Finite Group Databasebeta

← #11785799

Subgroups — #11785799

Order 1152.

670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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×#63900C211yesmaximal, characteristic
2C2×#63778C211yesmaximal, characteristic
3#10591355C211yesmaximal, characteristic
4#10590075C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—21no—
7C22×#622C2212yes—
8C2×C3×C4⋊Dic3—21no—
9C2×#3724C2212yes—
10C2×#3724C2212yes—
11C2×#3722—21no—
12#63900—22no—
13#63900C414yescomplemented
14#63778—22no—
15C3×C3⋊#95—21no—
16C2×D3×C4⋊C4—61no—
17#4667—61no—
18C23×C3⋊D3D411yescharacteristic
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C2×C4×C3⋊D3—24no—
22C2×C4×C3⋊D3C2×C412yes—
23C2×C4×C3⋊D3D412yes—
24C22×C3×Dic3—22no—
25C22×C3×Dic3—22no—
26C2×#624—24no—
27C2×#624—44no—
28C2×#622—22no—
29C2×#622—24no—
30C3×C4⋊Dic3—24no—
31#3724—22no—
32#3724—24no—
33#3724C2×C414yes—
34#3722—42no—
35#1824—91nomaximal, Sylow
36C22×C4×D3—61no—
37C22×C4×D3—61no—
38C22×C4×D3—62no—
39C2×C3×C4⋊C4—61no—
40C2×(C2×D3)⋊C4—62no—
41C2×C4⋊Dic3—21no—
42C2×Dic3⋊C4—62no—
43C2×Dic3⋊C4—62no—
44D3×C4⋊C4—64no—
45D3×C4⋊C4—64no—
46C3×#95—61no—
47C3⋊#95—21no—
48C23×C32C2×D411yescharacteristic
49C22×C3⋊D3—22no—
50C22×C3⋊D3—22no—
51C22×C3⋊D3C22⋊C412yes—
52C22×C3⋊D3SD1612yes—
53C22×C3⋊D3Q1612yes—
54C2×C32×C4—22no—
55C2×C32×C4C22⋊C412yes—
56C2×C3⋊Dic3C22×C411yescharacteristic
57C2×C3⋊Dic3C2×D411yescharacteristic
58C2×C3⋊Dic3#4114yes—
59C4×C3⋊D3—24no—
60C4×C3⋊D3—24no—
61C2×C3×Dic3—24no—
62C2×C3×Dic3—44no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66#624—48no—
67#622—42no—
68C22×C4⋊C4—91no—
69C2×C22⋊C8—91no—
70#380—91no—
71#340—94no—
72C23×D3—61no—
73C23×D3—61no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—62no—
77C22×C3×C4—62no—
78C22×Dic3—22no—
79C22×Dic3—22no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C2×C4×D3—62no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—68no—
87C2×C4×D3—68no—
88C2×C4×D3—124no—
89C2×C4×D3—128no—
90C3×C4⋊C4—64no—
91(C2×D3)⋊C4—124no—
92C4⋊Dic3—24no—
93Dic3⋊C4—64no—
94Dic3⋊C4—64no—
95Dic3⋊C4—124no—
96C22×C32C2×C22⋊C411yescharacteristic
97C22×C32#12312yes—
98C22×C32C2×SD1611yescharacteristic
99C22×C32C2×Q1611yescharacteristic
100C22×C32AGL(1,ℤ/8)12yes—
101C2×C3⋊D3—22no—
102C2×C3⋊D3—22no—
103C2×C3⋊D3—24no—
104C2×C3⋊D3—24no—
105C2×C3⋊D3#10314yes—
106C32×C4—22no—
107C3⋊Dic3#11712yes—
108C3⋊Dic3#12312yes—
109C3×Dic3—44no—
110C3×Dic3—82no—
111C23×C4—91no—
112C23×C4—181no—
113C22×C8—92no—
114C2×C4⋊C4—61no—
115C2×C4⋊C4—94no—
116C2×C4⋊C4—92no—
117C2×C4⋊C4—92no—
118C2×C4⋊C4—182no—
119C2×C22⋊C4—181no—
120C22⋊C8—182no—
121#95—61no—
122C23×C3—21no—
123C23×C3—21no—
124C22×D3—62no—
125C22×D3—62no—
126C22×D3—62no—
127C22×D3—62no—
128C22×D3—62no—
129C22×D3—62no—
130C22×D3—64no—
131C22×D3—64no—
132C22×D3—122no—
133C22×D3—122no—
134C2×C3×C4—24no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—42no—
138C2×C3×C4—64no—
139C2×C3×C4—124no—
140C2×C3×C4—122no—
141C2×C3×C4—122no—
142C2×C3×C4—122no—
143C2×Dic3—24no—
144C2×Dic3—44no—
145C2×Dic3—42no—
146C2×Dic3—42no—
147C2×Dic3—42no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C4×D3—68no—
155C4×D3—68no—
156C4×D3—124no—
157C4×D3—124no—
158C4×D3—1216no—
159C2×C32#38111yescharacteristic
160C2×C32C2×#10311yescharacteristic
161C2×C32#41811yescharacteristic
162C2×C32#48112yes—
163C2×C32#48412yes—
164C3⋊D3—24no—
165C24—91no—
166C22×C4—62no—
167C22×C4—62no—
168C22×C4—91no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—184no—
172C22×C4—184no—
173C22×C4—364no—
174C22×C4GO+(4,𝔽2)11yescharacteristic
175C2×C8—182no—
176C2×C8—184no—
177C4⋊C4—64no—
178C4⋊C4—94no—
179C4⋊C4—182no—
180C4⋊C4—184no—
181C22⋊C4—362no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—22no—
191C22×C3—22no—
192C2×D3—64no—
193C2×D3—64no—
194C2×D3—64no—
195C2×D3—64no—
196C2×D3—68no—
197C2×D3—68no—
198C2×D3—122no—
199C2×D3—124no—
200C2×D3—122no—
201C2×D3—124no—
202C3×C4—24no—
203C3×C4—42no—
204C3×C4—124no—
205C3×C4—242no—
206Dic3—44no—
207Dic3—62no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—82no—
212C32#182411yescharacteristic, complemented, Sylow
213C23—92no—
214C23—92no—
215C23—92no—
216C23—182no—
217C23—182no—
218C23C2×GO+(4,𝔽2)11yescharacteristic
219C2×C4—22no—
220C2×C4—64no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—94no—
224C2×C4—124no—
225C2×C4—122no—
226C2×C4—122no—
227C2×C4—122no—
228C2×C4—184no—
229C2×C4—184no—
230C2×C4—368no—
231C2×C4D32⋊C412yes—
232C8—362no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—22no—
238C2×C3—22no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243D3—68no—
244D3—124no—
245C22—94no—
246C22—184no—
247C22—182no—
248C22—184no—
249C22—182no—
250C22#6422412yes—
251C22#6422711yescharacteristic
252C22#6422811yescharacteristic
253C22C2×D32⋊C411yescharacteristic
254C22#6423312yes—
255C4—22no—
256C4—92no—
257C4—92no—
258C4—124no—
259C4—242no—
260C3—21no—
261C3—21no—
262C2—184no—
263C2#1059336112yes—
264C2#1059336311yescharacteristic
265C2#1059337212yes—
266C2#1059337511yescharacteristic
267C2#1059348811yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1824
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
4. #10590075C2semidirect
13. #63900C4semidirect
212. C32#1824semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#637782
#105913552
#105900752
#18249