Finite Group Databasebeta

← #11783909

Subgroups — #11783909

Order 1152.

795 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 795 conjugacy classes of subgroups — too many to draw. Only its 156 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#10595993C211yesmaximal, characteristic
2#10591222C211yesmaximal, characteristic, complemented
3C2×#63570C212yesmaximal
4#10591060C211yesmaximal, characteristic, complemented
5C3×#4532C212yesmaximal, complemented
6#68729—32nomaximal
7C2×#3828C2211yescharacteristic
8C32×#117C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64102C412yescomplemented
11#64096C412yescomplemented
12#64090—22no—
13#64081—21no—
14C42×C3⋊D3—21no—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17#63579—22no—
18#63570C418yescomplemented
19#63555—21no—
20#63553—21no—
21#5522—32no—
22#5522—61no—
23C2×#825—32no—
24Dic3×M16—32no—
25#4932—32no—
26C2×#805—32no—
27C3×#339—32no—
28#4532D312yescomplemented
29C22×C32×C4C2311yescharacteristic
30C2×#638—21no—
31C22×C3⋊Dic3D412yes—
32#3828—22no—
33#3828C2×C414yes—
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—22no—
37C2×#634C2×C411yescharacteristic
38C22×C3×Dic3—22no—
39C32×C4⋊C4C2×C412yes—
40C32×C22⋊C4—21no—
41C32×C42—21no—
42#3752—22no—
43#3750—22no—
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×#235—32no—
55C2×#235—61no—
56C2×C3×M16—32no—
57C3×#117—21no—
58C3×#117C2×D312yes—
59C2×C3×C42—32no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3C2×D312yes—
63C2×#208C2×D312yes—
64#893—34no—
65#893—62no—
66#887—34no—
67#887—62no—
68#67⋊C4—64no—
69#67⋊C4—64no—
70#872—62no—
71#872—62no—
72C42×D3—62no—
73C42×D3—62no—
74C3⋊#95—64no—
75#825—38no—
76#815—62no—
77C8×Dic3—62no—
78#805—38no—
79C23×C32C2×D411yescharacteristic
80C22×C3⋊D3—21no—
81C2×C32×C4—22no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C22×C412yes—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4#4112yes—
86#638—24no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3C22⋊C412yes—
90C2×C3⋊Dic3C22⋊C412yes—
91C4⋊(C3⋊D3)—21no—
92C4⋊(C3⋊D3)C4212yes—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—44no—
95#634—21no—
96#634C4212yes—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—44no—
99C3×C3⋊C8—24no—
100C4×#41—91no—
101C2×#104—92no—
102C4×M16—91no—
103#376—91no—
104#339—32no—
105C22×C3×C4—21no—
106C22×C3×C4—62no—
107C22×C3×C4C22×D312yes—
108C2×#67—62no—
109C2×#67—62no—
110C22×Dic3—22no—
111C22×Dic3—34no—
112C22×Dic3—62no—
113#235—34no—
114#235—34no—
115#235—64no—
116#235—64no—
117#235—62no—
118#235—62no—
119C2×D12—32no—
120C2×D12—61no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—64no—
124C2×C4×D3—64no—
125C2×Dic6—32no—
126C2×Dic6—61no—
127C3×M16—34no—
128C3×M16—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4C4×D314yes—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—22no—
134C3×C42—22no—
135C3×C42—22no—
136C3×C42—34no—
137C3×C42—62no—
138(C2×D3)⋊C4—64no—
139(C2×D3)⋊C4—64no—
140Dic3⋊C4—64no—
141Dic3⋊C4—64no—
142C4×Dic3—22no—
143C4×Dic3—34no—
144C4×Dic3—32no—
145C4×Dic3—32no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—62no—
149C4×Dic3—64no—
150C4×Dic3—64no—
151C4×Dic3C4×D314yescomplemented
152#208—22no—
153#208C4×D314yescomplemented
154C2×C3⋊C8—22no—
155C22×C32—22no—
156C22×C32C2×C22⋊C411yescharacteristic
157C22×C32C4×D412yes—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—42no—
160C32×C4—42no—
161C32×C4C2×C4211yescharacteristic
162C32×C4#11711yescharacteristic
163C32×C4C4×D412yes—
164C3⋊Dic3—22no—
165C3⋊Dic3—22no—
166C3⋊Dic3—22no—
167C3×Dic3—44no—
168C2×#41—91no—
169C2×M16—32no—
170C4×Q8—92no—
171C4×D4—92no—
172C4×D4—182no—
173#117—181no—
174#117D3211yescharacteristic
175C2×C42—32no—
176C2×C42—91no—
177C2×C42—181no—
178#104—98no—
179#97—181no—
180C4×C8—181no—
181#95—182no—
182C23×C3—21no—
183C23×C3D3×D412yes—
184C22×D3—62no—
185C22×D3—62no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—64no—
193C2×C3×C4—124no—
194C2×C3×C4C2×C4×D312yes—
195C2×C3×C4C2×C4×D312yes—
196C2×C3×C4C2×C4×D312yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4#23712yes—
199C2×C3×C4#23912yes—
200#67—68no—
201#67—64no—
202#67—64no—
203C2×Dic3—24no—
204C2×Dic3—34no—
205C2×Dic3—34no—
206C2×Dic3—44no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213D12—34no—
214D12—62no—
215D12—62no—
216D12—62no—
217C4×D3—68no—
218C4×D3—64no—
219C4×D3—64no—
220C4×D3—128no—
221C4×D3—128no—
222Dic6—34no—
223Dic6—62no—
224Dic6—62no—
225Dic6—62no—
226C3×C8—64no—
227C3⋊C8—24no—
228C2×C32—22no—
229C2×C32C4×C22⋊C411yescharacteristic
230C2×C32#42112yes—
231C3⋊D3—42no—
232#41—94no—
233#41—182no—
234C2×Q8—91no—
235C2×D4—91no—
236C2×D4—181no—
237C22×C4—62no—
238C22×C4—92no—
239C22×C4—182no—
240C22×C4—181no—
241C22×C4C2×D3211yescharacteristic
242M16—34no—
243M16—62no—
244C2×C8—62no—
245C4⋊C4—182no—
246C4⋊C4#62412yes—
247C22⋊C4—21no—
248C22⋊C4—182no—
249C42—21no—
250C42—34no—
251C42—62no—
252C42—92no—
253C42—91no—
254C42—91no—
255C42—182no—
256C22×C3—24no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—42no—
260C22×C3D3×C22⋊C412yes—
261C22×C3#67⋊C412yes—
262C22×C3#89312yes—
263C2×D3—64no—
264C2×D3—64no—
265C2×D3—124no—
266C2×D3—124no—
267C3×C4—21no—
268C3×C4—22no—
269C3×C4—21no—
270C3×C4—44no—
271C3×C4—44no—
272C3×C4—124no—
273C3×C4C42×D312yes—
274C3×C4#67⋊C412yes—
275C3×C4#89212yes—
276C3×C4#89312yes—
277Dic3—44no—
278Dic3—64no—
279Dic3—64no—
280Dic3—64no—
281Dic3—64no—
282Dic3—64no—
283Dic3—122no—
284C32#175911yescharacteristic, complemented, Sylow
285C23—181no—
286C23#381111yescharacteristic
287Q8—92no—
288Q8—181no—
289D4—92no—
290D4—184no—
291D4—181no—
292C2×C4—22no—
293C2×C4—64no—
294C2×C4—92no—
295C2×C4—92no—
296C2×C4—124no—
297C2×C4—181no—
298C2×C4—184no—
299C2×C4—364no—
300C2×C4—362no—
301C2×C4#379612yes—
302C2×C4C4×D3212yes—
303C2×C4C2×#62411yescharacteristic
304C2×C4#381111yescharacteristic
305C8—64no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—22no—
310C2×C3—42no—
311C2×C3#466612yes—
312C2×C3#482114yes—
313D3—124no—
314D3—124no—
315C22—22no—
316C22—182no—
317C22—362no—
318C22#6388112yes—
319C22#6397411yescharacteristic
320C4—42no—
321C4—124no—
322C4—182no—
323C4—182no—
324C4—182no—
325C4#6384911yescharacteristic
326C4#6388112yes—
327C4C4×#62411yescharacteristic
328C3—21no—
329C3#6872912yescomplemented
330C2—22no—
331C2—362no—
332C2#1059126011yescharacteristic
333C2#1059167212yes—
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10591222C2semidirect
4. #10591060C2semidirect
5. C3×#4532C2semidirect
10. #64102C4semidirect
11. #64096C4semidirect
18. #63570C4semidirect
28. #4532D3semidirect
49. C3×C4×Dic3C2×C4semidirect
51. C3×#208C2×C4semidirect
151. C4×Dic3C4×D3semidirect
153. #208C4×D3semidirect
284. C32#1759semidirect
329. C3#68729semidirect

Maximal subgroups

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

subgroupindex
#105959932
#105912222
C2×#635702
#105910602
C3×#45322
#687293