Finite Group Databasebeta

← #14662863

Subgroups — #14662863

Order 2816.

734 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622163C212yesmaximal, complemented
2#13066546C212yesmaximal, complemented
3#13066544C212yesmaximal, complemented
4C11×#2308C211yesmaximal, characteristic
5C23×D4×C11C411yescharacteristic
6C22×C11×C22⋊C4C411yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#386—22no—
9C11×#386—22no—
10C11×#381C411yescharacteristic
11C11×#381C2211yescharacteristic
12C11×#379C411yescharacteristic
13C11×#379C2211yescharacteristic
14C2×C22⋊(C11⋊C8)—22no—
15#10622163—22no—
16#10622163C2214yes—
17C25×C11C2×C411yescharacteristic
18C25×C11C2×C411yescharacteristic
19C22×D4×C11—21no—
20C22×D4×C11—21no—
21C22×D4×C11—22no—
22C22×D4×C11—42no—
23C22×D4×C11—42no—
24C22×D4×C11C814yescomplemented
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D412yes—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—42no—
32C2×C11×C22⋊C4—42no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D412yes—
37C2×C11×C22⋊C4C2311yescharacteristic
38C22×C11⋊C8—42no—
39C11×#95—22no—
40C11×#95—22no—
41C22⋊(C11⋊C8)—24no—
42C22⋊(C11⋊C8)—42no—
43#11426—111nomaximal, Sylow
44C24×C11—22no—
45C24×C11—22no—
46C24×C11—21no—
47C24×C11—21no—
48C24×C11—41no—
49C24×C11—41no—
50C24×C11—82no—
51C24×C11—82no—
52C24×C11C22⋊C411yescharacteristic
53C24×C11C22⋊C411yescharacteristic
54C24×C11C2×C812yes—
55C24×C11C2×C812yescomplemented
56C24×C11M1612yes—
57C24×C11C22×C411yescharacteristic
58C2×D4×C11—24no—
59C2×D4×C11—24no—
60C2×D4×C11—48no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—48no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—42no—
75C22×C4×C11—82no—
76C22×C4×C11—82no—
77C22×C4×C11C22⋊C412yes—
78C22×C4×C11C2×C812yescomplemented
79C22×C4×C11C2×D412yes—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—82no—
87C11×C22⋊C4—82no—
88C2×C11⋊C8—44no—
89C2×C11⋊C8—84no—
90#2308D1111yescharacteristic
91C2×#323—112no—
92#1317—112no—
93#1316—112no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—24no—
99C23×C11—24no—
100C23×C11—22no—
101C23×C11—42no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11—42no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—82no—
111C23×C11—82no—
112C23×C11—82no—
113C23×C11—82no—
114C23×C11—82no—
115C23×C11—84no—
116C23×C11—82no—
117C23×C11—84no—
118C23×C11—84no—
119C23×C11C22⋊C812yes—
120C23×C11C22⋊C812yes—
121C23×C11#9912yes—
122C23×C11#10012yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11C22×C811yescharacteristic
125C23×C11C2×M1611yescharacteristic
126D4×C11—48no—
127D4×C11—48no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—44no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—82no—
143C2×C4×C11—84no—
144C11⋊C8—84no—
145C23×D4Dic1111yescharacteristic
146C22×C22⋊C4Dic1111yescharacteristic
147C22×C22⋊C4C2×D1111yescharacteristic
148C2×C22⋊C8—222no—
149#386—22no—
150#386—22no—
151#381Dic1111yescharacteristic
152#381C2×D1111yescharacteristic
153#379Dic1111yescharacteristic
154#379C2×D1111yescharacteristic
155#323—114no—
156#323—222no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—84no—
176C22×C11—84no—
177C22×C11—82no—
178C22×C11—84no—
179C22×C11—84no—
180C22×C11—82no—
181C22×C11#32314yes—
182C22×C11C2×C22⋊C811yescharacteristic
183C22×C11C2×#9911yescharacteristic
184C22×C11C2×#10011yescharacteristic
185C4×C11—42no—
186C4×C11—42no—
187C4×C11—42no—
188C4×C11—81no—
189C4×C11—81no—
190C25C2×Dic1111yescharacteristic
191C25C2×Dic1111yescharacteristic
192C22×D4—22no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—42no—
196C22×D4—42no—
197C22×D4C11⋊C814yescomplemented
198C23×C4—21no—
199C23×C4C2×Dic1111yescharacteristic
200C23×C4C22⋊D1112yes—
201C22×C8—442no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—42no—
206C2×C22⋊C4—42no—
207C2×C22⋊C4C2×Dic1111yescharacteristic
208C2×C22⋊C4C2×Dic1111yescharacteristic
209C2×C22⋊C4C2×Dic1111yescharacteristic
210C2×C22⋊C4C22⋊D1112yes—
211C2×C22⋊C4C22×D1111yescharacteristic
212C22⋊C8—224no—
213C22⋊C8—442no—
214#95—22no—
215#95—22no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11—24no—
219C2×C11—42no—
220C2×C11—41no—
221C2×C11—41no—
222C2×C11—82no—
223C2×C11C2×#32311yescharacteristic
224C2×C11#212112yes—
225C24—22no—
226C24—22no—
227C24—21no—
228C24—21no—
229C24—41no—
230C24—41no—
231C24—82no—
232C24—82no—
233C24C2×C11⋊C812yes—
234C24C2×C11⋊C812yescomplemented
235C24#431812yes—
236C24C22⋊Dic1111yescharacteristic
237C24C22⋊Dic1111yescharacteristic
238C24C22×Dic1111yescharacteristic
239C2×D4—24no—
240C2×D4—24no—
241C2×D4—48no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—48no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—82no—
257C22×C4—82no—
258C22×C4C2×C11⋊C812yescomplemented
259C22×C4C22⋊Dic1112yes—
260C22×C4C2×C22⋊D1112yes—
261C2×C8—444no—
262C2×C8—884no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—82no—
270C22⋊C4—82no—
271C11#1142611yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—24no—
277C23—24no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—42no—
285C23—42no—
286C23—41no—
287C23—41no—
288C23—82no—
289C23—82no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23—84no—
294C23—82no—
295C23—84no—
296C23—84no—
297C23C22⋊(C11⋊C8)12yes—
298C23C22⋊(C11⋊C8)12yes—
299C23#6689712yes—
300C23#6689812yes—
301C23C22×C11⋊C811yescharacteristic
302C23C2×#431811yescharacteristic
303C23C2×C22⋊Dic1111yescharacteristic
304D4—48no—
305D4—48no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—84no—
322C8—884no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—42no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—84no—
342C22—84no—
343C22—82no—
344C22—84no—
345C22—84no—
346C22—82no—
347C22#1062216314yes—
348C22C2×C22⋊(C11⋊C8)11yescharacteristic
349C22C2×#6689711yescharacteristic
350C22C2×#6689811yescharacteristic
351C4—42no—
352C4—42no—
353C4—42no—
354C4—81no—
355C4—81no—
356C2—21no—
357C2—21no—
358C2—24no—
359C2—41no—
360C2—41no—
361C2—42no—
362C2—82no—
363C2C2×#1062216311yescharacteristic
364C2#1307026212yes—
subgroupG/H
centerC22C2×#66898
commutatorC23×C11C22×C8
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2308C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C4
cosocleC2×C11×C22⋊C4C23
hypercenter#2308D11
hypocenterC11#11426
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2308

Complements

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

NH ≅ G/Ntype
1. C2×#10622163C2semidirect
2. #13066546C2semidirect
3. #13066544C2semidirect
24. C22×D4×C11C8semidirect
55. C24×C11C2×C8semidirect
78. C22×C4×C11C2×C8semidirect
197. C22×D4C11⋊C8semidirect
234. C24C2×C11⋊C8semidirect
258. C22×C4C2×C11⋊C8semidirect
271. C11#11426semidirect

Maximal subgroups

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

subgroupindex
C2×#106221632
#130665462
#130665442
C11×#23082
#1142611