Finite Group Databasebeta

← #11781219

Subgroups — #11781219

Order 1152.

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

normal subgroups only

This group has 315 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×#4850C211yesmaximal, characteristic
2#10590312C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic
4#10590250C211yesmaximal, characteristic
5#10589345C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71149—31nomaximal
9#68509—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#63576—21no—
20#63576—21no—
21#63576—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24Dic3×C3⋊C8—21no—
25C3×#477—31no—
26#5091—31no—
27#5078—31no—
28#5078—31no—
29Q8×C3⋊C8—31no—
30#5021—31no—
31#4850D311yescharacteristic
32#4830—31no—
33C3×#333—31no—
34#4546—31no—
35#4481—31no—
36#4481D311yescharacteristic
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#1676—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#818—21no—
71#816—21no—
72Dic3⋊C8—61no—
73C8×Dic3—61no—
74#810—61no—
75#807—61no—
76#807—61no—
77#807—61no—
78#807—61no—
79#807—61no—
80#807—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—81no—
99C3×Dic6—81no—
100C3×Dic6Q1612yes—
101C32×C8—41no—
102C3⋊(C3⋊C8)—21no—
103C3⋊(C3⋊C8)—41no—
104C3⋊(C3⋊C8)Q1612yes—
105C3×C3⋊C8—41no—
106#500—91no—
107#477—31no—
108#477—91no—
109C8×Q8—91no—
110#335—91no—
111#333—31no—
112#333—91no—
113C2×C3×Q8—31no—
114C2×C3×Q8—61no—
115C2×C3×Q8—61no—
116C2×Dic6—21no—
117C2×Dic6—21no—
118C2×Dic6#6711yescharacteristic
119C2×C3×C8—21no—
120C2×C3×C8—21no—
121C2×C3×C8—41no—
122C2×C3×C8—61no—
123C3×C4⋊C4—31no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C42—21no—
130C3×C42—61no—
131C3×C42C22×D311yescharacteristic
132C3×C42C22×D311yescharacteristic
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3#6711yescharacteristic
138Dic3⋊C4—21no—
139C4×Dic3—21no—
140C2×C3⋊C8—21no—
141C2×C3⋊C8—31no—
142C2×C3⋊C8—31no—
143C2×C3⋊C8—31no—
144C2×C3⋊C8—31no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—121no—
150C22×C32#12111yescharacteristic
151C32×C4—21no—
152C32×C4C2×Q1611yescharacteristic
153C32×C4C2×Q1611yescharacteristic
154C32×C4#13511yescharacteristic
155C32×C4#13711yescharacteristic
156C3×Dic3—22no—
157C3×Dic3—41no—
158C3×Dic3—81no—
159C3×Dic3—81no—
160C4⋊Q8—31no—
161C4⋊Q8—31no—
162C4×Q8—31no—
163#107—61no—
164#107—181no—
165#107—181no—
166#107—181no—
167C4⋊C8—31no—
168C4⋊C8—91no—
169C4⋊C8—181no—
170C4⋊C8D3211yescharacteristic
171#103—61no—
172#103—181no—
173C4×C8—91no—
174C4×C8—181no—
175C3×Q8—32no—
176C3×Q8—61no—
177C3×Q8—241no—
178C3×Q8—241no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—61no—
183C2×C3×C4—61no—
184C2×C3×C4—121no—
185C2×C3×C4—121no—
186C2×C3×C4#23511yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4#23711yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—41no—
195C2×Dic3—41no—
196Dic6—21no—
197Dic6—81no—
198Dic6—81no—
199Dic6#21612yes—
200C3×C8—41no—
201C3×C8—41no—
202C3×C8—81no—
203C3×C8—121no—
204C3⋊C8—32no—
205C3⋊C8—32no—
206C3⋊C8—41no—
207C3⋊C8—62no—
208C3⋊C8—61no—
209C3⋊C8—61no—
210C3⋊C8—121no—
211C3⋊C8—121no—
212C3⋊C8—121no—
213C3⋊C8—241no—
214C2×C32#46211yescharacteristic
215C2×C32#46711yescharacteristic
216C2×C32#47211yescharacteristic
217C2×Q8—31no—
218C2×Q8—61no—
219C2×Q8—61no—
220C2×C8—21no—
221C2×C8—61no—
222C2×C8—91no—
223C2×C8—91no—
224C2×C8—181no—
225C4⋊C4—31no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C42—61no—
232C42C2×D3211yescharacteristic
233C22×C3—21no—
234C22×C3#88411yescharacteristic
235C22×C3#93911yescharacteristic
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—41no—
243C3×C4—62no—
244C3×C4—121no—
245C3×C4—241no—
246C3×C4—241no—
247C3×C4#91511yescharacteristic
248C3×C4#91611yescharacteristic
249C3×C4D3×Q1611yescharacteristic
250C3×C4D3×Q1611yescharacteristic
251C3×C4D3×Q1611yescharacteristic
252C3×C4#91811yescharacteristic
253C3×C4C2×#21611yescharacteristic
254C3×C4#95011yescharacteristic
255Dic3—22no—
256Dic3—41no—
257Dic3—81no—
258Dic3—81no—
259C32#167611yescharacteristic, complemented, Sylow
260Q8—32no—
261Q8—61no—
262Q8—241no—
263Q8—241no—
264C2×C4—61no—
265C2×C4—61no—
266C2×C4—121no—
267C2×C4—121no—
268C2×C4#379511yescharacteristic
269C2×C4#380211yescharacteristic
270C2×C4D3×#6711yescharacteristic
271C8—41no—
272C8—92no—
273C8—121no—
274C8—181no—
275C8—361no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3#474911yescharacteristic
280C2×C3#479511yescharacteristic
281C2×C3#481311yescharacteristic
282C2×C3#505111yescharacteristic
283C2×C3#518211yescharacteristic
284C2×C3#519911yescharacteristic
285C22#6388511yescharacteristic
286C4—21no—
287C4—62no—
288C4—121no—
289C4—241no—
290C4—241no—
291C4#6380211yescharacteristic
292C4#6381111yescharacteristic
293C4#6393511yescharacteristic
294C4D3×#21611yescharacteristic
295C3—21no—
296C3#6850911yescharacteristic, complemented
297C3#7114911yescharacteristic, complemented
298C2#1059051811yescharacteristic
299C2#1059079811yescharacteristic
300C2#1059098211yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1676
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
259. C32#1676semidirect
296. C3#68509semidirect
297. C3#71149semidirect

Maximal subgroups

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

subgroupindex
C3×#48502
#105903122
#105903102
#105902502
#105893452
C3×#44812
#105890952
#711493
#685093