Finite Group Databasebeta

← #11776369

Subgroups — #11776369

Order 1152.

448 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#10593727C211yesmaximal, characteristic
3#10590340C211yesmaximal, characteristic
4#10590040C214yesmaximal, complemented
5C2×#3797C412yes—
6C42×C3⋊D3C2211yescharacteristic
7C3×#869—21no—
8#63919C412yes—
9#63919C2212yes—
10#63900—21no—
11#63900—21no—
12#63873—21no—
13C2×#3712—21no—
14#63778—21no—
15C4⋊#622C2212yes—
16C4×#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63572C2212yes—
19D3×C4⋊Q8—61no—
20#4837—61no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627C2×C414yes—
26C2×#624—22no—
27#3797—44no—
28C2×#622—22no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—22no—
34C3×C4⋊Dic3—22no—
35C2×C3×C3⋊C8—22no—
36#3724—22no—
37#3724—22no—
38#3712—42no—
39#1548—91nomaximal, Sylow
40C2×D3×Q8—62no—
41C3×C4⋊Q8—61no—
42#944—62no—
43C2×ΓL(1,𝔽25)—62no—
44D3×C4⋊C4—62no—
45D3×C4⋊C4—62no—
46#888—62no—
47#888—62no—
48C42×D3—61no—
49C42×D3—61no—
50#869—21no—
51C3×C4⋊C8—61no—
52Dic3⋊C8—62no—
53C4⋊(C3⋊C8)—21no—
54C22×C3⋊D3C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3C22⋊C411yescharacteristic
59C2×C3⋊Dic3C22×C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3—22no—
63C4×C3⋊D3SD1612yes—
64C4×C3⋊D3Q1612yes—
65C2×C3×Dic3—24no—
66C3×Dic6—44no—
67#627—44no—
68#624—44no—
69#622—42no—
70C3×C3⋊C8—42no—
71C2×C4⋊Q8—91no—
72#431—91no—
73#423—91no—
74#333—94no—
75C2×C3×Q8—62no—
76D3×Q8—128no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—64no—
84C2×Dic6—22no—
85C2×Dic6—64no—
86C2×C3×C8—62no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C42—21no—
90C3×C42—21no—
91C4⋊Dic3—22no—
92C4⋊Dic3—22no—
93Dic3⋊C4—64no—
94Dic3⋊C4—64no—
95C4×Dic3—61no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—22no—
102ΓL(1,𝔽25)—124no—
103C22×C32C2×C22⋊C411yescharacteristic
104C2×C3⋊D3—21no—
105C2×C3⋊D3—21no—
106C2×C3⋊D3#10312yes—
107C32×C4—21no—
108C32×C4#10012yes—
109C32×C4C2×SD1611yescharacteristic
110C32×C4C2×Q1611yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3#10312yes—
113C3⋊Dic3#13712yes—
114C3×Dic3—44no—
115C22×Q8—92no—
116C2×M16—181no—
117C4⋊Q8—61no—
118C4⋊Q8—92no—
119C4⋊Q8—92no—
120C4⋊Q8—181no—
121C2×C4⋊C4—181no—
122C2×C4⋊C4—181no—
123C2×C42—91no—
124C4⋊C8—61no—
125C4⋊C8—92no—
126C4⋊C8—92no—
127C22⋊C8—181no—
128C4×C8—181no—
129C22×D3—61no—
130C22×D3—61no—
131C3×Q8—124no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—64no—
139C2×Dic3—24no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—64no—
151C4×D3—64no—
152C4×D3—122no—
153C4×D3—122no—
154C4×D3—128no—
155Dic6—44no—
156Dic6—128no—
157C3×C8—122no—
158C3⋊C8—42no—
159C2×C32C2×#10011yescharacteristic
160C2×C32C2×#10311yescharacteristic
161C2×C32#41911yescharacteristic
162C3⋊D3—22no—
163C2×Q8—62no—
164C2×Q8—94no—
165C2×Q8—364no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—182no—
170M16—362no—
171C2×C8—62no—
172C2×C8—182no—
173C4⋊C4—62no—
174C4⋊C4—62no—
175C4⋊C4—182no—
176C4⋊C4—182no—
177C42—91no—
178C42—91no—
179C42—91no—
180C42GO+(4,𝔽2)11yescharacteristic
181C22×C3—21no—
182C22×C3—21no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—62no—
187C2×D3—121no—
188C2×D3—121no—
189C3×C4—22no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—41no—
197C3×C4—124no—
198Dic3—44no—
199Dic3—62no—
200Dic3—62no—
201Dic3—62no—
202Dic3—62no—
203Dic3—62no—
204Dic3—121no—
205C32#154811yescharacteristic, complemented, Sylow
206C23—91no—
207Q8—124no—
208Q8—364no—
209C2×C4—64no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—91no—
215C2×C4—182no—
216C2×C4—182no—
217C2×C4—364no—
218C2×C4D32⋊C411yescharacteristic
219C2×C4D32⋊C411yescharacteristic
220C2×C4C2×GO+(4,𝔽2)11yescharacteristic
221C8—122no—
222C8—362no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229D3—64no—
230D3—122no—
231C22—92no—
232C22—181no—
233C22—181no—
234C22C2×D32⋊C411yescharacteristic
235C4—21no—
236C4—92no—
237C4—92no—
238C4—124no—
239C4—181no—
240C4#6372712yes—
241C4#6422711yescharacteristic
242C4#6422811yescharacteristic
243C3—21no—
244C3—21no—
245C2—182no—
246C2C2×#6372711yescharacteristic
247C2#1059332111yescharacteristic
248C2#1059337511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1548
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590040C2semidirect
205. C32#1548semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105937272
#105903402
#105900402
#15489