Finite Group Databasebeta

← C2×#10590444 #11869614

Subgroups — C2×#10590444 #11869614

Order 1152.

1081 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1081 conjugacy classes of subgroups — too many to draw. Only its 220 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×#64106C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×C3×#807C212yesmaximal, complemented
4C2×#63567C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic
6#10590444C218yesmaximal, direct product factor
7C2×#4884—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×#624—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×C4⋊(C3⋊Dic3)—21no—
14#64106—22no—
15#64106C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—21no—
19#63900—22no—
20#63900C2214yes—
21C3×#807C2218yescomplemented
22#63567C2218yescomplemented
23#63557C2214yes—
24C2×#897—32no—
25C2×#897—61no—
26C2×D3×C4⋊C4—32no—
27C2×C3×#107—32no—
28C2×(C2×D3)⋊C8—32no—
29C2×#816—32no—
30C2×#810—32no—
31C2×#807D312yescomplemented
32#4884—316no—
33C23×C3⋊D3D411yescharacteristic
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C2×C4×C3⋊D3—24no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3C2312yes—
41C2×#634—24no—
42C2×#634—21no—
43C2×#634C2312yes—
44C22×C3×Dic3—22no—
45C2×#624—24no—
46C2×#624—44no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2312yes—
49#3752—24no—
50C4⋊(C3⋊Dic3)—24no—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3C2314yes—
53C2×C3×C3⋊C8—24no—
54C2×C3×C3⋊C8C2314yes—
55#3724—24no—
56C2×#484—91noSylow
57C22×C4×D3—32no—
58C22×C4×D3—61no—
59C22×C4×D3—62no—
60C22×Dic6—32no—
61C22×Dic6—61no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4C2×D312yes—
66C2×(C2×D3)⋊C4—62no—
67C2×(C2×D3)⋊C4—62no—
68C2×C4⋊Dic3—62no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—62no—
72C22×C3⋊C8C2×D312yes—
73#897—38no—
74#897—64no—
75#897—64no—
76#897—64no—
77D3×C4⋊C4—38no—
78D3×C4⋊C4—64no—
79C3×#107—38no—
80(C2×D3)⋊C8—38no—
81#816—38no—
82#810—38no—
83#807C2×D318yescomplemented
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3Q1614yes—
88C22×C3⋊D3C2×D412yes—
89C2×C32×C4—22no—
90C2×C32×C4—42no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4114yes—
93C2×C32×C4C2411yescharacteristic
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3C2×D412yes—
98C4×C3⋊D3—24no—
99C4×C3⋊D3—24no—
100#634—24no—
101#634—42no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—44no—
104#624—48no—
105C3×C3⋊C8—24no—
106C2×C22⋊Q8—91no—
107C22×C4⋊C4—91no—
108#484—98no—
109C2×#107—32no—
110C2×#103—92no—
111C2×C22⋊C8—91no—
112C23×D3—32no—
113C23×D3—61no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4—62no—
118C22×C3×C4C22×D312yes—
119C22×Dic3—22no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C2×C4×D3—34no—
125C2×C4×D3—34no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—64no—
129C2×C4×D3—64no—
130C2×C4×D3—68no—
131C2×C4×D3—124no—
132C2×C4×D3—128no—
133C2×Dic6—34no—
134C2×Dic6—62no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—62no—
138C2×Dic6—62no—
139C2×Dic6—124no—
140C2×C3×C8—34no—
141C2×C3×C8—64no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—34no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4C22×D314yes—
148(C2×D3)⋊C4—68no—
149(C2×D3)⋊C4—68no—
150C4⋊Dic3—22no—
151C4⋊Dic3—68no—
152C4⋊Dic3—68no—
153C4⋊Dic3C22×D314yes—
154Dic3⋊C4—68no—
155C2×C3⋊C8—24no—
156C2×C3⋊C8C22×D314yes—
157C22×C32#12312yes—
158C22×C32C2×Q1612yes—
159C22×C32AGL(1,ℤ/8)12yes—
160C22×C32C22×D411yescharacteristic
161C2×C3⋊D3—22no—
162C2×C3⋊D3—22no—
163C2×C3⋊D3—28no—
164C2×C3⋊D3C2×Q1614yes—
165C32×C4—42no—
166C32×C4#12312yes—
167C32×C4C2×#4112yes—
168C3⋊Dic3—22no—
169C3⋊Dic3—42no—
170C3×Dic3—44no—
171C22×Q8—91no—
172C23×C4—91no—
173C23×C4—181no—
174C22×C8—32no—
175C22⋊Q8—94no—
176C22⋊Q8—182no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—94no—
179C2×C4⋊C4—182no—
180C2×C4⋊C4—181no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4D3211yescharacteristic
183C2×C22⋊C4—181no—
184#107—38no—
185#103—98no—
186C22⋊C8—94no—
187C23×C3—21no—
188C23×C3D3×D412yes—
189C22×D3—38no—
190C22×D3—34no—
191C22×D3—64no—
192C22×D3—62no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—122no—
196C22×D3—122no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—21no—
200C2×C3×C4—24no—
201C2×C3×C4—21no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4—64no—
205C2×C3×C4—124no—
206C2×C3×C4#23514yes—
207C2×C3×C4D3×D412yes—
208C2×C3×C4#23914yes—
209C2×C3×C4C23×D312yes—
210C2×Dic3—24no—
211C2×Dic3—34no—
212C2×Dic3—44no—
213C2×Dic3—62no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—122no—
218C2×Dic3—124no—
219C2×Dic3—124no—
220C4×D3—68no—
221C4×D3—64no—
222C4×D3—64no—
223C4×D3—124no—
224C4×D3—124no—
225C4×D3—1216no—
226Dic6—64no—
227Dic6—64no—
228Dic6—124no—
229Dic6—124no—
230Dic6—124no—
231C3×C8—64no—
232C3⋊C8—24no—
233C2×C32#48414yescomplemented
234C2×C32C2×#12311yescharacteristic
235C2×C32C22×Q1611yescharacteristic
236C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
237C3⋊D3—24no—
238C24—91no—
239C2×Q8—92no—
240C2×Q8—181no—
241C2×Q8—184no—
242C22×C4—21no—
243C22×C4—62no—
244C22×C4—91no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—184no—
248C22×C4—184no—
249C22×C4—181no—
250C22×C4—364no—
251C22×C4C2×D3211yescharacteristic
252C2×C8—34no—
253C2×C8—64no—
254C4⋊C4—21no—
255C4⋊C4—34no—
256C4⋊C4—62no—
257C4⋊C4—184no—
258C4⋊C4—184no—
259C4⋊C4C2×D3212yes—
260C22⋊C4—184no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3#89414yes—
266C22×C3#91114yes—
267C22×C3D3×Q1614yes—
268C22×C3C2×D3×D412yes—
269C2×D3—38no—
270C2×D3—64no—
271C2×D3—616no—
272C2×D3—64no—
273C2×D3—64no—
274C2×D3—122no—
275C2×D3—122no—
276C2×D3—128no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—44no—
280C3×C4—44no—
281C3×C4—124no—
282C3×C4#89414yes—
283C3×C4C2×#23512yes—
284C3×C4C2×#23912yes—
285Dic3—44no—
286Dic3—64no—
287Dic3—122no—
288Dic3—124no—
289Dic3—124no—
290C32C2×#48411yescharacteristic, complemented, Sylow
291C23—92no—
292C23—94no—
293C23—182no—
294C23—182no—
295C23#381111yescharacteristic
296Q8—184no—
297Q8—362no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—64no—
301C2×C4—92no—
302C2×C4—124no—
303C2×C4—182no—
304C2×C4—184no—
305C2×C4—184no—
306C2×C4—182no—
307C2×C4—368no—
308C2×C4—362no—
309C2×C4#379914yes—
310C2×C4#381111yescharacteristic
311C2×C4C22×D3211yescharacteristic
312C8—64no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—24no—
317C2×C3#488418yescomplemented
318C2×C3C2×#89412yes—
319C2×C3C2×#91112yes—
320C2×C3C2×D3×Q1612yes—
321D3—68no—
322D3—124no—
323C22—94no—
324C22—182no—
325C22—182no—
326C22—188no—
327C22#6389712yes—
328C22#6392712yes—
329C22#6394412yes—
330C22C2×#381111yescharacteristic
331C4—42no—
332C4—124no—
333C4—182no—
334C4—362no—
335C4#6389712yes—
336C4C2×#379912yes—
337C3—21no—
338C3C2×#488412yescomplemented
339C2—184no—
340C2#1059044414yesdirect product factor
341C2C2×#6389711yescharacteristic
342C2C2×#6392711yescharacteristic
343C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#484
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
3. C2×C3×#807C2semidirect
4. C2×#63567C2semidirect
6. #10590444C2direct (N × H)
21. C3×#807C22semidirect
22. #63567C22semidirect
31. C2×#807D3semidirect
83. #807C2×D3semidirect
233. C2×C32#484semidirect
290. C32C2×#484semidirect
317. C2×C3#4884semidirect
338. C3C2×#4884semidirect
340. C2#10590444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#639002
C2×C3×#8072
C2×#635672
C2×#635572
#105904442
C2×#48843