Finite Group Databasebeta

← C2×#10595052 #11901926

Subgroups — C2×#10595052 #11901926

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3C2×#63982C214yesmaximal
4#10595052C2116yesmaximal, direct product factor
5C2×#63918C214yesmaximal, complemented
6C2×#63869C214yesmaximal, complemented
7C2×#5519—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C22×#627C2214yes—
11C2×C4⋊(C3⋊Dic3)C2214yes—
12C2×C4⋊(C3⋊Dic3)C2218yes—
13C2×C3×#217C2214yes—
14C3×#926C22116yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic3C2214yes—
18#63982C22132yes—
19C2×#3724C2214yes—
20C2×Dic3⋊Dic3C2218yes—
21#63918C22132yescomplemented
22#63869C22132yescomplemented
23C2×C3×#117—32no—
24C2×#926D312yes—
25C22×C4⋊Dic3—32no—
26C22×C4⋊Dic3—61no—
27#5519—332no—
28C2×#890—34no—
29C2×#888—34no—
30C2×#878—38no—
31C2×#870—34no—
32C2×#869—34no—
33C24×C32C2311yescharacteristic
34C22×C32×C4Q818yescomplemented
35C22×C32×C4C2312yes—
36C22×C32×C4C2314yes—
37C22×C3⋊Dic3—44no—
38C22×C3⋊Dic3C2314yes—
39C22×C3⋊Dic3C2318yes—
40C22×C3×Dic3C2314yes—
41C22×C3×Dic3C2314yes—
42C2×#627—48no—
43C2×#627C23116yes—
44C4⋊(C3⋊Dic3)C23116yes—
45C3×#217C23116yes—
46C3×C4⋊Dic3C2318yes—
47C3×C4⋊Dic3C2318yes—
48C3×C4×Dic3C23116yes—
49#3724C23116yes—
50Dic3⋊Dic3C23132yes—
51C2×#544—91noSylow
52C23×C3×C4—21no—
53C23×C3×C4C2×D312yes—
54C23×Dic3—34no—
55C23×Dic3—62no—
56C22×Dic6—38no—
57C3×#117—316no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C22⋊C4—34no—
61C2×C3×C42—34no—
62C2×#217C2×D314yes—
63#926C2×D3116yes—
64C2×C4⋊Dic3—34no—
65C2×C4⋊Dic3—34no—
66C2×C4⋊Dic3—316no—
67C2×C4⋊Dic3—38no—
68C2×C4⋊Dic3—64no—
69C2×C4⋊Dic3—68no—
70C2×C4⋊Dic3C2×D312yes—
71C2×C4⋊Dic3C2×D312yes—
72C2×Dic3⋊C4—38no—
73C2×Dic3⋊C4—38no—
74C2×C4×Dic3C2×D314yes—
75#890—332no—
76#888—332no—
77#878—364no—
78#870—332no—
79#869—332no—
80C23×C32—22no—
81C23×C32—22no—
82C23×C32C2×Q814yes—
83C23×C32C2412yes—
84C23×C32C2411yescharacteristic
85C2×C32×C4C2×Q818yes—
86C2×C32×C4C2×Q8116yescomplemented
87C2×C32×C4C2414yes—
88C2×C3⋊Dic3—28no—
89C2×C3⋊Dic3—48no—
90C2×C3⋊Dic3C2418yes—
91C2×C3×Dic3—28no—
92C2×C3×Dic3—28no—
93C2×C3×Dic3C2418yes—
94C2×C3×Dic3C2418yes—
95#627—416no—
96#544—916no—
97C2×C4⋊Q8—94no—
98C2×#125—94no—
99C2×C22⋊Q8—94no—
100C2×#117—32no—
101C22×C4⋊C4—91no—
102C24×C3—21no—
103C24×C3C22×D312yes—
104C22×C3×C4—28no—
105C22×C3×C4—22no—
106C22×C3×C4—24no—
107C22×C3×C4—34no—
108C22×C3×C4—34no—
109C22×C3×C4Dic6116yescomplemented
110C22×C3×C4C22×D312yes—
111C22×C3×C4C22×D312yes—
112C22×C3×C4C22×D318yes—
113C22×Dic3—38no—
114C22×Dic3—316no—
115C22×Dic3—64no—
116C22×Dic3—68no—
117C22×Dic3—128no—
118C22×Dic3—128no—
119C22×Dic3C22×D314yes—
120C22×Dic3C22×D314yes—
121C2×Dic6—332no—
122C2×Dic6—1216no—
123C3×C4⋊C4—38no—
124C3×C4⋊C4—38no—
125C3×C22⋊C4—316no—
126C3×C42—316no—
127#217C22×D3116yes—
128C4⋊Dic3—316no—
129C4⋊Dic3—316no—
130C4⋊Dic3—332no—
131C4⋊Dic3—616no—
132C4⋊Dic3C22×D318yes—
133C4⋊Dic3C22×D318yes—
134Dic3⋊C4—332no—
135Dic3⋊C4—332no—
136C4×Dic3C22×D3116yes—
137C22×C32—28no—
138C22×C32—22no—
139C22×C32—22no—
140C22×C32C22×Q814yes—
141C22×C32C22×Q812yes—
142C22×C32H(5,𝔽2)12yes—
143C22×C322−1+412yes—
144C22×C32C2511yescharacteristic
145C32×C4C22×Q818yes—
146C3⋊Dic3—28no—
147C3×Dic3—28no—
148C3×Dic3—28no—
149C22×Q8—94no—
150C23×C4—92no—
151C23×C4D3211yescharacteristic
152C4⋊Q8—932no—
153#125—932no—
154C22⋊Q8—932no—
155#117—316no—
156C2×C4⋊C4—32no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—94no—
159C2×C4⋊C4—98no—
160C2×C4⋊C4—94no—
161C2×C4⋊C4—98no—
162C2×C22⋊C4—34no—
163C2×C42—34no—
164C23×C3—24no—
165C23×C3—24no—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3—22no—
169C23×C3—21no—
170C23×C3—24no—
171C23×C3C2×Dic618yes—
172C23×C3C23×D314yes—
173C23×C3C23×D312yes—
174C2×C3×C4—24no—
175C2×C3×C4—28no—
176C2×C3×C4—216no—
177C2×C3×C4—38no—
178C2×C3×C4—38no—
179C2×C3×C4—68no—
180C2×C3×C4—68no—
181C2×C3×C4C2×Dic618yes—
182C2×C3×C4C2×Dic618yes—
183C2×C3×C4C2×Dic6132yescomplemented
184C2×C3×C4C23×D314yes—
185C2×C3×C4C23×D314yes—
186C2×Dic3—28no—
187C2×Dic3—28no—
188C2×Dic3—316no—
189C2×Dic3—68no—
190C2×Dic3—616no—
191C2×Dic3—128no—
192C2×Dic3—1216no—
193C2×Dic3—1216no—
194C2×Dic3C23×D318yes—
195C2×Dic3C23×D318yes—
196Dic6—1232no—
197C2×C32—24no—
198C2×C32#54414yescomplemented
199C2×C32C23×Q811yescharacteristic
200C2×C32C2×H(5,𝔽2)11yescharacteristic
201C2×C32C2×2−1+411yescharacteristic
202C24C2×D3211yescharacteristic
203C2×Q8—916no—
204C2×Q8—368no—
205C22×C4—34no—
206C22×C4—34no—
207C22×C4—94no—
208C22×C4—98no—
209C22×C4—364no—
210C22×C4#62718yescomplemented
211C22×C4C2×D3212yes—
212C22×C4C2×D3214yes—
213C4⋊C4—38no—
214C4⋊C4—38no—
215C4⋊C4—916no—
216C4⋊C4—932no—
217C4⋊C4—916no—
218C22⋊C4—316no—
219C42—316no—
220C22×C3—24no—
221C22×C3—24no—
222C22×C3—216no—
223C22×C3—24no—
224C22×C3—24no—
225C22×C3—216no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—24no—
229C22×C3—22no—
230C22×C3—21no—
231C22×C3C22×Dic618yes—
232C22×C3C22×Dic614yes—
233C22×C3#100914yes—
234C22×C3#101014yes—
235C22×C3C24×D312yes—
236C3×C4—28no—
237C3×C4—68no—
238C3×C4—68no—
239C3×C4C22×Dic618yes—
240C3×C4C22×Dic618yes—
241Dic3—28no—
242Dic3—28no—
243Dic3—616no—
244Dic3—128no—
245C32C2×#54411yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23C2×#62714yes—
249C23C22×D3212yes—
250C23C22×D3211yescharacteristic
251Q8—3616no—
252C2×C4—38no—
253C2×C4—38no—
254C2×C4—68no—
255C2×C4—68no—
256C2×C4—98no—
257C2×C4—188no—
258C2×C4—368no—
259C2×C4C2×#62718yes—
260C2×C4C2×#627116yescomplemented
261C2×C4C22×D3214yes—
262C2×C3—28no—
263C2×C3—28no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—24no—
268C2×C3#551918yescomplemented
269C2×C3C23×Dic612yes—
270C2×C3C2×#100912yes—
271C2×C3C2×#101012yes—
272C22—22no—
273C22—22no—
274C22—28no—
275C22#6429812yes—
276C22#6430812yes—
277C22C22×#62714yes—
278C22C22×#62712yes—
279C22C23×D3211yescharacteristic
280C4—68no—
281C4—68no—
282C4—188no—
283C4C22×#62718yes—
284C3—21no—
285C3C2×#551912yescomplemented
286C2—24no—
287C2#1059505214yesdirect product factor
288C2C2×#6429811yescharacteristic
289C2C2×#6430811yescharacteristic
290C2C23×#62711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10595052C2direct (N × H)
5. C2×#63918C2semidirect
6. C2×#63869C2semidirect
21. #63918C22semidirect
22. #63869C22semidirect
34. C22×C32×C4Q8semidirect
86. C2×C32×C4C2×Q8semidirect
109. C22×C3×C4Dic6semidirect
183. C2×C3×C4C2×Dic6semidirect
198. C2×C32#544semidirect
210. C22×C4#627semidirect
245. C32C2×#544semidirect
260. C2×C4C2×#627semidirect
268. C2×C3#5519semidirect
285. C3C2×#5519semidirect
287. C2#10595052direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C2×C3×#9262
C2×#639822
#105950522
C2×#639182
C2×#638692
C2×#55193