Finite Group Databasebeta

← #11796924

Subgroups — #11796924

Order 1152.

398 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#63802C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic
3#10590913C211yesmaximal, characteristic
4#10590066C214yesmaximal, complemented
5C2×#3797—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C2×C3×Dic12—21no—
8C2×#3718C2212yes—
9#63818—21no—
10#63802—21no—
11#63802—21no—
12#63802C412yes—
13#63802C412yes—
14#63773C2212yes—
15#63765—21no—
16#63764—21no—
17C3×#819—21no—
18#63578C2212yes—
19C2×D3×Q16—61no—
20D3×#108—61no—
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627—41no—
24C2×#624—41no—
25#3797—22no—
26#3797—22no—
27#3797—41no—
28#3797—41no—
29C2×C32×C8D411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31C8×C3⋊D3C2×C411yescharacteristic
32C8×C3⋊D3C2×C411yescharacteristic
33C8×C3⋊D3D411yescharacteristic
34C8×C3⋊D3D411yescharacteristic
35C3×#208—22no—
36C3×Dic12—22no—
37C3×Dic12—22no—
38#3718—22no—
39#3718C2×C414yes—
40#3712—41no—
41#3710—41no—
42#3708—22no—
43C2×#362—91nomaximal, Sylow
44C2×D3×Q8—62no—
45C2×C3×Q16—61no—
46C2×#216—62no—
47D3×Q16—62no—
48D3×Q16—62no—
49D3×Q16—62no—
50D3×Q16—62no—
51D3×M16—62no—
52C2×Dic12—21no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55C3×#108—61no—
56#822—62no—
57#819—21no—
58C22×C3⋊D3SD1611yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3SD1611yescharacteristic
61C4×C3⋊D3C22⋊C411yescharacteristic
62C4×C3⋊D3C22⋊C411yescharacteristic
63C4×C3⋊D3D811yescharacteristic
64C4×C3⋊D3D811yescharacteristic
65C2×C3×Dic3—42no—
66C3×Dic6—24no—
67C3×Dic6—42no—
68#627—42no—
69#627—42no—
70#624—42no—
71#624—42no—
72C32×C8C22⋊C411yescharacteristic
73C32×C8C22⋊C411yescharacteristic
74C3⋊(C3⋊C8)C22×C411yescharacteristic
75C3⋊(C3⋊C8)C2×D411yescharacteristic
76C3×C3⋊C8—42no—
77C22×Q16—91no—
78C2×M32—91no—
79C2×#108—91no—
80#362—94no—
81C2×C3×Q8—62no—
82D3×Q8—64no—
83D3×Q8—64no—
84D3×Q8—122no—
85D3×Q8—122no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—122no—
89C2×Dic6—22no—
90C2×Dic6—122no—
91C3×Q16—62no—
92C3×Q16—62no—
93C3×M16—62no—
94C2×C3×C8—21no—
95C2×C3×C8—21no—
96#216—64no—
97#216—64no—
98#208—22no—
99C2×C3⋊C8—61no—
100C2×C3⋊C8—61no—
101Dic12—22no—
102Dic12—22no—
103ΓL(1,𝔽25)—122no—
104D3×C8—61no—
105D3×C8—61no—
106D3×C8—61no—
107D3×C8—61no—
108D3×C8—61no—
109D3×C8—61no—
110D3×C8—61no—
111D3×C8—61no—
112D3×C8—122no—
113C22×C32C2×SD1611yescharacteristic
114C2×C3⋊D3—22no—
115C2×C3⋊D3#10211yescharacteristic
116C2×C3⋊D3#10211yescharacteristic
117C32×C4C2×C22⋊C411yescharacteristic
118C32×C4C2×D811yescharacteristic
119C3⋊Dic3#10211yescharacteristic
120C3⋊Dic3#10211yescharacteristic
121C3×Dic3—44no—
122C22×Q8—181no—
123C2×Q16—61no—
124C2×Q16—92no—
125C2×Q16—92no—
126C2×Q16—92no—
127C2×Q16—181no—
128C2×Q16—181no—
129C2×M16—181no—
130C22×C8—91no—
131M32—92no—
132M32—181no—
133C2×C16—181no—
134#108—61no—
135#108—92no—
136C22×D3—61no—
137C22×D3—61no—
138C3×Q8—64no—
139C3×Q8—122no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—122no—
143C2×Dic3—42no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C4×D3—61no—
147C4×D3—61no—
148C4×D3—61no—
149C4×D3—61no—
150C4×D3—61no—
151C4×D3—61no—
152C4×D3—61no—
153C4×D3—61no—
154C4×D3—124no—
155C4×D3—124no—
156Dic6—24no—
157Dic6—42no—
158Dic6—124no—
159Dic6—124no—
160C3×C8—21no—
161C3×C8—21no—
162C3×C8—21no—
163C3×C8—21no—
164C3×C8—122no—
165C3⋊C8—42no—
166C3⋊C8—61no—
167C3⋊C8—61no—
168C3⋊C8—61no—
169C3⋊C8—61no—
170C2×C32—21no—
171C2×C32C2×#10211yescharacteristic
172C3⋊D3—21no—
173C3⋊D3#36212yescomplemented
174C2×Q8—62no—
175C2×Q8—182no—
176C2×Q8—182no—
177C2×Q8—361no—
178C2×Q8—361no—
179C2×Q8—361no—
180C22×C4—91no—
181C22×C4—361no—
182Q16—62no—
183Q16—62no—
184Q16—94no—
185Q16—182no—
186M16—62no—
187M16—361no—
188C2×C8—91no—
189C2×C8—91no—
190C2×C8—91no—
191C2×C8—91no—
192C2×C8—91no—
193C2×C8—361no—
194C2×C8GO+(4,𝔽2)11yescharacteristic
195C16—182no—
196C22×C3—21no—
197C22×C3—21no—
198C2×D3—61no—
199C2×D3—61no—
200C2×D3—61no—
201C2×D3—61no—
202C2×D3—64no—
203C2×D3—122no—
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—124no—
209Dic3—44no—
210Dic3—61no—
211Dic3—61no—
212Dic3—61no—
213Dic3—61no—
214C32C2×#36211yescharacteristic, complemented, Sylow
215C23—91no—
216Q8—64no—
217Q8—122no—
218Q8—362no—
219Q8—362no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—122no—
226C2×C4—362no—
227C2×C4—362no—
228C2×C4C2×GO+(4,𝔽2)11yescharacteristic
229C8—91no—
230C8—91no—
231C8—122no—
232C8D32⋊C411yescharacteristic
233C8D32⋊C411yescharacteristic
234C2×C3—22no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—41no—
238D3—62no—
239D3—62no—
240D3—62no—
241D3—121no—
242C22—91no—
243C22—91no—
244C22—182no—
245C22#6422711yescharacteristic
246C4—91no—
247C4—91no—
248C4—124no—
249C4#6422511yescharacteristic
250C4C2×D32⋊C411yescharacteristic
251C3—21no—
252C3—21no—
253C2—21no—
254C2—92no—
255C2—181no—
256C2#1059336511yescharacteristic
subgroupG/H
centerC2#10593365
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#362
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590066C2semidirect
173. C3⋊D3#362semidirect
214. C32C2×#362semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
#105937622
#105909132
#105900662
C2×#3629