Finite Group Databasebeta

← #11773766

Subgroups — #11773766

Order 1152.

693 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 693 conjugacy classes of subgroups — too many to draw. Only its 114 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×#64086C211yesmaximal, characteristic
2#10591061C212yesmaximal, complemented
3C3×#4525C212yesmaximal
4#10589148C212yesmaximal, complemented
5#68100—32nomaximal
6C23×C3⋊Dic3C411yescharacteristic
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×#3757C411yescharacteristic
9C2×#3750C411yescharacteristic
10C2×#3750C2211yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64086—22no—
14#64086—22no—
15C3×#830C2214yes—
16#63572—22no—
17#63553—22no—
18C2×#877—32no—
19C2×#877—61no—
20#4718—34no—
21C3×#323—32no—
22#4525D312yes—
23#4469—34no—
24C24×C32C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—22no—
30C22×C3⋊Dic3C814yescomplemented
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C32×C22⋊C4—22no—
36#3757—22no—
37#3750—22no—
38#3750—22no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3D412yes—
43C2×C3×C3⋊C8—24no—
44#1458—91noSylow
45C23×Dic3—32no—
46C23×Dic3—61no—
47C2×C3×C22⋊C4—21no—
48C2×C3×C22⋊C4C2×D312yes—
49C2×#217—32no—
50C2×#217—61no—
51C2×Dic3⋊C4—32no—
52C2×Dic3⋊C4—32no—
53C2×Dic3⋊C4—61no—
54C2×Dic3⋊C4—61no—
55C2×C4×Dic3—32no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59#877—64no—
60#877—64no—
61#877—64no—
62#877—64no—
63C3×C22⋊C8—34no—
64#830C2×D314yes—
65Dic3⋊C8—64no—
66C8×Dic3—64no—
67C23×C32—21no—
68C23×C32—21no—
69C23×C32—41no—
70C23×C32—41no—
71C23×C32C2×C812yes—
72C23×C32C22×C411yescharacteristic
73C2×C32×C4—21no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—24no—
80C2×C3⋊Dic3—24no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3C22⋊C412yes—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C2×C812yes—
88C2×C3⋊Dic3C2×C812yes—
89C2×C3⋊Dic3M1612yes—
90C3×C3⋊C8—44no—
91C2×#117—91no—
92#431—92no—
93#324—92no—
94#323—32no—
95C24×C3—21no—
96C24×C3C4×D312yes—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4C4×D312yes—
100C22×C3×C4C22×D312yes—
101C22×Dic3—32no—
102C22×Dic3—38no—
103C22×Dic3—32no—
104C22×Dic3—32no—
105C22×Dic3—32no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—64no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C22×Dic3—64no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—64no—
117C2×C3×C8—64no—
118C3×C22⋊C4—24no—
119C3×C22⋊C4—24no—
120#217—64no—
121#217—64no—
122Dic3⋊C4—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125Dic3⋊C4—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×C32—22no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—41no—
141C22×C32—41no—
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32C22×C811yescharacteristic
144C22×C32C2×M1611yescharacteristic
145C32×C4—22no—
146C32×C4—41no—
147C3⋊Dic3—22no—
148C3⋊Dic3—22no—
149C3⋊Dic3—41no—
150C3⋊Dic3C22⋊C812yes—
151C3⋊Dic3C22⋊C812yes—
152C23×C4—91no—
153#117—182no—
154#117—182no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4—91no—
157C2×C22⋊C4—91no—
158C2×C22⋊C4D3211yescharacteristic
159C2×C42—91no—
160C2×C42—91no—
161C4⋊C8—182no—
162C22⋊C8—34no—
163C4×C8—182no—
164C23×C3—22no—
165C23×C3—22no—
166C23×C3—22no—
167C23×C3—22no—
168C23×C3—22no—
169C23×C3—21no—
170C23×C3—42no—
171C23×C3—42no—
172C23×C3—42no—
173C23×C3—42no—
174C23×C3D3×C814yes—
175C23×C3C2×C4×D312yes—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4D3×D414yes—
184C2×Dic3—32no—
185C2×Dic3—32no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—34no—
189C2×Dic3—34no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—68no—
197C2×Dic3—68no—
198C2×Dic3—62no—
199C2×Dic3—68no—
200C2×Dic3—68no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208C2×Dic3—122no—
209C2×Dic3—122no—
210C3×C8—124no—
211C3⋊C8—44no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32—42no—
215C2×C32C2×C22⋊C811yescharacteristic
216C2×C32#41011yescharacteristic
217C2×C32#41311yescharacteristic
218C24#62411yescharacteristic
219C22×C4—91no—
220C22×C4—94no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—181no—
225C22×C4—181no—
226C22×C4—182no—
227C22×C4#62411yescharacteristic
228C22×C4C2×D3211yescharacteristic
229C2×C8—64no—
230C4⋊C4—182no—
231C4⋊C4—182no—
232C22⋊C4—22no—
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—24no—
243C22×C3—24no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—44no—
248C22×C3—44no—
249C22×C3—44no—
250C22×C3—44no—
251C22×C3—42no—
252C22×C3—42no—
253C22×C3—42no—
254C22×C3—42no—
255C22×C3D3×C22⋊C412yes—
256C22×C3C2×D3×C812yes—
257C22×C3D3×M1612yes—
258C3×C4—24no—
259C3×C4—42no—
260C3×C4—42no—
261C3×C4—42no—
262Dic3—34no—
263Dic3—34no—
264Dic3—62no—
265Dic3—62no—
266Dic3—64no—
267Dic3—64no—
268Dic3—64no—
269Dic3—122no—
270Dic3—122no—
271Dic3—122no—
272C32#145811yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23#371012yes—
278C23C2×#62411yescharacteristic
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—184no—
289C2×C4—184no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—361no—
294C2×C4—361no—
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—44no—
305C2×C3—44no—
306C2×C3D3×C22⋊C812yes—
307C2×C3#474012yes—
308C2×C3#474512yes—
309C22—21no—
310C22—21no—
311C22—22no—
312C22—42no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22C2×#371011yescharacteristic
317C22#6381811yescharacteristic
318C22#6397411yescharacteristic
319C4—22no—
320C4—41no—
321C4—92no—
322C4—92no—
323C4—182no—
324C4—182no—
325C4—361no—
326C3—21no—
327C3#6810012yescomplemented
328C2—21no—
329C2—21no—
330C2—42no—
331C2#1059115211yescharacteristic
332C2#1059150411yescharacteristic
333C2#1059152911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1458
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591061C2semidirect
4. #10589148C2semidirect
30. C22×C3⋊Dic3C8semidirect
272. C32#1458semidirect
327. C3#68100semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
#105910612
C3×#45252
#105891482
#681003