Finite Group Databasebeta

← #14656763

Subgroups — #14656763

Order 2816.

856 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 107 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#13074586C211yesmaximal, characteristic, complemented
2#13068547C212yesmaximal
3#13066495C212yesmaximal, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#1438C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—22no—
8C2×C11×#95C2211yescharacteristic
9C2×C11×#95C2211yescharacteristic
10C2×#66896—22no—
11C2×#66896—22no—
12#10622825C2212yes—
13#10622823—22no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622273—22no—
16#10622270—22no—
17C25×C11—21no—
18C22×D4×C11—22no—
19C22×D4×C11—22no—
20C22×D4×C11—21no—
21C22×D4×C11—44no—
22C22×D4×C11Q812yes—
23C23×C4×C11—21no—
24C23×C4×C11D412yes—
25C23×C4×C11C2311yescharacteristic
26C2×C11×C22⋊C4—44no—
27C2×C11×C22⋊C4—44no—
28C2×C11×C22⋊C4—44no—
29C2×C22⋊Dic11—22no—
30C2×C4⋊Dic11D412yes—
31C2×C4⋊Dic11D412yes—
32C2×Dic11⋊C4—22no—
33C2×Dic11⋊C4—22no—
34C22×C11⋊C8—22no—
35C11×#95—22no—
36C11×#95—22no—
37#66896—44no—
38#66896—44no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C22⋊(C11⋊C8)—22no—
43C22⋊(C11⋊C8)—22no—
44#10344—111nomaximal, Sylow
45C24×C11—24no—
46C24×C11—22no—
47C24×C11—42no—
48C24×C11—42no—
49C24×C11—42no—
50C24×C11—41no—
51C24×C11—41no—
52C24×C11—42no—
53C24×C11—42no—
54C24×C11C2×D411yescharacteristic
55C2×D4×C11—24no—
56C2×D4×C11—24no—
57C2×D4×C11—24no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—44no—
61C2×D4×C11—48no—
62C2×D4×C11—44no—
63C2×D4×C11—42no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—42no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—42no—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×Q811yescharacteristic
77C22×C4×C11#4112yes—
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C22×Dic11—22no—
81C11×C22⋊C4—416no—
82C22⋊Dic11—42no—
83C22⋊Dic11—42no—
84C4⋊Dic11—42no—
85C4⋊Dic11—42no—
86Dic11⋊C4—82no—
87Dic11⋊C4—82no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91#2646—111no—
92#1786—112no—
93#1438D1111yescharacteristic
94#1294—112no—
95#1280—111no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—22no—
99C23×C11—24no—
100C23×C11—44no—
101C23×C11—44no—
102C23×C11—42no—
103C23×C11—44no—
104C23×C11—44no—
105C23×C11—44no—
106C23×C11—44no—
107C23×C11—42no—
108C23×C11—44no—
109C23×C11—44no—
110C23×C11—82no—
111C23×C11—82no—
112C23×C11—82no—
113C23×C11—82no—
114C23×C11—82no—
115C23×C11—82no—
116C23×C11—81no—
117C23×C11—81no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11#12011yescharacteristic
121C23×C11C22⋊Q811yescharacteristic
122C23×C11#12411yescharacteristic
123C23×C11#13512yes—
124C23×C11AGL(1,ℤ/8)12yes—
125D4×C11—28no—
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—44no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—44no—
135C2×C4×C11—44no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—82no—
144C2×C4×C11C22⋊Q812yes—
145C2×C4×C11#12412yes—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C11⋊C8—82no—
153C23×D4C2×D1111yescharacteristic
154C22×C22⋊C4—22no—
155C2×#102—222no—
156C2×#102—222no—
157C2×C22⋊C8—112no—
158#400—222no—
159#398—222no—
160#385—222no—
161#380—112no—
162C2×#95C2×D1111yescharacteristic
163C2×#95C2×D1111yescharacteristic
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—48no—
173C22×C11—44no—
174C22×C11—84no—
175C22×C11—84no—
176C22×C11—84no—
177C22×C11—84no—
178C22×C11—84no—
179C22×C11—82no—
180C22×C11—82no—
181C22×C11#39311yescharacteristic
182C22×C11#44912yes—
183C22×C11#45311yescharacteristic
184C22×C11#45411yescharacteristic
185C22×C11B(4,𝔽2)12yes—
186C22×C11#47812yes—
187C22×C11#48811yescharacteristic
188C22×C11#49011yescharacteristic
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—82no—
192C4×C11—82no—
193Dic11—82no—
194Dic11—82no—
195C25—21no—
196C22×D4—21no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—44no—
200C22×D4Dic2212yes—
201C23×C4—21no—
202C23×C4C22⋊D1112yes—
203C23×C4C22×D1111yescharacteristic
204C22×C8—222no—
205C2×C4⋊C4—112no—
206C2×C4⋊C4—112no—
207C2×C4⋊C4—222no—
208C2×C4⋊C4—222no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—44no—
211C2×C22⋊C4—44no—
212C2×C22⋊C4—222no—
213#102—444no—
214#102—444no—
215C22⋊C8—222no—
216C22⋊C8—222no—
217#95—22no—
218#95—22no—
219#95—222no—
220#95—222no—
221#95—222no—
222C2×C11—21no—
223C2×C11—22no—
224C2×C11—21no—
225C2×C11—84no—
226C2×C11#159712yes—
227C2×C11#160012yes—
228C2×C11#202511yescharacteristic
229C2×C11#202711yescharacteristic
230C2×C11#202911yescharacteristic
231C24—24no—
232C24—22no—
233C24—42no—
234C24—42no—
235C24—42no—
236C24—42no—
237C24—41no—
238C24—41no—
239C24—42no—
240C24C2×C22⋊D1111yescharacteristic
241C2×D4—24no—
242C2×D4—24no—
243C2×D4—24no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—44no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—42no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—41no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4C2×Dic2211yescharacteristic
264C22×C4#433911yescharacteristic
265C22×C4D4×D1112yes—
266C22×C4#434112yes—
267C2×C8—442no—
268C2×C8—442no—
269C2×C8—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—882no—
273C4⋊C4—882no—
274C22⋊C4—416no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C11#1034411yescharacteristic, complemented, Sylow
278C23—22no—
279C23—21no—
280C23—21no—
281C23—24no—
282C23—44no—
283C23—44no—
284C23—42no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—42no—
290C23—44no—
291C23—44no—
292C23—82no—
293C23—82no—
294C23—82no—
295C23—82no—
296C23—82no—
297C23—82no—
298C23—81no—
299C23—81no—
300C23—81no—
301C23—81no—
302C23#6697711yescharacteristic
303C23#6698512yes—
304C23#6698911yescharacteristic
305C23#6699011yescharacteristic
306C23#6700312yes—
307D4—28no—
308D4—44no—
309D4—44no—
310D4—44no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
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—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—48no—
344C22—44no—
345C22—84no—
346C22—84no—
347C22—84no—
348C22—84no—
349C22—84no—
350C22—82no—
351C22—82no—
352C22#1062256011yescharacteristic
353C22#1062262212yes—
354C22#1062264512yes—
355C22#1062265012yes—
356C22#1062266911yescharacteristic
357C22#1062267511yescharacteristic
358C22#1062268411yescharacteristic
359C22#1062269011yescharacteristic
360C4—22no—
361C4—22no—
362C4—82no—
363C4—82no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—84no—
370C2#1306754312yes—
371C2#1306756012yes—
372C2#1306976211yescharacteristic
373C2#1306977211yescharacteristic
374C2#1306978011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1438C2
socleC23×C11#120
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#10344
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13074586C2semidirect
3. #13066495C2semidirect
4. #13066459C2semidirect
277. C11#10344semidirect

Maximal subgroups

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

subgroupindex
#130745862
#130685472
#130664952
#130664592
C11×#14382
#1034411