Finite Group Databasebeta

← #11794368

Subgroups — #11794368

Order 1152.

624 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×C32×#101C211yesmaximal, characteristic
2#10592924C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63649C211yesmaximal, characteristic
5#10592820C211yesmaximal, characteristic
6#10592818C211yesmaximal, characteristic
7#10589420C211yesmaximal, characteristic
8#70109—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C32×#101—22no—
17#63662—21no—
18#63662—21no—
19#63662—22no—
20#63649—22no—
21#63645—21no—
22#63644—21no—
23#63641—22no—
24C2×C3×#101D314yes—
25#5225—34no—
26C2×#835—34no—
27C2×#822—34no—
28#5121—34no—
29#5119—34no—
30#4554—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8Q812yes—
37C22×C32×C4—21no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C32×M16—21no—
41C32×M16—21no—
42C32×M16—21no—
43C32×M16D412yes—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46#3757—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4×C3⋊Dic3—21no—
52#3748—21no—
53#3748—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)D412yes—
58#2064—91noSylow
59C22×C3×Q8C2×D314yes—
60C2×C3×M16C2×D314yes—
61C2×C3×M16C2×D314yes—
62#926—34no—
63C2×C4⋊Dic3—34no—
64C2×#208—34no—
65C22×C3⋊C8—34no—
66C3×#101—28no—
67#835—68no—
68#835—64no—
69#835—64no—
70#822—68no—
71#818—64no—
72#817—64no—
73Dic3⋊C8—68no—
74C23×C32#4111yescharacteristic
75C32×Q8—22no—
76C32×Q8—22no—
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×Q811yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—81no—
92C32×C8—22no—
93C32×C8—41no—
94C3⋊(C3⋊C8)—22no—
95C3⋊(C3⋊C8)—41no—
96C2×#108—91no—
97#428—91no—
98#424—91no—
99#419—91no—
100C2×#103—91no—
101C2×#101C3⋊D311yescharacteristic
102#343—91no—
103C2×C3×Q8—24no—
104C2×C3×Q8—24no—
105C2×C3×Q8—24no—
106C2×C3×Q8—24no—
107C2×C3×Q8—24no—
108C2×C3×Q8Dic618yes—
109C22×C3×C4—24no—
110C22×C3×C4C22×D314yes—
111C22×Dic3—64no—
112C3×M16—24no—
113C3×M16—24no—
114C3×M16—24no—
115C3×M16#6718yes—
116C2×C3×C8—24no—
117C2×C3×C8—24no—
118#217—64no—
119C4⋊Dic3—34no—
120C4⋊Dic3—34no—
121C4⋊Dic3—64no—
122C4⋊Dic3—64no—
123C4×Dic3—64no—
124#208—64no—
125#208—64no—
126C2×C3⋊C8—38no—
127C2×C3⋊C8—64no—
128C2×C3⋊C8—64no—
129C2×C3⋊C8—64no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32#12111yescharacteristic
133C22×C32C22⋊Q811yescharacteristic
134C22×C32#12611yescharacteristic
135C32×C4—42no—
136C32×C4#12111yescharacteristic
137C32×C4#12111yescharacteristic
138C32×C4C22⋊Q811yescharacteristic
139C32×C4C22⋊Q811yescharacteristic
140C3⋊Dic3—41no—
141C3⋊Dic3—41no—
142C3⋊Dic3—81no—
143C22×Q8C2×C3⋊D311yescharacteristic
144C2×M16—91no—
145C2×M16C2×C3⋊D311yescharacteristic
146C2×M16C2×C3⋊D311yescharacteristic
147C22×C8—91no—
148#117—91no—
149C2×C4⋊C4—91no—
150#108—182no—
151#107—181no—
152#106—181no—
153C4⋊C8—182no—
154#103—181no—
155#103—181no—
156#103—182no—
157#101—22no—
158C23×C3#23514yes—
159C3×Q8—28no—
160C3×Q8—28no—
161C3×Q8—44no—
162C3×Q8—44no—
163C2×C3×C4—28no—
164C2×C3×C4—44no—
165C2×C3×C4—44no—
166C2×C3×C4C2×Dic614yes—
167C2×C3×C4D3×D414yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4#23714yes—
170C2×C3×C4#23714yes—
171C2×C3×C4C2×#6714yes—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—124no—
175C2×Dic3—244no—
176C3×C8—28no—
177C3×C8—44no—
178C3⋊C8—68no—
179C3⋊C8—124no—
180C2×C32—21no—
181C2×C32—21no—
182C2×C32#39611yescharacteristic
183C2×C32#47111yescharacteristic
184C2×C32#47311yescharacteristic
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8#63412yes—
191C22×C4—21no—
192C22×C4—181no—
193C22×C4C22×C3⋊D311yescharacteristic
194M16—21no—
195M16—21no—
196M16—21no—
197M16—181no—
198M16—181no—
199M16#63812yes—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—92no—
203C2×C8—181no—
204C2×C8—181no—
205C2×C8—181no—
206C4⋊C4—91no—
207C4⋊C4—91no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C22⋊C4—181no—
211C42—181no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3#87914yes—
215C22×C3#88414yes—
216C22×C3#92414yes—
217C3×C4—48no—
218C3×C4#87814yes—
219C3×C4#87814yes—
220C3×C4#93814yes—
221C3×C4#93914yes—
222Dic3—124no—
223Dic3—124no—
224Dic3—244no—
225C32#206411yescharacteristic, complemented, Sylow
226C23#382811yescharacteristic
227Q8—22no—
228Q8—22no—
229Q8—41no—
230Q8—41no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—361no—
237C2×C4—721no—
238C2×C4C2×#63411yescharacteristic
239C2×C4D4×C3⋊D311yescharacteristic
240C2×C4D4×C3⋊D311yescharacteristic
241C2×C4#383011yescharacteristic
242C2×C4#383011yescharacteristic
243C2×C4C2×#63811yescharacteristic
244C8—22no—
245C8—41no—
246C8—182no—
247C8—361no—
248C2×C3—24no—
249C2×C3—24no—
250C2×C3#475414yes—
251C2×C3#475514yes—
252C2×C3#494814yes—
253C22—21no—
254C22—21no—
255C22#6408811yescharacteristic
256C22#6409311yescharacteristic
257C22#6413311yescharacteristic
258C4—42no—
259C4—361no—
260C4—361no—
261C4—721no—
262C4#6408711yescharacteristic
263C4#6408711yescharacteristic
264C4#6414711yescharacteristic
265C4#6414811yescharacteristic
266C3#7010914yescomplemented
267C2—21no—
268C2—21no—
269C2#1059245311yescharacteristic
270C2#1059245411yescharacteristic
271C2#1059264711yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32#121
prime radicalC23×C32#41
hypercenterC2×#101C3⋊D3
hypocenterC32#2064
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
225. C32#2064semidirect
266. C3#70109semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1012
#105929242
C2×#636622
C2×#636492
#105928202
#105928182
#105894202
#701093