Finite Group Databasebeta

← #14656754

Subgroups — #14656754

Order 2816.

544 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074730C211yesmaximal, characteristic
2#13068703C212yesmaximal
3#13066883C211yesmaximal, characteristic
4#13066496C212yesmaximal
5C11×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic11C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×C22⋊C8C2212yes—
9C2×C11×#95C2211yescharacteristic
10#10622825—21no—
11#10622825C2212yes—
12C2×C11⋊#95—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2211yescharacteristic
15#10622274—22no—
16#10622269—22no—
17#10622189—22no—
18#10622189—22no—
19C23×C4×C11D411yescharacteristic
20C23×C4×C11D411yescharacteristic
21C23×C4×C11C2311yescharacteristic
22C23×Dic11—21no—
23C23×Dic11—21no—
24C22×Dic22—21no—
25C22×C8×C11—22no—
26C2×C22⋊Dic11—22no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—22no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11D412yes—
34C2×C4⋊Dic11D412yes—
35C2×C4⋊Dic11Q812yescomplemented
36#66977—42no—
37#66977—42no—
38C2×Dic11⋊C4—22no—
39C11×C22⋊C8—22no—
40C11×C22⋊C8—22no—
41C11×#95—22no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—42no—
46C11⋊#95—42no—
47#10342—111nomaximal, Sylow
48C24×C11C2×D411yescharacteristic
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11D812yes—
60C22×C4×C11SD1612yes—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×Q811yescharacteristic
63C22×C4×C11#4112yes—
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—41no—
70C22×Dic11—41no—
71C22×Dic11—41no—
72C22×Dic11—41no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C2×Dic22—42no—
82C2×Dic22—81no—
83C2×Dic22—81no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94C4⋊Dic11—81no—
95C4⋊Dic11—81no—
96Dic11⋊C4—44no—
97#2659—111no—
98#1823—112no—
99#1445—111no—
100#1294—112no—
101#1280D1111yescharacteristic
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#12011yescharacteristic
107C23×C11C22⋊Q811yescharacteristic
108C23×C11#12411yescharacteristic
109C23×C11C2×D811yescharacteristic
110C23×C11C2×SD1611yescharacteristic
111C23×C11AGL(1,ℤ/8)11yescharacteristic
112C23×C11#13711yescharacteristic
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C22⋊Q812yes—
129C2×C4×C11#12412yes—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—81no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150Dic22—84no—
151C8×C11—82no—
152C2×C22⋊Q8—221no—
153C22×C4⋊C4—111no—
154C2×C22⋊C8C2×D1112yes—
155#398—222no—
156#395—222no—
157#380—112no—
158#380—221no—
159C2×#95—111no—
160C2×#95—221no—
161C2×#95—221no—
162C2×#95C2×D1111yescharacteristic
163#340—222no—
164#340—222no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39311yescharacteristic
178C22×C11#44711yescharacteristic
179C22×C11#44811yescharacteristic
180C22×C11#45511yescharacteristic
181C22×C11#45611yescharacteristic
182C22×C11#45811yescharacteristic
183C22×C11#45811yescharacteristic
184C22×C11#47411yescharacteristic
185C22×C11#47611yescharacteristic
186C22×C11#48611yescharacteristic
187C22×C11#48911yescharacteristic
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—42no—
191C4×C11—42no—
192Dic11—82no—
193Dic11—82no—
194Dic11—82no—
195Dic11—82no—
196C22×Q8—221no—
197C23×C4—221no—
198C23×C4—221no—
199C23×C4D4411yescharacteristic
200C23×C4D4411yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C22×C8—22no—
203C22⋊Q8—442no—
204C22⋊Q8—442no—
205C2×C4⋊C4—112no—
206C2×C4⋊C4—112no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—222no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C22⋊C4—222no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218#95—22no—
219#95—222no—
220#95—222no—
221#95—222no—
222#95—442no—
223#95—442no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#160711yescharacteristic
229C2×C11#160811yescharacteristic
230C2×C11#161011yescharacteristic
231C2×C11#161111yescharacteristic
232C2×C11#202311yescharacteristic
233C2×C11#202811yescharacteristic
234C2×C11#203011yescharacteristic
235C24C2×D4411yescharacteristic
236C2×Q8—442no—
237C2×Q8—881no—
238C2×Q8—881no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4#431412yes—
266C22×C4D8812yes—
267C22×C4#433912yes—
268C22×C4D4×D1112yes—
269C22×C4#434111yescharacteristic
270C22×C4Q8×D1111yescharacteristic
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—224no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—444no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—881no—
281C4⋊C4—881no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C11#1034211yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#6692811yescharacteristic
290C23#6693511yescharacteristic
291C23#6695011yescharacteristic
292C23C2×#431411yescharacteristic
293C23C2×D8811yescharacteristic
294C23#6696111yescharacteristic
295C23#6696211yescharacteristic
296Q8—884no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4#6693812yes—
333C2×C4#6694912yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#1062228611yescharacteristic
348C22#1062230711yescharacteristic
349C22#1062232711yescharacteristic
350C22#1062234511yescharacteristic
351C22#1062235111yescharacteristic
352C22#1062235511yescharacteristic
353C22#1062235511yescharacteristic
354C22#1062235911yescharacteristic
355C22#1062236511yescharacteristic
356C22#1062245511yescharacteristic
357C22#1062245911yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—882no—
363C4—882no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1306760411yescharacteristic
371C2#1306760911yescharacteristic
372C2#1306762111yescharacteristic
373C2#1306762611yescharacteristic
374C2#1306975311yescharacteristic
375C2#1306977811yescharacteristic
376C2#1306978411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1280D11
hypocenterC11#10342
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
35. C2×C4⋊Dic11Q8semidirect
284. C11#10342semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130687032
#130668832
#130664962
C11×#12802
#1034211