Finite Group Databasebeta

← C3×#3347 #85211

Subgroups — C3×#3347 #85211

Order 384.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#555C211yesmaximal, characteristic, complemented
2C3×#553C211yesmaximal, characteristic, complemented
3C3×#501C211yesmaximal, characteristic, complemented
4C3×#482C211yesmaximal, characteristic, complemented
5C3×#482C211yesmaximal, characteristic, complemented
6C3×#482C211yesmaximal, characteristic, complemented
7C3×#480C211yesmaximal, characteristic, complemented
8C3×#478C211yesmaximal, characteristic, complemented
9C3×#474C211yesmaximal, characteristic, complemented
10C3×#469C211yesmaximal, characteristic, complemented
11C3×#466C211yesmaximal, characteristic, complemented
12C3×#442C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#428C211yesmaximal, characteristic, complemented
15C3×#427C211yesmaximal, characteristic, complemented
16#3347C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×D8C2211yescharacteristic
18C2×C3×M16C2211yescharacteristic
19C22×C3×C8C2211yescharacteristic
20C3×C4⋊Q8C2211yescharacteristic
21C3×#126—21no—
22C3×#125C2211yescharacteristic
23C3×#124—21no—
24C3×#124—21no—
25C3×#123—21no—
26C3×#121—21no—
27C3×#121—21no—
28C3×#121C2211yescharacteristic
29C3×#121C2211yescharacteristic
30C3×#121C2211yescharacteristic
31C3×#121C2211yescharacteristic
32C3×C4×D4—21no—
33C3×C4×D4C2211yescharacteristic
34C3×C4×D4C2211yescharacteristic
35C3×C4×D4C2211yescharacteristic
36C3×#117—21no—
37C3×#117C2211yescharacteristic
38C3×#117C2211yescharacteristic
39C3×#117C2211yescharacteristic
40C2×C3×C4⋊C4C2211yescharacteristic
41C3×#107C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#107C2211yescharacteristic
46C3×#106C2211yescharacteristic
47C3×#106C2211yescharacteristic
48C3×#106C2211yescharacteristic
49C3×#106C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#102C2211yescharacteristic
52C3×#102C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#555C2×C311yescharacteristic, complemented
61#553C2×C311yescharacteristic, complemented
62#501C2×C311yescharacteristic, complemented
63#482C2×C311yescharacteristic, complemented
64#482C2×C311yescharacteristic, complemented
65#482C2×C311yescharacteristic, complemented
66#480C2×C311yescharacteristic, complemented
67#478C2×C311yescharacteristic, complemented
68#474C2×C311yescharacteristic, complemented
69#469C2×C311yescharacteristic, complemented
70#466C2×C311yescharacteristic, complemented
71#442C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#428C2×C311yescharacteristic, complemented
74#427C2×C311yescharacteristic, complemented
75C2×C3×Q8—21no—
76C2×C3×D4—21no—
77C2×C3×D4—21no—
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4D411yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C3×D8—22no—
89C3×M16—22no—
90C2×C3×C8—22no—
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4D411yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C4⋊C4C2311yescharacteristic
105C3×C4⋊C4C2311yescharacteristic
106C3×C22⋊C4—21no—
107C3×C22⋊C4—21no—
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×C22⋊C4—21no—
115C3×C22⋊C4D411yescharacteristic
116C3×C22⋊C4D411yescharacteristic
117C3×C42—21no—
118C3×C42—21no—
119C3×C42—21no—
120C3×C42C2311yescharacteristic
121C2×D8C22×C311yescharacteristic
122C2×M16C22×C311yescharacteristic
123C22×C8C22×C311yescharacteristic
124C4⋊Q8C22×C311yescharacteristic
125#126—21no—
126#125C22×C311yescharacteristic
127#124—21no—
128#124—21no—
129#123—21no—
130#121—21no—
131#121—21no—
132#121C22×C311yescharacteristic
133#121C22×C311yescharacteristic
134#121C22×C311yescharacteristic
135#121C22×C311yescharacteristic
136C4×D4—21no—
137C4×D4C22×C311yescharacteristic
138C4×D4C22×C311yescharacteristic
139C4×D4C22×C311yescharacteristic
140#117—21no—
141#117C22×C311yescharacteristic
142#117C22×C311yescharacteristic
143#117C22×C311yescharacteristic
144C2×C4⋊C4C22×C311yescharacteristic
145#107C22×C311yescharacteristic
146#107C22×C311yescharacteristic
147#107C22×C311yescharacteristic
148#107C22×C311yescharacteristic
149#107C22×C311yescharacteristic
150#106C22×C311yescharacteristic
151#106C22×C311yescharacteristic
152#106C22×C311yescharacteristic
153#106C22×C311yescharacteristic
154C4⋊C8C22×C311yescharacteristic
155#102C22×C311yescharacteristic
156#102C22×C311yescharacteristic
157#102C22×C311yescharacteristic
158#102C22×C311yescharacteristic
159#102C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161C22⋊C8C22×C311yescharacteristic
162C22⋊C8C22×C311yescharacteristic
163#97C22×C311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
166C23×C3C2×D411yescharacteristic
167C23×C3C2×D411yescharacteristic
168C3×Q8—81no—
169C3×D4—21no—
170C3×D4—21no—
171C3×D4—21no—
172C3×D4—21no—
173C3×D4—41no—
174C3×D4—42no—
175C3×D4—81no—
176C3×D4—81no—
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—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—81no—
190C2×C3×C4—81no—
191C2×C3×C4C2×D411yescharacteristic
192C2×C3×C4C2×D411yescharacteristic
193C2×C3×C4C2×D411yescharacteristic
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2411yescharacteristic
196C3×C8—21no—
197C3×C8—21no—
198C3×C8—21no—
199C3×C8#4112yes—
200C2×Q8—21no—
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4C3×D411yescharacteristic
206C2×D4C23×C311yescharacteristic
207C2×D4C23×C311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C23×C311yescharacteristic
212C22×C4C23×C311yescharacteristic
213D8—22no—
214M16—22no—
215C2×C8—22no—
216C2×C8C23×C311yescharacteristic
217C2×C8C23×C311yescharacteristic
218C2×C8C23×C311yescharacteristic
219C2×C8C23×C311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4C3×D411yescharacteristic
225C4⋊C4C23×C311yescharacteristic
226C4⋊C4C23×C311yescharacteristic
227C4⋊C4C23×C311yescharacteristic
228C4⋊C4C23×C311yescharacteristic
229C4⋊C4C23×C311yescharacteristic
230C4⋊C4C23×C311yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—21no—
233C22⋊C4—21no—
234C22⋊C4—21no—
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4C3×D411yescharacteristic
241C22⋊C4C3×D411yescharacteristic
242C42—21no—
243C42—21no—
244C42—21no—
245C42C23×C311yescharacteristic
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3C22×D411yescharacteristic
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4C2×#4111yescharacteristic
270C3×C42−1+411yescharacteristic
271C23—21no—
272C23—21no—
273C23C2×C3×D411yescharacteristic
274C23C2×C3×D411yescharacteristic
275Q8—81no—
276D4—21no—
277D4—21no—
278D4—21no—
279D4—21no—
280D4—41no—
281D4—42no—
282D4—81no—
283D4—81no—
284D4—81no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4C2×C3×D411yescharacteristic
299C2×C4C2×C3×D411yescharacteristic
300C2×C4C2×C3×D411yescharacteristic
301C2×C4C2×C3×D411yescharacteristic
302C2×C4C24×C311yescharacteristic
303C8—21no—
304C8—21no—
305C8—21no—
306C8C3×#4112yes—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3—81no—
310C2×C3—81no—
311C2×C3#54711yescharacteristic
312C2×C3#57511yescharacteristic
313C2×C3#57611yescharacteristic
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22C22×C3×D411yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4C2×C3×#4111yescharacteristic
338C4C3×2−1+411yescharacteristic
339C3#334711yescharacteristic, direct product factor, Sylow
340C2—41no—
341C2—41no—
342C2—81no—
343C2—81no—
344C2C3×#54711yescharacteristic
345C2C3×#57511yescharacteristic
346C2C3×#57611yescharacteristic
subgroupG/H
center, socleC22×C3C22×D4
commutator, Frattini, cosocleC2×C4C24×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#555C2semidirect
2. C3×#553C2semidirect
3. C3×#501C2semidirect
4. C3×#482C2semidirect
5. C3×#482C2semidirect
6. C3×#482C2semidirect
7. C3×#480C2semidirect
8. C3×#478C2semidirect
9. C3×#474C2semidirect
10. C3×#469C2semidirect
11. C3×#466C2semidirect
12. C3×#442C2semidirect
13. C3×#435C2semidirect
14. C3×#428C2semidirect
15. C3×#427C2semidirect
16. #3347C3direct (N × H)
60. #555C2×C3semidirect
61. #553C2×C3semidirect
62. #501C2×C3semidirect
63. #482C2×C3semidirect
64. #482C2×C3semidirect
65. #482C2×C3semidirect
66. #480C2×C3semidirect
67. #478C2×C3semidirect
68. #474C2×C3semidirect
69. #469C2×C3semidirect
70. #466C2×C3semidirect
71. #442C2×C3semidirect
72. #435C2×C3semidirect
73. #428C2×C3semidirect
74. #427C2×C3semidirect
339. C3#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5552
C3×#5532
C3×#5012
C3×#4822
C3×#4802
C3×#4782
C3×#4742
C3×#4692
C3×#4662
C3×#4422
C3×#4352
C3×#4282
C3×#4272
#33473