Finite Group Databasebeta

← #11796776

Subgroups — #11796776

Order 1152.

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

normal subgroups only

This group has 410 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
2C2×#63764C211yesmaximal, characteristic, complemented
3#10590913C211yesmaximal, characteristic, complemented
4#10590063C214yesmaximal, complemented
5#64306—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C3×#904—21no—
8#63822C2212yes—
9#63818—21no—
10#63810—21no—
11#63809C412yes—
12#63802C411yescharacteristic
13#63797C411yescharacteristic
14#63796—21no—
15C2×#3708C2212yescomplemented
16#63764—21no—
17#63764—21no—
18C3×#819—21no—
19#63578C2212yescomplemented
20D3×#135—61no—
21D3×#108—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—
31C2×C32×C8D411yescharacteristic
32C2×C3⋊(C3⋊C8)C2311yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C3×#208—22no—
38C3×Dic12—21no—
39C3×D24—21no—
40C3×#204—22no—
41#3718C2×C412yes—
42#3715—22no—
43#3713C2×C412yes—
44#3712—41no—
45#3710—41no—
46#3708—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—
57D3×M16—62no—
58#904—21no—
59C2×D3×C8—61no—
60C2×D3×C8—61no—
61C3×#108—61no—
62#822—62no—
63#819—21no—
64C22×C3⋊D3SD1611yescharacteristic
65C2×D32—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3SD1611yescharacteristic
68C4×C3⋊D3C22⋊C411yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3D811yescharacteristic
71C4×C3⋊D3D811yescharacteristic
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—
81C32×C8C22⋊C411yescharacteristic
82C32×C8C22⋊C411yescharacteristic
83C3⋊(C3⋊C8)C22×C411yescharacteristic
84C3⋊(C3⋊C8)C2×D411yescharacteristic
85C3×C3⋊C8—42no—
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—
105C3×M16—62no—
106C2×C3×C8—21no—
107C2×C3×C8—21no—
108#216—62no—
109#215—62no—
110#214—62no—
111#213—62no—
112#208—22no—
113C2×C3⋊C8—61no—
114C2×C3⋊C8—61no—
115Dic12—21no—
116D24—21no—
117#204—22no—
118ΓL(1,𝔽25)—122no—
119D3×C8—61no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124D3×C8—61no—
125D3×C8—61no—
126D3×C8—61no—
127D3×C8—122no—
128C22×C32C2×SD1611yescharacteristic
129C2×C3⋊D3—22no—
130C2×C3⋊D3#10211yescharacteristic
131C2×C3⋊D3#10211yescharacteristic
132C2×C3×D3—42no—
133D32—82no—
134C32×C4C2×C22⋊C411yescharacteristic
135C32×C4C2×D811yescharacteristic
136C3⋊Dic3#10211yescharacteristic
137C3⋊Dic3#10211yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140#135—61no—
141#135—92no—
142#135—92no—
143#135—181no—
144C2×Q16—91no—
145C2×SD16—181no—
146C2×D8—91no—
147C2×M16—181no—
148C22×C8—91no—
149C2×C16—92no—
150C2×C16—181no—
151C2×C16—181no—
152#108—61no—
153#108—92no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—122no—
157C3×Q8—62no—
158C3×D4—62no—
159C3×D4—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—122no—
163#67—42no—
164#67—122no—
165#67—122no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—122no—
169D12—22no—
170D12—122no—
171C4×D3—42no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—122no—
181C4×D3—122no—
182Dic6—22no—
183Dic6—122no—
184C3×C8—21no—
185C3×C8—21no—
186C3×C8—21no—
187C3×C8—21no—
188C3×C8—122no—
189C3⋊C8—42no—
190C3⋊C8—61no—
191C3⋊C8—61no—
192C3⋊C8—61no—
193C3⋊C8—61no—
194C2×C32—21no—
195C2×C32C2×#10211yescharacteristic
196C3⋊D3—21no—
197C3⋊D3#35912yescomplemented
198C3×D3—82no—
199#41—62no—
200#41—182no—
201#41—361no—
202#41—361no—
203C2×Q8—181no—
204C2×D4—181no—
205C2×D4—361no—
206C22×C4—91no—
207C22×C4—361no—
208Q16—61no—
209Q16—92no—
210SD16—62no—
211SD16—182no—
212D8—61no—
213D8—92no—
214M16—62no—
215M16—361no—
216C2×C8—91no—
217C2×C8—91no—
218C2×C8—91no—
219C2×C8—91no—
220C2×C8—91no—
221C2×C8—361no—
222C2×C8GO+(4,𝔽2)11yescharacteristic
223C16—182no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—122no—
227C2×D3—42no—
228C2×D3—61no—
229C2×D3—61no—
230C2×D3—61no—
231C2×D3—61no—
232C2×D3—122no—
233C2×D3—122no—
234C2×D3—244no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—122no—
240Dic3—42no—
241Dic3—61no—
242Dic3—61no—
243Dic3—61no—
244Dic3—61no—
245C32C2×#35911yescharacteristic, complemented, Sylow
246C23—91no—
247C23—361no—
248Q8—62no—
249Q8—361no—
250D4—62no—
251D4—122no—
252D4—361no—
253D4—362no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—122no—
260C2×C4—362no—
261C2×C4—361no—
262C2×C4C2×GO+(4,𝔽2)11yescharacteristic
263C8—91no—
264C8—91no—
265C8—122no—
266C8D32⋊C411yescharacteristic
267C8D32⋊C411yescharacteristic
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—41no—
271C2×C3—41no—
272C2×C3—242no—
273D3—62no—
274D3—62no—
275D3—82no—
276D3—121no—
277D3—121no—
278C22—91no—
279C22—91no—
280C22—122no—
281C22—182no—
282C22—722no—
283C22#6422711yescharacteristic
284C4—91no—
285C4—91no—
286C4—122no—
287C4#6422511yescharacteristic
288C4C2×D32⋊C411yescharacteristic
289C3—21no—
290C3—21no—
291C2—21no—
292C2—92no—
293C2—181no—
294C2—242no—
295C2#1059336511yescharacteristic
subgroupG/H
centerC4#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC2×C3⋊(C3⋊C8)C23
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. C2×#63764C2semidirect
3. #10590913C2semidirect
4. #10590063C2semidirect
15. C2×#3708C22semidirect
19. #63578C22semidirect
197. C3⋊D3#359semidirect
245. C32C2×#359semidirect

Maximal subgroups

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

subgroupindex
#105946842
C2×#637642
#105909132
#105900632
C2×#3599