Finite Group Databasebeta

← #11779498

Subgroups — #11779498

Order 1152.

468 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5734C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic, complemented
3#10590266C212yesmaximal, complemented
4#10589412C211yesmaximal, characteristic, complemented
5#10589081C212yesmaximal, complemented
6#71928—31nomaximal
7#71304—31nomaximal
8C32×C4⋊Q8C2211yescharacteristic
9C3×#947—22no—
10C2×C3×#216—22no—
11C3×#895—22no—
12C3×#892—22no—
13C3×C4×D12C2212yes—
14C3×#869C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2212yes—
16C3×C4×C3⋊C8C2211yescharacteristic
17#63574—22no—
18#63562—22no—
19C3×#555—31no—
20#5734D311yescharacteristic
21C3×#494—31no—
22#5092D311yescharacteristic, complemented
23#5084—32no—
24#5008—32no—
25#4546—31no—
26#4546—31no—
27#4546—61no—
28D4⋊(C3⋊C8)—32no—
29#4459—32no—
30C2×C32×Q8D412yes—
31C2×C3×D12—22no—
32C2×C3×D12D412yes—
33C2×C3×C4×D3—22no—
34C2×C3×Dic6—21no—
35C32×C4⋊C4—22no—
36C32×C42C2311yescharacteristic
37C2×C3⋊(C3⋊C8)—22no—
38C3×#216—44no—
39C3×(C2×D3)⋊C4—24no—
40C3×(C2×D3)⋊C4—22no—
41C3×C4⋊Dic3—22no—
42C3×C4⋊Dic3D412yes—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—21no—
45#1634—91noSylow
46C2×C3×Q16—62no—
47C3×C4⋊Q8—21no—
48C3×C4⋊Q8—31no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C2×D311yescharacteristic
51C3×#124—62no—
52C3×#121—62no—
53C3×C4×D4—32no—
54C3×#117—62no—
55#947—22no—
56C2×#216—22no—
57#895—22no—
58#892—22no—
59C4×D12C2×D312yes—
60#869C2×D311yescharacteristic
61C3×C4×C8—31no—
62#832—62no—
63#809—62no—
64#808—62no—
65#808—62no—
66C4⋊(C3⋊C8)—32no—
67C4⋊(C3⋊C8)—32no—
68C4⋊(C3⋊C8)—62no—
69C4×C3⋊C8C2×D311yescharacteristic
70C22×C3×D3—22no—
71C32×Q8—42no—
72C2×C32×C4—22no—
73C2×C32×C4C2×D412yes—
74C2×C32×C4C2×D411yescharacteristic
75C2×C3×Dic3—22no—
76C2×C3×Dic3—41no—
77C3×D12—22no—
78C3×D12—22no—
79C3×D12—82no—
80C3×C4×D3—42no—
81C3×C4×D3—42no—
82C3×Dic6—42no—
83C3⋊(C3⋊C8)—42no—
84C3×C3⋊C8—22no—
85#555—31no—
86#494—31no—
87#476—92no—
88#333—91no—
89D4⋊C8—92no—
90C2×C3×Q8—22no—
91C2×C3×Q8—61no—
92C2×C3×Q8#6712yes—
93C2×C3×Q8#6712yes—
94C2×C3×D4—32no—
95C2×C3×D4—62no—
96C22×C3×C4—62no—
97C2×D12—22no—
98C2×D12#6712yes—
99C2×C4×D3—22no—
100C2×Dic6—21no—
101C3×Q16—124no—
102C2×C3×C8—61no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—32no—
106C3×C4⋊C4—42no—
107C3×C4⋊C4—62no—
108C3×C22⋊C4—64no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42—62no—
112C3×C42C22×D311yescharacteristic
113C3×C42C22×D311yescharacteristic
114#216—44no—
115(C2×D3)⋊C4—24no—
116(C2×D3)⋊C4—22no—
117C4⋊Dic3—22no—
118C4⋊Dic3#6712yes—
119C4×Dic3—22no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123C2×C3⋊C8—122no—
124C22×C32#12011yescharacteristic
125C2×C3×D3—42no—
126C2×C3×D3—42no—
127C2×C3×D3—42no—
128C32×C4—21no—
129C32×C4—42no—
130C32×C4#13512yes—
131C32×C4#13712yes—
132C3×Dic3—42no—
133C3×Dic3—81no—
134C2×Q16—62no—
135C4⋊Q8—31no—
136C4⋊Q8D3211yescharacteristic
137#124—62no—
138#121—62no—
139C4×D4—32no—
140#117—62no—
141#106—182no—
142C4⋊C8—92no—
143#102—182no—
144C4×C8—31no—
145C23×C3—62no—
146C22×D3—22no—
147C3×Q8—42no—
148C3×Q8—42no—
149C3×Q8—82no—
150C3×Q8—122no—
151C3×D4—62no—
152C3×D4—62no—
153C3×D4—242no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—21no—
157C2×C3×C4—22no—
158C2×C3×C4—42no—
159C2×C3×C4—62no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×C3×C4—121no—
163C2×C3×C4D3×D412yes—
164C2×C3×C4C2×#6711yescharacteristic
165C2×C3×C4C2×#6711yescharacteristic
166C2×C3×C4C2×#6712yes—
167C2×Dic3—22no—
168C2×Dic3—41no—
169D12—22no—
170D12—22no—
171D12—82no—
172C4×D3—42no—
173C4×D3—42no—
174Dic6—42no—
175C3×C8—62no—
176C3⋊C8—22no—
177C3⋊C8—122no—
178C3⋊C8—122no—
179C3⋊C8—242no—
180C2×C32#45212yes—
181C2×C32#45311yescharacteristic
182C3×D3—82no—
183C2×Q8—61no—
184C2×Q8#62512yes—
185C2×D4—32no—
186C2×D4—62no—
187C22×C4—62no—
188Q16—124no—
189C2×C8—61no—
190C2×C8—182no—
191C4⋊C4—22no—
192C4⋊C4—32no—
193C4⋊C4—62no—
194C22⋊C4—64no—
195C22⋊C4—62no—
196C42—62no—
197C42C2×D3211yescharacteristic
198C22×C3—21no—
199C22×C3—122no—
200C22×C3—122no—
201C22×C3—122no—
202C22×C3#93711yescharacteristic
203C22×C3#95311yescharacteristic
204C2×D3—42no—
205C2×D3—42no—
206C2×D3—42no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—41no—
212C3×C4—42no—
213C3×C4—42no—
214C3×C4—82no—
215C3×C4—122no—
216C3×C4—241no—
217C3×C4#91812yes—
218C3×C4#91912yes—
219C3×C4#95012yes—
220C3×C4#95112yes—
221Dic3—42no—
222Dic3—81no—
223C32#163411yescharacteristic, complemented, Sylow
224C23—62no—
225Q8—42no—
226Q8—122no—
227D4—62no—
228D4—62no—
229D4—242no—
230C2×C4—22no—
231C2×C4—62no—
232C2×C4—122no—
233C2×C4—122no—
234C2×C4—121no—
235C2×C4C2×#62511yescharacteristic
236C2×C4D3×#6712yes—
237C8—62no—
238C8—362no—
239C2×C3—21no—
240C2×C3—22no—
241C2×C3—242no—
242C2×C3#507711yescharacteristic
243C2×C3#518712yes—
244C2×C3#523912yes—
245C2×C3#524111yescharacteristic
246D3—82no—
247C22—122no—
248C22—122no—
249C22—122no—
250C22#6397611yescharacteristic
251C4—21no—
252C4—42no—
253C4—122no—
254C4—241no—
255C4#6394312yes—
256C4#6394912yes—
257C3—21no—
258C3#7130411yescharacteristic, complemented
259C3#7192811yescharacteristic, complemented
260C2—242no—
261C2#1059150911yescharacteristic
262C2#1059159712yes—
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC3×#5734C2
hypercenterC4⋊Q8D32
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5092C2semidirect
3. #10590266C2semidirect
4. #10589412C2semidirect
5. #10589081C2semidirect
22. #5092D3semidirect
223. C32#1634semidirect
258. C3#71304semidirect
259. C3#71928semidirect

Maximal subgroups

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

subgroupindex
C3×#57342
C3×#50922
#105902662
#105894122
#105890812
#719283
#713043