Finite Group Databasebeta

← #11781896

Subgroups — #11781896

Order 1152.

319 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#4680C211yesmaximal, characteristic
2C3×#4679C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4#10590310C211yesmaximal, characteristic
5#10589324C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71349—31nomaximal
9#70963—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C32×C4×C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#817—21no—
18C3×#817—21no—
19C3×#815—21no—
20C3×Dic3⋊C8—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63576—21no—
23#63565—21no—
24#63565—21no—
25C3×#498—31no—
26C3×#446—31no—
27#5091—31no—
28#5090—31no—
29#5031—31no—
30#5021—31no—
31#4680D311yescharacteristic
32#4679D311yescharacteristic
33#4547—31no—
34#4546—31no—
35#4486—31no—
36#4481—31no—
37#4458—31no—
38#4458—31no—
39#4458—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#1692—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×#216—61no—
62C2×#216—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C4×Dic6C2×D311yescharacteristic
66C3×#106—61no—
67C3×#106—61no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—61no—
70C3×#97—61no—
71C3×C4×C8—21no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#835—61no—
75#835—61no—
76#817—21no—
77#817—21no—
78#815—21no—
79Dic3⋊C8—21no—
80#810—61no—
81#810—61no—
82#807—61no—
83#807—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C3×Dic6—21no—
99C3×Dic6—21no—
100C3×Dic6—41no—
101C3×Dic6—41no—
102C3×Dic6—81no—
103C32×C8—21no—
104C32×C8Q1612yescomplemented
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—41no—
108#498—31no—
109#477—91no—
110#462—91no—
111#446—31no—
112#335—91no—
113#333—91no—
114#332—91no—
115C2×C3×Q8—31no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C2×Dic6D1211yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C2×C3×C8—61no—
124C2×C3×C8#6711yescharacteristic
125C2×C3×C8#6711yescharacteristic
126C2×C3×C8#6711yescharacteristic
127C2×C3×C8#6711yescharacteristic
128C3×C4⋊C4—31no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42—61no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138#216—122no—
139#216—122no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3D1211yescharacteristic
145Dic3⋊C4—21no—
146C4×Dic3—21no—
147C2×C3⋊C8—21no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8—121no—
154C22×C32#12111yescharacteristic
155C32×C4—21no—
156C32×C4C2×Q1611yescharacteristic
157C32×C4AGL(1,ℤ/8)11yescharacteristic
158C32×C4#13711yescharacteristic
159C32×C4#13711yescharacteristic
160C3×Dic3—41no—
161C3×Dic3—41no—
162C3×Dic3—81no—
163C3×Dic3—81no—
164C2×Q16—181no—
165C4⋊Q8—31no—
166C4⋊Q8—31no—
167C4×Q8—31no—
168#107—181no—
169#106—61no—
170#106—61no—
171C4⋊C8—31no—
172C4⋊C8—61no—
173C4⋊C8—91no—
174C4⋊C8—91no—
175#103—181no—
176#103—181no—
177#97—61no—
178C4×C8D3211yescharacteristic
179C3×Q8—61no—
180C3×Q8—61no—
181C3×Q8—121no—
182C3×Q8—121no—
183C3×Q8—241no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4—121no—
190C2×C3×C4—121no—
191C2×C3×C4C2×D1211yescharacteristic
192C2×C3×C4#23511yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4#23711yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—41no—
200C2×Dic3—41no—
201Dic6—21no—
202Dic6—21no—
203Dic6—41no—
204Dic6—41no—
205Dic6—81no—
206C3×C8—21no—
207C3×C8—21no—
208C3×C8—22no—
209C3×C8—41no—
210C3×C8—121no—
211C3×C8#21612yescomplemented
212C3×C8#21612yescomplemented
213C3⋊C8—41no—
214C3⋊C8—121no—
215C3⋊C8—121no—
216C3⋊C8—121no—
217C3⋊C8—121no—
218C3⋊C8—241no—
219C3⋊C8—241no—
220C2×C32#46211yescharacteristic
221C2×C32#46811yescharacteristic
222C2×C32#47111yescharacteristic
223C2×Q8—31no—
224C2×Q8—61no—
225C2×Q8—61no—
226Q16—362no—
227C2×C8—61no—
228C2×C8—181no—
229C2×C8—181no—
230C2×C8#62511yescharacteristic
231C2×C8#62511yescharacteristic
232C4⋊C4—31no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C42—61no—
239C42C2×D3211yescharacteristic
240C22×C3—21no—
241C22×C3#93011yescharacteristic
242C22×C3#93811yescharacteristic
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—41no—
250C3×C4—121no—
251C3×C4—121no—
252C3×C4—241no—
253C3×C4—241no—
254C3×C4#90811yescharacteristic
255C3×C4#90911yescharacteristic
256C3×C4#91411yescharacteristic
257C3×C4#91511yescharacteristic
258C3×C4#94211yescharacteristic
259C3×C4C2×#21611yescharacteristic
260C3×C4C2×#21611yescharacteristic
261C3×C4#95111yescharacteristic
262Dic3—41no—
263Dic3—41no—
264Dic3—81no—
265Dic3—81no—
266C32#169211yescharacteristic, complemented, Sylow
267Q8—61no—
268Q8—61no—
269Q8—121no—
270Q8—121no—
271Q8—241no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4#379511yescharacteristic
277C2×C4D3×D1211yescharacteristic
278C2×C4C2×#62511yescharacteristic
279C8—21no—
280C8—121no—
281C8—361no—
282C8—361no—
283C8#371812yescomplemented
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3#503111yescharacteristic
288C2×C3#509011yescharacteristic
289C2×C3#513411yescharacteristic
290C2×C3#514111yescharacteristic
291C2×C3#517411yescharacteristic
292C2×C3#517711yescharacteristic
293C22#6390811yescharacteristic
294C4—21no—
295C4—121no—
296C4—121no—
297C4—241no—
298C4—241no—
299C4#6379411yescharacteristic
300C4#6380011yescharacteristic
301C4#6382711yescharacteristic
302C4C2×#371811yescharacteristic
303C3—21no—
304C3#7096311yescharacteristic, complemented
305C3#7134911yescharacteristic, complemented
306C2#1059038411yescharacteristic
307C2#1059083311yescharacteristic
308C2#1059092511yescharacteristic
subgroupG/H
centerC22#63908
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
104. C32×C8Q16semidirect
211. C3×C8#216semidirect
212. C3×C8#216semidirect
266. C32#1692semidirect
283. C8#3718semidirect
304. C3#70963semidirect
305. C3#71349semidirect

Maximal subgroups

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

subgroupindex
C3×#46802
C3×#46792
#105903842
#105903102
#105893242
#105890952
#105890922
#713493
#709633