Finite Group Databasebeta

← #11790625

Subgroups — #11790625

Order 1152.

809 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 809 conjugacy classes of subgroups — too many to draw. Only its 180 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×#64153C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal
3#10591359C211yesmaximal, characteristic
4C2×#63567C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#70225—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×#634C2211yescharacteristic
9#64153—22no—
10#64153C414yescomplemented
11C2×#3750—22no—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C22×C3×C3⋊C8C2212yes—
15C2×#3724—22no—
16C3×#835—24no—
17#63567—24no—
18#63553—22no—
19C2×#944—32no—
20C2×#944—61no—
21C2×C3×#103—32no—
22C2×#835D312yes—
23C2×#816—32no—
24C2×C8×Dic3—32no—
25#4975—32no—
26C2×#810—32no—
27C2×C32×Q8—21no—
28C2×C32×Q8—22no—
29C2×C32×Q8—22no—
30C2×C32×Q8C2×C412yes—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D412yes—
35C2×#634—22no—
36C2×#634—22no—
37C2×#634—21no—
38C2×#634C2×C412yes—
39C22×C3×Dic3—22no—
40#3750—28no—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3D412yes—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8D414yes—
48#3724—44no—
49#1956—91noSylow
50C22×C3×Q8—21no—
51C22×C3×Q8C2×D312yes—
52C22×Dic6—32no—
53C22×Dic6—61no—
54C22×C3×C8—32no—
55C2×C3×C4⋊C4—32no—
56#944—38no—
57#944—64no—
58#944—64no—
59#944—64no—
60C2×C4⋊Dic3C2×D312yes—
61C2×Dic3⋊C4—64no—
62C2×Dic3⋊C4—64no—
63C2×Dic3⋊C4—64no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C22×C3⋊C8C2×D312yes—
67C3×#103—64no—
68#835—24no—
69#816—64no—
70C8×Dic3—64no—
71#810—64no—
72C23×C32C2×D411yescharacteristic
73C32×Q8—24no—
74C32×Q8—42no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D412yes—
81C2×C32×C4#4112yes—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C22⋊C414yes—
86C2×C3⋊Dic3SD1614yes—
87C2×C3⋊Dic3Q1614yes—
88#634—24no—
89#634—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—44no—
92C3×C3⋊C8—24no—
93C2×C4⋊Q8—91no—
94C2×#103—32no—
95C2×#103—92no—
96C2×C4×C8—91no—
97#384—91no—
98C2×C3×Q8—22no—
99C2×C3×Q8—22no—
100C2×C3×Q8—22no—
101C2×C3×Q8—22no—
102C2×C3×Q8—22no—
103C2×C3×Q8—22no—
104C2×C3×Q8—22no—
105C2×C3×Q8—42no—
106C2×C3×Q8—42no—
107C2×C3×Q8C4×D314yes—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—62no—
112C22×C3×C4C22×D312yes—
113C22×Dic3—22no—
114C22×Dic3—34no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C2×Dic6—34no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—62no—
126C2×Dic6—122no—
127C2×Dic6—122no—
128C2×C3×C8—34no—
129C2×C3×C8—62no—
130C2×C3×C8—62no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—62no—
133C4⋊Dic3—22no—
134C4⋊Dic3—22no—
135Dic3⋊C4—616no—
136Dic3⋊C4—616no—
137Dic3⋊C4—128no—
138C4×Dic3—34no—
139C4×Dic3—34no—
140C4×Dic3—62no—
141C4×Dic3—62no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8#6714yes—
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#12411yescharacteristic
147C22×C32#12711yescharacteristic
148C22×C32C2×SD1612yes—
149C22×C32C2×Q1612yes—
150C32×C4—42no—
151C32×C4C4×D412yes—
152C32×C4#12112yes—
153C3⋊Dic3—42no—
154C3⋊Dic3#10318yescomplemented
155C3×Dic3—82no—
156C22×Q8—91no—
157C22×Q8D3211yescharacteristic
158C22×C8—32no—
159C4⋊Q8—94no—
160C4⋊Q8—182no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—182no—
163C2×C4⋊C4—182no—
164C2×C42—91no—
165#103—64no—
166#103—184no—
167C4×C8—182no—
168C23×C3—21no—
169C23×C3D3×D412yes—
170C3×Q8—24no—
171C3×Q8—24no—
172C3×Q8—44no—
173C3×Q8—44no—
174C3×Q8—42no—
175C3×Q8—42no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—124no—
187C2×C3×C4—122no—
188C2×C3×C4C2×C4×D312yes—
189C2×C3×C4#23512yes—
190C2×C3×C4D3×D412yes—
191C2×C3×C4D3×D412yes—
192C2×C3×C4#23712yes—
193C2×C3×C4C2×#6712yes—
194C2×Dic3—38no—
195C2×Dic3—38no—
196C2×Dic3—38no—
197C2×Dic3—44no—
198C2×Dic3—42no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208Dic6—64no—
209Dic6—64no—
210Dic6—124no—
211Dic6—124no—
212Dic6—122no—
213Dic6—122no—
214C3×C8—64no—
215C3⋊C8—24no—
216C2×C32#39011yescharacteristic
217C2×C32C2×#10312yes—
218C2×C32#48712yes—
219C2×C32#49211yescharacteristic
220C2×C32#49411yescharacteristic
221C2×Q8—21no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—92no—
225C2×Q8—181no—
226C2×Q8—182no—
227C2×Q8—182no—
228C2×Q8#62412yes—
229C22×C4—21no—
230C22×C4—62no—
231C22×C4—92no—
232C22×C4—181no—
233C22×C4C2×D3211yescharacteristic
234C2×C8—34no—
235C2×C8—62no—
236C2×C8—62no—
237C4⋊C4—62no—
238C4⋊C4—62no—
239C4⋊C4—188no—
240C4⋊C4—364no—
241C42—92no—
242C42—92no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3D3×C22⋊C412yes—
249C22×C3#88512yes—
250C22×C3D3×SD1614yes—
251C22×C3D3×Q1614yes—
252C22×C3#94012yes—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—44no—
256C3×C4—44no—
257C3×C4—242no—
258C3×C4#67⋊C412yes—
259C3×C4#88412yes—
260C3×C4C4×#6712yes—
261C3×C4#93912yes—
262Dic3—316no—
263Dic3—68no—
264Dic3—82no—
265Dic3—124no—
266Dic3—124no—
267C32#195611yescharacteristic, complemented, Sylow
268C23#381111yescharacteristic
269Q8—24no—
270Q8—42no—
271Q8—184no—
272Q8—362no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—94no—
277C2×C4—94no—
278C2×C4—94no—
279C2×C4—124no—
280C2×C4—122no—
281C2×C4—182no—
282C2×C4—361no—
283C2×C4—361no—
284C2×C4#380412yes—
285C2×C4C2×#62411yescharacteristic
286C2×C4D3×#6712yes—
287C2×C4#381111yescharacteristic
288C8—64no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3#479214yes—
295C2×C3D3×#10314yes—
296C2×C3#495712yes—
297C2×C3#517512yes—
298C2×C3#518312yes—
299C22#6394012yes—
300C22#6394412yes—
301C22#6395311yescharacteristic
302C22#6397411yescharacteristic
303C22#6397911yescharacteristic
304C4—42no—
305C4—98no—
306C4—242no—
307C4—362no—
308C4#6395212yes—
309C4#6397112yes—
310C3—21no—
311C3#7022512yescomplemented
312C2#1059153812yes—
313C2#1059155212yes—
314C2#1059162011yescharacteristic
315C2#1059162811yescharacteristic
316C2#1059170411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1956
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
10. #64153C4semidirect
154. C3⋊Dic3#103semidirect
267. C32#1956semidirect
311. C3#70225semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#8352
#105913592
C2×#635672
C2×#635532
#702253