Finite Group Databasebeta

← C2×#10590567 #11873407

Subgroups — C2×#10590567 #11873407

Order 1152.

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

normal subgroups only

This group has 993 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×#64097C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×#63566C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#10590567C218yesmaximal, direct product factor
7C2×#4792—32nomaximal
8C22×#634—21no—
9C22×C3×Dic6C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64097—22no—
15#64097C2214yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18C2×#3724—21no—
19#63873—22no—
20#63873C2214yes—
21C3×#810C2218yes—
22#63566C2218yes—
23#63553C2214yes—
24C2×#944—32no—
25C2×#888—32no—
26C2×#888—61no—
27C2×C3×#103—32no—
28C2×#835—32no—
29C2×#816—32no—
30C2×C8×Dic3—32no—
31C2×#810D312yes—
32#4792—316no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×#634—24no—
39C2×#634—44no—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2314yes—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2312yes—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2312yes—
49#3750—24no—
50C4×C3⋊Dic3D412yes—
51C4×C3⋊Dic3C2312yes—
52C2×C3×C3⋊C8—24no—
53C2×C3×C3⋊C8C2314yes—
54#3724—24no—
55#3724—24no—
56C2×#487—91noSylow
57C22×C3×Q8—32no—
58C22×Dic6—62no—
59C22×Dic6—62no—
60C22×Dic6C2×D312yes—
61C22×C3×C8—32no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4C2×D312yes—
64#944—38no—
65#944—64no—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—61no—
68C2×Dic3⋊C4—62no—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—62no—
71C2×Dic3⋊C4—62no—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—61no—
74C22×C3⋊C8C2×D312yes—
75#888—38no—
76#888—64no—
77#888—64no—
78#888—64no—
79C3×#103—38no—
80#835—38no—
81#816—38no—
82C8×Dic3—38no—
83#810C2×D318yes—
84C23×C32C2×D411yescharacteristic
85C2×C32×C4—22no—
86C2×C32×C4—42no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4#4114yes—
89C2×C32×C4C2411yescharacteristic
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3SD1614yes—
93C2×C3⋊Dic3Q1614yes—
94C2×C3⋊Dic3C2×D412yes—
95C2×C3⋊Dic3C2×D412yes—
96#634—48no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99C3×Dic6—24no—
100C3×Dic6—24no—
101C3×Dic6—44no—
102C3×C3⋊C8—24no—
103C2×C4⋊Q8—91no—
104C2×C4⋊Q8—91no—
105#487—98no—
106C2×#103—32no—
107C2×#103—92no—
108C2×C4×C8—91no—
109C2×C3×Q8—34no—
110C2×C3×Q8—62no—
111C2×C3×Q8—64no—
112C2×C3×Q8—64no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—62no—
117C22×C3×C4C22×D312yes—
118C22×Dic3—22no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C2×Dic6—24no—
126C2×Dic6—24no—
127C2×Dic6—22no—
128C2×Dic6—68no—
129C2×Dic6—68no—
130C2×Dic6—128no—
131C2×Dic6—128no—
132C2×Dic6C22×D314yes—
133C2×C3×C8—34no—
134C2×C3×C8—64no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4C22×D314yes—
139C4⋊Dic3—34no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142C4⋊Dic3—62no—
143Dic3⋊C4—68no—
144Dic3⋊C4—68no—
145Dic3⋊C4—68no—
146Dic3⋊C4—68no—
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C2×C3⋊C8—24no—
152C2×C3⋊C8C22×D314yes—
153C22×C32#12412yes—
154C22×C32C2×SD1612yes—
155C22×C32C2×Q1612yes—
156C22×C32C22×D411yescharacteristic
157C32×C4—42no—
158C32×C4#12412yes—
159C32×C4C2×#4112yes—
160C3⋊Dic3—42no—
161C3⋊Dic3C2×SD1614yes—
162C3⋊Dic3C2×Q1614yes—
163C3×Dic3—44no—
164C22×Q8—32no—
165C22×Q8—181no—
166C22×C8—32no—
167C4⋊Q8—94no—
168C4⋊Q8—94no—
169C4⋊Q8—182no—
170C4⋊Q8—182no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—181no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4D3211yescharacteristic
176C2×C42—91no—
177#103—38no—
178#103—98no—
179C4×C8—94no—
180C23×C3—21no—
181C23×C3D3×D412yes—
182C3×Q8—64no—
183C3×Q8—64no—
184C3×Q8—124no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—21no—
188C2×C3×C4—24no—
189C2×C3×C4—21no—
190C2×C3×C4—44no—
191C2×C3×C4—44no—
192C2×C3×C4—64no—
193C2×C3×C4—124no—
194C2×C3×C4#23514yes—
195C2×C3×C4D3×D412yes—
196C2×C3×C4#23714yes—
197C2×C3×C4C23×D312yes—
198C2×Dic3—24no—
199C2×Dic3—38no—
200C2×Dic3—38no—
201C2×Dic3—34no—
202C2×Dic3—34no—
203C2×Dic3—44no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212Dic6—24no—
213Dic6—24no—
214Dic6—44no—
215Dic6—1216no—
216Dic6—1216no—
217C3×C8—64no—
218C3⋊C8—24no—
219C2×C32#48714yescomplemented
220C2×C32C2×#12411yescharacteristic
221C2×C32C22×SD1611yescharacteristic
222C2×C32C22×Q1611yescharacteristic
223C2×Q8—34no—
224C2×Q8—62no—
225C2×Q8—64no—
226C2×Q8—64no—
227C2×Q8—184no—
228C2×Q8—364no—
229C22×C4—21no—
230C22×C4—62no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—181no—
234C22×C4C2×D3211yescharacteristic
235C2×C8—34no—
236C2×C8—64no—
237C4⋊C4—21no—
238C4⋊C4—92no—
239C4⋊C4—184no—
240C4⋊C4—184no—
241C4⋊C4—184no—
242C4⋊C4—181no—
243C4⋊C4C2×D3212yes—
244C42—92no—
245C42—92no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3#88514yes—
251C22×C3D3×SD1614yes—
252C22×C3D3×Q1614yes—
253C22×C3C2×D3×D412yes—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—44no—
257C3×C4—44no—
258C3×C4—124no—
259C3×C4#88514yes—
260C3×C4C2×#23512yes—
261C3×C4C2×#23712yes—
262Dic3—38no—
263Dic3—38no—
264Dic3—44no—
265Dic3—64no—
266Dic3—64no—
267Dic3—124no—
268Dic3—124no—
269C32C2×#48711yescharacteristic, complemented, Sylow
270C23#381111yescharacteristic
271Q8—64no—
272Q8—64no—
273Q8—124no—
274Q8—368no—
275C2×C4—22no—
276C2×C4—42no—
277C2×C4—64no—
278C2×C4—92no—
279C2×C4—92no—
280C2×C4—94no—
281C2×C4—94no—
282C2×C4—124no—
283C2×C4—182no—
284C2×C4—362no—
285C2×C4#379514yes—
286C2×C4#381111yescharacteristic
287C2×C4C22×D3211yescharacteristic
288C8—64no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—24no—
292C2×C3—21no—
293C2×C3#479218yescomplemented
294C2×C3C2×#88512yes—
295C2×C3C2×D3×SD1612yes—
296C2×C3C2×D3×Q1612yes—
297C22#6391312yes—
298C22#6393012yes—
299C22#6394412yes—
300C22C2×#381111yescharacteristic
301C4—42no—
302C4—94no—
303C4—94no—
304C4—124no—
305C4—362no—
306C4#6391312yes—
307C4C2×#379512yes—
308C3—21no—
309C3C2×#479212yescomplemented
310C2#1059056714yesdirect product factor
311C2C2×#6391311yescharacteristic
312C2C2×#6393011yescharacteristic
313C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#487
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. #10590567C2direct (N × H)
219. C2×C32#487semidirect
269. C32C2×#487semidirect
293. C2×C3#4792semidirect
309. C3C2×#4792semidirect
310. C2#10590567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#638732
C2×C3×#8102
C2×#635662
C2×#635532
#105905672
C2×#47923