Finite Group Databasebeta

← C3×#3309 #85173

Subgroups — C3×#3309 #85173

Order 384.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic, complemented
2C3×#550C211yesmaximal, characteristic, complemented
3C3×#490C211yesmaximal, characteristic, complemented
4C3×#482C211yesmaximal, characteristic, complemented
5C3×#480C211yesmaximal, characteristic, complemented
6C3×#479C211yesmaximal, characteristic, complemented
7C3×#469C211yesmaximal, characteristic, complemented
8C3×#466C211yesmaximal, characteristic, complemented
9C3×#459C211yesmaximal, characteristic, complemented
10C3×#449C211yesmaximal, characteristic, complemented
11C3×#449C211yesmaximal, characteristic, complemented
12C3×#440C211yesmaximal, characteristic, complemented
13C3×#435C211yesmaximal, characteristic, complemented
14C3×#417C211yesmaximal, characteristic, complemented
15C3×#416C211yesmaximal, characteristic, complemented
16#3309C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×C3×#41C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C2×C3×D8C2211yescharacteristic
21C2×C3×D8C2211yescharacteristic
22C2×C3×M16C2211yescharacteristic
23C22×C3×C8C2211yescharacteristic
24C3×#127—21no—
25C3×#127C2211yescharacteristic
26C3×#126—21no—
27C3×#125C2211yescharacteristic
28C3×#123—21no—
29C3×#121—21no—
30C3×#121—21no—
31C3×#121—21no—
32C3×#121C2211yescharacteristic
33C3×#121C2211yescharacteristic
34C3×#121C2211yescharacteristic
35C3×#121C2211yescharacteristic
36C3×C4×Q8C2211yescharacteristic
37C3×C4×D4—21no—
38C3×C4×D4—21no—
39C3×C4×D4C2211yescharacteristic
40C3×C4×D4C2211yescharacteristic
41C3×#117C2211yescharacteristic
42C2×C3×C4⋊C4C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45C3×#106C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×#103C2211yescharacteristic
48C3×#103C2211yescharacteristic
49C3×#103C2211yescharacteristic
50C3×#102C2211yescharacteristic
51C3×#102C2211yescharacteristic
52C3×#102C2211yescharacteristic
53C3×#102C2211yescharacteristic
54C3×#102C2211yescharacteristic
55C3×#102C2211yescharacteristic
56C3×#102C2211yescharacteristic
57C3×C22⋊C8C2211yescharacteristic
58C3×C22⋊C8C2211yescharacteristic
59C3×#97C2211yescharacteristic
60#553C2×C311yescharacteristic, complemented
61#550C2×C311yescharacteristic, complemented
62#490C2×C311yescharacteristic, complemented
63#482C2×C311yescharacteristic, complemented
64#480C2×C311yescharacteristic, complemented
65#479C2×C311yescharacteristic, complemented
66#469C2×C311yescharacteristic, complemented
67#466C2×C311yescharacteristic, complemented
68#459C2×C311yescharacteristic, complemented
69#449C2×C311yescharacteristic, complemented
70#449C2×C311yescharacteristic, complemented
71#440C2×C311yescharacteristic, complemented
72#435C2×C311yescharacteristic, complemented
73#417C2×C311yescharacteristic, complemented
74#416C2×C311yescharacteristic, complemented
75C3×#41—22no—
76C3×#41—22no—
77C3×#41—41no—
78C3×#41—41no—
79C2×C3×Q8C2311yescharacteristic
80C2×C3×D4—21no—
81C2×C3×D4—21no—
82C2×C3×D4—21no—
83C2×C3×D4—21no—
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4—21no—
87C2×C3×D4—21no—
88C2×C3×D4D411yescharacteristic
89C2×C3×D4C2311yescharacteristic
90C2×C3×D4C2311yescharacteristic
91C2×C3×D4C2311yescharacteristic
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C3×SD16—22no—
99C3×D8—41no—
100C3×D8—41no—
101C3×M16—41no—
102C2×C3×C8—41no—
103C2×C3×C8C2311yescharacteristic
104C2×C3×C8C2311yescharacteristic
105C2×C3×C8C2311yescharacteristic
106C2×C3×C8C2311yescharacteristic
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4—21no—
110C3×C4⋊C4—21no—
111C3×C4⋊C4D411yescharacteristic
112C3×C4⋊C4C2311yescharacteristic
113C3×C4⋊C4C2311yescharacteristic
114C3×C4⋊C4C2311yescharacteristic
115C3×C4⋊C4C2311yescharacteristic
116C3×C22⋊C4—21no—
117C3×C22⋊C4—21no—
118C3×C22⋊C4—21no—
119C3×C22⋊C4—21no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4—21no—
122C3×C22⋊C4D411yescharacteristic
123C3×C22⋊C4D411yescharacteristic
124C3×C42—21no—
125C3×C42—21no—
126C3×C42C2311yescharacteristic
127C2×#41C22×C311yescharacteristic
128C2×#41C22×C311yescharacteristic
129C2×SD16C22×C311yescharacteristic
130C2×D8C22×C311yescharacteristic
131C2×D8C22×C311yescharacteristic
132C2×M16C22×C311yescharacteristic
133C22×C8C22×C311yescharacteristic
134#127—21no—
135#127C22×C311yescharacteristic
136#126—21no—
137#125C22×C311yescharacteristic
138#123—21no—
139#121—21no—
140#121—21no—
141#121—21no—
142#121C22×C311yescharacteristic
143#121C22×C311yescharacteristic
144#121C22×C311yescharacteristic
145#121C22×C311yescharacteristic
146C4×Q8C22×C311yescharacteristic
147C4×D4—21no—
148C4×D4—21no—
149C4×D4C22×C311yescharacteristic
150C4×D4C22×C311yescharacteristic
151#117C22×C311yescharacteristic
152C2×C4⋊C4C22×C311yescharacteristic
153#107C22×C311yescharacteristic
154#107C22×C311yescharacteristic
155#106C22×C311yescharacteristic
156C4⋊C8C22×C311yescharacteristic
157#103C22×C311yescharacteristic
158#103C22×C311yescharacteristic
159#103C22×C311yescharacteristic
160#102C22×C311yescharacteristic
161#102C22×C311yescharacteristic
162#102C22×C311yescharacteristic
163#102C22×C311yescharacteristic
164#102C22×C311yescharacteristic
165#102C22×C311yescharacteristic
166#102C22×C311yescharacteristic
167C22⋊C8C22×C311yescharacteristic
168C22⋊C8C22×C311yescharacteristic
169#97C22×C311yescharacteristic
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3C2×D411yescharacteristic
174C23×C3C2×D411yescharacteristic
175C3×Q8—21no—
176C3×Q8#4112yes—
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—21no—
181C3×D4—21no—
182C3×D4—21no—
183C3×D4—41no—
184C3×D4—42no—
185C3×D4—42no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—81no—
189C3×D4—81no—
190C3×D4—81no—
191C3×D4—81no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—81no—
204C2×C3×C4—81no—
205C2×C3×C4C2×D411yescharacteristic
206C2×C3×C4C2×D411yescharacteristic
207C2×C3×C4C2×D411yescharacteristic
208C2×C3×C4C2×D411yescharacteristic
209C2×C3×C4C2411yescharacteristic
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8—21no—
214#41—22no—
215#41—22no—
216#41—41no—
217#41—41no—
218C2×Q8C23×C311yescharacteristic
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—21no—
227C2×D4C3×D411yescharacteristic
228C2×D4C23×C311yescharacteristic
229C2×D4C23×C311yescharacteristic
230C2×D4C23×C311yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C23×C311yescharacteristic
236C22×C4C23×C311yescharacteristic
237SD16—22no—
238D8—41no—
239D8—41no—
240M16—41no—
241C2×C8—41no—
242C2×C8C23×C311yescharacteristic
243C2×C8C23×C311yescharacteristic
244C2×C8C23×C311yescharacteristic
245C2×C8C23×C311yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4C3×D411yescharacteristic
251C4⋊C4C23×C311yescharacteristic
252C4⋊C4C23×C311yescharacteristic
253C4⋊C4C23×C311yescharacteristic
254C4⋊C4C23×C311yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4C3×D411yescharacteristic
262C22⋊C4C3×D411yescharacteristic
263C42—21no—
264C42—21no—
265C42C23×C311yescharacteristic
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3C22×D411yescharacteristic
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4C2×#4111yescharacteristic
292C3×C4H(5,𝔽2)11yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×C3×D411yescharacteristic
297C23C2×C3×D411yescharacteristic
298Q8—21no—
299Q8C3×#4112yes—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—81no—
312D4—81no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4C2×C3×D411yescharacteristic
329C2×C4C2×C3×D411yescharacteristic
330C2×C4C2×C3×D411yescharacteristic
331C2×C4C2×C3×D411yescharacteristic
332C2×C4C24×C311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C2×C3—41no—
338C2×C3—41no—
339C2×C3—81no—
340C2×C3—81no—
341C2×C3—81no—
342C2×C3#54611yescharacteristic
343C2×C3#57511yescharacteristic
344C2×C3#57611yescharacteristic
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22C22×C3×D411yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4C2×C3×#4111yescharacteristic
371C4C3×H(5,𝔽2)11yescharacteristic
372C3#330911yescharacteristic, direct product factor, Sylow
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—81no—
378C2C3×#54611yescharacteristic
379C2C3×#57511yescharacteristic
380C2C3×#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×#553C2semidirect
2. C3×#550C2semidirect
3. C3×#490C2semidirect
4. C3×#482C2semidirect
5. C3×#480C2semidirect
6. C3×#479C2semidirect
7. C3×#469C2semidirect
8. C3×#466C2semidirect
9. C3×#459C2semidirect
10. C3×#449C2semidirect
11. C3×#449C2semidirect
12. C3×#440C2semidirect
13. C3×#435C2semidirect
14. C3×#417C2semidirect
15. C3×#416C2semidirect
16. #3309C3direct (N × H)
60. #553C2×C3semidirect
61. #550C2×C3semidirect
62. #490C2×C3semidirect
63. #482C2×C3semidirect
64. #480C2×C3semidirect
65. #479C2×C3semidirect
66. #469C2×C3semidirect
67. #466C2×C3semidirect
68. #459C2×C3semidirect
69. #449C2×C3semidirect
70. #449C2×C3semidirect
71. #440C2×C3semidirect
72. #435C2×C3semidirect
73. #417C2×C3semidirect
74. #416C2×C3semidirect
372. C3#3309direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#5532
C3×#5502
C3×#4902
C3×#4822
C3×#4802
C3×#4792
C3×#4692
C3×#4662
C3×#4592
C3×#4492
C3×#4402
C3×#4352
C3×#4172
C3×#4162
#33093