Finite Group Databasebeta

← #11783742

Subgroups — #11783742

Order 1152.

1236 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 223 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
1C2×#64090C211yesmaximal, characteristic
2C2×#63633C212yesmaximal
3C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
4C32×#342C211yesmaximal, characteristic, complemented
5#10589392C211yesmaximal, characteristic, complemented
6#68952—34nomaximal
7C22×#638C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C22×C4×C3⋊D3C411yescharacteristic, complemented
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C2212yes—
12C2×#3757C2212yes—
13C2×#3752C411yescharacteristic, complemented
14C2×#3750C411yescharacteristic, complemented
15C2×C4×C3⋊Dic3—22no—
16C2×C4×C3⋊Dic3C411yescharacteristic, complemented
17#64090—22no—
18#64090—22no—
19#63658—22no—
20#63633C418yescomplemented
21C2×#67⋊C4—34no—
22C2×#806—38no—
23Dic3×C22⋊C4—38no—
24C3×#342D314yescomplemented
25#4526—34no—
26C24×C32C2311yescharacteristic
27C23×C3⋊D3C2×C411yescharacteristic
28C22×C32×C4—22no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C2×#638—22no—
32C2×#638—21no—
33C2×#638—21no—
34C2×#638C2×C414yes—
35C22×C3⋊Dic3—22no—
36C22×C3⋊Dic3—42no—
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C22×C3⋊Dic3D412yes—
41C22×C3⋊Dic3D412yes—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—42no—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C22⋊C4C2×C414yescomplemented
48#3757—22no—
49#3757C2×C414yescomplemented
50#3752—22no—
51#3750—22no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—44no—
55C4×#99—91noSylow
56C22×#67—34no—
57C23×Dic3—34no—
58C22×C4×D3—34no—
59C2×C3×C22⋊C4C2×D314yes—
60C2×C3×C22⋊C4C2×D318yes—
61C2×#217—38no—
62C2×(C2×D3)⋊C4—34no—
63C2×Dic3⋊C4—34no—
64C2×C4×Dic3—34no—
65C2×C4×Dic3—68no—
66#67⋊C4—68no—
67#67⋊C4—68no—
68C3⋊#95—68no—
69#806—332no—
70C23×C32—41no—
71C23×C32—41no—
72C23×C32C22×C411yescharacteristic
73C23×C32C22×C412yes—
74C23×C32C2×D412yes—
75C23×C32#4111yescharacteristic
76C23×C32#4111yescharacteristic
77C22×C3⋊D3—21no—
78C22×C3⋊D3—21no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3C4212yescomplemented
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4—24no—
85C2×C32×C4—42no—
86C2×C32×C4—42no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89#638—24no—
90#638—24no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—42no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3—42no—
100C2×C3⋊Dic3C4212yescomplemented
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C412yes—
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4×C3⋊D3—42no—
105C4×C3⋊D3—42no—
106C2×C4×D4—91no—
107C2×#99—92no—
108C4×C22⋊C4—92no—
109#342—91no—
110#342C3⋊D311yescharacteristic, complemented
111C24×C3C22×D314yes—
112C23×D3—34no—
113C22×C3×C4—28no—
114C22×C3×C4C4×D314yes—
115C22×C3×C4C4×D314yes—
116C2×#67—316no—
117C2×#67—68no—
118C2×#67—64no—
119C2×#67—64no—
120C22×Dic3—34no—
121C22×Dic3—34no—
122C22×Dic3—38no—
123C22×Dic3—34no—
124C22×Dic3—38no—
125C22×Dic3—68no—
126C22×Dic3—128no—
127C2×C4×D3—64no—
128C2×C4×D3—64no—
129C2×C4×D3—128no—
130C3×C22⋊C4—28no—
131C3×C22⋊C4—28no—
132C3×C22⋊C4C4×D3116yescomplemented
133#217—316no—
134#217—68no—
135(C2×D3)⋊C4—68no—
136Dic3⋊C4—68no—
137C4×Dic3—64no—
138C4×Dic3—64no—
139C4×Dic3—1216no—
140C22×C32—22no—
141C22×C32—21no—
142C22×C32—22no—
143C22×C32—21no—
144C22×C32—42no—
145C22×C32—41no—
146C22×C32—41no—
147C22×C32C2×C4211yescharacteristic
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32#11711yescharacteristic
150C22×C32C4×D412yes—
151C22×C32C4×D412yes—
152C2×C3⋊D3—22no—
153C2×C3⋊D3—42no—
154C2×C3⋊D3—41no—
155C2×C3⋊D3—41no—
156C2×C3⋊D3—42no—
157C32×C4—44no—
158C32×C4—41no—
159C32×C4—41no—
160C3⋊Dic3—22no—
161C3⋊Dic3—21no—
162C3⋊Dic3—22no—
163C3⋊Dic3—44no—
164C3⋊Dic3#9912yescomplemented
165C22×D4—91no—
166C23×C4—91no—
167C23×C4—91no—
168C4×D4—182no—
169C4×D4—182no—
170C2×C4⋊C4—91no—
171C2×C22⋊C4—92no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4C2×C3⋊D311yescharacteristic
174C2×C22⋊C4C2×C3⋊D312yes—
175C2×C42—91no—
176C2×C42—182no—
177#99—98no—
178#95—182no—
179C23×C3—44no—
180C23×C3—44no—
181C23×C3C2×C4×D314yes—
182C23×C3C2×C4×D318yes—
183C23×C3D3×D418yes—
184C23×C3#23714yes—
185C23×C3#23914yes—
186C22×D3—38no—
187C22×D3—64no—
188C22×D3—64no—
189C22×D3—124no—
190C22×D3—124no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—216no—
194C2×C3×C4—48no—
195C2×C3×C4—48no—
196C2×C3×C4—44no—
197C2×C3×C4—44no—
198#67—616no—
199#67—616no—
200C2×Dic3—34no—
201C2×Dic3—38no—
202C2×Dic3—34no—
203C2×Dic3—38no—
204C2×Dic3—616no—
205C2×Dic3—68no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—616no—
209C2×Dic3—128no—
210C2×Dic3—124no—
211C2×Dic3—128no—
212C2×Dic3—128no—
213C4×D3—128no—
214C4×D3—128no—
215C2×C32—22no—
216C2×C32—22no—
217C2×C32—21no—
218C2×C32—21no—
219C2×C32C4×C22⋊C411yescharacteristic
220C2×C32C2×#9911yescharacteristic
221C2×C32#41011yescharacteristic
222C3⋊D3—42no—
223C24—91no—
224C24C22×C3⋊D311yescharacteristic
225C2×D4—94no—
226C2×D4—182no—
227C2×D4—181no—
228C2×D4—181no—
229C22×C4—22no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—92no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4—182no—
238C22×C4—362no—
239C22×C4—362no—
240C22×C4C4×C3⋊D311yescharacteristic
241C22×C4C4×C3⋊D311yescharacteristic
242C4⋊C4—182no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—94no—
246C22⋊C4—182no—
247C22⋊C4—182no—
248C22⋊C4C4×C3⋊D314yescomplemented
249C42—181no—
250C42—181no—
251C42—364no—
252C22×C3—28no—
253C22×C3—24no—
254C22×C3—28no—
255C22×C3—24no—
256C22×C3—48no—
257C22×C3—44no—
258C22×C3—44no—
259C22×C3C42×D314yes—
260C22×C3D3×C22⋊C414yes—
261C22×C3#67⋊C418yes—
262C22×C3#89214yes—
263C22×C3#89318yes—
264C2×D3—68no—
265C2×D3—128no—
266C2×D3—124no—
267C2×D3—124no—
268C2×D3—128no—
269C3×C4—416no—
270C3×C4—44no—
271C3×C4—44no—
272Dic3—38no—
273Dic3—68no—
274Dic3—64no—
275Dic3—68no—
276Dic3—1216no—
277C32C4×#9911yescharacteristic, complemented, Sylow
278C23—41no—
279C23—41no—
280C23—92no—
281C23—181no—
282C23—181no—
283C23—361no—
284C23—361no—
285C23C2×C4×C3⋊D311yescharacteristic
286C23C2×C4×C3⋊D312yes—
287C23D4×C3⋊D312yes—
288C23#383011yescharacteristic
289C23#383211yescharacteristic
290D4—184no—
291D4—184no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—91no—
300C2×C4—92no—
301C2×C4—91no—
302C2×C4—92no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—184no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4—361no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C3—28no—
315C2×C3—28no—
316C2×C3—24no—
317C2×C3—24no—
318C2×C3#466614yes—
319C2×C3#474014yes—
320C2×C3D3×#9914yes—
321D3—128no—
322C22—22no—
323C22—21no—
324C22—22no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—182no—
330C22—362no—
331C22—362no—
332C22—361no—
333C22—361no—
334C22C42×C3⋊D311yescharacteristic
335C22C22⋊C4×C3⋊D311yescharacteristic
336C22#6409012yes—
337C22#6410111yescharacteristic
338C22#6410212yes—
339C4—44no—
340C4—41no—
341C4—41no—
342C4—92no—
343C4—182no—
344C4—181no—
345C4—182no—
346C4—364no—
347C3#6895214yescomplemented
348C2—22no—
349C2—22no—
350C2—21no—
351C2—21no—
352C2—362no—
353C2#1059236511yescharacteristic
354C2#1059243911yescharacteristic
355C2C3⋊D3×#9911yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC24C22×C3⋊D3
FittingC32×#342C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenter#342C3⋊D3
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×C3⋊Dic3C2semidirect
4. C32×#342C2semidirect
5. #10589392C2semidirect
9. C22×C4×C3⋊D3C4semidirect
13. C2×#3752C4semidirect
14. C2×#3750C4semidirect
16. C2×C4×C3⋊Dic3C4semidirect
20. #63633C4semidirect
24. C3×#342D3semidirect
47. C32×C22⋊C4C2×C4semidirect
49. #3757C2×C4semidirect
81. C22×C3⋊D3C42semidirect
100. C2×C3⋊Dic3C42semidirect
110. #342C3⋊D3semidirect
132. C3×C22⋊C4C4×D3semidirect
164. C3⋊Dic3#99semidirect
248. C22⋊C4C4×C3⋊D3semidirect
277. C32C4×#99semidirect
347. C3#68952semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#636332
C22⋊C4×C3⋊Dic32
C32×#3422
#105893922
#689523