Finite Group Databasebeta

← #11776231

Subgroups — #11776231

Order 1152.

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

normal subgroups only

This group has 460 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#10594929C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4#10590040C212yesmaximal, complemented
5#10590037C212yesmaximal, complemented
6C2×#3805C412yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9#63980—21no—
10#63919C2211yescharacteristic
11#63915C412yes—
12#63914C2211yescharacteristic
13#63902—21no—
14#63898—21no—
15C22⋊#622—21no—
16C4⋊#622C2212yes—
17C4×#622—21no—
18C3×#830—21no—
19#63572C2212yes—
20#63553—21no—
21#5596—61no—
22#4718—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C3×#67—22no—
27C2×C3×D12—21no—
28C2×#627C2×C412yes—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3805—44no—
32C2×D3×Dic3—22no—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×C4⋊Dic3—21no—
40C2×C3×C3⋊C8—22no—
41#3724—21no—
42(C2×D3)⋊Dic3—22no—
43#1543—91nomaximal, Sylow
44C2×#237—62no—
45C3×#121—61no—
46#940—61no—
47#939—62no—
48D4×Dic3—61no—
49#930—21no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52#893—61no—
53#888—61no—
54#885—62no—
55#67⋊C4—62no—
56C3×C22⋊C8—61no—
57#830—21no—
58Dic3⋊C8—62no—
59C8×Dic3—62no—
60C23×C32C22⋊C411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C3×#67—44no—
72C2×C3×Dic3—22no—
73C3×D12—42no—
74#627—42no—
75#625—42no—
76#625—42no—
77D3×Dic3—44no—
78#622—42no—
79C3×C3⋊C8—42no—
80#532—91no—
81#431—91no—
82#431—91no—
83#333—92no—
84#331—92no—
85C2×C3×D4—61no—
86C2×C3×D4—62no—
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C2×#67—22no—
90C2×#67—62no—
91C2×#67—62no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C22×Dic3—62no—
97#237—128no—
98C2×D12—21no—
99C2×C4×D3—62no—
100C2×Dic6—62no—
101C2×C3×C8—62no—
102C3×C4⋊C4—61no—
103C3×C22⋊C4—62no—
104#217—62no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—62no—
107C4⋊Dic3—21no—
108Dic3⋊C4—62no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C2×C3⋊C8—22no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C32×C4—21no—
126C32×C4#13512yes—
127C3⋊Dic3—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3#10012yes—
130C3⋊Dic3#13512yes—
131C3×Dic3—42no—
132C2×#41—92no—
133C4⋊Q8—91no—
134#127—91no—
135#124—92no—
136#121—61no—
137#121—181no—
138C4×D4—181no—
139C4×D4—181no—
140C2×C42—91no—
141C4⋊C8—92no—
142C4⋊C8—92no—
143C22⋊C8—61no—
144C22⋊C8—181no—
145C4×C8—181no—
146C4×C8—181no—
147C23×C3—21no—
148C23×C3—21no—
149C23×C3—62no—
150C22×D3—22no—
151C3×D4—122no—
152C3×D4—124no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—62no—
160#67—44no—
161#67—124no—
162#67—124no—
163C2×Dic3—22no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—122no—
175C2×Dic3—122no—
176C2×Dic3—124no—
177D12—42no—
178C4×D3—124no—
179Dic6—124no—
180C3×C8—122no—
181C3⋊C8—42no—
182C2×C32—41no—
183C2×C32C2×#10011yescharacteristic
184C2×C32#41611yescharacteristic
185C2×C32#41611yescharacteristic
186C3×D3—82no—
187#41—364no—
188C2×Q8—92no—
189C2×D4—62no—
190C2×D4—61no—
191C2×D4—92no—
192C2×D4—181no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—182no—
196C22×C4GO+(4,𝔽2)11yescharacteristic
197C2×C8—62no—
198C2×C8—182no—
199C4⋊C4—61no—
200C4⋊C4—181no—
201C22⋊C4—62no—
202C22⋊C4—182no—
203C42—91no—
204C42—91no—
205C42—91no—
206C42—91no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—41no—
212C22×C3—41no—
213C22×C3—41no—
214C22×C3—41no—
215C22×C3—122no—
216C22×C3—122no—
217C22×C3—122no—
218C2×D3—42no—
219C2×D3—42no—
220C2×D3—42no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—41no—
224C3×C4—41no—
225C3×C4—122no—
226Dic3—42no—
227Dic3—62no—
228Dic3—62no—
229Dic3—62no—
230Dic3—62no—
231Dic3—62no—
232Dic3—62no—
233Dic3—121no—
234Dic3—121no—
235C32#154311yescharacteristic, complemented, Sylow
236C23—62no—
237C23D32⋊C411yescharacteristic
238Q8—362no—
239D4—124no—
240D4—122no—
241D4—362no—
242D4—362no—
243C2×C4—22no—
244C2×C4—62no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4—364no—
252C2×C4D32⋊C411yescharacteristic
253C2×C4C2×GO+(4,𝔽2)11yescharacteristic
254C8—122no—
255C8—362no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—42no—
263C2×C3—42no—
264C2×C3—242no—
265D3—82no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—122no—
270C22—122no—
271C22—122no—
272C22C2×D32⋊C411yescharacteristic
273C4—21no—
274C4—92no—
275C4—92no—
276C4—122no—
277C4—181no—
278C4—181no—
279C4#6423712yes—
280C3—21no—
281C3—21no—
282C2—41no—
283C2—242no—
284C2#1059331211yescharacteristic
285C2#1059331711yescharacteristic
286C2#1059349811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1543
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
3. #10591061C2semidirect
4. #10590040C2semidirect
5. #10590037C2semidirect
235. C32#1543semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105937952
#105910612
#105900402
#105900372
#15439