Finite Group Databasebeta

← C2×#10589181 #11796350

Subgroups — C2×#10589181 #11796350

Order 1152.

733 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 116 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×#64145C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3#10589181C214yesmaximal, direct product factor
4C2×#4473—32nomaximal
5C22×C32×D4C2211yescharacteristic
6C22×#634C411yescharacteristic, complemented
7C2×#3757—22no—
8#64145—22no—
9#64145C412yescomplemented
10#64145C2212yes—
11C2×C4×C3⋊Dic3C411yescharacteristic, complemented
12C2×C3×#217—22no—
13C3×#834—22no—
14C3×#834C2214yes—
15C2×#936—32no—
16C2×#936—61no—
17C2×C3×#99—32no—
18C2×#834D312yes—
19#4473—38no—
20C24×C32D412yes—
21C2×C32×D4—41no—
22C2×C32×D4—41no—
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4D412yes—
25C2×C32×D4C2311yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29C2×#634—21no—
30C2×#634—41no—
31C2×#634—41no—
32C2×#634C2×C412yescomplemented
33C22×C3×Dic3—42no—
34#3757—24no—
35#3757—24no—
36C4×C3⋊Dic3—21no—
37C4×C3⋊Dic3C2×C412yescomplemented
38C3×#217—24no—
39C3×#217—42no—
40C2×#354—91noSylow
41C22×C3×D4—21no—
42C22×C3×D4C2×D312yes—
43C22×Dic6—32no—
44C22×Dic6—61no—
45C2×C3×C22⋊C4—62no—
46C2×#217—22no—
47C2×#217—64no—
48C2×#217—62no—
49C2×#217—62no—
50#936—34no—
51#936—34no—
52#936—62no—
53#936—62no—
54#936—64no—
55#936—62no—
56#936—62no—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59C3×#99—34no—
60C3×#99—62no—
61#834—22no—
62#834C2×D314yes—
63C23×C32—22no—
64C23×C32—22no—
65C23×C32—44no—
66C23×C32C22⋊C411yescharacteristic
67C23×C32C22⋊C412yes—
68C23×C32C2×D412yes—
69C32×D4—41no—
70C32×D4—42no—
71C32×D4—41no—
72C2×C32×C4—21no—
73C2×C32×C4—21no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22×C411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—42no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81#634—42no—
82#634—42no—
83C2×C3×Dic3—44no—
84C2×C3×Dic3—84no—
85C2×#124—91no—
86C2×#99—32no—
87#354—94no—
88C24×C3—22no—
89C24×C3D1212yes—
90C24×C3#6712yes—
91C2×C3×D4—21no—
92C2×C3×D4—22no—
93C2×C3×D4—21no—
94C2×C3×D4—42no—
95C2×C3×D4—42no—
96C2×C3×D4—42no—
97C2×C3×D4—42no—
98C2×C3×D4C4×D312yes—
99C2×C3×D4D1212yes—
100C2×C3×D4#6712yes—
101C2×C3×D4C22×D312yes—
102C22×C3×C4—21no—
103C22×C3×C4—122no—
104C22×C3×C4C4×D312yes—
105C22×Dic3—42no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C2×Dic6—34no—
111C2×Dic6—62no—
112C2×Dic6—62no—
113C2×Dic6—62no—
114C2×Dic6—122no—
115C2×Dic6—122no—
116C2×Dic6—122no—
117C2×Dic6—122no—
118C3×C22⋊C4—64no—
119C3×C22⋊C4—122no—
120#217—24no—
121#217—42no—
122#217—68no—
123#217—68no—
124#217—64no—
125#217—64no—
126#217—64no—
127#217—64no—
128C4×Dic3—34no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C22×C32—22no—
133C22×C32—22no—
134C22×C32—22no—
135C22×C32—42no—
136C22×C32—42no—
137C22×C32—44no—
138C22×C32—82no—
139C22×C32#9911yescharacteristic
140C22×C32#9911yescharacteristic
141C22×C32C2×C22⋊C411yescharacteristic
142C32×C4—21no—
143C32×C4—21no—
144C3⋊Dic3—42no—
145C3⋊Dic3—42no—
146C3×Dic3—84no—
147C22×Q8—91no—
148C22×D4D3211yescharacteristic
149#124—92no—
150#124—92no—
151#124—182no—
152C2×C22⋊C4—62no—
153C2×C22⋊C4—182no—
154C2×C42—91no—
155#99—34no—
156#99—62no—
157C23×C3—22no—
158C23×C3—22no—
159C23×C3—22no—
160C23×C3—22no—
161C23×C3—22no—
162C23×C3—21no—
163C23×C3—22no—
164C23×C3—42no—
165C23×C3—42no—
166C23×C3—44no—
167C23×C3—44no—
168C23×C3—48no—
169C23×C3(C2×D3)⋊C412yes—
170C23×C3(C2×D3)⋊C412yes—
171C23×C3(C2×D3)⋊C412yes—
172C23×C3C2×D1212yes—
173C23×C3C2×#6712yes—
174C3×D4—42no—
175C3×D4—42no—
176C3×D4—42no—
177C3×D4—42no—
178C3×D4—42no—
179C3×D4—44no—
180C3×D4—42no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—124no—
188C2×C3×C4—244no—
189C2×C3×C4(C2×D3)⋊C412yes—
190C2×C3×C4C2×C4×D312yes—
191C2×Dic3—44no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—84no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199C2×Dic3—124no—
200C2×Dic3—124no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203Dic6—124no—
204Dic6—124no—
205Dic6—124no—
206Dic6—124no—
207C2×C32—21no—
208C2×C32—21no—
209C2×C32—42no—
210C2×C32—42no—
211C2×C32#35412yescomplemented
212C2×C32C2×#9911yescharacteristic
213C24#62612yes—
214C2×Q8—92no—
215C2×Q8—181no—
216C2×Q8—361no—
217C2×Q8—361no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4#62411yescharacteristic
221C2×D4#62612yes—
222C2×D4C2×D3211yescharacteristic
223C22×C4—122no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4#62411yescharacteristic
227C22⋊C4—64no—
228C22⋊C4—122no—
229C22⋊C4—184no—
230C22⋊C4—184no—
231C42—92no—
232C42—181no—
233C22×C3—24no—
234C22×C3—24no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—42no—
245C22×C3—42no—
246C22×C3—42no—
247C22×C3—42no—
248C22×C3—44no—
249C22×C3—44no—
250C22×C3—44no—
251C22×C3—44no—
252C22×C3—84no—
253C22×C3—82no—
254C22×C3—82no—
255C22×C3—84no—
256C22×C3#80612yes—
257C22×C3#80612yes—
258C22×C3C2×(C2×D3)⋊C412yes—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—22no—
263C3×C4—244no—
264Dic3—84no—
265Dic3—124no—
266Dic3—124no—
267Dic3—124no—
268Dic3—124no—
269C32C2×#35411yescharacteristic, complemented, Sylow
270C23—22no—
271C23—22no—
272C23—44no—
273C23#372212yes—
274C23#372211yescharacteristic
275C23C2×#62612yes—
276Q8—362no—
277Q8—362no—
278D4—41no—
279D4—42no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—124no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—244no—
287C2×C4—362no—
288C2×C4—361no—
289C2×C4—361no—
290C2×C4#372211yescharacteristic
291C2×C4C2×#62411yescharacteristic
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—22no—
295C2×C3—22no—
296C2×C3—21no—
297C2×C3—22no—
298C2×C3—42no—
299C2×C3—42no—
300C2×C3—42no—
301C2×C3—42no—
302C2×C3—82no—
303C2×C3—82no—
304C2×C3#447314yescomplemented
305C2×C3C2×#80612yes—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—44no—
312C22—82no—
313C22#6358111yescharacteristic
314C22#6358111yescharacteristic
315C22C2×#372211yescharacteristic
316C4—21no—
317C4—21no—
318C4—244no—
319C4—362no—
320C4—362no—
321C3—21no—
322C3C2×#447312yescomplemented
323C2—21no—
324C2—21no—
325C2—42no—
326C2—42no—
327C2#1058918112yesdirect product factor
328C2C2×#6358111yescharacteristic
subgroupG/H
centerC22#63581
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#99
cosocleC2×C32×D4C23
hypercenterC22×D4D32
hypocenterC32C2×#354
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10589181C2direct (N × H)
6. C22×#634C4semidirect
9. #64145C4semidirect
11. C2×C4×C3⋊Dic3C4semidirect
32. C2×#634C2×C4semidirect
37. C4×C3⋊Dic3C2×C4semidirect
211. C2×C32#354semidirect
269. C32C2×#354semidirect
304. C2×C3#4473semidirect
322. C3C2×#4473semidirect
327. C2#10589181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×C3×#8342
#105891812
C2×#44733