Finite Group Databasebeta

← #14656753

Subgroups — #14656753

Order 2816.

544 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068702C212yesmaximal
3#13066495C212yesmaximal
4#13066459C211yesmaximal, characteristic
5C11×#1445C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×#95—21no—
9C2×C11×#95—21no—
10C2×C11×#95C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12#10622825—21no—
13#10622825C2212yes—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622274—22no—
16#10622269—22no—
17#10622167—22no—
18#10622167—22no—
19C23×C4×C11—21no—
20C23×C4×C11—21no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4Q812yescomplemented
29C2×C22⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11D412yes—
34C2×C4⋊Dic11D412yes—
35#66977—42no—
36#66977—42no—
37C2×Dic11⋊C4—22no—
38C22×C11⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—42no—
42C11×#95—42no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)—22no—
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—22no—
54C22×C4×C11—22no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11D812yes—
74C22×C4×C11SD1612yes—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×Q811yescharacteristic
77C22×C4×C11#4112yes—
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C22×Dic11—22no—
81C2×Dic22—42no—
82C2×Dic22—81no—
83C2×Dic22—81no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—42no—
86C22⋊Dic11—42no—
87C22⋊Dic11—42no—
88C4⋊Dic11—42no—
89C4⋊Dic11—42no—
90C4⋊Dic11—42no—
91C4⋊Dic11—81no—
92C4⋊Dic11—81no—
93Dic11⋊C4—44no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97#2659—111no—
98#1823—112no—
99#1445D1111yescharacteristic
100#1294—112no—
101#1280—111no—
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—41no—
119C2×C4×C11—42no—
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—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11C22⋊Q812yes—
143C2×C4×C11#12412yes—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150Dic22—84no—
151C11⋊C8—82no—
152C2×C22⋊Q8—221no—
153C22×C4⋊C4C2×D1111yescharacteristic
154C2×C22⋊C8—112no—
155#398—222no—
156#395—222no—
157#380—112no—
158#380—221no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95C2×D1111yescharacteristic
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—
192C4×C11—82no—
193C4×C11—82no—
194Dic11—82no—
195Dic11—82no—
196C22×Q8—221no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4C22⋊D1111yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22×D1111yescharacteristic
202C22×C8—222no—
203C22⋊Q8—442no—
204C22⋊Q8—442no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4Dic2212yescomplemented
215C2×C22⋊C4—222no—
216C22⋊C8—222no—
217C22⋊C8—222no—
218#95—22no—
219#95—22no—
220#95—42no—
221#95—42no—
222#95—222no—
223#95—222no—
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×C22⋊D1111yescharacteristic
236C2×Q8—442no—
237C2×Q8—881no—
238C2×Q8—881no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4#432312yes—
266C22×C4#432412yes—
267C22×C4C2×Dic2211yescharacteristic
268C22×C4#433911yescharacteristic
269C22×C4D4×D1112yes—
270C22×C4#434112yes—
271C2×C8—442no—
272C2×C8—442no—
273C2×C8—442no—
274C4⋊C4—24no—
275C4⋊C4—42no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—444no—
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#6697711yescharacteristic
290C23C2×#432311yescharacteristic
291C23C2×#432411yescharacteristic
292C23#6698911yescharacteristic
293C23#6699011yescharacteristic
294C23#6700211yescharacteristic
295C23#6700411yescharacteristic
296Q8—884no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4#6693112yes—
333C2×C4#6693812yes—
334C8—882no—
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#1062256011yescharacteristic
348C22#1062262011yescharacteristic
349C22#1062262111yescharacteristic
350C22#1062264911yescharacteristic
351C22#1062265311yescharacteristic
352C22#1062266611yescharacteristic
353C22#1062266611yescharacteristic
354C22#1062266811yescharacteristic
355C22#1062267411yescharacteristic
356C22#1062268311yescharacteristic
357C22#1062270811yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1306760111yescharacteristic
371C2#1306760611yescharacteristic
372C2#1306761811yescharacteristic
373C2#1306762311yescharacteristic
374C2#1306975211yescharacteristic
375C2#1306977711yescharacteristic
376C2#1306978311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1445C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1445D11
hypocenterC11#10342
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
28. C2×C11×C4⋊C4Q8semidirect
214. C2×C4⋊C4Dic22semidirect
284. C11#10342semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130687022
#130664952
#130664592
C11×#14452
#1034211