Finite Group Databasebeta

← #11783612

Subgroups — #11783612

Order 1152.

837 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 837 conjugacy classes of subgroups — too many to draw. Only its 188 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×#64081C211yesmaximal, characteristic
2C2×#63557C212yesmaximal
3C2×#63555C211yesmaximal, characteristic, complemented
4C2×#63553C211yesmaximal, characteristic, complemented
5C3×#4524C212yesmaximal, complemented
6#68601—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×#3752C412yes—
10C2×#3750C412yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64081—22no—
13#64081—22no—
14C22×C3×C3⋊C8C2212yes—
15C22×C3×C3⋊C8C2212yes—
16#63557C418yescomplemented
17#63555—22no—
18#63553—22no—
19C2×#872—32no—
20C2×#872—61no—
21C2×(C2×D3)⋊C8—32no—
22C2×(C2×D3)⋊C8—32no—
23C2×#815—32no—
24C2×C8×Dic3—32no—
25C3×#336—32no—
26#4524D312yescomplemented
27C23×C3⋊D3C2×C411yescharacteristic
28C22×C32×C4C2×C412yes—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C412yes—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3C2×C414yes—
36C32×C42—21no—
37C32×C42—21no—
38#3752—24no—
39#3750—24no—
40C4×C3⋊Dic3D412yes—
41C4×C3⋊Dic3D412yes—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8C2×C414yes—
47C2×C3×C3⋊C8C2×C414yes—
48#1750—91noSylow
49C22×C4×D3—32no—
50C22×C4×D3—61no—
51C22×C3×C8—32no—
52C22×C3×C8—32no—
53C2×C3×C42—21no—
54C2×C3×C42C2×D312yes—
55C2×(C2×D3)⋊C4—34no—
56C2×(C2×D3)⋊C4—62no—
57C2×Dic3⋊C4—34no—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61C22×C3⋊C8C2×D312yes—
62C22×C3⋊C8C2×D312yes—
63#872—64no—
64#872—64no—
65#872—64no—
66#872—64no—
67(C2×D3)⋊C8—38no—
68(C2×D3)⋊C8—38no—
69#815—64no—
70C8×Dic3—64no—
71C23×C32C22×C411yescharacteristic
72C22×C3⋊D3—21no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3—24no—
75C22×C3⋊D3C4212yes—
76C2×C32×C4—22no—
77C2×C32×C4—24no—
78C2×C32×C4C22×C412yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—24no—
85C2×C3⋊Dic3C4212yes—
86C2×C3⋊Dic3C22⋊C414yes—
87C4×C3⋊D3—24no—
88C4×C3⋊D3—24no—
89C3×C3⋊C8—24no—
90C3×C3⋊C8—24no—
91C2×#117—91no—
92C2×C22⋊C8—92no—
93C2×#97—91no—
94C2×C4×C8—91no—
95#336—32no—
96C23×D3—32no—
97C23×D3—61no—
98C22×C3×C4—22no—
99C22×C3×C4—21no—
100C22×C3×C4C4×D314yes—
101C22×C3×C4C22×D312yes—
102C22×Dic3—34no—
103C22×Dic3—32no—
104C22×Dic3—61no—
105C22×Dic3—62no—
106C2×C4×D3—34no—
107C2×C4×D3—34no—
108C2×C4×D3—64no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—64no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C3×C8—34no—
117C2×C3×C8—34no—
118C2×C3×C8—62no—
119C2×C3×C8—62no—
120C2×C3×C8—62no—
121C2×C3×C8—62no—
122C3×C42—22no—
123C3×C42—22no—
124C3×C42—22no—
125C3×C42—22no—
126(C2×D3)⋊C4—68no—
127(C2×D3)⋊C4—68no—
128Dic3⋊C4—68no—
129Dic3⋊C4—68no—
130C4×Dic3—34no—
131C4×Dic3—34no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—22no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8C4×D314yes—
139C2×C3⋊C8C4×D314yes—
140C22×C32C2×C4211yescharacteristic
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32#11711yescharacteristic
143C22×C32#13114yes—
144C2×C3⋊D3—22no—
145C2×C3⋊D3—24no—
146C2×C3⋊D3—42no—
147C2×C3⋊D3—42no—
148C32×C4—42no—
149C32×C4C4×D412yes—
150C32×C4C4×D412yes—
151C3⋊Dic3—22no—
152C3⋊Dic3—24no—
153C23×C4—91no—
154C22×C8—32no—
155C22×C8—32no—
156#117—182no—
157#117—182no—
158C2×C4⋊C4—92no—
159C2×C22⋊C4—92no—
160C2×C42—91no—
161C2×C42D3211yescharacteristic
162C22⋊C8—98no—
163#97—182no—
164C4×C8—182no—
165C23×C3—21no—
166C23×C3C2×C4×D312yes—
167C22×D3—34no—
168C22×D3—62no—
169C22×D3—62no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—124no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—44no—
185C2×C3×C4C2×C4×D312yes—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4#23712yes—
190C2×C3×C4#23912yes—
191C2×Dic3—34no—
192C2×Dic3—38no—
193C2×Dic3—62no—
194C2×Dic3—64no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—124no—
202C4×D3—68no—
203C4×D3—68no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—64no—
207C4×D3—64no—
208C3×C8—64no—
209C3×C8—64no—
210C3⋊C8—24no—
211C3⋊C8—24no—
212C2×C32C4×C22⋊C411yescharacteristic
213C2×C32#40512yes—
214C2×C32#40812yes—
215C2×C32#43312yes—
216C3⋊D3—42no—
217C24—91no—
218C22×C4—92no—
219C22×C4—91no—
220C22×C4—94no—
221C22×C4—182no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4#62412yes—
225C22×C4C2×D3211yescharacteristic
226C2×C8—34no—
227C2×C8—34no—
228C2×C8—62no—
229C2×C8—62no—
230C2×C8—62no—
231C2×C8—62no—
232C4⋊C4—184no—
233C22⋊C4—184no—
234C42—21no—
235C42—21no—
236C42—92no—
237C42—92no—
238C22×C3—24no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3C42×D312yes—
243C22×C3D3×C22⋊C412yes—
244C22×C3#89212yes—
245C22×C3#90114yes—
246C22×C3#90714yes—
247C2×D3—64no—
248C2×D3—64no—
249C2×D3—64no—
250C2×D3—64no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—124no—
254C2×D3—124no—
255C2×D3—124no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—44no—
259C3×C4—44no—
260C3×C4#67⋊C412yes—
261C3×C4#67⋊C412yes—
262C3×C4#89312yes—
263C3×C4#89312yes—
264Dic3—64no—
265Dic3—64no—
266Dic3—68no—
267Dic3—124no—
268C32#175011yescharacteristic, complemented, Sylow
269C23—92no—
270C23—184no—
271C23—181no—
272C23—181no—
273C23C2×#62411yescharacteristic
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—92no—
277C2×C4—94no—
278C2×C4—184no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—184no—
282C2×C4—184no—
283C2×C4#379612yes—
284C2×C4C4×D3212yes—
285C2×C4#381111yescharacteristic
286C2×C4#381111yescharacteristic
287C8—64no—
288C8—64no—
289C2×C3—21no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3#466612yes—
294C2×C3#468912yes—
295C2×C3#470812yes—
296C2×C3#472714yes—
297C2×C3#484014yes—
298D3—124no—
299D3—124no—
300C22—182no—
301C22—184no—
302C22—362no—
303C22—362no—
304C22#6381714yes—
305C22#6384911yescharacteristic
306C22C4×#62411yescharacteristic
307C22#6397411yescharacteristic
308C4—42no—
309C4—182no—
310C4—184no—
311C4#6388112yes—
312C4#6388112yes—
313C3—21no—
314C3#6860112yescomplemented
315C2—362no—
316C2#1059025712yes—
317C2#1059032112yes—
318C2#1059115312yes—
319C2#1059126011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63555C2semidirect
4. C2×#63553C2semidirect
5. C3×#4524C2semidirect
16. #63557C4semidirect
26. #4524D3semidirect
268. C32#1750semidirect
314. C3#68601semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#635572
C2×#635552
C2×#635532
C3×#45242
#686013