Finite Group Databasebeta

← #11906304

Subgroups — #11906304

Order 1152.

2077 conjugacy classes of subgroups.

The subgroup lattice has 267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5812C212yesmaximal
3#10595422C218yesmaximal, complemented
4Q8×#627C214yesmaximal, complemented
5#10595351C214yesmaximal, complemented
6#10595052C216yesmaximal
7#10595050C216yesmaximal
8#85875—32nomaximal
9C22×C32×Q8C2211yescharacteristic
10Q8×C3⋊Dic3C2214yes—
11Q8×C3⋊Dic3C2214yes—
12C2×C4⋊(C3⋊Dic3)C2213yes—
13C2×C4×C3⋊Dic3C2213yes—
14C3×Q8×Dic3C2218yes—
15C3×Q8×Dic3C2218yes—
16C3×#926C22112yes—
17#63982C2214yes—
18#63982C22112yes—
19#63919C2216yes—
20#63919C2216yes—
21#63918C22124yes—
22C4×#627C22112yes—
23C4×#627C22112yes—
24#63872C22112yes—
25#63869C22124yes—
26C3×#519—32no—
27#5812D312yes—
28C2×Q8×Dic3—32no—
29C2×Q8×Dic3—61no—
30#5570—38no—
31#5569—38no—
32#5569—38no—
33Q8×Dic6—38no—
34#5519—312no—
35#5517—312no—
36C2×C32×Q8Q818yescomplemented
37C2×C32×Q8C2314yes—
38C22×C32×C4C2313yes—
39C22×C3⋊Dic3C2311yescharacteristic
40C22×C3⋊Dic3C2313yes—
41C2×#627C2314yes—
42C2×#627C23112yes—
43C4⋊(C3⋊Dic3)C23112yes—
44C4×C3⋊Dic3C2316yes—
45C4×C3⋊Dic3C2316yes—
46C3×#217C2318yes—
47C3×C4⋊Dic3C23112yes—
48C3×C4⋊Dic3C23112yes—
49C3×C4×Dic3C23124yes—
50#3724C23112yes—
51#3724C2314yes—
52Dic3⋊Dic3C23124yes—
53Dic3⋊Dic3C2318yes—
54#3502—91noSylow
55C22×C3×Q8—21no—
56C22×C3×Q8C2×D312yes—
57C3×C4×Q8—38no—
58C3×C4×Q8—38no—
59C3×#117—312no—
60Q8×Dic3—38no—
61Q8×Dic3—38no—
62Q8×Dic3—64no—
63Q8×Dic3—64no—
64Q8×Dic3C2×D318yes—
65Q8×Dic3C2×D318yes—
66#926C2×D3112yes—
67C2×C4⋊Dic3—36no—
68C2×C4⋊Dic3—63no—
69C2×C4×Dic3—36no—
70C2×C4×Dic3—63no—
71#890—312no—
72#890—312no—
73#890—324no—
74#888—312no—
75#888—312no—
76#888—324no—
77#878—38no—
78#878—324no—
79#870—324no—
80#869—324no—
81C4×Dic6—324no—
82C4×Dic6—324no—
83C23×C32C2411yescharacteristic
84C32×Q8C2×Q8116yes—
85C2×C32×C4C2×Q8112yes—
86C2×C32×C4C2416yes—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—43no—
89C2×C3⋊Dic3C2411yescharacteristic
90C2×C3⋊Dic3C2416yes—
91C2×C3⋊Dic3C2411yescharacteristic
92C2×C3×Dic3C2418yes—
93C2×C3×Dic3C2418yes—
94#627—28no—
95#627—412no—
96Q82—94no—
97#557—94no—
98#557—98no—
99#544—96no—
100#533—96no—
101#519—32no—
102C2×C4×Q8—91no—
103C2×C3×Q8—28no—
104C2×C3×Q8—24no—
105C2×C3×Q8Dic6116yescomplemented
106C2×C3×Q8C22×D318yes—
107C22×C3×C4—23no—
108C22×C3×C4C22×D316yes—
109C22×Dic3—32no—
110C22×Dic3—36no—
111C22×Dic3—61no—
112C22×Dic3—63no—
113C2×Dic6—38no—
114C2×Dic6—324no—
115C3×C4⋊C4—312no—
116C3×C4⋊C4—312no—
117C3×C22⋊C4—38no—
118C3×C42—324no—
119#217C22×D318yes—
120C4⋊Dic3—324no—
121C4⋊Dic3—38no—
122C4⋊Dic3—324no—
123C4⋊Dic3—612no—
124C4⋊Dic3C22×D3112yes—
125C4⋊Dic3C22×D3112yes—
126Dic3⋊C4—38no—
127Dic3⋊C4—38no—
128Dic3⋊C4—324no—
129Dic3⋊C4—324no—
130C4×Dic3—312no—
131C4×Dic3—312no—
132C4×Dic3—66no—
133C4×Dic3—66no—
134C4×Dic3C22×D3124yes—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C22×Q812yes—
138C22×C32C2511yescharacteristic
139C32×C4C22×Q8112yes—
140C3⋊Dic3—21no—
141C3⋊Dic3—26no—
142C3⋊Dic32−1+412yes—
143C3×Dic3—28no—
144C3×Dic3—28no—
145C22×Q8D3211yescharacteristic
146C4⋊Q8—924no—
147C4⋊Q8—96no—
148C4⋊Q8—96no—
149#125—924no—
150#125—912no—
151C22⋊Q8—94no—
152C22⋊Q8—912no—
153C4×Q8—38no—
154C4×Q8—38no—
155C4×Q8—912no—
156C4×Q8—912no—
157C4×Q8—94no—
158C4×Q8—94no—
159#117—312no—
160C2×C4⋊C4—93no—
161C2×C42—93no—
162C23×C3—21no—
163C23×C3C23×D312yes—
164C3×Q8—216no—
165C3×Q8C2×Dic6132yes—
166C2×C3×C4—26no—
167C2×C3×C4—212no—
168C2×C3×C4—38no—
169C2×C3×C4—38no—
170C2×C3×C4C2×Dic6124yes—
171C2×C3×C4C23×D3112yes—
172C2×Dic3—32no—
173C2×Dic3—32no—
174C2×Dic3—312no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—66no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—126no—
181C2×Dic3—126no—
182C2×Dic3C23×D318yes—
183C2×Dic3C23×D318yes—
184Dic6—616no—
185Dic6—1224no—
186C2×C32—22no—
187C2×C32C23×Q811yescharacteristic
188C2×C32C2×2−1+411yescharacteristic
189C2×C32#58511yescharacteristic
190C2×Q8—94no—
191C2×Q8—912no—
192C2×Q8#62718yescomplemented
193C2×Q8C2×D3214yes—
194C22×C4—91no—
195C22×C4—93no—
196C22×C4C2×D3213yes—
197C4⋊C4—312no—
198C4⋊C4—312no—
199C4⋊C4—98no—
200C4⋊C4—94no—
201C4⋊C4—912no—
202C4⋊C4—924no—
203C4⋊C4—912no—
204C22⋊C4—38no—
205C42—324no—
206C42—96no—
207C42—96no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—21no—
214C22×C3C22×Dic614yes—
215C22×C3C24×D312yes—
216C3×C4—212no—
217C3×C4—68no—
218C3×C4—68no—
219C3×C4C22×Dic6124yes—
220Dic3—28no—
221Dic3—28no—
222Dic3—34no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—612no—
227Dic3—126no—
228C32#350211yescharacteristic, complemented, Sylow
229C23C22×D3211yescharacteristic
230Q8—188no—
231Q8—3612no—
232Q8C2×#627116yes—
233C2×C4—38no—
234C2×C4—38no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—96no—
238C2×C4—182no—
239C2×C4—363no—
240C2×C4C2×#627112yes—
241C2×C4C22×D3216yes—
242C2×C3—24no—
243C2×C3—24no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3C23×Dic612yes—
248C2×C3D3×2−1+412yes—
249C2×C3#596812yes—
250C22—21no—
251C22—21no—
252C22C22×#62712yes—
253C22C23×D3211yescharacteristic
254C4—68no—
255C4—68no—
256C4—92no—
257C4—181no—
258C4—186no—
259C4C22×#627112yes—
260C3—21no—
261C3#8587512yescomplemented
262C2—22no—
263C2#1059668711yescharacteristic
264C2#1059668911yescharacteristic
265C2C23×#62711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
prime radicalC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10595422C2semidirect
4. Q8×#627C2semidirect
5. #10595351C2semidirect
36. C2×C32×Q8Q8semidirect
105. C2×C3×Q8Dic6semidirect
192. C2×Q8#627semidirect
228. C32#3502semidirect
261. C3#85875semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C3×#58122
#105954222
Q8×#6272
#105953512
#105950522
#105950502
#858753