Finite Group Databasebeta

← #11776582

Subgroups — #11776582

Order 1152.

719 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 719 conjugacy classes of subgroups — too many to draw. Only its 100 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#10594008C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4C3×#4485C212yesmaximal, complemented
5#10589090C212yesmaximal, complemented
6#68387—32nomaximal
7C2×#3802—21no—
8C2×#3802—21no—
9C2×#3802C412yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#874C2212yes—
12#63914—21no—
13#63914—21no—
14#63914C412yes—
15C32×C4⋊C8C2211yescharacteristic, complemented
16#63647—21no—
17#63642—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
19C3×C4⋊(C3⋊C8)C2212yescomplemented
20#63557—21no—
21#63555—21no—
22D3×#127—32no—
23#4835—32no—
24#4835—32no—
25#4835—61no—
26C3×#331—32no—
27#4544—32no—
28#4485—32no—
29#4485D312yescomplemented
30C22×D32—22no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×D12—22no—
35C2×C3×D12—22no—
36C2×C3×D12C2×C414yes—
37C2×#625—22no—
38C2×#625—22no—
39C2×#625—22no—
40#3802—42no—
41#3802—44no—
42#3802—42no—
43#3802—44no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3×C3⋊C8—22no—
51#1555—91noSylow
52C2×D3×D4—34no—
53C2×D3×D4—62no—
54C2×D3×D4—62no—
55C3×#127—32no—
56#940—34no—
57#940—62no—
58#940—62no—
59#874C2×D312yes—
60C42×D3—32no—
61C42×D3—61no—
62C3×C4⋊C8—21no—
63C3×C4⋊C8—32no—
64C3×C4⋊C8C2×D312yescomplemented
65(C2×D3)⋊C8—62no—
66(C2×D3)⋊C8—62no—
67(C2×D3)⋊C8—62no—
68#815—62no—
69#815—62no—
70#815—62no—
71C4⋊(C3⋊C8)—32no—
72C4⋊(C3⋊C8)—61no—
73C4⋊(C3⋊C8)C2×D312yescomplemented
74C22×C3⋊D3C22⋊C411yescharacteristic
75C22×C3×D3—24no—
76C2×D32—44no—
77C2×D32—44no—
78C2×D32—44no—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—21no—
89C3×D12—44no—
90C3×D12—42no—
91C3×D12—42no—
92C3×D12—42no—
93C3×D12—42no—
94#625—44no—
95#625—44no—
96#625—44no—
97C32×C8—41no—
98C3⋊(C3⋊C8)—41no—
99C3×C3⋊C8—42no—
100C2×#127—91no—
101#432—91no—
102#432—91no—
103#331—32no—
104#331—92no—
105C23×D3—64no—
106C2×C3×D4—34no—
107C2×C3×D4—62no—
108C2×C3×D4—62no—
109C2×#67—64no—
110C2×#67—64no—
111C2×#67—64no—
112D3×D4—128no—
113D3×D4—124no—
114D3×D4—124no—
115D3×D4—124no—
116D3×D4—124no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12C4×D314yes—
120C2×C4×D3—32no—
121C2×C4×D3—32no—
122C2×C4×D3—32no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C3×C8—22no—
127C2×C3×C8—22no—
128C2×C3×C8—62no—
129C3×C42—21no—
130C3×C42C22×D312yes—
131C4×Dic3—32no—
132C4×Dic3—32no—
133C4×Dic3—32no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C22×C32C2×C22⋊C411yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3#10012yes—
144C2×C3×D3—44no—
145C2×C3×D3—44no—
146C2×C3×D3—44no—
147D32—88no—
148C32×C4—21no—
149C32×C4AGL(1,ℤ/8)11yescharacteristic
150C32×C4AGL(1,ℤ/8)12yes—
151C32×C4AGL(1,ℤ/8)11yescharacteristic
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3—21no—
155C22×D4—92no—
156C22×D4—181no—
157C22×D4—181no—
158#127—32no—
159#127—92no—
160#127—181no—
161#127—181no—
162C2×C42—91no—
163C4⋊C8—32no—
164C4⋊C8—91no—
165C4⋊C8D3211yescharacteristic, complemented
166C22⋊C8—181no—
167C22⋊C8—181no—
168#97—181no—
169#97—181no—
170C23×C3—64no—
171C22×D3—24no—
172C22×D3—32no—
173C22×D3—61no—
174C22×D3—128no—
175C22×D3—128no—
176C22×D3—128no—
177C3×D4—124no—
178C3×D4—122no—
179C3×D4—122no—
180C3×D4—122no—
181C3×D4—122no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4C2×C4×D312yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4D3×D412yes—
188#67—128no—
189#67—128no—
190#67—128no—
191C2×Dic3—32no—
192C2×Dic3—32no—
193C2×Dic3—32no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197D12—44no—
198D12—42no—
199D12—42no—
200D12—42no—
201D12—42no—
202C4×D3—64no—
203C4×D3—62no—
204C4×D3—62no—
205C4×D3—62no—
206C4×D3—62no—
207C4×D3—122no—
208C4×D3—121no—
209C4×D3—121no—
210C4×D3—122no—
211C3×C8—42no—
212C3×C8—42no—
213C3×C8—122no—
214C3⋊C8—42no—
215C3⋊C8—122no—
216C3⋊C8—122no—
217C2×C32C2×#10011yescharacteristic
218C2×C32#41811yescharacteristic
219C2×C32#41811yescharacteristic
220C3⋊D3—22no—
221C3×D3—84no—
222C24—182no—
223C2×D4—34no—
224C2×D4—62no—
225C2×D4—62no—
226C2×D4—182no—
227C2×D4—182no—
228C2×D4—182no—
229C2×D4—364no—
230C2×D4—364no—
231C2×D4—362no—
232C2×D4—362no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—91no—
236C2×C8—21no—
237C2×C8—62no—
238C2×C8—181no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42C2×D3211yescharacteristic
243C22×C3—21no—
244C22×C3—124no—
245C22×C3—124no—
246C22×C3—124no—
247C22×C3D3×C22⋊C412yes—
248C2×D3—34no—
249C2×D3—44no—
250C2×D3—44no—
251C2×D3—44no—
252C2×D3—62no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—121no—
256C2×D3—121no—
257C2×D3—2416no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—41no—
263C3×C4#91112yes—
264C3×C4#91112yes—
265C3×C4#91412yes—
266C3×C4#91412yes—
267Dic3—62no—
268Dic3—62no—
269Dic3—62no—
270Dic3—121no—
271Dic3—121no—
272Dic3—121no—
273C32#155511yescharacteristic, complemented, Sylow
274C23—64no—
275C23—91no—
276C23—364no—
277C23—364no—
278C23—364no—
279D4—124no—
280D4—122no—
281D4—122no—
282D4—122no—
283D4—122no—
284D4—364no—
285D4—364no—
286D4—364no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4C4×D3211yescharacteristic
295C2×C4#380211yescharacteristic
296C2×C4#381111yescharacteristic
297C8—41no—
298C8—122no—
299C8—361no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—244no—
304C2×C3D3×#10012yes—
305C2×C3#477012yes—
306C2×C3#477012yes—
307D3—64no—
308D3—84no—
309D3—122no—
310C22—92no—
311C22—124no—
312C22—124no—
313C22—124no—
314C22—181no—
315C22—181no—
316C22—728no—
317C22#6392111yescharacteristic
318C4—21no—
319C4—181no—
320C4—181no—
321C4—181no—
322C4#6379812yes—
323C4#6392711yescharacteristic
324C4#6394111yescharacteristic
325C3—21no—
326C3#6838712yescomplemented
327C2—182no—
328C2—244no—
329C2#1059059411yescharacteristic
330C2#1059094111yescharacteristic
331C2#1059100111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594008C2
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1555
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592534C2semidirect
3. #10590260C2semidirect
4. C3×#4485C2semidirect
5. #10589090C2semidirect
15. C32×C4⋊C8C22semidirect
18. C4⋊(C3⋊(C3⋊C8))C22semidirect
19. C3×C4⋊(C3⋊C8)C22semidirect
29. #4485D3semidirect
64. C3×C4⋊C8C2×D3semidirect
73. C4⋊(C3⋊C8)C2×D3semidirect
165. C4⋊C8D32semidirect
273. C32#1555semidirect
326. C3#68387semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105925342
#105902602
C3×#44852
#105890902
#683873