Finite Group Databasebeta

← #14663226

Subgroups — #14663226

Order 2816.

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

normal subgroups only

This group has 470 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#13066957C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066564C212yesmaximal, complemented
4#13066546C212yesmaximal, complemented
5C4×C11×#123C211yesmaximal, characteristic
6C2×C11×#123C411yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C22×C42×C11C411yescharacteristic
9C11×#388—21no—
10C11×#387—21no—
11C11×#386C411yescharacteristic
12C11×#385C2211yescharacteristic
13C11×#381C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C4×C11×C22⋊C4—21no—
16C4×C11×C22⋊C4C411yescharacteristic
17#10622820—21no—
18#10622539—21no—
19#10622166—21no—
20#10622163—21no—
21#10622163C2212yes—
22#10622163C2212yes—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#123—22no—
29C11×#123—22no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11—21no—
44C2×C42×C11—41no—
45C2×C42×C11—41no—
46C2×C42×C11D411yescharacteristic
47C2×#4318—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—41no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11526—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22×C411yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11M1612yescomplemented
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×C4⋊C4—24no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—42no—
89C11×C22⋊C4—24no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4M1612yescomplemented
96C42×C11—21no—
97C42×C11—21no—
98C42×C11—42no—
99C42×C11—42no—
100C42×C11—41no—
101C42×C11—41no—
102#4318—82no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—42no—
105C4×#123D1111yescharacteristic
106#1466—111no—
107#1465—111no—
108#1326—112no—
109#1317—112no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11C2×C22⋊C411yescharacteristic
120C23×C11C2×M1611yescharacteristic
121C23×C11C2×M1611yescharacteristic
122D4×C11—42no—
123D4×C11—42no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C2×C4×C11#9911yescharacteristic
155C2×C4×C11#9911yescharacteristic
156C11⋊C8—82no—
157C11⋊C8—82no—
158C2×#123Dic1111yescharacteristic
159C2×C4×D4C2×D1111yescharacteristic
160C22×C42Dic1111yescharacteristic
161#432—221no—
162#407—221no—
163#388—21no—
164#387—21no—
165#386Dic1111yescharacteristic
166#385C2×D1111yescharacteristic
167#381C2×D1111yescharacteristic
168C4×C4⋊C4—21no—
169C4×C22⋊C4—21no—
170C4×C22⋊C4Dic1111yescharacteristic
171#324—221no—
172#323—112no—
173#323—112no—
174#323—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—81no—
189C22×C11#40711yescharacteristic
190C22×C11C2×#9911yescharacteristic
191C22×C11#41311yescharacteristic
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—42no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—42no—
200C4×C11—81no—
201C4×C11#35212yes—
202C22×D4C2×Dic1111yescharacteristic
203C23×C4C2×Dic1111yescharacteristic
204C23×C4C2×Dic1111yescharacteristic
205C23×C4C2×Dic1111yescharacteristic
206C23×C4C22⋊D1111yescharacteristic
207C2×M16—441no—
208#123—22no—
209#123—22no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4C2×Dic1111yescharacteristic
218C2×C22⋊C4C2×Dic1111yescharacteristic
219C2×C22⋊C4C22⋊D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—41no—
225C2×C42—41no—
226C2×C42C22⋊D1111yescharacteristic
227C4⋊C8—441no—
228C22⋊C8—222no—
229C22⋊C8—222no—
230C22⋊C8—441no—
231#97—441no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—41no—
241C2×C11—81no—
242C2×C11#146511yescharacteristic
243C2×C11C2×#35211yescharacteristic
244C2×C11#212011yescharacteristic
245C24C22⋊Dic1111yescharacteristic
246C24C22×Dic1111yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4#431812yescomplemented
267C22×C4C22⋊Dic1111yescharacteristic
268C22×C4C22⋊Dic1111yescharacteristic
269C22×C4C22⋊Dic1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—882no—
273C2×C8—442no—
274C2×C8—442no—
275C4⋊C4—24no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C22⋊C4—24no—
279C22⋊C4—21no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4#431812yescomplemented
285C42—21no—
286C42—21no—
287C42—42no—
288C42—42no—
289C42—41no—
290C42—41no—
291C11#1152611yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23C2×#431811yescharacteristic
302C23C2×#431811yescharacteristic
303C23C2×C22⋊Dic1111yescharacteristic
304D4—42no—
305D4—42no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4#6689811yescharacteristic
337C2×C4#6689811yescharacteristic
338C8—882no—
339C8—882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22#1062282011yescharacteristic
355C22C2×#6689811yescharacteristic
356C22#1062285011yescharacteristic
357C4—21no—
358C4—42no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—42no—
363C4—41no—
364C4—42no—
365C4—81no—
366C4#1062217712yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—81no—
372C2#1306695411yescharacteristic
373C2C2×#1062217711yescharacteristic
374C2#1307025711yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC4×C11×#123C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenterC4×#123D11
hypocenterC11#11526
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
3. #13066564C2semidirect
4. #13066546C2semidirect
83. C22×C4×C11M16semidirect
95. C11×C22⋊C4M16semidirect
266. C22×C4#4318semidirect
284. C22⋊C4#4318semidirect
291. C11#11526semidirect

Maximal subgroups

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

subgroupindex
#130669572
#130669542
#130665642
#130665462
C4×C11×#1232
#1152611