Finite Group Databasebeta

← #11790618

Subgroups — #11790618

Order 1152.

757 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 757 conjugacy classes of subgroups — too many to draw. Only its 178 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×#63873C211yesmaximal, characteristic
2#10592674C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×#63566C212yesmaximal
5C2×#63553C211yesmaximal, characteristic
6#70225—32nomaximal
7C22×C3×Dic6C2212yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750—22no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—22no—
14#63873—22no—
15#63873C414yescomplemented
16C3×#810—24no—
17#63566—24no—
18#63553—22no—
19C2×#944—32no—
20C2×C3×#103—32no—
21C2×#835—32no—
22C2×#816—32no—
23C2×C8×Dic3—32no—
24#4975—32no—
25#4975—61no—
26C2×#810D312yes—
27C22×C32×C4—21no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3D412yes—
31C22×C3×Dic3—22no—
32C2×C3×Dic6—22no—
33C2×C3×Dic6—22no—
34C2×C3×Dic6—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6C2×C414yes—
38C32×C4⋊C4—22no—
39C4⋊(C3⋊Dic3)—22no—
40#3750—44no—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3D412yes—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—22no—
45C2×C3×C3⋊C8D414yes—
46#3724—28no—
47#1956—91noSylow
48C22×C3×Q8—32no—
49C22×Dic6C2×D312yes—
50C22×C3×C8—32no—
51C2×C3×C4⋊C4—21no—
52C2×C3×C4⋊C4C2×D312yes—
53#944—38no—
54#944—64no—
55C2×C4⋊Dic3—32no—
56C2×C4⋊Dic3—61no—
57C2×Dic3⋊C4—64no—
58C2×Dic3⋊C4—64no—
59C2×Dic3⋊C4—64no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C22×C3⋊C8C2×D312yes—
63C3×#103—64no—
64#835—64no—
65#816—64no—
66C8×Dic3—64no—
67#810—24no—
68C23×C32C2×D411yescharacteristic
69C2×C32×C4—41no—
70C2×C32×C4—42no—
71C2×C32×C4C22×C411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4#4112yes—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3C22⋊C414yes—
78C2×C3⋊Dic3SD1614yes—
79C2×C3⋊Dic3Q1614yes—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C3×Dic6—24no—
84C3×Dic6—24no—
85C3×Dic6—42no—
86C3×Dic6—42no—
87C3×C3⋊C8—24no—
88C2×C4⋊Q8—91no—
89C2×#103—32no—
90C2×#103—92no—
91C2×C4×C8—91no—
92#384—91no—
93C2×C3×Q8—34no—
94C2×C3×Q8—62no—
95C2×C3×Q8—62no—
96C2×C3×Q8—62no—
97C2×C3×Q8—62no—
98C2×C3×Q8—62no—
99C22×C3×C4—22no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4—62no—
103C22×C3×C4C22×D312yes—
104C22×Dic3—22no—
105C22×Dic3—34no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C2×Dic6—22no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—22no—
113C2×Dic6—22no—
114C2×Dic6C4×D314yes—
115C2×C3×C8—34no—
116C2×C3×C8—62no—
117C2×C3×C8—62no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—42no—
121C4⋊Dic3—62no—
122C4⋊Dic3—62no—
123C4⋊Dic3—122no—
124Dic3⋊C4—616no—
125Dic3⋊C4—128no—
126Dic3⋊C4—128no—
127C4×Dic3—34no—
128C4×Dic3—34no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C2×C3⋊C8—22no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8#6714yes—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32#12411yescharacteristic
136C22×C32#12711yescharacteristic
137C22×C32C2×SD1612yes—
138C22×C32C2×Q1612yes—
139C32×C4—81no—
140C32×C4C4×D412yes—
141C32×C4#12112yes—
142C3⋊Dic3—81no—
143C3⋊Dic3#10318yescomplemented
144C3×Dic3—44no—
145C22×Q8—32no—
146C22×C8—32no—
147C4⋊Q8—94no—
148C4⋊Q8—182no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—182no—
151C2×C4⋊C4—182no—
152C2×C4⋊C4D3211yescharacteristic
153C2×C42—91no—
154#103—64no—
155#103—184no—
156C4×C8—182no—
157C23×C3—21no—
158C23×C3D3×D412yes—
159C3×Q8—64no—
160C3×Q8—64no—
161C3×Q8—122no—
162C3×Q8—122no—
163C2×C3×C4—22no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—22no—
167C2×C3×C4—44no—
168C2×C3×C4—42no—
169C2×C3×C4—44no—
170C2×C3×C4—42no—
171C2×C3×C4—64no—
172C2×C3×C4—122no—
173C2×C3×C4—122no—
174C2×C3×C4C2×C4×D312yes—
175C2×C3×C4#23512yes—
176C2×C3×C4D3×D412yes—
177C2×C3×C4D3×D412yes—
178C2×C3×C4#23712yes—
179C2×C3×C4C2×#6712yes—
180C2×Dic3—24no—
181C2×Dic3—38no—
182C2×Dic3—38no—
183C2×Dic3—38no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—124no—
190C2×Dic3—122no—
191C2×Dic3—124no—
192C2×Dic3—122no—
193Dic6—24no—
194Dic6—24no—
195Dic6—42no—
196Dic6—42no—
197C3×C8—64no—
198C3⋊C8—24no—
199C2×C32#39011yescharacteristic
200C2×C32C2×#10312yes—
201C2×C32#48712yes—
202C2×C32#49211yescharacteristic
203C2×C32#49411yescharacteristic
204C2×Q8—34no—
205C2×Q8—62no—
206C2×Q8—62no—
207C2×Q8—62no—
208C2×Q8—62no—
209C2×Q8—62no—
210C22×C4—21no—
211C22×C4—62no—
212C22×C4—92no—
213C22×C4—181no—
214C22×C4C2×D3211yescharacteristic
215C2×C8—34no—
216C2×C8—62no—
217C2×C8—62no—
218C4⋊C4—22no—
219C4⋊C4—188no—
220C4⋊C4—182no—
221C4⋊C4—364no—
222C42—92no—
223C42—92no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3D3×C22⋊C412yes—
230C22×C3#88512yes—
231C22×C3D3×SD1614yes—
232C22×C3D3×Q1614yes—
233C22×C3#94012yes—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—82no—
237C3×C4—82no—
238C3×C4—124no—
239C3×C4#67⋊C412yes—
240C3×C4#88412yes—
241C3×C4C4×#6712yes—
242C3×C4#93912yes—
243Dic3—316no—
244Dic3—44no—
245Dic3—68no—
246Dic3—242no—
247Dic3—242no—
248C32#195611yescharacteristic, complemented, Sylow
249C23#381111yescharacteristic
250Q8—64no—
251Q8—64no—
252Q8—122no—
253Q8—122no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—64no—
257C2×C4—94no—
258C2×C4—94no—
259C2×C4—94no—
260C2×C4—122no—
261C2×C4—122no—
262C2×C4—362no—
263C2×C4—361no—
264C2×C4#379512yes—
265C2×C4C4×D3211yescharacteristic
266C2×C4#380211yescharacteristic
267C2×C4D3×#6712yes—
268C8—64no—
269C2×C3—21no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3#479214yes—
275C2×C3D3×#10314yes—
276C2×C3#495712yes—
277C2×C3#517512yes—
278C2×C3#518312yes—
279C22#6391311yescharacteristic
280C22#6392111yescharacteristic
281C22#6393012yes—
282C22#6394412yes—
283C22#6397911yescharacteristic
284C4—81no—
285C4—98no—
286C4—124no—
287C4—721no—
288C4#6387912yes—
289C4#6388512yes—
290C3—21no—
291C3#7022512yescomplemented
292C2#1059056712yes—
293C2#1059060112yes—
294C2#1059138611yescharacteristic
295C2#1059149211yescharacteristic
296C2#1059162811yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1956
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #63873C4semidirect
143. C3⋊Dic3#103semidirect
248. C32#1956semidirect
291. C3#70225semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
#105926742
C2×C3×#8102
C2×#635662
C2×#635532
#702253