Finite Group Databasebeta

← C3×#71955 #11780516

Subgroups — C3×#71955 #11780516

Order 1152.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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×#563C211yesmaximal, characteristic, complemented
2C3×#5067C212yesmaximal, complemented
3C3×#5058C211yesmaximal, characteristic
4C3×#4543C212yesmaximal, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6C3×#1657—31nomaximal
7#71955C311yesmaximal, characteristic, direct product factor
8C32×C4⋊Q8—21no—
9C32×#126—22no—
10C32×#125C2212yes—
11C32×#124C2211yescharacteristic
12C32×#123—21no—
13C32×C22⋊Q8—22no—
14C2×C3×#215—21no—
15C2×C3×#213—21no—
16C3×#874C2211yescharacteristic
17C3×#809—22no—
18C3×#809—22no—
19C3×#803C2212yes—
20C3×#803C2211yescharacteristic
21C3×#563—21no—
22C3×#563D311yescharacteristic, complemented
23C3×#563C2×C311yescharacteristic, complemented
24C3×#496—31no—
25C3×#490—32no—
26#5067C2×C312yescomplemented
27#5058C2×C311yescharacteristic
28C3×#330—32no—
29C3×#329—31no—
30#4543C2×C312yescomplemented
31#4540C2×C311yescharacteristic, complemented
32C2×C32×Q8—21no—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4D411yescharacteristic
35C22×C32×C4—21no—
36C2×C3×D12—21no—
37C2×C3×D12—22no—
38C32×C4⋊C4—22no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4—22no—
41C32×C4⋊C4D412yes—
42C32×C4⋊C4D412yes—
43C32×C22⋊C4—22no—
44C32×C22⋊C4—21no—
45C32×C22⋊C4—22no—
46C32×C42—21no—
47C32×C42C2311yescharacteristic
48C3×#215—42no—
49C3×#213—42no—
50C2×C3×C3⋊C8—21no—
51C2×C3×C3⋊C8—22no—
52#1657—31noSylow
53C2×C3×SD16—61no—
54C2×C3×D8—61no—
55C3×C4⋊Q8—22no—
56C3×C4⋊Q8—21no—
57C3×C4⋊Q8—21no—
58C3×#127—31no—
59C3×#126—24no—
60C3×#126—22no—
61C3×#126—22no—
62C3×#125—22no—
63C3×#125C2×D312yes—
64C3×#125C22×C312yes—
65C3×#124—21no—
66C3×#124C2×D311yescharacteristic
67C3×#124C22×C311yescharacteristic
68C3×#123—22no—
69C3×#123—21no—
70C3×#123—21no—
71C3×C22⋊Q8—24no—
72C3×C22⋊Q8—22no—
73C3×C22⋊Q8—22no—
74C2×#215—21no—
75C2×#213—21no—
76#874C22×C311yescharacteristic
77C3×#102—62no—
78C3×#102—62no—
79C3×#97—32no—
80C3×#97—31no—
81#809—22no—
82#809—22no—
83#803C22×C312yes—
84#803C22×C311yescharacteristic
85C23×C32—21no—
86C22×C3×D3—41no—
87C32×Q8—41no—
88C32×Q8—81no—
89C32×D4—41no—
90C2×C32×C4—22no—
91C2×C32×C4—21no—
92C2×C32×C4—22no—
93C2×C32×C4—81no—
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C3×D12—41no—
97C3×D12—41no—
98C3×D12—44no—
99C3×C3⋊C8—22no—
100C3×C3⋊C8—42no—
101#563C3×D311yescharacteristic, complemented
102#496—31no—
103#490—32no—
104#330—32no—
105#329—31no—
106C2×C3×Q8—22no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109C2×C3×Q8—21no—
110C2×C3×Q8#6711yescharacteristic
111C2×C3×Q8C3×D411yescharacteristic
112C2×C3×D4—21no—
113C2×C3×D4—62no—
114C2×C3×D4—61no—
115C2×C3×D4#6711yescharacteristic
116C2×C3×D4C3×D411yescharacteristic
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C2×D12—22no—
121C2×D12—21no—
122C3×SD16—122no—
123C3×D8—122no—
124C2×C3×C8—61no—
125C2×C3×C8—62no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4—24no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—24no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—22no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4#6712yes—
138C3×C4⋊C4#6712yes—
139C3×C4⋊C4C3×D412yes—
140C3×C4⋊C4C3×D412yes—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—22no—
144C3×C22⋊C4—24no—
145C3×C22⋊C4—22no—
146C3×C22⋊C4—21no—
147C3×C22⋊C4—21no—
148C3×C22⋊C4—22no—
149C3×C22⋊C4—22no—
150C3×C42—22no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156#215—42no—
157#213—42no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—22no—
160C22×C32—41no—
161C22×C32—42no—
162C22×C32#12011yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—82no—
165C32×C4—21no—
166C32×C4—22no—
167C32×C4—42no—
168C32×C4—41no—
169C32×C4—42no—
170C2×SD16—61no—
171C2×D8—61no—
172C4⋊Q8—21no—
173#127—31no—
174#126—22no—
175#125C2×C3×D312yes—
176#124C2×C3×D311yescharacteristic
177#123—21no—
178C22⋊Q8—22no—
179#102—62no—
180#102—62no—
181#97—32no—
182#97—31no—
183C23×C3—22no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—121no—
187C22×D3—41no—
188C3×Q8—41no—
189C3×Q8—41no—
190C3×Q8—81no—
191C3×Q8—82no—
192C3×Q8—81no—
193C3×Q8—81no—
194C3×D4—41no—
195C3×D4—41no—
196C3×D4—81no—
197C3×D4—121no—
198C3×D4—121no—
199C3×D4—124no—
200C2×C3×C4—24no—
201C2×C3×C4—22no—
202C2×C3×C4—24no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—21no—
211C2×C3×C4—82no—
212C2×C3×C4—81no—
213C2×C3×C4—81no—
214C2×C3×C4C2×#6712yes—
215C2×C3×C4C2×#6711yescharacteristic
216C2×C3×C4C2×C3×D412yes—
217C2×C3×C4C2×C3×D411yescharacteristic
218D12—41no—
219D12—41no—
220D12—44no—
221C3×C8—62no—
222C3×C8—122no—
223C3⋊C8—22no—
224C3⋊C8—42no—
225C2×C32—81no—
226C2×C32#45311yescharacteristic
227C2×C32#45412yes—
228C3×D3—161no—
229C2×Q8—21no—
230C2×Q8C3×#6711yescharacteristic
231C2×D4—62no—
232C2×D4—61no—
233C2×D4C3×#6711yescharacteristic
234C22×C4—21no—
235SD16—122no—
236D8—122no—
237C2×C8—61no—
238C2×C8—62no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4C3×#6712yes—
243C4⋊C4C3×#6712yes—
244C22⋊C4—22no—
245C22⋊C4—21no—
246C22⋊C4—22no—
247C42—21no—
248C42C22×C3×D311yescharacteristic
249C22×C3—21no—
250C22×C3—42no—
251C22×C3—44no—
252C22×C3—41no—
253C22×C3—42no—
254C22×C3—41no—
255C22×C3—42no—
256C22×C3—241no—
257C22×C3—242no—
258C22×C3#95311yescharacteristic
259C22×C3C3×#12011yescharacteristic
260C2×D3—81no—
261C2×D3—82no—
262C3×C4—21no—
263C3×C4—22no—
264C3×C4—21no—
265C3×C4—22no—
266C3×C4—41no—
267C3×C4—42no—
268C3×C4—44no—
269C3×C4—42no—
270C3×C4—44no—
271C3×C4—42no—
272C3×C4—41no—
273C3×C4—42no—
274C3×C4—42no—
275C3×C4—41no—
276C3×C4—42no—
277C32#165711yescharacteristic, complemented, Sylow
278C23—21no—
279C23—121no—
280Q8—41no—
281Q8—81no—
282D4—41no—
283D4—121no—
284D4—121no—
285D4—124no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—81no—
290C2×C4C2×C3×#6712yes—
291C2×C4C2×C3×#6711yescharacteristic
292C8—62no—
293C8—122no—
294C2×C3—21no—
295C2×C3—22no—
296C2×C3—82no—
297C2×C3—81no—
298C2×C3—81no—
299C2×C3—481no—
300C2×C3#524111yescharacteristic
301C2×C3#524512yes—
302C2×C3C3×#45311yescharacteristic
303C2×C3C3×#45412yes—
304D3—161no—
305C22—41no—
306C22—42no—
307C22—241no—
308C22—242no—
309C22C3×#95311yescharacteristic
310C4—21no—
311C4—22no—
312C4—42no—
313C4—41no—
314C4—42no—
315C3—21no—
316C3#7195511yescharacteristic, direct product factor
317C3C3×#165711yescharacteristic, complemented
318C2—81no—
319C2—481no—
320C2C3×#524111yescharacteristic
321C2C3×#524512yes—
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#563C2
socleC22×C32#120
prime radicalC3×#5058C2
hypercenterC3×#563D3
hypocenterC3C3×#1657
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#563

Complements

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

NH ≅ G/Ntype
1. C32×#563C2semidirect
2. C3×#5067C2semidirect
4. C3×#4543C2semidirect
5. C3×#4540C2semidirect
7. #71955C3direct (N × H)
22. C3×#563D3semidirect
23. C3×#563C2×C3semidirect
26. #5067C2×C3semidirect
30. #4543C2×C3semidirect
31. #4540C2×C3semidirect
101. #563C3×D3semidirect
277. C32#1657semidirect
316. C3#71955direct (N × H)
317. C3C3×#1657semidirect

Maximal subgroups

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

subgroupindex
C32×#5632
C3×#50672
C3×#50582
C3×#45432
C3×#45402
C3×#16573
#719553