Finite Group Databasebeta

← #11858602

Subgroups — #11858602

Order 1152.

770 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64287C211yesmaximal, characteristic
2#10595219C212yesmaximal
3#10593511C212yesmaximal, complemented
4C2×#63743C212yesmaximal, complemented
5#10593507C214yesmaximal, complemented
6#10593396C211yesmaximal, characteristic, complemented
7#10593394C212yesmaximal, complemented
8#10593389C211yesmaximal, characteristic, complemented
9C2×#3830C2211yescharacteristic
10C2×#3792C2212yes—
11C22×#622C2212yes—
12#64287C418yescomplemented
13C2×#3788C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C3×D4×Dic3—22no—
16C2×#3724C2214yes—
17#63957C2214yes—
18#63952—24no—
19#63900C2212yes—
20#63874C2212yes—
21#63844—22no—
22#63743C2211yescharacteristic
23#63743C2211yescharacteristic
24#63743C2214yes—
25#63743C2212yes—
26#63743C2212yes—
27#63742C2212yes—
28#63742C2214yes—
29#5546—62no—
30C2×C32×D4D411yescharacteristic
31C2×#638D412yes—
32C22×C3⋊Dic3C2312yes—
33#3830C2×C414yes—
34#3830Q814yes—
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#634D411yescharacteristic
37C22×C3×Dic3—24no—
38C2×#624—22no—
39#3792C2×C418yescomplemented
40C2×#622C2×C418yescomplemented
41C2×#622C2311yescharacteristic
42C2×#622C2311yescharacteristic
43C2×#622C2312yes—
44#3788C2×C414yescomplemented
45#3787C2×C414yescomplemented
46C3×#217—24no—
47C3×C4⋊Dic3—22no—
48C3×C4×Dic3—22no—
49#3724—24no—
50#3724C2312yes—
51#3724C2312yes—
52#3724C2314yes—
53#3722—22no—
54Dic32—24no—
55#2913—91nomaximal, Sylow
56C2×#237—62no—
57C3×C4×D4—62no—
58D4×Dic3—22no—
59C4×#67—64no—
60C2×Dic3⋊C4—64no—
61D3×C4⋊C4—62no—
62#887—62no—
63#67⋊C4—64no—
64#877—64no—
65#872—62no—
66C4×Dic6—62no—
67C23×C32C2×D412yes—
68C22×C3⋊D3C2×D411yescharacteristic
69C32×D4C4⋊C414yes—
70C2×C32×C4C2×D411yescharacteristic
71#638C4⋊C418yes—
72C2×C3⋊Dic3C22×C414yes—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×Q814yes—
75C2×C3⋊Dic3C2411yescharacteristic
76C4×C3⋊D3C22×C412yes—
77C4×C3⋊D3C2×Q812yes—
78#634C4⋊C414yes—
79C2×C3×Dic3—22no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—84no—
83#624—82no—
84#622C22×C412yes—
85#622C22×C412yes—
86#622C22×C414yes—
87C2×#131—91no—
88#520—92no—
89#428—92no—
90#428—94no—
91#427—91no—
92#427—92no—
93C2×#107—91no—
94C2×#107—92no—
95C2×C3×D4—22no—
96C22×C3×C4—64no—
97C2×#67—64no—
98C22×Dic3—24no—
99C22×Dic3—64no—
100#237—68no—
101#237—68no—
102C2×C4×D3—62no—
103C2×C4×D3—64no—
104C2×Dic6—62no—
105C3×C4⋊C4—62no—
106C3×C22⋊C4—64no—
107C3×C42—62no—
108#217—24no—
109(C2×D3)⋊C4—62no—
110(C2×D3)⋊C4—62no—
111C4⋊Dic3—22no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114Dic3⋊C4—64no—
115Dic3⋊C4—64no—
116Dic3⋊C4—64no—
117C4×Dic3—22no—
118C4×Dic3—64no—
119C4×Dic3—64no—
120C22×C32—22no—
121C22×C32—22no—
122C22×C32C2×C4⋊C414yes—
123C22×C32C22×D411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3C2×C4⋊C412yes—
127C32×C4C2×C4⋊C412yes—
128C3⋊Dic3C2×C4⋊C414yes—
129C3⋊Dic3C23×C411yescharacteristic
130C3⋊Dic3C22×Q811yescharacteristic
131C3×Dic3—44no—
132C3×Dic3—42no—
133C3×Dic3—42no—
134C2×#41—91no—
135#131—98no—
136C2×M16—91no—
137C2×M16—92no—
138C22×C8—91no—
139C22×C8—92no—
140C4×Q8—182no—
141C4×D4—62no—
142C4×D4—184no—
143#117—92no—
144#117—94no—
145C2×C4⋊C4—92no—
146C2×C4⋊C4—94no—
147#107—92no—
148#107—91no—
149#107—92no—
150#107—94no—
151#107—91no—
152#106—92no—
153#106—94no—
154C23×C3—24no—
155C22×D3—62no—
156C3×D4—28no—
157C2×C3×C4—22no—
158C2×C3×C4—62no—
159C2×C3×C4—64no—
160C2×C3×C4—62no—
161C2×C3×C4—244no—
162#67—616no—
163C2×Dic3—22no—
164C2×Dic3—22no—
165C2×Dic3—24no—
166C2×Dic3—68no—
167C2×Dic3—64no—
168C2×Dic3—68no—
169C2×Dic3—62no—
170C2×Dic3—84no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—244no—
174Dic6—68no—
175C2×C32—24no—
176C2×C32C22×C4⋊C411yescharacteristic
177C2×C32#57611yescharacteristic
178C2×C32#57811yescharacteristic
179C3⋊D3—22no—
180#41—94no—
181#41—94no—
182C2×Q8—91no—
183C2×D4—92no—
184C2×D4GO+(4,𝔽2)11yescharacteristic
185C22×C4—64no—
186C22×C4—92no—
187C22×C4—91no—
188C22×C4—182no—
189M16—94no—
190M16—98no—
191C2×C8—91no—
192C2×C8—92no—
193C2×C8—91no—
194C2×C8—94no—
195C2×C8—98no—
196C4⋊C4—62no—
197C4⋊C4—92no—
198C4⋊C4—92no—
199C4⋊C4—94no—
200C4⋊C4—184no—
201C22⋊C4—64no—
202C22⋊C4—182no—
203C42—62no—
204C42—184no—
205C22×C3—22no—
206C22×C3—28no—
207C22×C3—44no—
208C22×C3—44no—
209C2×D3—64no—
210C2×D3—122no—
211C2×D3—122no—
212C3×C4—24no—
213C3×C4—124no—
214C3×C4—122no—
215C3×C4—122no—
216Dic3—44no—
217Dic3—42no—
218Dic3—42no—
219Dic3—68no—
220Dic3—62no—
221Dic3—62no—
222C32#291311yescharacteristic, complemented, Sylow
223C23—91no—
224C23C2×GO+(4,𝔽2)12yes—
225Q8—94no—
226D4—98no—
227D4#377314yes—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—64no—
231C2×C4—92no—
232C2×C4—91no—
233C2×C4—94no—
234C2×C4—94no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—244no—
238C2×C4—722no—
239C2×C4C2×GO+(4,𝔽2)11yescharacteristic
240C8—92no—
241C8—92no—
242C8—94no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—48no—
247D3—124no—
248C22—22no—
249C22—22no—
250C22—92no—
251C22—181no—
252C22—181no—
253C22C2×#377314yes—
254C22C22×GO+(4,𝔽2)11yescharacteristic
255C4—91no—
256C4—91no—
257C4—94no—
258C4—122no—
259C4—124no—
260C4—122no—
261C4C2×#377312yes—
262C3—22no—
263C2—24no—
264C2—182no—
265C2#1059651411yescharacteristic
266C2#1059651611yescharacteristic
267C2C22×#377311yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC2×C32×D4D4
socleC22×C32C22×D4
prime radicalC2×#3830C22
cosocleC2×C3⋊Dic3C24
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#2913
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. #10593511C2semidirect
4. C2×#63743C2semidirect
5. #10593507C2semidirect
6. #10593396C2semidirect
7. #10593394C2semidirect
8. #10593389C2semidirect
12. #64287C4semidirect
39. #3792C2×C4semidirect
40. C2×#622C2×C4semidirect
44. #3788C2×C4semidirect
45. #3787C2×C4semidirect
222. C32#2913semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
#105952192
#105935112
C2×#637432
#105935072
#105933962
#105933942
#105933892
#29139