Finite Group Databasebeta

← #11772639

Subgroups — #11772639

Order 1152.

316 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593822C211yesmaximal, characteristic
2#10591529C211yesmaximal, characteristic
3#10591504C211yesmaximal, characteristic
4C2×#3830C2211yescharacteristic
5C2×#3792C411yescharacteristic, complemented
6C22×#622C411yescharacteristic, complemented
7#63957—21no—
8#63818—21no—
9C22⋊#622—21no—
10#63778—21no—
11C3×#834—21no—
12C3×#833—21no—
13#63581C412yes—
14#63561C412yescomplemented
15#4745—61no—
16#4740—61no—
17C2×C32×D4D411yescharacteristic
18C2×#638C2×C411yescharacteristic
19C2×#638Q811yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22#3830—41no—
23#3830—41no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#634C2×C411yescharacteristic
26#3792—41no—
27C2×#622—21no—
28C2×#622—21no—
29C2×#622—41no—
30C3×#217—22no—
31C3×#208—22no—
32#3724—41no—
33Dic32—41no—
34#3712—41no—
35#3710—41no—
36#1395—91nomaximal, Sylow
37C2×#237—61no—
38C2×#237—61no—
39D3×M16—62no—
40#877—62no—
41C3×#100—61no—
42C3×#99—61no—
43#834—21no—
44#833—21no—
45#824—62no—
46#806—62no—
47C23×C32C22⋊C411yescharacteristic
48C23×C32C4⋊C411yescharacteristic
49C22×C3⋊D3C4⋊C411yescharacteristic
50C32×D4—41no—
51C2×C32×C4C22⋊C411yescharacteristic
52#638—41no—
53#638—41no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3C4211yescharacteristic
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63#634—41no—
64C2×C3×Dic3—42no—
65#622—41no—
66#622—41no—
67C3×C3⋊C8—42no—
68#413—91no—
69#410—91no—
70#408—91no—
71C2×C3×D4—21no—
72C2×C3×D4—21no—
73C2×#67—61no—
74C2×#67—61no—
75C2×#67—61no—
76C2×#67—61no—
77C22×Dic3—61no—
78C22×Dic3—61no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81#237—122no—
82#237—122no—
83#237—122no—
84#237—122no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C3×M16—62no—
90C3×C22⋊C4—62no—
91#217—22no—
92Dic3⋊C4—122no—
93C4×Dic3—122no—
94#208—22no—
95ΓL(1,𝔽25)—122no—
96D3×C8—122no—
97C22×C32—21no—
98C22×C32—21no—
99C22×C32—41no—
100C22×C32—41no—
101C22×C32#9511yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—41no—
104C32×C4—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3#9911yescharacteristic
108C3⋊Dic3#9911yescharacteristic
109C3×Dic3—82no—
110C2×#41—91no—
111C2×M16—91no—
112C2×M16—181no—
113C22×C8—91no—
114#117—181no—
115#101—92no—
116#100—61no—
117#99—61no—
118#99—92no—
119C22⋊C8—181no—
120C22⋊C8—181no—
121C23×C3—21no—
122C23×C3—21no—
123C23×C3—21no—
124C23×C3—21no—
125C22×D3—61no—
126C22×D3—61no—
127C3×D4—42no—
128C3×D4—42no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—122no—
132#67—122no—
133#67—122no—
134#67—122no—
135#67—122no—
136C2×Dic3—42no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—121no—
146C2×Dic3—121no—
147C2×Dic3—121no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C4×D3—62no—
152C4×D3—62no—
153C4×D3—121no—
154C4×D3—121no—
155Dic6—122no—
156Dic6—122no—
157C3×C8—122no—
158C3⋊C8—42no—
159C2×C32—21no—
160C2×C32—41no—
161C2×C32—41no—
162C2×C32#34211yescharacteristic
163C3⋊D3—41no—
164#41—361no—
165#41—361no—
166C2×Q8—91no—
167C2×D4—91no—
168C2×D4—91no—
169C2×D4GO+(4,𝔽2)11yescharacteristic
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173M16—62no—
174M16—361no—
175M16—361no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8—361no—
179C2×C8—361no—
180C4⋊C4—361no—
181C22⋊C4—62no—
182C42—361no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—41no—
187C22×C3—41no—
188C22×C3—41no—
189C22×C3—81no—
190C22×C3—81no—
191C22×C3—81no—
192C22×C3—81no—
193C2×D3—62no—
194C2×D3—121no—
195C2×D3—241no—
196C2×D3—241no—
197C3×C4—22no—
198C3×C4—41no—
199C3×C4—242no—
200Dic3—61no—
201Dic3—61no—
202Dic3—61no—
203Dic3—61no—
204Dic3—62no—
205Dic3—82no—
206Dic3—121no—
207Dic3—121no—
208Dic3—121no—
209C32#139511yescharacteristic, complemented, Sylow
210C23—91no—
211C23D32⋊C411yescharacteristic
212C23#377311yescharacteristic
213Q8—361no—
214D4—41no—
215D4—361no—
216D4—361no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—122no—
221C2×C4—181no—
222C2×C4—181no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4D32⋊C411yescharacteristic
228C8—122no—
229C8—361no—
230C8—361no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—41no—
234C2×C3—41no—
235C2×C3—42no—
236C2×C3—81no—
237C2×C3—81no—
238C2×C3—81no—
239D3—122no—
240D3—241no—
241C22—21no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—181no—
246C22—361no—
247C22#6373711yescharacteristic
248C4—21no—
249C4—91no—
250C4—91no—
251C4—181no—
252C4—181no—
253C4—242no—
254C3—21no—
255C3—21no—
256C2—21no—
257C2—41no—
258C2—41no—
259C2—361no—
260C2#1059007711yescharacteristic
subgroupG/H
centerC2#10590077
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC2×D4GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#342
prime radical, cosocleC2×#3830C22
hypocenterC32#1395
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
5. C2×#3792C4semidirect
6. C22×#622C4semidirect
14. #63561C4semidirect
209. C32#1395semidirect

Maximal subgroups

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

subgroupindex
#105938222
#105915292
#105915042
#13959