Finite Group Databasebeta

← C22⋊C4×#634 #11804875

Subgroups — C22⋊C4×#634 #11804875

Order 1152.

2460 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic
2C2×C4×#634C212yesmaximal, complemented
3C32×C4×C22⋊C4C211yesmaximal, characteristic
4#10592911C211yesmaximal, characteristic
5#10592641C212yesmaximal
6C22⋊C4×C3⋊Dic3C212yesmaximal
7#10592628C212yesmaximal, complemented
8#10592345C214yesmaximal, complemented
9C22⋊C4×Dic6—34nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C22×#634—28no—
13C22×#634C418yescomplemented
14C22×#634C2212yes—
15C22×#634C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×C32×C42C2212yes—
20C2×#3757C2212yes—
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×#3750C2214yes—
23C2×C4×C3⋊Dic3C2214yes—
24C4×#634—28no—
25C32×#95C2212yes—
26#63658C2212yes—
27#63658C2214yes—
28#63658C2214yes—
29C23×Dic6—34no—
30C2×C4×Dic6—38no—
31C3×C4×C22⋊C4D314yes—
32#5212—34no—
33#4942—38no—
34Dic3×C22⋊C4—38no—
35#4929—38no—
36#4646—316no—
37C24×C32C2311yescharacteristic
38C22×C32×C4—24no—
39C22×C32×C4C2×C414yes—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—28no—
45C22×C3⋊Dic3C2×C418yes—
46C22×C3⋊Dic3C2314yes—
47C22×C3⋊Dic3C2312yes—
48C22×C3⋊Dic3C2312yes—
49C2×#634—24no—
50C2×#634—28no—
51C2×#634—232no—
52C2×#634C2×C414yes—
53C2×#634C2×C418yes—
54C2×#634C2×C414yes—
55C2×#634D418yes—
56C32×C22⋊C4—22no—
57C32×C22⋊C4Q814yescomplemented
58C32×C42—24no—
59#3757—24no—
60C4⋊(C3⋊Dic3)—24no—
61#3750—28no—
62C4×C3⋊Dic3—28no—
63Q8×C22⋊C4—91noSylow
64C23×C3×C4C2×D314yes—
65C23×Dic3—38no—
66C22×Dic6—34no—
67C22×Dic6—332no—
68C22×Dic6—38no—
69C22×Dic6—34no—
70C22×Dic6—632no—
71C2×C3×C22⋊C4C2×D314yes—
72C2×C3×C22⋊C4C2×D314yes—
73C2×C3×C42C2×D318yes—
74C2×#217—38no—
75C2×C4⋊Dic3—38no—
76C2×Dic3⋊C4—316no—
77C2×C4×Dic3—316no—
78C4×Dic6—632no—
79C3×#95C2×D318yes—
80C3⋊#95—38no—
81C3⋊#95—316no—
82C3⋊#95—316no—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32C22×C412yes—
86C23×C32C2×Q812yes—
87C23×C32#4112yes—
88C23×C32C2411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—28no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C22×C412yes—
97C2×C32×C4C22×C412yes—
98C2×C32×C4C2×D414yes—
99C2×C32×C4C2×Q814yescomplemented
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—216no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3C22×C414yes—
106C2×C3⋊Dic3C22×C414yes—
107C2×C3⋊Dic3C2×D418yes—
108#634—28no—
109#634—216no—
110#634C22⋊C4116yesdirect product factor
111C23×Q8—91no—
112C2×C4×Q8—92no—
113#391—92no—
114#391—94no—
115#380—91no—
116#380—92no—
117C4×C22⋊C4—92no—
118C4×C22⋊C4C3⋊D311yescharacteristic
119C24×C3C22×D314yes—
120C22×C3×C4—216no—
121C22×C3×C4C4×D3116yes—
122C22×C3×C4C22×D318yes—
123C22×C3×C4C22×D318yes—
124C22×C3×C4C22×D314yes—
125C22×C3×C4C22×D314yes—
126C22×Dic3—38no—
127C22×Dic3—332no—
128C22×Dic3—38no—
129C22×Dic3—316no—
130C22×Dic3—632no—
131C2×Dic6—316no—
132C2×Dic6—332no—
133C2×Dic6—332no—
134C2×Dic6—316no—
135C2×Dic6—6128no—
136C2×Dic6—632no—
137C2×Dic6—616no—
138C3×C22⋊C4—28no—
139C3×C22⋊C4Dic6116yescomplemented
140C3×C42—216no—
141#217—616no—
142C4⋊Dic3—616no—
143Dic3⋊C4—632no—
144C4×Dic3—632no—
145C22×C32—22no—
146C22×C32—22no—
147C22×C32—24no—
148C22×C32—24no—
149C22×C32C4×Q814yescomplemented
150C22×C32C23×C411yescharacteristic
151C22×C32C22×D412yes—
152C22×C32C22×Q811yescharacteristic
153C22×C32C2×#4111yescharacteristic
154C22×C322−1+412yes—
155C32×C4—22no—
156C32×C4—24no—
157C32×C4—42no—
158C32×C4C2×C22⋊C414yes—
159C3⋊Dic3—24no—
160C3⋊Dic3—44no—
161C3⋊Dic3C2×C22⋊C418yes—
162C22×Q8—98no—
163C22×Q8—91no—
164C22×Q8—92no—
165C22×Q8—91no—
166C22×Q8—188no—
167C23×C4—92no—
168C23×C4C2×C3⋊D311yescharacteristic
169C4×Q8—188no—
170C2×C4⋊C4—94no—
171C2×C4⋊C4—92no—
172C2×C22⋊C4—92no—
173C2×C22⋊C4C2×C3⋊D311yescharacteristic
174C2×C22⋊C4C2×C3⋊D311yescharacteristic
175C2×C42—94no—
176C2×C42C2×C3⋊D312yes—
177#95—94no—
178#95—94no—
179#95—92no—
180#95C2×C3⋊D312yes—
181C23×C3—28no—
182C23×C3—28no—
183C23×C3C2×Dic618yes—
184C23×C3C2×C4×D318yes—
185C23×C3#23518yes—
186C23×C3C23×D314yes—
187C2×C3×C4—28no—
188C2×C3×C4—28no—
189C2×C3×C4—28no—
190C2×C3×C4—232no—
191C2×C3×C4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4C2×Dic6116yescomplemented
195C2×C3×C4C2×C4×D318yes—
196C2×C3×C4C2×C4×D318yes—
197C2×C3×C4D3×D4116yes—
198C2×Dic3—316no—
199C2×Dic3—332no—
200C2×Dic3—316no—
201C2×Dic3—664no—
202C2×Dic3—616no—
203C2×Dic3—616no—
204C2×Dic3—616no—
205C2×Dic3—616no—
206Dic6—364no—
207Dic6—664no—
208Dic6—632no—
209C2×C32—24no—
210C2×C32C22×C22⋊C411yescharacteristic
211C2×C32C2×C4×Q811yescharacteristic
212C2×C32#51911yescharacteristic
213C2×C32#54812yes—
214C2×C32D4×Q812yes—
215C24C22×C3⋊D311yescharacteristic
216C2×Q8—94no—
217C2×Q8—98no—
218C2×Q8—94no—
219C2×Q8—98no—
220C2×Q8—188no—
221C2×Q8—1832no—
222C2×Q8—184no—
223C22×C4—24no—
224C22×C4—92no—
225C22×C4—92no—
226C22×C4—98no—
227C22×C4—94no—
228C22×C4—188no—
229C22×C4C4×C3⋊D314yes—
230C22×C4C22×C3⋊D312yes—
231C22×C4C22×C3⋊D312yes—
232C22×C4C22×C3⋊D311yescharacteristic
233C22×C4C22×C3⋊D311yescharacteristic
234C4⋊C4—188no—
235C4⋊C4—184no—
236C22⋊C4—22no—
237C22⋊C4—184no—
238C22⋊C4#63414yesdirect product factor
239C42—24no—
240C42—188no—
241C22×C3—28no—
242C22×C3—28no—
243C22×C3—216no—
244C22×C3—216no—
245C22×C3C4×Dic6116yescomplemented
246C22×C3C22×Dic614yes—
247C22×C3C22×C4×D314yes—
248C22×C3C2×#23514yes—
249C22×C3C2×D3×D418yes—
250C22×C3#101018yes—
251C3×C4—28no—
252C3×C4—216no—
253C3×C4—48no—
254C3×C4D3×C22⋊C4116yes—
255Dic3—332no—
256Dic3—616no—
257Dic3—1216no—
258C32Q8×C22⋊C411yescharacteristic, complemented, Sylow
259C23—22no—
260C23—22no—
261C23C2×#63412yes—
262C23C2×C4×C3⋊D312yes—
263C23#382812yes—
264C23C23×C3⋊D311yescharacteristic
265Q8—916no—
266Q8—1816no—
267Q8—188no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—28no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—94no—
276C2×C4—98no—
277C2×C4—94no—
278C2×C4—1816no—
279C2×C4—184no—
280C2×C4—184no—
281C2×C4—184no—
282C2×C4—184no—
283C2×C4C2×#63414yescomplemented
284C2×C4C2×C4×C3⋊D312yes—
285C2×C4C2×C4×C3⋊D312yes—
286C2×C4D4×C3⋊D314yes—
287C2×C3—216no—
288C2×C3C2×C4×Dic614yes—
289C2×C3C2×D3×C22⋊C414yes—
290C2×C3#551614yes—
291C2×C3D4×Dic618yes—
292C2×C3#555218yes—
293C22—22no—
294C22—22no—
295C22—24no—
296C22—24no—
297C22C4×#63414yescomplemented
298C22C22×#63411yescharacteristic
299C22C22×C4×C3⋊D311yescharacteristic
300C22C2×#382811yescharacteristic
301C22C2×D4×C3⋊D312yes—
302C22#6436712yes—
303C4—22no—
304C4—24no—
305C4—42no—
306C4—98no—
307C4—184no—
308C4—364no—
309C4C22⋊C4×C3⋊D314yes—
310C3C22⋊C4×Dic614yescomplemented
311C2—24no—
312C2C2×C4×#63411yescharacteristic
313C2C2×C22⋊C4×C3⋊D311yescharacteristic
314C2#1059598711yescharacteristic
315C2D4×#63412yes—
316C2#1059602312yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×C4×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32Q8×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#634C2semidirect
7. #10592628C2semidirect
8. #10592345C2semidirect
13. C22×#634C4semidirect
57. C32×C22⋊C4Q8semidirect
99. C2×C32×C4C2×Q8semidirect
110. #634C22⋊C4direct (N × H)
139. C3×C22⋊C4Dic6semidirect
149. C22×C32C4×Q8semidirect
194. C2×C3×C4C2×Dic6semidirect
238. C22⋊C4#634direct (N × H)
245. C22×C3C4×Dic6semidirect
258. C32Q8×C22⋊C4semidirect
283. C2×C4C2×#634semidirect
297. C22C4×#634semidirect
310. C3C22⋊C4×Dic6semidirect

Maximal subgroups

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

subgroupindex
C23×#6342
C2×C4×#6342
C32×C4×C22⋊C42
#105929112
#105926412
C22⋊C4×C3⋊Dic32
#105926282
#105923452
C22⋊C4×Dic63