Finite Group Databasebeta

← C3×#3371 #85235

Subgroups — C3×#3371 #85235

Order 384.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#559C211yesmaximal, characteristic
2C3×#557C211yesmaximal, characteristic, complemented
3C3×#490C211yesmaximal, characteristic
4C3×#489C211yesmaximal, characteristic, complemented
5C3×#488C211yesmaximal, characteristic, complemented
6C3×#479C211yesmaximal, characteristic, complemented
7C3×#478C211yesmaximal, characteristic, complemented
8C3×#476C211yesmaximal, characteristic, complemented
9C3×#464C211yesmaximal, characteristic, complemented
10C3×#464C211yesmaximal, characteristic, complemented
11C3×#460C211yesmaximal, characteristic
12C3×#446C211yesmaximal, characteristic, complemented
13C3×#441C211yesmaximal, characteristic, complemented
14C3×#440C211yesmaximal, characteristic, complemented
15C3×C4×SD16C211yesmaximal, characteristic, complemented
16#3371C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×Q16C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4⋊Q8—21no—
21C3×C4⋊Q8C2211yescharacteristic
22C3×#127C2211yescharacteristic
23C3×#125—21no—
24C3×#125—21no—
25C3×#125C2211yescharacteristic
26C3×#125C2211yescharacteristic
27C3×#124—21no—
28C3×#124C2211yescharacteristic
29C3×#124C2211yescharacteristic
30C3×#123—21no—
31C3×#123—21no—
32C3×C4×Q8—21no—
33C3×C4×Q8C2211yescharacteristic
34C3×C4×Q8C2211yescharacteristic
35C3×C4×Q8C2211yescharacteristic
36C3×C4×Q8C2211yescharacteristic
37C3×C4×Q8C2211yescharacteristic
38C3×C4×D4—21no—
39C3×C4×D4C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic
41C3×#107C2211yescharacteristic
42C3×#106C2211yescharacteristic
43C3×#106C2211yescharacteristic
44C3×C4⋊C8C2211yescharacteristic
45C3×C4⋊C8C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×#103C2211yescharacteristic
48C3×#103C2211yescharacteristic
49C3×#103C2211yescharacteristic
50C3×#103C2211yescharacteristic
51C3×#102C2211yescharacteristic
52C3×#102C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×#97C2211yescharacteristic
58C3×#97C2211yescharacteristic
59C3×C4×C8C2211yescharacteristic
60#559C2×C311yescharacteristic
61#557C2×C311yescharacteristic, complemented
62#490C2×C311yescharacteristic
63#489C2×C311yescharacteristic, complemented
64#488C2×C311yescharacteristic, complemented
65#479C2×C311yescharacteristic, complemented
66#478C2×C311yescharacteristic, complemented
67#476C2×C311yescharacteristic, complemented
68#464C2×C311yescharacteristic, complemented
69#464C2×C311yescharacteristic, complemented
70#460C2×C311yescharacteristic
71#446C2×C311yescharacteristic, complemented
72#441C2×C311yescharacteristic, complemented
73#440C2×C311yescharacteristic, complemented
74C4×SD16C2×C311yescharacteristic, complemented
75C2×C3×Q8—21no—
76C2×C3×Q8D411yescharacteristic
77C2×C3×Q8C2311yescharacteristic
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4—21no—
80C2×C3×D4—21no—
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C3×Q16—22no—
86C3×SD16—22no—
87C3×SD16—22no—
88C2×C3×C8C2311yescharacteristic
89C2×C3×C8C2311yescharacteristic
90C2×C3×C8C2311yescharacteristic
91C2×C3×C8C2311yescharacteristic
92C3×C4⋊C4—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4—21no—
100C3×C4⋊C4—21no—
101C3×C4⋊C4D411yescharacteristic
102C3×C4⋊C4D411yescharacteristic
103C3×C4⋊C4D411yescharacteristic
104C3×C4⋊C4C2311yescharacteristic
105C3×C4⋊C4C2311yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C4⋊C4C2311yescharacteristic
108C3×C22⋊C4—21no—
109C3×C22⋊C4—21no—
110C3×C22⋊C4—21no—
111C3×C22⋊C4—21no—
112C3×C22⋊C4—21no—
113C3×C22⋊C4—21no—
114C3×C42—21no—
115C3×C42—21no—
116C3×C42—21no—
117C3×C42—21no—
118C3×C42C2311yescharacteristic
119C3×C42C2311yescharacteristic
120C3×C42C2311yescharacteristic
121C2×Q16C22×C311yescharacteristic
122C2×SD16C22×C311yescharacteristic
123C2×SD16C22×C311yescharacteristic
124C4⋊Q8—21no—
125C4⋊Q8C22×C311yescharacteristic
126#127C22×C311yescharacteristic
127#125—21no—
128#125—21no—
129#125C22×C311yescharacteristic
130#125C22×C311yescharacteristic
131#124—21no—
132#124C22×C311yescharacteristic
133#124C22×C311yescharacteristic
134#123—21no—
135#123—21no—
136C4×Q8—21no—
137C4×Q8C22×C311yescharacteristic
138C4×Q8C22×C311yescharacteristic
139C4×Q8C22×C311yescharacteristic
140C4×Q8C22×C311yescharacteristic
141C4×Q8C22×C311yescharacteristic
142C4×D4—21no—
143C4×D4C22×C311yescharacteristic
144C4×D4C22×C311yescharacteristic
145#107C22×C311yescharacteristic
146#106C22×C311yescharacteristic
147#106C22×C311yescharacteristic
148C4⋊C8C22×C311yescharacteristic
149C4⋊C8C22×C311yescharacteristic
150C4⋊C8C22×C311yescharacteristic
151#103C22×C311yescharacteristic
152#103C22×C311yescharacteristic
153#103C22×C311yescharacteristic
154#103C22×C311yescharacteristic
155#102C22×C311yescharacteristic
156#102C22×C311yescharacteristic
157#102C22×C311yescharacteristic
158#102C22×C311yescharacteristic
159#102C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161#97C22×C311yescharacteristic
162#97C22×C311yescharacteristic
163C4×C8C22×C311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
166C3×Q8—21no—
167C3×Q8—21no—
168C3×Q8—21no—
169C3×Q8—41no—
170C3×Q8—42no—
171C3×Q8#4112yes—
172C3×D4—21no—
173C3×D4—21no—
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—42no—
177C3×D4—81no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—81no—
185C2×C3×C4—81no—
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2×D411yescharacteristic
191C2×C3×C4C2×D411yescharacteristic
192C2×C3×C4C2411yescharacteristic
193C3×C8—21no—
194C3×C8—21no—
195C3×C8—21no—
196C3×C8—21no—
197C2×Q8—21no—
198C2×Q8C3×D411yescharacteristic
199C2×Q8C23×C311yescharacteristic
200C2×Q8C23×C311yescharacteristic
201C2×D4—21no—
202C2×D4—21no—
203C2×D4C23×C311yescharacteristic
204C2×D4C23×C311yescharacteristic
205C22×C4—21no—
206C22×C4—21no—
207Q16—22no—
208SD16—22no—
209SD16—22no—
210C2×C8C23×C311yescharacteristic
211C2×C8C23×C311yescharacteristic
212C2×C8C23×C311yescharacteristic
213C2×C8C23×C311yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4C3×D411yescharacteristic
224C4⋊C4C3×D411yescharacteristic
225C4⋊C4C3×D411yescharacteristic
226C4⋊C4C23×C311yescharacteristic
227C4⋊C4C23×C311yescharacteristic
228C4⋊C4C23×C311yescharacteristic
229C4⋊C4C23×C311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—21no—
233C22⋊C4—21no—
234C22⋊C4—21no—
235C22⋊C4—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42C23×C311yescharacteristic
241C42C23×C311yescharacteristic
242C42C23×C311yescharacteristic
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3C22×D411yescharacteristic
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4C2×#4111yescharacteristic
263C3×C42−1+411yescharacteristic
264C23—21no—
265C23—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—41no—
270Q8—42no—
271Q8C3×#4112yes—
272D4—21no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—42no—
277D4—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C2×C3×D411yescharacteristic
287C2×C4C2×C3×D411yescharacteristic
288C2×C4C2×C3×D411yescharacteristic
289C2×C4C2×C3×D411yescharacteristic
290C2×C4C2×C3×D411yescharacteristic
291C2×C4C2×C3×D411yescharacteristic
292C2×C4C24×C311yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8—21no—
297C2×C3—81no—
298C2×C3—81no—
299C2×C3#54811yescharacteristic
300C2×C3#57511yescharacteristic
301C2×C3#57711yescharacteristic
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22C22×C3×D411yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4C2×C3×#4111yescharacteristic
322C4C3×2−1+411yescharacteristic
323C3#337111yescharacteristic, direct product factor, Sylow
324C2—81no—
325C2—81no—
326C2C3×#54811yescharacteristic
327C2C3×#57511yescharacteristic
328C2C3×#57711yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
prime radicalC3×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#557C2semidirect
4. C3×#489C2semidirect
5. C3×#488C2semidirect
6. C3×#479C2semidirect
7. C3×#478C2semidirect
8. C3×#476C2semidirect
9. C3×#464C2semidirect
10. C3×#464C2semidirect
12. C3×#446C2semidirect
13. C3×#441C2semidirect
14. C3×#440C2semidirect
15. C3×C4×SD16C2semidirect
16. #3371C3direct (N × H)
61. #557C2×C3semidirect
63. #489C2×C3semidirect
64. #488C2×C3semidirect
65. #479C2×C3semidirect
66. #478C2×C3semidirect
67. #476C2×C3semidirect
68. #464C2×C3semidirect
69. #464C2×C3semidirect
71. #446C2×C3semidirect
72. #441C2×C3semidirect
73. #440C2×C3semidirect
74. C4×SD16C2×C3semidirect
323. C3#3371direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5592
C3×#5572
C3×#4902
C3×#4892
C3×#4882
C3×#4792
C3×#4782
C3×#4762
C3×#4642
C3×#4602
C3×#4462
C3×#4412
C3×#4402
C3×C4×SD162
#33713