Finite Group Databasebeta

← #11779467

Subgroups — #11779467

Order 1152.

444 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5722C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic
3#10590310C212yesmaximal
4#10589412C211yesmaximal, characteristic
5#10589084C212yesmaximal
6#71940—31nomaximal
7#71307—31nomaximal
8C32×C4⋊Q8C2211yescharacteristic
9C3×#944—22no—
10C2×C3×#216—22no—
11C3×#888—22no—
12C3×#887—22no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2212yes—
15C4⋊(C3⋊(C3⋊C8))C2212yes—
16C3×C4×C3⋊C8C2211yescharacteristic
17#63576—22no—
18#63565—22no—
19C3×Q82—31no—
20#5722D311yescharacteristic
21C3×#494—31no—
22#5092D311yescharacteristic
23#5091—32no—
24#5021—32no—
25#4546—31no—
26#4546—31no—
27#4546—61no—
28#4535—32no—
29#4456—32no—
30C2×C32×Q8D412yes—
31C2×C3×Dic6—21no—
32C2×C3×Dic6—22no—
33C2×C3×Dic6D412yes—
34C32×C4⋊C4—22no—
35C32×C42C2311yescharacteristic
36C2×C3⋊(C3⋊C8)—22no—
37C3×#216—44no—
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3D412yes—
40C3×Dic3⋊C4—24no—
41C3×Dic3⋊C4—22no—
42C3×C4×Dic3—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—21no—
45#1633—91noSylow
46C2×C3×Q16—62no—
47C3×C4⋊Q8—21no—
48C3×C4⋊Q8—31no—
49C3×C4⋊Q8—62no—
50C3×C4⋊Q8—62no—
51C3×C4⋊Q8C2×D311yescharacteristic
52C3×C4⋊Q8C2×D311yescharacteristic
53C3×C4×Q8—32no—
54C3×C4×Q8—62no—
55#944—22no—
56C2×#216—22no—
57#888—22no—
58#887—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
70C32×Q8—42no—
71C2×C32×C4—22no—
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3×Dic3—22no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—41no—
77C3×Dic6—22no—
78C3×Dic6—42no—
79C3×Dic6—82no—
80C3×Dic6Q1614yescomplemented
81C3⋊(C3⋊C8)—42no—
82C3×C3⋊C8—22no—
83Q82—31no—
84#494—31no—
85#477—92no—
86#333—91no—
87Q8⋊C8—92no—
88C2×C3×Q8—22no—
89C2×C3×Q8—32no—
90C2×C3×Q8—62no—
91C2×C3×Q8—61no—
92C2×C3×Q8#6712yes—
93C2×C3×Q8#6712yes—
94C2×Dic6—21no—
95C2×Dic6—22no—
96C2×Dic6#6712yes—
97C3×Q16—124no—
98C2×C3×C8—61no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—32no—
102C3×C4⋊C4—42no—
103C3×C4⋊C4—64no—
104C3×C4⋊C4—62no—
105C3×C4⋊C4—62no—
106C3×C42—21no—
107C3×C42—62no—
108C3×C42—62no—
109C3×C42C22×D311yescharacteristic
110C3×C42C22×D311yescharacteristic
111#216—44no—
112C4⋊Dic3—22no—
113C4⋊Dic3#6712yes—
114Dic3⋊C4—24no—
115Dic3⋊C4—22no—
116C4×Dic3—22no—
117C4×Dic3—22no—
118C2×C3⋊C8—21no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—122no—
122C22×C32#12011yescharacteristic
123C32×C4—21no—
124C32×C4—42no—
125C32×C4C2×Q1612yes—
126C32×C4#13712yes—
127C3×Dic3—24no—
128C3×Dic3—42no—
129C3×Dic3—81no—
130C2×Q16—62no—
131C4⋊Q8—31no—
132C4⋊Q8—62no—
133C4⋊Q8—62no—
134C4⋊Q8D3211yescharacteristic
135C4×Q8—32no—
136C4×Q8—62no—
137#107—182no—
138C4⋊C8—92no—
139#103—182no—
140C4×C8—31no—
141C3×Q8—34no—
142C3×Q8—42no—
143C3×Q8—42no—
144C3×Q8—62no—
145C3×Q8—82no—
146C3×Q8—122no—
147C3×Q8—242no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—21no—
151C2×C3×C4—22no—
152C2×C3×C4—42no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×C3×C4—121no—
156C2×C3×C4D3×D412yes—
157C2×C3×C4C2×#6711yescharacteristic
158C2×C3×C4C2×#6711yescharacteristic
159C2×C3×C4C2×#6712yes—
160C2×Dic3—22no—
161C2×Dic3—22no—
162C2×Dic3—41no—
163Dic6—22no—
164Dic6—42no—
165Dic6—82no—
166Dic6#21614yescomplemented
167C3×C8—62no—
168C3⋊C8—22no—
169C3⋊C8—122no—
170C3⋊C8—122no—
171C3⋊C8—242no—
172C2×C32#45112yes—
173C2×C32#45311yescharacteristic
174C2×Q8—32no—
175C2×Q8—62no—
176C2×Q8—61no—
177C2×Q8#62512yes—
178Q16—124no—
179C2×C8—61no—
180C2×C8—182no—
181C4⋊C4—22no—
182C4⋊C4—32no—
183C4⋊C4—64no—
184C4⋊C4—62no—
185C4⋊C4—62no—
186C42—62no—
187C42—62no—
188C42C2×D3211yescharacteristic
189C22×C3—21no—
190C22×C3#93711yescharacteristic
191C22×C3#95311yescharacteristic
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—41no—
197C3×C4—42no—
198C3×C4—42no—
199C3×C4—64no—
200C3×C4—82no—
201C3×C4—122no—
202C3×C4—241no—
203C3×C4D3×Q1612yes—
204C3×C4#91812yes—
205C3×C4#94212yes—
206C3×C4C2×#21612yes—
207Dic3—24no—
208Dic3—42no—
209Dic3—81no—
210C32#163311yescharacteristic, complemented, Sylow
211Q8—34no—
212Q8—42no—
213Q8—62no—
214Q8—122no—
215Q8—242no—
216C2×C4—22no—
217C2×C4—62no—
218C2×C4—62no—
219C2×C4—121no—
220C2×C4C2×#62511yescharacteristic
221C2×C4D3×#6712yes—
222C8—62no—
223C8—362no—
224C2×C3—21no—
225C2×C3—22no—
226C2×C3#507711yescharacteristic
227C2×C3#518612yes—
228C2×C3#522812yes—
229C2×C3#524111yescharacteristic
230C22#6397611yescharacteristic
231C4—21no—
232C4—42no—
233C4—64no—
234C4—122no—
235C4—241no—
236C4D3×#21612yes—
237C4#6394812yes—
238C3—21no—
239C3#7130711yescharacteristic, complemented
240C3#7194011yescharacteristic, complemented
241C2#1059150911yescharacteristic
242C2#1059159412yes—
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1633
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
80. C3×Dic6Q16semidirect
166. Dic6#216semidirect
210. C32#1633semidirect
239. C3#71307semidirect
240. C3#71940semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#50922
#105903102
#105894122
#105890842
#719403
#713073