Finite Group Databasebeta

← #11799751

Subgroups — #11799751

Order 1152.

269 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 269 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5196C211yesmaximal, characteristic
2#10590871C211yesmaximal, characteristic, complemented
3#10589432C211yesmaximal, characteristic
4C3×#4566C211yesmaximal, characteristic
5#10589138C211yesmaximal, characteristic, complemented
6#10589137C211yesmaximal, characteristic, complemented
7#10589134C211yesmaximal, characteristic, complemented
8#70920—31nomaximal
9#69247—31nomaximal
10C32×#135C2211yescharacteristic
11C3×#948—21no—
12#63869—21no—
13#63644C2211yescharacteristic
14#63639C2211yescharacteristic
15C3×#837—21no—
16C3×#819C2211yescharacteristic
17C3×#817C2211yescharacteristic
18C3×C8×Dic3C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63575—21no—
21C3×#443—31no—
22#5196D311yescharacteristic
23#4858—31no—
24#4683—31no—
25C3×#360—31no—
26#4566—31no—
27#4566—31no—
28#4566—61no—
29#4566D311yescharacteristic
30#4513—31no—
31#4511—31no—
32#4494—31no—
33#4494—31no—
34#4487—31no—
35#4463—31no—
36C32×#41—21no—
37C32×Q16Q811yescharacteristic
38C32×SD16—21no—
39C32×D8Q811yescharacteristic
40C2×C32×C8C2311yescharacteristic
41C4⋊(C3⋊Dic3)—21no—
42C3×C4⋊Dic3—21no—
43C3×C4×Dic3D411yescharacteristic
44C3×#208—21no—
45C3×#208—41no—
46C2×C3×C3⋊C8—41no—
47C2×C3×C3⋊C8D411yescharacteristic
48#3724—41no—
49Dic3⋊Dic3—41no—
50C3⋊(C3⋊C16)—21no—
51C3×C3⋊C16—21no—
52#2231—91noSylow
53C3×#135—21no—
54C3×#135C2×D311yescharacteristic
55C3×#135C2×D311yescharacteristic
56C3×#131—61no—
57#948—21no—
58#890—61no—
59#870—61no—
60C3×M32—31no—
61C3×#108—31no—
62C3×#106—31no—
63C3×#104—61no—
64C3×C4×C8—31no—
65#837—21no—
66#819C2×D311yescharacteristic
67#818—61no—
68#817—31no—
69#817—31no—
70#817—61no—
71#817C2×D311yescharacteristic
72C8×Dic3C2×D311yescharacteristic
73#812—31no—
74#812—31no—
75#812—61no—
76#812C2×D311yescharacteristic
77#807—61no—
78C32×Q8—21no—
79C32×D4—21no—
80C32×D4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—41no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—41no—
86C32×C8C2×Q811yescharacteristic
87C32×C8#4111yescharacteristic
88C3×C3⋊C8—41no—
89C3×C3⋊C8SD1611yescharacteristic
90C3×C3⋊C8SD1611yescharacteristic
91#499—91no—
92#443—31no—
93#365—91no—
94#365—91no—
95#364—91no—
96#360—31no—
97#360—91no—
98C3×#41—21no—
99C3×#41—21no—
100C3×#41—41no—
101C3×Q16—21no—
102C3×Q16Dic611yescharacteristic
103C3×Q16Dic611yescharacteristic
104C3×SD16—21no—
105C3×SD16—21no—
106C3×SD16—41no—
107C3×D8—21no—
108C3×D8Dic611yescharacteristic
109C3×D8Dic611yescharacteristic
110C3×M16—61no—
111C3×M16—121no—
112C2×C3×C8—21no—
113C2×C3×C8—31no—
114C2×C3×C8—121no—
115C2×C3×C8C22×D311yescharacteristic
116C2×C3×C8C22×D311yescharacteristic
117C3×C4⋊C4—61no—
118C3×C42—31no—
119C4⋊Dic3—21no—
120C4⋊Dic3—61no—
121C4⋊Dic3—61no—
122C4⋊Dic3—121no—
123C4⋊Dic3—121no—
124Dic3⋊C4—121no—
125Dic3⋊C4—121no—
126Dic3⋊C4—121no—
127C4×Dic3#6711yescharacteristic
128#208—21no—
129#208—41no—
130C2×C3⋊C8—41no—
131C2×C3⋊C8#6711yescharacteristic
132C3×C16—61no—
133C3⋊C16—21no—
134C3⋊C16—61no—
135C3⋊C16—61no—
136C3⋊C16—121no—
137C22×C32—41no—
138C22×C32AGL(1,ℤ/8)11yescharacteristic
139C32×C4—41no—
140C32×C4C22⋊Q811yescharacteristic
141C32×C4C2×SD1611yescharacteristic
142C3⋊Dic3—81no—
143C3×Dic3—41no—
144C3×Dic3—81no—
145#135D3211yescharacteristic
146#131—61no—
147#125—181no—
148M32—31no—
149M32—91no—
150#108—31no—
151#107—181no—
152#106—31no—
153#106—91no—
154#104—61no—
155C4×C8—31no—
156C3×Q8—21no—
157C3×Q8—21no—
158C3×Q8—41no—
159C3×D4—21no—
160C3×D4—21no—
161C3×D4—41no—
162C3×D4—41no—
163C3×D4—41no—
164C3×D4—81no—
165C2×C3×C4—21no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—61no—
169C2×C3×C4—81no—
170C2×C3×C4—121no—
171C2×C3×C4D3×D411yescharacteristic
172C2×C3×C4C2×#6711yescharacteristic
173C2×Dic3—21no—
174C2×Dic3—41no—
175C2×Dic3—121no—
176C2×Dic3—121no—
177C2×Dic3—241no—
178C3×C8—21no—
179C3×C8—21no—
180C3×C8—31no—
181C3×C8—31no—
182C3×C8—121no—
183C3×C8C2×Dic611yescharacteristic
184C3×C8C2×Dic611yescharacteristic
185C3×C8#23511yescharacteristic
186C3×C8#23711yescharacteristic
187C3⋊C8—41no—
188C3⋊C8#21411yescharacteristic
189C3⋊C8#21411yescharacteristic
190C2×C32—21no—
191C2×C32—81no—
192C2×C32#47611yescharacteristic
193#41—21no—
194Q16#62711yescharacteristic
195SD16—21no—
196D8#62711yescharacteristic
197M16—61no—
198M16—121no—
199C2×C8—31no—
200C2×C8—121no—
201C2×C8C2×D3211yescharacteristic
202C4⋊C4—61no—
203C4⋊C4—181no—
204C4⋊C4—361no—
205C4⋊C4—361no—
206C42—31no—
207C16—61no—
208C16—181no—
209C22×C3—21no—
210C22×C3—41no—
211C22×C3—41no—
212C22×C3—81no—
213C22×C3#91111yescharacteristic
214C22×C3#94911yescharacteristic
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—41no—
218C3×C4—41no—
219C3×C4—81no—
220C3×C4—121no—
221C3×C4—241no—
222C3×C4#87811yescharacteristic
223C3×C4D3×SD1611yescharacteristic
224C3×C4#92411yescharacteristic
225C3×C4C2×#21411yescharacteristic
226Dic3—41no—
227Dic3—81no—
228Dic3—241no—
229Dic3—241no—
230Dic3—481no—
231C32#223111yescharacteristic, complemented, Sylow
232Q8—21no—
233D4—21no—
234D4—41no—
235C2×C4—41no—
236C2×C4—61no—
237C2×C4—121no—
238C2×C4—361no—
239C2×C4D3×#6711yescharacteristic
240C8—31no—
241C8—31no—
242C8—121no—
243C8#380411yescharacteristic
244C8C2×#62711yescharacteristic
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—41no—
249C2×C3—81no—
250C2×C3—81no—
251C2×C3—161no—
252C2×C3#476111yescharacteristic
253C2×C3#500811yescharacteristic
254C22—41no—
255C22#6392511yescharacteristic
256C4—41no—
257C4—121no—
258C4—241no—
259C4—721no—
260C4D3×#21411yescharacteristic
261C4#6396411yescharacteristic
262C3—21no—
263C3#6924711yescharacteristic, complemented
264C3#7092011yescharacteristic, complemented
265C2—21no—
266C2—81no—
267C2#1059140811yescharacteristic
subgroupG/H
centerC2#10591408
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
Fitting, prime radicalC32×#135C22
socleC2×C32#476
hypercenter#135D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10590871C2semidirect
5. #10589138C2semidirect
6. #10589137C2semidirect
7. #10589134C2semidirect
231. C32#2231semidirect
263. C3#69247semidirect
264. C3#70920semidirect

Maximal subgroups

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

subgroupindex
C3×#51962
#105908712
#105894322
C3×#45662
#105891382
#105891372
#105891342
#709203
#692473