Finite Group Databasebeta

← C3⋊D3×#342 #11783343

Subgroups — C3⋊D3×#342 #11783343

Order 1152.

2040 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 2040 conjugacy classes of subgroups — too many to draw. Only its 261 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×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×C22⋊C4×C3⋊D3C212yesmaximal
3C32×#342C211yesmaximal, characteristic, complemented
4#10589393C212yesmaximal, complemented
5#10589392C211yesmaximal, characteristic, complemented
6D3×#342—34nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C22×C4×C3⋊D3—22no—
9C22×C4×C3⋊D3C412yescomplemented
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×C32×C22⋊C4C2212yes—
12C2×#3757C2211yescharacteristic
13C2×#3757C2212yes—
14C2×#3752—22no—
15C2×#3752C412yescomplemented
16C22⋊C4×C3⋊D3—22no—
17C22⋊C4×C3⋊D3—24no—
18C22⋊C4×C3⋊D3—22no—
19C22⋊C4×C3⋊D3C418yescomplemented
20C2×D3×C22⋊C4—38no—
21C2×D3×C22⋊C4—34no—
22C3×#342D314yescomplemented
23#4527—38no—
24#4526—34no—
25C24×C32C2311yescharacteristic
26C23×C3⋊D3—44no—
27C23×C3⋊D3C2×C411yescharacteristic
28C23×C3⋊D3C2×C414yes—
29C23×C3⋊D3C2×C411yescharacteristic
30C23×C3⋊D3D412yes—
31C23×C3⋊D3D412yes—
32C23×C3⋊D3D412yes—
33C23×C3⋊D3Q812yes—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yescomplemented
36C22×C3⋊Dic3—22no—
37C22×C3⋊Dic3C2×C412yescomplemented
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—22no—
40C2×C4×C3⋊D3—28no—
41C2×C4×C3⋊D3—48no—
42C2×C4×C3⋊D3—44no—
43C32×C22⋊C4—22no—
44C32×C22⋊C4—22no—
45C32×C22⋊C4C2×C414yescomplemented
46#3757—22no—
47#3757—22no—
48#3757C2×C414yescomplemented
49#3752—24no—
50#3752—28no—
51C2×#342—91noSylow
52C24×D3—34no—
53C22×C4×D3—38no—
54C22×C4×D3—68no—
55C2×C3×C22⋊C4C2×D314yes—
56C2×C3×C22⋊C4C2×D318yes—
57C2×#217—38no—
58C2×#217—34no—
59C2×(C2×D3)⋊C4—38no—
60C2×(C2×D3)⋊C4—68no—
61D3×C22⋊C4—332no—
62D3×C22⋊C4—616no—
63D3×C22⋊C4—68no—
64D3×C22⋊C4—68no—
65C23×C32—42no—
66C23×C32C22×C411yescharacteristic
67C23×C32C22×C412yes—
68C23×C32C2×D412yes—
69C23×C32C2×D411yescharacteristic
70C23×C32C2×Q811yescharacteristic
71C22×C3⋊D3—24no—
72C22×C3⋊D3—28no—
73C22×C3⋊D3—48no—
74C22×C3⋊D3—44no—
75C22×C3⋊D3—44no—
76C22×C3⋊D3—42no—
77C22×C3⋊D3—44no—
78C22×C3⋊D3C4212yes—
79C22×C3⋊D3C4212yes—
80C22×C3⋊D3C22⋊C412yes—
81C22×C3⋊D3C22⋊C411yescharacteristic
82C22×C3⋊D3C22⋊C414yes—
83C22×C3⋊D3C22⋊C414yes—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C22×C3⋊D3C4⋊C412yes—
86C22×C3⋊D3C4⋊C414yes—
87C22×C3⋊D3C4⋊C414yes—
88C22×C3⋊D3C4⋊C412yes—
89C2×C32×C4—22no—
90C2×C32×C4—24no—
91C2×C32×C4—44no—
92C2×C32×C4—42no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—24no—
95C2×C3⋊Dic3—44no—
96C2×C3⋊Dic3—42no—
97C4×C3⋊D3—416no—
98C4×C3⋊D3—44no—
99C4×C3⋊D3—44no—
100C22×C22⋊C4—92no—
101C22×C22⋊C4—91no—
102#342—91no—
103#342—92no—
104#342C3⋊D311yescharacteristic, direct product factor
105C24×C3C22×D314yes—
106C23×D3—34no—
107C23×D3—38no—
108C23×D3—316no—
109C23×D3—34no—
110C23×D3—38no—
111C23×D3—38no—
112C23×D3—38no—
113C23×D3—1216no—
114C22×C3×C4—28no—
115C22×C3×C4C4×D318yescomplemented
116C22×Dic3—38no—
117C22×Dic3—68no—
118C2×C4×D3—632no—
119C2×C4×D3—68no—
120C2×C4×D3—68no—
121C2×C4×D3—1232no—
122C2×C4×D3—1216no—
123C3×C22⋊C4—28no—
124C3×C22⋊C4—28no—
125C3×C22⋊C4C4×D3116yescomplemented
126#217—316no—
127#217—68no—
128#217—68no—
129(C2×D3)⋊C4—632no—
130(C2×D3)⋊C4—616no—
131C22×C32—22no—
132C22×C32—24no—
133C22×C32—42no—
134C22×C32—41no—
135C22×C32—41no—
136C22×C32C2×C4211yescharacteristic
137C22×C32C2×C22⋊C412yes—
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32C2×C4⋊C411yescharacteristic
140C22×C32C2×C4⋊C412yes—
141C2×C3⋊D3—22no—
142C2×C3⋊D3—24no—
143C2×C3⋊D3—28no—
144C2×C3⋊D3—24no—
145C2×C3⋊D3—24no—
146C2×C3⋊D3—28no—
147C2×C3⋊D3—42no—
148C2×C3⋊D3—44no—
149C2×C3⋊D3—44no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3#9512yes—
152C2×C3⋊D3#9514yes—
153C2×C3⋊D3#9512yes—
154C2×C3⋊D3#9914yes—
155C32×C4—44no—
156C32×C4—42no—
157C3⋊Dic3—44no—
158C3⋊Dic3—42no—
159C25—91no—
160C23×C4—92no—
161C23×C4—182no—
162C2×C22⋊C4—92no—
163C2×C22⋊C4—98no—
164C2×C22⋊C4—91no—
165C2×C22⋊C4—92no—
166C2×C22⋊C4—184no—
167C2×C22⋊C4—182no—
168C2×C22⋊C4—182no—
169C2×C22⋊C4—182no—
170C2×C22⋊C4C2×C3⋊D311yescharacteristic
171C2×C22⋊C4C2×C3⋊D312yes—
172C23×C3—48no—
173C23×C3C2×C4×D314yes—
174C23×C3C2×C4×D318yes—
175C23×C3D3×D418yes—
176C23×C3D3×D414yes—
177C23×C3D3×Q814yes—
178C22×D3—34no—
179C22×D3—38no—
180C22×D3—38no—
181C22×D3—316no—
182C22×D3—34no—
183C22×D3—38no—
184C22×D3—316no—
185C22×D3—38no—
186C22×D3—316no—
187C22×D3—316no—
188C22×D3—38no—
189C22×D3—632no—
190C22×D3—616no—
191C22×D3—1216no—
192C22×D3—1232no—
193C22×D3—1216no—
194C22×D3—1216no—
195C22×D3—128no—
196C2×C3×C4—28no—
197C2×C3×C4—216no—
198C2×C3×C4—416no—
199C2×C3×C4—48no—
200C2×Dic3—616no—
201C2×Dic3—68no—
202C2×Dic3—1216no—
203C2×Dic3—128no—
204C4×D3—1216no—
205C4×D3—1264no—
206C4×D3—1216no—
207C2×C32—22no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32—22no—
211C2×C32C2×#9511yescharacteristic
212C2×C32C2×#9912yes—
213C3⋊D3—22no—
214C3⋊D3—24no—
215C3⋊D3#34214yesdirect product factor
216C24—91no—
217C24—92no—
218C24—94no—
219C24—91no—
220C24—92no—
221C24—92no—
222C24—92no—
223C24—364no—
224C24C22×C3⋊D311yescharacteristic
225C22×C4—22no—
226C22×C4—92no—
227C22×C4—188no—
228C22×C4—182no—
229C22×C4—182no—
230C22×C4—182no—
231C22×C4—368no—
232C22×C4—364no—
233C22×C4C4×C3⋊D312yescomplemented
234C22⋊C4—22no—
235C22⋊C4—22no—
236C22⋊C4—94no—
237C22⋊C4—188no—
238C22⋊C4—184no—
239C22⋊C4—182no—
240C22⋊C4—182no—
241C22⋊C4C4×C3⋊D314yescomplemented
242C22×C3—28no—
243C22×C3—216no—
244C22×C3—48no—
245C22×C3—44no—
246C22×C3—44no—
247C22×C3C42×D314yes—
248C22×C3D3×C22⋊C418yes—
249C22×C3D3×C22⋊C414yes—
250C22×C3D3×C4⋊C414yes—
251C22×C3D3×C4⋊C418yes—
252C2×D3—38no—
253C2×D3—316no—
254C2×D3—38no—
255C2×D3—316no—
256C2×D3—632no—
257C2×D3—616no—
258C2×D3—632no—
259C2×D3—616no—
260C2×D3—68no—
261C2×D3—616no—
262C2×D3—1216no—
263C2×D3—128no—
264C2×D3—128no—
265C2×D3—1216no—
266C3×C4—416no—
267C3×C4—48no—
268Dic3—1216no—
269Dic3—128no—
270C32C2×#34211yescharacteristic, complemented, Sylow
271C23—42no—
272C23—91no—
273C23—92no—
274C23—94no—
275C23—92no—
276C23—91no—
277C23—92no—
278C23—94no—
279C23—92no—
280C23—94no—
281C23—94no—
282C23—92no—
283C23—184no—
284C23—188no—
285C23—362no—
286C23—364no—
287C23—368no—
288C23—364no—
289C23—364no—
290C23C2×C4×C3⋊D311yescharacteristic
291C23C2×C4×C3⋊D312yes—
292C23D4×C3⋊D312yes—
293C23D4×C3⋊D311yescharacteristic
294C23Q8×C3⋊D311yescharacteristic
295C2×C4—24no—
296C2×C4—22no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—184no—
300C2×C4—182no—
301C2×C4—364no—
302C2×C4—3616no—
303C2×C4—364no—
304C2×C4—364no—
305C2×C4—362no—
306C2×C3—28no—
307C2×C3—24no—
308C2×C3—24no—
309C2×C3—28no—
310C2×C3D3×#9514yes—
311C2×C3D3×#9918yes—
312D3—316no—
313D3—616no—
314D3—68no—
315C22—22no—
316C22—24no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—92no—
321C22—94no—
322C22—92no—
323C22—94no—
324C22—188no—
325C22—184no—
326C22—184no—
327C22—188no—
328C22—182no—
329C22—184no—
330C22—364no—
331C22—362no—
332C22—362no—
333C22—364no—
334C22C42×C3⋊D311yescharacteristic
335C22C22⋊C4×C3⋊D312yes—
336C22C22⋊C4×C3⋊D311yescharacteristic
337C22C4⋊C4×C3⋊D311yescharacteristic
338C22C4⋊C4×C3⋊D312yes—
339C4—44no—
340C4—42no—
341C4—364no—
342C4—362no—
343C3D3×#34214yescomplemented
344C2—22no—
345C2—21no—
346C2—21no—
347C2—22no—
348C2—94no—
349C2—184no—
350C2—182no—
351C2C3⋊D3×#9511yescharacteristic
352C2C3⋊D3×#9912yes—
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C2×C42
FrattiniC24C22×C3⋊D3
FittingC32×#342C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C22
cosocleC24×C32C23
hypercenter#342C3⋊D3
hypocenterC32C2×#342
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. C32×#342C2semidirect
4. #10589393C2semidirect
5. #10589392C2semidirect
9. C22×C4×C3⋊D3C4semidirect
15. C2×#3752C4semidirect
19. C22⋊C4×C3⋊D3C4semidirect
22. C3×#342D3semidirect
35. C22×C32×C4C2×C4semidirect
37. C22×C3⋊Dic3C2×C4semidirect
45. C32×C22⋊C4C2×C4semidirect
48. #3757C2×C4semidirect
104. #342C3⋊D3direct (N × H)
115. C22×C3×C4C4×D3semidirect
125. C3×C22⋊C4C4×D3semidirect
215. C3⋊D3#342direct (N × H)
233. C22×C4C4×C3⋊D3semidirect
241. C22⋊C4C4×C3⋊D3semidirect
270. C32C2×#342semidirect
343. C3D3×#342semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C32×#3422
#105893932
#105893922
D3×#3423