Finite Group Databasebeta

← #11780571

Subgroups — #11780571

Order 1152.

518 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 70 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#10594021C211yesmaximal, characteristic
2#10592785C211yesmaximal, characteristic, complemented
3C3×#5089C212yesmaximal, complemented
4#10589087C211yesmaximal, characteristic, complemented
5#10589086C212yesmaximal, complemented
6#71244—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic, complemented
8C2×#3756—21no—
9C2×#3755—21no—
10#64084C2211yescharacteristic
11C3×#875C2212yes—
12#63923—21no—
13#63922—22no—
14#63913—21no—
15#63907—22no—
16#63630C2211yescharacteristic, complemented
17C3×#810—22no—
18C3×#809—22no—
19C3×#803C2212yescomplemented
20#5683—32no—
21C3×#489—32no—
22#5089D312yescomplemented
23#5086—32no—
24#5086—61no—
25#4540—32no—
26#4464—32no—
27#4464—32no—
28C22×D32—21no—
29C2×C32×Q8—21no—
30C2×C4⋊(C3⋊D3)D411yescharacteristic
31C2×#634D411yescharacteristic
32C2×C3×D12D412yes—
33C2×C3×Dic6D412yes—
34C2×#626—22no—
35C2×#625—21no—
36C32×C4⋊C4—22no—
37C32×C42C2311yescharacteristic
38#3756—42no—
39#3755—42no—
40#3752—22no—
41C2×C3⋊(C3⋊C8)—21no—
42C3×(C2×D3)⋊C4—22no—
43C3×(C2×D3)⋊C4—22no—
44C2×C3×C3⋊C8—22no—
45#3722—21no—
46(C2×D3)⋊Dic3—22no—
47Dic32—21no—
48#1659—91noSylow
49C3×C4⋊Q8—21no—
50C3×C4⋊Q8C2×D312yescomplemented
51C3×#124—32no—
52#947—62no—
53C2×#216—62no—
54C2×#216—62no—
55C2×#215—62no—
56C2×#215—62no—
57#937—62no—
58#885—62no—
59#885—62no—
60#882—62no—
61#882—62no—
62#875—32no—
63#875—61no—
64#875C2×D312yes—
65C3×#103—62no—
66C3×#102—62no—
67C3×#97—32no—
68#810—22no—
69#809—22no—
70#803—32no—
71#803—61no—
72#803C2×D312yescomplemented
73C22×C3⋊D3—21no—
74C22×C3×D3—22no—
75C2×D32—81no—
76C2×D32—82no—
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—41no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D412yes—
82C2×C3⋊Dic3—21no—
83C4⋊(C3⋊D3)—41no—
84#634—41no—
85C2×C3×Dic3—22no—
86C3×D12—42no—
87C3×Dic6—42no—
88#626—82no—
89#625—81no—
90C3⋊(C3⋊C8)—22no—
91C3×C3⋊C8—42no—
92H(3,𝔽4)—91no—
93#497—91no—
94#489—32no—
95#329—91no—
96#329—92no—
97C23×D3—62no—
98C2×C3×Q8—22no—
99C2×C3×Q8—22no—
100C2×C3×Q8—32no—
101C2×C3×D4—32no—
102C2×#67—62no—
103C2×#67—62no—
104C2×D12—32no—
105C2×D12—61no—
106C2×D12—62no—
107C2×D12#6712yes—
108C2×Dic6—32no—
109C2×Dic6—61no—
110C2×Dic6#6712yes—
111C2×C3×C8—62no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—42no—
115C3×C22⋊C4—62no—
116C3×C22⋊C4—62no—
117C3×C42—21no—
118C3×C42C22×D312yes—
119#217—62no—
120#216—124no—
121#216—124no—
122#215—124no—
123#215—124no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—62no—
127(C2×D3)⋊C4—62no—
128(C2×D3)⋊C4—62no—
129(C2×D3)⋊C4—62no—
130(C2×D3)⋊C4—122no—
131C4×Dic3—62no—
132C2×C3⋊C8—22no—
133C2×C3⋊C8—62no—
134C2×C3⋊C8—62no—
135C22×C32#12011yescharacteristic
136C2×C3⋊D3—41no—
137C2×C3⋊D3—42no—
138C2×C3×D3—42no—
139C2×C3×D3—42no—
140C2×C3×D3—42no—
141D32—84no—
142C32×C4—21no—
143C32×C4—22no—
144C32×C4—81no—
145C3⋊Dic3—41no—
146C3×Dic3—42no—
147C2×Q16—181no—
148C2×SD16—181no—
149C4⋊Q8D3211yescharacteristic, complemented
150#124—32no—
151#124—91no—
152#124—181no—
153#124—182no—
154#120—181no—
155#120—182no—
156#103—62no—
157#102—62no—
158#97—32no—
159#97—91no—
160C23×C3—62no—
161C22×D3—22no—
162C22×D3—62no—
163C22×D3—121no—
164C22×D3—242no—
165C22×D3—242no—
166C22×D3—242no—
167C3×Q8—42no—
168C3×Q8—42no—
169C3×Q8—42no—
170C3×Q8—42no—
171C3×Q8—122no—
172C3×D4—122no—
173C2×C3×C4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—42no—
176C2×C3×C4—42no—
177C2×C3×C4—62no—
178C2×C3×C4D3×D412yes—
179C2×C3×C4D3×D412yes—
180C2×C3×C4C2×#6712yes—
181#67—242no—
182#67—242no—
183C2×Dic3—22no—
184C2×Dic3—62no—
185C2×Dic3—121no—
186D12—42no—
187D12—122no—
188D12—122no—
189D12—242no—
190Dic6—42no—
191Dic6—122no—
192Dic6—122no—
193C3×C8—122no—
194C3⋊C8—42no—
195C3⋊C8—64no—
196C3⋊C8—64no—
197C2×C32#45311yescharacteristic
198C2×C32#45512yes—
199C3⋊D3—81no—
200C3×D3—82no—
201C24—181no—
202C2×Q8—21no—
203C2×Q8—32no—
204C2×Q8—91no—
205C2×D4—32no—
206C2×D4—91no—
207C2×D4—182no—
208C2×D4—181no—
209Q16—362no—
210SD16—362no—
211C2×C8—62no—
212C2×C8—181no—
213C4⋊C4—22no—
214C22⋊C4—62no—
215C22⋊C4—62no—
216C22⋊C4—181no—
217C22⋊C4—182no—
218C22⋊C4—182no—
219C42—181no—
220C42C2×D3211yescharacteristic
221C22×C3—21no—
222C22×C3—122no—
223C22×C3—122no—
224C22×C3—122no—
225C22×C3#93712yes—
226C2×D3—42no—
227C2×D3—42no—
228C2×D3—42no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—241no—
233C2×D3—242no—
234C2×D3—248no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—42no—
240C3×C4—82no—
241C3×C4—82no—
242C3×C4—122no—
243Dic3—42no—
244Dic3—122no—
245Dic3—241no—
246C32#165911yescharacteristic, complemented, Sylow
247C23—62no—
248C23—181no—
249C23—721no—
250C23—722no—
251Q8—41no—
252Q8—41no—
253Q8—122no—
254Q8—361no—
255D4—122no—
256D4—361no—
257D4—722no—
258D4—721no—
259C2×C4—41no—
260C2×C4—62no—
261C2×C4—181no—
262C2×C4D3×#6712yes—
263C2×C4#381111yescharacteristic
264C8—122no—
265C8—182no—
266C2×C3—21no—
267C2×C3—22no—
268C2×C3—242no—
269C2×C3#506112yes—
270C2×C3#519812yes—
271C2×C3#520212yes—
272D3—82no—
273D3—242no—
274D3—481no—
275C22—122no—
276C22—122no—
277C22—122no—
278C22—361no—
279C22—362no—
280C22—724no—
281C22#6398311yescharacteristic
282C4—21no—
283C4—22no—
284C4—81no—
285C4—122no—
286C4—361no—
287C3—21no—
288C3#7124412yescomplemented
289C2—242no—
290C2—721no—
291C2#1059152211yescharacteristic
292C2#1059165912yes—
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10594021C2
hypercenterC4⋊Q8D32
hypocenterC32#1659
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. #10592785C2semidirect
3. C3×#5089C2semidirect
4. #10589087C2semidirect
5. #10589086C2semidirect
7. C32×C4⋊Q8C22semidirect
16. #63630C22semidirect
19. C3×#803C22semidirect
22. #5089D3semidirect
50. C3×C4⋊Q8C2×D3semidirect
72. #803C2×D3semidirect
149. C4⋊Q8D32semidirect
246. C32#1659semidirect
288. C3#71244semidirect

Maximal subgroups

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

subgroupindex
#105940212
#105927852
C3×#50892
#105890872
#105890862
#712443