Finite Group Databasebeta

← C2×#10591480 #11873580

Subgroups — C2×#10591480 #11873580

Order 1152.

1225 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1225 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×#64149C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal, complemented
4#10591480C218yesmaximal, direct product factor
5C2×#63564C212yesmaximal, complemented
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×#4764—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638—22no—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64149—22no—
12#64149C2214yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic3⋊Dic3—22no—
17#63872—22no—
18#63872C2214yescomplemented
19C3×#832C2218yescomplemented
20#63564C2218yescomplemented
21#63555C2214yescomplemented
22C2×#940—32no—
23C2×#940—61no—
24C2×#890—32no—
25C2×C3×#102—32no—
26C2×#832D312yescomplemented
27C2×#821—32no—
28C2×#815—32no—
29C2×#809—32no—
30#4764—316no—
31C24×C32—21no—
32C23×C3⋊D3—21no—
33C2×C32×D4—21no—
34C2×C32×D4—24no—
35C2×C32×D4C2312yes—
36C22×C32×C4C2311yescharacteristic
37C2×#638—28no—
38C2×#638—48no—
39C22×C3⋊Dic3D412yes—
40C2×C4⋊(C3⋊D3)—24no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2312yes—
43C22×C3×Dic3—22no—
44C4×C3⋊Dic3D412yes—
45C4×C3⋊Dic3C2312yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3C2314yes—
48C2×C3×C3⋊C8—24no—
49C2×C3×C3⋊C8C2314yes—
50Dic3⋊Dic3—28no—
51C2×#490—91noSylow
52C22×C3×D4—21no—
53C22×C3×D4C2×D312yes—
54C22×#67—62no—
55C22×#67—62no—
56C22×#67—64no—
57C22×D12—32no—
58C22×D12—61no—
59C22×C3×C8—32no—
60C2×C3×C4⋊C4—32no—
61#940—38no—
62#940—64no—
63#940—64no—
64#940—64no—
65C2×C4⋊Dic3—62no—
66C2×C4⋊Dic3C2×D312yes—
67C2×Dic3⋊C4—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8C2×D312yes—
71#890—38no—
72#890—64no—
73C3×#102—38no—
74#832C2×D318yescomplemented
75#821—38no—
76#815—38no—
77#809—38no—
78C23×C32—22no—
79C23×C32—42no—
80C23×C32—44no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—42no—
84C22×C3⋊D3—44no—
85C32×D4—24no—
86C32×D4—42no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4#4114yes—
89C2×C32×C4C2411yescharacteristic
90#638—416no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C2×D414yes—
93C4⋊(C3⋊D3)—24no—
94C4⋊(C3⋊D3)—42no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—44no—
97C3×C3⋊C8—24no—
98C2×#127—91no—
99C2×#125—91no—
100#490—98no—
101C2×#102—32no—
102C2×#102—92no—
103C2×#97—91no—
104C24×C3—22no—
105C24×C3—22no—
106C23×D3—62no—
107C23×D3—62no—
108C2×C3×D4—22no—
109C2×C3×D4—24no—
110C2×C3×D4—22no—
111C2×C3×D4—24no—
112C2×C3×D4—22no—
113C2×C3×D4—44no—
114C2×C3×D4C22×D314yes—
115C22×C3×C4—21no—
116C22×C3×C4—62no—
117C22×C3×C4C22×D312yes—
118C2×#67—68no—
119C2×#67—68no—
120C2×#67—616no—
121C2×#67—1216no—
122C2×#67—128no—
123C2×#67—128no—
124C22×Dic3—22no—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—62no—
128C2×D12—34no—
129C2×D12—62no—
130C2×D12—64no—
131C2×D12—64no—
132C2×D12—62no—
133C2×D12—62no—
134C2×D12—124no—
135C2×C3×C8—34no—
136C2×C3×C8—64no—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—62no—
139C4⋊Dic3—22no—
140C4⋊Dic3—68no—
141C4⋊Dic3C22×D314yes—
142Dic3⋊C4—68no—
143C4×Dic3—34no—
144C4×Dic3—34no—
145C4×Dic3—62no—
146C4×Dic3—62no—
147C2×C3⋊C8—24no—
148C2×C3⋊C8C22×D314yes—
149C22×C32—42no—
150C22×C32—44no—
151C22×C32—84no—
152C22×C32#12412yes—
153C22×C32AGL(1,ℤ/8)14yes—
154C22×C32C22×D411yescharacteristic
155C2×C3⋊D3—42no—
156C2×C3⋊D3—44no—
157C2×C3⋊D3—84no—
158C32×C4#12412yes—
159C32×C4C2×#4112yes—
160C3⋊Dic3—24no—
161C3×Dic3—44no—
162C22×D4—91no—
163C22×D4—182no—
164C22×D4D3211yescharacteristic
165C22×C8—32no—
166#127—94no—
167#127—182no—
168#125—94no—
169#125—182no—
170C2×C4⋊C4—32no—
171C2×C4⋊C4—182no—
172C2×C42—91no—
173#102—38no—
174#102—98no—
175#97—94no—
176C23×C3—24no—
177C23×C3—24no—
178C23×C3—21no—
179C23×C3—48no—
180C23×C3—44no—
181C23×C3—44no—
182C23×C3—44no—
183C23×C3—44no—
184C23×C3D3×D412yes—
185C22×D3—64no—
186C22×D3—64no—
187C22×D3—124no—
188C22×D3—128no—
189C22×D3—124no—
190C22×D3—124no—
191C22×D3—124no—
192C3×D4—24no—
193C3×D4—24no—
194C3×D4—44no—
195C3×D4—44no—
196C3×D4—44no—
197C2×C3×C4—21no—
198C2×C3×C4—24no—
199C2×C3×C4—21no—
200C2×C3×C4—64no—
201C2×C3×C4—124no—
202C2×C3×C4#23514yes—
203C2×C3×C4D3×D412yes—
204C2×C3×C4#23714yes—
205C2×C3×C4C23×D312yes—
206#67—1232no—
207#67—1216no—
208#67—1216no—
209C2×Dic3—24no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—44no—
213C2×Dic3—64no—
214C2×Dic3—68no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217D12—64no—
218D12—64no—
219D12—124no—
220D12—124no—
221D12—124no—
222C3×C8—64no—
223C3⋊C8—24no—
224C2×C32—82no—
225C2×C32#49014yescomplemented
226C2×C32C2×#12411yescharacteristic
227C2×C32C2×AGL(1,ℤ/8)12yes—
228C3⋊D3—82no—
229C24—21no—
230C24—181no—
231C2×D4—24no—
232C2×D4—21no—
233C2×D4—92no—
234C2×D4—188no—
235C2×D4—184no—
236C2×D4—181no—
237C2×D4—368no—
238C2×D4C2×D3212yes—
239C22×C4—62no—
240C22×C4—92no—
241C22×C4C2×D3211yescharacteristic
242C2×C8—34no—
243C2×C8—64no—
244C4⋊C4—34no—
245C4⋊C4—62no—
246C4⋊C4—188no—
247C42—92no—
248C42—92no—
249C22×C3—21no—
250C22×C3—24no—
251C22×C3—22no—
252C22×C3—48no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—44no—
256C22×C3—44no—
257C22×C3—88no—
258C22×C3—88no—
259C22×C3#88514yes—
260C22×C3#91114yes—
261C22×C3#91414yes—
262C22×C3C2×D3×D412yes—
263C2×D3—124no—
264C2×D3—128no—
265C2×D3—124no—
266C2×D3—124no—
267C2×D3—124no—
268C2×D3—248no—
269C2×D3—248no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—124no—
273C3×C4#88514yes—
274C3×C4C2×#23512yes—
275C3×C4C2×#23712yes—
276Dic3—44no—
277Dic3—68no—
278Dic3—64no—
279Dic3—64no—
280C32C2×#49011yescharacteristic, complemented, Sylow
281C23—22no—
282C23—44no—
283C23—42no—
284C23—182no—
285C23—364no—
286C23—362no—
287C23#381111yescharacteristic
288D4—24no—
289D4—42no—
290D4—184no—
291D4—3616no—
292D4—362no—
293C2×C4—64no—
294C2×C4—94no—
295C2×C4—124no—
296C2×C4—184no—
297C2×C4#380414yes—
298C2×C4#381111yescharacteristic
299C2×C4C22×D3211yescharacteristic
300C8—64no—
301C2×C3—22no—
302C2×C3—21no—
303C2×C3—24no—
304C2×C3—84no—
305C2×C3—84no—
306C2×C3#476418yescomplemented
307C2×C3C2×#88512yes—
308C2×C3C2×#91112yes—
309C2×C3C2×#91412yes—
310D3—244no—
311D3—244no—
312C22—44no—
313C22—42no—
314C22—84no—
315C22—364no—
316C22—362no—
317C22—724no—
318C22#6393714yes—
319C22#6395312yes—
320C22C2×#381111yescharacteristic
321C4—124no—
322C4—184no—
323C4#6395312yes—
324C4C2×#380412yes—
325C3—21no—
326C3C2×#476412yescomplemented
327C2—82no—
328C2—722no—
329C2#1059148014yesdirect product factor
330C2C2×#6393712yes—
331C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64149C2
hypercenterC22×D4D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63872C2semidirect
3. C2×C3×#832C2semidirect
4. #10591480C2direct (N × H)
5. C2×#63564C2semidirect
6. C2×#63555C2semidirect
18. #63872C22semidirect
19. C3×#832C22semidirect
20. #63564C22semidirect
21. #63555C22semidirect
26. C2×#832D3semidirect
74. #832C2×D3semidirect
225. C2×C32#490semidirect
280. C32C2×#490semidirect
306. C2×C3#4764semidirect
326. C3C2×#4764semidirect
329. C2#10591480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641492
C2×#638722
C2×C3×#8322
#105914802
C2×#635642
C2×#635552
C2×#47643