Finite Group Databasebeta

← #14656217

Subgroups — #14656217

Order 2816.

604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079557C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic
4#13067114C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2548C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C2×C11×#124—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#394—22no—
13C11×#390—22no—
14C11×#390—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16#10622838—21no—
17#10622831—22no—
18#10622689—21no—
19#10622688—22no—
20#10622683—21no—
21#10622635—22no—
22#10622634—21no—
23#10622633—21no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622090—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#124—42no—
40C11×#124—42no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—24no—
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4324—24no—
54#66979—21no—
55#66977—21no—
56#66977—21no—
57C2×#4318—21no—
58#66923—21no—
59#66922D411yescharacteristic
60#66922D411yescharacteristic
61C4×Dic22—21no—
62C4×Dic22—21no—
63C11×#95D412yes—
64#66899—22no—
65#66899—22no—
66#66896—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10250—111nomaximal, Sylow
78C24×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11SD1612yescomplemented
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—82no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C2×Dic22—21no—
104C2×Dic22—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—48no—
111C11×C22⋊C4—84no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C22⋊Dic11—41no—
121#4324—84no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129#4318—41no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3208—111no—
135#3078—111no—
136#2548D1111yescharacteristic
137#1545—111no—
138#1503—111no—
139#1479—111no—
140#1303—111no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11#12011yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151D4×C11—44no—
152D4×C11—82no—
153D4×C11—82no—
154D4×C11—82no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×SD1611yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—41no—
180C2×Dic11—41no—
181Dic22—42no—
182Dic22—81no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186#533—111no—
187C2×#127C2×D1111yescharacteristic
188C2×#124—21no—
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#431—111no—
198#431—111no—
199#428—221no—
200#423—111no—
201#419—221no—
202#394—22no—
203#390—22no—
204#390—21no—
205C4×C4⋊C4C2×D1111yescharacteristic
206#331—222no—
207#328—222no—
208Q8⋊C8—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—84no—
212C22×C11—84no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11#39211yescharacteristic
217C22×C11#45011yescharacteristic
218C22×C11#45211yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—42no—
223C4×C11—82no—
224C4×C11—81no—
225C4×C11#44811yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#45512yes—
228C4×C11#46511yescharacteristic
229C4×C11#46811yescharacteristic
230Dic11—81no—
231Dic11—81no—
232C22×Q8C22⋊D1111yescharacteristic
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C22⋊D1112yes—
236C2×SD16—224no—
237C2×M16—221no—
238C4⋊Q8—111no—
239C4⋊Q8—111no—
240#127—21no—
241#127—21no—
242#127—21no—
243#127—21no—
244#125—221no—
245#124—42no—
246#124—42no—
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—21no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270#103—222no—
271#103—222no—
272#102—224no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C4×C8—221no—
276C4×C8—221no—
277#95C22⋊D1112yes—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—162no—
281C2×C11#200011yescharacteristic
282C2×C11#200411yescharacteristic
283C2×C11#200811yescharacteristic
284C24—22no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—221no—
291C2×Q8—221no—
292C2×Q8#432412yescomplemented
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—44no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—82no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311SD16—884no—
312M16—441no—
313M16—441no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—441no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—48no—
329C22⋊C4—84no—
330C22⋊C4—441no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—441no—
336C42D4×D1111yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42#434111yescharacteristic
340C11#1025011yescharacteristic, complemented, Sylow
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23#6700611yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—442no—
352Q8—881no—
353D4—44no—
354D4—82no—
355D4—82no—
356D4—82no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4#6698511yescharacteristic
374C2×C4C2×#432411yescharacteristic
375C2×C4#6699011yescharacteristic
376C2×C4#6699011yescharacteristic
377C2×C4#6699111yescharacteristic
378C2×C4#6699211yescharacteristic
379C2×C4#6699211yescharacteristic
380C2×C4#6699311yescharacteristic
381C2×C4#6700311yescharacteristic
382C2×C4#6700411yescharacteristic
383C8—442no—
384C8—442no—
385C8—881no—
386C22—21no—
387C22—21no—
388C22—84no—
389C22—84no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22#1062283111yescharacteristic
394C22#1062283611yescharacteristic
395C22#1062285211yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4—881no—
403C4—881no—
404C4#1062265011yescharacteristic
405C4#1062265311yescharacteristic
406C4#1062265411yescharacteristic
407C4#1062265511yescharacteristic
408C4#1062267412yes—
409C2—21no—
410C2—21no—
411C2—162no—
412C2#1306961911yescharacteristic
413C2#1306964511yescharacteristic
414C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2548C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#2548D11
hypocenterC11#10250
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2548

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
4. #13067114C2semidirect
5. #13067011C2semidirect
6. #13066519C2semidirect
84. C2×Q8×C11SD16semidirect
292. C2×Q8#4324semidirect
340. C11#10250semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784212
#130672842
#130671142
#130670112
#130665192
C11×#25482
#1025011