Finite Group Databasebeta

← #11773908

Subgroups — #11773908

Order 1152.

669 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 669 conjugacy classes of subgroups — too many to draw. Only its 102 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×#64101C211yesmaximal, characteristic
2#10591066C212yesmaximal, complemented
3C3×#4528C212yesmaximal, complemented
4#10589146C212yesmaximal
5#68126—32nomaximal
6C22×C4×C3⋊D3C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3752C411yescharacteristic
9C2×#3752C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64101—22no—
14#64101—22no—
15C3×#830C2214yes—
16#63572—22no—
17#63555—22no—
18C2×#892—32no—
19C2×#892—61no—
20#4719—34no—
21C3×#324—32no—
22#4528D312yescomplemented
23#4468—34no—
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C32×C4⋊C4—22no—
36#3752—22no—
37#3752—22no—
38C4⋊(C3⋊Dic3)—22no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43C2×C3×C3⋊C8—24no—
44#1464—91noSylow
45C22×C4×D3—32no—
46C22×C4×D3—61no—
47C2×C3×C4⋊C4—21no—
48C2×C3×C4⋊C4C2×D312yes—
49C2×(C2×D3)⋊C4—32no—
50C2×(C2×D3)⋊C4—32no—
51C2×(C2×D3)⋊C4—61no—
52C2×(C2×D3)⋊C4—61no—
53C2×C4⋊Dic3—32no—
54C2×C4⋊Dic3—61no—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59#892—64no—
60#892—64no—
61#892—64no—
62#892—64no—
63C3×C22⋊C8—34no—
64#830C2×D314yes—
65#815—64no—
66Dic3⋊C8—64no—
67C23×C32C22×C411yescharacteristic
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3M1612yes—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4M1612yes—
79C2×C32×C4C2×D412yes—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C412yes—
88C4×C3⋊D3—24no—
89C4×C3⋊D3—24no—
90C3×C3⋊C8—44no—
91C2×#117—91no—
92#432—92no—
93#324—32no—
94#323—92no—
95C23×D3—32no—
96C23×D3—61no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4C4×D312yes—
101C22×C3×C4C4×D312yes—
102C22×C3×C4C22×D312yes—
103C22×Dic3—32no—
104C22×Dic3—32no—
105C22×Dic3—32no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—64no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C3×C8—64no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—24no—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—64no—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124C4⋊Dic3—64no—
125C4⋊Dic3—64no—
126C4×Dic3—34no—
127C4×Dic3—34no—
128C4×Dic3—62no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C2×C3⋊C8—24no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×C22⋊C411yescharacteristic
138C22×C32C2×M1611yescharacteristic
139C22×C32C2×M1611yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3—42no—
142C2×C3⋊D3—41no—
143C2×C3⋊D3—41no—
144C2×C3⋊D3—42no—
145C32×C4—22no—
146C32×C4—22no—
147C32×C4—41no—
148C3⋊Dic3—21no—
149C3⋊Dic3—21no—
150C3⋊Dic3—22no—
151C3⋊Dic3—41no—
152C23×C4—91no—
153#117—182no—
154#117—182no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4D3211yescharacteristic
157C2×C22⋊C4—91no—
158C2×C22⋊C4—91no—
159C2×C42—91no—
160C2×C42—91no—
161C4⋊C8—182no—
162C22⋊C8—34no—
163#97—182no—
164C23×C3—21no—
165C23×C3C2×C4×D312yes—
166C22×D3—34no—
167C22×D3—62no—
168C22×D3—62no—
169C22×D3—62no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—122no—
173C22×D3—122no—
174C22×D3—122no—
175C22×D3—122no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187C2×C3×C4—42no—
188C2×C3×C4ΓL(1,𝔽25)14yes—
189C2×C3×C4D3×D414yes—
190C2×Dic3—32no—
191C2×Dic3—32no—
192C2×Dic3—34no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206C4×D3—68no—
207C4×D3—68no—
208C4×D3—68no—
209C4×D3—68no—
210C3×C8—124no—
211C3⋊C8—44no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32#40711yescharacteristic
215C2×C32#41011yescharacteristic
216C2×C32#41311yescharacteristic
217C3⋊D3—42no—
218C24—91no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—181no—
223C22×C4—181no—
224C22×C4—182no—
225C22×C4—182no—
226C22×C4#62411yescharacteristic
227C22×C4#62411yescharacteristic
228C22×C4C2×D3211yescharacteristic
229C2×C8—64no—
230C4⋊C4—22no—
231C4⋊C4—182no—
232C22⋊C4—182no—
233C22⋊C4—182no—
234C42—92no—
235C42—92no—
236C42—181no—
237C42—181no—
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3D3×C22⋊C412yes—
246C22×C3C2×ΓL(1,𝔽25)12yes—
247C22×C3D3×M1612yes—
248C2×D3—64no—
249C2×D3—64no—
250C2×D3—124no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—122no—
254C2×D3—122no—
255C2×D3—122no—
256C2×D3—122no—
257C2×D3—124no—
258C3×C4—24no—
259C3×C4—24no—
260C3×C4—24no—
261C3×C4—42no—
262C3×C4—42no—
263C3×C4—42no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—64no—
269Dic3—122no—
270Dic3—122no—
271Dic3—122no—
272C32#146411yescharacteristic, complemented, Sylow
273C23—92no—
274C23—181no—
275C23—181no—
276C23—361no—
277C23—361no—
278C23C2×#62411yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—92no—
287C2×C4—184no—
288C2×C4—184no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—361no—
293C2×C4—361no—
294C2×C4#371212yes—
295C2×C4#381112yes—
296C8—124no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3#472612yes—
305C2×C3#474012yes—
306C2×C3#475112yes—
307D3—124no—
308D3—124no—
309C22—21no—
310C22—21no—
311C22—182no—
312C22—362no—
313C22—362no—
314C22—361no—
315C22—361no—
316C22#6381811yescharacteristic
317C22C2×#371211yescharacteristic
318C22#6397411yescharacteristic
319C4—22no—
320C4—22no—
321C4—41no—
322C4—182no—
323C4—181no—
324C4—181no—
325C4—361no—
326C3—21no—
327C3#6812612yescomplemented
328C2—21no—
329C2—21no—
330C2—362no—
331C2#1059115911yescharacteristic
332C2#1059152911yescharacteristic
333C2#1059164011yescharacteristic
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#1464
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
2. #10591066C2semidirect
3. C3×#4528C2semidirect
22. #4528D3semidirect
272. C32#1464semidirect
327. C3#68126semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105910662
C3×#45282
#105891462
#681263