Finite Group Databasebeta

← C22×#63844 #11899939

Subgroups — C22×#63844 #11899939

Order 1152.

3753 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C22×C3×C4×Dic3C211yesmaximal, characteristic
4C22×#3724C212yesmaximal
5C22×Dic32C212yesmaximal
6C2×#63844C2124yesmaximal, direct product factor
7C22×#887—31nomaximal
8C22×C4×Dic6—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C22×#634C4116yescomplemented
12C22×#634C22112yes—
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2212yes—
15C23×C3×Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C22112yes—
17C2×C3×C4×Dic3C22112yes—
18C2×#3724C22124yes—
19C2×Dic32C22124yes—
20#63844C22164yesdirect product factor
21C23×Dic6—31no—
22C23×Dic6—31no—
23C23×Dic6—61no—
24C22×C3×C4⋊C4—31no—
25C22×C3×C42—31no—
26C22×C4⋊Dic3D311yescharacteristic
27C22×Dic3⋊C4—32no—
28C22×Dic3⋊C4—32no—
29C22×C4×Dic3—32no—
30C22×C4×Dic3—32no—
31C22×C4×Dic3D311yescharacteristic
32C2×#887—324no—
33C2×C4×Dic6—324no—
34C24×C32C2311yescharacteristic
35C22×C32×C4C2×C418yes—
36C22×C32×C4C2316yes—
37C22×C3⋊Dic3C2×C4116yes—
38C22×C3⋊Dic3C23112yes—
39C2×#634C2×C4196yescomplemented
40C2×#634C23116yes—
41C22×C3×Dic3—24no—
42C22×C3×Dic3—28no—
43C22×C3×Dic3Q818yescomplemented
44C22×C3×Dic3C2316yes—
45C22×C3×Dic3C23112yes—
46C22×C3×Dic3C2316yes—
47C3×C4⋊Dic3C23116yes—
48C3×C4×Dic3C23116yes—
49#3724C23132yes—
50Dic32C23132yes—
51C22×C4×Q8—91noSylow
52C23×C3×C4—21no—
53C23×C3×C4—31no—
54C23×C3×C4—32no—
55C23×C3×C4—31no—
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C2×D311yescharacteristic
58C23×Dic3—32no—
59C23×Dic3—32no—
60C23×Dic3—62no—
61C23×Dic3C2×D312yes—
62C23×Dic3C2×D311yescharacteristic
63C23×Dic3C2×D311yescharacteristic
64C22×Dic6—316no—
65C22×Dic6—316no—
66C22×Dic6—312no—
67C22×Dic6—312no—
68C22×Dic6—616no—
69C22×Dic6—612no—
70C2×C3×C4⋊C4—312no—
71C2×C3×C42—312no—
72C2×C4⋊Dic3C2×D3112yes—
73C2×Dic3⋊C4—324no—
74C2×Dic3⋊C4—324no—
75C2×C4×Dic3—324no—
76C2×C4×Dic3—324no—
77C2×C4×Dic3C2×D3112yes—
78#887—364no—
79C4×Dic6—364no—
80C23×C32C22×C414yes—
81C23×C32C2×Q814yes—
82C23×C32#4114yes—
83C23×C32C2413yes—
84C2×C32×C4C22×C4124yes—
85C2×C32×C4C2414yes—
86C2×C3⋊Dic3C22×C4148yes—
87C2×C3⋊Dic3C2418yes—
88#634C22×C4164yescomplemented
89C2×C3×Dic3—212no—
90C2×C3×Dic3—224no—
91C2×C3×Dic3C2×Q8124yescomplemented
92C2×C3×Dic3C2418yes—
93C2×C3×Dic3C2414yes—
94C2×C3×Dic3C2414yes—
95C23×Q8—91no—
96C2×C4×Q8—924no—
97C22×C4⋊C4—31no—
98C22×C4⋊C4—92no—
99C22×C42—31no—
100C22×C42—92no—
101C24×C3—21no—
102C24×C3C22×D311yescharacteristic
103C24×C3C22×D311yescharacteristic
104C22×C3×C4—28no—
105C22×C3×C4—26no—
106C22×C3×C4—38no—
107C22×C3×C4—36no—
108C22×C3×C4—312no—
109C22×C3×C4—36no—
110C22×C3×C4—68no—
111C22×C3×C4—64no—
112C22×C3×C4C4×D318yes—
113C22×C3×C4C4×D318yes—
114C22×C3×C4C22×D316yes—
115C22×C3×C4C22×D316yes—
116C22×Dic3—24no—
117C22×Dic3—28no—
118C22×Dic3—316no—
119C22×Dic3—316no—
120C22×Dic3—312no—
121C22×Dic3—312no—
122C22×Dic3—616no—
123C22×Dic3—612no—
124C22×Dic3Dic618yescomplemented
125C22×Dic3C22×D3112yes—
126C22×Dic3C22×D316yes—
127C22×Dic3C22×D316yes—
128C2×Dic6—396no—
129C2×Dic6—396no—
130C2×Dic6—316no—
131C2×Dic6—316no—
132C2×Dic6—696no—
133C2×Dic6—616no—
134C3×C4⋊C4—316no—
135C3×C42—316no—
136C4⋊Dic3C22×D3116yes—
137Dic3⋊C4—332no—
138Dic3⋊C4—332no—
139C4×Dic3—332no—
140C4×Dic3—332no—
141C4×Dic3C22×D3116yes—
142C22×C32C4×Q8116yescomplemented
143C22×C32C23×C416yes—
144C22×C32C22×Q816yes—
145C22×C32C2×#4116yes—
146C22×C32C2511yescharacteristic
147C32×C4C23×C418yes—
148C3⋊Dic3C23×C4116yes—
149C3×Dic3—24no—
150C3×Dic3—28no—
151C3×Dic3C22×Q818yescomplemented
152C22×Q8—916no—
153C22×Q8—912no—
154C23×C4—31no—
155C23×C4—32no—
156C23×C4—31no—
157C23×C4—92no—
158C23×C4D3211yescharacteristic
159C4×Q8—964no—
160C2×C4⋊C4—312no—
161C2×C4⋊C4—924no—
162C2×C42—312no—
163C2×C42—924no—
164C23×C3—23no—
165C23×C3—24no—
166C23×C3—24no—
167C23×C3—24no—
168C23×C3C2×Dic614yes—
169C23×C3C2×C4×D314yes—
170C23×C3C2×C4×D314yes—
171C23×C3#23514yes—
172C23×C3#23714yes—
173C23×C3D3×Q814yes—
174C23×C3C23×D313yes—
175C23×C3C23×D313yes—
176C2×C3×C4—24no—
177C2×C3×C4—224no—
178C2×C3×C4—324no—
179C2×C3×C4—34no—
180C2×C3×C4—38no—
181C2×C3×C4—34no—
182C2×C3×C4—624no—
183C2×C3×C4—612no—
184C2×C3×C4C2×C4×D3124yes—
185C2×C3×C4C2×C4×D3124yes—
186C2×C3×C4C23×D314yes—
187C2×C3×C4C23×D314yes—
188C2×Dic3—212no—
189C2×Dic3—224no—
190C2×Dic3—348no—
191C2×Dic3—348no—
192C2×Dic3—38no—
193C2×Dic3—38no—
194C2×Dic3—648no—
195C2×Dic3—68no—
196C2×Dic3C2×Dic6124yescomplemented
197C2×Dic3C23×D318yes—
198C2×Dic3C23×D314yes—
199C2×Dic3C23×D314yes—
200Dic6—364no—
201Dic6—364no—
202Dic6—664no—
203C2×C32C2×C4×Q8112yescomplemented
204C2×C32C24×C411yescharacteristic
205C2×C32C23×Q811yescharacteristic
206C2×C32C22×#4111yescharacteristic
207C24C2×D3211yescharacteristic
208C2×Q8—916no—
209C2×Q8—996no—
210C22×C4—36no—
211C22×C4—38no—
212C22×C4—36no—
213C22×C4—312no—
214C22×C4—68no—
215C22×C4—64no—
216C22×C4—912no—
217C22×C4—916no—
218C22×C4#62418yes—
219C22×C4C2×D3216yes—
220C4⋊C4—316no—
221C4⋊C4—932no—
222C42—316no—
223C42—932no—
224C22×C3—26no—
225C22×C3—26no—
226C22×C3—26no—
227C22×C3—216no—
228C22×C3—21no—
229C22×C3C4×Dic6116yescomplemented
230C22×C3#887116yescomplemented
231C22×C3C22×Dic616yes—
232C22×C3C22×C4×D316yes—
233C22×C3C22×C4×D316yes—
234C22×C3C2×#23516yes—
235C22×C3C2×#23716yes—
236C22×C3C2×D3×Q816yes—
237C22×C3C24×D311yescharacteristic
238C22×C3C24×D311yescharacteristic
239C3×C4—28no—
240C3×C4—38no—
241C3×C4—68no—
242C3×C4—64no—
243C3×C4C22×C4×D318yes—
244C3×C4C22×C4×D318yes—
245Dic3—24no—
246Dic3—28no—
247Dic3—316no—
248Dic3—316no—
249Dic3—616no—
250Dic3C22×Dic618yescomplemented
251C32C22×C4×Q811yescharacteristic, complemented, Sylow
252C23D3×Dic614yes—
253C23#379514yes—
254C23C2×#62414yes—
255C23C22×D3213yes—
256Q8—964no—
257C2×C4—324no—
258C2×C4—34no—
259C2×C4—34no—
260C2×C4—38no—
261C2×C4—612no—
262C2×C4—624no—
263C2×C4—948no—
264C2×C4—98no—
265C2×C4C2×#624124yes—
266C2×C4C22×D3214yes—
267C2×C3—212no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3C2×C4×Dic6112yescomplemented
272C2×C3C2×#887112yescomplemented
273C2×C3C23×Dic611yescharacteristic
274C2×C3C23×C4×D311yescharacteristic
275C2×C3C23×C4×D311yescharacteristic
276C2×C3C22×#23511yescharacteristic
277C2×C3C22×#23711yescharacteristic
278C2×C3C22×D3×Q811yescharacteristic
279C22#63844116yesdirect product factor
280C22C2×D3×Dic616yes—
281C22C2×#379516yes—
282C22C22×#62416yes—
283C22C23×D3211yescharacteristic
284C4—38no—
285C4—64no—
286C4—68no—
287C4—916no—
288C4C22×#62418yes—
289C3—21no—
290C3C22×C4×Dic611yescharacteristic, complemented
291C3C22×#88711yescharacteristic, complemented
292C2C2×#63844112yesdirect product factor
293C2C22×D3×Dic611yescharacteristic
294C2C22×#379511yescharacteristic
295C2C23×#62411yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC22×C32C25
hypercenterC23×C4D32
hypocenterC32C22×C4×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. C2×#63844C2direct (N × H)
11. C22×#634C4semidirect
20. #63844C22direct (N × H)
39. C2×#634C2×C4semidirect
43. C22×C3×Dic3Q8semidirect
88. #634C22×C4semidirect
91. C2×C3×Dic3C2×Q8semidirect
124. C22×Dic3Dic6semidirect
142. C22×C32C4×Q8semidirect
151. C3×Dic3C22×Q8semidirect
196. C2×Dic3C2×Dic6semidirect
203. C2×C32C2×C4×Q8semidirect
229. C22×C3C4×Dic6semidirect
230. C22×C3#887semidirect
250. Dic3C22×Dic6semidirect
251. C32C22×C4×Q8semidirect
271. C2×C3C2×C4×Dic6semidirect
272. C2×C3C2×#887semidirect
279. C22#63844direct (N × H)
290. C3C22×C4×Dic6semidirect
291. C3C22×#887semidirect
292. C2C2×#63844direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6342
C22×C3×C4⋊Dic32
C22×C3×C4×Dic32
C22×#37242
C22×Dic322
C2×#638442
C22×#8873
C22×C4×Dic63