Finite Group Databasebeta

← #11776201

Subgroups — #11776201

Order 1152.

535 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 108 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#10596199C211yesmaximal, characteristic
2#10590331C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4547C212yesmaximal, complemented
5#10589096C212yesmaximal, complemented
6#68418—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8#64155—21no—
9Q8×C3⋊Dic3—21no—
10#64106C412yes—
11#64101—21no—
12#64099—21no—
13#64096C412yes—
14C42×C3⋊D3C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×#3710—21no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×C4⋊(C3⋊C8)C2212yes—
19#63572—21no—
20#63557—21no—
21#63553—21no—
22#5728—32no—
23#5728—61no—
24#4833—32no—
25D3×C4⋊C8—32no—
26C3×#332—32no—
27#4547D312yescomplemented
28#4481—32no—
29#4481—32no—
30C2×C32×Q8—21no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#634C2×C412yes—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C412yes—
37C32×C42C2311yescharacteristic
38#3752—22no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—22no—
42#3750—22no—
43C4×C3⋊Dic3—22no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49#3710—42no—
50#1542—91noSylow
51C3×C4⋊Q8—21no—
52C3×C4⋊Q8C2×D312yes—
53#946—62no—
54#946—62no—
55Q8×Dic3—62no—
56Q8×Dic3—62no—
57C2×D3×C8—62no—
58#897—34no—
59#897—62no—
60#892—62no—
61#892—62no—
62#890—62no—
63#890—62no—
64#887—34no—
65#887—62no—
66C42×D3—32no—
67C42×D3—61no—
68#869—32no—
69#869—61no—
70C3×C4⋊C8—32no—
71C3×C4⋊C8—32no—
72(C2×D3)⋊C8—62no—
73Dic3⋊C8—62no—
74C8×Dic3—62no—
75C4⋊(C3⋊C8)C2×D312yes—
76C4⋊(C3⋊C8)C2×D312yes—
77C22×C3⋊D3C22⋊C411yescharacteristic
78C32×Q8—42no—
79C2×C32×C4—22no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C4×C3⋊D3—22no—
88C4×C3⋊D3—41no—
89C4×C3⋊D3SD1612yes—
90C4×C3⋊D3Q1612yes—
91#634—42no—
92C3×C3⋊C8—42no—
93C3×C3⋊C8—42no—
94#533—91no—
95#431—91no—
96C2×C4⋊C8—91no—
97#333—92no—
98#332—32no—
99C2×C3×Q8—22no—
100C2×C3×Q8—22no—
101C2×C4×D3—32no—
102C2×C4×D3—32no—
103C2×C4×D3—32no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×Dic6—34no—
108C2×Dic6—62no—
109C2×C3×C8—62no—
110C2×C3×C8—62no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4C4×D314yes—
115C3×C42—21no—
116C3×C42C22×D312yes—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119C4⋊Dic3—64no—
120C4⋊Dic3—62no—
121C4⋊Dic3—62no—
122C4⋊Dic3—64no—
123C4⋊Dic3—62no—
124C4⋊Dic3—62no—
125Dic3⋊C4—64no—
126Dic3⋊C4—64no—
127C4×Dic3—32no—
128C4×Dic3—32no—
129C4×Dic3—32no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—64no—
134C4×Dic3—64no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—22no—
137D3×C8—124no—
138C22×C32C2×C22⋊C411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3#10312yes—
142C32×C4—21no—
143C32×C4—42no—
144C32×C4C2×SD1611yescharacteristic
145C32×C4C2×Q1611yescharacteristic
146C32×C4#13512yes—
147C3⋊Dic3—21no—
148C3⋊Dic3—21no—
149C3⋊Dic3—42no—
150C3⋊Dic3#10312yes—
151C22×C8—181no—
152C4⋊Q8—91no—
153C4⋊Q8D3211yescharacteristic
154#125—181no—
155C22⋊Q8—92no—
156C22⋊Q8—181no—
157C4×Q8—92no—
158C4×Q8—181no—
159#117—181no—
160C2×C42—91no—
161C4⋊C8—32no—
162C4⋊C8—32no—
163C4⋊C8—181no—
164C22⋊C8—181no—
165C4×C8—181no—
166C22×D3—32no—
167C22×D3—61no—
168C3×Q8—44no—
169C3×Q8—42no—
170C3×Q8—42no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4C2×C4×D312yes—
177C2×C3×C4D3×D412yes—
178C2×C3×C4D3×D412yes—
179C2×Dic3—32no—
180C2×Dic3—32no—
181C2×Dic3—32no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C4×D3—34no—
188C4×D3—34no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—122no—
194C4×D3—122no—
195C4×D3—122no—
196Dic6—124no—
197Dic6—124no—
198C3×C8—122no—
199C3×C8—122no—
200C3⋊C8—42no—
201C3⋊C8—42no—
202C2×C32#41311yescharacteristic
203C2×C32C2×#10311yescharacteristic
204C2×C32#41611yescharacteristic
205C3⋊D3—22no—
206C2×Q8—21no—
207C2×Q8—92no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—91no—
211C2×C8—62no—
212C2×C8—62no—
213C2×C8—362no—
214C4⋊C4—21no—
215C4⋊C4—182no—
216C4⋊C4—182no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4#62412yes—
220C22⋊C4—182no—
221C42—91no—
222C42—91no—
223C42—91no—
224C42—182no—
225C42C2×D3211yescharacteristic
226C22×C3—21no—
227C22×C3D3×C22⋊C412yes—
228C2×D3—34no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—121no—
233C2×D3—121no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—44no—
240C3×C4—44no—
241C3×C4#91212yes—
242C3×C4D3×SD1612yes—
243C3×C4#91612yes—
244C3×C4D3×Q1612yes—
245Dic3—34no—
246Dic3—62no—
247Dic3—62no—
248Dic3—62no—
249Dic3—121no—
250Dic3—121no—
251Dic3—124no—
252Dic3—124no—
253C32#154211yescharacteristic, complemented, Sylow
254C23—91no—
255Q8—42no—
256Q8—362no—
257C2×C4—22no—
258C2×C4—91no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—182no—
264C2×C4—182no—
265C2×C4—361no—
266C2×C4C2×#62411yescharacteristic
267C2×C4#381111yescharacteristic
268C2×C4#381111yescharacteristic
269C8—122no—
270C8—122no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3#475112yes—
275C2×C3#477212yes—
276C2×C3D3×#10312yes—
277D3—64no—
278D3—122no—
279C22—92no—
280C22—181no—
281C22—181no—
282C22#6397411yescharacteristic
283C4—21no—
284C4—42no—
285C4—92no—
286C4—181no—
287C4—181no—
288C4—362no—
289C4#6393612yes—
290C4#6394011yescharacteristic
291C4#6394411yescharacteristic
292C3—21no—
293C3#6841812yescomplemented
294C2—182no—
295C2#1059142411yescharacteristic
296C2#1059155211yescharacteristic
297C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1542
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4547C2semidirect
5. #10589096C2semidirect
27. #4547D3semidirect
253. C32#1542semidirect
293. C3#68418semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105903312
#105902562
C3×#45472
#105890962
#684183