Finite Group Databasebeta

← #11794377

Subgroups — #11794377

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
1C32×#424C211yesmaximal, characteristic
2C2×#63651C211yesmaximal, characteristic
3C2×#63646C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic
5#10592703C211yesmaximal, characteristic
6#10592694C211yesmaximal, characteristic
7#10589420C211yesmaximal, characteristic
8#70544—34nomaximal
9C22×#634C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C32×C4⋊C8—22no—
17#63651—22no—
18#63646—22no—
19#63643—22no—
20#63637—21no—
21#63637—21no—
22#63635—21no—
23#63634—21no—
24C3×#424D314yes—
25C2×#824—34no—
26C2×#819—34no—
27C2×#816—34no—
28#5004—34no—
29#4995—34no—
30#4554—34no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C2×#634—21no—
35C2×#634—21no—
36C2×#634—21no—
37C2×#634—21no—
38C2×#634—21no—
39C2×#634Q812yes—
40C32×M16—21no—
41C32×M16—21no—
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C2×C32×C8D412yes—
46C32×C4⋊C4D411yescharacteristic
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52#3748—21no—
53#3748—21no—
54#3748—21no—
55#3748D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58#2064—91noSylow
59C22×Dic6—34no—
60C2×C3×M16C2×D314yes—
61C22×C3×C8C2×D314yes—
62C3×#117C2×D314yes—
63C2×C4⋊Dic3—34no—
64C2×#208—34no—
65C2×#208—34no—
66C3×C4⋊C8—28no—
67#824—68no—
68#819—68no—
69#816—68no—
70#810—64no—
71#810—64no—
72#808—64no—
73#807—64no—
74C23×C32#4111yescharacteristic
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×Q811yescharacteristic
81C2×C32×C4#4111yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—81no—
88#634—22no—
89#634—22no—
90#634—41no—
91#634—41no—
92C32×C8—22no—
93C32×C8—41no—
94C3⋊(C3⋊C8)—22no—
95C3⋊(C3⋊C8)—41no—
96C2×#108—91no—
97#428—91no—
98#424C3⋊D311yescharacteristic
99#419—91no—
100C2×#103—91no—
101C2×#101—91no—
102#343—91no—
103C22×C3×C4C22×D314yes—
104C22×Dic3—64no—
105C22×Dic3—64no—
106C2×Dic6—38no—
107C2×Dic6—64no—
108C2×Dic6—64no—
109C2×Dic6—64no—
110C2×Dic6—64no—
111C2×Dic6—64no—
112C3×M16—24no—
113C3×M16—24no—
114C2×C3×C8—24no—
115C2×C3×C8—24no—
116C2×C3×C8—24no—
117C2×C3×C8#6718yes—
118C3×C4⋊C4D1214yes—
119C3×C4⋊C4D1214yes—
120C3×C22⋊C4—24no—
121C3×C42—24no—
122C4⋊Dic3—64no—
123C4⋊Dic3—64no—
124#208—38no—
125#208—64no—
126#208—64no—
127#208—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—41no—
136C32×C4—41no—
137C32×C4#12111yescharacteristic
138C32×C4#12111yescharacteristic
139C32×C4C22⋊Q811yescharacteristic
140C32×C4C22⋊Q811yescharacteristic
141C3⋊Dic3—42no—
142C3⋊Dic3—81no—
143C22×Q8—91no—
144C2×M16—91no—
145C2×M16—91no—
146C2×M16C2×C3⋊D311yescharacteristic
147C22×C8C2×C3⋊D311yescharacteristic
148#117C2×C3⋊D311yescharacteristic
149C2×C4⋊C4—91no—
150#108—182no—
151#107—181no—
152#106—181no—
153C4⋊C8—22no—
154#103—182no—
155#103—181no—
156#103—181no—
157#101—182no—
158C23×C3#23514yes—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4C2×D1214yes—
162C2×C3×C4D3×D414yes—
163C2×C3×C4#23714yes—
164C2×C3×C4D3×Q814yes—
165C2×C3×C4#23914yes—
166C2×C3×C4C2×#6714yes—
167C2×Dic3—68no—
168C2×Dic3—124no—
169C2×Dic3—124no—
170C2×Dic3—124no—
171C2×Dic3—244no—
172Dic6—68no—
173Dic6—68no—
174Dic6—124no—
175Dic6—124no—
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—92no—
186C2×Q8—181no—
187C2×Q8—181no—
188C2×Q8—181no—
189C2×Q8—181no—
190C2×Q8—181no—
191C22×C4—181no—
192C22×C4—181no—
193C22×C4C22×C3⋊D311yescharacteristic
194M16—21no—
195M16—21no—
196M16—92no—
197M16—181no—
198M16—181no—
199M16—181no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—181no—
204C2×C8—181no—
205C2×C8#63812yes—
206C4⋊C4—181no—
207C4⋊C4—181no—
208C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
209C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
210C22⋊C4—21no—
211C42—21no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3#89614yes—
215C22×C3#89814yes—
216C22×C3#93014yes—
217C3×C4—44no—
218C3×C4—44no—
219C3×C4#89514yes—
220C3×C4#89714yes—
221C3×C4#93914yes—
222C3×C4#94614yes—
223Dic3—128no—
224Dic3—244no—
225C32#206411yescharacteristic, complemented, Sylow
226C23#382811yescharacteristic
227Q8—182no—
228Q8—182no—
229Q8—361no—
230Q8—361no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—182no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4—721no—
238C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
239C2×C4D4×C3⋊D311yescharacteristic
240C2×C4#383011yescharacteristic
241C2×C4Q8×C3⋊D311yescharacteristic
242C2×C4#383211yescharacteristic
243C2×C4C2×#63811yescharacteristic
244C8—22no—
245C8—41no—
246C8—182no—
247C8—361no—
248C2×C3—24no—
249C2×C3—24no—
250C2×C3#499414yes—
251C2×C3#514114yes—
252C2×C3#514314yes—
253C22—21no—
254C22—21no—
255C22#6410511yescharacteristic
256C22#6410711yescharacteristic
257C22#6413911yescharacteristic
258C4—41no—
259C4—41no—
260C4—362no—
261C4—721no—
262C4#6410411yescharacteristic
263C4#6410611yescharacteristic
264C4#6414811yescharacteristic
265C4#6415511yescharacteristic
266C3#7054414yescomplemented
267C2—21no—
268C2—21no—
269C2#1059269311yescharacteristic
270C2#1059284011yescharacteristic
271C2#1059284211yescharacteristic
subgroupG/H
centerC22#64139
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#424C2
socleC22×C32#121
prime radicalC23×C32#41
hypercenter#424C3⋊D3
hypocenterC32#2064
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
225. C32#2064semidirect
266. C3#70544semidirect

Maximal subgroups

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

subgroupindex
C32×#4242
C2×#636512
C2×#636462
C2×#636432
#105927032
#105926942
#105894202
#705443