Finite Group Databasebeta

← C3⋊D3×#323 #11773705

Subgroups — C3⋊D3×#323 #11773705

Order 1152.

1368 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 163 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
2C3⋊D3×C22⋊C8C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4#10589391C211yesmaximal, characteristic, complemented
5#10589334C212yesmaximal, complemented
6D3×#323—34nomaximal
7C24×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3757C411yescharacteristic
12C2×#3752C411yescharacteristic
13C2×#3752C2211yescharacteristic
14C2×C8×C3⋊D3—22no—
15C22⋊C4×C3⋊D3—22no—
16C22⋊C4×C3⋊D3—22no—
17C32×C22⋊C8C2212yescomplemented
18#63657C2212yescomplemented
19#63647—22no—
20C2×D3×C22⋊C4—34no—
21D3×C22⋊C8—38no—
22C3×#323D314yescomplemented
23#4525—34no—
24#4468—38no—
25C24×C32C2×C411yescharacteristic
26C23×C3⋊D3—21no—
27C23×C3⋊D3—21no—
28C23×C3⋊D3—22no—
29C23×C3⋊D3—42no—
30C23×C3⋊D3—42no—
31C23×C3⋊D3C814yescomplemented
32C23×C3⋊D3C2×C411yescharacteristic
33C23×C3⋊D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3—42no—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3D412yes—
44C2×C32×C8—22no—
45C32×C22⋊C4—22no—
46#3757—22no—
47#3752—22no—
48#3752—22no—
49C2×C3⋊(C3⋊C8)—22no—
50C8×C3⋊D3—44no—
51C2×#323—91noSylow
52C24×D3—34no—
53C22×C4×D3—34no—
54C22×C4×D3—34no—
55C2×C3×C22⋊C4C2×D314yes—
56C2×#217—34no—
57C2×(C2×D3)⋊C4—34no—
58C2×(C2×D3)⋊C4—34no—
59C2×D3×C8—68no—
60D3×C22⋊C4—68no—
61D3×C22⋊C4—68no—
62C3×C22⋊C8C2×D318yescomplemented
63#830—38no—
64(C2×D3)⋊C8—68no—
65C23×C32—21no—
66C23×C32—21no—
67C23×C32—41no—
68C23×C32—41no—
69C23×C32C2×C812yescomplemented
70C23×C32C22×C411yescharacteristic
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3—24no—
76C22×C3⋊D3—24no—
77C22×C3⋊D3—42no—
78C22×C3⋊D3—42no—
79C22×C3⋊D3—48no—
80C22×C3⋊D3—48no—
81C22×C3⋊D3—42no—
82C22×C3⋊D3—42no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3C22⋊C411yescharacteristic
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C2×C812yes—
88C22×C3⋊D3C2×C812yescomplemented
89C22×C3⋊D3M1612yes—
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C2×D412yes—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3C22⋊C412yes—
98C4×C3⋊D3—24no—
99C4×C3⋊D3—42no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3—42no—
102C32×C8—42no—
103C3⋊(C3⋊C8)—42no—
104C22×C22⋊C4—91no—
105C2×C22⋊C8—92no—
106#323—91no—
107#323—92no—
108#323C3⋊D311yescharacteristic, direct product factor
109C24×C3C4×D314yes—
110C23×D3—34no—
111C23×D3—316no—
112C23×D3—34no—
113C23×D3—64no—
114C23×D3—64no—
115C23×D3—68no—
116C23×D3—128no—
117C23×D3—128no—
118C22×C3×C4C4×D314yes—
119C22×C3×C4C22×D314yes—
120C22×Dic3—34no—
121C22×Dic3—34no—
122C2×C4×D3—38no—
123C2×C4×D3—38no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×C4×D3—128no—
127C2×C4×D3—128no—
128C2×C3×C8—28no—
129C3×C22⋊C4—28no—
130#217—68no—
131(C2×D3)⋊C4—68no—
132(C2×D3)⋊C4—68no—
133C2×C3⋊C8—68no—
134D3×C8—1216no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—22no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—41no—
141C22×C32—41no—
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32C22×C811yescharacteristic
144C22×C32C2×M1611yescharacteristic
145C2×C3⋊D3—21no—
146C2×C3⋊D3—21no—
147C2×C3⋊D3—24no—
148C2×C3⋊D3—24no—
149C2×C3⋊D3—22no—
150C2×C3⋊D3—48no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—48no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3C22⋊C812yes—
157C2×C3⋊D3C22⋊C812yes—
158C2×C3⋊D3#9912yes—
159C2×C3⋊D3#10012yes—
160C32×C4—22no—
161C32×C4—41no—
162C3⋊Dic3—22no—
163C3⋊Dic3—41no—
164C25—91no—
165C23×C4—91no—
166C23×C4—91no—
167C22×C8—182no—
168C2×C22⋊C4—91no—
169C2×C22⋊C4—91no—
170C2×C22⋊C4—91no—
171C2×C22⋊C4—182no—
172C2×C22⋊C4—182no—
173C2×C22⋊C4C2×C3⋊D311yescharacteristic
174C22⋊C8—92no—
175C22⋊C8—182no—
176C22⋊C8C2×C3⋊D312yescomplemented
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—44no—
180C23×C3—44no—
181C23×C3D3×C818yescomplemented
182C23×C3C2×C4×D314yes—
183C22×D3—34no—
184C22×D3—34no—
185C22×D3—38no—
186C22×D3—38no—
187C22×D3—38no—
188C22×D3—68no—
189C22×D3—68no—
190C22×D3—616no—
191C22×D3—616no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—128no—
195C22×D3—128no—
196C22×D3—1232no—
197C22×D3—128no—
198C22×D3—128no—
199C22×D3—1232no—
200C22×D3—124no—
201C22×D3—124no—
202C2×C3×C4—24no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4D3×D418yes—
206C2×Dic3—38no—
207C2×Dic3—64no—
208C2×Dic3—124no—
209C2×Dic3—124no—
210C4×D3—616no—
211C4×D3—128no—
212C4×D3—128no—
213C4×D3—128no—
214C3×C8—48no—
215C3⋊C8—128no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32—42no—
219C2×C32C2×C22⋊C811yescharacteristic
220C2×C32C2×#9911yescharacteristic
221C2×C32C2×#10011yescharacteristic
222C3⋊D3—22no—
223C3⋊D3—42no—
224C3⋊D3#32314yesdirect product factor
225C24—91no—
226C24—94no—
227C24—91no—
228C24—181no—
229C24—181no—
230C24—182no—
231C24—362no—
232C24—362no—
233C24C4×C3⋊D311yescharacteristic
234C22×C4—91no—
235C22×C4—92no—
236C22×C4—92no—
237C22×C4—91no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4—362no—
241C22×C4—362no—
242C22×C4C4×C3⋊D311yescharacteristic
243C22×C4C22×C3⋊D311yescharacteristic
244C2×C8—22no—
245C2×C8—182no—
246C2×C8—364no—
247C22⋊C4—22no—
248C22⋊C4—182no—
249C22⋊C4—182no—
250C22⋊C4—182no—
251C22×C3—24no—
252C22×C3—24no—
253C22×C3—28no—
254C22×C3—48no—
255C22×C3—48no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3D3×C22⋊C414yes—
259C22×C3C2×D3×C814yes—
260C22×C3D3×M1614yes—
261C2×D3—38no—
262C2×D3—38no—
263C2×D3—38no—
264C2×D3—38no—
265C2×D3—616no—
266C2×D3—616no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—68no—
270C2×D3—1232no—
271C2×D3—1232no—
272C2×D3—128no—
273C2×D3—124no—
274C2×D3—124no—
275C2×D3—128no—
276C3×C4—28no—
277C3×C4—44no—
278Dic3—68no—
279Dic3—124no—
280C32C2×#32311yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23—91no—
286C23—91no—
287C23—92no—
288C23—92no—
289C23—92no—
290C23—182no—
291C23—182no—
292C23—184no—
293C23—184no—
294C23—181no—
295C23—181no—
296C23—361no—
297C23—361no—
298C23—362no—
299C23—362no—
300C23—368no—
301C23—368no—
302C23—362no—
303C23—362no—
304C23C8×C3⋊D312yescomplemented
305C23C2×C4×C3⋊D311yescharacteristic
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—92no—
310C2×C4—184no—
311C2×C4—181no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C4—362no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4D4×C3⋊D312yes—
318C8—42no—
319C8—362no—
320C2×C3—24no—
321C2×C3—24no—
322C2×C3—48no—
323C2×C3D3×C22⋊C814yes—
324C2×C3D3×#9914yes—
325C2×C3D3×#10014yes—
326D3—316no—
327D3—68no—
328D3—128no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—92no—
337C22—92no—
338C22—92no—
339C22—92no—
340C22—184no—
341C22—184no—
342C22—181no—
343C22—181no—
344C22—182no—
345C22—362no—
346C22—362no—
347C22—368no—
348C22—368no—
349C22—361no—
350C22—361no—
351C22C22⋊C4×C3⋊D311yescharacteristic
352C22C2×C8×C3⋊D311yescharacteristic
353C22M16×C3⋊D311yescharacteristic
354C4—22no—
355C4—41no—
356C4—182no—
357C4—361no—
358C3D3×#32314yescomplemented
359C2—21no—
360C2—21no—
361C2—42no—
362C2—94no—
363C2—182no—
364C2—362no—
365C2C3⋊D3×C22⋊C811yescharacteristic
366C2C3⋊D3×#9911yescharacteristic
367C2C3⋊D3×#10011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C4
cosocleC22×C32×C4C23
hypercenter#323C3⋊D3
hypocenterC32C2×#323
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C22⋊C8C2semidirect
3. C32×#323C2semidirect
4. #10589391C2semidirect
5. #10589334C2semidirect
17. C32×C22⋊C8C22semidirect
18. #63657C22semidirect
22. C3×#323D3semidirect
31. C23×C3⋊D3C8semidirect
62. C3×C22⋊C8C2×D3semidirect
69. C23×C32C2×C8semidirect
88. C22×C3⋊D3C2×C8semidirect
108. #323C3⋊D3direct (N × H)
176. C22⋊C8C2×C3⋊D3semidirect
181. C23×C3D3×C8semidirect
224. C3⋊D3#323direct (N × H)
280. C32C2×#323semidirect
304. C23C8×C3⋊D3semidirect
358. C3D3×#323semidirect

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
C3⋊D3×C22⋊C82
C32×#3232
#105893912
#105893342
D3×#3233