Finite Group Databasebeta

← #11785773

Subgroups — #11785773

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—42no—
28C2×#624—42no—
29C2×#622—22no—
30C2×#622—24no—
31C3×C4⋊Dic3—24no—
32#3724—22no—
33#3724—24no—
34#3724C2×C414yes—
35#3722—42no—
36#1823—91nomaximal, Sylow
37C22×C4×D3—61no—
38C22×C4×D3—61no—
39C22×C4×D3—62no—
40C2×C3×C4⋊C4—61no—
41C2×(C2×D3)⋊C4—62no—
42C2×C4⋊Dic3—21no—
43C2×Dic3⋊C4—62no—
44C2×Dic3⋊C4—62no—
45D3×C4⋊C4—64no—
46D3×C4⋊C4—64no—
47C3×#95—61no—
48C3⋊#95—21no—
49C23×C32C2×D411yescharacteristic
50C22×C3⋊D3—22no—
51C22×C3⋊D3—22no—
52C22×C3⋊D3C22⋊C412yes—
53C22×C3⋊D3D812yes—
54C22×C3⋊D3SD1612yes—
55C2×C32×C4—22no—
56C2×C32×C4C22⋊C412yes—
57C2×C3⋊Dic3C22×C411yescharacteristic
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3#4114yes—
60C4×C3⋊D3—24no—
61C4×C3⋊D3—24no—
62C2×C3×Dic3—24no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68#624—48no—
69#622—42no—
70C22×C4⋊C4—91no—
71C2×C22⋊C8—91no—
72#380—91no—
73#340—94no—
74C23×D3—61no—
75C23×D3—61no—
76C22×C3×C4—21no—
77C22×C3×C4—21no—
78C22×C3×C4—62no—
79C22×C3×C4—62no—
80C22×Dic3—22no—
81C22×Dic3—22no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—68no—
89C2×C4×D3—68no—
90C2×C4×D3—124no—
91C2×C4×D3—124no—
92C2×C4×D3—124no—
93C3×C4⋊C4—64no—
94(C2×D3)⋊C4—124no—
95C4⋊Dic3—24no—
96Dic3⋊C4—64no—
97Dic3⋊C4—64no—
98Dic3⋊C4—124no—
99C22×C32C2×C22⋊C411yescharacteristic
100C22×C32#12312yes—
101C22×C32C2×D811yescharacteristic
102C22×C32C2×SD1611yescharacteristic
103C22×C32#13712yes—
104C2×C3⋊D3—22no—
105C2×C3⋊D3—22no—
106C2×C3⋊D3—24no—
107C2×C3⋊D3—24no—
108C2×C3⋊D3#10214yes—
109C32×C4—22no—
110C3⋊Dic3#11712yes—
111C3⋊Dic3#12312yes—
112C3×Dic3—44no—
113C3×Dic3—82no—
114C23×C4—91no—
115C23×C4—181no—
116C22×C8—92no—
117C2×C4⋊C4—61no—
118C2×C4⋊C4—94no—
119C2×C4⋊C4—92no—
120C2×C4⋊C4—92no—
121C2×C4⋊C4—182no—
122C2×C22⋊C4—181no—
123C22⋊C8—182no—
124#95—61no—
125C23×C3—21no—
126C23×C3—21no—
127C22×D3—62no—
128C22×D3—62no—
129C22×D3—62no—
130C22×D3—62no—
131C22×D3—62no—
132C22×D3—62no—
133C22×D3—64no—
134C22×D3—64no—
135C22×D3—122no—
136C22×D3—122no—
137C2×C3×C4—24no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—42no—
141C2×C3×C4—64no—
142C2×C3×C4—122no—
143C2×C3×C4—122no—
144C2×C3×C4—122no—
145C2×C3×C4—122no—
146C2×C3×C4—122no—
147C2×Dic3—24no—
148C2×Dic3—42no—
149C2×Dic3—42no—
150C2×Dic3—42no—
151C2×Dic3—42no—
152C2×Dic3—42no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C4×D3—68no—
160C4×D3—68no—
161C4×D3—124no—
162C4×D3—124no—
163C4×D3—1216no—
164C2×C32#38111yescharacteristic
165C2×C32C2×#10211yescharacteristic
166C2×C32#41911yescharacteristic
167C2×C32#48012yes—
168C2×C32#48312yes—
169C3⋊D3—24no—
170C24—91no—
171C22×C4—62no—
172C22×C4—62no—
173C22×C4—91no—
174C22×C4—92no—
175C22×C4—92no—
176C22×C4—184no—
177C22×C4—184no—
178C22×C4—362no—
179C22×C4—362no—
180C22×C4GO+(4,𝔽2)11yescharacteristic
181C2×C8—182no—
182C2×C8—184no—
183C4⋊C4—64no—
184C4⋊C4—94no—
185C4⋊C4—182no—
186C4⋊C4—184no—
187C22⋊C4—362no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—22no—
197C22×C3—22no—
198C2×D3—64no—
199C2×D3—64no—
200C2×D3—64no—
201C2×D3—68no—
202C2×D3—64no—
203C2×D3—68no—
204C2×D3—122no—
205C2×D3—124no—
206C2×D3—122no—
207C2×D3—124no—
208C3×C4—24no—
209C3×C4—42no—
210C3×C4—124no—
211C3×C4—242no—
212Dic3—44no—
213Dic3—62no—
214Dic3—62no—
215Dic3—62no—
216Dic3—62no—
217Dic3—82no—
218C32#182311yescharacteristic, complemented, Sylow
219C23—92no—
220C23—92no—
221C23—92no—
222C23—182no—
223C23—182no—
224C23C2×GO+(4,𝔽2)11yescharacteristic
225C2×C4—22no—
226C2×C4—64no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—94no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—122no—
233C2×C4—122no—
234C2×C4—122no—
235C2×C4—184no—
236C2×C4—184no—
237C2×C4—368no—
238C2×C4D32⋊C412yes—
239C8—362no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—21no—
250D3—68no—
251D3—124no—
252C22—94no—
253C22—184no—
254C22—182no—
255C22—184no—
256C22—182no—
257C22#6422511yescharacteristic
258C22#6422612yes—
259C22#6422711yescharacteristic
260C22C2×D32⋊C411yescharacteristic
261C22#6423312yes—
262C4—22no—
263C4—92no—
264C4—92no—
265C4—124no—
266C4—242no—
267C3—21no—
268C3—21no—
269C2—184no—
270C2#1059336511yescharacteristic
271C2#1059336812yes—
272C2#1059337411yescharacteristic
273C2#1059338612yes—
274C2#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#1823
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
218. C32#1823semidirect

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
#18239