Finite Group Databasebeta

← #14656218

Subgroups — #14656218

Order 2816.

604 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079559C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13073615C211yesmaximal, characteristic
4#13067283C211yesmaximal, characteristic
5#13067116C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#67000—21no—
10C2×#66927C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622838—21no—
15#10622635—22no—
16#10622634—21no—
17#10622633—21no—
18#10622604—22no—
19#10622601—21no—
20#10622577—21no—
21#10622552—22no—
22C4×C4⋊Dic11C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622461—22no—
25#10622344—22no—
26#10622307—21no—
27#10622306—21no—
28C11×Q8⋊C8—22no—
29#10622123—22no—
30#10622105—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44D412yes—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#67000—42no—
44#67000—42no—
45C2×(C2×D11)⋊C4—24no—
46C2×(C2×D11)⋊C4—24no—
47#66979—21no—
48C2×C4⋊Dic11—21no—
49#66977—21no—
50#66977—21no—
51C2×C4×Dic11—21no—
52C2×#4318—21no—
53C2×#4314—24no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66923—21no—
59#66922D411yescharacteristic
60#66922D411yescharacteristic
61C4×Dic22—21no—
62C4×Dic22—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69#66899—22no—
70#66899—22no—
71C11⋊#95D412yes—
72#66885—24no—
73#66872—22no—
74#66871—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77#10250—111nomaximal, Sylow
78C23×D11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11SD1612yescomplemented
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—44no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—82no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—48no—
119(C2×D11)⋊C4—84no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—42no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—22no—
133#4314—84no—
134#3208—111no—
135#3078—111no—
136#2548—111no—
137#1545—111no—
138#1503—111no—
139#1479D1111yescharacteristic, complemented
140#1303—111no—
141C23×C11#12011yescharacteristic
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173D44—44no—
174D44—82no—
175D44—82no—
176D44—82no—
177D44—81no—
178D44—81no—
179D44—81no—
180D44—81no—
181Dic22—42no—
182Dic22—81no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—42no—
186#533—111no—
187C2×#127—111no—
188C2×#124—221no—
189C2×C4×Q8C2×D1111yescharacteristic
190#492—221no—
191#486—221no—
192#479—222no—
193#477—221no—
194#475—221no—
195#460—222no—
196#450—222no—
197#431C2×D1111yescharacteristic
198#431C2×D1111yescharacteristic
199#428—221no—
200#423—111no—
201#419—221no—
202#394—222no—
203#390—222no—
204#390—221no—
205C4×C4⋊C4—111no—
206#331—222no—
207#328—222no—
208Q8⋊C8—22no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#39211yescharacteristic
212C22×C11#45011yescharacteristic
213C22×C11#45211yescharacteristic
214C2×D11—84no—
215C2×D11—84no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—42no—
223C4×C11—81no—
224C4×C11#44811yescharacteristic
225C4×C11#44911yescharacteristic
226C4×C11#45512yes—
227C4×C11#46511yescharacteristic
228C4×C11#46811yescharacteristic
229Dic11—82no—
230Dic11—81no—
231Dic11—81no—
232C22×Q8D4411yescharacteristic
233C22×D4—112no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—224no—
237C2×M16—221no—
238C4⋊Q8—111no—
239C4⋊Q8—111no—
240#127—221no—
241#127—221no—
242#127—221no—
243#127—221no—
244#125—221no—
245#124—442no—
246#124—442no—
247C22⋊Q8—221no—
248C22⋊Q8—221no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—221no—
254C4×Q8—221no—
255#117—221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4D4411yescharacteristic
259C2×C22⋊C4—224no—
260C2×C22⋊C4—224no—
261C2×C42—21no—
262C2×C42—221no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—222no—
271#103—222no—
272#102—224no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277#95—112no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11#200011yescharacteristic
281C2×C11#200411yescharacteristic
282C2×C11#200811yescharacteristic
283D11—162no—
284C24—222no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—221no—
291C2×Q8—221no—
292C2×Q8#431412yescomplemented
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—444no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—882no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—222no—
308C22×C4C2×D4411yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311SD16—884no—
312M16—441no—
313M16—441no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—222no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—442no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—448no—
329C22⋊C4—441no—
330C22⋊C4—884no—
331C42—41no—
332C42—41no—
333C42—441no—
334C42—441no—
335C42—441no—
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C11#1025011yescharacteristic, complemented, Sylow
341C23—444no—
342C23—444no—
343C23—442no—
344C23—442no—
345C23—442no—
346C23#6693511yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—442no—
352Q8—881no—
353D4—444no—
354D4—882no—
355D4—882no—
356D4—882no—
357D4—881no—
358D4—881no—
359D4—881no—
360D4—881no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4#6693511yescharacteristic
374C2×C4#6693711yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4C2×#431411yescharacteristic
377C2×C4#6695711yescharacteristic
378C2×C4#6696111yescharacteristic
379C2×C4#6696211yescharacteristic
380C2×C4#6698311yescharacteristic
381C2×C4#6699011yescharacteristic
382C2×C4#6699311yescharacteristic
383C8—42no—
384C8—81no—
385C8—442no—
386C22—21no—
387C22—21no—
388C22—884no—
389C22—884no—
390C22—882no—
391C22—882no—
392C22—882no—
393C22#1062234411yescharacteristic
394C22#1062234611yescharacteristic
395C22#1062257311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—882no—
402C4—881no—
403C4—881no—
404C4#1062234711yescharacteristic
405C4#1062235111yescharacteristic
406C4#1062272711yescharacteristic
407C4#1062274711yescharacteristic
408C4#1062281512yes—
409C2—21no—
410C2—21no—
411C2—1762no—
412C2#1306962111yescharacteristic
413C2#1306964611yescharacteristic
414C2#1306967011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1479D11
hypocenterC11#10250
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
5. #13067116C2semidirect
6. #13066518C2semidirect
7. C11×#1479C2semidirect
84. C2×Q8×C11SD16semidirect
139. #1479D11semidirect
292. C2×Q8#4314semidirect
340. C11#10250semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784212
#130736152
#130672832
#130671162
#130665182
C11×#14792
#1025011