Finite Group Databasebeta

← #11781086

Subgroups — #11781086

Order 1152.

332 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 92 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×#4849C211yesmaximal, characteristic
2#10590303C211yesmaximal, characteristic
3#10590283C211yesmaximal, characteristic
4C3⋊C8×Dic6C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71052—31nomaximal
9#68547—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×Dic12—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#816—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—21no—
20#63573—21no—
21#63573—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63566—21no—
24Dic3×C3⋊C8—21no—
25C3×#462—31no—
26#5080—31no—
27Q8×C3⋊C8—31no—
28#5021—31no—
29#4850—31no—
30#4849D311yescharacteristic
31#4680—31no—
32C8×Dic6—31no—
33C3×#334—31no—
34#4547—31no—
35#4482—31no—
36#4481—31no—
37#4481—31no—
38#4481—61no—
39#4480D311yescharacteristic
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—42no—
57#1672—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×Dic12—21no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#103—61no—
72C3×C4×C8—31no—
73#835—61no—
74#818—61no—
75#817—61no—
76#817—61no—
77#816—21no—
78#816—61no—
79Dic3⋊C8—61no—
80C8×Dic3—61no—
81#808—61no—
82#808—61no—
83#807—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—41no—
95#634—81no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×Dic6—21no—
100C3×Dic6—41no—
101C3×Dic6—41no—
102C3×Dic6SD1612yes—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yescomplemented
108#498—91no—
109#477—91no—
110#462—31no—
111C8×Q8—91no—
112#334—31no—
113#333—91no—
114#332—91no—
115C2×C3×Q8—31no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—62no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6#6711yescharacteristic
122C3×Q16—122no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C2×C3×C8—31no—
126C2×C3×C8—31no—
127C2×C3×C8—41no—
128C2×C3×C8—61no—
129C3×C4⋊C4—31no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42—61no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C4⋊Dic3—121no—
145C4⋊Dic3#6711yescharacteristic
146Dic3⋊C4—21no—
147C4×Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—121no—
152C2×C3⋊C8D1211yescharacteristic
153C2×C3⋊C8D1211yescharacteristic
154Dic12—42no—
155C22×C32#12111yescharacteristic
156C32×C4—21no—
157C32×C4C2×SD1611yescharacteristic
158C32×C4C2×Q1611yescharacteristic
159C32×C4#13511yescharacteristic
160C32×C4#13711yescharacteristic
161C3⋊Dic3—81no—
162C3×Dic3—22no—
163C3×Dic3—41no—
164C3×Dic3—81no—
165C2×Q16—61no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4×Q8—31no—
169#107—181no—
170#106—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—91no—
174C4⋊C8—181no—
175C4⋊C8D3211yescharacteristic
176#103—61no—
177#103—181no—
178C4×C8—31no—
179C4×C8—181no—
180C3×Q8—32no—
181C3×Q8—61no—
182C3×Q8—121no—
183C3×Q8—121no—
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×C4C2×D1211yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4#23711yescharacteristic
194C2×C3×C4#23911yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—41no—
199C2×Dic3—122no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202Dic6—21no—
203Dic6—41no—
204Dic6—41no—
205Dic6—241no—
206Dic6—241no—
207Dic6—242no—
208Dic6#21412yes—
209C3×C8—32no—
210C3×C8—41no—
211C3×C8—41no—
212C3×C8—61no—
213C3×C8—81no—
214C3×C8—121no—
215C3⋊C8—21no—
216C3⋊C8—41no—
217C3⋊C8—121no—
218C3⋊C8—121no—
219C3⋊C8—241no—
220C3⋊C8Dic1212yescomplemented
221C2×C32#46211yescharacteristic
222C2×C32#46511yescharacteristic
223C2×C32#47111yescharacteristic
224C2×Q8—31no—
225C2×Q8—61no—
226C2×Q8—181no—
227Q16—122no—
228C2×C8—21no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—61no—
232C2×C8—181no—
233C4⋊C4—31no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C42—61no—
240C42C2×D3211yescharacteristic
241C22×C3—21no—
242C22×C3#89511yescharacteristic
243C22×C3#93911yescharacteristic
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—62no—
252C3×C4—121no—
253C3×C4—241no—
254C3×C4C2×Dic1211yescharacteristic
255C3×C4#90911yescharacteristic
256C3×C4D3×SD1611yescharacteristic
257C3×C4#91611yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4#91811yescharacteristic
260C3×C4C2×#21411yescharacteristic
261C3×C4#95011yescharacteristic
262Dic3—22no—
263Dic3—41no—
264Dic3—81no—
265Dic3—242no—
266Dic3—241no—
267Dic3—241no—
268C32#167211yescharacteristic, complemented, Sylow
269Q8—32no—
270Q8—61no—
271Q8—121no—
272Q8—121no—
273Q8—721no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—121no—
277C2×C4—361no—
278C2×C4#379611yescharacteristic
279C2×C4D3×D1211yescharacteristic
280C2×C4D3×#6711yescharacteristic
281C8—32no—
282C8—41no—
283C8—61no—
284C8—121no—
285C8—361no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#484911yescharacteristic
290C2×C3#486411yescharacteristic
291C2×C3#489811yescharacteristic
292C2×C3#504111yescharacteristic
293C2×C3#518211yescharacteristic
294C2×C3#520311yescharacteristic
295C22#6388611yescharacteristic
296C4—21no—
297C4—62no—
298C4—121no—
299C4—241no—
300C4—721no—
301C4D3×Dic1211yescharacteristic
302C4#6380111yescharacteristic
303C4D3×#21411yescharacteristic
304C4#6394711yescharacteristic
305C3—21no—
306C3#6854711yescharacteristic, complemented
307C3#7105211yescharacteristic, complemented
308C2#1059057811yescharacteristic
309C2#1059080011yescharacteristic
310C2#1059098511yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1672
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
107. C3×C3⋊C8Q16semidirect
220. C3⋊C8Dic12semidirect
268. C32#1672semidirect
306. C3#68547semidirect
307. C3#71052semidirect

Maximal subgroups

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

subgroupindex
C3×#48492
#105903032
#105902832
C3⋊C8×Dic62
#105893472
C3×#44802
#105890932
#710523
#685473