Finite Group Databasebeta

← #11779497

Subgroups — #11779497

Order 1152.

554 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596205C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic, complemented
3#10590300C212yesmaximal, complemented
4C3×#4546C211yesmaximal, characteristic, complemented
5#10589082C212yesmaximal, complemented
6#71304—31nomaximal
7#68493—31nomaximal
8C32×C4⋊Q8C2211yescharacteristic
9#64156—22no—
10#64104—22no—
11#64101—22no—
12C4×C4⋊(C3⋊D3)C2212yes—
13C2×C3×#216—22no—
14C3×#869C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16C3×C4×C3⋊C8C2211yescharacteristic
17#63573—22no—
18#63564—22no—
19#5734—31no—
20#5734—31no—
21#5734—61no—
22C3×#494—31no—
23#5092D311yescharacteristic, complemented
24#5084—32no—
25#4842—32no—
26C3×#333—31no—
27#4546D311yescharacteristic, complemented
28#4483—32no—
29#4459—32no—
30C2×C32×Q8D412yes—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)D412yes—
33C2×C4×C3⋊D3—22no—
34C2×C3×Dic6—21no—
35C32×C4⋊C4—22no—
36C32×C42C2311yescharacteristic
37#3752—24no—
38#3752—22no—
39C4⋊(C3⋊Dic3)D412yes—
40C4×C3⋊Dic3—22no—
41C3×#216—44no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8—22no—
45#1634—91noSylow
46C2×C3×Q16—62no—
47C3×C4⋊Q8—21no—
48C3×C4⋊Q8—31no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C2×D311yescharacteristic
51#947—64no—
52#947—62no—
53#947—62no—
54C2×#216—22no—
55#895—62no—
56#895—62no—
57#895—64no—
58#892—62no—
59#892—62no—
60#892—64no—
61C4×D12—32no—
62C4×D12—32no—
63C4×D12—62no—
64#869C2×D311yescharacteristic
65C3×C4⋊C8—32no—
66C3×C4×C8—31no—
67#821—62no—
68#817—62no—
69#809—62no—
70#808—62no—
71C4⋊(C3⋊C8)C2×D312yes—
72C4×C3⋊C8C2×D311yescharacteristic
73C22×C3⋊D3—22no—
74C32×Q8—42no—
75C2×C32×C4—22no—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D412yes—
78C2×C3⋊Dic3—22no—
79C4⋊(C3⋊D3)—22no—
80C4⋊(C3⋊D3)—22no—
81C4⋊(C3⋊D3)—82no—
82C4×C3⋊D3—42no—
83C4×C3⋊D3—42no—
84C2×C3×Dic3—41no—
85C3×Dic6—42no—
86C3×C3⋊C8—22no—
87C3×C3⋊C8—42no—
88#555—91no—
89#494—31no—
90#476—92no—
91#333—31no—
92D4⋊C8—92no—
93C2×C3×Q8—22no—
94C2×C3×Q8—61no—
95C2×C3×Q8D1212yes—
96C2×C3×Q8#6712yes—
97C2×D12—32no—
98C2×D12—32no—
99C2×D12—62no—
100C2×D12—64no—
101C2×D12—62no—
102C2×D12—62no—
103C2×C4×D3—64no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×Dic6—21no—
107C3×Q16—124no—
108C2×C3×C8—61no—
109C2×C3×C8—62no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—62no—
114C3×C42—21no—
115C3×C42C22×D311yescharacteristic
116C3×C42C22×D311yescharacteristic
117#216—44no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—68no—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—64no—
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—62no—
124C4⋊Dic3—22no—
125C4⋊Dic3—32no—
126C4⋊Dic3—32no—
127C4⋊Dic3—62no—
128C4×Dic3—64no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C2×C3⋊C8—21no—
132C2×C3⋊C8—22no—
133C22×C32#12011yescharacteristic
134C2×C3⋊D3—42no—
135C2×C3⋊D3—42no—
136C2×C3⋊D3—42no—
137C32×C4—21no—
138C32×C4—42no—
139C32×C4#13512yes—
140C32×C4#13712yes—
141C3⋊Dic3—42no—
142C3×Dic3—81no—
143C2×Q16—62no—
144C4⋊Q8—31no—
145C4⋊Q8D3211yescharacteristic
146#124—182no—
147#121—182no—
148C4×D4—92no—
149#117—182no—
150#106—182no—
151C4⋊C8—32no—
152#102—182no—
153C4×C8—31no—
154C22×D3—64no—
155C22×D3—62no—
156C22×D3—62no—
157C3×Q8—42no—
158C3×Q8—42no—
159C3×Q8—82no—
160C3×Q8—122no—
161C2×C3×C4—24no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—21no—
165C2×C3×C4—22no—
166C2×C3×C4—121no—
167C2×C3×C4C2×D1211yescharacteristic
168C2×C3×C4D3×D412yes—
169C2×C3×C4D3×D412yes—
170C2×C3×C4C2×#6711yescharacteristic
171C2×Dic3—41no—
172C2×Dic3—64no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175D12—62no—
176D12—62no—
177D12—62no—
178D12—62no—
179D12—122no—
180D12—122no—
181D12—244no—
182D12—242no—
183D12—242no—
184C4×D3—124no—
185C4×D3—124no—
186C4×D3—122no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—122no—
190Dic6—42no—
191C3×C8—62no—
192C3×C8—122no—
193C3⋊C8—22no—
194C3⋊C8—42no—
195C2×C32#45212yes—
196C2×C32#45311yescharacteristic
197C3⋊D3—82no—
198C2×Q8—61no—
199C2×Q8#62612yes—
200C2×D4—92no—
201C2×D4—182no—
202C22×C4—182no—
203Q16—124no—
204C2×C8—61no—
205C2×C8—62no—
206C4⋊C4—22no—
207C4⋊C4—62no—
208C4⋊C4—92no—
209C22⋊C4—184no—
210C22⋊C4—182no—
211C42—182no—
212C42C2×D3211yescharacteristic
213C22×C3—21no—
214C22×C3#88211yescharacteristic
215C22×C3#93711yescharacteristic
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—124no—
219C2×D3—122no—
220C2×D3—122no—
221C2×D3—122no—
222C2×D3—122no—
223C2×D3—122no—
224C2×D3—122no—
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—22no—
229C3×C4—41no—
230C3×C4—44no—
231C3×C4—42no—
232C3×C4—42no—
233C3×C4—241no—
234C3×C4#91612yes—
235C3×C4#91812yes—
236C3×C4#91812yes—
237C3×C4#91912yes—
238Dic3—81no—
239Dic3—124no—
240Dic3—122no—
241Dic3—122no—
242C32#163411yescharacteristic, complemented, Sylow
243C23—182no—
244Q8—42no—
245Q8—122no—
246D4—182no—
247D4—182no—
248D4—722no—
249C2×C4—22no—
250C2×C4—121no—
251C2×C4—182no—
252C2×C4—362no—
253C2×C4—362no—
254C2×C4C2×#62611yescharacteristic
255C2×C4#381112yes—
256C8—62no—
257C8—122no—
258C2×C3—21no—
259C2×C3—22no—
260C2×C3#474711yescharacteristic
261C2×C3#480812yes—
262C2×C3#507711yescharacteristic
263C2×C3#518712yes—
264D3—244no—
265D3—242no—
266D3—242no—
267C22—362no—
268C22—362no—
269C22—362no—
270C22#6398111yescharacteristic
271C4—21no—
272C4—42no—
273C4—241no—
274C4—362no—
275C4#6394512yes—
276C4#6395012yes—
277C3—21no—
278C3#6849311yescharacteristic, complemented
279C3#7130411yescharacteristic, complemented
280C2—722no—
281C2#1059151111yescharacteristic
282C2#1059160212yes—
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10596205C2
hypercenterC4⋊Q8D32
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5092C2semidirect
3. #10590300C2semidirect
4. C3×#4546C2semidirect
5. #10589082C2semidirect
23. #5092D3semidirect
27. #4546D3semidirect
242. C32#1634semidirect
278. C3#68493semidirect
279. C3#71304semidirect

Maximal subgroups

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

subgroupindex
#105962052
C3×#50922
#105903002
C3×#45462
#105890822
#713043
#684933