Finite Group Databasebeta

← #11793998

Subgroups — #11793998

Order 1152.

585 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 585 conjugacy classes of subgroups — too many to draw. Only its 110 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#10594786C211yesmaximal, characteristic
2#10592698C211yesmaximal, characteristic, complemented
3C3×#5006C212yesmaximal, complemented
4#10591083C212yesmaximal, complemented
5#10589157C211yesmaximal, characteristic, complemented
6#70043—32nomaximal
7C2×C3×#235C2212yes—
8C32×#117C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C3×#926C2212yes—
12#63827—22no—
13#63823—22no—
14#63822—22no—
15C4⋊(C3⋊(C3⋊C8))—22no—
16C3×#806—24no—
17#63565—22no—
18#63562—22no—
19#5822—32no—
20C3×#410—32no—
21#5233—32no—
22#5006D312yescomplemented
23#5002—32no—
24#4999—32no—
25#4999—61no—
26#4531—32no—
27C22×C32×C4C2311yescharacteristic
28C2×C3×#67—22no—
29C3×#235—22no—
30C3×#235—22no—
31C3×#235—22no—
32C3×#235—22no—
33C2×C3×D12D412yes—
34C2×C3×C4×D3—22no—
35C2×C3×Dic6D412yes—
36C32×C4⋊C4—21no—
37C32×C22⋊C4D412yes—
38C32×C42—21no—
39#3748—22no—
40C2×C3⋊(C3⋊C8)—21no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)D412yes—
43C3×#217—22no—
44C3×C4⋊Dic3—22no—
45C3×C4×Dic3—22no—
46#3718—22no—
47#3715—24no—
48#3713—22no—
49#2053—91noSylow
50C2×C3×#41—32no—
51C2×#235C2×D312yes—
52C3×#117—21no—
53C3×#117—32no—
54C3×#117C2×D312yes—
55#951—62no—
56#950—64no—
57#949—62no—
58#942—62no—
59#932—62no—
60#926C2×D312yes—
61C2×#208—32no—
62C2×#208—61no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—61no—
65C3×#99—64no—
66#835—62no—
67#832—62no—
68#810—62no—
69#809—62no—
70#806—24no—
71C4⋊(C3⋊C8)—64no—
72C4⋊(C3⋊C8)—64no—
73C23×C32C2×D411yescharacteristic
74C22×C3×D3—22no—
75C2×C32×C4—22no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4#4112yes—
79C2×C32×C4#4111yescharacteristic
80C3×#67—42no—
81C3×#67—42no—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—42no—
84C3×D12—22no—
85C3×D12—22no—
86C3×C4×D3—42no—
87C3×C4×D3—42no—
88C3×Dic6—22no—
89C3×Dic6—22no—
90C3⋊(C3⋊C8)—22no—
91C3⋊(C3⋊C8)—41no—
92#575—91no—
93#424—91no—
94#416—92no—
95#410—32no—
96H(3,ℤ/4)—91no—
97C3×#41—62no—
98C3×#41—62no—
99C3×#41—62no—
100C3×#41—62no—
101C2×C3×Q8—32no—
102C2×C3×D4—32no—
103C2×C3×D4—62no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C22×C3×C4C22×D312yes—
107C2×#67—22no—
108#235—22no—
109#235—22no—
110#235—22no—
111#235—22no—
112C2×D12D1212yes—
113C2×C4×D3—22no—
114C2×Dic6D1212yes—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4—62no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—62no—
120C3×C22⋊C4#6714yes—
121C3×C42—22no—
122C3×C42—22no—
123C3×C42—62no—
124#217—22no—
125#216—64no—
126#215—64no—
127#214—64no—
128#213—64no—
129C4⋊Dic3—22no—
130C4×Dic3—22no—
131#208—62no—
132#208—62no—
133#208—122no—
134C2×C3⋊C8—34no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—122no—
141C22×C32—41no—
142C22×C32#12112yes—
143C22×C32#12111yescharacteristic
144C2×C3×D3—42no—
145C2×C3×D3—82no—
146C32×C4—42no—
147C32×C4#12011yescharacteristic
148C32×C4#12312yes—
149C32×C4#12411yescharacteristic
150C3×Dic3—42no—
151C3×Dic3—82no—
152C2×#41—32no—
153#137—182no—
154AGL(1,ℤ/8)—182no—
155#135—182no—
156C2×M16—91no—
157C22×C8—91no—
158#117—32no—
159#117D3211yescharacteristic
160C4⋊C8—182no—
161#103—182no—
162#102—182no—
163#99—64no—
164C23×C3—21no—
165C23×C3—62no—
166C23×C3C2×#6712yes—
167C22×D3—22no—
168C3×Q8—62no—
169C3×Q8—62no—
170C3×D4—62no—
171C3×D4—62no—
172C3×D4—122no—
173C3×D4—122no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—62no—
181C2×C3×C4—122no—
182C2×C3×C4—122no—
183C2×C3×C4—122no—
184C2×C3×C4C2×D1212yes—
185C2×C3×C4#23512yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4#23712yes—
189C2×C3×C4#23712yes—
190#67—42no—
191#67—42no—
192C2×Dic3—22no—
193C2×Dic3—42no—
194D12—22no—
195D12—22no—
196C4×D3—42no—
197C4×D3—42no—
198Dic6—22no—
199Dic6—22no—
200C3⋊C8—64no—
201C3⋊C8—122no—
202C3⋊C8—122no—
203C3⋊C8—122no—
204C2×C32—21no—
205C2×C32—22no—
206C2×C32#39411yescharacteristic
207C3×D3—82no—
208#41—62no—
209#41—62no—
210#41—62no—
211#41—62no—
212C2×Q8—32no—
213C2×D4—32no—
214C2×D4—62no—
215C22×C4—62no—
216C22×C4C2×D3211yescharacteristic
217Q16—182no—
218SD16—184no—
219D8—182no—
220M16—182no—
221C2×C8—92no—
222C2×C8—182no—
223C2×C8—181no—
224C4⋊C4—21no—
225C4⋊C4—62no—
226C22⋊C4—62no—
227C22⋊C4#62512yes—
228C42—21no—
229C42—62no—
230C22×C3—22no—
231C22×C3—21no—
232C22×C3—42no—
233C22×C3—42no—
234C22×C3—122no—
235C22×C3—242no—
236C22×C3#93012yes—
237C22×C3#93812yes—
238C22×C3#93912yes—
239C2×D3—42no—
240C2×D3—82no—
241C3×C4—22no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—44no—
245C3×C4—44no—
246C3×C4—122no—
247C3×C4—242no—
248C3×C4#88212yes—
249C3×C4#88312yes—
250C3×C4#88512yes—
251C3×C4#88612yes—
252Dic3—42no—
253Dic3—82no—
254C32#205311yescharacteristic, complemented, Sylow
255C23—62no—
256C23C2×#62511yescharacteristic
257Q8—62no—
258Q8—62no—
259D4—62no—
260D4—62no—
261D4—122no—
262D4—122no—
263C2×C4—22no—
264C2×C4—62no—
265C2×C4—122no—
266C2×C4—122no—
267C2×C4—122no—
268C2×C4#379512yes—
269C2×C4D3×D1212yes—
270C2×C4#380511yescharacteristic
271C2×C4#381111yescharacteristic
272C8—182no—
273C8—361no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—22no—
278C2×C3—21no—
279C2×C3—42no—
280C2×C3—242no—
281C2×C3#496112yes—
282D3—82no—
283C22—41no—
284C22—122no—
285C22—242no—
286C22#6390812yes—
287C22#6398011yescharacteristic
288C4—42no—
289C4—122no—
290C4—242no—
291C4#6389112yes—
292C4#6391311yescharacteristic
293C4#6392311yescharacteristic
294C3—21no—
295C3#7004312yescomplemented
296C2—21no—
297C2—22no—
298C2—242no—
299C2#1059139411yescharacteristic
subgroupG/H
centerC4#63913
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#394
prime radical#10594786C2
hypercenter#117D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592698C2semidirect
3. C3×#5006C2semidirect
4. #10591083C2semidirect
5. #10589157C2semidirect
22. #5006D3semidirect
254. C32#2053semidirect
295. C3#70043semidirect

Maximal subgroups

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

subgroupindex
#105947862
#105926982
C3×#50062
#105910832
#105891572
#700433