Finite Group Databasebeta

← #11795370

Subgroups — #11795370

Order 1152.

368 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593330C212yesmaximal, complemented
2#10593307C212yesmaximal
3#10590937C211yesmaximal, characteristic
4#10590914C211yesmaximal, characteristic, complemented
5#10590186C211yesmaximal, characteristic, complemented
6C2×C4×D32C2211yescharacteristic
7#64283C2212yes—
8C2×#3743C2211yescharacteristic
9C2×#3712C2211yescharacteristic
10#63818C2212yes—
11#63733—24no—
12D32⋊C8—24no—
13C3×(C2×D3)⋊C8—21no—
14C3×#819—21no—
15#63578—21no—
16(C2×D3)⋊(C3⋊C8)—21no—
17#4893—61no—
18#4726—61no—
19C22×D32Q811yescharacteristic
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×C3×C4×D3—21no—
22C2×#624Q811yescharacteristic
23C2×D3×Dic3—21no—
24C4×D32—22no—
25C4×D32—22no—
26#3792—22no—
27#3788—22no—
28#3787D414yes—
29C2×C32×C8D411yescharacteristic
30C2×C3⋊(C3⋊C8)D411yescharacteristic
31#3743—22no—
32C3×#208—22no—
33C2×C3×C3⋊C8—21no—
34#3712—22no—
35#3712—22no—
36#3710—22no—
37#2091—91nomaximal, Sylow
38C22×C4×D3—61no—
39D3×M16—62no—
40C2×ΓL(1,𝔽25)—61no—
41C2×ΓL(1,𝔽25)—61no—
42C2×ΓL(1,𝔽25)—61no—
43C3×#108—61no—
44C3×C22⋊C8—61no—
45#830—61no—
46#822—62no—
47(C2×D3)⋊C8—21no—
48(C2×D3)⋊C8—61no—
49#819—21no—
50C22×C3⋊D3C2×Q811yescharacteristic
51C22×C3×D3—21no—
52C2×D32—22no—
53C2×D32—42no—
54C2×C32×C4C2×D411yescharacteristic
55C2×C3⋊Dic3#4111yescharacteristic
56C4×C3⋊D3C2×D412yes—
57C4×C3⋊D3#4112yes—
58C2×C3×Dic3—21no—
59C3×C4×D3—41no—
60C3×C4×D3—41no—
61#624—22no—
62D3×Dic3—42no—
63#622—24no—
64C32×C8—21no—
65C3⋊(C3⋊C8)—21no—
66C3×C3⋊C8—42no—
67C3×C3⋊C8—41no—
68#430—91no—
69#430—92no—
70#407—91no—
71#407—92no—
72#338—91no—
73C23×D3—61no—
74C22×C3×C4—61no—
75C22×Dic3—61no—
76C2×C4×D3—21no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—122no—
82C2×C4×D3—122no—
83C3×M16—62no—
84C2×C3×C8—21no—
85C2×C3×C8—21no—
86C2×C3×C8—61no—
87#208—22no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91ΓL(1,𝔽25)—64no—
92ΓL(1,𝔽25)—122no—
93ΓL(1,𝔽25)—122no—
94ΓL(1,𝔽25)—122no—
95D3×C8—122no—
96C22×C32C22⋊Q811yescharacteristic
97C2×C3⋊D3—41no—
98C2×C3⋊D3C22⋊Q812yes—
99C2×C3×D3—22no—
100C2×C3×D3—41no—
101C2×C3×D3—41no—
102D32—24no—
103D32—42no—
104C32×C4#12311yescharacteristic
105C32×C4#12711yescharacteristic
106C3⋊Dic3#12312yes—
107C3×Dic3—41no—
108C23×C4—91no—
109C2×M16—91no—
110C2×M16—92no—
111C2×M16—91no—
112C2×M16—92no—
113#108—61no—
114#108—181no—
115#108—184no—
116C22⋊C8—61no—
117C22⋊C8—181no—
118C22⋊C8—184no—
119C23×C3—61no—
120C22×D3—21no—
121C22×D3—61no—
122C22×D3—61no—
123C22×D3—122no—
124C22×D3—122no—
125C22×D3—122no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—61no—
129C2×C3×C4—121no—
130C2×C3×C4—121no—
131C2×Dic3—21no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—122no—
135C4×D3—41no—
136C4×D3—41no—
137C4×D3—62no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—62no—
141C4×D3—122no—
142C4×D3—122no—
143C3×C8—22no—
144C3×C8—41no—
145C3×C8—122no—
146C3×C8—121no—
147C3⋊C8—42no—
148C3⋊C8—41no—
149C3⋊C8—62no—
150C3⋊C8—121no—
151C2×C32—21no—
152C2×C32#39911yescharacteristic
153C3⋊D3—22no—
154C3×D3—42no—
155C24—91no—
156C22×C4—61no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—181no—
160C22×C4—182no—
161C22×C4—182no—
162M16—62no—
163M16—182no—
164M16—182no—
165M16—182no—
166M16—182no—
167M16—182no—
168C2×C8—61no—
169C2×C8—94no—
170C2×C8—91no—
171C2×C8—182no—
172C2×C8GO+(4,𝔽2)11yescharacteristic
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—62no—
176C22×C3—121no—
177C22×C3—121no—
178C2×D3—22no—
179C2×D3—41no—
180C2×D3—41no—
181C2×D3—62no—
182C2×D3—62no—
183C2×D3—124no—
184C2×D3—124no—
185C2×D3—121no—
186C2×D3—121no—
187C2×D3—241no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—121no—
193Dic3—41no—
194Dic3—62no—
195Dic3—62no—
196C32#209111yescharacteristic, complemented, Sylow
197C23—61no—
198C23—91no—
199C23—182no—
200C23—362no—
201C2×C4—61no—
202C2×C4—91no—
203C2×C4—92no—
204C2×C4—92no—
205C2×C4—121no—
206C2×C4—121no—
207C2×C4—182no—
208C2×C4—362no—
209C2×C4C2×GO+(4,𝔽2)11yescharacteristic
210C8—21no—
211C8—121no—
212C8—122no—
213C8—184no—
214C8—181no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—41no—
220C2×C3—122no—
221D3—42no—
222D3—122no—
223D3—122no—
224C22—62no—
225C22—92no—
226C22—121no—
227C22—121no—
228C22—184no—
229C22—361no—
230C22—362no—
231C22D32⋊Q811yescharacteristic
232C4—92no—
233C4—121no—
234C4#6423111yescharacteristic
235C4#6423311yescharacteristic
236C3—21no—
237C3—21no—
238C2—21no—
239C2—122no—
240C2—182no—
241C2#1059340811yescharacteristic
subgroupG/H
centerC4#64231
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#399
prime radicalC22×D32Q8
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2091
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10593330C2semidirect
4. #10590914C2semidirect
5. #10590186C2semidirect
196. C32#2091semidirect

Maximal subgroups

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

subgroupindex
#105933302
#105933072
#105909372
#105909142
#105901862
#20919