Finite Group Databasebeta

← #11781893

Subgroups — #11781893

Order 1152.

324 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5090C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic
4#10590258C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589099C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71349—31nomaximal
9#71056—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#835—21no—
17C3×#808—21no—
18C3×#808—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63576—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24#63554—21no—
25C3×#498—31no—
26C3×#462—31no—
27#5091—31no—
28#5090D311yescharacteristic
29#5080D311yescharacteristic
30#5024—31no—
31#5021—31no—
32#4679—31no—
33#4547—31no—
34#4547—31no—
35#4547—61no—
36#4546—31no—
37#4481—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×#216—42no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1692—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4×Q8—31no—
64C2×#216—21no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×#106—61no—
68C3×#106—61no—
69C3×C4⋊C8—31no—
70C3×#103—61no—
71C3×C4×C8—31no—
72#835—21no—
73#835—61no—
74#815—61no—
75Dic3⋊C8—61no—
76#810—61no—
77#808—21no—
78#808—21no—
79#807—61no—
80#807—61no—
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89#803—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C32×Q8—41no—
92C32×Q8—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×Dic6—21no—
101C3×Dic6—21no—
102C3×Dic6—81no—
103C3⋊(C3⋊C8)—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yescomplemented
108#498—31no—
109#477—91no—
110#462—31no—
111#446—91no—
112#335—91no—
113#333—91no—
114#332—91no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×Q8—31no—
118C2×C3×Q8—41no—
119C2×C3×Q8—61no—
120C2×Dic6—21no—
121C2×Dic6#6711yescharacteristic
122C3×Q16—122no—
123C2×C3×C8—31no—
124C2×C3×C8—31no—
125C2×C3×C8—61no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42—61no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#216—42no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3#6711yescharacteristic
144Dic3⋊C4—21no—
145C4×Dic3—21no—
146C2×C3⋊C8—21no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—121no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8#6711yescharacteristic
154C2×C3⋊C8#6711yescharacteristic
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4—81no—
158C32×C4C2×Q1611yescharacteristic
159C32×C4AGL(1,ℤ/8)11yescharacteristic
160C32×C4#13711yescharacteristic
161C32×C4#13711yescharacteristic
162C3×Dic3—41no—
163C3×Dic3—41no—
164C3×Dic3—81no—
165C2×Q16—61no—
166C4⋊Q8—31no—
167C4⋊Q8D3211yescharacteristic
168C4×Q8—31no—
169#107—181no—
170#106—61no—
171#106—61no—
172C4⋊C8—31no—
173C4⋊C8—91no—
174C4⋊C8—91no—
175C4⋊C8—181no—
176#103—61no—
177#103—181no—
178#97—181no—
179C4×C8—31no—
180C3×Q8—41no—
181C3×Q8—41no—
182C3×Q8—41no—
183C3×Q8—41no—
184C3×Q8—61no—
185C3×Q8—61no—
186C3×Q8—81no—
187C3×Q8—81no—
188C3×Q8—241no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—121no—
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4#23711yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4C2×#6711yescharacteristic
203C2×C3×C4C2×#6711yescharacteristic
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—41no—
207Dic6—21no—
208Dic6—21no—
209Dic6—81no—
210C3×C8—32no—
211C3×C8—61no—
212C3×C8—121no—
213C3⋊C8—21no—
214C3⋊C8—41no—
215C3⋊C8—121no—
216C3⋊C8—121no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—241no—
220C3⋊C8—241no—
221C3⋊C8#21612yescomplemented
222C2×C32#46211yescharacteristic
223C2×C32#46811yescharacteristic
224C2×C32#47111yescharacteristic
225C2×Q8—21no—
226C2×Q8—31no—
227C2×Q8—61no—
228Q16—122no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—61no—
232C2×C8—181no—
233C2×C8—181no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—31no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C42—61no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3#93811yescharacteristic
244C22×C3#93911yescharacteristic
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—41no—
252C3×C4—82no—
253C3×C4—81no—
254C3×C4—81no—
255C3×C4—121no—
256C3×C4—121no—
257C3×C4—241no—
258C3×C4#91411yescharacteristic
259C3×C4#91511yescharacteristic
260C3×C4D3×Q1611yescharacteristic
261C3×C4#91811yescharacteristic
262C3×C4#93211yescharacteristic
263C3×C4#94211yescharacteristic
264C3×C4C2×#21611yescharacteristic
265C3×C4#95111yescharacteristic
266Dic3—41no—
267Dic3—41no—
268Dic3—81no—
269C32#169211yescharacteristic, complemented, Sylow
270Q8—41no—
271Q8—41no—
272Q8—61no—
273Q8—61no—
274Q8—241no—
275C2×C4—41no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—121no—
279C2×C4#380511yescharacteristic
280C2×C4D3×#6711yescharacteristic
281C2×C4D3×#6711yescharacteristic
282C8—32no—
283C8—61no—
284C8—121no—
285C8—361no—
286C8—361no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3#504211yescharacteristic
291C2×C3#509011yescharacteristic
292C2×C3#517411yescharacteristic
293C2×C3#517711yescharacteristic
294C2×C3#518211yescharacteristic
295C2×C3#520311yescharacteristic
296C22#6397011yescharacteristic
297C4—21no—
298C4—81no—
299C4—121no—
300C4—121no—
301C4—241no—
302C4#6392911yescharacteristic
303C4#6393411yescharacteristic
304C4D3×#21611yescharacteristic
305C4#6394811yescharacteristic
306C3—21no—
307C3#7105611yescharacteristic, complemented
308C3#7134911yescharacteristic, complemented
309C2#1059150211yescharacteristic
310C2#1059157411yescharacteristic
311C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
107. C3×C3⋊C8Q16semidirect
221. C3⋊C8#216semidirect
269. C32#1692semidirect
307. C3#71056semidirect
308. C3#71349semidirect

Maximal subgroups

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

subgroupindex
C3×#50902
C3×#50802
#105903102
#105902582
#105894132
#105890992
#105890952
#713493
#710563