Finite Group Databasebeta

← #11782986

Subgroups — #11782986

Order 1152.

413 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 413 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#10592398C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic
3#10590311C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic
5#10590303C211yesmaximal, characteristic
6#10590287C211yesmaximal, characteristic
7C3×#4454C211yesmaximal, characteristic
8#71226—31nomaximal
9#68099—31nomaximal
10C2×#3746—22no—
11#64078C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16C3×#816—22no—
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—22no—
20#63575—22no—
21#63573—22no—
22#63566—22no—
23C3×#487—31no—
24#5080—31no—
25#5079—31no—
26#5078—31no—
27#5078—31no—
28#4699—31no—
29#4699—31no—
30#4699—61no—
31#4682—31no—
32#4682—31no—
33#4681—31no—
34#4681D311yescharacteristic
35#4680—31no—
36C3×#322—31no—
37#4454D311yescharacteristic
38C2×#634—21no—
39C2×#634—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C32×C8D412yes—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48#3746—44no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#1723—91noSylow
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C2×Dic12—64no—
59C2×Dic12—62no—
60C2×Dic12—62no—
61#869—31no—
62#869—31no—
63#869—31no—
64#869—31no—
65#869—61no—
66#869—61no—
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#103—62no—
70C3×C4×C8—21no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73C3×C4×C8C2×D311yescharacteristic
74C3×C4×C8C2×D311yescharacteristic
75#835—62no—
76#818—62no—
77#818—62no—
78#817—62no—
79#816—22no—
80#816—62no—
81#808—62no—
82#807—62no—
83#807—62no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91#634—42no—
92#634—42no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C3×Dic6—42no—
96C3×Dic6—42no—
97C32×C8—22no—
98C3×C3⋊C8—22no—
99C3×C3⋊C8Q1614yescomplemented
100#500—91no—
101#500—91no—
102#498—91no—
103#494—91no—
104#487—31no—
105#487—91no—
106#322—31no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×Dic6—21no—
110C2×Dic6—21no—
111C2×Dic6—62no—
112C2×Dic6—62no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×Dic6—61no—
116C2×Dic6—61no—
117C2×C3×C8—22no—
118C2×C3×C8—32no—
119C2×C3×C8—32no—
120C2×C3×C8D1212yes—
121C2×C3×C8#6712yes—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C42—21no—
127C3×C42C22×D311yescharacteristic
128C3×C42C22×D311yescharacteristic
129C4⋊Dic3—21no—
130C4⋊Dic3—21no—
131C4⋊Dic3—21no—
132C4⋊Dic3—21no—
133C4⋊Dic3—61no—
134C4⋊Dic3—61no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—121no—
142C4⋊Dic3—121no—
143C4⋊Dic3—121no—
144C4⋊Dic3—121no—
145C2×C3⋊C8D1212yes—
146C2×C3⋊C8D1212yes—
147Dic12—128no—
148Dic12—124no—
149Dic12—124no—
150C22×C32#12711yescharacteristic
151C32×C4C2×Q1612yes—
152C32×C4AGL(1,ℤ/8)12yes—
153C32×C4#13712yes—
154C3⋊Dic3—81no—
155C3⋊Dic3—81no—
156C3×Dic3—81no—
157C3×Dic3—81no—
158C2×Q16—182no—
159C4⋊Q8—31no—
160C4⋊Q8—31no—
161C4⋊Q8—91no—
162C4⋊Q8—91no—
163#107—182no—
164#107—182no—
165#106—182no—
166#103—62no—
167#103—182no—
168C4×C8—31no—
169C4×C8—31no—
170C4×C8D3211yescharacteristic
171C3×Q8—122no—
172C3×Q8—122no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4C2×D1211yescharacteristic
179C2×C3×C4C2×D1211yescharacteristic
180C2×C3×C4C2×D1211yescharacteristic
181C2×C3×C4D3×D411yescharacteristic
182C2×C3×C4D3×D411yescharacteristic
183C2×C3×C4C2×#6711yescharacteristic
184C2×Dic3—41no—
185C2×Dic3—41no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192Dic6—42no—
193Dic6—42no—
194Dic6—124no—
195Dic6—124no—
196Dic6—122no—
197Dic6—122no—
198Dic6—122no—
199Dic6—122no—
200C3×C8—24no—
201C3×C8—22no—
202C3×C8—22no—
203C3×C8—34no—
204C3×C8—62no—
205C3⋊C8—22no—
206C3⋊C8Dic1214yescomplemented
207C2×C32#49411yescharacteristic
208C2×C32#49611yescharacteristic
209C2×C32#49711yescharacteristic
210C2×Q8—61no—
211C2×Q8—61no—
212C2×Q8—181no—
213C2×Q8—181no—
214Q16—364no—
215C2×C8—32no—
216C2×C8—32no—
217C2×C8#62612yes—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C42C2×D3211yescharacteristic
227C22×C3—21no—
228C22×C3#87411yescharacteristic
229C22×C3#94011yescharacteristic
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—241no—
234C3×C4—241no—
235C3×C4C2×Dic1212yes—
236C3×C4#90812yes—
237C3×C4#90912yes—
238C3×C4#91512yes—
239C3×C4D3×Q1612yes—
240C3×C4#94912yes—
241Dic3—81no—
242Dic3—81no—
243Dic3—242no—
244Dic3—242no—
245Dic3—241no—
246Dic3—241no—
247Dic3—241no—
248Dic3—241no—
249C32#172311yescharacteristic, complemented, Sylow
250Q8—122no—
251Q8—122no—
252Q8—362no—
253Q8—362no—
254C2×C4—121no—
255C2×C4—121no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4D3×D1211yescharacteristic
259C2×C4D3×D1211yescharacteristic
260C2×C4C2×#62611yescharacteristic
261C8—22no—
262C8—34no—
263C8—62no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3#469911yescharacteristic
268C2×C3#471211yescharacteristic
269C2×C3#471511yescharacteristic
270C2×C3#505811yescharacteristic
271C2×C3#516711yescharacteristic
272C2×C3#518311yescharacteristic
273C22#6391111yescharacteristic
274C4—241no—
275C4—241no—
276C4—721no—
277C4—721no—
278C4D3×Dic1212yes—
279C4#6380012yes—
280C4#6382512yes—
281C3—21no—
282C3#6809911yescharacteristic, complemented
283C3#7122611yescharacteristic, complemented
284C2#1059035111yescharacteristic
285C2#1059089611yescharacteristic
286C2#1059089711yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1723
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
99. C3×C3⋊C8Q16semidirect
206. C3⋊C8Dic12semidirect
249. C32#1723semidirect
282. C3#68099semidirect
283. C3#71226semidirect

Maximal subgroups

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

subgroupindex
#105923982
C3×#46812
#105903112
#105903032
#105902872
C3×#44542
#712263
#680993