Finite Group Databasebeta

← #11858328

Subgroups — #11858328

Order 1152.

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

normal subgroups only

This group has 602 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×#64286C211yesmaximal, characteristic
2C2×#64283C212yesmaximal
3#10593540C218yesmaximal, complemented
4#10593539C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157C412yes—
7C2×#3792—22no—
8#64286C414yes—
9#64286C2214yes—
10C2×C4⋊#157C412yes—
11C2×C4×#157C2212yes—
12#64283—22no—
13#64283—22no—
14#64283C2214yes—
15#64283C2214yes—
16C2×#3788—22no—
17C2×#3787C2214yes—
18#63744C22116yescomplemented
19C23×C3⋊D3C2×C411yescharacteristic
20C22×#157C2×C414yes—
21C22×C32×C4Q811yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3Q812yes—
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×C4×C3⋊D3C2312yes—
30C2×C4×C3⋊D3C2311yescharacteristic
31C22⋊#157C2×C418yes—
32#3792—24no—
33#3792—24no—
34C2×#622—24no—
35C4⋊#157C2×C418yes—
36C4×#157C2×C414yes—
37C4×#157C2314yes—
38#3788—24no—
39#3788—24no—
40#3787—24no—
41#3787C2318yes—
42#2905—91nomaximal, Sylow
43C22×C4×D3—121no—
44C23×C32C4⋊C411yescharacteristic
45C22×C3⋊D3—42no—
46C22×C3⋊D3C4⋊C412yes—
47C22×C3⋊D3C4⋊C411yescharacteristic
48C22×C3⋊D3C22×C411yescharacteristic
49C22×C3⋊D3C22×C412yes—
50C2×#157—44no—
51C2×#157C22×C418yes—
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C32×C4C4⋊C412yes—
54C2×C32×C4C2×Q812yes—
55C2×C32×C4C2×Q811yescharacteristic
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C4⋊C412yes—
58C2×C3⋊Dic3C2×D412yes—
59C2×C3⋊Dic3C2×D411yescharacteristic
60C4×C3⋊D3C4⋊C412yes—
61C4×C3⋊D3C4⋊C412yes—
62C4×C3⋊D3C4⋊C412yes—
63C4×C3⋊D3C22×C411yescharacteristic
64C4×C3⋊D3C22×C412yes—
65C4×C3⋊D3C2×D412yes—
66C4×C3⋊D3C2×D411yescharacteristic
67C4×C3⋊D3C2×Q812yes—
68C4×C3⋊D3C2×Q811yescharacteristic
69C4×C3⋊D3C2411yescharacteristic
70#622—28no—
71C22×M16—92no—
72C2×#117—91no—
73#424—98no—
74#423—94no—
75C23×D3—121no—
76C22×C3×C4—41no—
77C22×Dic3—121no—
78C2×C4×D3—121no—
79C2×C4×D3—122no—
80C2×C4×D3—122no—
81C2×C4×D3—121no—
82C2×C4×D3—121no—
83C2×C4×D3—122no—
84C2×C4×D3—121no—
85C2×C4×D3—122no—
86C22×C32—41no—
87C22×C32C2×C4⋊C412yes—
88C22×C32C2×C4⋊C411yescharacteristic
89C2×C3⋊D3—22no—
90C2×C3⋊D3—24no—
91C2×C3⋊D3—42no—
92C2×C3⋊D3—41no—
93C2×C3⋊D3C2×C4⋊C412yes—
94C2×C3⋊D3C2×C4⋊C411yescharacteristic
95C2×C3⋊D3C23×C411yescharacteristic
96#157—28no—
97C32×C4C2×C4⋊C411yescharacteristic
98C32×C4C2×C4⋊C412yes—
99C32×C4C22×Q811yescharacteristic
100C3⋊Dic3C2×C4⋊C411yescharacteristic
101C3⋊Dic3C2×C4⋊C412yes—
102C3⋊Dic3C22×D411yescharacteristic
103C23×C4—91no—
104C2×M16—94no—
105C2×M16—94no—
106C2×M16—182no—
107C2×M16—182no—
108C2×M16—182no—
109C2×M16—182no—
110C22×C8—94no—
111#117—94no—
112#117—94no—
113C2×C4⋊C4—92no—
114C2×C22⋊C4—92no—
115C2×C42—92no—
116C4⋊C8—916no—
117C23×C3—41no—
118C22×D3—122no—
119C22×D3—121no—
120C22×D3—122no—
121C22×D3—121no—
122C22×D3—128no—
123C2×C3×C4—41no—
124C2×C3×C4—42no—
125C2×C3×C4—41no—
126C2×C3×C4—42no—
127C2×Dic3—121no—
128C2×Dic3—122no—
129C2×Dic3—122no—
130C2×Dic3—121no—
131C4×D3—122no—
132C4×D3—122no—
133C4×D3—122no—
134C4×D3—121no—
135C4×D3—122no—
136C4×D3—122no—
137C4×D3—121no—
138C4×D3—121no—
139C4×D3—122no—
140C4×D3—121no—
141C2×C32—21no—
142C2×C32—22no—
143C2×C32C22×C4⋊C411yescharacteristic
144C3⋊D3—21no—
145C3⋊D3—22no—
146C3⋊D3#56812yes—
147C24—91no—
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—92no—
151C22×C4—91no—
152C22×C4—92no—
153C22×C4—91no—
154C22×C4—92no—
155C22×C4—92no—
156C22×C4—91no—
157C22×C4—94no—
158C22×C4PSU(3,𝔽2)11yescharacteristic
159M16—184no—
160M16—184no—
161M16—184no—
162M16—184no—
163C2×C8—98no—
164C2×C8—184no—
165C2×C8—184no—
166C4⋊C4—98no—
167C22⋊C4—98no—
168C42—94no—
169C42—94no—
170C22×C3—44no—
171C22×C3—42no—
172C22×C3—41no—
173C2×D3—122no—
174C2×D3—121no—
175C2×D3—121no—
176C2×D3—124no—
177C2×D3—128no—
178C2×D3—124no—
179C2×D3—128no—
180C3×C4—41no—
181C3×C4—41no—
182C3×C4—42no—
183Dic3—122no—
184Dic3—121no—
185Dic3—121no—
186C32#290511yescharacteristic, complemented, Sylow
187C23—92no—
188C23—91no—
189C23—91no—
190C23—92no—
191C23—362no—
192C23#377711yescharacteristic
193C2×C4—92no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—92no—
197C2×C4—91no—
198C2×C4—91no—
199C2×C4—92no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—92no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—98no—
208C2×C4—364no—
209C2×C4#377711yescharacteristic
210C2×C4#377712yes—
211C2×C4C2×PSU(3,𝔽2)11yescharacteristic
212C2×C4C2×PSU(3,𝔽2)12yes—
213C8—188no—
214C2×C3—42no—
215C2×C3—44no—
216C2×C3—41no—
217D3—122no—
218D3—122no—
219D3—124no—
220C22—41no—
221C22—91no—
222C22—92no—
223C22—91no—
224C22—182no—
225C22—184no—
226C22—361no—
227C22—362no—
228C22C2×#377712yes—
229C22C2×#377711yescharacteristic
230C4—91no—
231C4—92no—
232C4—91no—
233C4—188no—
234C4C2×#377711yescharacteristic
235C4C2×#377712yes—
236C4C22×PSU(3,𝔽2)11yescharacteristic
237C3—41no—
238C2—21no—
239C2—22no—
240C2—92no—
241C2—181no—
242C2—182no—
243C2C22×#377711yescharacteristic
subgroupG/H
center, FrattiniC4C22×PSU(3,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC22×C32×C4Q8
socleC2×C32C22×C4⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC4×C3⋊D3C24
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#2905
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10593540C2semidirect
4. #10593539C2semidirect
18. #63744C22semidirect
186. C32#2905semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#642832
#105935402
#105935392
#29059