Finite Group Databasebeta

← #11783680

Subgroups — #11783680

Order 1152.

889 conjugacy classes of subgroups; only the 196 normal subgroups are shown.

normal subgroups only

This group has 889 conjugacy classes of subgroups — too many to draw. Only its 196 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×C8×C3⋊D3C211yesmaximal, characteristic
2C4×#3722C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C2×#63554C212yesmaximal, complemented
5C3×#4550C212yesmaximal, complemented
6#68648—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C8×C3⋊D3—24no—
11C2×C8×C3⋊D3C414yescomplemented
12C2×C3×C4×Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3722C412yes—
15#63579C412yes—
16#63557C414yescomplemented
17#63554—24no—
18C22×D3×C8—32no—
19C22×D3×C8—61no—
20C2×(C2×D3)⋊C8—32no—
21C2×#815—32no—
22C4×(C2×D3)⋊C4—32no—
23C2×#803—32no—
24C3×#336—32no—
25#4550D312yescomplemented
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3C2×C412yes—
32C2×C4×C3⋊D3C2×C412yes—
33C22×C3×Dic3C2×C414yes—
34C2×C32×C8—22no—
35C2×C32×C8C2×C412yes—
36C2×C3⋊(C3⋊C8)C2×C412yes—
37C2×C3⋊(C3⋊C8)D414yes—
38C8×C3⋊D3—28no—
39C3×C4×Dic3—22no—
40C3×C4×Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8C2×C414yes—
44#3722—24no—
45#1752—91noSylow
46C22×C4×D3—32no—
47C22×C4×D3—61no—
48C22×C3×C8—21no—
49C22×C3×C8—32no—
50C22×C3×C8C2×D312yes—
51C2×C3×C42—32no—
52C2×(C2×D3)⋊C4—34no—
53C2×C4×Dic3C2×D312yes—
54C22×C3⋊C8—32no—
55C22×C3⋊C8—61no—
56C22×C3⋊C8C2×D312yes—
57C2×D3×C8—38no—
58C2×D3×C8—64no—
59C2×D3×C8—64no—
60C2×D3×C8—64no—
61C2×D3×C8—68no—
62C3⋊#95—34no—
63(C2×D3)⋊C8—38no—
64#815—64no—
65#803—64no—
66C23×C32C22×C411yescharacteristic
67C22×C3⋊D3—22no—
68C22×C3⋊D3—22no—
69C22×C3⋊D3C4212yes—
70C22×C3⋊D3M1614yes—
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4#4112yes—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3C4212yes—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—24no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—24no—
83C32×C8—22no—
84C3⋊(C3⋊C8)C22⋊C414yescomplemented
85C3×C3⋊C8—24no—
86C23×C8—91no—
87C2×C22⋊C8—91no—
88C2×#97—92no—
89C4×C22⋊C4—91no—
90#336—32no—
91C23×D3—32no—
92C23×D3—61no—
93C22×C3×C4—21no—
94C22×C3×C4—34no—
95C22×C3×C4C22×D312yes—
96C22×Dic3—32no—
97C22×Dic3—61no—
98C22×Dic3C4×D314yes—
99C2×C4×D3—34no—
100C2×C4×D3—34no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C3×C8—24no—
110C2×C3×C8—22no—
111C2×C3×C8—22no—
112C2×C3×C8—22no—
113C2×C3×C8—34no—
114C2×C3×C8—62no—
115C2×C3×C8—62no—
116C2×C3×C8C4×D314yes—
117C3×C42—62no—
118C3×C42—62no—
119(C2×D3)⋊C4—68no—
120C4×Dic3—22no—
121C4×Dic3—22no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—34no—
125C2×C3⋊C8—34no—
126C2×C3⋊C8—34no—
127C2×C3⋊C8—62no—
128C2×C3⋊C8—64no—
129C2×C3⋊C8C4×D314yes—
130D3×C8—616no—
131D3×C8—616no—
132C22×C32C2×C4211yescharacteristic
133C22×C32C4×D412yes—
134C22×C32C2×M1612yes—
135C22×C32#13112yes—
136C2×C3⋊D3—22no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3—28no—
139C2×C3⋊D3#9714yescomplemented
140C32×C4C2×C22⋊C411yescharacteristic
141C32×C4#11711yescharacteristic
142C32×C4C4×D412yes—
143C3⋊Dic3—22no—
144C3×Dic3—44no—
145C23×C4—91no—
146C22×C8—32no—
147C22×C8—91no—
148C22×C8—94no—
149C22×C8—184no—
150C22×C8D3211yescharacteristic
151C2×C22⋊C4—92no—
152C2×C42—32no—
153C22⋊C8—94no—
154#97—184no—
155#95—92no—
156C23×C3—21no—
157C23×C3C2×C4×D312yes—
158C22×D3—34no—
159C22×D3—38no—
160C22×D3—62no—
161C22×D3—64no—
162C22×D3—64no—
163C22×D3—64no—
164C22×D3—62no—
165C22×D3—62no—
166C22×D3—64no—
167C2×C3×C4—22no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—22no—
171C2×C3×C4—64no—
172C2×C3×C4—64no—
173C2×C3×C4—64no—
174C2×C3×C4C2×C4×D312yes—
175C2×C3×C4C2×C4×D312yes—
176C2×C3×C4D3×D412yes—
177C2×C3×C4D3×D412yes—
178C2×C3×C4#23712yes—
179C2×C3×C4#23912yes—
180C2×Dic3—24no—
181C2×Dic3—24no—
182C2×Dic3—24no—
183C2×Dic3—34no—
184C2×Dic3—62no—
185C2×Dic3—64no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—68no—
191C4×D3—64no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—64no—
195C3×C8—24no—
196C3×C8—24no—
197C3×C8—64no—
198C3⋊C8—24no—
199C3⋊C8—38no—
200C3⋊C8—64no—
201C2×C32C4×C22⋊C411yescharacteristic
202C2×C32C2×#9711yescharacteristic
203C2×C32#40511yescharacteristic
204C2×C32#43514yes—
205C3⋊D3—24no—
206C24—91no—
207C22×C4—34no—
208C22×C4—91no—
209C22×C4—92no—
210C22×C4—92no—
211C22×C4—182no—
212C22×C4—182no—
213C22×C4C2×D3211yescharacteristic
214C2×C8—22no—
215C2×C8—34no—
216C2×C8—62no—
217C2×C8—62no—
218C2×C8—92no—
219C2×C8—94no—
220C2×C8—188no—
221C2×C8#62412yes—
222C22⋊C4—184no—
223C42—62no—
224C42—62no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3C42×D312yes—
230C22×C3#67⋊C412yes—
231C22×C3#89312yes—
232C22×C3#90114yes—
233C22×C3D3×M1614yes—
234C2×D3—38no—
235C2×D3—64no—
236C2×D3—64no—
237C2×D3—616no—
238C2×D3—64no—
239C2×D3—64no—
240C2×D3—64no—
241C2×D3—68no—
242C2×D3—68no—
243C3×C4—21no—
244C3×C4—22no—
245C3×C4—21no—
246C3×C4—124no—
247C3×C4D3×C22⋊C412yes—
248C3×C4#67⋊C412yes—
249C3×C4#89212yes—
250C3×C4#89312yes—
251Dic3—44no—
252Dic3—64no—
253Dic3—64no—
254C32#175211yescharacteristic, complemented, Sylow
255C23—94no—
256C23—92no—
257C23—182no—
258C23—182no—
259C23C4×D3211yescharacteristic
260C2×C4—64no—
261C2×C4—64no—
262C2×C4—64no—
263C2×C4—92no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4—184no—
267C2×C4—182no—
268C2×C4#379612yes—
269C2×C4C4×D3211yescharacteristic
270C2×C4C2×#62411yescharacteristic
271C2×C4#381112yes—
272C8—22no—
273C8—64no—
274C8—94no—
275C2×C3—24no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3#466612yes—
280C2×C3#468912yes—
281C2×C3D3×#9712yes—
282C2×C3#472814yes—
283C2×C3#483614yes—
284D3—68no—
285D3—68no—
286C22—94no—
287C22—188no—
288C22—182no—
289C22—182no—
290C22#6379112yes—
291C22#6380312yes—
292C22#6388112yes—
293C22C4×#62411yescharacteristic
294C4—124no—
295C4—182no—
296C4#6384911yescharacteristic
297C4#6388112yes—
298C4#6397411yescharacteristic
299C3—21no—
300C3#6864812yescomplemented
301C2—184no—
302C2#1059066811yescharacteristic
303C2#1059070011yescharacteristic
304C2#1059073714yes—
305C2#1059126011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1752
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×#63554C2semidirect
5. C3×#4550C2semidirect
11. C2×C8×C3⋊D3C4semidirect
16. #63557C4semidirect
25. #4550D3semidirect
84. C3⋊(C3⋊C8)C22⋊C4semidirect
139. C2×C3⋊D3#97semidirect
254. C32#1752semidirect
300. C3#68648semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C4×#37222
C2×#635572
C2×#635542
C3×#45502
#686483