Finite Group Databasebeta

← #11782604

Subgroups — #11782604

Order 1152.

433 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 433 conjugacy classes of subgroups — too many to draw. Only its 114 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#10592777C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic
3C3×#5078C211yesmaximal, characteristic
4#10590386C211yesmaximal, characteristic
5#10590312C211yesmaximal, characteristic
6#10590311C211yesmaximal, characteristic
7C3⋊C82C211yesmaximal, characteristic
8#71362—31nomaximal
9#71298—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—22no—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3719—22no—
16#63634—22no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#807—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63576—22no—
22#63575—22no—
23C3×#500—31no—
24C3×#494—31no—
25#5092—31no—
26#5092D311yescharacteristic
27#5078—31no—
28#5078—31no—
29#5078—31no—
30#5078—31no—
31#5078—31no—
32#5078—61no—
33#5078D311yescharacteristic
34#4699—31no—
35#4682—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×Q8—21no—
39C2×#634—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×#216—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#3719—44no—
56#1713—91noSylow
57C2×C3×Q16—62no—
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C2×#216—22no—
64C2×#216—62no—
65C2×Dic12—62no—
66#869—31no—
67#869—31no—
68#869—61no—
69#869C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C3×#107—62no—
72C3×C4×C8—31no—
73C3×C4×C8—31no—
74#818—62no—
75#807—22no—
76#807—62no—
77#807—62no—
78#807—62no—
79#807—62no—
80#807—64no—
81#807—62no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—61no—
85C4×C3⋊C8C2×D311yescharacteristic
86C4×C3⋊C8C2×D311yescharacteristic
87C32×Q8—42no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C3⋊Dic3—41no—
93#634—42no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3×Dic6—42no—
97C3×Dic6—42no—
98C3⋊(C3⋊C8)Q1614yescomplemented
99C3×C3⋊C8D814yes—
100C3×C3⋊C8Q1614yescomplemented
101#500—31no—
102#500—91no—
103#500—91no—
104#500—91no—
105#494—31no—
106#494—91no—
107C82—91no—
108C2×C3×Q8—21no—
109C2×C3×Q8—21no—
110C2×C3×Q8—41no—
111C2×C3×Q8—61no—
112C2×C3×Q8—61no—
113C2×Dic6—21no—
114C2×Dic6—21no—
115C2×Dic6—61no—
116C2×Dic6—61no—
117C2×Dic6—121no—
118C3×Q16—124no—
119C2×C3×C8—32no—
120C2×C3×C8—32no—
121C3×C4⋊C4—22no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—41no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C42—21no—
132C3×C42C22×D311yescharacteristic
133C3×C42C22×D311yescharacteristic
134#216—44no—
135#216—124no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—121no—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—32no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8#6712yes—
150C2×C3⋊C8#6712yes—
151Dic12—124no—
152C22×C32#12711yescharacteristic
153C32×C4—81no—
154C32×C4C2×D812yes—
155C32×C4C2×Q1612yes—
156C32×C4C2×Q1612yes—
157C3⋊Dic3—81no—
158C3×Dic3—81no—
159C3×Dic3—81no—
160C2×Q16—62no—
161C2×Q16—182no—
162C4⋊Q8—31no—
163C4⋊Q8—31no—
164C4⋊Q8—91no—
165C4⋊Q8D3211yescharacteristic
166#107—62no—
167#107—182no—
168#107—182no—
169#107—182no—
170C4×C8—31no—
171C4×C8—31no—
172C4×C8—91no—
173C3×Q8—42no—
174C3×Q8—42no—
175C3×Q8—82no—
176C3×Q8—122no—
177C3×Q8—122no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—42no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4—121no—
185C2×C3×C4—121no—
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—41no—
193C2×Dic3—41no—
194C2×Dic3—122no—
195C2×Dic3—121no—
196C2×Dic3—121no—
197Dic6—42no—
198Dic6—42no—
199Dic6—122no—
200Dic6—122no—
201Dic6—242no—
202C3×C8—34no—
203C3×C8—34no—
204C3⋊C8—34no—
205C3⋊C8—34no—
206C3⋊C8—64no—
207C3⋊C8#21314yes—
208C3⋊C8#21614yescomplemented
209C2×C32#49311yescharacteristic
210C2×C32#49411yescharacteristic
211C2×C32#49411yescharacteristic
212C2×Q8—21no—
213C2×Q8—61no—
214C2×Q8—61no—
215C2×Q8—181no—
216Q16—124no—
217Q16—364no—
218C2×C8—32no—
219C2×C8—32no—
220C2×C8—92no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C42C2×D3211yescharacteristic
230C22×C3—21no—
231C22×C3#94011yescharacteristic
232C22×C3#94011yescharacteristic
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—82no—
237C3×C4—81no—
238C3×C4—81no—
239C3×C4—241no—
240C3×C4—241no—
241C3×C4D3×D812yes—
242C3×C4D3×Q1612yes—
243C3×C4D3×Q1612yes—
244C3×C4D3×Q1612yes—
245C3×C4C2×#21312yes—
246C3×C4C2×#21612yes—
247Dic3—81no—
248Dic3—81no—
249Dic3—242no—
250Dic3—241no—
251Dic3—241no—
252C32#171311yescharacteristic, complemented, Sylow
253Q8—42no—
254Q8—122no—
255Q8—122no—
256Q8—362no—
257C2×C4—41no—
258C2×C4—121no—
259C2×C4—121no—
260C2×C4—361no—
261C2×C4D3×#6711yescharacteristic
262C2×C4D3×#6711yescharacteristic
263C2×C4#381111yescharacteristic
264C8—34no—
265C8—34no—
266C8—94no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3#507311yescharacteristic
271C2×C3#509211yescharacteristic
272C2×C3#515111yescharacteristic
273C2×C3#518311yescharacteristic
274C2×C3#518311yescharacteristic
275C2×C3#518311yescharacteristic
276C22#6397911yescharacteristic
277C4—81no—
278C4—241no—
279C4—241no—
280C4—721no—
281C4D3×#21312yes—
282C4D3×#21612yes—
283C4#6394412yes—
284C3—21no—
285C3#7129811yescharacteristic, complemented
286C3#7136211yescharacteristic, complemented
287C2#1059148211yescharacteristic
288C2#1059162611yescharacteristic
289C2#1059162811yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1713
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
98. C3⋊(C3⋊C8)Q16semidirect
100. C3×C3⋊C8Q16semidirect
208. C3⋊C8#216semidirect
252. C32#1713semidirect
285. C3#71298semidirect
286. C3#71362semidirect

Maximal subgroups

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

subgroupindex
#105927772
C3×#50922
C3×#50782
#105903862
#105903122
#105903112
C3⋊C822
#713623
#712983