Finite Group Databasebeta

← #11791671

Subgroups — #11791671

Order 1152.

470 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 83 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×#63870C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3C4×#3724C211yesmaximal, characteristic
4#10590075C212yesmaximal
5#10590075C212yesmaximal
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×Dic3⋊C4—21no—
9C2×C3×C4×Dic3—21no—
10C2×#3724C2211yescharacteristic
11C2×#3724C2211yescharacteristic
12C2×#3724C2212yes—
13C2×Dic3⋊Dic3—21no—
14#63870—22no—
15#63870C414yescomplemented
16#63779—22no—
17#63579—21no—
18C2×#889—61no—
19C4×Dic3⋊C4—61no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C22×C3×Dic3—22no—
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C2×#622—22no—
27C2×#622—24no—
28C4×C3⋊Dic3C2×C412yes—
29C4×C3⋊Dic3D412yes—
30C3×Dic3⋊C4—24no—
31C3×C4×Dic3—42no—
32#3724—21no—
33#3724—21no—
34#3724—22no—
35#3724C2×C412yes—
36#3724C2×C412yes—
37#3724Q814yes—
38Dic3⋊Dic3—24no—
39#1989—91nomaximal, Sylow
40C2×C3×C4⋊C4—61no—
41C2×C3×C42—61no—
42C2×C4⋊Dic3—61no—
43C2×Dic3⋊C4—21no—
44C2×Dic3⋊C4—62no—
45C2×Dic3⋊C4—61no—
46C2×Dic3⋊C4—61no—
47C2×Dic3⋊C4—61no—
48C2×C4×Dic3—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51#889—64no—
52#889—64no—
53C3⋊#95—62no—
54C23×C32C2×D411yescharacteristic
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4C22⋊C412yes—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C22⋊C412yes—
60C2×C3⋊Dic3C22×C411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3C2×Q812yes—
63C2×C3⋊Dic3#4112yes—
64C2×C3×Dic3—22no—
65C2×C3×Dic3—22no—
66C2×C3×Dic3—24no—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—42no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—41no—
72#622—42no—
73C2×#125—91no—
74C2×C4⋊C8—91no—
75C4×C4⋊C4—91no—
76#340—92no—
77#340—92no—
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—62no—
81C22×C3×C4—61no—
82C22×C3×C4—61no—
83C22×Dic3—22no—
84C22×Dic3—21no—
85C22×Dic3—21no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C3×C4⋊C4—64no—
91C3×C42—122no—
92C4⋊Dic3—64no—
93Dic3⋊C4—24no—
94Dic3⋊C4—62no—
95Dic3⋊C4—62no—
96Dic3⋊C4—64no—
97Dic3⋊C4—64no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100Dic3⋊C4—64no—
101C4×Dic3—42no—
102C4×Dic3—62no—
103C4×Dic3—62no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C22×C32C2×C22⋊C411yescharacteristic
107C22×C32C22⋊Q812yes—
108C22×C32#13512yes—
109C22×C32AGL(1,ℤ/8)11yescharacteristic
110C22×C32#13711yescharacteristic
111C32×C4—22no—
112C3⋊Dic3—22no—
113C3⋊Dic3C4×Q812yes—
114C3⋊Dic3#12411yescharacteristic
115C3⋊Dic3C4⋊Q811yescharacteristic
116C3×Dic3—42no—
117C3×Dic3—42no—
118C3×Dic3—44no—
119C22×C8—92no—
120#125—94no—
121#125—182no—
122C2×C4⋊C4—61no—
123C2×C4⋊C4—91no—
124C2×C4⋊C4—91no—
125C2×C4⋊C4—92no—
126C2×C4⋊C4—181no—
127C2×C42—61no—
128C2×C42—91no—
129C4⋊C8—182no—
130#95—181no—
131C23×C3—21no—
132C23×C3—21no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—41no—
138C2×C3×C4—41no—
139C2×C3×C4—62no—
140C2×C3×C4—62no—
141C2×C3×C4—64no—
142C2×C3×C4—122no—
143C2×C3×C4—122no—
144C2×C3×C4—122no—
145C2×C3×C4—121no—
146C2×C3×C4—121no—
147C2×Dic3—22no—
148C2×Dic3—22no—
149C2×Dic3—24no—
150C2×Dic3—42no—
151C2×Dic3—42no—
152C2×Dic3—42no—
153C2×Dic3—41no—
154C2×Dic3—41no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167C2×C32#39111yescharacteristic
168C2×C32#41611yescharacteristic
169C2×C32#41711yescharacteristic
170C2×C32#47812yes—
171C2×C32#47912yes—
172C22×C4—62no—
173C22×C4—61no—
174C22×C4—61no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4GO+(4,𝔽2)11yescharacteristic
178C2×C8—182no—
179C2×C8—184no—
180C4⋊C4—64no—
181C4⋊C4—92no—
182C4⋊C4—92no—
183C4⋊C4—94no—
184C4⋊C4—181no—
185C4⋊C4—181no—
186C4⋊C4—182no—
187C4⋊C4—184no—
188C42—92no—
189C42—92no—
190C42—122no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C3×C4—24no—
202C3×C4—42no—
203C3×C4—122no—
204C3×C4—124no—
205C3×C4—122no—
206Dic3—42no—
207Dic3—44no—
208Dic3—42no—
209Dic3—62no—
210Dic3—62no—
211Dic3—61no—
212Dic3—61no—
213Dic3—61no—
214Dic3—61no—
215Dic3—122no—
216Dic3—122no—
217C32#198911yescharacteristic, complemented, Sylow
218C23C2×GO+(4,𝔽2)11yescharacteristic
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—64no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—122no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—182no—
235C2×C4D32⋊C412yes—
236C8—362no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—21no—
246C2×C3—21no—
247C22D32⋊Q812yes—
248C22#6422312yes—
249C22C2×D32⋊C411yescharacteristic
250C22#6423611yescharacteristic
251C22#6423911yescharacteristic
252C4—22no—
253C4—91no—
254C4—91no—
255C4—92no—
256C4—122no—
257C4—124no—
258C4—122no—
259C4—182no—
260C3—21no—
261C3—21no—
262C2#1059334111yescharacteristic
263C2#1059334911yescharacteristic
264C2#1059335012yes—
265C2#1059338212yes—
266C2#1059349611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1989
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
15. #63870C4semidirect
217. C32#1989semidirect

Maximal subgroups

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

subgroupindex
C2×#638702
C2×#637792
C4×#37242
#105900752
#19899