Finite Group Databasebeta

← #11775768

Subgroups — #11775768

Order 1152.

408 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#10593882C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic
3C4×#3712C211yesmaximal, characteristic
4#10590036C214yesmaximal, complemented
5C2×#3788—21no—
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×Dic6—21no—
8#63919C411yescharacteristic
9C4×#627—21no—
10#63874C412yes—
11#63873C411yescharacteristic
12#63871—21no—
13#63870C2212yes—
14#63865—21no—
15C2×#3712—21no—
16#63777C2212yes—
17C4×#622—21no—
18C3×C4×C3⋊C8—21no—
19#63555C2212yes—
20#5578—61no—
21C4×ΓL(1,𝔽25)—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627—21no—
27C2×#622—22no—
28#3788—24no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—21no—
34C3×Dic3⋊C4—22no—
35C3×C4×Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—21no—
38#3724C2×C412yes—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41#3722—22no—
42#3712—24no—
43#1526—91nomaximal, Sylow
44C3×C4×Q8—61no—
45#946—61no—
46#944—61no—
47C2×ΓL(1,𝔽25)—62no—
48#897—61no—
49#896—62no—
50#889—62no—
51#888—61no—
52#872—62no—
53C42×D3—61no—
54C42×D3—61no—
55C4×Dic6—21no—
56C4×Dic6—62no—
57C3×C4×C8—61no—
58#815—62no—
59C4×C3⋊C8—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3—22no—
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C3×Dic6—42no—
73#627—42no—
74#622—24no—
75C3×C3⋊C8—24no—
76#533—91no—
77C4×M16—91no—
78C4×M16—91no—
79#330—94no—
80C2×C3×Q8—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×Dic6—21no—
88C2×Dic6—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—62no—
92C3×C42—21no—
93C3×C42—21no—
94C3×C42—62no—
95(C2×D3)⋊C4—62no—
96(C2×D3)⋊C4—62no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—22no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C2×C3⋊C8—22no—
112ΓL(1,𝔽25)—68no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C2×C3⋊D3—21no—
117C32×C4—21no—
118C32×C4#10112yes—
119C32×C4#10412yes—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3#10412yes—
123C3×Dic3—42no—
124C3×Dic3—42no—
125C2×M16—181no—
126C2×M16—181no—
127C4⋊Q8—91no—
128C4⋊Q8—91no—
129#125—92no—
130C22⋊Q8—181no—
131C22⋊Q8—181no—
132C4×Q8—61no—
133C4×Q8—181no—
134#117—92no—
135C2×C42—91no—
136#97—92no—
137#97—92no—
138C4×C8—61no—
139C4×C8—181no—
140C22×D3—61no—
141C22×D3—61no—
142C3×Q8—122no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—62no—
150C2×C3×C4—62no—
151C2×Dic3—22no—
152C2×Dic3—22no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C4×D3—64no—
160C4×D3—64no—
161C4×D3—122no—
162C4×D3—122no—
163C4×D3—122no—
164C4×D3—122no—
165Dic6—42no—
166Dic6—124no—
167C3×C8—64no—
168C3⋊C8—24no—
169C2×C32C2×#10111yescharacteristic
170C2×C32C2×#10411yescharacteristic
171C2×C32C2×#10411yescharacteristic
172C3⋊D3—41no—
173C2×Q8—61no—
174C2×Q8—181no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178M16—184no—
179M16—184no—
180C2×C8—62no—
181C2×C8—182no—
182C4⋊C4—62no—
183C4⋊C4—61no—
184C4⋊C4—92no—
185C4⋊C4—92no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C22⋊C4—182no—
189C42—62no—
190C42—91no—
191C42—91no—
192C42—91no—
193C42GO+(4,𝔽2)11yescharacteristic
194C22×C3—21no—
195C22×C3—21no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—121no—
199C2×D3—121no—
200C2×D3—121no—
201C2×D3—121no—
202C3×C4—22no—
203C3×C4—22no—
204C3×C4—22no—
205C3×C4—22no—
206C3×C4—22no—
207C3×C4—41no—
208C3×C4—122no—
209C3×C4—122no—
210Dic3—42no—
211Dic3—42no—
212Dic3—62no—
213Dic3—62no—
214Dic3—62no—
215Dic3—121no—
216Dic3—121no—
217Dic3—121no—
218C32#152611yescharacteristic, complemented, Sylow
219C23—91no—
220Q8—122no—
221Q8—362no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—182no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4D32⋊C411yescharacteristic
231C2×C4D32⋊C411yescharacteristic
232C2×C4C2×GO+(4,𝔽2)11yescharacteristic
233C8—64no—
234C8—184no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241D3—122no—
242D3—122no—
243C22—181no—
244C22—181no—
245C22—181no—
246C22C2×D32⋊C411yescharacteristic
247C4—21no—
248C4—92no—
249C4—122no—
250C4—122no—
251C4—181no—
252C4—181no—
253C4#6372812yes—
254C4#6373112yes—
255C3—21no—
256C3—21no—
257C2—361no—
258C2C2×#6372811yescharacteristic
259C2C2×#6373111yescharacteristic
260C2#1059338011yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1526
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590036C2semidirect
218. C32#1526semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×#37882
C4×#37122
#105900362
#15269