Finite Group Databasebeta

← #14642920

Subgroups — #14642920

Order 2816.

422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 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#13076560C211yesmaximal, characteristic
2#13070159C211yesmaximal, characteristic, complemented
3#13070026C211yesmaximal, characteristic, complemented
4#13070021C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic, complemented
8C11×#391C2211yescharacteristic
9#10622844—21no—
10C2×#66899—21no—
11C2×#66885—21no—
12C2×#66880—21no—
13#10622602—21no—
14C2×#66872—21no—
15#10622552C2211yescharacteristic
16#10622548C2211yescharacteristic
17#10622542C2211yescharacteristic
18#10622286—21no—
19#10622281—21no—
20#10622278—21no—
21#10622273—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622189—21no—
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C22×C11⋊C8—21no—
47C11×#95—21no—
48C11×#95—21no—
49#66899—42no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66885—42no—
56#66880—42no—
57#66872—42no—
58#7804—111nomaximal, Sylow
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×D44—21no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44SD1612yes—
77C2×C4×D11—81no—
78C2×C4×D11—81no—
79C2×C4×D11—81no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C42×C11—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—81no—
97(C2×D11)⋊C4—81no—
98(C2×D11)⋊C4—81no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—81no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2804—111no—
112#2096—111no—
113#2072—111no—
114#2071—111no—
115#1272—111no—
116#1272D1111yescharacteristic, complemented
117#1270—111no—
118C23×C11#12011yescharacteristic
119C22×D11—22no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126Q8×C11—42no—
127Q8×C11—81no—
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—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158D44—42no—
159D44—81no—
160C4×D11—84no—
161Dic22—42no—
162Dic22—81no—
163C8×C11—81no—
164C8×C11—81no—
165C11⋊C8—42no—
166C2×#106—221no—
167C2×#103—221no—
168C2×#103—221no—
169C2×#102—221no—
170#400—221no—
171#393—221no—
172#393—221no—
173#391—111no—
174#391C2×D1111yescharacteristic
175#390—111no—
176#386—221no—
177#385—221no—
178#385—221no—
179#384—111no—
180#340—221no—
181#340—221no—
182#336—111no—
183#336C2×D1111yescharacteristic
184#336C2×D1111yescharacteristic
185C22×C11#44811yescharacteristic
186C22×C11#44911yescharacteristic
187C22×C11#45211yescharacteristic
188C22×C11#45311yescharacteristic
189C22×C11#45511yescharacteristic
190C22×C11#45511yescharacteristic
191C22×C11#45811yescharacteristic
192C2×D11—42no—
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—81no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210Dic11—161no—
211C22×Q8—111no—
212C22×Q8D4411yescharacteristic
213C22×D4—111no—
214C23×C4—221no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—221no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4D4411yescharacteristic
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42C22×D1111yescharacteristic
231#106—442no—
232#103—442no—
233#103—442no—
234#102—442no—
235#95—21no—
236#95—21no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242C2×C11#160811yescharacteristic
243C2×C11#161211yescharacteristic
244C2×C11#161811yescharacteristic
245C2×C11#162211yescharacteristic
246C2×C11#164011yescharacteristic
247C2×C11#164311yescharacteristic
248C2×C11#165911yescharacteristic
249D11—82no—
250C24—221no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×D4—112no—
260C2×D4—221no—
261C2×D4—441no—
262C2×D4—441no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—441no—
269C22×C4—881no—
270C22×C4—881no—
271C22×C4—881no—
272C22×C4C2×D4411yescharacteristic
273C22×C4D4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—881no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—881no—
299C22⋊C4—881no—
300C22⋊C4—881no—
301C42—41no—
302C11#780411yescharacteristic, complemented, Sylow
303C23—222no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23#6693511yescharacteristic
311Q8—42no—
312Q8—81no—
313Q8—442no—
314Q8—881no—
315D4—442no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—884no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4#6695711yescharacteristic
343C2×C4#6696211yescharacteristic
344C2×C4SD16×D1111yescharacteristic
345C2×C4#6696711yescharacteristic
346C2×C4#6697111yescharacteristic
347C2×C4#6697211yescharacteristic
348C8—81no—
349C8—81no—
350C8—442no—
351C22—442no—
352C22—442no—
353C22—442no—
354C22—881no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22#1062234611yescharacteristic
359C22#1062235511yescharacteristic
360C22#1062236011yescharacteristic
361C22#1062241911yescharacteristic
362C22#1062242411yescharacteristic
363C22#1062243811yescharacteristic
364C22#1062243811yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—81no—
372C4—81no—
373C4—881no—
374C4—881no—
375C4—881no—
376C4—1761no—
377C2—882no—
378C2#1306760811yescharacteristic
379C2#1306763311yescharacteristic
380C2#1306766611yescharacteristic
381C2#1306768911yescharacteristic
382C2#1306780511yescharacteristic
383C2#1306782611yescharacteristic
384C2#1306792311yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1272D11
hypocenterC11#7804
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13070159C2semidirect
3. #13070026C2semidirect
5. #13066441C2semidirect
7. C11×#1272C2semidirect
116. #1272D11semidirect
302. C11#7804semidirect

Maximal subgroups

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

subgroupindex
#130765602
#130701592
#130700262
#130700212
#130664412
#130664362
C11×#12722
#780411