Finite Group Databasebeta

← #11792636

Subgroups — #11792636

Order 1152.

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

normal subgroups only

This group has 833 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
1C22×C3×#216C212yesmaximal
2C2×#63873C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic
4C2×#63566C212yesmaximal
5#10589156C211yesmaximal, characteristic
6#72073—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×C3×Dic6C2212yes—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×#216—24no—
12C2×C3×#216—24no—
13C2×C3×#216—24no—
14C22×C3×C3⋊C8C2212yes—
15C2×#3724—22no—
16#63873—24no—
17#63658—22no—
18#63566—24no—
19C22×C3×Q16—32no—
20C2×#944—32no—
21C22×#216D312yes—
22#5229—32no—
23#5229—61no—
24C2×#835—32no—
25C2×#816—32no—
26#4550—32no—
27C2×C32×Q8—21no—
28C2×C32×Q8—22no—
29C2×C32×Q8—22no—
30C2×C32×Q8D412yes—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D412yes—
35C22×C3×Dic3—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6—22no—
39C2×C3×Dic6—22no—
40C2×C3×Dic6—22no—
41C2×C3×Dic6D414yes—
42C4⋊(C3⋊Dic3)—22no—
43C4×C3⋊Dic3—22no—
44C3×#216—216no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8D414yes—
48#3724—28no—
49#2016—91noSylow
50C22×C3×Q8—21no—
51C22×C3×Q8—32no—
52C22×C3×Q8C2×D312yes—
53C22×Dic6C2×D312yes—
54C2×C3×Q16—64no—
55C2×C3×Q16—64no—
56C2×C3×Q16—64no—
57C22×C3×C8—32no—
58#944—64no—
59#944—64no—
60C2×#216—24no—
61C2×#216—24no—
62C2×#216—24no—
63C2×C4⋊Dic3—32no—
64C2×C4⋊Dic3—61no—
65C2×Dic3⋊C4—64no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—61no—
68C22×C3⋊C8C2×D312yes—
69#835—64no—
70C3⋊#95—64no—
71C3⋊#95—64no—
72#816—64no—
73C23×C32C2×D411yescharacteristic
74C32×Q8—24no—
75C32×Q8—42no—
76C2×C32×C4—22no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C2×D412yes—
80C2×C32×C4C2×D412yes—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3Q1614yescomplemented
88C2×C3×Dic3—24no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3×Dic6—24no—
92C3×Dic6—24no—
93C3×Dic6—42no—
94C3×Dic6—42no—
95C3×C3⋊C8—24no—
96C22×Q16—32no—
97C2×C4⋊Q8—91no—
98C2×#103—92no—
99#391—91no—
100#336—91no—
101C2×C3×Q8—22no—
102C2×C3×Q8—22no—
103C2×C3×Q8—22no—
104C2×C3×Q8—22no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—34no—
109C2×C3×Q8—42no—
110C2×C3×Q8—42no—
111C2×C3×Q8—62no—
112C2×C3×Q8—62no—
113C2×C3×Q8—62no—
114C2×C3×Q8—62no—
115C2×C3×Q8—62no—
116C2×C3×Q8#6714yes—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—22no—
123C22×Dic3—34no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C2×Dic6—22no—
128C2×Dic6—22no—
129C2×Dic6—22no—
130C2×Dic6—22no—
131C2×Dic6—22no—
132C2×Dic6#6714yes—
133C3×Q16—616no—
134C2×C3×C8—34no—
135C2×C3×C8—62no—
136C2×C3×C8—62no—
137#216—216no—
138C4⋊Dic3—62no—
139C4⋊Dic3—62no—
140C4⋊Dic3—122no—
141Dic3⋊C4—616no—
142C4×Dic3—62no—
143C4×Dic3—62no—
144C4×Dic3—122no—
145C2×C3⋊C8—22no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8#6714yes—
148C22×C32#12011yescharacteristic
149C22×C32#12111yescharacteristic
150C22×C32#12711yescharacteristic
151C22×C32C2×Q1612yes—
152C22×C32#13712yes—
153C32×C4—42no—
154C32×C4#12012yes—
155C32×C4#12112yes—
156C3⋊Dic3—24no—
157C3⋊Dic3—81no—
158C3×Dic3—44no—
159C22×Q8—32no—
160C22×Q8D3211yescharacteristic
161C2×Q16—64no—
162C2×Q16—64no—
163C2×Q16—64no—
164C22×C8—32no—
165C4⋊Q8—184no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—182no—
168C2×C42—91no—
169#103—184no—
170#95—182no—
171C23×C3—21no—
172C23×C3D3×D412yes—
173C3×Q8—24no—
174C3×Q8—24no—
175C3×Q8—44no—
176C3×Q8—44no—
177C3×Q8—42no—
178C3×Q8—42no—
179C3×Q8—64no—
180C3×Q8—64no—
181C3×Q8—122no—
182C3×Q8—122no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—64no—
194C2×C3×C4—122no—
195C2×C3×C4—122no—
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4#23712yes—
199C2×C3×C4C2×#6712yes—
200C2×C3×C4C2×#6712yes—
201C2×C3×C4C2×#6712yes—
202C2×Dic3—24no—
203C2×Dic3—38no—
204C2×Dic3—42no—
205C2×Dic3—42no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—122no—
210C2×Dic3—122no—
211C2×Dic3—122no—
212C2×Dic3—124no—
213C2×Dic3—124no—
214C2×Dic3—122no—
215Dic6—24no—
216Dic6—24no—
217Dic6—42no—
218Dic6—42no—
219C3×C8—64no—
220C3⋊C8—24no—
221C2×C32#39211yescharacteristic
222C2×C32#45112yes—
223C2×C32#46212yes—
224C2×C32#49411yescharacteristic
225C2×C32#49711yescharacteristic
226C2×Q8—21no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—34no—
230C2×Q8—62no—
231C2×Q8—62no—
232C2×Q8—62no—
233C2×Q8—62no—
234C2×Q8—62no—
235C2×Q8#62512yes—
236C22×C4—21no—
237C22×C4—62no—
238C22×C4—92no—
239C22×C4—181no—
240C22×C4C2×D3211yescharacteristic
241Q16—616no—
242C2×C8—34no—
243C2×C8—62no—
244C2×C8—62no—
245C4⋊C4—188no—
246C4⋊C4—182no—
247C42—182no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3D3×Q1614yes—
254C22×C3#91814yes—
255C22×C3#93712yes—
256C22×C3#93912yes—
257C22×C3#94012yes—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—44no—
261C3×C4—44no—
262C3×C4—124no—
263C3×C4#93712yes—
264C3×C4#93812yes—
265C3×C4#93912yes—
266C3×C4#95312yes—
267Dic3—44no—
268Dic3—68no—
269Dic3—124no—
270Dic3—242no—
271Dic3—242no—
272C32#201611yescharacteristic, complemented, Sylow
273C23#381111yescharacteristic
274Q8—24no—
275Q8—42no—
276Q8—64no—
277Q8—64no—
278Q8—122no—
279Q8—122no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—64no—
284C2×C4—94no—
285C2×C4—122no—
286C2×C4—122no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—362no—
290C2×C4—361no—
291C2×C4#380511yescharacteristic
292C2×C4C2×#62511yescharacteristic
293C2×C4D3×#6712yes—
294C2×C4D3×#6712yes—
295C8—64no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3#518214yes—
302C2×C3#518312yes—
303C2×C3#518614yes—
304C2×C3#519012yes—
305C2×C3#522312yes—
306C22#6394412yes—
307C22#6394512yes—
308C22#6397911yescharacteristic
309C22#6398011yescharacteristic
310C22#6398311yescharacteristic
311C4—42no—
312C4—124no—
313C4—184no—
314C4—721no—
315C4#6397012yes—
316C4#6397612yes—
317C3—21no—
318C3#7207312yescomplemented
319C2#1059162811yescharacteristic
320C2#1059162911yescharacteristic
321C2#1059163312yes—
322C2#1059165412yes—
323C2#1059172311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#2016
LCSG ▷ C22×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
87. C2×C3⋊Dic3Q16semidirect
272. C32#2016semidirect
318. C3#72073semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2162
C2×#638732
#105929282
C2×#635662
#105891562
#720733