Finite Group Databasebeta

← #11785729

Subgroups — #11785729

Order 1152.

841 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10591074C212yesmaximal
3C3×#4530C212yesmaximal, complemented
4#10589168C212yesmaximal, complemented
5#68990—32nomaximal
6C22×C4×C3⋊D3C412yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750C412yes—
11C4⋊C4×C3⋊D3—22no—
12C4⋊C4×C3⋊D3—22no—
13C2×C3×#208C2214yes—
14#63557—22no—
15#63557—22no—
16C2×D3×C4⋊C4—32no—
17C2×D3×C4⋊C4—61no—
18#5126—34no—
19C3×#343—32no—
20#4554—34no—
21#4530D312yescomplemented
22C23×C3⋊D3C2×C411yescharacteristic
23C22×C32×C4C2×C412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C412yes—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—44no—
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3D412yes—
34C32×C4⋊C4—22no—
35C4⋊(C3⋊Dic3)—22no—
36#3750—24no—
37C3×#208—24no—
38C3×#208—24no—
39C2×C3×C3⋊C8—24no—
40#1821—91noSylow
41C22×C4×D3—32no—
42C22×C4×D3—34no—
43C22×C4×D3—61no—
44C22×C4×D3—62no—
45C2×C3×M16—34no—
46C2×C3×C4⋊C4—21no—
47C2×C3×C4⋊C4C2×D312yes—
48C2×C4⋊Dic3—32no—
49C2×C4⋊Dic3—61no—
50C2×Dic3⋊C4—34no—
51C2×Dic3⋊C4—62no—
52C2×#208C2×D314yes—
53D3×C4⋊C4—64no—
54D3×C4⋊C4—64no—
55D3×C4⋊C4—64no—
56D3×C4⋊C4—64no—
57(C2×D3)⋊C8—64no—
58(C2×D3)⋊C8—64no—
59C23×C32C22×C411yescharacteristic
60C22×C3⋊D3—21no—
61C22×C3⋊D3—21no—
62C22×C3⋊D3—22no—
63C22×C3⋊D3—22no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C22×C3⋊D3C22⋊C411yescharacteristic
66C2×C32×C4—22no—
67C2×C32×C4—42no—
68C2×C32×C4C2×D412yes—
69C2×C32×C4#4112yes—
70C2×C32×C4#4112yes—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—42no—
75C2×C3⋊Dic3C22⋊C412yes—
76C4×C3⋊D3—24no—
77C4×C3⋊D3—24no—
78C4×C3⋊D3—44no—
79C4×C3⋊D3—44no—
80C3×C3⋊C8—44no—
81C22×C4⋊C4—91no—
82#407—92no—
83#343—32no—
84#343—92no—
85C23×D3—32no—
86C23×D3—61no—
87C22×C3×C4—22no—
88C22×C3×C4—21no—
89C22×C3×C4C4×D314yes—
90C22×C3×C4C22×D312yes—
91C22×Dic3—32no—
92C22×Dic3—34no—
93C22×Dic3—61no—
94C22×Dic3—62no—
95C2×C4×D3—34no—
96C2×C4×D3—34no—
97C2×C4×D3—62no—
98C2×C4×D3—62no—
99C2×C4×D3—64no—
100C2×C4×D3—64no—
101C2×C4×D3—64no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—64no—
108C2×C4×D3—128no—
109C2×C4×D3—128no—
110C3×M16—64no—
111C3×M16—64no—
112C2×C3×C8—64no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C4⋊Dic3—64no—
116C4⋊Dic3—64no—
117Dic3⋊C4—68no—
118Dic3⋊C4—68no—
119#208—24no—
120#208—24no—
121C2×C3⋊C8—24no—
122C22×C32—21no—
123C22×C32—21no—
124C22×C32C2×C22⋊C411yescharacteristic
125C22×C32#11711yescharacteristic
126C22×C32#11711yescharacteristic
127C2×C3⋊D3—24no—
128C2×C3⋊D3—24no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—21no—
133C2×C3⋊D3#10012yes—
134C2×C3⋊D3#10112yes—
135C32×C4—42no—
136C32×C4#12314yes—
137C3⋊Dic3—22no—
138C3⋊Dic3—42no—
139C23×C4—91no—
140C23×C4—92no—
141C2×M16—34no—
142C2×C4⋊C4—92no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—182no—
145C2×C4⋊C4—182no—
146C2×C4⋊C4D3211yescharacteristic
147C22⋊C8—182no—
148C22⋊C8—182no—
149C23×C3—21no—
150C23×C3C2×C4×D312yes—
151C22×D3—32no—
152C22×D3—32no—
153C22×D3—61no—
154C22×D3—61no—
155C22×D3—64no—
156C22×D3—64no—
157C22×D3—62no—
158C22×D3—62no—
159C22×D3—64no—
160C22×D3—64no—
161C22×D3—62no—
162C22×D3—62no—
163C2×C3×C4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—44no—
169C2×C3×C4—44no—
170C2×C3×C4#23514yes—
171C2×C3×C4D3×D414yes—
172C2×C3×C4#23712yes—
173C2×C3×C4#23912yes—
174C2×Dic3—34no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—124no—
183C2×Dic3—124no—
184C4×D3—68no—
185C4×D3—68no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—128no—
191C4×D3—128no—
192C4×D3—128no—
193C4×D3—128no—
194C3×C8—124no—
195C3⋊C8—44no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32#38111yescharacteristic
199C2×C32C2×#10011yescharacteristic
200C2×C32C2×#10111yescharacteristic
201C3⋊D3—22no—
202C3⋊D3—22no—
203C24—91no—
204C22×C4—91no—
205C22×C4—92no—
206C22×C4—92no—
207C22×C4—92no—
208C22×C4—182no—
209C22×C4—182no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—364no—
213C22×C4#62412yes—
214C22×C4C2×D3211yescharacteristic
215M16—64no—
216M16—64no—
217C2×C8—64no—
218C4⋊C4—22no—
219C4⋊C4—184no—
220C4⋊C4—182no—
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3#87212yes—
229C22×C3D3×C22⋊C412yes—
230C22×C3#89212yes—
231C2×D3—34no—
232C2×D3—34no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—62no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—68no—
239C2×D3—68no—
240C2×D3—68no—
241C2×D3—68no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—62no—
247C3×C4—24no—
248C3×C4—44no—
249C3×C4—44no—
250C3×C4#88314yes—
251C3×C4#89414yes—
252Dic3—64no—
253Dic3—64no—
254Dic3—124no—
255Dic3—124no—
256C32#182111yescharacteristic, complemented, Sylow
257C23—91no—
258C23—91no—
259C23—182no—
260C23—182no—
261C23—181no—
262C23—181no—
263C23C2×#62411yescharacteristic
264C2×C4—22no—
265C2×C4—42no—
266C2×C4—92no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4—184no—
270C2×C4—184no—
271C2×C4—182no—
272C2×C4—364no—
273C2×C4—364no—
274C2×C4—362no—
275C2×C4#379612yes—
276C2×C4#379812yes—
277C2×C4#381112yes—
278C8—124no—
279C2×C3—22no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3#466412yes—
287C2×C3D3×#10012yes—
288C2×C3D3×#10112yes—
289D3—64no—
290D3—64no—
291D3—64no—
292D3—64no—
293C22—21no—
294C22—21no—
295C22—92no—
296C22—92no—
297C22—184no—
298C22—184no—
299C22—181no—
300C22—181no—
301C22—181no—
302C22—181no—
303C22#6384911yescharacteristic
304C22#6387411yescharacteristic
305C22#6397411yescharacteristic
306C4—42no—
307C4—182no—
308C4—362no—
309C4#6385314yes—
310C3—21no—
311C3#6899012yescomplemented
312C2—21no—
313C2—21no—
314C2—182no—
315C2—182no—
316C2#1059121911yescharacteristic
317C2#1059150311yescharacteristic
318C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1821
LCSG ▷ C23×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. C3×#4530C2semidirect
4. #10589168C2semidirect
21. #4530D3semidirect
256. C32#1821semidirect
311. C3#68990semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105910742
C3×#45302
#105891682
#689903