Finite Group Databasebeta

← #11774510

Subgroups — #11774510

Order 1152.

488 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593971C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C2×#3796—21no—
6C42×C3⋊D3C2211yescharacteristic
7C3×#875—21no—
8#63914C411yescharacteristic
9#63912—21no—
10#63912C412yes—
11#63902—21no—
12#63902C2212yes—
13#63873C411yescharacteristic
14C2×#3712—21no—
15#63779C2212yes—
16#63778—21no—
17C4×#622—21no—
18C3×#803—21no—
19#63553C2212yes—
20#5668—61no—
21#4707—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×Dic6—21no—
27C2×#626—22no—
28C2×#625—21no—
29C2×#625C2×C412yes—
30C2×D3×Dic3—22no—
31#3796—44no—
32C2×#622—22no—
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×(C2×D3)⋊C4—22no—
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41#3724C2×C412yes—
42#3712—24no—
43#1484—91nomaximal, Sylow
44C2×#239—61no—
45C2×#237—61no—
46C3×#124—61no—
47#944—61no—
48#940—61no—
49C2×ΓL(1,𝔽25)—62no—
50#884—62no—
51#884—62no—
52#67⋊C4—62no—
53#67⋊C4—62no—
54#875—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×#97—61no—
58C8×Dic3—62no—
59#803—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×Dic6—42no—
74#626—44no—
75#625—24no—
76#625—42no—
77D3×Dic3—44no—
78#622—42no—
79C3×C3⋊C8—24no—
80#532—91no—
81#431—91no—
82C4×M16—91no—
83D4⋊C8—94no—
84C2×C3×Q8—61no—
85C2×C3×D4—61no—
86C2×#67—62no—
87C2×#67—62no—
88C2×#67—62no—
89C22×Dic3—62no—
90#239—124no—
91#237—124no—
92C2×D12—21no—
93C2×D12—62no—
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×C4×D3—62no—
101C2×Dic6—21no—
102C2×C3×C8—62no—
103C3×C22⋊C4—62no—
104C3×C22⋊C4—62no—
105C3×C42—21no—
106C3×C42—21no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—22no—
109Dic3⋊C4—62no—
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—
118ΓL(1,𝔽25)—68no—
119C22×C32C2×C22⋊C411yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—21no—
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C32×C4—21no—
127C32×C4—21no—
128C32×C4—21no—
129C3⋊Dic3#10412yes—
130C3⋊Dic3#13112yes—
131C3⋊Dic3AGL(1,ℤ/8)12yes—
132C3×Dic3—42no—
133C2×#41—181no—
134C2×M16—181no—
135C4⋊Q8—91no—
136#127—91no—
137#124—61no—
138#121—92no—
139#121—181no—
140C4×D4—92no—
141C4×D4—181no—
142C2×C42—91no—
143C4⋊C8—92no—
144C22⋊C8—181no—
145#97—61no—
146C4×C8—92no—
147C4×C8—181no—
148C23×C3—62no—
149C22×D3—22no—
150C22×D3—61no—
151C22×D3—61no—
152C3×Q8—122no—
153C3×D4—122no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—62no—
161#67—124no—
162#67—124no—
163#67—124no—
164C2×Dic3—22no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—124no—
172D12—42no—
173D12—124no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—122no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—122no—
180C4×D3—124no—
181Dic6—42no—
182C3×C8—64no—
183C3⋊C8—24no—
184C2×C32#40811yescharacteristic
185C2×C32#41811yescharacteristic
186C2×C32C2×#10411yescharacteristic
187C3⋊D3—41no—
188C3×D3—82no—
189#41—364no—
190C2×Q8—61no—
191C2×D4—61no—
192C2×D4—92no—
193C2×D4—182no—
194C2×D4—181no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—182no—
199M16—184no—
200C2×C8—62no—
201C2×C8—182no—
202C4⋊C4—92no—
203C4⋊C4—181no—
204C22⋊C4—62no—
205C22⋊C4—62no—
206C42—91no—
207C42—91no—
208C42—91no—
209C42GO+(4,𝔽2)11yescharacteristic
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—122no—
213C22×C3—122no—
214C22×C3—122no—
215C2×D3—42no—
216C2×D3—42no—
217C2×D3—42no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—121no—
221C2×D3—121no—
222C2×D3—121no—
223C2×D3—121no—
224C3×C4—22no—
225C3×C4—22no—
226C3×C4—41no—
227C3×C4—41no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4—122no—
231Dic3—42no—
232Dic3—62no—
233Dic3—62no—
234Dic3—62no—
235Dic3—62no—
236Dic3—62no—
237Dic3—62no—
238C32#148411yescharacteristic, complemented, Sylow
239C23—62no—
240C23—91no—
241Q8—122no—
242D4—122no—
243D4—184no—
244D4—362no—
245D4—364no—
246C2×C4—62no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—182no—
251C2×C4—182no—
252C2×C4—182no—
253C2×C4—364no—
254C2×C4D32⋊C411yescharacteristic
255C2×C4D32⋊C411yescharacteristic
256C2×C4C2×GO+(4,𝔽2)11yescharacteristic
257C8—64no—
258C8—362no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—242no—
266D3—82no—
267D3—122no—
268D3—122no—
269C22—122no—
270C22—122no—
271C22—122no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22C2×D32⋊C411yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—92no—
280C4—92no—
281C4—92no—
282C4—122no—
283C3—21no—
284C3—21no—
285C2—242no—
286C2—361no—
287C2#1059330911yescharacteristic
288C2#1059331811yescharacteristic
289C2#1059338011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1484
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593725C2semidirect
3. #10590247C2semidirect
4. #10590030C2semidirect
238. C32#1484semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105937252
#105902472
#105900302
#14849