Finite Group Databasebeta

← #74375⋊C3 #11921161

Subgroups — #74375⋊C3 #11921161

Order 1152.

397 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C2×D3×C42⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#127⋊C3)C211yesmaximal, characteristic, complemented
3C3×#384⋊C3C211yesmaximal, characteristic, complemented
4#74375C311yesmaximal, characteristic, complemented
5#2856⋊C3—31nomaximal
6A4×D12—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8D3×C42⋊C3—21no—
9C3⋊(#127⋊C3)—21no—
10C2×#895—31no—
11C2×#895—31no—
12C2×#874C2×C311yescharacteristic, complemented
13C2×C42×D3C2×C311yescharacteristic, complemented
14C2×#127⋊C3—31no—
15C22×C42⋊C3—31no—
16C3×#384C2×C311yescharacteristic, complemented
17#4988—31no—
18#4988—31no—
19#384⋊C3—21no—
20#384⋊C3D311yescharacteristic, complemented
21C2×D3×A4—41no—
22C2×D3×A4—41no—
23C3×C4×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2856—31noSylow
26C22×D12—31no—
27C22×D12—31no—
28C22×D12—31no—
29C22×D12A411yescharacteristic
30C22×C4×D3—31no—
31D4×A4—121no—
32C2×C3×C4⋊C4—31no—
33C2×C3×C4⋊C4—31no—
34C2×C3×C42C22×C311yescharacteristic
35C2×(C2×D3)⋊C4—32no—
36C2×(C2×D3)⋊C4—31no—
37C2×(C2×D3)⋊C4—31no—
38C2×C4×Dic3—31no—
39#895—62no—
40#895—62no—
41#895—62no—
42#895—62no—
43#874—21no—
44#874—61no—
45C42×D3—21no—
46C42×D3—61no—
47#127⋊C3—61no—
48C2×C42⋊C3—21no—
49C2×C42⋊C3—61no—
50C2×C42⋊C3C2×D311yescharacteristic
51C2×C3×A4—41no—
52D3×A4—81no—
53D3×A4—81no—
54C3×D12—161no—
55C2×#127—31no—
56C2×#121—91no—
57C2×#121—91no—
58C22×C42—31no—
59#390—91no—
60#390—91no—
61#384C3×D311yescharacteristic, complemented
62C23×D3—31no—
63C23×D3C2×A411yescharacteristic
64C23×D3C2×A411yescharacteristic
65C22×A4—121no—
66C22×A4—121no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4C2×A411yescharacteristic
70C22×Dic3—31no—
71C2×D12—61no—
72C2×D12—61no—
73C2×D12—61no—
74C2×D12—61no—
75C2×D12—61no—
76C2×D12—62no—
77C2×D12—62no—
78C2×D12—62no—
79C2×D12—62no—
80C2×D12—62no—
81C2×D12—61no—
82C2×D12—61no—
83C2×D12—62no—
84C2×D12—61no—
85C2×C4×D3—32no—
86C2×C4×D3—32no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—62no—
90C4×A4—41no—
91C4×A4—81no—
92C3×C4⋊C4—62no—
93C3×C4⋊C4—62no—
94C3×C42—31no—
95C3×C42C3×D411yescharacteristic, complemented
96(C2×D3)⋊C4—62no—
97(C2×D3)⋊C4—62no—
98(C2×D3)⋊C4—64no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C42⋊C3—21no—
102C42⋊C3D1211yescharacteristic, complemented
103C2×C3×D3—161no—
104C2×C3×D3—161no—
105C3×A4—41no—
106C32×C4—161no—
107C22×D4—31no—
108C22×D4—91no—
109C22×D4—91no—
110C22×D4—91no—
111C23×C4—91no—
112#127—61no—
113#127—181no—
114#121—182no—
115#121—182no—
116#121—182no—
117#121—182no—
118C2×C4⋊C4—31no—
119C2×C4⋊C4—31no—
120C2×C22⋊C4—91no—
121C2×C22⋊C4—92no—
122C2×C22⋊C4—91no—
123C2×C42—61no—
124C2×C42—91no—
125C2×C42—181no—
126C2×C42C2×C3×D311yescharacteristic
127C23×C3C22×A411yescharacteristic
128C22×D3—21no—
129C22×D3—21no—
130C22×D3—31no—
131C22×D3—31no—
132C22×D3—61no—
133C22×D3—61no—
134C22×D3—61no—
135C22×D3—62no—
136C22×D3—62no—
137C22×D3—61no—
138C22×D3—61no—
139C22×D3—61no—
140C2×A4—41no—
141C2×A4—81no—
142C2×A4—241no—
143C2×A4—241no—
144C3×D4—481no—
145C2×C3×C4—32no—
146C2×C3×C4—32no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—61no—
150C2×C3×C4—61no—
151C2×C3×C4—62no—
152C2×Dic3—32no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155D12—41no—
156D12—122no—
157D12—122no—
158D12—122no—
159D12—122no—
160D12—121no—
161D12—121no—
162D12—122no—
163D12—121no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C2×C32—161no—
169C3×D3—321no—
170C3×D3—321no—
171C24—31no—
172C24—31no—
173C24—91no—
174C2×D4—181no—
175C2×D4—181no—
176C2×D4—181no—
177C2×D4—181no—
178C2×D4—182no—
179C2×D4—182no—
180C2×D4—182no—
181C2×D4—182no—
182C2×D4—181no—
183C2×D4—181no—
184C2×D4—182no—
185C2×D4—182no—
186C2×D4—181no—
187C2×D4—181no—
188C22×C4—31no—
189C22×C4—31no—
190C22×C4—92no—
191C22×C4—92no—
192C22×C4—91no—
193C22×C4—181no—
194C22×C4—181no—
195C22×C4—182no—
196C22×C4D3×A411yescharacteristic
197C4⋊C4—62no—
198C4⋊C4—62no—
199C22⋊C4—182no—
200C22⋊C4—182no—
201C22⋊C4—184no—
202C42—31no—
203C42—181no—
204C42—181no—
205C42C3×D1211yescharacteristic, complemented
206C22×C3—31no—
207C22×C3—31no—
208C22×C3—481no—
209C22×C3—481no—
210C22×C3D4×A411yescharacteristic
211C2×D3—31no—
212C2×D3—41no—
213C2×D3—61no—
214C2×D3—61no—
215C2×D3—61no—
216C2×D3—61no—
217C2×D3—121no—
218C2×D3—121no—
219C2×D3—121no—
220C2×D3—122no—
221C2×D3—121no—
222C2×D3—122no—
223C2×D3—121no—
224C2×D3#127⋊C311yescharacteristic, complemented
225A4—41no—
226A4—81no—
227C3×C4—32no—
228C3×C4—32no—
229C3×C4—41no—
230C3×C4—121no—
231C3×C4—161no—
232C3×C4—321no—
233Dic3—62no—
234C32—161noSylow
235C23—61no—
236C23—61no—
237C23—91no—
238C23—91no—
239C23—181no—
240C23—181no—
241C23—181no—
242C23—181no—
243C23—182no—
244C23—181no—
245C23—182no—
246C23—181no—
247C23C2×D3×A411yescharacteristic
248D4—121no—
249D4—362no—
250D4—362no—
251D4—362no—
252D4—362no—
253D4—361no—
254D4—361no—
255D4—361no—
256D4—362no—
257C2×C4—32no—
258C2×C4—32no—
259C2×C4—31no—
260C2×C4—31no—
261C2×C4—61no—
262C2×C4—61no—
263C2×C4—62no—
264C2×C4—92no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C3—31no—
272C2×C3—31no—
273C2×C3—161no—
274C2×C3—321no—
275C2×C3—961no—
276C2×C3—961no—
277C2×C3C2×#127⋊C311yescharacteristic
278D3—21no—
279D3—61no—
280D3—81no—
281D3—241no—
282C22—31no—
283C22—31no—
284C22—31no—
285C22—91no—
286C22—121no—
287C22—181no—
288C22—181no—
289C22—181no—
290C22—181no—
291C22—361no—
292C22—361no—
293C22—361no—
294C22—362no—
295C22—361no—
296C22—362no—
297C22—361no—
298C22A4×D1211yescharacteristic
299C4—32no—
300C4—32no—
301C4—41no—
302C4—121no—
303C4—182no—
304C3—161no—
305C3—321no—
306C3#2856⋊C311yescharacteristic, complemented
307C2—31no—
308C2—31no—
309C2—61no—
310C2—181no—
311C2—241no—
312C2—721no—
313C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#384C2×C3
socleC23×C3C22×A4
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D3×C42⋊C3C2semidirect
2. C2×C3⋊(#127⋊C3)C2semidirect
3. C3×#384⋊C3C2semidirect
4. #74375C3semidirect
12. C2×#874C2×C3semidirect
13. C2×C42×D3C2×C3semidirect
16. C3×#384C2×C3semidirect
20. #384⋊C3D3semidirect
24. C3×C42⋊C3D4semidirect
61. #384C3×D3semidirect
95. C3×C42C3×D4semidirect
102. C42⋊C3D12semidirect
205. C42C3×D12semidirect
224. C2×D3#127⋊C3semidirect
306. C3#2856⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C42⋊C32
C2×C3⋊(#127⋊C3)2
C3×#384⋊C32
#743753
#2856⋊C33
A4×D124