Finite Group Databasebeta

← #11790741

Subgroups — #11790741

Order 1152.

761 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 761 conjugacy classes of subgroups — too many to draw. Only its 164 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#10591230C211yesmaximal, characteristic
4C2×#63567C212yesmaximal
5C2×#63555C211yesmaximal, characteristic
6#70228—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—
15C3×#835—24no—
16#63579—22no—
17#63567—24no—
18#63555—22no—
19C2×#944—32no—
20C2×#944—61no—
21C2×C3×#103—32no—
22C2×#835D312yes—
23C2×#816—32no—
24C2×#815—32no—
25#4977—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#1960—91noSylow
49C22×C3×Q8—21no—
50C22×C3×Q8C2×D312yes—
51C22×Dic6—32no—
52C22×Dic6—61no—
53C22×C3×C8—32no—
54C2×C3×C4⋊C4—32no—
55#944—38no—
56#944—64no—
57#944—64no—
58#944—64no—
59C2×C4⋊Dic3C2×D312yes—
60C2×Dic3⋊C4—64no—
61C2×Dic3⋊C4—64no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C22×C3⋊C8C2×D312yes—
65C3×#103—64no—
66#835—24no—
67C3⋊#95—64no—
68#816—64no—
69#815—64no—
70#810—64no—
71C23×C32C2×D411yescharacteristic
72C32×Q8—24no—
73C32×Q8—42no—
74C2×C32×C4—22no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D412yes—
80C2×C32×C4#4112yes—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C22⋊C414yes—
86#634—24no—
87#634—42no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—44no—
90C3×C3⋊C8—24no—
91C2×C4⋊Q8—91no—
92C2×#103—32no—
93C2×#103—92no—
94C2×#97—91no—
95#382—91no—
96C2×C3×Q8—22no—
97C2×C3×Q8—22no—
98C2×C3×Q8—22no—
99C2×C3×Q8—22no—
100C2×C3×Q8—22no—
101C2×C3×Q8—22no—
102C2×C3×Q8—22no—
103C2×C3×Q8—42no—
104C2×C3×Q8—42no—
105C2×C3×Q8C4×D314yes—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C22×Dic3—22no—
112C22×Dic3—34no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×Dic6—34no—
117C2×Dic6—62no—
118C2×Dic6—62no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×Dic6—62no—
124C2×Dic6—122no—
125C2×Dic6—122no—
126C2×C3×C8—34no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4—62no—
131C4⋊Dic3—22no—
132C4⋊Dic3—22no—
133Dic3⋊C4—616no—
134Dic3⋊C4—616no—
135C4×Dic3—34no—
136C4×Dic3—34no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—22no—
141C2×C3⋊C8#6714yes—
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32#12411yescharacteristic
144C22×C32#12711yescharacteristic
145C22×C32#13714yes—
146C32×C4—42no—
147C32×C4C4×D412yes—
148C32×C4#12112yes—
149C3⋊Dic3—24no—
150C3⋊Dic3—42no—
151C3×Dic3—82no—
152C22×Q8—91no—
153C22×Q8D3211yescharacteristic
154C22×C8—32no—
155C4⋊Q8—94no—
156C4⋊Q8—182no—
157C2×C4⋊C4—32no—
158C2×C4⋊C4—182no—
159C2×C42—91no—
160#103—64no—
161#103—184no—
162#97—182no—
163#95—182no—
164C23×C3—21no—
165C23×C3D3×D412yes—
166C3×Q8—24no—
167C3×Q8—24no—
168C3×Q8—44no—
169C3×Q8—44no—
170C3×Q8—42no—
171C3×Q8—42no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—22no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—124no—
183C2×C3×C4—122no—
184C2×C3×C4C2×C4×D312yes—
185C2×C3×C4#23512yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4#23712yes—
189C2×C3×C4C2×#6712yes—
190C2×Dic3—38no—
191C2×Dic3—44no—
192C2×Dic3—42no—
193C2×Dic3—64no—
194C2×Dic3—68no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—122no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203Dic6—64no—
204Dic6—64no—
205Dic6—124no—
206Dic6—124no—
207Dic6—122no—
208Dic6—122no—
209C3×C8—64no—
210C3⋊C8—24no—
211C2×C32#39011yescharacteristic
212C2×C32#41912yes—
213C2×C32#49112yes—
214C2×C32#49712yes—
215C2×Q8—21no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—182no—
221C2×Q8—182no—
222C2×Q8#62412yes—
223C22×C4—21no—
224C22×C4—62no—
225C22×C4—92no—
226C22×C4—181no—
227C22×C4C2×D3211yescharacteristic
228C2×C8—34no—
229C2×C8—62no—
230C2×C8—62no—
231C4⋊C4—62no—
232C4⋊C4—62no—
233C4⋊C4—188no—
234C42—92no—
235C42—92no—
236C22×C3—24no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3D3×C22⋊C412yes—
241C22×C3#88512yes—
242C22×C3#91514yes—
243C22×C3#91814yes—
244C22×C3#94012yes—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—44no—
248C3×C4—44no—
249C3×C4—242no—
250C3×C4#67⋊C412yes—
251C3×C4#88412yes—
252C3×C4C4×#6712yes—
253C3×C4#93912yes—
254Dic3—68no—
255Dic3—68no—
256Dic3—82no—
257Dic3—124no—
258Dic3—124no—
259C32#196011yescharacteristic, complemented, Sylow
260C23#381111yescharacteristic
261Q8—24no—
262Q8—42no—
263Q8—184no—
264Q8—362no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—94no—
269C2×C4—124no—
270C2×C4—122no—
271C2×C4—184no—
272C2×C4—182no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4#380412yes—
276C2×C4C2×#62411yescharacteristic
277C2×C4D3×#6712yes—
278C2×C4#381111yescharacteristic
279C8—64no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3#479714yes—
285C2×C3#480214yes—
286C2×C3#495712yes—
287C2×C3#516712yes—
288C2×C3#519012yes—
289C22#6395114yes—
290C22#6395311yescharacteristic
291C22#6397411yescharacteristic
292C22#6397911yescharacteristic
293C4—42no—
294C4—184no—
295C4—242no—
296C4—362no—
297C4#6395212yes—
298C4#6397112yes—
299C3—21no—
300C3#7022812yescomplemented
301C2#1059156212yes—
302C2#1059161112yes—
303C2#1059161612yes—
304C2#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#1960
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
259. C32#1960semidirect
300. C3#70228semidirect

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
#105912302
C2×#635672
C2×#635552
#702283