Finite Group Databasebeta

← #11799688

Subgroups — #11799688

Order 1152.

303 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592572C211yesmaximal, characteristic
2#10590875C211yesmaximal, characteristic
3C3×#4490C211yesmaximal, characteristic
4C3×#4489C211yesmaximal, characteristic
5#10589133C211yesmaximal, characteristic
6#10589119C211yesmaximal, characteristic
7#10589119C211yesmaximal, characteristic
8#69356—31nomaximal
9#69336—31nomaximal
10C2×#3746C2211yescharacteristic
11#64096—21no—
12#63872—21no—
13C32×#107C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15#63637—21no—
16C3×#818C2211yescharacteristic
17C3×#818C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20#63574—21no—
21#4878—31no—
22#4878—31no—
23#4873—31no—
24#4873—31no—
25#4873—61no—
26C3×#367—31no—
27C3×#366—31no—
28#4503—31no—
29#4503—31no—
30Dic3⋊C16—31no—
31Dic3⋊C16—31no—
32#4492—31no—
33#4492—31no—
34#4490D311yescharacteristic
35#4489D311yescharacteristic
36C2×#634—21no—
37C2×C32×C8C2311yescharacteristic
38C32×C4⋊C4—21no—
39#3750—41no—
40C4×C3⋊Dic3—41no—
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746—21no—
44#3746Q812yes—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47Dic3⋊Dic3—41no—
48Dic3⋊Dic3—41no—
49C3×C3⋊C16—21no—
50C3×C3⋊C16—21no—
51#2229—91noSylow
52C2×Dic12—31no—
53C2×Dic12—31no—
54C2×Dic12—61no—
55#890—61no—
56#890—61no—
57#887—61no—
58#887—61no—
59#887—62no—
60C2×C3×C16—31no—
61C2×C3×C16—31no—
62C3×#107—21no—
63C3×#107—31no—
64C3×#107—31no—
65C3×#107C2×D311yescharacteristic
66C3×#107C2×D311yescharacteristic
67#818C2×D311yescharacteristic
68#818C2×D311yescharacteristic
69C8×Dic3—31no—
70C8×Dic3—31no—
71C8×Dic3—61no—
72C2×C3⋊C16C2×D311yescharacteristic
73C2×C3⋊C16C2×D311yescharacteristic
74#810—61no—
75#810—61no—
76#810—62no—
77#808—61no—
78#808—61no—
79C2×C32×C4—41no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3D811yescharacteristic
83C2×C3⋊Dic3D811yescharacteristic
84#634—22no—
85#634—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3—41no—
88C32×C8C2×Q811yescharacteristic
89C32×C8#4111yescharacteristic
90C3⋊(C3⋊C8)—21no—
91#499—91no—
92C4×Q16—91no—
93#367—31no—
94#366—31no—
95C4⋊C16—91no—
96#358—91no—
97#358—91no—
98C2×Dic6—62no—
99C2×Dic6—61no—
100C2×Dic6—61no—
101C2×C3×C8—21no—
102C2×C3×C8C22×D311yescharacteristic
103C2×C3×C8C22×D311yescharacteristic
104C3×C4⋊C4—22no—
105C3×C4⋊C4—21no—
106C3×C4⋊C4—21no—
107C3×C4⋊C4—61no—
108C3×C4⋊C4—61no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—121no—
112C4⋊Dic3—121no—
113Dic3⋊C4—121no—
114Dic3⋊C4—121no—
115Dic3⋊C4—121no—
116Dic3⋊C4—121no—
117Dic3⋊C4—122no—
118C4×Dic3—31no—
119C4×Dic3—31no—
120C4×Dic3—61no—
121C4×Dic3—121no—
122C4×Dic3—121no—
123C4×Dic3—122no—
124C2×C3⋊C8—31no—
125C2×C3⋊C8—31no—
126C2×C3⋊C8—61no—
127Dic12—32no—
128Dic12—32no—
129Dic12—62no—
130Dic12—62no—
131Dic12—61no—
132Dic12—61no—
133C3×C16—61no—
134C3×C16—61no—
135C3⋊C16—21no—
136C3⋊C16—21no—
137C22×C32C2×D811yescharacteristic
138C32×C4—81no—
139C32×C4C22⋊Q811yescharacteristic
140C32×C4#13711yescharacteristic
141C3⋊Dic3—21no—
142C3⋊Dic3—21no—
143C3⋊Dic3—42no—
144C3×Dic3—81no—
145C3×Dic3—81no—
146C2×Q16—91no—
147#125—181no—
148C4×Q8—181no—
149C2×C16—31no—
150C2×C16—31no—
151#107—31no—
152#107—31no—
153#107D3211yescharacteristic
154#106—181no—
155#103—181no—
156C4×C8—91no—
157C2×C3×C4—21no—
158C2×C3×C4—42no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—121no—
162C2×C3×C4—121no—
163C2×C3×C4D3×D411yescharacteristic
164C2×C3×C4D3×D411yescharacteristic
165C2×Dic3—31no—
166C2×Dic3—31no—
167C2×Dic3—31no—
168C2×Dic3—31no—
169C2×Dic3—41no—
170C2×Dic3—41no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—122no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176Dic6—64no—
177Dic6—62no—
178Dic6—62no—
179Dic6—122no—
180Dic6—121no—
181Dic6—121no—
182C3×C8—21no—
183C3×C8—21no—
184C3×C8#23511yescharacteristic
185C3×C8#23511yescharacteristic
186C3×C8D3×Q811yescharacteristic
187C3×C8D3×Q811yescharacteristic
188C3⋊C8—61no—
189C3⋊C8—61no—
190C3⋊C8—121no—
191C2×C32#47411yescharacteristic
192C2×C32#50811yescharacteristic
193C2×C32#51011yescharacteristic
194C2×Q8—181no—
195Q16—92no—
196Q16—181no—
197C2×C8—91no—
198C2×C8C2×D3211yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—61no—
201C4⋊C4—61no—
202C4⋊C4—361no—
203C4⋊C4—361no—
204C4⋊C4—361no—
205C42—91no—
206C42—361no—
207C16—61no—
208C16—61no—
209C22×C3—21no—
210C22×C3D3×D811yescharacteristic
211C22×C3D3×D811yescharacteristic
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—82no—
215C3×C4—81no—
216C3×C4—81no—
217C3×C4—241no—
218C3×C4—241no—
219C3×C4#89611yescharacteristic
220C3×C4#89611yescharacteristic
221C3×C4#91811yescharacteristic
222C3×C4#91811yescharacteristic
223Dic3—62no—
224Dic3—61no—
225Dic3—61no—
226Dic3—61no—
227Dic3—61no—
228Dic3—81no—
229Dic3—81no—
230Dic3—121no—
231Dic3—124no—
232Dic3—122no—
233Dic3—122no—
234C32#222911yescharacteristic, complemented, Sylow
235Q8—182no—
236Q8—361no—
237C2×C4—41no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—121no—
241C2×C4—121no—
242C2×C4—361no—
243C2×C4#381111yescharacteristic
244C8—181no—
245C8#379711yescharacteristic
246C8#379811yescharacteristic
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3#489011yescharacteristic
251C2×C3#489011yescharacteristic
252C2×C3#491211yescharacteristic
253C2×C3#491511yescharacteristic
254C2×C3#491611yescharacteristic
255C2×C3#491811yescharacteristic
256C22#6392611yescharacteristic
257C4—81no—
258C4—181no—
259C4—181no—
260C4—241no—
261C4—241no—
262C4—362no—
263C4#6386511yescharacteristic
264C4#6394511yescharacteristic
265C3—21no—
266C3#6933611yescharacteristic, complemented
267C3#6935611yescharacteristic, complemented
268C2#1059043011yescharacteristic
269C2#1059103511yescharacteristic
270C2#1059105011yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socle, prime radicalC22×C32C2×D8
hypercenter#107D32
hypocenterC32#2229
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
234. C32#2229semidirect
266. C3#69336semidirect
267. C3#69356semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105908752
C3×#44902
C3×#44892
#105891332
#105891192
#693563
#693363