Finite Group Databasebeta

← #11791117

Subgroups — #11791117

Order 1152.

634 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×#3774C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic, complemented
3C2×#63742C211yesmaximal, characteristic, complemented
4C2×#63739C212yesmaximal, complemented
5#10591385C212yesmaximal, complemented
6C22×#625C2212yes—
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×#3774—22no—
10C2×#3774—22no—
11C2×#3774C414yescomplemented
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—22no—
14C2×#3724C2212yes—
15C2×(C2×D3)⋊Dic3—22no—
16#63777—22no—
17#63742—22no—
18#63739—24no—
19#4957—62no—
20C23×C3×D3—22no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—22no—
25C2×#625—22no—
26C2×#625—22no—
27C2×#625—22no—
28C2×#625—22no—
29C2×#625—22no—
30C2×#625C2×C414yes—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622C2×C412yes—
34C2×#622D412yes—
35C2×#622D412yes—
36C2×#622D412yes—
37#3774—28no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3—21no—
40C3×(C2×D3)⋊C4—44no—
41#3724—22no—
42#3724—22no—
43(C2×D3)⋊Dic3—44no—
44#1972—91nomaximal, Sylow
45C22×#67—62no—
46C2×C3×C22⋊C4—62no—
47C2×#217—62no—
48C2×(C2×D3)⋊C4—22no—
49C2×(C2×D3)⋊C4—62no—
50C2×Dic3⋊C4—62no—
51C2×C4×Dic3—62no—
52C23×C32C2×D411yescharacteristic
53C22×C3×D3—24no—
54C22×C3×D3—42no—
55C22×C3×D3—42no—
56C22×C3×D3—42no—
57C22×C3×D3—42no—
58C22×C3×D3—42no—
59C22×C3×D3—42no—
60C2×C32×C4—22no—
61C2×C32×C4—21no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C2×C3⋊Dic3#4111yescharacteristic
69C2×C3⋊Dic3#4111yescharacteristic
70C2×C3×Dic3—42no—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—42no—
73#625—24no—
74#625—24no—
75#625—42no—
76#625—42no—
77#622—22no—
78#622C22⋊C414yescomplemented
79C22×D8—91no—
80C2×#106—91no—
81C2×#102—92no—
82C2×#97—91no—
83#390—92no—
84C24×C3—62no—
85C23×D3—22no—
86C22×C3×C4—22no—
87C22×C3×C4—62no—
88C2×#67—64no—
89C2×#67—64no—
90C2×#67—122no—
91C2×#67—122no—
92C2×#67—122no—
93C2×#67—122no—
94C22×Dic3—22no—
95C22×Dic3—62no—
96C22×Dic3—62no—
97C3×C22⋊C4—124no—
98#217—124no—
99(C2×D3)⋊C4—44no—
100(C2×D3)⋊C4—124no—
101Dic3⋊C4—122no—
102Dic3⋊C4—122no—
103C4×Dic3—122no—
104C4×Dic3—122no—
105C22×C32C4×D411yescharacteristic
106C22×C32#12111yescharacteristic
107C22×C32#12711yescharacteristic
108C22×C32AGL(1,ℤ/8)12yes—
109C22×C32AGL(1,ℤ/8)12yes—
110C2×C3×D3—44no—
111C2×C3×D3—44no—
112C2×C3×D3—44no—
113C2×C3×D3—82no—
114C2×C3×D3—82no—
115C2×C3×D3—82no—
116C2×C3×D3—82no—
117C32×C4—41no—
118C3⋊Dic3—41no—
119C3⋊Dic3C2×C22⋊C411yescharacteristic
120C3⋊Dic3C4×D411yescharacteristic
121C3⋊Dic3#12111yescharacteristic
122C3⋊Dic3#12411yescharacteristic
123C3×Dic3—82no—
124C22×D4—92no—
125C2×D8—94no—
126C2×D8—182no—
127C2×D8—182no—
128C22×C8—91no—
129C22×C8—91no—
130C2×C4⋊C4—92no—
131C2×C22⋊C4—62no—
132C2×C22⋊C4—182no—
133C2×C42—91no—
134#106—182no—
135#102—184no—
136#97—182no—
137C23×C3—22no—
138C23×C3—64no—
139C23×C3—122no—
140C23×C3—122no—
141C23×C3—122no—
142C23×C3—122no—
143C23×C3—122no—
144C23×C3—122no—
145C22×D3—24no—
146C22×D3—42no—
147C22×D3—42no—
148C22×D3—42no—
149C22×D3—42no—
150C22×D3—42no—
151C22×D3—42no—
152C2×C3×C4—24no—
153C2×C3×C4—42no—
154C2×C3×C4—42no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158#67—124no—
159#67—124no—
160#67—124no—
161#67—124no—
162C2×Dic3—42no—
163C2×Dic3—42no—
164C2×Dic3—42no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—64no—
172C2×Dic3—122no—
173C2×Dic3—122no—
174C2×C32#39011yescharacteristic
175C2×C32#44212yes—
176C2×C32#46911yescharacteristic
177C2×C32#46911yescharacteristic
178C2×C32#49612yes—
179C3×D3—84no—
180C24—62no—
181C2×D4—94no—
182C2×D4—182no—
183C2×D4—182no—
184C2×D4—182no—
185C2×D4—182no—
186C2×D4—182no—
187C22×C4—62no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4GO+(4,𝔽2)11yescharacteristic
191D8—188no—
192C2×C8—92no—
193C2×C8—92no—
194C2×C8—92no—
195C2×C8—92no—
196C2×C8—181no—
197C2×C8—181no—
198C4⋊C4—182no—
199C4⋊C4—182no—
200C22⋊C4—124no—
201C22⋊C4—364no—
202C42—181no—
203C42—181no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—124no—
212C22×C3—124no—
213C22×C3—124no—
214C22×C3—242no—
215C22×C3—242no—
216C22×C3—242no—
217C22×C3—242no—
218C2×D3—44no—
219C2×D3—44no—
220C2×D3—44no—
221C2×D3—82no—
222C2×D3—82no—
223C2×D3—82no—
224C2×D3—82no—
225C3×C4—44no—
226C3×C4—242no—
227Dic3—62no—
228Dic3—62no—
229Dic3—62no—
230Dic3—62no—
231Dic3—82no—
232Dic3—124no—
233C32#197211yescharacteristic, complemented, Sylow
234C23—64no—
235C23—122no—
236C23—122no—
237C23—122no—
238C23—122no—
239C23—122no—
240C23—122no—
241C23C2×GO+(4,𝔽2)11yescharacteristic
242D4—184no—
243D4—184no—
244D4—362no—
245D4—362no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—122no—
257C2×C4—182no—
258C2×C4—181no—
259C8—94no—
260C8—182no—
261C2×C3—22no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—22no—
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—244no—
269D3—84no—
270C22—124no—
271C22—124no—
272C22—124no—
273C22—242no—
274C22—242no—
275C22—242no—
276C22—242no—
277C22#6422412yes—
278C22C4×GO+(4,𝔽2)11yescharacteristic
279C22#6423111yescharacteristic
280C22#6423612yes—
281C22#6424211yescharacteristic
282C4—41no—
283C4—91no—
284C4—91no—
285C4—91no—
286C4—91no—
287C4—242no—
288C4—361no—
289C3—22no—
290C2—244no—
291C2#1059341912yes—
292C2#1059342712yes—
293C2#1059342911yescharacteristic
294C2#1059345411yescharacteristic
295C2#1059352211yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3774C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1972
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63777C2semidirect
3. C2×#63742C2semidirect
4. C2×#63739C2semidirect
5. #10591385C2semidirect
11. C2×#3774C4semidirect
78. #622C22⋊C4semidirect
233. C32#1972semidirect

Maximal subgroups

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

subgroupindex
C22×#37742
C2×#637772
C2×#637422
C2×#637392
#105913852
#19729