Finite Group Databasebeta

← #11783920

Subgroups — #11783920

Order 1152.

795 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 795 conjugacy classes of subgroups — too many to draw. Only its 188 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#41×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#837C212yesmaximal
3#10591222C211yesmaximal, characteristic, complemented
4#10591060C211yesmaximal, characteristic, complemented
5#10589162C212yesmaximal, complemented
6#70354—32nomaximal
7C2×C32×#41C2211yescharacteristic
8Q8×C3⋊Dic3C412yescomplemented
9D4×C3⋊Dic3—22no—
10D4×C3⋊Dic3C412yescomplemented
11#64135—21no—
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17C3×#837C418yescomplemented
18#63579—22no—
19#63555—21no—
20#63553—21no—
21Dic3×#41—32no—
22Dic3×#41—61no—
23C2×C3×#104—32no—
24C2×#837D312yes—
25Dic3×M16—32no—
26#4932—32no—
27#4555—32no—
28#4523—32no—
29C32×#41—22no—
30C32×#41C2×C414yes—
31C2×C32×Q8C2×C411yescharacteristic
32C2×C32×D4—21no—
33C2×C32×D4C2×C411yescharacteristic
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3D412yes—
38C22×C3×Dic3—22no—
39#3757—21no—
40#3757—22no—
41C4⋊(C3⋊Dic3)—22no—
42C4⋊(C3⋊Dic3)C2×C412yes—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—22no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C3×C4×Dic3—22no—
49C3×C4×Dic3C2×C414yescomplemented
50C3×#208—22no—
51C3×#208C2×C414yescomplemented
52C2×C3×C3⋊C8—22no—
53#1759—91noSylow
54C2×C3×#41—21no—
55C2×C3×#41C2×D312yes—
56C2×C3×M16—32no—
57C2×C3×C42—32no—
58Q8×Dic3—34no—
59Q8×Dic3—62no—
60D4×Dic3—34no—
61D4×Dic3—62no—
62D4×Dic3—64no—
63D4×Dic3—64no—
64#926—32no—
65#926—61no—
66#926—62no—
67#926—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—62no—
71C2×C4×Dic3—62no—
72C2×C4×Dic3C2×D312yes—
73C2×#208C2×D312yes—
74C3×#104—38no—
75#837Dic318yescomplemented
76C3⋊#95—64no—
77#815—62no—
78C8×Dic3—62no—
79C23×C32—21no—
80C23×C32C2×D411yescharacteristic
81C32×Q8—21no—
82C32×Q8C4212yes—
83C32×D4—24no—
84C32×D4—21no—
85C32×D4C4212yes—
86C2×C32×C4—21no—
87C2×C32×C4—24no—
88C2×C32×C4C22×C411yescharacteristic
89C2×C32×C4C22×C412yes—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4#4112yes—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—42no—
94C2×C3⋊Dic3—44no—
95C2×C3⋊Dic3C22⋊C412yes—
96C2×C3⋊Dic3C22⋊C412yes—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99C3×C3⋊C8—24no—
100C4×#41—91no—
101C2×#104—32no—
102C4×M16—91no—
103#376—91no—
104#339—92no—
105C3×#41—24no—
106C3×#41—22no—
107C3×#41—22no—
108C3×#41—24no—
109C3×#41C4×D314yes—
110C3×#41C2×Dic314yes—
111C2×C3×Q8—21no—
112C2×C3×Q8C4×D312yes—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—21no—
116C2×C3×D4C4×D312yes—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—34no—
124C22×Dic3—62no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127C3×M16—34no—
128C3×M16—62no—
129C2×C3×C8—62no—
130C3×C42—34no—
131C3×C42—62no—
132#217—64no—
133#217—64no—
134#217—62no—
135#217—62no—
136C4⋊Dic3—34no—
137C4⋊Dic3—62no—
138C4⋊Dic3—64no—
139C4⋊Dic3—64no—
140C4×Dic3—22no—
141C4×Dic3—34no—
142C4×Dic3—32no—
143C4×Dic3—32no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—62no—
147C4×Dic3—64no—
148C4×Dic3—62no—
149C4×Dic3—64no—
150C4×Dic3—62no—
151C4×Dic3C2×Dic314yescomplemented
152#208—22no—
153#208C2×Dic314yescomplemented
154C2×C3⋊C8—22no—
155C22×C32—22no—
156C22×C32—22no—
157C22×C32—42no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32C4×D412yes—
160C32×C4—22no—
161C32×C4C2×C4211yescharacteristic
162C32×C4#11711yescharacteristic
163C32×C4C4×D412yes—
164C3⋊Dic3—22no—
165C3⋊Dic3—22no—
166C3⋊Dic3—42no—
167C3×Dic3—44no—
168C2×#41D3211yescharacteristic
169C2×M16—32no—
170C4×Q8—92no—
171C4×D4—92no—
172C4×D4—182no—
173#117—91no—
174#117—181no—
175C2×C42—32no—
176C2×C42—91no—
177C2×C42—181no—
178#104—38no—
179#97—181no—
180C4×C8—181no—
181#95—182no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—21no—
185C23×C3D3×D412yes—
186C3×Q8—22no—
187C3×Q8—22no—
188C3×Q8—22no—
189C3×Q8C4×Dic314yes—
190C3×D4—28no—
191C3×D4—22no—
192C3×D4—24no—
193C3×D4—24no—
194C3×D4—22no—
195C3×D4—22no—
196C3×D4C4×Dic314yes—
197C2×C3×C4—22no—
198C2×C3×C4—28no—
199C2×C3×C4—22no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—64no—
207C2×C3×C4—124no—
208C2×C3×C4C2×C4×D312yes—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4D3×D412yes—
211C2×C3×C4#23712yes—
212C2×C3×C4#23712yes—
213C2×C3×C4C22×Dic312yes—
214C2×Dic3—24no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—44no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C2×Dic3—128no—
225C2×Dic3—128no—
226C3×C8—64no—
227C3⋊C8—24no—
228C2×C32—22no—
229C2×C32—42no—
230C2×C32C4×C22⋊C411yescharacteristic
231C2×C32#42112yes—
232#41—22no—
233#41D3×Dic314yes—
234C2×Q8#62411yescharacteristic
235C2×D4—21no—
236C2×D4#62411yescharacteristic
237C22×C4—21no—
238C22×C4—62no—
239C22×C4—92no—
240C22×C4—182no—
241C22×C4C2×D3211yescharacteristic
242M16—34no—
243M16—62no—
244C2×C8—62no—
245C4⋊C4—92no—
246C4⋊C4—182no—
247C22⋊C4—182no—
248C22⋊C4—181no—
249C42—34no—
250C42—62no—
251C42—92no—
252C42—91no—
253C42—91no—
254C42—182no—
255C42—181no—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3—24no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—42no—
262C22×C3—44no—
263C22×C3—44no—
264C22×C3D3×C22⋊C412yes—
265C22×C3#67⋊C412yes—
266C22×C3D4×Dic312yes—
267C3×C4—24no—
268C3×C4—24no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—124no—
273C3×C4#87712yes—
274C3×C4#67⋊C412yes—
275C3×C4C2×C4×Dic312yes—
276C3×C4D4×Dic312yes—
277Dic3—44no—
278Dic3—64no—
279Dic3—64no—
280Dic3—64no—
281Dic3—122no—
282Dic3—124no—
283Dic3—124no—
284C32#175911yescharacteristic, complemented, Sylow
285C23—21no—
286C23#381111yescharacteristic
287Q8—21no—
288Q8Dic3212yes—
289D4—24no—
290D4—21no—
291D4Dic3212yes—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—64no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—124no—
298C2×C4—182no—
299C2×C4—362no—
300C2×C4—364no—
301C2×C4C2×D3×Dic312yes—
302C2×C4#380512yes—
303C2×C4C2×#62411yescharacteristic
304C2×C4#381111yescharacteristic
305C8—64no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—42no—
311C2×C3—44no—
312C2×C3—44no—
313C2×C3#482114yes—
314C2×C3Dic3×C22⋊C412yes—
315C22—22no—
316C22—22no—
317C22—42no—
318C22#67⋊Dic312yes—
319C22#6397411yescharacteristic
320C4—22no—
321C4—124no—
322C4—182no—
323C4—182no—
324C4—362no—
325C4C2×Dic3211yescharacteristic
326C4#6395711yescharacteristic
327C4#67⋊Dic312yes—
328C3—21no—
329C3#7035412yescomplemented
330C2—22no—
331C2—42no—
332C2#1059167212yes—
333C2#1059170511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10591222C2semidirect
4. #10591060C2semidirect
5. #10589162C2semidirect
8. Q8×C3⋊Dic3C4semidirect
10. D4×C3⋊Dic3C4semidirect
17. C3×#837C4semidirect
49. C3×C4×Dic3C2×C4semidirect
51. C3×#208C2×C4semidirect
75. #837Dic3semidirect
151. C4×Dic3C2×Dic3semidirect
153. #208C2×Dic3semidirect
284. C32#1759semidirect
329. C3#70354semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C3×#8372
#105912222
#105910602
#105891622
#703543