Finite Group Databasebeta

← #11797759

Subgroups — #11797759

Order 1152.

375 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 96 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
1Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic
3#10590777C211yesmaximal, characteristic
4C3×#4564C211yesmaximal, characteristic, complemented
5#10589139C211yesmaximal, characteristic, complemented
6#10589115C211yesmaximal, characteristic
7#10589104C211yesmaximal, characteristic, complemented
8#71474—31nomaximal
9#69208—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12C2×C3×D24C2211yescharacteristic
13#63898—21no—
14#63662—21no—
15#63645C2211yescharacteristic
16C8×C3⋊Dic3C2211yescharacteristic
17C3×#828C414yescomplemented
18C3×#818C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#63562—21no—
22C2×C3×SD32—31no—
23Dic3×Q16—31no—
24Dic3×Q16—31no—
25Dic3×Q16—61no—
26C2×#828D311yescharacteristic
27Dic3×D8—31no—
28#4872—31no—
29C3×#358—31no—
30#4564D311yescharacteristic, complemented
31#4562—31no—
32#4509—31no—
33#4504—31no—
34#4502—31no—
35#4502—31no—
36#4489—31no—
37C2×C32×Q8—21no—
38C2×C3×D12—21no—
39C2×D3×Dic3—41no—
40C32×Q16—21no—
41C32×Q16C2×C412yescomplemented
42C2×C32×C8C2311yescharacteristic
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—41no—
45C4×C3⋊Dic3—41no—
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×C4⋊Dic3—21no—
49C3×D24—21no—
50C3×D24C2×C412yes—
51(C2×D3)⋊Dic3—41no—
52C3×C3⋊C16—21no—
53C3×C3⋊C16C2×C412yescomplemented
54#2175—91noSylow
55C2×C3×Q16—21no—
56C2×C3×Q16C2×D311yescharacteristic
57C2×C3×Q16C2×D311yescharacteristic
58C2×C3×D8—31no—
59Q8×Dic3—61no—
60Q8×Dic3—61no—
61Q8×Dic3—62no—
62D4×Dic3—61no—
63C2×D24C2×D311yescharacteristic
64#893—61no—
65C3×SD32—34no—
66C2×C3×C16—31no—
67C2×C3×C16—31no—
68C3×#107—31no—
69#835—61no—
70#835—61no—
71#835—62no—
72#832—61no—
73#828Dic314yescomplemented
74#818—31no—
75#818—31no—
76#818—61no—
77#818C2×D311yescharacteristic
78C8×Dic3—31no—
79C8×Dic3—31no—
80C8×Dic3—61no—
81C2×C3⋊C16C2×D311yescharacteristic
82C2×C3⋊C16C2×D311yescharacteristic
83#809—61no—
84C22×C3×D3—41no—
85C32×Q8—22no—
86C32×Q8—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3D811yescharacteristic
91C2×C3⋊Dic3D811yescharacteristic
92C2×C3×Dic3—41no—
93C3×D12—22no—
94C3×D12—41no—
95D3×Dic3—82no—
96C32×C8C22×C411yescharacteristic
97C32×C8#4111yescharacteristic
98C3⋊(C3⋊C8)—21no—
99C2×SD32—31no—
100C4×Q16—91no—
101C4×D8—91no—
102#366—91no—
103#358—31no—
104#357—91no—
105#346—91no—
106C2×C3×Q8—22no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109C2×C3×D4—61no—
110C22×Dic3—121no—
111C2×D12—21no—
112C2×C4×D3—121no—
113C3×Q16—22no—
114C3×Q16—21no—
115C3×Q16—21no—
116C3×Q16—22no—
117C3×Q16C4×D312yescomplemented
118C3×Q16C2×Dic312yescomplemented
119C3×D8—32no—
120C3×D8—61no—
121C2×C3×C8—21no—
122C2×C3×C8C22×D311yescharacteristic
123C2×C3×C8C22×D311yescharacteristic
124C3×C4⋊C4—61no—
125#217—121no—
126(C2×D3)⋊C4—121no—
127C4⋊Dic3—21no—
128C4⋊Dic3—62no—
129C4⋊Dic3—61no—
130C4⋊Dic3—61no—
131C4⋊Dic3—121no—
132C4⋊Dic3—121no—
133C4⋊Dic3—122no—
134C4×Dic3—31no—
135C4×Dic3—31no—
136C4×Dic3—61no—
137C4×Dic3—121no—
138C4×Dic3—121no—
139C4×Dic3—122no—
140C2×C3⋊C8—31no—
141C2×C3⋊C8—31no—
142C2×C3⋊C8—61no—
143D24—21no—
144D24C2×Dic312yes—
145C3×C16—32no—
146C3×C16—61no—
147C3⋊C16—21no—
148C3⋊C16C2×Dic312yescomplemented
149C22×C32C2×D811yescharacteristic
150C2×C3×D3—42no—
151C2×C3×D3—81no—
152C2×C3×D3—81no—
153C32×C4—42no—
154C32×C4C4×D411yescharacteristic
155C32×C4#13511yescharacteristic
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3—81no—
159C3×Dic3—81no—
160C2×Q16D3211yescharacteristic
161C2×D8—31no—
162C4×Q8—181no—
163C4×D4—181no—
164SD32—34no—
165C2×C16—31no—
166C2×C16—31no—
167#107—31no—
168#107—91no—
169#103—181no—
170#102—181no—
171C4×C8—91no—
172C23×C3—121no—
173C22×D3—41no—
174C3×Q8—24no—
175C3×Q8—22no—
176C3×Q8—22no—
177C3×Q8—42no—
178C3×Q8—41no—
179C3×Q8—41no—
180C3×D4—62no—
181C3×D4—121no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—121no—
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—31no—
192C2×Dic3—31no—
193C2×Dic3—41no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—122no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—242no—
200D12—22no—
201D12—41no—
202C4×D3—242no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8C2×C4×D311yescharacteristic
206C3×C8#23711yescharacteristic
207C3×C8#23711yescharacteristic
208C3×C8C22×Dic311yescharacteristic
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—121no—
212C2×C32C4×D811yescharacteristic
213C2×C32#50911yescharacteristic
214C2×C32#51011yescharacteristic
215C3×D3—82no—
216C2×Q8—21no—
217C2×D4—61no—
218C22×C4—361no—
219Q16—21no—
220Q16D3×Dic312yescomplemented
221D8—32no—
222D8—61no—
223C2×C8—91no—
224C2×C8C2×D3211yescharacteristic
225C4⋊C4—61no—
226C4⋊C4—181no—
227C4⋊C4—361no—
228C22⋊C4—361no—
229C42—91no—
230C42—361no—
231C16—32no—
232C16—61no—
233C22×C3—21no—
234C22×C3—122no—
235C22×C3—241no—
236C22×C3—241no—
237C22×C3D3×D811yescharacteristic
238C22×C3D3×D811yescharacteristic
239C2×D3—42no—
240C2×D3—81no—
241C2×D3—81no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—44no—
245C3×C4—42no—
246C3×C4—42no—
247C3×C4—241no—
248C3×C4#67⋊C411yescharacteristic
249C3×C4#91211yescharacteristic
250C3×C4#91611yescharacteristic
251C3×C4D4×Dic311yescharacteristic
252Dic3—62no—
253Dic3—61no—
254Dic3—61no—
255Dic3—61no—
256Dic3—61no—
257Dic3—81no—
258Dic3—121no—
259Dic3—242no—
260Dic3—241no—
261Dic3—241no—
262C32#217511yescharacteristic, complemented, Sylow
263C23—121no—
264Q8—22no—
265Q8—41no—
266D4—62no—
267D4—121no—
268C2×C4—41no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—121no—
272C2×C4—361no—
273C2×C4—722no—
274C2×C4#381111yescharacteristic
275C8—181no—
276C8C2×D3×Dic311yescharacteristic
277C8#380511yescharacteristic
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—242no—
282C2×C3#475611yescharacteristic
283C2×C3#491411yescharacteristic
284C2×C3#491411yescharacteristic
285C2×C3#491511yescharacteristic
286C2×C3#491811yescharacteristic
287C2×C3Dic3×D811yescharacteristic
288D3—82no—
289C22—122no—
290C22—241no—
291C22—241no—
292C22#6392611yescharacteristic
293C4—42no—
294C4—181no—
295C4—181no—
296C4—241no—
297C4—721no—
298C4#6393611yescharacteristic
299C4#67⋊Dic311yescharacteristic
300C3—21no—
301C3#6920811yescharacteristic, complemented
302C3#7147411yescharacteristic, complemented
303C2—242no—
304C2#1059104011yescharacteristic
305C2#1059105011yescharacteristic
306C2#1059143511yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×C3×D24C22
cosocleC2×C32×C8C23
hypercenterC2×Q16D32
hypocenterC32#2175
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. Q16×C3⋊Dic3C2semidirect
4. C3×#4564C2semidirect
5. #10589139C2semidirect
7. #10589104C2semidirect
17. C3×#828C4semidirect
30. #4564D3semidirect
41. C32×Q16C2×C4semidirect
53. C3×C3⋊C16C2×C4semidirect
73. #828Dic3semidirect
117. C3×Q16C4×D3semidirect
118. C3×Q16C2×Dic3semidirect
148. C3⋊C16C2×Dic3semidirect
220. Q16D3×Dic3semidirect
262. C32#2175semidirect
301. C3#69208semidirect
302. C3#71474semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
C2×C3×#8282
#105907772
C3×#45642
#105891392
#105891152
#105891042
#714743
#692083