Finite Group Databasebeta

← C3×#71907 #11779298

Subgroups — C3×#71907 #11779298

Order 1152.

842 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 130 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×D42C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic, complemented
3C3×#5008C212yesmaximal, complemented
4C3×#4544C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1629—31nomaximal
7#71907C311yesmaximal, characteristic, direct product factor
8C22×C32×D4—22no—
9C32×#127C2211yescharacteristic
10C32×#121—22no—
11C32×#120—22no—
12C32×C4×D4C2212yes—
13C2×C3×#214—22no—
14C3×#869C2211yescharacteristic, complemented
15C3×#832—22no—
16C3×#808—22no—
17C3×C4⋊(C3⋊C8)C2212yescomplemented
18C3×C4×C3⋊C8C2211yescharacteristic, complemented
19C3×D42—21no—
20C3×D42D311yescharacteristic
21C3×D42C2×C311yescharacteristic
22C3×#492—31no—
23C3×#476—32no—
24#5076C2×C311yescharacteristic, complemented
25#5008C2×C312yescomplemented
26C3×#331—31no—
27C3×D4⋊C8—32no—
28#4544C2×C311yescharacteristic, complemented
29D4⋊(C3⋊C8)C2×C312yescomplemented
30C24×C32—22no—
31C2×C32×D4—24no—
32C2×C32×D4—22no—
33C2×C32×D4—44no—
34C2×C32×D4—44no—
35C2×C32×D4D412yes—
36C2×C32×D4D412yes—
37C22×C32×C4—22no—
38C2×C3×Dic6—21no—
39C32×C4⋊C4D412yes—
40C32×C22⋊C4—22no—
41C32×C22⋊C4—22no—
42C32×C42C2311yescharacteristic
43C3×#214—44no—
44C3×C4⋊Dic3—22no—
45C2×C3×C3⋊C8—21no—
46C2×C3×C3⋊C8—22no—
47#1629—31noSylow
48C22×C3×D4—24no—
49C22×C3×D4—22no—
50C22×C3×D4—22no—
51C2×C3×SD16—62no—
52C3×C4⋊Q8—31no—
53C3×#127—21no—
54C3×#127C2×D311yescharacteristic
55C3×#127C22×C311yescharacteristic
56C3×#121—24no—
57C3×#121—22no—
58C3×#121—22no—
59C3×#120—24no—
60C3×#120—22no—
61C3×#120—22no—
62C3×C4×D4—22no—
63C3×C4×D4C2×D312yes—
64C3×C4×D4C22×C312yes—
65C2×#214—22no—
66#869C22×C311yescharacteristic, complemented
67C3×#106—62no—
68C3×C4⋊C8—32no—
69C3×#102—62no—
70C3×C4×C8—31no—
71#832—22no—
72#808—22no—
73C4⋊(C3⋊C8)C22×C312yescomplemented
74C4×C3⋊C8C22×C311yescharacteristic, complemented
75C23×C32—22no—
76C23×C32—22no—
77C23×C32—48no—
78C23×C32—82no—
79C32×D4—22no—
80C32×D4—48no—
81C32×D4—42no—
82C32×D4—42no—
83C32×D4—42no—
84C32×D4SD1614yescomplemented
85C2×C32×C4—22no—
86C2×C32×C4—42no—
87C2×C32×C4—42no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D412yes—
90C2×C3×Dic3—41no—
91C3×Dic6—42no—
92C3×C3⋊C8—22no—
93C3×C3⋊C8—42no—
94D42C3×D311yescharacteristic
95#492—31no—
96#476—32no—
97#331—31no—
98D4⋊C8—32no—
99C24×C3—24no—
100C24×C3—22no—
101C24×C3—22no—
102C2×C3×Q8—61no—
103C2×C3×D4—28no—
104C2×C3×D4—24no—
105C2×C3×D4—24no—
106C2×C3×D4—24no—
107C2×C3×D4—22no—
108C2×C3×D4—22no—
109C2×C3×D4—22no—
110C2×C3×D4—22no—
111C2×C3×D4—48no—
112C2×C3×D4—44no—
113C2×C3×D4—44no—
114C2×C3×D4—48no—
115C2×C3×D4—44no—
116C2×C3×D4—44no—
117C2×C3×D4#6712yes—
118C2×C3×D4#6712yes—
119C2×C3×D4C3×D412yes—
120C2×C3×D4C3×D412yes—
121C22×C3×C4—24no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C2×Dic6—21no—
125C3×SD16—124no—
126C2×C3×C8—61no—
127C2×C3×C8—62no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4#6712yes—
131C3×C4⋊C4C3×D412yes—
132C3×C22⋊C4—24no—
133C3×C22⋊C4—24no—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4—22no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C23×C311yescharacteristic
141#214—44no—
142C4⋊Dic3—22no—
143C2×C3⋊C8—21no—
144C2×C3⋊C8—22no—
145C22×C32—24no—
146C22×C32—42no—
147C22×C32—42no—
148C22×C32—44no—
149C22×C32—42no—
150C22×C32—88no—
151C22×C32#12011yescharacteristic
152C32×C4—21no—
153C32×C4—42no—
154C32×C4C2×SD1612yes—
155C32×C4AGL(1,ℤ/8)12yes—
156C3×Dic3—81no—
157C22×D4—22no—
158C2×SD16—62no—
159C4⋊Q8—31no—
160#127C2×C3×D311yescharacteristic
161#121—22no—
162#120—22no—
163C4×D4C2×C3×D312yes—
164#106—62no—
165C4⋊C8—32no—
166#102—62no—
167C4×C8—31no—
168C23×C3—24no—
169C23×C3—22no—
170C23×C3—22no—
171C23×C3—24no—
172C23×C3—22no—
173C23×C3—22no—
174C23×C3—416no—
175C23×C3—48no—
176C23×C3—48no—
177C23×C3—84no—
178C23×C3—82no—
179C23×C3—82no—
180C3×Q8—122no—
181C3×D4—24no—
182C3×D4—22no—
183C3×D4—22no—
184C3×D4—24no—
185C3×D4—42no—
186C3×D4—42no—
187C3×D4—44no—
188C3×D4—44no—
189C3×D4—416no—
190C3×D4—48no—
191C3×D4—48no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—82no—
197C3×D4#21414yescomplemented
198C3×D4C3×SD1614yescomplemented
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4—121no—
211C2×C3×C4C2×#6711yescharacteristic
212C2×C3×C4C2×#6712yes—
213C2×C3×C4C2×C3×D411yescharacteristic
214C2×C3×C4C2×C3×D412yes—
215C2×Dic3—41no—
216Dic6—42no—
217C3×C8—62no—
218C3×C8—122no—
219C3⋊C8—22no—
220C3⋊C8—42no—
221C2×C32—44no—
222C2×C32—82no—
223C2×C32#45012yes—
224C2×C32#45311yescharacteristic
225C24—22no—
226C2×Q8—61no—
227C2×D4—24no—
228C2×D4—22no—
229C2×D4—44no—
230C2×D4—44no—
231C2×D4C3×#6712yes—
232C2×D4C3×#6712yes—
233C22×C4—22no—
234SD16—124no—
235C2×C8—61no—
236C2×C8—62no—
237C4⋊C4—62no—
238C4⋊C4C3×#6712yes—
239C22⋊C4—22no—
240C22⋊C4—22no—
241C42C22×C3×D311yescharacteristic
242C22×C3—28no—
243C22×C3—24no—
244C22×C3—24no—
245C22×C3—21no—
246C22×C3—44no—
247C22×C3—44no—
248C22×C3—48no—
249C22×C3—44no—
250C22×C3—42no—
251C22×C3—42no—
252C22×C3—42no—
253C22×C3—42no—
254C22×C3—44no—
255C22×C3—42no—
256C22×C3—44no—
257C22×C3—42no—
258C22×C3—816no—
259C22×C3—88no—
260C22×C3—88no—
261C22×C3#95311yescharacteristic
262C22×C3C3×#12011yescharacteristic
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—41no—
268C3×C4—44no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—241no—
272C3×C4#93212yes—
273C3×C4C2×#21412yes—
274C3×C4C2×C3×SD1612yes—
275C3×C4C3×AGL(1,ℤ/8)12yes—
276Dic3—81no—
277C32#162911yescharacteristic, complemented, Sylow
278C23—22no—
279C23—22no—
280C23—48no—
281C23—82no—
282Q8—122no—
283D4—22no—
284D4—42no—
285D4—48no—
286D4—42no—
287D4—42no—
288D4C3×#21414yescomplemented
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—121no—
293C2×C4C2×C3×#6711yescharacteristic
294C2×C4C2×C3×#6712yes—
295C8—62no—
296C8—122no—
297C2×C3—22no—
298C2×C3—21no—
299C2×C3—48no—
300C2×C3—44no—
301C2×C3—44no—
302C2×C3—84no—
303C2×C3—82no—
304C2×C3—82no—
305C2×C3#521812yes—
306C2×C3#524111yescharacteristic
307C2×C3C3×#45012yes—
308C2×C3C3×#45311yescharacteristic
309C22—24no—
310C22—42no—
311C22—42no—
312C22—44no—
313C22—42no—
314C22—88no—
315C22C3×#95311yescharacteristic
316C4—21no—
317C4—42no—
318C4—241no—
319C4C3×#93212yes—
320C4C2×C3×#21412yes—
321C3—21no—
322C3#7190711yescharacteristic, direct product factor
323C3C3×#162911yescharacteristic, complemented
324C2—44no—
325C2—82no—
326C2C3×#521812yes—
327C2C3×#524111yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×D42C2
socleC22×C32#120
hypercenterC3×D42D3
hypocenterC3C3×#1629
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D42

Complements

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

NH ≅ G/Ntype
2. C3×#5076C2semidirect
3. C3×#5008C2semidirect
4. C3×#4544C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71907C3direct (N × H)
14. C3×#869C22semidirect
17. C3×C4⋊(C3⋊C8)C22semidirect
18. C3×C4×C3⋊C8C22semidirect
24. #5076C2×C3semidirect
25. #5008C2×C3semidirect
28. #4544C2×C3semidirect
29. D4⋊(C3⋊C8)C2×C3semidirect
66. #869C22×C3semidirect
73. C4⋊(C3⋊C8)C22×C3semidirect
74. C4×C3⋊C8C22×C3semidirect
84. C32×D4SD16semidirect
197. C3×D4#214semidirect
198. C3×D4C3×SD16semidirect
277. C32#1629semidirect
288. D4C3×#214semidirect
322. C3#71907direct (N × H)
323. C3C3×#1629semidirect

Maximal subgroups

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

subgroupindex
C32×D422
C3×#50762
C3×#50082
C3×#45442
C3×D4⋊(C3⋊C8)2
C3×#16293
#719073