Finite Group Databasebeta

← #14651157

Subgroups — #14651157

Order 2816.

730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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#13077639C211yesmaximal, characteristic, complemented
2#13073558C211yesmaximal, characteristic
3#13068605C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic, complemented
5#13067283C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×#66948—22no—
9C2×#66927—21no—
10C2×#66927C2211yescharacteristic
11C2×C4×D44C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C2×#66887—21no—
16#10622552—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622447—22no—
20D11×C22⋊C8—22no—
21C8×D44—22no—
22#10622284C414yes—
23#10622192—21no—
24#10622123—22no—
25#10622123—22no—
26C22×D44—21no—
27C22×D44—21no—
28C22×D44—24no—
29C22×D44C2×C412yes—
30C22×D44D411yescharacteristic
31C22×C4×D11D412yes—
32C2×C11×M16—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—24no—
37C2×(C2×D11)⋊C4C2×C412yes—
38C2×C4⋊Dic11D411yescharacteristic
39C2×#4318—21no—
40C2×C8×D11—24no—
41#66948—48no—
42#66927—21no—
43#66927—21no—
44#66927—21no—
45#66927—21no—
46#66927—42no—
47#66927—42no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yescomplemented
55C11×C22⋊C8—21no—
56C4×C8×C11—21no—
57C11×#95C2×C412yes—
58C22⋊(C11⋊C8)—21no—
59#66887—42no—
60(C2×D11)⋊C8—24no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yescomplemented
64C4×C11⋊C8—21no—
65#9397—111nomaximal, Sylow
66C23×D11—22no—
67C23×D11C22⋊C412yes—
68C22×C4×C11—22no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11C22⋊C412yes—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—44no—
80C2×D44—48no—
81C2×D44—48no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—82no—
91C2×D44—84no—
92C2×D44D812yes—
93C2×D44SD1612yes—
94C2×C4×D11—22no—
95C2×C4×D11—22no—
96C2×C4×D11—44no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C11×C4⋊C4—24no—
102C42×C11—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—48no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113#4318—41no—
114#4318—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117C8×D11—84no—
118#2972—111no—
119#2541—111no—
120#1800—111no—
121#1545—111no—
122#1545—111no—
123#1303—111no—
124#1303D1111yescharacteristic, complemented
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—22no—
127C22×D11—22no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—44no—
131C22×D11—44no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11#10214yes—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—42no—
153D44—22no—
154D44—22no—
155D44—22no—
156D44—22no—
157D44—82no—
158D44—82no—
159D44—82no—
160D44—816no—
161D44—82no—
162D44—81no—
163D44—81no—
164D44—81no—
165D44—81no—
166C4×D11—44no—
167C4×D11—82no—
168C8×C11—42no—
169C8×C11—81no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C2×#127—111no—
173C2×#127—221no—
174C2×#121—222no—
175C2×C4×D4—111no—
176C8×D4—222no—
177C8×D4—222no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#423—111no—
181#423C2×D1111yescharacteristic
182C2×#100—221no—
183C2×C22⋊C8—222no—
184#392—114no—
185#390—221no—
186C4×C4⋊C4C2×D1111yescharacteristic
187#343—221no—
188#331—222no—
189#331—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11C2×#10211yescharacteristic
194C22×C11#41611yescharacteristic
195C2×D11—24no—
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—44no—
199C2×D11—82no—
200C2×D11—84no—
201C2×D11—84no—
202C2×D11—82no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—44no—
209C4×C11#45312yes—
210C4×C11#46511yescharacteristic
211C4×C11#46511yescharacteristic
212C4×C11#46611yescharacteristic
213C4×C11#46611yescharacteristic
214Dic11—42no—
215C22×D4—112no—
216C22×D4—111no—
217C22×D4—224no—
218C22×D4—221no—
219C22×D4—221no—
220C23×C4—112no—
221C2×M16—21no—
222C2×M16—221no—
223C22×C8—224no—
224#127—221no—
225#127—221no—
226#127—221no—
227#127—221no—
228#127—442no—
229#127—442no—
230#121—448no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234C4×D4—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—111no—
237C2×C22⋊C4—112no—
238C2×C22⋊C4—224no—
239C2×C42—21no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8D4412yescomplemented
247#100—442no—
248C22⋊C8—21no—
249C22⋊C8—224no—
250C22⋊C8—221no—
251C4×C8—21no—
252C4×C8—221no—
253#95C4×D1112yes—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#188711yescharacteristic
257C2×C11#189311yescharacteristic
258C2×C11#191411yescharacteristic
259D11—44no—
260D11—162no—
261C24—112no—
262C24—222no—
263C2×D4—112no—
264C2×D4—112no—
265C2×D4—222no—
266C2×D4—221no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—444no—
272C2×D4—448no—
273C2×D4—448no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—884no—
283C2×D4—882no—
284C22×C4—22no—
285C22×C4—112no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—444no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292M16—41no—
293M16—41no—
294M16—441no—
295M16—441no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—222no—
299C2×C8—441no—
300C2×C8—884no—
301C4⋊C4—24no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—448no—
307C42—41no—
308C42—41no—
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42#434311yescharacteristic
313C11#939711yescharacteristic, complemented, Sylow
314C23—114no—
315C23—222no—
316C23—222no—
317C23—442no—
318C23—442no—
319C23—444no—
320C23—444no—
321C23—442no—
322C23—442no—
323C23—442no—
324C23C22⋊C4×D1111yescharacteristic
325D4—222no—
326D4—222no—
327D4—222no—
328D4—222no—
329D4—882no—
330D4—882no—
331D4—882no—
332D4—8816no—
333D4—881no—
334D4—881no—
335D4—881no—
336D4—881no—
337D4—882no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—222no—
344C2×C4—444no—
345C2×C4—442no—
346C2×C4—882no—
347C2×C4C4×D4411yescharacteristic
348C2×C4#6693511yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6694611yescharacteristic
351C2×C4#6694711yescharacteristic
352C2×C4#6694811yescharacteristic
353C2×C4D8×D1111yescharacteristic
354C2×C4SD16×D1111yescharacteristic
355C2×C4#6696911yescharacteristic
356C2×C4#6697211yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—224no—
364C22—444no—
365C22—442no—
366C22—442no—
367C22—882no—
368C22—884no—
369C22—884no—
370C22—882no—
371C22—882no—
372C22—882no—
373C22#1062227811yescharacteristic
374C22D11×#10211yescharacteristic
375C22#1062241711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—442no—
381C4#1062238811yescharacteristic
382C4#1062242011yescharacteristic
383C4#1062243512yes—
384C4#1062247711yescharacteristic
385C4#1062249611yescharacteristic
386C2—21no—
387C2—21no—
388C2—444no—
389C2—1762no—
390C2#1306901311yescharacteristic
391C2#1306904311yescharacteristic
392C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radical#13073558C2
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9397
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
1. #13077639C2semidirect
3. #13068605C2semidirect
4. #13067285C2semidirect
5. #13067283C2semidirect
6. #13066519C2semidirect
7. C11×#1303C2semidirect
54. C11×C4⋊C8D4semidirect
63. C4⋊(C11⋊C8)D4semidirect
124. #1303D11semidirect
246. C4⋊C8D44semidirect
313. C11#9397semidirect

Maximal subgroups

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

subgroupindex
#130776392
#130735582
#130686052
#130672852
#130672832
#130665192
C11×#13032
#939711