Finite Group Databasebeta

← #83185⋊C3 #11921297

Subgroups — #83185⋊C3 #11921297

Order 1152.

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

normal subgroups only

This group has 519 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×C3×#127⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#127⋊C3)C211yesmaximal, characteristic, complemented
3Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
4#83185C311yesmaximal, characteristic, complemented
5C4⋊(#127⋊C3)—31nomaximal
6A4×#67—41nomaximal
7C3×#127⋊C3—21no—
8C2×C3×C42⋊C3C2211yescharacteristic
9C3⋊(#127⋊C3)—21no—
10C2×C3×#127C2×C311yescharacteristic, complemented
11C2×#940—31no—
12C2×#940—31no—
13C2×#940—31no—
14C2×#940—31no—
15C2×#874C2×C311yescharacteristic, complemented
16C2×#127⋊C3—21no—
17C2×#127⋊C3—31no—
18C2×#127⋊C3D311yescharacteristic, complemented
19C42×Dic3C2×C311yescharacteristic, complemented
20C4×C42⋊C3—31no—
21C22×C3×A4—41no—
22C2×D3×A4—41no—
23Dic3×A4—41no—
24C3×C42⋊C3D411yescharacteristic, complemented
25#2867—31noSylow
26C22×C3×D4—31no—
27C22×C3×D4—31no—
28C22×#67—32no—
29C22×#67—31no—
30C22×#67—31no—
31C22×#67—31no—
32C22×#67A411yescharacteristic
33C22×D12—31no—
34C22×D12—31no—
35D4×A4—121no—
36C3×#127—21no—
37C3×#127—61no—
38C2×C3×C42C22×C311yescharacteristic
39#940—62no—
40#940—64no—
41#940—64no—
42#940—62no—
43#940—62no—
44#940—62no—
45C2×C4×Dic3—31no—
46C2×C4×Dic3—31no—
47#874—21no—
48#874—61no—
49#127⋊C3—22no—
50#127⋊C3—21no—
51#127⋊C3—61no—
52C2×C42⋊C3—21no—
53C2×C42⋊C3C2×D311yescharacteristic
54C2×C3×A4—41no—
55C2×C3×A4—81no—
56D3×A4—81no—
57C3×#67—161no—
58C2×#127—31no—
59C2×#127—91no—
60C2×#127—91no—
61C2×#127—91no—
62C2×#127—91no—
63C2×#127C3×D311yescharacteristic, complemented
64C43—31no—
65C24×C3—31no—
66C24×C3C2×A411yescharacteristic
67C23×D3—31no—
68C23×D3C2×A411yescharacteristic
69C22×A4—41no—
70C22×A4—81no—
71C22×A4—121no—
72C2×C3×D4—61no—
73C2×C3×D4—61no—
74C2×C3×D4—61no—
75C2×C3×D4—61no—
76C2×C3×D4—62no—
77C2×C3×D4—62no—
78C2×C3×D4—62no—
79C2×C3×D4—62no—
80C22×C3×C4—31no—
81C2×#67—61no—
82C2×#67—62no—
83C2×#67—62no—
84C2×#67—64no—
85C2×#67—64no—
86C2×#67—64no—
87C2×#67—64no—
88C2×#67—64no—
89C2×#67—61no—
90C2×#67—62no—
91C2×#67—62no—
92C2×#67—61no—
93C2×#67—61no—
94C22×Dic3—31no—
95C22×Dic3C2×A411yescharacteristic
96C2×D12—61no—
97C2×D12—61no—
98C2×D12—61no—
99C2×D12—61no—
100C2×D12—62no—
101C2×D12—62no—
102C2×D12—62no—
103C2×D12—62no—
104C4×A4—121no—
105C3×C42—31no—
106C3×C42C3×D411yescharacteristic, complemented
107C4×Dic3—34no—
108C4×Dic3—32no—
109C4×Dic3—32no—
110C42⋊C3—21no—
111C42⋊C3#6711yescharacteristic, complemented
112C22×C32—161no—
113C2×C3×D3—161no—
114C3×A4—41no—
115C3×Dic3—161no—
116C22×D4—31no—
117C22×D4—31no—
118C22×D4—31no—
119C22×D4—91no—
120C22×D4—91no—
121C22×D4—91no—
122C22×D4—91no—
123C22×D4—92no—
124C22×D4—91no—
125#127—21no—
126#127—61no—
127#127—61no—
128#127—181no—
129#127—182no—
130#127—182no—
131#127—184no—
132#127—184no—
133#127—182no—
134#127—182no—
135C2×C42—91no—
136C2×C42—91no—
137C2×C42C2×C3×D311yescharacteristic
138C23×C3—21no—
139C23×C3—61no—
140C23×C3—61no—
141C23×C3—61no—
142C23×C3—62no—
143C23×C3—61no—
144C23×C3—62no—
145C23×C3—61no—
146C23×C3C22×A411yescharacteristic
147C22×D3—21no—
148C22×D3—61no—
149C22×D3—62no—
150C22×D3—61no—
151C22×D3—61no—
152C22×D3—62no—
153C22×D3—61no—
154C22×D3—61no—
155C2×A4—41no—
156C2×A4—81no—
157C2×A4—82no—
158C2×A4—81no—
159C2×A4—241no—
160C3×D4—122no—
161C3×D4—122no—
162C3×D4—122no—
163C3×D4—122no—
164C3×D4—481no—
165C2×C3×C4—32no—
166C2×C3×C4—32no—
167C2×C3×C4—31no—
168C2×C3×C4—31no—
169#67—41no—
170#67—121no—
171#67—124no—
172#67—124no—
173#67—128no—
174#67—121no—
175#67—122no—
176#67—121no—
177C2×Dic3—34no—
178C2×Dic3—32no—
179C2×Dic3—31no—
180C2×Dic3—31no—
181D12—122no—
182D12—122no—
183D12—122no—
184D12—122no—
185C2×C32—161no—
186C2×C32—321no—
187C3×D3—321no—
188C24—31no—
189C24—31no—
190C24—91no—
191C24D3×A411yescharacteristic
192C2×D4—61no—
193C2×D4—61no—
194C2×D4—61no—
195C2×D4—61no—
196C2×D4—62no—
197C2×D4—62no—
198C2×D4—62no—
199C2×D4—62no—
200C2×D4—181no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4—181no—
204C2×D4—182no—
205C2×D4—182no—
206C2×D4—182no—
207C2×D4—182no—
208C2×D4—181no—
209C2×D4—181no—
210C2×D4—182no—
211C2×D4—182no—
212C2×D4—184no—
213C2×D4—182no—
214C2×D4—184no—
215C2×D4—184no—
216C2×D4—184no—
217C2×D4—184no—
218C2×D4—182no—
219C2×D4—181no—
220C2×D4—181no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—91no—
224C42—31no—
225C42—92no—
226C42—94no—
227C42—92no—
228C42C3×#6711yescharacteristic, complemented
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—41no—
232C22×C3—121no—
233C22×C3—121no—
234C22×C3—121no—
235C22×C3—122no—
236C22×C3—121no—
237C22×C3—122no—
238C22×C3—121no—
239C22×C3—161no—
240C22×C3—321no—
241C22×C3—481no—
242C22×C3D4×A411yescharacteristic
243C2×D3—41no—
244C2×D3—121no—
245C2×D3—121no—
246C2×D3—121no—
247C2×D3—122no—
248C2×D3—121no—
249C2×D3—122no—
250C2×D3—121no—
251A4—41no—
252A4—81no—
253C3×C4—32no—
254C3×C4—32no—
255C3×C4—481no—
256Dic3—34no—
257Dic3—31no—
258Dic3#127⋊C311yescharacteristic, complemented
259C32—161noSylow
260C23—21no—
261C23—61no—
262C23—61no—
263C23—61no—
264C23—62no—
265C23—61no—
266C23—62no—
267C23—61no—
268C23—61no—
269C23—181no—
270C23—181no—
271C23—181no—
272C23—182no—
273C23—181no—
274C23—182no—
275C23—181no—
276C23C2×D3×A411yescharacteristic
277D4—121no—
278D4—122no—
279D4—122no—
280D4—122no—
281D4—122no—
282D4—361no—
283D4—362no—
284D4—362no—
285D4—362no—
286D4—362no—
287D4—361no—
288D4—364no—
289D4—364no—
290D4—368no—
291D4—361no—
292D4—362no—
293C2×C4—32no—
294C2×C4—32no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—91no—
298C2×C4—94no—
299C2×C4—92no—
300C2×C4—91no—
301C2×C3—31no—
302C2×C3—31no—
303C2×C3—81no—
304C2×C3—161no—
305C2×C3—241no—
306C2×C3—321no—
307C2×C3—322no—
308C2×C3—321no—
309C2×C3—961no—
310C2×C3C2×#127⋊C311yescharacteristic
311D3—81no—
312D3—241no—
313C22—31no—
314C22—31no—
315C22—41no—
316C22—121no—
317C22—121no—
318C22—121no—
319C22—122no—
320C22—121no—
321C22—122no—
322C22—121no—
323C22—121no—
324C22—361no—
325C22—361no—
326C22—361no—
327C22—362no—
328C22—361no—
329C22—362no—
330C22—361no—
331C22A4×#6711yescharacteristic
332C4—32no—
333C4—32no—
334C4—31no—
335C4—94no—
336C4—91no—
337C3—161no—
338C3—321no—
339C3C4⋊(#127⋊C3)11yescharacteristic, complemented
340C2—31no—
341C2—31no—
342C2—81no—
343C2—241no—
344C2—241no—
345C2—721no—
346C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC2×C3×#127C2×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×C3×#127⋊C3C2semidirect
2. C2×C3⋊(#127⋊C3)C2semidirect
3. Dic3×C42⋊C3C2semidirect
4. #83185C3semidirect
10. C2×C3×#127C2×C3semidirect
15. C2×#874C2×C3semidirect
18. C2×#127⋊C3D3semidirect
19. C42×Dic3C2×C3semidirect
24. C3×C42⋊C3D4semidirect
63. C2×#127C3×D3semidirect
106. C3×C42C3×D4semidirect
111. C42⋊C3#67semidirect
228. C42C3×#67semidirect
258. Dic3#127⋊C3semidirect
339. C3C4⋊(#127⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
C2×C3⋊(#127⋊C3)2
Dic3×C42⋊C32
#831853
C4⋊(#127⋊C3)3
A4×#674