Finite Group Databasebeta

← #11779466

Subgroups — #11779466

Order 1152.

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

normal subgroups only

This group has 518 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
1#10596193C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic
3#10590284C212yesmaximal
4C3×#4546C211yesmaximal, characteristic
5#10589085C212yesmaximal
6#71307—31nomaximal
7#68505—31nomaximal
8C32×C4⋊Q8C2211yescharacteristic
9#64153—22no—
10#64097—22no—
11#64096—22no—
12C4×#634C2212yes—
13C2×C3×#216—22no—
14C3×#869C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16C3×C4×C3⋊C8C2211yescharacteristic
17#63575—22no—
18#63567—22no—
19#5722—31no—
20#5722—31no—
21#5722—61no—
22C3×#494—31no—
23#5092D311yescharacteristic
24#5091—32no—
25#4850—32no—
26C3×#333—31no—
27#4546D311yescharacteristic
28#4484—32no—
29#4456—32no—
30C2×C32×Q8D412yes—
31C2×#634—22no—
32C2×#634D412yes—
33C2×C3×Dic6—21no—
34C32×C4⋊C4—22no—
35C32×C42C2311yescharacteristic
36C4⋊(C3⋊Dic3)D412yes—
37#3750—24no—
38#3750—22no—
39C4×C3⋊Dic3—22no—
40C4×C3⋊Dic3—22no—
41C3×#216—44no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8—22no—
45#1633—91noSylow
46C2×C3×Q16—62no—
47C3×C4⋊Q8—21no—
48C3×C4⋊Q8—31no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C2×D311yescharacteristic
51#944—64no—
52#944—62no—
53#944—62no—
54C2×#216—22no—
55#888—62no—
56#888—62no—
57#888—64no—
58#887—62no—
59#887—62no—
60#887—64no—
61#869C2×D311yescharacteristic
62C4×Dic6—32no—
63C4×Dic6—32no—
64C4×Dic6—62no—
65C3×C4⋊C8—32no—
66C3×C4×C8—31no—
67#818—62no—
68#816—62no—
69#810—62no—
70#807—62no—
71C4⋊(C3⋊C8)C2×D312yes—
72C4×C3⋊C8C2×D311yescharacteristic
73C32×Q8—42no—
74C2×C32×C4—22no—
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79#634—22no—
80#634—82no—
81#634Q1614yescomplemented
82C2×C3×Dic3—41no—
83C3×Dic6—42no—
84C3×C3⋊C8—22no—
85C3×C3⋊C8—42no—
86Q82—91no—
87#494—31no—
88#477—92no—
89#333—31no—
90Q8⋊C8—92no—
91C2×C3×Q8—22no—
92C2×C3×Q8—61no—
93C2×C3×Q8D1212yes—
94C2×C3×Q8#6712yes—
95C2×Dic6—21no—
96C2×Dic6—32no—
97C2×Dic6—32no—
98C2×Dic6—62no—
99C2×Dic6—64no—
100C2×Dic6—62no—
101C2×Dic6—62no—
102C3×Q16—124no—
103C2×C3×C8—61no—
104C2×C3×C8—62no—
105C3×C4⋊C4—24no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—62no—
109C3×C42—21no—
110C3×C42C22×D311yescharacteristic
111C3×C42C22×D311yescharacteristic
112#216—44no—
113C4⋊Dic3—22no—
114C4⋊Dic3—32no—
115C4⋊Dic3—32no—
116C4⋊Dic3—62no—
117Dic3⋊C4—64no—
118Dic3⋊C4—68no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123C4×Dic3—64no—
124C4×Dic3—64no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C2×C3⋊C8—21no—
130C2×C3⋊C8—22no—
131C22×C32#12011yescharacteristic
132C32×C4—21no—
133C32×C4—42no—
134C32×C4C2×Q1612yes—
135C32×C4#13712yes—
136C3⋊Dic3—24no—
137C3⋊Dic3—42no—
138C3×Dic3—81no—
139C2×Q16—62no—
140C4⋊Q8—31no—
141C4⋊Q8—182no—
142C4⋊Q8—182no—
143C4⋊Q8D3211yescharacteristic
144C4×Q8—92no—
145C4×Q8—182no—
146#107—182no—
147C4⋊C8—32no—
148#103—182no—
149C4×C8—31no—
150C3×Q8—42no—
151C3×Q8—42no—
152C3×Q8—82no—
153C3×Q8—122no—
154C2×C3×C4—24no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—21no—
158C2×C3×C4—22no—
159C2×C3×C4—121no—
160C2×C3×C4C2×D1211yescharacteristic
161C2×C3×C4D3×D412yes—
162C2×C3×C4D3×D412yes—
163C2×C3×C4C2×#6711yescharacteristic
164C2×Dic3—41no—
165C2×Dic3—64no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—64no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171Dic6—34no—
172Dic6—34no—
173Dic6—42no—
174Dic6—64no—
175Dic6—64no—
176Dic6—62no—
177Dic6—62no—
178Dic6—244no—
179Dic6—242no—
180Dic6—242no—
181C3×C8—62no—
182C3×C8—122no—
183C3⋊C8—22no—
184C3⋊C8—42no—
185C2×C32#45112yes—
186C2×C32#45311yescharacteristic
187C2×Q8—61no—
188C2×Q8—92no—
189C2×Q8—182no—
190C2×Q8#62612yes—
191Q16—124no—
192C2×C8—61no—
193C2×C8—62no—
194C4⋊C4—22no—
195C4⋊C4—62no—
196C4⋊C4—92no—
197C4⋊C4—184no—
198C4⋊C4—182no—
199C42—182no—
200C42—182no—
201C42C2×D3211yescharacteristic
202C22×C3—21no—
203C22×C3#88211yescharacteristic
204C22×C3#93711yescharacteristic
205C3×C4—21no—
206C3×C4—21no—
207C3×C4—22no—
208C3×C4—22no—
209C3×C4—41no—
210C3×C4—44no—
211C3×C4—42no—
212C3×C4—42no—
213C3×C4—241no—
214C3×C4#91512yes—
215C3×C4D3×Q1612yes—
216C3×C4D3×Q1612yes—
217C3×C4#91812yes—
218Dic3—68no—
219Dic3—64no—
220Dic3—64no—
221Dic3—81no—
222Dic3—124no—
223Dic3—122no—
224Dic3—122no—
225C32#163311yescharacteristic, complemented, Sylow
226Q8—42no—
227Q8—94no—
228Q8—122no—
229Q8—182no—
230Q8—722no—
231C2×C4—22no—
232C2×C4—121no—
233C2×C4—182no—
234C2×C4—182no—
235C2×C4C2×#62611yescharacteristic
236C2×C4#381112yes—
237C8—62no—
238C8—122no—
239C2×C3—21no—
240C2×C3—22no—
241C2×C3#474711yescharacteristic
242C2×C3#480912yes—
243C2×C3#507711yescharacteristic
244C2×C3#518612yes—
245C22#6398111yescharacteristic
246C4—21no—
247C4—42no—
248C4—184no—
249C4—241no—
250C4—362no—
251C4#6394412yes—
252C4#6395112yes—
253C3—21no—
254C3#6850511yescharacteristic, complemented
255C3#7130711yescharacteristic, complemented
256C2#1059151111yescharacteristic
257C2#1059160312yes—
subgroupG/H
centerC22#63981
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
81. #634Q16semidirect
225. C32#1633semidirect
254. C3#68505semidirect
255. C3#71307semidirect

Maximal subgroups

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

subgroupindex
#105961932
C3×#50922
#105902842
C3×#45462
#105890852
#713073
#685053