Finite Group Databasebeta

← C3×#67641 #11772600

Subgroups — C3×#67641 #11772600

Order 1152.

593 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C32×#390C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal
3C3×#1393—31nomaximal
4#67641C311yesmaximal, characteristic, direct product factor
5C22×C32×D4C2211yescharacteristic
6C2×C32×C4⋊C4C411yescharacteristic, complemented
7C2×C32×C22⋊C4—22no—
8C2×C32×C42C411yescharacteristic, complemented
9C2×C3×#217—22no—
10C3×#834—22no—
11C3×#834C414yescomplemented
12C2×C3×#99—32no—
13C3×#390—21no—
14C3×#390D311yescharacteristic
15C3×#390C2×C311yescharacteristic
16C2×#834C2×C312yes—
17C24×C32D412yes—
18C2×C32×D4—41no—
19C2×C32×D4—41no—
20C2×C32×D4C2×C412yes—
21C2×C32×D4D411yescharacteristic
22C2×C32×D4Q811yescharacteristic
23C22×C32×C4—21no—
24C22×C32×C4—21no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C3×Dic3—42no—
27C32×C4⋊C4—41no—
28C32×C22⋊C4—44no—
29C32×C42—41no—
30C3×#217—24no—
31C3×#217—42no—
32#1393—31noSylow
33C22×C3×D4—21no—
34C22×C3×D4C2×D311yescharacteristic
35C22×C3×D4C22×C311yescharacteristic
36C2×C3×C4⋊C4—21no—
37C2×C3×C4⋊C4Dic311yescharacteristic, complemented
38C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
39C2×C3×C22⋊C4—24no—
40C2×C3×C22⋊C4—22no—
41C2×C3×C22⋊C4—22no—
42C2×C3×C22⋊C4—62no—
43C2×C3×C42—21no—
44C2×C3×C42Dic311yescharacteristic, complemented
45C2×C3×C42C3×C411yescharacteristic, complemented
46C2×#217—22no—
47C3×#99—34no—
48C3×#99—62no—
49#834—22no—
50#834C3×C414yescomplemented
51C23×C32—22no—
52C23×C32—22no—
53C23×C32—42no—
54C23×C32—42no—
55C23×C32C22⋊C412yes—
56C23×C32C22⋊C411yescharacteristic
57C23×C32C4⋊C412yes—
58C32×D4—42no—
59C32×D4—41no—
60C32×D4—41no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—22no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4—42no—
67C2×C32×C4—41no—
68C2×C32×C4C4211yescharacteristic
69C2×C32×C4C4⋊C411yescharacteristic
70C2×C3×Dic3—44no—
71C2×C3×Dic3—82no—
72C2×C3×Dic3—82no—
73C2×#99—32no—
74#390C3×D311yescharacteristic
75C24×C3—22no—
76C24×C3#6712yes—
77C24×C3C3×D412yes—
78C2×C3×D4—21no—
79C2×C3×D4—22no—
80C2×C3×D4—21no—
81C2×C3×D4—41no—
82C2×C3×D4—41no—
83C2×C3×D4—41no—
84C2×C3×D4—41no—
85C2×C3×D4—42no—
86C2×C3×D4—42no—
87C2×C3×D4Dic611yescharacteristic
88C2×C3×D4C4×D312yes—
89C2×C3×D4D1211yescharacteristic
90C2×C3×D4C2×C3×C412yes—
91C2×C3×D4C3×D411yescharacteristic
92C2×C3×D4C3×Q811yescharacteristic
93C22×C3×C4—22no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—22no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—122no—
101C22×C3×C4C2×Dic311yescharacteristic
102C22×C3×C4C2×C3×C411yescharacteristic
103C22×Dic3—42no—
104C3×C4⋊C4—41no—
105C3×C4⋊C4—41no—
106C3×C4⋊C4—42no—
107C3×C22⋊C4—44no—
108C3×C22⋊C4—44no—
109C3×C22⋊C4—48no—
110C3×C22⋊C4—64no—
111C3×C22⋊C4—122no—
112C3×C42—41no—
113C3×C42—41no—
114C3×C42—42no—
115#217—24no—
116#217—42no—
117C22×C32—21no—
118C22×C32—21no—
119C22×C32—22no—
120C22×C32—22no—
121C22×C32—42no—
122C22×C32—42no—
123C22×C32—42no—
124C22×C32—42no—
125C22×C32—82no—
126C22×C32#9511yescharacteristic
127C22×C32#9911yescharacteristic
128C22×C32#9911yescharacteristic
129C32×C4—21no—
130C32×C4—21no—
131C32×C4—42no—
132C32×C4—81no—
133C3×Dic3—84no—
134C22×D4C2×C3×D311yescharacteristic
135C2×C4⋊C4C3×Dic311yescharacteristic, complemented
136C2×C22⋊C4—22no—
137C2×C22⋊C4—62no—
138C2×C42C3×Dic311yescharacteristic, complemented
139#99—34no—
140#99—62no—
141C23×C3—22no—
142C23×C3—22no—
143C23×C3—22no—
144C23×C3—22no—
145C23×C3—22no—
146C23×C3—22no—
147C23×C3—21no—
148C23×C3—42no—
149C23×C3—42no—
150C23×C3—42no—
151C23×C3—42no—
152C23×C3—42no—
153C23×C3—42no—
154C23×C3—44no—
155C23×C3—44no—
156C23×C3Dic3⋊C412yes—
157C23×C3(C2×D3)⋊C412yes—
158C23×C3#21711yescharacteristic
159C23×C3C3×C22⋊C412yes—
160C23×C3C3×C22⋊C411yescharacteristic
161C23×C3C3×C4⋊C412yes—
162C3×D4—41no—
163C3×D4—42no—
164C3×D4—41no—
165C3×D4—42no—
166C3×D4—41no—
167C3×D4—41no—
168C3×D4—42no—
169C3×D4—44no—
170C3×D4—42no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—44no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—124no—
195C2×C3×C4—242no—
196C2×C3×C4—242no—
197C2×C3×C4C4×Dic311yescharacteristic
198C2×C3×C4C4⋊Dic311yescharacteristic
199C2×C3×C4C3×C4211yescharacteristic
200C2×C3×C4C3×C4⋊C411yescharacteristic
201C2×Dic3—44no—
202C2×Dic3—82no—
203C2×Dic3—82no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32—42no—
207C2×C32—42no—
208C2×C32#34211yescharacteristic
209C2×C32#35311yescharacteristic
210C2×C32#35411yescharacteristic
211C24C3×#6712yes—
212C2×D4—41no—
213C2×D4—41no—
214C2×D4C3×Dic611yescharacteristic
215C2×D4C3×C4×D312yes—
216C2×D4C3×D1211yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—122no—
220C22×C4C2×C3×Dic311yescharacteristic
221C4⋊C4—41no—
222C22⋊C4—44no—
223C22⋊C4—64no—
224C22⋊C4—122no—
225C42—41no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—42no—
245C22×C3—44no—
246C22×C3—44no—
247C22×C3—42no—
248C22×C3—42no—
249C22×C3—42no—
250C22×C3—42no—
251C22×C3—82no—
252C22×C3—82no—
253C22×C3—82no—
254C22×C3—82no—
255C22×C3—84no—
256C22×C3C3⋊#9511yescharacteristic
257C22×C3#83411yescharacteristic
258C22×C3#83411yescharacteristic
259C22×C3C3×#9511yescharacteristic
260C22×C3C3×#9911yescharacteristic
261C22×C3C3×#9911yescharacteristic
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—44no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—82no—
272C3×C4—81no—
273C3×C4—81no—
274C3×C4—244no—
275Dic3—84no—
276C32#139311yescharacteristic, complemented, Sylow
277C23—22no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23C3×Dic3⋊C412yes—
282C23C3×(C2×D3)⋊C412yes—
283C23C3×#21711yescharacteristic
284D4—41no—
285D4—42no—
286D4—41no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—124no—
295C2×C4—242no—
296C2×C4—242no—
297C2×C4C3×C4×Dic311yescharacteristic
298C2×C4C3×C4⋊Dic311yescharacteristic
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—42no—
309C2×C3—42no—
310C2×C3—42no—
311C2×C3—42no—
312C2×C3—82no—
313C2×C3—82no—
314C2×C3#452611yescharacteristic
315C2×C3#454111yescharacteristic
316C2×C3#454511yescharacteristic
317C2×C3C3×#34211yescharacteristic
318C2×C3C3×#35311yescharacteristic
319C2×C3C3×#35411yescharacteristic
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22C3×C3⋊#9511yescharacteristic
330C22C3×#83411yescharacteristic
331C22C3×#83411yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—244no—
337C3—21no—
338C3#6764111yescharacteristic, direct product factor
339C3C3×#139311yescharacteristic, complemented
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2C3×#452611yescharacteristic
345C2C3×#454111yescharacteristic
346C2C3×#454511yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC2×C3×C4C3×C42
FrattiniC22×D4C2×C3×D3
FittingC32×#390C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC22×C3×D4C22×C3
hypercenterC3×#390D3
hypocenterC3C3×#1393
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
4. #67641C3direct (N × H)
6. C2×C32×C4⋊C4C4semidirect
8. C2×C32×C42C4semidirect
11. C3×#834C4semidirect
37. C2×C3×C4⋊C4Dic3semidirect
38. C2×C3×C4⋊C4C3×C4semidirect
44. C2×C3×C42Dic3semidirect
45. C2×C3×C42C3×C4semidirect
50. #834C3×C4semidirect
135. C2×C4⋊C4C3×Dic3semidirect
138. C2×C42C3×Dic3semidirect
276. C32#1393semidirect
338. C3#67641direct (N × H)
339. C3C3×#1393semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×C3×#8342
C3×#13933
#676413