Finite Group Databasebeta

← C3×#67492 #11771934

Subgroups — C3×#67492 #11771934

Order 1152.

379 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 379 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C3×#4949C211yesmaximal, characteristic
2C32×#342C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4C3×#1352—31nomaximal
5#67492C311yesmaximal, characteristic, direct product factor
6C2×C32×C22⋊C4—21no—
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×C3×#217—21no—
9C2×C3×C4⋊Dic3C411yescharacteristic, complemented
10C2×C3×Dic3⋊C4—21no—
11C3×C3⋊#95C411yescharacteristic, complemented
12C3×#830—21no—
13C3×#399—31no—
14#4949C2×C311yescharacteristic
15C3×#342—21no—
16C3×#342D311yescharacteristic
17C3×#342C2×C311yescharacteristic
18C3×#323—31no—
19#4525C2×C311yescharacteristic
20C24×C32D411yescharacteristic
21C22×C32×C4—41no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C32×C22⋊C4—22no—
27C32×C22⋊C4—41no—
28C32×C22⋊C4—41no—
29C3×#217—42no—
30C3×C4⋊Dic3—41no—
31C3×Dic3⋊C4—42no—
32C2×C3×C3⋊C8—41no—
33#1352—31noSylow
34C2×C3×C4⋊C4—31no—
35C2×C3×C4⋊C4—61no—
36C2×C3×C22⋊C4—22no—
37C2×C3×C22⋊C4—21no—
38C2×C3×C22⋊C4—21no—
39C2×C3×C22⋊C4—21no—
40C2×C3×C22⋊C4—61no—
41C2×C3×C22⋊C4C2×D311yescharacteristic
42C2×C3×C22⋊C4C22×C311yescharacteristic
43C2×#217—21no—
44C2×C4⋊Dic3C3×C411yescharacteristic, complemented
45C2×Dic3⋊C4—21no—
46C3×C22⋊C8—61no—
47C3×#95—31no—
48C3⋊#95C3×C411yescharacteristic, complemented
49#830—21no—
50C23×C32—21no—
51C23×C32—21no—
52C23×C32—41no—
53C23×C32—41no—
54C23×C32C22⋊C411yescharacteristic
55C23×C32SD1611yescharacteristic
56C23×C32Q1611yescharacteristic
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—42no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4—81no—
63C2×C32×C4—81no—
64C2×C3×Dic3—22no—
65C2×C3×Dic3—41no—
66C2×C3×Dic3—41no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C3×C3⋊C8—81no—
71#399—31no—
72#342C3×D311yescharacteristic
73#323—31no—
74C24×C3—21no—
75C24×C3#6711yescharacteristic
76C24×C3C3×D411yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—42no—
80C22×C3×C4—41no—
81C22×C3×C4—41no—
82C22×C3×C4—61no—
83C22×C3×C4—61no—
84C22×C3×C4C4×D311yescharacteristic
85C22×C3×C4D1211yescharacteristic
86C22×C3×C4C2×C3×C411yescharacteristic
87C22×C3×C4C3×D411yescharacteristic
88C22×Dic3—21no—
89C22×Dic3—21no—
90C2×C3×C8—121no—
91C3×C4⋊C4—121no—
92C3×C4⋊C4—122no—
93C3×C22⋊C4—24no—
94C3×C22⋊C4—22no—
95C3×C22⋊C4—22no—
96C3×C22⋊C4—41no—
97C3×C22⋊C4—41no—
98C3×C22⋊C4—42no—
99C3×C22⋊C4—42no—
100C3×C22⋊C4—41no—
101C3×C22⋊C4—41no—
102C3×C22⋊C4—122no—
103#217—42no—
104C4⋊Dic3—41no—
105Dic3⋊C4—42no—
106C2×C3⋊C8—41no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32—41no—
114C22×C32—41no—
115C22×C32—81no—
116C22×C32#9911yescharacteristic
117C22×C32#10311yescharacteristic
118C22×C32#10411yescharacteristic
119C32×C4—41no—
120C32×C4—41no—
121C32×C4—82no—
122C3×Dic3—42no—
123C3×Dic3—81no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—61no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—61no—
128C2×C22⋊C4C2×C3×D311yescharacteristic
129C22⋊C8—61no—
130#95—31no—
131C23×C3—22no—
132C23×C3—22no—
133C23×C3—21no—
134C23×C3—21no—
135C23×C3—21no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—41no—
141C23×C3—41no—
142C23×C3—41no—
143C23×C3—41no—
144C23×C3—81no—
145C23×C3—81no—
146C23×C3(C2×D3)⋊C411yescharacteristic
147C23×C3#21411yescharacteristic
148C23×C3#21611yescharacteristic
149C23×C3C3×C22⋊C411yescharacteristic
150C23×C3C3×SD1611yescharacteristic
151C23×C3C3×Q1611yescharacteristic
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—41no—
157C2×C3×C4—41no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—44no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4—62no—
166C2×C3×C4—81no—
167C2×C3×C4—81no—
168C2×C3×C4—82no—
169C2×C3×C4—82no—
170C2×C3×C4—81no—
171C2×C3×C4—81no—
172C2×C3×C4—81no—
173C2×C3×C4—81no—
174C2×C3×C4—121no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×Dic3—22no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C3×C8—241no—
186C3⋊C8—81no—
187C2×C32—21no—
188C2×C32—21no—
189C2×C32—41no—
190C2×C32—41no—
191C2×C32#32811yescharacteristic
192C2×C32#35211yescharacteristic
193C2×C32#35311yescharacteristic
194C24C3×#6711yescharacteristic
195C22×C4—41no—
196C22×C4—61no—
197C22×C4—61no—
198C22×C4C3×C4×D311yescharacteristic
199C22×C4C3×D1211yescharacteristic
200C2×C8—121no—
201C4⋊C4—121no—
202C4⋊C4—122no—
203C22⋊C4—22no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—122no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—41no—
221C22×C3—41no—
222C22×C3—41no—
223C22×C3—41no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—42no—
227C22×C3—42no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—81no—
233C22×C3—81no—
234C22×C3—81no—
235C22×C3—81no—
236C22×C3—82no—
237C22×C3#80511yescharacteristic
238C22×C3#80611yescharacteristic
239C22×C3#81011yescharacteristic
240C22×C3C3×#9911yescharacteristic
241C22×C3C3×#10311yescharacteristic
242C22×C3C3×#10411yescharacteristic
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—81no—
248C3×C4—81no—
249C3×C4—84no—
250C3×C4—82no—
251C3×C4—82no—
252C3×C4—122no—
253C3×C4—241no—
254Dic3—42no—
255Dic3—81no—
256C32#135211yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23C3×(C2×D3)⋊C411yescharacteristic
262C23C3×#21411yescharacteristic
263C23C3×#21611yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—62no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—121no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4—121no—
277C8—241no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—42no—
288C2×C3—42no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3—41no—
292C2×C3—41no—
293C2×C3#445211yescharacteristic
294C2×C3#447211yescharacteristic
295C2×C3#447411yescharacteristic
296C2×C3C3×#32811yescharacteristic
297C2×C3C3×#35211yescharacteristic
298C2×C3C3×#35311yescharacteristic
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C3×#80511yescharacteristic
309C22C3×#80611yescharacteristic
310C22C3×#81011yescharacteristic
311C4—41no—
312C4—41no—
313C4—82no—
314C4—122no—
315C4—241no—
316C3—21no—
317C3#6749211yescharacteristic, direct product factor
318C3C3×#135211yescharacteristic, complemented
319C2—21no—
320C2—21no—
321C2—41no—
322C2—41no—
323C2C3×#445211yescharacteristic
324C2C3×#447211yescharacteristic
325C2C3×#447411yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C22⋊C4C2×C3×D3
FittingC32×#342C2
socleC22×C32#99
prime radicalC24×C32D4
cosocleC2×C3×C22⋊C4C22×C3
hypercenterC3×#342D3
hypocenterC3C3×#1352
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C22⋊C4 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
5. #67492C3direct (N × H)
9. C2×C3×C4⋊Dic3C4semidirect
11. C3×C3⋊#95C4semidirect
44. C2×C4⋊Dic3C3×C4semidirect
48. C3⋊#95C3×C4semidirect
256. C32#1352semidirect
317. C3#67492direct (N × H)
318. C3C3×#1352semidirect

Maximal subgroups

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

subgroupindex
C3×#49492
C32×#3422
C3×#45252
C3×#13523
#674923