Finite Group Databasebeta

← #11784040

Subgroups — #11784040

Order 1152.

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

normal subgroups only

This group has 622 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
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63784C212yesmaximal
3C4×C4⋊#157C211yesmaximal, characteristic
4#10593723C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C2×C4×#157—21no—
9C2×#3787C2212yes—
10C32×C4×Q8C411yescharacteristic, complemented
11Q8×C3⋊Dic3C411yescharacteristic, complemented
12C4⋊C4×C3⋊D3—21no—
13C4⋊C4×C3⋊D3C2211yescharacteristic
14#64096—21no—
15#64096C411yescharacteristic, complemented
16C42×C3⋊D3—21no—
17C42×C3⋊D3C2211yescharacteristic
18C4×#634—21no—
19C4×#634C411yescharacteristic, complemented
20#63784C418yescomplemented
21#63781—21no—
22#63777—21no—
23#63777—21no—
24C4×D3×Q8—62no—
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27Q8×C3⋊D3—22no—
28Q8×C3⋊D3C2×C414yes—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×#634—21no—
35C2×#634C2×C411yescharacteristic
36C2×#622—22no—
37C4⋊#157—22no—
38C4⋊#157C2×C414yes—
39C4×#157—42no—
40#3787—22no—
41#3787C2×C414yes—
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C42—21no—
45C32×C42C2×C411yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57#1763—91nomaximal, Sylow
58C2×D3×Q8—62no—
59C3×C4×Q8—22no—
60Q8×Dic3—62no—
61D3×C4⋊C4—62no—
62D3×C4⋊C4—64no—
63#887—62no—
64#887—64no—
65C42×D3—62no—
66C42×D3—64no—
67C4×Dic6—62no—
68C4×Dic6—64no—
69C22×C3⋊D3C2×D411yescharacteristic
70C2×#157—24no—
71C2×#157—42no—
72C2×#157—42no—
73C32×Q8—21no—
74C32×Q8C4212yescomplemented
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4×C3⋊D3—24no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3C22×C412yes—
92C4×C3⋊D3#4112yes—
93#634—21no—
94#634—24no—
95#634C4212yescomplemented
96#622—24no—
97C2×C4×Q8—91no—
98C2×#103—92no—
99C2×#97—91no—
100C4×C4⋊C4—91no—
101#340—92no—
102C2×C3×Q8—22no—
103D3×Q8—68no—
104D3×Q8—68no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×Dic6—62no—
111C2×Dic6—64no—
112C3×C4⋊C4—24no—
113C3×C4⋊C4—22no—
114C3×C42—24no—
115C3×C42—22no—
116C4⋊Dic3—62no—
117C4⋊Dic3—64no—
118Dic3⋊C4—64no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—64no—
125C4×Dic3—64no—
126C4×Dic3—64no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3C4×D412yes—
129C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
130C2×C3⋊D3#13712yes—
131C2×C3⋊D3#13711yescharacteristic
132#157—44no—
133C32×C4—22no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4—41no—
137C32×C4C2×C4211yescharacteristic
138C32×C4#11711yescharacteristic
139C3⋊Dic3—22no—
140C3⋊Dic3—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3C4×D412yes—
144C22×Q8—91no—
145C22×C8—92no—
146C4×Q8—91no—
147C4×Q8—91no—
148C4×Q8—91no—
149C4×Q8—181no—
150C4×Q8—181no—
151C4×Q8#15711yescharacteristic, complemented
152C2×C4⋊C4—92no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—181no—
155C2×C42—91no—
156C2×C42—181no—
157C2×C42—181no—
158#103—98no—
159#97—181no—
160#97—181no—
161#95—181no—
162C22×D3—62no—
163C3×Q8—24no—
164C3×Q8—24no—
165C2×C3×C4—24no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C4×D3—64no—
176C4×D3—64no—
177C4×D3—68no—
178C4×D3—616no—
179C4×D3—122no—
180C4×D3—122no—
181C4×D3—124no—
182C4×D3—124no—
183Dic6—64no—
184Dic6—616no—
185Dic6—64no—
186C2×C32C4×C22⋊C411yescharacteristic
187C2×C32#41711yescharacteristic
188C2×C32#41911yescharacteristic
189C3⋊D3#44012yes—
190C3⋊D3#44112yes—
191C2×Q8—94no—
192C2×Q8—91no—
193C2×Q8—181no—
194C2×Q8—182no—
195C2×Q8C2×#15711yescharacteristic
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—182no—
202C2×C8—94no—
203C2×C8—182no—
204C2×C8—182no—
205C4⋊C4—21no—
206C4⋊C4—94no—
207C4⋊C4—91no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4—182no—
212C4⋊C4—181no—
213C4⋊C4C2×#15711yescharacteristic
214C42—21no—
215C42—91no—
216C42—91no—
217C42—91no—
218C42—181no—
219C42—181no—
220C42—181no—
221C42—362no—
222C42C2×#15711yescharacteristic
223C22×C3—22no—
224C2×D3—64no—
225C2×D3—64no—
226C2×D3—62no—
227C2×D3—62no—
228C3×C4—28no—
229C3×C4—24no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—42no—
233C3×C4—44no—
234Dic3—64no—
235Dic3—68no—
236Dic3—64no—
237Dic3—122no—
238Dic3—124no—
239C32#176311yescharacteristic, complemented, Sylow
240C23—91no—
241Q8—21no—
242Q8—92no—
243Q8—184no—
244Q8—181no—
245Q8C4×#15712yescomplemented
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—91no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—181no—
254C2×C4—182no—
255C2×C4—181no—
256C2×C4—184no—
257C2×C4—181no—
258C2×C4—184no—
259C2×C4—181no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—362no—
263C2×C4—362no—
264C2×C4C22⋊#15711yescharacteristic
265C2×C4C22⋊#15711yescharacteristic
266C2×C4C22×#15711yescharacteristic
267C8—184no—
268C2×C3—22no—
269C2×C3—22no—
270C2×C3—22no—
271D3—64no—
272D3—64no—
273C22—92no—
274C22—92no—
275C22—91no—
276C22—91no—
277C22C2×C22⋊#15711yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—41no—
282C4—92no—
283C4—182no—
284C4—181no—
285C4—181no—
286C4—364no—
287C4—361no—
288C4C2×C4×#15711yescharacteristic
289C4#6428611yescharacteristic
290C3—22no—
291C2—92no—
292C2—92no—
293C2C4×C22⋊#15711yescharacteristic
294C2#1059382911yescharacteristic
295C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1763
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
10. C32×C4×Q8C4semidirect
11. Q8×C3⋊Dic3C4semidirect
15. #64096C4semidirect
19. C4×#634C4semidirect
20. #63784C4semidirect
74. C32×Q8C42semidirect
95. #634C42semidirect
151. C4×Q8#157semidirect
239. C32#1763semidirect
245. Q8C4×#157semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C2×#637842
C4×C4⋊#1572
#105937232
#105901632
#17639