Finite Group Databasebeta

← #11790734

Subgroups — #11790734

Order 1152.

693 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 693 conjugacy classes of subgroups — too many to draw. Only its 162 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#10592676C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal
4C2×#63566C212yesmaximal
5C2×#63555C211yesmaximal, characteristic
6#70228—32nomaximal
7C22×C3×Dic6C2212yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3×C3⋊C8C2212yes—
12C2×#3724—22no—
13#63873—22no—
14#63873C414yescomplemented
15#63658—22no—
16C3×#810—24no—
17#63566—24no—
18#63555—22no—
19C2×#944—32no—
20C2×C3×#103—32no—
21C2×#835—32no—
22C2×#816—32no—
23C2×#815—32no—
24#4977—32no—
25#4977—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—
40C4×C3⋊Dic3C2×C412yes—
41C4×C3⋊Dic3D412yes—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8D414yes—
45#3724—28no—
46#1960—91noSylow
47C22×C3×Q8—32no—
48C22×Dic6C2×D312yes—
49C22×C3×C8—32no—
50C2×C3×C4⋊C4—21no—
51C2×C3×C4⋊C4C2×D312yes—
52#944—38no—
53#944—64no—
54C2×C4⋊Dic3—32no—
55C2×C4⋊Dic3—61no—
56C2×Dic3⋊C4—64no—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59C22×C3⋊C8C2×D312yes—
60C3×#103—64no—
61#835—64no—
62C3⋊#95—64no—
63C3⋊#95—64no—
64#816—64no—
65#815—64no—
66#810—24no—
67C23×C32C2×D411yescharacteristic
68C2×C32×C4—41no—
69C2×C32×C4—42no—
70C2×C32×C4C22×C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D412yes—
73C2×C32×C4#4112yes—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—42no—
78C2×C3⋊Dic3C22⋊C414yes—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C3×Dic6—24no—
83C3×Dic6—24no—
84C3×Dic6—42no—
85C3×Dic6—42no—
86C3×C3⋊C8—24no—
87C2×C4⋊Q8—91no—
88C2×#103—32no—
89C2×#103—92no—
90C2×#97—91no—
91#382—91no—
92C2×C3×Q8—34no—
93C2×C3×Q8—62no—
94C2×C3×Q8—62no—
95C2×C3×Q8—62no—
96C2×C3×Q8—62no—
97C2×C3×Q8—62no—
98C22×C3×C4—22no—
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—62no—
102C22×C3×C4C22×D312yes—
103C22×Dic3—22no—
104C22×Dic3—34no—
105C22×Dic3—62no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C2×Dic6—22no—
109C2×Dic6—22no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—22no—
113C2×Dic6C4×D314yes—
114C2×C3×C8—34no—
115C2×C3×C8—62no—
116C2×C3×C8—62no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—42no—
120C4⋊Dic3—62no—
121C4⋊Dic3—62no—
122C4⋊Dic3—122no—
123Dic3⋊C4—616no—
124C4×Dic3—34no—
125C4×Dic3—34no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C2×C3⋊C8—22no—
129C2×C3⋊C8—22no—
130C2×C3⋊C8#6714yes—
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32#12411yescharacteristic
133C22×C32#12711yescharacteristic
134C22×C32#13712yes—
135C22×C32#13712yes—
136C32×C4—81no—
137C32×C4C4×D412yes—
138C32×C4#12112yes—
139C3⋊Dic3—24no—
140C3⋊Dic3—81no—
141C3×Dic3—44no—
142C22×Q8—32no—
143C22×C8—32no—
144C4⋊Q8—94no—
145C4⋊Q8—182no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—182no—
148C2×C4⋊C4D3211yescharacteristic
149C2×C42—91no—
150#103—64no—
151#103—184no—
152#97—182no—
153#95—182no—
154C23×C3—21no—
155C23×C3D3×D412yes—
156C3×Q8—64no—
157C3×Q8—64no—
158C3×Q8—122no—
159C3×Q8—122no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—22no—
164C2×C3×C4—42no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4—42no—
168C2×C3×C4—64no—
169C2×C3×C4—122no—
170C2×C3×C4—122no—
171C2×C3×C4C2×C4×D312yes—
172C2×C3×C4#23512yes—
173C2×C3×C4D3×D412yes—
174C2×C3×C4D3×D412yes—
175C2×C3×C4#23712yes—
176C2×C3×C4C2×#6712yes—
177C2×Dic3—24no—
178C2×Dic3—38no—
179C2×Dic3—42no—
180C2×Dic3—42no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—122no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189C2×Dic3—122no—
190Dic6—24no—
191Dic6—24no—
192Dic6—42no—
193Dic6—42no—
194C3×C8—64no—
195C3⋊C8—24no—
196C2×C32#39011yescharacteristic
197C2×C32#41912yes—
198C2×C32#49112yes—
199C2×C32#49711yescharacteristic
200C2×C32#49711yescharacteristic
201C2×Q8—34no—
202C2×Q8—62no—
203C2×Q8—62no—
204C2×Q8—62no—
205C2×Q8—62no—
206C2×Q8—62no—
207C22×C4—21no—
208C22×C4—62no—
209C22×C4—92no—
210C22×C4—181no—
211C22×C4C2×D3211yescharacteristic
212C2×C8—34no—
213C2×C8—62no—
214C2×C8—62no—
215C4⋊C4—22no—
216C4⋊C4—188no—
217C4⋊C4—182no—
218C42—92no—
219C42—92no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—21no—
225C22×C3D3×C22⋊C412yes—
226C22×C3#88512yes—
227C22×C3#91514yes—
228C22×C3#91814yes—
229C22×C3#94012yes—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—82no—
233C3×C4—82no—
234C3×C4—124no—
235C3×C4#67⋊C412yes—
236C3×C4#88412yes—
237C3×C4C4×#6712yes—
238C3×C4#93912yes—
239Dic3—44no—
240Dic3—68no—
241Dic3—124no—
242Dic3—242no—
243Dic3—242no—
244C32#196011yescharacteristic, complemented, Sylow
245C23#381111yescharacteristic
246Q8—64no—
247Q8—64no—
248Q8—122no—
249Q8—122no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—64no—
253C2×C4—94no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—362no—
259C2×C4—361no—
260C2×C4#379512yes—
261C2×C4C4×D3211yescharacteristic
262C2×C4#380211yescharacteristic
263C2×C4D3×#6712yes—
264C8—64no—
265C2×C3—21no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3#479714yes—
271C2×C3#480214yes—
272C2×C3#495712yes—
273C2×C3#516712yes—
274C2×C3#519012yes—
275C22#6391311yescharacteristic
276C22#6392111yescharacteristic
277C22#6393112yes—
278C22#6394512yes—
279C22#6397911yescharacteristic
280C4—81no—
281C4—124no—
282C4—184no—
283C4—721no—
284C4#6387912yes—
285C4#6388512yes—
286C3—21no—
287C3#7022812yescomplemented
288C2#1059056812yes—
289C2#1059060212yes—
290C2#1059138611yescharacteristic
291C2#1059149311yescharacteristic
292C2#1059162911yescharacteristic
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#1960
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
14. #63873C4semidirect
244. C32#1960semidirect
287. C3#70228semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
#105926762
C2×C3×#8102
C2×#635662
C2×#635552
#702283