Finite Group Databasebeta

← #11783785

Subgroups — #11783785

Order 1152.

933 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 933 conjugacy classes of subgroups — too many to draw. Only its 158 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×#64102C211yesmaximal, characteristic
2C2×#63559C212yesmaximal
3#10591060C212yesmaximal, complemented
4C3×#4530C212yesmaximal, complemented
5#68972—32nomaximal
6C22×C4⋊(C3⋊D3)C2211yescharacteristic
7C22×C4×C3⋊D3C412yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752C412yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11#64102—22no—
12#64102—22no—
13C2×C3×#208C2214yes—
14#63559C418yescomplemented
15#63555—22no—
16#63553—22no—
17C2×#893—32no—
18C2×#893—61no—
19C2×#823—34no—
20Dic3×M16—34no—
21C3×#343—32no—
22#4530D312yescomplemented
23C23×C3⋊D3C2×C412yes—
24C22×C32×C4C2×C412yes—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)C2×C414yes—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—44no—
34C32×C4⋊C4—22no—
35#3752—24no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38C3×#208—24no—
39C3×#208C2×C418yescomplemented
40C2×C3×C3⋊C8—24no—
41C4×#100—91noSylow
42C22×D12—32no—
43C22×D12—61no—
44C22×C4×D3—34no—
45C22×C4×D3—62no—
46C2×C3×M16—34no—
47C2×C3×C4⋊C4—21no—
48C2×C3×C4⋊C4C2×D312yes—
49C2×(C2×D3)⋊C4—34no—
50C2×(C2×D3)⋊C4—62no—
51C2×C4×Dic3—32no—
52C2×C4×Dic3—61no—
53C2×#208C2×D314yes—
54#893—64no—
55#893—64no—
56#893—64no—
57#893—64no—
58#823—316no—
59#815—64no—
60C8×Dic3—64no—
61C23×C32C22×C411yescharacteristic
62C22×C3⋊D3—22no—
63C22×C3⋊D3—22no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3—42no—
66C22×C3⋊D3C4214yes—
67C2×C32×C4—22no—
68C2×C32×C4—42no—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C2×D412yes—
71C2×C32×C4#4112yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3C22⋊C412yes—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C4⋊(C3⋊D3)—28no—
78C4×C3⋊D3—44no—
79C4×C3⋊D3—44no—
80C3×C3⋊C8—28no—
81C2×C4×D4—91no—
82C2×#100—92no—
83C4×M16—92no—
84#343—32no—
85C23×D3—34no—
86C23×D3—62no—
87C22×C3×C4—22no—
88C22×C3×C4—21no—
89C22×C3×C4C4×D314yes—
90C22×C3×C4C22×D312yes—
91C22×Dic3—32no—
92C22×Dic3—32no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C2×D12—38no—
96C2×D12—64no—
97C2×D12—64no—
98C2×D12—64no—
99C2×D12—64no—
100C2×D12—62no—
101C2×D12—62no—
102C2×C4×D3—64no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—128no—
107C2×C4×D3—128no—
108C3×M16—38no—
109C3×M16—64no—
110C2×C3×C8—64no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4—24no—
113(C2×D3)⋊C4—68no—
114(C2×D3)⋊C4—68no—
115C4×Dic3—34no—
116C4×Dic3—34no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119#208—24no—
120#208C4×D318yescomplemented
121C2×C3⋊C8—24no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32C2×C4211yescharacteristic
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32#11711yescharacteristic
127C2×C3⋊D3—24no—
128C2×C3⋊D3—44no—
129C2×C3⋊D3—42no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—44no—
132C32×C4—42no—
133C32×C4C4×D414yes—
134C3⋊Dic3—21no—
135C3⋊Dic3—22no—
136C3⋊Dic3#10012yescomplemented
137C22×D4—91no—
138C23×C4—92no—
139C2×M16—34no—
140C4×D4—182no—
141C4×D4—182no—
142C2×C4⋊C4D3211yescharacteristic
143C2×C22⋊C4—92no—
144C2×C42—91no—
145#100—98no—
146#97—182no—
147C4×C8—182no—
148C23×C3—21no—
149C23×C3C2×C4×D312yes—
150C22×D3—38no—
151C22×D3—64no—
152C22×D3—64no—
153C22×D3—64no—
154C22×D3—64no—
155C22×D3—64no—
156C22×D3—124no—
157C22×D3—124no—
158C22×D3—124no—
159C22×D3—124no—
160C2×C3×C4—24no—
161C2×C3×C4—24no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4C2×C4×D314yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4#23712yes—
170C2×C3×C4#23912yes—
171C2×Dic3—32no—
172C2×Dic3—34no—
173C2×Dic3—32no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—62no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—122no—
180C2×Dic3—122no—
181D12—616no—
182D12—68no—
183D12—68no—
184C4×D3—128no—
185C4×D3—128no—
186C4×D3—128no—
187C4×D3—128no—
188C3×C8—68no—
189C3⋊C8—28no—
190C2×C32—21no—
191C2×C32—21no—
192C2×C32C4×C22⋊C411yescharacteristic
193C2×C32C2×#10011yescharacteristic
194C2×C32#41311yescharacteristic
195C3⋊D3—44no—
196C24—92no—
197C2×D4—94no—
198C2×D4—182no—
199C2×D4—182no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—182no—
203C22×C4—182no—
204C22×C4—364no—
205C22×C4#62412yes—
206C22×C4C2×D3211yescharacteristic
207M16—38no—
208M16—64no—
209C2×C8—64no—
210C4⋊C4—22no—
211C22⋊C4—184no—
212C42—92no—
213C42—92no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3C42×D312yes—
222C22×C3D3×C22⋊C412yes—
223C22×C3#89212yes—
224C2×D3—68no—
225C2×D3—68no—
226C2×D3—124no—
227C2×D3—128no—
228C2×D3—128no—
229C2×D3—128no—
230C2×D3—124no—
231C2×D3—124no—
232C2×D3—124no—
233C2×D3—128no—
234C3×C4—24no—
235C3×C4—44no—
236C3×C4—44no—
237C3×C4#67⋊C414yes—
238C3×C4#89314yes—
239Dic3—34no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—64no—
244Dic3—122no—
245C32C4×#10011yescharacteristic, complemented, Sylow
246C23—94no—
247C23—182no—
248C23—182no—
249C23—362no—
250C23—362no—
251C23C2×#62411yescharacteristic
252D4—188no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—91no—
256C2×C4—92no—
257C2×C4—91no—
258C2×C4—182no—
259C2×C4—364no—
260C2×C4—364no—
261C2×C4—361no—
262C2×C4#379612yes—
263C2×C4C4×D3212yes—
264C2×C4#381112yes—
265C8—68no—
266C2×C3—22no—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—22no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3#466612yes—
274C2×C3D3×#10012yes—
275C2×C3#475112yes—
276D3—128no—
277D3—128no—
278C22—21no—
279C22—21no—
280C22—184no—
281C22—364no—
282C22—364no—
283C22—362no—
284C22—362no—
285C22#6384911yescharacteristic
286C22C4×#62411yescharacteristic
287C22#6397411yescharacteristic
288C4—42no—
289C4—92no—
290C4—181no—
291C4—182no—
292C4#6388114yes—
293C3—21no—
294C3#6897212yescomplemented
295C2—21no—
296C2—21no—
297C2—364no—
298C2#1059126011yescharacteristic
299C2#1059150311yescharacteristic
300C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10591060C2semidirect
4. C3×#4530C2semidirect
14. #63559C4semidirect
22. #4530D3semidirect
39. C3×#208C2×C4semidirect
120. #208C4×D3semidirect
136. C3⋊Dic3#100semidirect
245. C32C4×#100semidirect
294. C3#68972semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#635592
#105910602
C3×#45302
#689723