Finite Group Databasebeta

← #11795084

Subgroups — #11795084

Order 1152.

545 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 154 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
1#10592683C211yesmaximal, characteristic
2C2×C3×#807C212yesmaximal
3#10591359C211yesmaximal, characteristic
4#10589164C212yesmaximal
5#10589156C211yesmaximal, characteristic
6#70619—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)—21no—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—21no—
14C2×#3724—21no—
15#63658—21no—
16C3×#807—24no—
17C2×C3×#107—32no—
18#4984—32no—
19#4984—61no—
20#4975—32no—
21C2×#807D312yes—
22#4551—32no—
23#4550—32no—
24#4529—32no—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3×Dic3—22no—
31C32×C4⋊C4—21no—
32C32×C4⋊C4D412yes—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—42no—
35C4×C3⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8Q814yes—
41#3724—42no—
42#3724—42no—
43#2083—91noSylow
44C22×C3×C8—32no—
45C2×C3×C4⋊C4—21no—
46C2×C3×C4⋊C4—32no—
47C2×C3×C4⋊C4C2×D312yes—
48C2×C4⋊Dic3—32no—
49C2×C4⋊Dic3—61no—
50C2×C4⋊Dic3—62no—
51C2×C4⋊Dic3—62no—
52C2×C4⋊Dic3C2×D312yes—
53C2×Dic3⋊C4—62no—
54C2×Dic3⋊C4—62no—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—61no—
57C22×C3⋊C8C2×D312yes—
58C3×#107—64no—
59C3⋊#95—62no—
60C3⋊#95—62no—
61#807—24no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4—22no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×Q812yes—
68C2×C32×C4#4112yes—
69C2×C32×C4#4111yescharacteristic
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3D812yes—
78C2×C3⋊Dic3Q1612yes—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C3×C3⋊C8—24no—
83C2×#107—32no—
84#389—91no—
85#384—91no—
86#340—92no—
87#336—91no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—21no—
91C22×C3×C4—62no—
92C22×C3×C4C22×D312yes—
93C22×Dic3—22no—
94C22×Dic3—32no—
95C22×Dic3—32no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C2×C3×C8—34no—
101C2×C3×C8—62no—
102C2×C3×C8—62no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—62no—
107C3×C4⋊C4—62no—
108C3×C4⋊C4#6714yes—
109C4⋊Dic3—22no—
110C4⋊Dic3—22no—
111C4⋊Dic3—62no—
112C4⋊Dic3—62no—
113C4⋊Dic3—122no—
114C4⋊Dic3—124no—
115C4⋊Dic3—124no—
116Dic3⋊C4—124no—
117Dic3⋊C4—124no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—122no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8Dic614yes—
124C22×C32#12111yescharacteristic
125C22×C32#12311yescharacteristic
126C22×C32C4⋊Q811yescharacteristic
127C22×C32C2×D811yescharacteristic
128C22×C32C2×Q1611yescharacteristic
129C22×C32AGL(1,ℤ/8)11yescharacteristic
130C22×C32#13711yescharacteristic
131C32×C4—42no—
132C32×C4C22⋊Q812yes—
133C32×C4#12512yes—
134C3⋊Dic3—22no—
135C3⋊Dic3—22no—
136C3⋊Dic3—81no—
137C3×Dic3—82no—
138C22×C8—32no—
139C2×C4⋊C4—32no—
140C2×C4⋊C4—91no—
141C2×C4⋊C4—181no—
142C2×C4⋊C4—181no—
143C2×C4⋊C4—181no—
144C2×C4⋊C4D3211yescharacteristic
145C2×C42—91no—
146#107—64no—
147#95—181no—
148C23×C3—21no—
149C23×C3D3×D412yes—
150C2×C3×C4—24no—
151C2×C3×C4—24no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×C3×C4—122no—
163C2×C3×C4C2×Dic612yes—
164C2×C3×C4#23512yes—
165C2×C3×C4#23712yes—
166C2×C3×C4D3×Q812yes—
167C2×C3×C4#23912yes—
168C2×C3×C4C2×#6712yes—
169C2×Dic3—34no—
170C2×Dic3—34no—
171C2×Dic3—42no—
172C2×Dic3—42no—
173C2×Dic3—42no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—121no—
181C2×Dic3—121no—
182C2×Dic3—121no—
183C2×Dic3—121no—
184C2×Dic3—122no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C3×C8—64no—
191C3⋊C8—24no—
192C2×C32#39811yescharacteristic
193C2×C32#45911yescharacteristic
194C2×C32#46211yescharacteristic
195C2×C32#48011yescharacteristic
196C2×C32#48411yescharacteristic
197C2×C32#50011yescharacteristic
198C2×C32#50111yescharacteristic
199C22×C4—21no—
200C22×C4—62no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—181no—
204C22×C4C2×D3211yescharacteristic
205C2×C8—34no—
206C2×C8—62no—
207C2×C8—62no—
208C4⋊C4—21no—
209C4⋊C4—62no—
210C4⋊C4—62no—
211C4⋊C4—182no—
212C4⋊C4—362no—
213C4⋊C4—362no—
214C4⋊C4—362no—
215C4⋊C4#62512yes—
216C42—182no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3#88812yes—
225C22×C3#89412yes—
226C22×C3D3×D812yes—
227C22×C3#91112yes—
228C22×C3D3×Q1612yes—
229C22×C3#91812yes—
230C22×C3#93912yes—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—44no—
234C3×C4—44no—
235C3×C4—242no—
236C3×C4#88912yes—
237C3×C4#89012yes—
238C3×C4#92412yes—
239C3×C4#94612yes—
240Dic3—64no—
241Dic3—64no—
242Dic3—82no—
243Dic3—122no—
244Dic3—122no—
245Dic3—242no—
246Dic3—242no—
247C32#208311yescharacteristic, complemented, Sylow
248C23#381111yescharacteristic
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—122no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4—361no—
264C2×C4D3×Dic612yes—
265C2×C4#379912yes—
266C2×C4#380511yescharacteristic
267C2×C4C2×#62511yescharacteristic
268C8—64no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3#487412yes—
277C2×C3#487612yes—
278C2×C3#488212yes—
279C2×C3#488412yes—
280C2×C3#498212yes—
281C2×C3#515012yes—
282C2×C3#518212yes—
283C22#6384011yescharacteristic
284C22#6389711yescharacteristic
285C22#6392611yescharacteristic
286C22#6392711yescharacteristic
287C22#6394411yescharacteristic
288C22#6394511yescharacteristic
289C22#6398011yescharacteristic
290C4—42no—
291C4—182no—
292C4—182no—
293C4—242no—
294C4—721no—
295C4#6384512yes—
296C4#6385612yes—
297C3—21no—
298C3#7061912yescomplemented
299C2#1059041511yescharacteristic
300C2#1059044211yescharacteristic
301C2#1059044411yescharacteristic
302C2#1059056311yescharacteristic
303C2#1059121511yescharacteristic
304C2#1059148611yescharacteristic
305C2#1059163311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2083
LCSG ▷ C22×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
247. C32#2083semidirect
298. C3#70619semidirect

Maximal subgroups

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

subgroupindex
#105926832
C2×C3×#8072
#105913592
#105891642
#105891562
#706193