Finite Group Databasebeta

← #11782801

Subgroups — #11782801

Order 1152.

361 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4682C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic
3#10590309C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic
5#10590290C211yesmaximal, characteristic
6#10590290C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic
8#71364—31nomaximal
9#71222—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#818—22no—
18C3×#816—22no—
19#63574—22no—
20#63565—22no—
21#63565—22no—
22#63565—22no—
23C3×#500—31no—
24C3×#487—31no—
25#5093—31no—
26#5093—31no—
27#5093—31no—
28#5080—31no—
29#5080—31no—
30#5079—31no—
31#5079—31no—
32#5079—31no—
33#4682D311yescharacteristic
34#4681D311yescharacteristic
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C32×C8D412yes—
43C32×C42C2311yescharacteristic
44C2×C3⋊(C3⋊C8)D412yes—
45C2×C3⋊(C3⋊C8)D412yes—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54#1718—91noSylow
55C3×C4⋊Q8—31no—
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59#869C2×D311yescharacteristic
60#869C2×D311yescharacteristic
61#869C2×D311yescharacteristic
62#869C2×D311yescharacteristic
63C3×#107—62no—
64C3×#103—62no—
65C3×C4×C8—21no—
66C3×C4×C8C2×D311yescharacteristic
67C3×C4×C8C2×D311yescharacteristic
68#835—62no—
69#835—62no—
70#835—62no—
71#818—22no—
72#816—22no—
73#810—62no—
74#810—62no—
75#810—62no—
76#808—62no—
77#808—62no—
78C4×C3⋊C8—31no—
79C4×C3⋊C8—31no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—61no—
83C4×C3⋊C8—61no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C3×Dic6—42no—
92C3×Dic6—42no—
93C3×Dic6—42no—
94C3×Dic6—42no—
95C32×C8—22no—
96C3⋊(C3⋊C8)—22no—
97C3⋊(C3⋊C8)—22no—
98#500—31no—
99#498—91no—
100#487—31no—
101#487—91no—
102#487—91no—
103#487—91no—
104#322—91no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×Dic6—21no—
110C2×Dic6—21no—
111C2×Dic6—21no—
112C2×Dic6—21no—
113C2×C3×C8—22no—
114C2×C3×C8#6712yes—
115C2×C3×C8#6712yes—
116C3×C4⋊C4—61no—
117C3×C4⋊C4—61no—
118C3×C4⋊C4—61no—
119C3×C4⋊C4—61no—
120C3×C4⋊C4—61no—
121C3×C4⋊C4—61no—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C42—21no—
125C3×C42C22×D311yescharacteristic
126C3×C42C22×D311yescharacteristic
127C4⋊Dic3—21no—
128C4⋊Dic3—21no—
129C4⋊Dic3—21no—
130C4⋊Dic3—21no—
131C4⋊Dic3—21no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—32no—
137C2×C3⋊C8—32no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C22×C32#12711yescharacteristic
142C32×C4#13512yes—
143C32×C4#13712yes—
144C32×C4#13712yes—
145C3×Dic3—81no—
146C3×Dic3—81no—
147C3×Dic3—81no—
148C3×Dic3—81no—
149C4⋊Q8—31no—
150C4⋊Q8—31no—
151C4⋊Q8—31no—
152C4⋊Q8—31no—
153#107—62no—
154#106—182no—
155#103—62no—
156#103—182no—
157#103—182no—
158#103—182no—
159C4×C8—91no—
160C4×C8—91no—
161C4×C8D3211yescharacteristic
162C3×Q8—122no—
163C3×Q8—122no—
164C3×Q8—122no—
165C3×Q8—122no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4D3×D411yescharacteristic
174C2×C3×C4D3×D411yescharacteristic
175C2×C3×C4D3×D411yescharacteristic
176C2×C3×C4D3×D411yescharacteristic
177C2×C3×C4C2×#6711yescharacteristic
178C2×C3×C4C2×#6711yescharacteristic
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183Dic6—42no—
184Dic6—42no—
185Dic6—42no—
186Dic6—42no—
187C3×C8—22no—
188C3×C8—22no—
189C3×C8—42no—
190C3⋊C8—64no—
191C3⋊C8—62no—
192C3⋊C8—62no—
193C3⋊C8—62no—
194C3⋊C8—62no—
195C3⋊C8—122no—
196C2×C32#49511yescharacteristic
197C2×C32#49711yescharacteristic
198C2×C32#49711yescharacteristic
199C2×Q8—61no—
200C2×Q8—61no—
201C2×Q8—61no—
202C2×Q8—61no—
203C2×C8—92no—
204C2×C8—92no—
205C2×C8#62512yes—
206C4⋊C4—61no—
207C4⋊C4—61no—
208C4⋊C4—61no—
209C4⋊C4—61no—
210C4⋊C4—61no—
211C4⋊C4—61no—
212C4⋊C4—61no—
213C4⋊C4—61no—
214C42C2×D3211yescharacteristic
215C22×C3—21no—
216C22×C3#94011yescharacteristic
217C22×C3#94011yescharacteristic
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—241no—
222C3×C4—241no—
223C3×C4—241no—
224C3×C4—241no—
225C3×C4#91212yes—
226C3×C4#91512yes—
227C3×C4#91812yes—
228C3×C4#91912yes—
229C3×C4#94212yes—
230C3×C4#95112yes—
231Dic3—81no—
232Dic3—81no—
233Dic3—81no—
234Dic3—81no—
235C32#171811yescharacteristic, complemented, Sylow
236Q8—122no—
237Q8—122no—
238Q8—122no—
239Q8—122no—
240C2×C4—121no—
241C2×C4—121no—
242C2×C4—121no—
243C2×C4—121no—
244C2×C4#380211yescharacteristic
245C2×C4#380211yescharacteristic
246C2×C4C2×#62511yescharacteristic
247C8—22no—
248C8—182no—
249C8—182no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3#506011yescharacteristic
254C2×C3#508611yescharacteristic
255C2×C3#515511yescharacteristic
256C2×C3#516711yescharacteristic
257C2×C3#519011yescharacteristic
258C2×C3#519111yescharacteristic
259C22#6391411yescharacteristic
260C4—241no—
261C4—241no—
262C4—241no—
263C4—241no—
264C4#6381012yes—
265C4#6381112yes—
266C4#6382712yes—
267C3—21no—
268C3#7122211yescharacteristic, complemented
269C3#7136411yescharacteristic, complemented
270C2#1059037611yescharacteristic
271C2#1059086911yescharacteristic
272C2#1059087011yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1718
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
235. C32#1718semidirect
268. C3#71222semidirect
269. C3#71364semidirect

Maximal subgroups

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

subgroupindex
C3×#46822
C3×#46812
#105903092
#105902902
#105893202
#713643
#712223