Finite Group Databasebeta

← #11781593

Subgroups — #11781593

Order 1152.

315 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4850C211yesmaximal, characteristic
2#10590290C211yesmaximal, characteristic
3#10590285C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5#10589345C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71151—31nomaximal
9#68471—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#818—21no—
17C3×#816—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19#63574—21no—
20Dic3⋊(C3⋊C8)—21no—
21#63565—21no—
22#63565—21no—
23#63565—21no—
24Dic3×C3⋊C8—21no—
25C3×#477—31no—
26#5094—31no—
27#5093—31no—
28#5079—31no—
29Q8×C3⋊C8—31no—
30#5020—31no—
31#4850D311yescharacteristic
32#4830—31no—
33C3×#332—31no—
34#4546—31no—
35#4486D311yescharacteristic
36#4481—31no—
37#4479—31no—
38#4479—31no—
39#4479—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
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#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4×Q8—31no—
60#869C2×D311yescharacteristic
61#869C2×D311yescharacteristic
62C4×Dic6C2×D311yescharacteristic
63C3×#107—61no—
64C3×C4⋊C8—21no—
65C3×C4⋊C8—31no—
66C3×C4⋊C8C2×D311yescharacteristic
67C3×C4⋊C8C2×D311yescharacteristic
68C3×#103—61no—
69#835—61no—
70#835—61no—
71#835—61no—
72#818—21no—
73#816—21no—
74Dic3⋊C8—61no—
75C8×Dic3—61no—
76#810—61no—
77#810—61no—
78#810—61no—
79#808—61no—
80#808—61no—
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4×C3⋊C8—31no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—61no—
89C4×C3⋊C8—61no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C3×Dic3—21no—
94C2×C3×Dic3—21no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—21no—
98C3×Dic6—41no—
99C3×Dic6—41no—
100C3×Dic6—81no—
101C3×Dic6Q1612yes—
102C32×C8—41no—
103C3⋊(C3⋊C8)—21no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—41no—
107#487—91no—
108#477—31no—
109#475—91no—
110C8×Q8—91no—
111#335—91no—
112#333—91no—
113#332—31no—
114C2×C3×Q8—31no—
115C2×C3×Q8—61no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—21no—
119C2×Dic6#6711yescharacteristic
120C2×C3×C8—21no—
121C2×C3×C8—21no—
122C2×C3×C8—41no—
123C2×C3×C8—61no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C42—21no—
131C3×C42—61no—
132C3×C42C22×D311yescharacteristic
133C3×C42C22×D311yescharacteristic
134C4⋊Dic3—21no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3#6711yescharacteristic
139Dic3⋊C4—21no—
140C4×Dic3—21no—
141C2×C3⋊C8—21no—
142C2×C3⋊C8—31no—
143C2×C3⋊C8—31no—
144C2×C3⋊C8—31no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—121no—
151C22×C32#12111yescharacteristic
152C32×C4—21no—
153C32×C4C2×Q1611yescharacteristic
154C32×C4#13511yescharacteristic
155C32×C4#13511yescharacteristic
156C32×C4#13711yescharacteristic
157C3×Dic3—22no—
158C3×Dic3—41no—
159C3×Dic3—81no—
160C3×Dic3—81no—
161C4⋊Q8—31no—
162C4⋊Q8—31no—
163C4×Q8—31no—
164#107—61no—
165#106—181no—
166C4⋊C8—31no—
167C4⋊C8—91no—
168C4⋊C8—181no—
169C4⋊C8D3211yescharacteristic
170#103—61no—
171#103—181no—
172#103—181no—
173#103—181no—
174C4×C8—91no—
175C4×C8—181no—
176C3×Q8—32no—
177C3×Q8—61no—
178C3×Q8—121no—
179C3×Q8—121no—
180C3×Q8—241no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—121no—
187C2×C3×C4—121no—
188C2×C3×C4#23511yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4#23711yescharacteristic
193C2×C3×C4C2×#6711yescharacteristic
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—41no—
197C2×Dic3—41no—
198Dic6—21no—
199Dic6—41no—
200Dic6—41no—
201Dic6—81no—
202Dic6#21612yes—
203C3×C8—41no—
204C3×C8—41no—
205C3×C8—81no—
206C3×C8—121no—
207C3⋊C8—41no—
208C3⋊C8—62no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—61no—
212C3⋊C8—61no—
213C3⋊C8—121no—
214C3⋊C8—121no—
215C3⋊C8—121no—
216C3⋊C8—241no—
217C2×C32#46411yescharacteristic
218C2×C32#46711yescharacteristic
219C2×C32#47111yescharacteristic
220C2×Q8—31no—
221C2×Q8—61no—
222C2×Q8—61no—
223C2×C8—21no—
224C2×C8—61no—
225C2×C8—91no—
226C2×C8—91no—
227C2×C8—181no—
228C4⋊C4—31no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C42—61no—
235C42C2×D3211yescharacteristic
236C22×C3—21no—
237C22×C3#88411yescharacteristic
238C22×C3#93911yescharacteristic
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—41no—
246C3×C4—62no—
247C3×C4—121no—
248C3×C4—241no—
249C3×C4—241no—
250C3×C4#91211yescharacteristic
251C3×C4#91511yescharacteristic
252C3×C4#91611yescharacteristic
253C3×C4D3×Q1611yescharacteristic
254C3×C4#91811yescharacteristic
255C3×C4#91911yescharacteristic
256C3×C4C2×#21611yescharacteristic
257C3×C4#95011yescharacteristic
258Dic3—22no—
259Dic3—41no—
260Dic3—81no—
261Dic3—81no—
262C32#168411yescharacteristic, complemented, Sylow
263Q8—32no—
264Q8—61no—
265Q8—121no—
266Q8—121no—
267Q8—241no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4#379511yescharacteristic
273C2×C4#380211yescharacteristic
274C2×C4D3×#6711yescharacteristic
275C8—41no—
276C8—121no—
277C8—181no—
278C8—181no—
279C8—361no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3#475411yescharacteristic
284C2×C3#476711yescharacteristic
285C2×C3#481311yescharacteristic
286C2×C3#505111yescharacteristic
287C2×C3#518511yescharacteristic
288C2×C3#520011yescharacteristic
289C22#6388511yescharacteristic
290C4—21no—
291C4—62no—
292C4—121no—
293C4—241no—
294C4—241no—
295C4#6381011yescharacteristic
296C4#6381111yescharacteristic
297C4#6393511yescharacteristic
298C4D3×#21611yescharacteristic
299C3—21no—
300C3#6847111yescharacteristic, complemented
301C3#7115111yescharacteristic, complemented
302C2#1059051811yescharacteristic
303C2#1059079711yescharacteristic
304C2#1059098011yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1684
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
262. C32#1684semidirect
300. C3#68471semidirect
301. C3#71151semidirect

Maximal subgroups

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

subgroupindex
C3×#48502
#105902902
#105902852
#105902502
#105893452
C3×#44862
#105890952
#711513
#684713