Finite Group Databasebeta

← #11857085

Subgroups — #11857085

Order 1152.

1441 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 1441 conjugacy classes of subgroups — too many to draw. Only its 340 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×#64153C211yesmaximal, characteristic
2C2×C3×#944C212yesmaximal
3C2×#63873C211yesmaximal, characteristic
4C2×#63866C212yesmaximal
5#10591244C218yesmaximal
6C4×Dic32C211yesmaximal, characteristic
7#83253—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11#64153—24no—
12C2×#3750C2214yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#944—28no—
15C2×C3×Dic3⋊C4C2218yes—
16C2×C3×C4×Dic3C2212yes—
17C2×#3724C2214yes—
18C2×Dic3⋊Dic3C2218yes—
19C2×Dic32C2214yes—
20#63873—24no—
21#63866—28no—
22C2×C3×C4⋊Q8—32no—
23C2×#944—32no—
24C2×#944—32no—
25C2×#944—32no—
26C2×#944—61no—
27C2×#944D312yes—
28C2×#869—32no—
29#4975—316no—
30C42×Dic3—32no—
31C2×C32×Q8—22no—
32C2×C32×Q8—24no—
33C22×C32×C4C2312yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2312yes—
37C2×#634—22no—
38C2×#634—24no—
39C22×C3×Dic3C2314yes—
40C22×C3×Dic3C2314yes—
41C2×C3×Dic6—24no—
42C2×C3×Dic6—24no—
43C2×C3×Dic6—24no—
44#3750—28no—
45C4×C3⋊Dic3D414yes—
46C3×Dic3⋊C4—216no—
47C3×C4×Dic3D418yes—
48#3724—28no—
49Dic3⋊Dic3—216no—
50Dic32Q8116yescomplemented
51#2868—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8—32no—
54C22×C3×Q8C2×D312yes—
55C22×Dic6—32no—
56C22×Dic6—61no—
57C22×Dic6C2×D312yes—
58C3×C4⋊Q8—68no—
59C2×C3×C4⋊C4—38no—
60C2×C3×C42—32no—
61#944—28no—
62#944—68no—
63#944—68no—
64#944—68no—
65#944—68no—
66C2×C4⋊Dic3—38no—
67C2×Dic3⋊C4—38no—
68C2×Dic3⋊C4—38no—
69C2×Dic3⋊C4—38no—
70C2×Dic3⋊C4—64no—
71C2×Dic3⋊C4C2×D318yes—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—38no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3C2×D312yes—
76#869—68no—
77C23×C32C2411yescharacteristic
78C32×Q8—44no—
79C2×C32×C4—22no—
80C2×C32×C4—24no—
81C2×C32×C4C2×D412yes—
82C2×C32×C4C2×D414yes—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—24no—
85C2×C3⋊Dic3C2×D414yes—
86C2×C3⋊Dic3C2×Q818yes—
87#634—44no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3C2×D418yes—
92C2×C3×Dic3C2×Q8116yes—
93C3×Dic6—48no—
94C2×C4⋊Q8—32no—
95C2×C4⋊Q8—92no—
96C2×C4⋊Q8—91no—
97C2×C4⋊Q8—91no—
98#384—98no—
99C43—91no—
100C2×C3×Q8—24no—
101C2×C3×Q8—24no—
102C2×C3×Q8—24no—
103C2×C3×Q8—24no—
104C2×C3×Q8—44no—
105C2×C3×Q8—64no—
106C2×C3×Q8—64no—
107C2×C3×Q8—64no—
108C22×C3×C4—21no—
109C22×C3×C4—22no—
110C22×C3×C4—34no—
111C22×C3×C4—34no—
112C22×C3×C4C22×D314yes—
113C22×C3×C4C22×D312yes—
114C22×Dic3—34no—
115C22×Dic3—34no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C22×Dic3C22×D314yes—
119C22×Dic3C22×D314yes—
120C2×Dic6—24no—
121C2×Dic6—24no—
122C2×Dic6—24no—
123C2×Dic6—64no—
124C2×Dic6—64no—
125C2×Dic6—64no—
126C2×Dic6—64no—
127C2×Dic6—124no—
128C3×C4⋊C4—616no—
129C3×C42—38no—
130C4⋊Dic3—616no—
131Dic3⋊C4—216no—
132Dic3⋊C4—616no—
133Dic3⋊C4—616no—
134Dic3⋊C4—616no—
135Dic3⋊C4—616no—
136C4×Dic3—38no—
137C4×Dic3—332no—
138C4×Dic3—64no—
139C4×Dic3#6718yes—
140C22×C32C22×D411yescharacteristic
141C22×C32C22×D412yes—
142C22×C32C22×Q814yes—
143C32×C4—42no—
144C32×C4#12714yes—
145C3⋊Dic3—42no—
146C3⋊Dic3C4⋊Q818yescomplemented
147C3×Dic3—44no—
148C3×Dic3C4⋊Q8116yescomplemented
149C22×Q8—32no—
150C22×Q8—91no—
151C22×Q8D3211yescharacteristic
152C4⋊Q8—68no—
153C4⋊Q8—188no—
154C4⋊Q8—184no—
155C4⋊Q8—184no—
156C2×C4⋊C4—38no—
157C2×C4⋊C4—94no—
158C2×C4⋊C4—98no—
159C2×C4⋊C4—94no—
160C2×C42—32no—
161C2×C42—94no—
162C2×C42—91no—
163C23×C3—21no—
164C23×C3C23×D312yes—
165C3×Q8—48no—
166C3×Q8—48no—
167C3×Q8—128no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—38no—
175C2×C3×C4—316no—
176C2×C3×C4—44no—
177C2×C3×C4—64no—
178C2×C3×C4—64no—
179C2×C3×C4—64no—
180C2×C3×C4D3×D414yes—
181C2×C3×C4D3×D414yes—
182C2×C3×C4C2×#6714yes—
183C2×Dic3—24no—
184C2×Dic3—24no—
185C2×Dic3—24no—
186C2×Dic3—38no—
187C2×Dic3—316no—
188C2×Dic3—64no—
189C2×Dic3—68no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—124no—
195C2×Dic3D3×Q8116yes—
196C2×Dic3C2×#6718yes—
197Dic6—48no—
198Dic6—128no—
199Dic6—128no—
200C2×C32C2×#12711yescharacteristic
201C2×C32C2×C4⋊Q812yes—
202C2×C32C2×C4⋊Q814yes—
203C2×Q8—24no—
204C2×Q8—22no—
205C2×Q8—64no—
206C2×Q8—64no—
207C2×Q8—64no—
208C2×Q8—184no—
209C2×Q8—182no—
210C22×C4—34no—
211C22×C4—34no—
212C22×C4—92no—
213C22×C4—92no—
214C22×C4C2×D3212yes—
215C22×C4C2×D3211yescharacteristic
216C4⋊C4—616no—
217C4⋊C4—188no—
218C4⋊C4—1816no—
219C4⋊C4—188no—
220C42—38no—
221C42—916no—
222C42—94no—
223C22×C3—24no—
224C22×C3—22no—
225C22×C3—21no—
226C22×C3C2×D3×D412yes—
227C22×C3C2×D3×D412yes—
228C22×C3C2×D3×Q818yes—
229C22×C3C22×#6712yes—
230C3×C4—24no—
231C3×C4—316no—
232C3×C4—44no—
233C3×C4—44no—
234C3×C4—124no—
235C3×C4#94018yes—
236Dic3—316no—
237Dic3—44no—
238Dic3—68no—
239Dic3—124no—
240Dic3—124no—
241Dic3#944116yescomplemented
242C32#286811yescharacteristic, complemented, Sylow
243C23C22×D3211yescharacteristic
244Q8—44no—
245Q8—128no—
246Q8—364no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—316no—
250C2×C4—38no—
251C2×C4—64no—
252C2×C4—64no—
253C2×C4—64no—
254C2×C4—98no—
255C2×C4—94no—
256C2×C4—184no—
257C2×C4—182no—
258C2×C4D3×#6714yes—
259C2×C4#381112yes—
260C2×C3—24no—
261C2×C3—22no—
262C2×C3—21no—
263C2×C3D3×C4⋊Q814yes—
264C2×C3D3×C4⋊Q814yes—
265C2×C3C2×#94012yes—
266C2×C3C2×#94414yes—
267C22D32×Q814yes—
268C22C2×D3×#6712yes—
269C22C2×#381111yescharacteristic
270C4—316no—
271C4—42no—
272C4—98no—
273C4—124no—
274C4—362no—
275C4#6397914yes—
276C3—21no—
277C3#8325312yescomplemented
278C2D3×#94414yes—
279C2#1059536512yes—
280C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#2868
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
50. Dic32Q8semidirect
146. C3⋊Dic3C4⋊Q8semidirect
148. C3×Dic3C4⋊Q8semidirect
241. Dic3#944semidirect
242. C32#2868semidirect
277. C3#83253semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9442
C2×#638732
C2×#638662
#105912442
C4×Dic322
#832533