Finite Group Databasebeta

← #11858655

Subgroups — #11858655

Order 1152.

758 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 189 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×#64283C211yesmaximal, characteristic
2C2×#63818C212yesmaximal
3#10593331C214yesmaximal, complemented
4#10593330C218yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C412yes—
7#64283C414yes—
8#64283C2214yes—
9C2×#3788C412yes—
10C2×#3787C2212yes—
11C2×C3×#208—22no—
12C2×#3712C2214yes—
13#63818—22no—
14#63818—22no—
15#63818C2214yes—
16#63818C2214yes—
17C2×#3710—22no—
18#63733C22116yescomplemented
19C2×D3×M16—62no—
20C23×C3⋊D3Q811yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3Q811yescharacteristic
28C2×C4×C3⋊D3Q812yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C4×C3⋊D3C2312yes—
31#3792C2×C418yes—
32C2×#622C2×C414yes—
33#3788C2×C418yes—
34#3787C2×C414yes—
35#3787C2314yes—
36C3×#208—24no—
37C3×#208—24no—
38C2×C3×C3⋊C8—24no—
39#3712—24no—
40#3712C2318yes—
41#3710—24no—
42#3710—24no—
43C2×#430—91nomaximal, Sylow
44C22×C4×D3—62no—
45C2×C3×M16—62no—
46C2×#208—22no—
47D3×M16—64no—
48D3×M16—64no—
49D3×M16—64no—
50D3×M16—64no—
51C2×ΓL(1,𝔽25)—64no—
52C2×D3×C8—64no—
53C23×C32C4⋊C411yescharacteristic
54C22×C3⋊D3—42no—
55C22×C3⋊D3C4⋊C412yes—
56C22×C3⋊D3C4⋊C411yescharacteristic
57C22×C3⋊D3C2×Q811yescharacteristic
58C22×C3⋊D3C2×Q812yes—
59C2×C32×C4C4⋊C411yescharacteristic
60C2×C32×C4C4⋊C412yes—
61C2×C32×C4C2×D412yes—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C4⋊C412yes—
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C22×C412yes—
67C4×C3⋊D3C4⋊C412yes—
68C4×C3⋊D3C4⋊C412yes—
69C4×C3⋊D3C4⋊C412yes—
70C4×C3⋊D3C22×C411yescharacteristic
71C4×C3⋊D3C22×C412yes—
72C4×C3⋊D3C2×D411yescharacteristic
73C4×C3⋊D3C2×D412yes—
74C4×C3⋊D3C2×Q811yescharacteristic
75C4×C3⋊D3C2×Q812yes—
76C4×C3⋊D3C2411yescharacteristic
77#622C22×C418yes—
78C3×C3⋊C8—28no—
79C22×M16—91no—
80C22×M16—92no—
81#430—98no—
82C2×#108—94no—
83C23×D3—62no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C3×M16—64no—
99C3×M16—64no—
100C2×C3×C8—64no—
101#208—24no—
102#208—24no—
103C2×C3⋊C8—24no—
104ΓL(1,𝔽25)—68no—
105ΓL(1,𝔽25)—68no—
106D3×C8—68no—
107D3×C8—68no—
108C22×C32—41no—
109C22×C32C2×C4⋊C412yes—
110C22×C32C2×C4⋊C411yescharacteristic
111C2×C3⋊D3—24no—
112C2×C3⋊D3—22no—
113C2×C3⋊D3—41no—
114C2×C3⋊D3—42no—
115C2×C3⋊D3C2×C4⋊C412yes—
116C2×C3⋊D3C2×C4⋊C411yescharacteristic
117C2×C3⋊D3C22×Q811yescharacteristic
118C32×C4C2×C4⋊C411yescharacteristic
119C32×C4C2×C4⋊C412yes—
120C32×C4C22×D411yescharacteristic
121C3⋊Dic3C2×C4⋊C411yescharacteristic
122C3⋊Dic3C2×C4⋊C412yes—
123C3⋊Dic3C23×C411yescharacteristic
124C23×C4—91no—
125C2×M16—62no—
126C2×M16—94no—
127C2×M16—92no—
128C2×M16—94no—
129C2×M16—94no—
130C2×M16—92no—
131C2×M16—94no—
132C2×M16—94no—
133C2×M16—182no—
134C2×M16—182no—
135C22×C8—92no—
136C22×C8—182no—
137#108—916no—
138C23×C3—22no—
139C22×D3—62no—
140C22×D3—62no—
141C22×D3—62no—
142C22×D3—62no—
143C22×D3—62no—
144C22×D3—62no—
145C22×D3—128no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C4×D3—62no—
159C4×D3—62no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C3×C8—68no—
175C3⋊C8—28no—
176C2×C32—22no—
177C2×C32—21no—
178C2×C32C22×C4⋊C411yescharacteristic
179C3⋊D3—22no—
180C3⋊D3—21no—
181C3⋊D3#43012yescomplemented
182C24—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—92no—
190C22×C4—91no—
191C22×C4—92no—
192C22×C4GO+(4,𝔽2)11yescharacteristic
193M16—64no—
194M16—64no—
195M16—98no—
196M16—98no—
197M16—98no—
198M16—184no—
199C2×C8—64no—
200C2×C8—94no—
201C2×C8—94no—
202C2×C8—94no—
203C2×C8—184no—
204C2×C8—184no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—44no—
209C2×D3—62no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—62no—
213C2×D3—68no—
214C2×D3—124no—
215C2×D3—124no—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—124no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—22no—
222C3×C4—22no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—62no—
227C32C2×#43011yescharacteristic, complemented, Sylow
228C23—92no—
229C23—91no—
230C23—92no—
231C23—91no—
232C23—362no—
233C23#377311yescharacteristic
234C2×C4—91no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—92no—
241C2×C4—91no—
242C2×C4—92no—
243C2×C4—92no—
244C2×C4—91no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—92no—
248C2×C4#377312yes—
249C2×C4#377311yescharacteristic
250C2×C4C2×GO+(4,𝔽2)12yes—
251C2×C4C2×GO+(4,𝔽2)11yescharacteristic
252C8—68no—
253C8—98no—
254C2×C3—24no—
255C2×C3—22no—
256C2×C3—42no—
257C2×C3—42no—
258D3—64no—
259D3—64no—
260D3—122no—
261D3—122no—
262C22—41no—
263C22—91no—
264C22—92no—
265C22—91no—
266C22—184no—
267C22—182no—
268C22—362no—
269C22—361no—
270C22C2×#377312yes—
271C22C2×#377311yescharacteristic
272C4—91no—
273C4—91no—
274C4—92no—
275C4C2×#377311yescharacteristic
276C4C2×#377312yes—
277C4C22×GO+(4,𝔽2)11yescharacteristic
278C3—22no—
279C2—22no—
280C2—21no—
281C2—92no—
282C2—182no—
283C2—181no—
284C2C22×#377311yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC22×C32×C4D4
socleC2×C32C22×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#430
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593331C2semidirect
4. #10593330C2semidirect
18. #63733C22semidirect
181. C3⋊D3#430semidirect
227. C32C2×#430semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×#638182
#105933312
#105933302
C2×#4309