Finite Group Databasebeta

← #11779341

Subgroups — #11779341

Order 1152.

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

normal subgroups only

This group has 478 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×#5713C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic
3#10590310C212yesmaximal, complemented
4#10589410C211yesmaximal, characteristic
5#10589084C212yesmaximal, complemented
6#71944—31nomaximal
7#71270—31nomaximal
8C32×#127C2211yescharacteristic
9C3×#936—22no—
10C3×#935—22no—
11C3×D4×Dic3—22no—
12C2×C3×#214—22no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2212yes—
15C4⋊(C3⋊(C3⋊C8))C2212yes—
16C3×C4×C3⋊C8C2211yescharacteristic
17#63576—22no—
18#63565—22no—
19C3×#559—31no—
20#5713D311yescharacteristic
21C3×#492—31no—
22#5091—32no—
23#5076D311yescharacteristic
24#5021—32no—
25#4544—31no—
26#4544—31no—
27#4544—61no—
28#4535—32no—
29#4456—32no—
30C2×C32×D4—22no—
31C2×C32×D4D412yes—
32C22×C3×Dic3—22no—
33C2×C3×Dic6—21no—
34C2×C3×Dic6D412yes—
35C32×C42C2311yescharacteristic
36C2×C3⋊(C3⋊C8)—22no—
37C3×#217—24no—
38C3×#217—22no—
39C3×#214—44no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3D412yes—
42C3×Dic3⋊C4—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—21no—
45#1630—91noSylow
46C2×C3×SD16—62no—
47C3×C4⋊Q8—31no—
48C3×#127—21no—
49C3×#127C2×D311yescharacteristic
50C3×#127C2×D311yescharacteristic
51C3×#124—62no—
52C3×#123—62no—
53C3×C4×Q8—32no—
54C3×C4×D4—62no—
55#936—22no—
56#935—22no—
57D4×Dic3—22no—
58C2×#214—22no—
59#869C2×D311yescharacteristic
60C4×Dic6C2×D312yes—
61C3×C4×C8—31no—
62#835—62no—
63#810—62no—
64#807—62no—
65#807—62no—
66C4⋊(C3⋊C8)—32no—
67C4⋊(C3⋊C8)—32no—
68C4⋊(C3⋊C8)—62no—
69C4×C3⋊C8C2×D311yescharacteristic
70C23×C32—22no—
71C32×D4—42no—
72C32×D4—42no—
73C32×D4—42no—
74C2×C32×C4C2×D412yes—
75C2×C32×C4C2×D411yescharacteristic
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—82no—
80C3×Dic6—22no—
81C3×Dic6—22no—
82C3×Dic6—42no—
83C3⋊(C3⋊C8)—42no—
84C3×C3⋊C8—22no—
85#559—31no—
86#492—31no—
87#477—92no—
88#331—91no—
89Q8⋊C8—92no—
90C2×C3×Q8—32no—
91C2×C3×Q8—61no—
92C2×C3×D4—22no—
93C2×C3×D4—22no—
94C2×C3×D4—22no—
95C2×C3×D4—42no—
96C2×C3×D4#6712yes—
97C2×C3×D4#6712yes—
98C22×C3×C4—62no—
99C22×Dic3—22no—
100C2×Dic6—21no—
101C2×Dic6#6712yes—
102C3×SD16—124no—
103C2×C3×C8—61no—
104C3×C4⋊C4—32no—
105C3×C4⋊C4—62no—
106C3×C4⋊C4—62no—
107C3×C22⋊C4—64no—
108C3×C22⋊C4—62no—
109C3×C42—21no—
110C3×C42—62no—
111C3×C42C22×D311yescharacteristic
112C3×C42C22×D311yescharacteristic
113#217—24no—
114#217—22no—
115#214—44no—
116C4⋊Dic3—22no—
117C4⋊Dic3#6712yes—
118Dic3⋊C4—22no—
119C4×Dic3—22no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123C2×C3⋊C8—122no—
124C22×C32—44no—
125C22×C32—42no—
126C22×C32#12011yescharacteristic
127C32×C4—21no—
128C32×C4#13512yes—
129C32×C4#13712yes—
130C3×Dic3—42no—
131C3×Dic3—42no—
132C3×Dic3—81no—
133C2×SD16—62no—
134C4⋊Q8—31no—
135#127D3211yescharacteristic
136#124—62no—
137#123—62no—
138C4×Q8—32no—
139C4×D4—62no—
140#107—182no—
141C4⋊C8—92no—
142#103—182no—
143C4×C8—31no—
144C23×C3—22no—
145C23×C3—22no—
146C23×C3—42no—
147C3×Q8—62no—
148C3×Q8—62no—
149C3×Q8—122no—
150C3×D4—42no—
151C3×D4—42no—
152C3×D4—42no—
153C3×D4—42no—
154C3×D4—42no—
155C3×D4—42no—
156C3×D4—82no—
157C3×D4—82no—
158C3×D4—82no—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4—62no—
162C2×C3×C4—62no—
163C2×C3×C4—121no—
164C2×C3×C4—242no—
165C2×C3×C4D3×D412yes—
166C2×C3×C4C2×#6711yescharacteristic
167C2×C3×C4C2×#6711yescharacteristic
168C2×C3×C4C2×#6712yes—
169C2×Dic3—22no—
170C2×Dic3—22no—
171C2×Dic3—41no—
172C2×Dic3—82no—
173Dic6—22no—
174Dic6—22no—
175Dic6—42no—
176C3×C8—62no—
177C3⋊C8—22no—
178C3⋊C8—122no—
179C3⋊C8—122no—
180C3⋊C8—242no—
181C2×C32—82no—
182C2×C32#45212yes—
183C2×C32#45311yescharacteristic
184C2×Q8—32no—
185C2×Q8—61no—
186C2×D4—22no—
187C2×D4#62512yes—
188C22×C4—62no—
189SD16—124no—
190C2×C8—61no—
191C2×C8—182no—
192C4⋊C4—32no—
193C4⋊C4—62no—
194C4⋊C4—62no—
195C22⋊C4—64no—
196C22⋊C4—62no—
197C42—62no—
198C42C2×D3211yescharacteristic
199C22×C3—21no—
200C22×C3—44no—
201C22×C3—44no—
202C22×C3—42no—
203C22×C3—42no—
204C22×C3—84no—
205C22×C3—82no—
206C22×C3#93711yescharacteristic
207C22×C3#95311yescharacteristic
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213C3×C4—122no—
214C3×C4—122no—
215C3×C4—241no—
216C3×C4#91512yes—
217C3×C4#91612yes—
218C3×C4#95012yes—
219C3×C4#95112yes—
220Dic3—42no—
221Dic3—42no—
222Dic3—81no—
223C32#163011yescharacteristic, complemented, Sylow
224C23—22no—
225Q8—62no—
226Q8—62no—
227Q8—122no—
228D4—42no—
229D4—42no—
230D4—42no—
231C2×C4—62no—
232C2×C4—62no—
233C2×C4—121no—
234C2×C4—242no—
235C2×C4C2×#62511yescharacteristic
236C2×C4D3×#6712yes—
237C8—62no—
238C8—362no—
239C2×C3—21no—
240C2×C3—22no—
241C2×C3—82no—
242C2×C3—82no—
243C2×C3—162no—
244C2×C3#507711yescharacteristic
245C2×C3#517312yes—
246C2×C3#523912yes—
247C2×C3#524111yescharacteristic
248C22—42no—
249C22—44no—
250C22#6397611yescharacteristic
251C4—21no—
252C4—122no—
253C4—122no—
254C4—241no—
255C4#6392912yes—
256C4#6393512yes—
257C3—21no—
258C3#7127011yescharacteristic, complemented
259C3#7194411yescharacteristic, complemented
260C2—82no—
261C2#1059146112yes—
262C2#1059150911yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#120
hypercenter#127D32
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #10590310C2semidirect
5. #10589084C2semidirect
223. C32#1630semidirect
258. C3#71270semidirect
259. C3#71944semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#50762
#105903102
#105894102
#105890842
#719443
#712703