Finite Group Databasebeta

← #11774352

Subgroups — #11774352

Order 1152.

456 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#3797C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C2×#3797C411yescharacteristic
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×Dic6—21no—
8C4×#627C412yes—
9#63900C411yescharacteristic
10#63883—21no—
11C4×#624—21no—
12#63843—21no—
13#63838C2212yes—
14#63779C2212yes—
15#63778—21no—
16C4×#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63557—21no—
19#63553C2212yes—
20C4×D3×Q8—61no—
21#4833—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27C2×#624—21no—
28C2×#624—21no—
29#3797—22no—
30#3797C814yescomplemented
31C2×#622—22no—
32C32×C42D411yescharacteristic
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C3×C4⋊Dic3—21no—
37C3×Dic3⋊C4—22no—
38C3×C4×Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic32—22no—
43#1479—91nomaximal, Sylow
44C2×D3×Q8—61no—
45C3×C4×Q8—61no—
46Q8×Dic3—61no—
47D3×C4⋊C4—61no—
48D3×C4⋊C4—62no—
49#887—62no—
50#887—61no—
51C42×D3—61no—
52C42×D3—61no—
53C42×D3—62no—
54C4×Dic6—21no—
55C4×Dic6—62no—
56C3×C4⋊C8—61no—
57(C2×D3)⋊C8—62no—
58C8×Dic3—62no—
59C4⋊(C3⋊C8)—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3—22no—
68C4×C3⋊D3—41no—
69C4×C3⋊D3C2×C812yes—
70C4×C3⋊D3M1612yes—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C3×Dic6—24no—
74#627—22no—
75#627C2×C814yes—
76#624—24no—
77#624—42no—
78#622—42no—
79C3×C3⋊C8—42no—
80C2×C4×Q8—91no—
81#431—91no—
82#431—91no—
83Q8⋊C8—94no—
84C2×C3×Q8—61no—
85D3×Q8—64no—
86D3×Q8—64no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×Dic6—21no—
96C2×Dic6—62no—
97C2×C3×C8—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—61no—
100C3×C42—21no—
101C3×C42—21no—
102C3×C42—62no—
103C4⋊Dic3—21no—
104C4⋊Dic3—62no—
105Dic3⋊C4—22no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108C4×Dic3—22no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C2×C3⋊C8—22no—
118C22×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3C22⋊C812yes—
122C32×C4—21no—
123C32×C4—21no—
124C32×C4C22⋊C812yes—
125C3⋊Dic3—21no—
126C3⋊Dic3C22×C811yescharacteristic
127C3⋊Dic3C2×M1611yescharacteristic
128C3⋊Dic3#13712yes—
129C3×Dic3—24no—
130C3×Dic3—42no—
131C22×Q8—91no—
132C4×Q8—61no—
133C4×Q8—92no—
134C4×Q8—92no—
135C4×Q8—181no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—181no—
138C2×C42—91no—
139C2×C42—181no—
140C4⋊C8—61no—
141C4⋊C8—92no—
142C22⋊C8—181no—
143C22⋊C8—181no—
144C4×C8—92no—
145C4×C8—181no—
146C22×D3—61no—
147C22×D3—61no—
148C3×Q8—64no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—62no—
156C2×C3×C4—62no—
157C2×Dic3—22no—
158C2×Dic3—22no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—68no—
170C4×D3—64no—
171C4×D3—122no—
172C4×D3—124no—
173C4×D3—121no—
174C4×D3—121no—
175C4×D3—122no—
176Dic6—24no—
177Dic6—64no—
178Dic6—64no—
179C3×C8—122no—
180C3⋊C8—42no—
181C2×C32C2×C22⋊C811yescharacteristic
182C2×C32#41911yescharacteristic
183C2×C32#42111yescharacteristic
184C3⋊D3—22no—
185C2×Q8—61no—
186C2×Q8—92no—
187C2×Q8—94no—
188C2×Q8—182no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—181no—
193C22×C4—181no—
194C2×C8—62no—
195C2×C8—182no—
196C4⋊C4—62no—
197C4⋊C4—61no—
198C4⋊C4—92no—
199C4⋊C4—182no—
200C42—62no—
201C42—91no—
202C42—91no—
203C42—91no—
204C42—182no—
205C42GO+(4,𝔽2)11yescharacteristic
206C22×C3—21no—
207C22×C3—21no—
208C2×D3—62no—
209C2×D3—62no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—121no—
213C2×D3—121no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—22no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—41no—
220C3×C4—41no—
221C3×C4—64no—
222C3×C4—122no—
223Dic3—24no—
224Dic3—42no—
225Dic3—61no—
226Dic3—61no—
227Dic3—61no—
228Dic3—61no—
229Dic3—62no—
230Dic3—62no—
231Dic3—121no—
232Dic3—121no—
233C32#147911yescharacteristic, complemented, Sylow
234C23—91no—
235Q8—64no—
236Q8—94no—
237Q8—182no—
238C2×C4—62no—
239C2×C4—62no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—92no—
243C2×C4—92no—
244C2×C4—91no—
245C2×C4—182no—
246C2×C4—184no—
247C2×C4—361no—
248C2×C4—362no—
249C2×C4D32⋊C411yescharacteristic
250C2×C4D32⋊C411yescharacteristic
251C2×C4C2×GO+(4,𝔽2)11yescharacteristic
252C8—122no—
253C8—362no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260D3—64no—
261D3—122no—
262C22—92no—
263C22—181no—
264C22—181no—
265C22C2×D32⋊C411yescharacteristic
266C4—21no—
267C4—21no—
268C4—64no—
269C4—91no—
270C4—91no—
271C4—92no—
272C4—122no—
273C4—181no—
274C4D32⋊C812yes—
275C3—21no—
276C3—21no—
277C2—182no—
278C2C2×D32⋊C811yescharacteristic
279C2#1059332111yescharacteristic
280C2#1059338111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1479
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
30. #3797C8semidirect
233. C32#1479semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105937252
#105902562
#105900312
#14799