Finite Group Databasebeta

← #11796778

Subgroups — #11796778

Order 1152.

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

normal subgroups only

This group has 406 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#10594684C211yesmaximal, characteristic
2#10593771C211yesmaximal, characteristic, complemented
3C2×#63542C211yesmaximal, characteristic, complemented
4#10590018C214yesmaximal, complemented
5#64306—21no—
6#64283—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C3×#904—21no—
9#63822C412yes—
10#63810—21no—
11#63809C2212yes—
12#63802C411yescharacteristic
13#63797C411yescharacteristic
14#63796—21no—
15#63771—21no—
16#63770C2212yescomplemented
17C2×C3×C3⋊C16—21no—
18#63542—21no—
19#63542C2212yescomplemented
20D3×#135—61no—
21C2×D3×C16—61no—
22C2×C4×C3⋊D3D411yescharacteristic
23C3×#235—22no—
24#3811—41no—
25#3805—41no—
26#3802—21no—
27C4×D32—41no—
28#3798—41no—
29#3797—21no—
30#3796—22no—
31#3792—41no—
32#3788—22no—
33#3787—41no—
34C2×C32×C8D411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C8×C3⋊D3C2×C411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3C2311yescharacteristic
40C3×Dic12—21no—
41C3×D24—21no—
42C3×#204—22no—
43#3718C2×C412yes—
44#3715—22no—
45#3713C2×C412yes—
46C3×C3⋊C16—22no—
47C2×#359—91nomaximal, Sylow
48D3×#41—62no—
49C3×#135—61no—
50#950—62no—
51#919—61no—
52D3×Q16—61no—
53#916—62no—
54D3×SD16—62no—
55#912—61no—
56D3×D8—61no—
57#904—21no—
58C2×D3×C8—61no—
59C2×D3×C8—61no—
60C2×C3×C16—61no—
61C2×C3⋊C16—21no—
62D3×C16—62no—
63D3×C16—62no—
64C22×C3⋊D3SD1611yescharacteristic
65C2×D32—41no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C3⋊Dic3D811yescharacteristic
68C4×C3⋊D3C22⋊C411yescharacteristic
69C4×C3⋊D3D811yescharacteristic
70C4×C3⋊D3SD1611yescharacteristic
71C4×C3⋊D3C2×D411yescharacteristic
72C3×#67—42no—
73C3×D12—22no—
74C3×C4×D3—42no—
75C3×Dic6—22no—
76#627—41no—
77#626—42no—
78#625—41no—
79#624—41no—
80D3×Dic3—42no—
81#622—42no—
82C32×C8C22⋊C411yescharacteristic
83C32×C8C2×D411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C3⋊(C3⋊C8)C22×C411yescharacteristic
86C2×#135—91no—
87C22×C16—91no—
88C2×#108—91no—
89#359—94no—
90C3×#41—62no—
91#239—62no—
92D3×Q8—62no—
93#237—62no—
94#237—122no—
95D3×D4—62no—
96D3×D4—122no—
97#235—22no—
98#235—122no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—122no—
102C3×Q16—61no—
103C3×SD16—62no—
104C3×D8—61no—
105C2×C3×C8—21no—
106C2×C3×C8—21no—
107#216—62no—
108#215—62no—
109#214—62no—
110#213—62no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113Dic12—21no—
114D24—21no—
115#204—22no—
116D3×C8—61no—
117D3×C8—61no—
118D3×C8—61no—
119D3×C8—61no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124C3×C16—62no—
125C3⋊C16—22no—
126C22×C32#10211yescharacteristic
127C2×C3⋊D3—22no—
128C2×C3⋊D3#10211yescharacteristic
129C2×C3⋊D3C2×SD1611yescharacteristic
130C2×C3×D3—42no—
131D32—82no—
132C32×C4#10211yescharacteristic
133C32×C4C2×C22⋊C411yescharacteristic
134C3⋊Dic3#10211yescharacteristic
135C3⋊Dic3C2×D811yescharacteristic
136C3×Dic3—42no—
137C2×#41—181no—
138#135—61no—
139#135—92no—
140#135—92no—
141#135—181no—
142C2×Q16—91no—
143C2×SD16—181no—
144C2×D8—91no—
145C2×M16—181no—
146C22×C8—91no—
147C2×C16—61no—
148C2×C16—92no—
149C2×C16—181no—
150#108—92no—
151#108—181no—
152C22×D3—61no—
153C22×D3—61no—
154C22×D3—122no—
155C3×Q8—62no—
156C3×D4—62no—
157C3×D4—122no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—122no—
161#67—42no—
162#67—122no—
163#67—122no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—122no—
167D12—22no—
168D12—122no—
169C4×D3—42no—
170C4×D3—61no—
171C4×D3—61no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—122no—
179C4×D3—122no—
180Dic6—22no—
181Dic6—122no—
182C3×C8—21no—
183C3×C8—21no—
184C3×C8—21no—
185C3×C8—21no—
186C3⋊C8—61no—
187C3⋊C8—61no—
188C3⋊C8—61no—
189C3⋊C8—61no—
190C2×C32—21no—
191C2×C32C2×#10211yescharacteristic
192C3⋊D3—21no—
193C3⋊D3#35912yescomplemented
194C3×D3—82no—
195#41—62no—
196#41—182no—
197#41—361no—
198#41—361no—
199C2×Q8—181no—
200C2×D4—181no—
201C2×D4—361no—
202C22×C4—91no—
203C22×C4—361no—
204Q16—61no—
205Q16—92no—
206SD16—62no—
207SD16—182no—
208D8—61no—
209D8—92no—
210M16—182no—
211M16—361no—
212C2×C8—91no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—361no—
218C2×C8GO+(4,𝔽2)11yescharacteristic
219C16—62no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—122no—
223C2×D3—42no—
224C2×D3—61no—
225C2×D3—61no—
226C2×D3—61no—
227C2×D3—61no—
228C2×D3—64no—
229C2×D3—122no—
230C2×D3—244no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—122no—
236Dic3—42no—
237Dic3—61no—
238Dic3—61no—
239Dic3—61no—
240Dic3—61no—
241C32C2×#35911yescharacteristic, complemented, Sylow
242C23—91no—
243C23—361no—
244Q8—62no—
245Q8—361no—
246D4—62no—
247D4—122no—
248D4—361no—
249D4—362no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—122no—
256C2×C4—362no—
257C2×C4—361no—
258C2×C4D32⋊C411yescharacteristic
259C8—91no—
260C8—91no—
261C8—362no—
262C8D32⋊C411yescharacteristic
263C8C2×GO+(4,𝔽2)11yescharacteristic
264C2×C3—22no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—41no—
268C2×C3—242no—
269D3—62no—
270D3—62no—
271D3—62no—
272D3—82no—
273D3—121no—
274C22—91no—
275C22—91no—
276C22—122no—
277C22—182no—
278C22—722no—
279C22#6372911yescharacteristic
280C4—91no—
281C4—91no—
282C4—122no—
283C4#6372911yescharacteristic
284C4C2×D32⋊C411yescharacteristic
285C3—21no—
286C3—21no—
287C2—21no—
288C2—92no—
289C2—181no—
290C2—242no—
291C2C2×#6372911yescharacteristic
subgroupG/H
centerC4#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#359
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593771C2semidirect
3. C2×#63542C2semidirect
4. #10590018C2semidirect
16. #63770C22semidirect
19. #63542C22semidirect
193. C3⋊D3#359semidirect
241. C32C2×#359semidirect

Maximal subgroups

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

subgroupindex
#105946842
#105937712
C2×#635422
#105900182
C2×#3599