Finite Group Databasebeta

← #11770849

Subgroups — #11770849

Order 1152.

458 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 59 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#10593800C211yesmaximal, characteristic
2C4×#3722C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3787—21no—
6C2×C3×C4×Dic3—21no—
7C2×#3722C412yes—
8C2×#3710C412yescomplemented
9C22⋊#622—21no—
10#63778C412yescomplemented
11C3×#830—21no—
12#63579—21no—
13#63557—21no—
14C4×(C2×D3)⋊C4—61no—
15D3×C22⋊C8—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C22×C3×Dic3—22no—
25C2×#622—22no—
26#3787—42no—
27C3×C4×Dic3—42no—
28C2×C3×C3⋊C8—22no—
29#3722—22no—
30#3722C814yescomplemented
31#3710—42no—
32#1282—91nomaximal, Sylow
33C22×C4×D3—61no—
34C22×C4×D3—61no—
35C2×C3×C42—61no—
36C2×(C2×D3)⋊C4—62no—
37C2×C4×Dic3—21no—
38C2×D3×C8—62no—
39C3×C22⋊C8—61no—
40C3⋊#95—62no—
41#830—21no—
42(C2×D3)⋊C8—62no—
43C23×C32C22⋊C411yescharacteristic
44C22×C3⋊D3—41no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3C4211yescharacteristic
47C22×C3⋊D3C4⋊C411yescharacteristic
48C22×C3⋊D3C2×C812yes—
49C22×C3⋊D3M1612yes—
50C2×C32×C4—22no—
51C2×C32×C4C22⋊C411yescharacteristic
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3C22⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58C4×C3⋊D3—41no—
59C4×C3⋊D3—41no—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63#622—42no—
64C3×C3⋊C8—42no—
65C2×C22⋊C8—91no—
66C2×C22⋊C8—91no—
67C4×C22⋊C4—91no—
68C23×D3—61no—
69C23×D3—61no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—62no—
73C22×Dic3—22no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—124no—
85C2×C4×D3—122no—
86C2×C4×D3—122no—
87C2×C3×C8—62no—
88C3×C42—122no—
89(C2×D3)⋊C4—64no—
90(C2×D3)⋊C4—64no—
91C4×Dic3—42no—
92C2×C3⋊C8—22no—
93D3×C8—124no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32#9511yescharacteristic
97C22×C32C22⋊C812yes—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3—42no—
103C2×C3⋊D3—42no—
104C2×C3⋊D3C4×C811yescharacteristic
105C2×C3⋊D3#9711yescharacteristic
106C2×C3⋊D3C4⋊C812yes—
107C32×C4—21no—
108C32×C4#9912yes—
109C3⋊Dic3—21no—
110C3⋊Dic3—21no—
111C3×Dic3—44no—
112C23×C4—91no—
113C22×C8—92no—
114C22×C8—181no—
115C2×C22⋊C4—92no—
116C2×C42—61no—
117C22⋊C8—61no—
118C22⋊C8—92no—
119C22⋊C8—181no—
120C22⋊C8—181no—
121#95—181no—
122C23×C3—21no—
123C23×C3—21no—
124C22×D3—61no—
125C22×D3—61no—
126C22×D3—61no—
127C22×D3—61no—
128C22×D3—62no—
129C22×D3—62no—
130C22×D3—62no—
131C22×D3—62no—
132C22×D3—122no—
133C22×D3—122no—
134C22×D3—121no—
135C22×D3—121no—
136C22×D3—122no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—42no—
144C2×C3×C4—64no—
145C2×C3×C4—122no—
146C2×C3×C4—122no—
147C2×Dic3—24no—
148C2×Dic3—42no—
149C2×Dic3—42no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—122no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C4×D3—64no—
158C4×D3—122no—
159C4×D3—122no—
160C4×D3—122no—
161C4×D3—122no—
162C4×D3—122no—
163C4×D3—122no—
164C4×D3—122no—
165C3×C8—122no—
166C3⋊C8—42no—
167C2×C32—22no—
168C2×C32#33611yescharacteristic
169C2×C32#34211yescharacteristic
170C2×C32#34411yescharacteristic
171C3⋊D3—21no—
172C3⋊D3—21no—
173C3⋊D3—22no—
174C24—91no—
175C22×C4—62no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—362no—
182C22×C4GO+(4,𝔽2)11yescharacteristic
183C2×C8—62no—
184C2×C8—182no—
185C2×C8—362no—
186C2×C8—362no—
187C22⋊C4—94no—
188C22⋊C4—182no—
189C42—122no—
190C22×C3—21no—
191C22×C3—22no—
192C22×C3—21no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—41no—
198C22×C3—41no—
199C2×D3—61no—
200C2×D3—61no—
201C2×D3—61no—
202C2×D3—61no—
203C2×D3—62no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—121no—
211C2×D3—121no—
212C2×D3—121no—
213C2×D3—124no—
214C2×D3—124no—
215C2×D3—122no—
216C2×D3—122no—
217C2×D3—122no—
218C2×D3—122no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—22no—
222C3×C4—41no—
223C3×C4—124no—
224Dic3—44no—
225Dic3—62no—
226Dic3—121no—
227Dic3—121no—
228Dic3—121no—
229C32#128211yescharacteristic, complemented, Sylow
230C23—91no—
231C23—91no—
232C23—92no—
233C23—92no—
234C23—361no—
235C23—361no—
236C23D32⋊C411yescharacteristic
237C2×C4—22no—
238C2×C4—64no—
239C2×C4—91no—
240C2×C4—91no—
241C2×C4—122no—
242C2×C4—122no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4D32⋊C411yescharacteristic
249C2×C4#377311yescharacteristic
250C8—122no—
251C8—362no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—42no—
261D3—62no—
262D3—62no—
263D3—121no—
264D3—121no—
265D3—122no—
266D3—122no—
267C22—21no—
268C22—21no—
269C22—91no—
270C22—91no—
271C22—92no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22—181no—
276C22—362no—
277C22—362no—
278C22D32⋊C812yes—
279C22#6373711yescharacteristic
280C4—21no—
281C4—124no—
282C4—181no—
283C4—181no—
284C4#6373812yes—
285C3—21no—
286C3—21no—
287C2—22no—
288C2—181no—
289C2—181no—
290C2—182no—
291C2#1059004311yescharacteristic
292C2#1059005411yescharacteristic
293C2#1059007611yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1282
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×#3710C4semidirect
10. #63778C4semidirect
30. #3722C8semidirect
229. C32#1282semidirect

Maximal subgroups

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

subgroupindex
#105938002
C4×#37222
#105911522
#12829