D3×D412yes—
240C2×D3—124no—
241C2×D3—128no—
242C2×D3—124no—
243C2×D3—124no—
244C2×D3—124no—
245C2×D3—248no—
246C2×D3—248no—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—44no—
250C3×C4—44no—
251C3×C4—124no—
252C3×C4#88514yes—
253C3×C4C2×#23512yes—
254C3×C4C2×#23712yes—
255Dic3—44no—
256Dic3—64no—
257Dic3—64no—
258Dic3—124no—
259C32C2×#48811yescharacteristic, complemented, Sylow
260C23—182no—
261C23—364no—
262C23—362no—
263C23#381111yescharacteristic
264Q8—24no—
265Q8—42no—
266D4—184no—
267D4—362no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—64no—
271C2×C4—94no—
272C2×C4—124no—
273C2×C4—184no—
274C2×C4#380414yes—
275C2×C4#381111yescharacteristic
276C2×C4C22×D3211yescharacteristic
277C8—64no—
278C2×C3—22no—
279C2×C3—24no—
280C2×C3—21no—
281C2×C3#480018yescomplemented
282C2×C3C2×#88512yes—
283C2×C3C2×#91612yes—
284C2×C3C2×#91912yes—
285D3—244no—
286D3—244no—
287C22—364no—
288C22—362no—
289C22—724no—
290C22#6395014yes—
291C22#6395312yes—
292C22C2×#381111yescharacteristic
293C4—42no—
294C4—124no—
295C4—184no—
296C4#6395312yes—
297C4C2×#380412yes—
298C3—21no—
299C3C2×#480012yescomplemented
300C2—722no—
301C2#1059153914yesdirect product factor
302C2C2×#6395012yes—
303C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#488
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
2. C2×#63872C2semidirect
3. C2×C3×#835C2semidirect
4. #10591539C2direct (N × H)
6. C2×#63553C2semidirect
18. #63872C22semidirect
19. C3×#835C22semidirect
21. #63553C22semidirect
26. C2×#835D3semidirect
73. #835C2×D3semidirect
210. C2×C32#488semidirect
259. C32C2×#488semidirect
281. C2×C3#4800semidirect
299. C3C2×#4800semidirect
301. C2#10591539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×#638722
C2×C3×#8352
#105915392
C2×#635642
C2×#635532
C2×#48003