Finite Group Databasebeta

← #11791886

Subgroups — #11791886

Order 1152.

468 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 73 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#10593909C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic
3#10590340C211yesmaximal, characteristic
4#10590052C214yesmaximal
5C2×#3797C412yes—
6C2×#3788C2212yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×#869—21no—
9#63919—21no—
10#63919—21no—
11#63900C412yes—
12#63900C2212yes—
13#63873—21no—
14C2×#3712C2212yes—
15#63777—21no—
16C4×#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63572—21no—
19D3×C4⋊Q8—61no—
20#4837—61no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627—22no—
26C2×#624C2×C414yes—
27#3797—44no—
28C2×#622—22no—
29#3788—22no—
30#3788Q814yescomplemented
31C32×C42D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3724—22no—
39#3724—22no—
40#3712—24no—
41#1997—91nomaximal, Sylow
42C2×D3×Q8—62no—
43C3×C4⋊Q8—61no—
44#944—62no—
45C2×ΓL(1,𝔽25)—62no—
46D3×C4⋊C4—62no—
47D3×C4⋊C4—62no—
48#888—62no—
49#888—62no—
50C42×D3—61no—
51C42×D3—61no—
52#869—21no—
53C3×C4⋊C8—61no—
54Dic3⋊C8—62no—
55C4⋊(C3⋊C8)—21no—
56C22×C3⋊D3C22×C411yescharacteristic
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C2×D411yescharacteristic
63C4×C3⋊D3—22no—
64C4×C3⋊D3—22no—
65C4×C3⋊D3C2×Q812yes—
66C4×C3⋊D3#4112yes—
67C2×C3×Dic3—24no—
68C3×Dic6—44no—
69#627—44no—
70#624—44no—
71#622—24no—
72C3×C3⋊C8—42no—
73C2×C4⋊Q8—91no—
74#423—91no—
75C4×M16—91no—
76#343—94no—
77C2×C3×Q8—62no—
78D3×Q8—128no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—64no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×Dic6—22no—
87C2×Dic6—64no—
88C2×C3×C8—62no—
89C3×C4⋊C4—62no—
90C3×C4⋊C4—62no—
91C3×C42—21no—
92C3×C42—21no—
93C4⋊Dic3—22no—
94C4⋊Dic3—22no—
95Dic3⋊C4—64no—
96Dic3⋊C4—64no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3⋊C8—22no—
104ΓL(1,𝔽25)—124no—
105C22×C32C2×C22⋊C411yescharacteristic
106C2×C3⋊D3—21no—
107C2×C3⋊D3—21no—
108C2×C3⋊D3C4×Q812yes—
109C32×C4—21no—
110C32×C4#10112yes—
111C32×C4#12411yescharacteristic
112C32×C4C4⋊Q811yescharacteristic
113C3⋊Dic3—21no—
114C3⋊Dic3#10012yes—
115C3⋊Dic3C22⋊Q812yes—
116C3×Dic3—44no—
117C22×Q8—92no—
118C2×M16—92no—
119C2×M16—92no—
120C4⋊Q8—61no—
121C4⋊Q8—181no—
122C4⋊Q8—181no—
123C4⋊Q8—181no—
124C2×C4⋊C4—92no—
125C2×C4⋊C4—92no—
126C2×C42—91no—
127C4⋊C8—61no—
128C4⋊C8—181no—
129#97—181no—
130C4×C8—181no—
131C22×D3—61no—
132C22×D3—61no—
133C3×Q8—124no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—64no—
141C2×Dic3—24no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—62no—
152C4×D3—64no—
153C4×D3—64no—
154C4×D3—122no—
155C4×D3—122no—
156C4×D3—128no—
157Dic6—44no—
158Dic6—128no—
159C3×C8—122no—
160C3⋊C8—42no—
161C2×C32#39111yescharacteristic
162C2×C32C2×#10011yescharacteristic
163C2×C32C2×#10111yescharacteristic
164C3⋊D3—22no—
165C2×Q8—62no—
166C2×Q8—182no—
167C2×Q8—364no—
168C22×C4—94no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172M16—94no—
173M16—184no—
174M16—182no—
175C2×C8—62no—
176C2×C8—182no—
177C4⋊C4—62no—
178C4⋊C4—62no—
179C4⋊C4—182no—
180C4⋊C4—182no—
181C42—91no—
182C42—91no—
183C42—91no—
184C42GO+(4,𝔽2)11yescharacteristic
185C22×C3—21no—
186C22×C3—21no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—62no—
190C2×D3—62no—
191C2×D3—121no—
192C2×D3—121no—
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—41no—
201C3×C4—124no—
202Dic3—44no—
203Dic3—62no—
204Dic3—62no—
205Dic3—62no—
206Dic3—62no—
207Dic3—62no—
208Dic3—121no—
209C32#199711yescharacteristic, complemented, Sylow
210C23—91no—
211Q8—124no—
212Q8—364no—
213C2×C4—64no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—92no—
218C2×C4—91no—
219C2×C4—182no—
220C2×C4—182no—
221C2×C4—364no—
222C2×C4D32⋊C411yescharacteristic
223C2×C4D32⋊C411yescharacteristic
224C2×C4C2×GO+(4,𝔽2)11yescharacteristic
225C8—122no—
226C8—184no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233D3—64no—
234D3—122no—
235C22—92no—
236C22—181no—
237C22—181no—
238C22C2×D32⋊C411yescharacteristic
239C4—21no—
240C4—92no—
241C4—92no—
242C4—124no—
243C4—181no—
244C4#6372812yes—
245C4#6422111yescharacteristic
246C4#6422211yescharacteristic
247C3—21no—
248C3—21no—
249C2—182no—
250C2#1059331211yescharacteristic
251C2C2×#6372811yescharacteristic
252C2#1059334211yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutator, prime radicalC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1997
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
30. #3788Q8semidirect
209. C32#1997semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37882
#105903402
#105900522
#19979