Finite Group Databasebeta

← #11921004

Subgroups — #11921004

Order 1152.

382 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C22×C3×C42⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊#857C211yesmaximal, characteristic, complemented
3C3⋊#4623C211yesmaximal, characteristic, complemented
4#73048—33nomaximal
5#71532—31nomaximal
6#64269—41nomaximal
7C2×C3×C42⋊C3—21no—
8C2×C3×C42⋊C3C2211yescharacteristic
9C3⋊#857—21no—
10C22×C3×C42D311yescharacteristic, complemented
11#5791—31no—
12C22×C42⋊C3D313yescomplemented
13C2×#857—33no—
14#5207—31no—
15C2×#805—31no—
16C2×#805—31no—
17#4623—33no—
18#4523—31no—
19#4523—31no—
20C22×C3×A4—41no—
21C2×C3⋊S4—41no—
22C3⋊SL(2,ℤ/4)—41no—
23C3×C42⋊C3D411yescharacteristic, complemented
24#1896—91noSylow
25C23×C3×C4—31no—
26C2×#235—31no—
27GL(2,ℤ/4)—123no—
28C2×C3×C42—21no—
29C2×C3×C42—31no—
30C2×C3×C42—61no—
31C2×C3×C42C2×D311yescharacteristic
32#953—61no—
33#930—31no—
34#930—31no—
35#929—61no—
36C4×#67—61no—
37C4×#67—61no—
38#926—31no—
39#924—31no—
40#924—31no—
41C2×#208—31no—
42C2×#208—31no—
43C2×C42⋊C3—23no—
44C2×C42⋊C3C2×D313yes—
45#857—63no—
46#830—61no—
47#830—61no—
48#805—61no—
49#805—62no—
50#805—61no—
51C2×C3×A4—41no—
52C2×C3×A4—81no—
53C3⋊S4—81no—
54#638—161no—
55#525—91no—
56C22×C42C3⋊D311yescharacteristic, complemented
57C2×#104—91no—
58C2×#104—91no—
59#407—91no—
60#339—91no—
61#339—91no—
62C24×C3S411yescharacteristic
63C22×A4—43no—
64C2×S4—123no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—31no—
70C22×C3×C4—31no—
71C22×C3×C4—61no—
72C22×C3×C4—61no—
73C22×C3×C4—61no—
74C22×C3×C4—61no—
75C2×#67—61no—
76C2×#67—61no—
77C2×#67—61no—
78#235—61no—
79#235—61no—
80#235—61no—
81#235—61no—
82C2×D12—31no—
83C2×C4×D3—61no—
84C2×Dic6—31no—
85SL(2,ℤ/4)—123no—
86C3×C42—31no—
87C3×C42—32no—
88C3×C42—61no—
89C3×C42#6711yescharacteristic, complemented
90#217—61no—
91#217—61no—
92#217—61no—
93(C2×D3)⋊C4—61no—
94(C2×D3)⋊C4—61no—
95C4⋊Dic3—31no—
96C4⋊Dic3—31no—
97Dic3⋊C4—61no—
98Dic3⋊C4—61no—
99C4×Dic3—61no—
100#208—61no—
101#208—61no—
102#208—61no—
103#208—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C42⋊C3#6713yescomplemented
107C22×C32—161no—
108C2×C3⋊D3—161no—
109C3×A4—41no—
110C3⋊Dic3—161no—
111C2×#41—91no—
112C23×C4—31no—
113C2×M16—91no—
114C2×M16—91no—
115#123—181no—
116C22⋊Q8—91no—
117C22⋊Q8—91no—
118#121—91no—
119#121—91no—
120#120—181no—
121C4×D4—181no—
122C4×D4—181no—
123#117—91no—
124C2×C42—21no—
125C2×C42—31no—
126C2×C42—61no—
127C2×C42C2×C3⋊D311yescharacteristic
128#104—181no—
129#104—182no—
130#104—181no—
131C22⋊C8—181no—
132C22⋊C8—181no—
133C23×C3—21no—
134C23×C3—31no—
135C23×C3—31no—
136C23×C3—61no—
137C23×C3C2×S411yescharacteristic
138C22×D3—61no—
139C2×A4—43no—
140C2×A4—83no—
141S4—243no—
142C2×C3×C4—31no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—31no—
149C2×C3×C4—31no—
150C2×C3×C4—61no—
151C2×C3×C4—61no—
152C2×C3×C4—61no—
153C2×C3×C4—61no—
154C2×C3×C4—61no—
155C2×C3×C4—61no—
156C2×C3×C4—61no—
157C2×C3×C4—61no—
158C2×C3×C4—61no—
159C2×C3×C4—61no—
160#67—121no—
161#67—122no—
162#67—121no—
163#67—121no—
164#67—121no—
165#67—483no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169D12—61no—
170D12—61no—
171C4×D3—121no—
172C4×D3—121no—
173Dic6—61no—
174Dic6—61no—
175C3⋊C8—121no—
176C3⋊C8—121no—
177C2×C32—161no—
178C2×C32—321no—
179C3⋊D3—321no—
180C24C3⋊S411yescharacteristic
181#41—181no—
182#41—181no—
183#41—181no—
184#41—181no—
185C2×Q8—91no—
186C2×D4—91no—
187C2×D4—181no—
188C2×D4—181no—
189C2×D4—181no—
190C22×C4—31no—
191C22×C4—31no—
192C22×C4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—61no—
197C22×C4—61no—
198C22×C4—61no—
199C22×C4—61no—
200C22×C4—181no—
201M16—181no—
202M16—181no—
203M16—181no—
204M16—181no—
205C2×C8—181no—
206C2×C8—181no—
207C4⋊C4—91no—
208C4⋊C4—91no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C22⋊C4—181no—
214C22⋊C4—181no—
215C22⋊C4—181no—
216C42—31no—
217C42—32no—
218C42—61no—
219C42—181no—
220C42#63811yescharacteristic, complemented
221C22×C3—31no—
222C22×C3—31no—
223C22×C3—32no—
224C22×C3—31no—
225C22×C3—61no—
226C22×C3—61no—
227C22×C3—61no—
228C22×C3—163no—
229C22×C3#85711yescharacteristic, complemented
230C22×C3GL(2,ℤ/4)11yescharacteristic
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—121no—
234C2×D3—483no—
235A4—43no—
236C3×C4—31no—
237C3×C4—31no—
238C3×C4—31no—
239C3×C4—31no—
240C3×C4—61no—
241C3×C4—61no—
242Dic3—121no—
243Dic3—121no—
244Dic3—121no—
245Dic3—483no—
246C32—161noSylow
247C23—21no—
248C23—31no—
249C23—31no—
250C23—61no—
251C23—181no—
252C23C2×C3⋊S411yescharacteristic
253Q8—181no—
254Q8—181no—
255D4—181no—
256D4—181no—
257D4—361no—
258D4—362no—
259D4—361no—
260D4—361no—
261D4—361no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—361no—
284C2×C4—361no—
285C8—361no—
286C8—361no—
287C2×C3—21no—
288C2×C3—31no—
289C2×C3—31no—
290C2×C3—61no—
291C2×C3—163no—
292C2×C3—323no—
293C2×C3C2×#85711yescharacteristic
294D3—241no—
295D3—963no—
296C22—31no—
297C22—31no—
298C22—32no—
299C22—31no—
300C22—61no—
301C22—61no—
302C22—61no—
303C22—361no—
304C22—361no—
305C22—361no—
306C22C3⋊#85711yescharacteristic, complemented
307C22#6426911yescharacteristic
308C4—31no—
309C4—31no—
310C4—31no—
311C4—31no—
312C4—61no—
313C4—61no—
314C4—361no—
315C4—361no—
316C4—361no—
317C3—163no—
318C3#7304811yescharacteristic, complemented
319C2—21no—
320C2—31no—
321C2—31no—
322C2—61no—
323C2—721no—
324C2C2×C3⋊#85711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#857
commutator, cosocleC2×C3×C42⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC22×C3×C42D3
socleC23×C3C2×S4
hypercenterC22C3⋊#857
hypocenterC3×C42⋊C3D4
LCSG ▷ C2×C3×C42⋊C3 ▷ C3×C42⋊C3
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C42⋊C3C2semidirect
2. C2×C3⋊#857C2semidirect
3. C3⋊#4623C2semidirect
10. C22×C3×C42D3semidirect
12. C22×C42⋊C3D3semidirect
23. C3×C42⋊C3D4semidirect
56. C22×C42C3⋊D3semidirect
89. C3×C42#67semidirect
106. C42⋊C3#67semidirect
220. C42#638semidirect
229. C22×C3#857semidirect
306. C22C3⋊#857semidirect
318. C3#73048semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C42⋊C32
C2×C3⋊#8572
C3⋊#46232
#730483
#715323
#642694