Finite Group Databasebeta

← #11776230

Subgroups — #11776230

Order 1152.

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

normal subgroups only

This group has 460 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#10593972C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4#10590040C212yesmaximal, complemented
5#10590037C212yesmaximal, complemented
6C2×#3798C412yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63919C2211yescharacteristic
10#63916—21no—
11#63915C412yes—
12#63914C2211yescharacteristic
13#63912—21no—
14C4×#625—21no—
15#63778—21no—
16C4⋊#622C2212yes—
17C4×#622—21no—
18C3×C4×C3⋊C8—21no—
19#63572C2212yes—
20#63557—21no—
21#5548—61no—
22#4685—61no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#627C2×C412yes—
29C2×#626—22no—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3798—44no—
33C2×#622—22no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
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×#235—62no—
45C3×C4×D4—61no—
46#940—61no—
47#938—61no—
48C4×#67—62no—
49#895—61no—
50#888—61no—
51#885—62no—
52#884—62no—
53C4×D12—21no—
54C42×D3—61no—
55C42×D3—61no—
56C3×C4×C8—61no—
57(C2×D3)⋊C8—62no—
58Dic3⋊C8—62no—
59C4×C3⋊C8—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—22no—
71C2×C3×Dic3—22no—
72C3×D12—42no—
73C3×C4×D3—44no—
74#627—42no—
75#626—44no—
76#625—42no—
77#625—42no—
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—
86C22×C3×C4—62no—
87C2×#67—62no—
88C2×#67—62no—
89C2×#67—62no—
90#235—128no—
91C2×D12—21no—
92C2×D12—62no—
93C2×C4×D3—22no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×Dic6—62no—
101C2×C3×C8—62no—
102C3×C4⋊C4—61no—
103C3×C22⋊C4—62no—
104C3×C42—21no—
105C3×C42—21no—
106#217—62no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—62no—
109C4⋊Dic3—21no—
110Dic3⋊C4—62no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C2×C3⋊C8—22no—
118C22×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3×D3—42no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C32×C4—21no—
126C32×C4#10012yes—
127C32×C4#13512yes—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3#13512yes—
131C3×Dic3—42no—
132C2×#41—92no—
133C4⋊Q8—91no—
134#127—91no—
135#124—92no—
136#121—181no—
137#121—181no—
138C4×D4—61no—
139C4×D4—181no—
140C2×C42—91no—
141C4⋊C8—92no—
142C4⋊C8—92no—
143C22⋊C8—181no—
144C22⋊C8—181no—
145C4×C8—61no—
146C4×C8—181no—
147C23×C3—62no—
148C22×D3—22no—
149C22×D3—61no—
150C22×D3—61no—
151C3×D4—122no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—62no—
159C2×C3×C4—124no—
160#67—124no—
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—
170D12—42no—
171D12—124no—
172C4×D3—44no—
173C4×D3—64no—
174C4×D3—64no—
175C4×D3—122no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179Dic6—124no—
180C3×C8—122no—
181C3⋊C8—42no—
182C2×C32C2×#10011yescharacteristic
183C2×C32#41611yescharacteristic
184C2×C32#41611yescharacteristic
185C3⋊D3—41no—
186C3×D3—82no—
187#41—364no—
188C2×Q8—92no—
189C2×D4—61no—
190C2×D4—92no—
191C2×D4—182no—
192C2×D4—181no—
193C22×C4—62no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—91no—
197C2×C8—62no—
198C2×C8—182no—
199C4⋊C4—61no—
200C4⋊C4—181no—
201C22⋊C4—62no—
202C22⋊C4—182no—
203C42—91no—
204C42—91no—
205C42—91no—
206C42GO+(4,𝔽2)11yescharacteristic
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—122no—
210C22×C3—122no—
211C22×C3—122no—
212C2×D3—42no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—62no—
216C2×D3—62no—
217C2×D3—121no—
218C2×D3—121no—
219C2×D3—121no—
220C2×D3—121no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—41no—
227C3×C4—122no—
228Dic3—42no—
229Dic3—62no—
230Dic3—62no—
231Dic3—62no—
232Dic3—121no—
233Dic3—121no—
234Dic3—121no—
235C32#154311yescharacteristic, complemented, Sylow
236C23—62no—
237C23—91no—
238Q8—362no—
239D4—122no—
240D4—362no—
241D4—364no—
242D4—362no—
243C2×C4—62no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—124no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—182no—
251C2×C4D32⋊C411yescharacteristic
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—242no—
263D3—82no—
264D3—122no—
265D3—122no—
266C22—122no—
267C22—122no—
268C22—122no—
269C22—181no—
270C22—181no—
271C22—181no—
272C22C2×D32⋊C411yescharacteristic
273C4—21no—
274C4—92no—
275C4—122no—
276C4—181no—
277C4—181no—
278C4#6372712yes—
279C4#6422312yes—
280C3—21no—
281C3—21no—
282C2—242no—
283C2—361no—
284C2C2×#6372711yescharacteristic
285C2#1059331711yescharacteristic
286C2#1059334911yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1543
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
2. #10593727C2semidirect
3. #10590297C2semidirect
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
#105939722
#105937272
#105902972
#105900402
#105900372
#15439