Finite Group Databasebeta

← #14663157

Subgroups — #14663157

Order 2816.

586 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 99 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#13066950C212yesmaximal, complemented
2#13066550C212yesmaximal, complemented
3#13066548C212yesmaximal, complemented
4C11×#2297C211yesmaximal, characteristic
5C22×C11×#41C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C22×C42×C11C411yescharacteristic
8C11×#391C411yescharacteristic
9C11×#391C2211yescharacteristic
10C11×#390C411yescharacteristic
11C11×#390C2211yescharacteristic
12C11×#386—22no—
13C4×C11×C22⋊C4—22no—
14#10622539—22no—
15#10622166C2214yes—
16#10622163—22no—
17C2×C11×#41—22no—
18C2×C11×#41—22no—
19C2×C11×#41—42no—
20C2×C11×#41—41no—
21C2×C11×#41—41no—
22C22×Q8×C11C2×C411yescharacteristic
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11C2×C411yescharacteristic
28C11×#117—41no—
29C11×#117—41no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D412yes—
35C2×C42×C11—21no—
36C2×C42×C11—42no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11D412yes—
40C11×#95—22no—
41C11×#95—22no—
42C22⋊(C11⋊C8)—24no—
43C4⋊(C11⋊C8)—42no—
44#66867—42no—
45#11507—111nomaximal, Sylow
46C24×C11—21no—
47C24×C11C22⋊C411yescharacteristic
48C11×#41—44no—
49C11×#41—44no—
50C11×#41—44no—
51C11×#41—44no—
52C2×Q8×C11—21no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C2×Q8×C11M1612yes—
56C2×D4×C11—24no—
57C2×D4×C11—21no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—42no—
61C2×D4×C11—42no—
62C2×D4×C11M1612yes—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—24no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D412yes—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—44no—
86C11×C22⋊C4—44no—
87C42×C11—22no—
88C42×C11—22no—
89C42×C11—42no—
90C42×C11—41no—
91C42×C11—41no—
92C2×C11⋊C8—44no—
93#2297D1111yescharacteristic
94#1464—112no—
95#1319—112no—
96#1318—112no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—22no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11#10012yes—
107C23×C11C2×C22⋊C411yescharacteristic
108Q8×C11—42no—
109Q8×C11—42no—
110D4×C11—42no—
111D4×C11—42no—
112D4×C11—48no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—48no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11#9911yescharacteristic
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11C2×M1611yescharacteristic
140C2×C4×C11C2×M1611yescharacteristic
141C11⋊C8—84no—
142C22×#41Dic1111yescharacteristic
143C2×#117C2×D1111yescharacteristic
144C22×C42Dic1111yescharacteristic
145#432—222no—
146#391Dic1111yescharacteristic
147#391C2×D1111yescharacteristic
148#390Dic1111yescharacteristic
149#390C2×D1111yescharacteristic
150#386—22no—
151C4×C22⋊C4—22no—
152#324—114no—
153#323—222no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11—44no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—42no—
163C22×C11—82no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11#40711yescharacteristic
167C22×C11C2×#9911yescharacteristic
168C22×C11C2×#10011yescharacteristic
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—42no—
177C4×C11—42no—
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—42no—
181C2×#41—41no—
182C2×#41—41no—
183C22×Q8C2×Dic1111yescharacteristic
184C22×D4—21no—
185C22×D4C2×Dic1111yescharacteristic
186C23×C4—21no—
187C23×C4—21no—
188C23×C4C2×Dic1111yescharacteristic
189#117—41no—
190#117—41no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C22×D1111yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4C22⋊D1112yes—
196C2×C42—21no—
197C2×C42—42no—
198C2×C42C2×Dic1111yescharacteristic
199C2×C42C2×Dic1111yescharacteristic
200C2×C42C22⋊D1112yes—
201C4⋊C8—442no—
202C22⋊C8—224no—
203#97—442no—
204#95—22no—
205#95—22no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—42no—
209C2×C11—82no—
210C2×C11#146211yescharacteristic
211C2×C11#212611yescharacteristic
212C2×C11#213211yescharacteristic
213C24—21no—
214C24C22⋊Dic1111yescharacteristic
215#41—44no—
216#41—44no—
217#41—44no—
218#41—44no—
219C2×Q8—21no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8#431812yes—
223C2×D4—24no—
224C2×D4—21no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4#431812yes—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—24no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊Dic1112yes—
246C22×C4C22⋊Dic1111yescharacteristic
247C22×C4C22×Dic1111yescharacteristic
248C22×C4C2×C22⋊D1112yes—
249C2×C8—444no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—44no—
254C22⋊C4—44no—
255C42—22no—
256C42—22no—
257C42—41no—
258C42—41no—
259C42—42no—
260C11#1150711yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—22no—
264C23—41no—
265C23—41no—
266C23—42no—
267C23—42no—
268C23—41no—
269C23—41no—
270C23#6689712yes—
271C23C2×C22⋊Dic1111yescharacteristic
272Q8—42no—
273Q8—42no—
274D4—42no—
275D4—42no—
276D4—48no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—48no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4#6689811yescharacteristic
302C2×C4#6689811yescharacteristic
303C2×C4C2×#431811yescharacteristic
304C2×C4C2×#431811yescharacteristic
305C8—884no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—44no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—82no—
316C22—81no—
317C22—81no—
318C22#1062282011yescharacteristic
319C22C2×#6689711yescharacteristic
320C22C2×#6689811yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—42no—
328C4—42no—
329C4—42no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—82no—
334C2#1306694311yescharacteristic
335C2#1307028111yescharacteristic
336C2#1307030111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2297C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2297D11
hypocenterC11#11507
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13066950C2semidirect
2. #13066550C2semidirect
3. #13066548C2semidirect
260. C11#11507semidirect

Maximal subgroups

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

subgroupindex
#130669502
#130665502
#130665482
C11×#22972
#1150711