Finite Group Databasebeta

← #14656189

Subgroups — #14656189

Order 2816.

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

normal subgroups only

This group has 740 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, complemented
2#13078413C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067114C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2541C211yesmaximal, characteristic
8C2×C11×#127—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C11×#121—22no—
11C2×C4×D4×C11C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#392—22no—
14C11×#390—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16#10622831—22no—
17#10622828—21no—
18#10622689—21no—
19#10622688—22no—
20#10622683—21no—
21#10622622—22no—
22#10622621—21no—
23#10622620—21no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29D4⋊(C11⋊C8)—22no—
30#10622090—22no—
31C22×D4×C11—24no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11D412yes—
36C23×C4×C11—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—42no—
42C11×#127—42no—
43C11×#121—48no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4324—24no—
55#66979—21no—
56#66977—21no—
57#66977—21no—
58C2×#4318—21no—
59#66923—21no—
60#66922D411yescharacteristic, complemented
61#66922D411yescharacteristic, complemented
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×#95D412yes—
65#66896—22no—
66#66896—22no—
67#66896—24no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66872—22no—
71#66871—22no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yescomplemented
75C4⋊(C11⋊C8)D412yescomplemented
76C4×C11⋊C8—21no—
77C4×C11⋊C8—21no—
78#10246—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—44no—
89C2×D4×C11—48no—
90C2×D4×C11—48no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—82no—
100C2×D4×C11—84no—
101C2×D4×C11SD1612yescomplemented
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—44no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C2×Dic22—21no—
111C2×Dic22—21no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C22⋊C4—48no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C22⋊Dic11—41no—
125#4324—84no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—41no—
133#4318—41no—
134#4318—41no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3208—111no—
139#3077—111no—
140#2541D1111yescharacteristic
141#1545—111no—
142#1503—111no—
143#1478—111no—
144#1303—111no—
145C23×C11—22no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—44no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11#12011yescharacteristic
156D4×C11—22no—
157D4×C11—22no—
158D4×C11—41no—
159D4×C11—44no—
160D4×C11—41no—
161D4×C11—82no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—816no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×SD1611yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11#13711yescharacteristic
188C2×Dic11—41no—
189C2×Dic11—41no—
190Dic22—42no—
191Dic22—81no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194C11⋊C8—81no—
195#533—111no—
196C2×#127—21no—
197C2×#127C2×D1111yescharacteristic
198C2×#121—22no—
199C2×C4×D4C2×D1111yescharacteristic
200#492—221no—
201#486—221no—
202#478—222no—
203#476—221no—
204#474—221no—
205#460—222no—
206#450—222no—
207#431—111no—
208#431—111no—
209#428—221no—
210#423—111no—
211#418—221no—
212#392—22no—
213#390—21no—
214C4×C4⋊C4C2×D1111yescharacteristic
215#331—222no—
216#328—222no—
217D4⋊C8—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—84no—
224C22×C11—84no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11#39211yescharacteristic
231C22×C11#45011yescharacteristic
232C22×C11#45211yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—44no—
237C4×C11—81no—
238C4×C11#44811yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#45312yes—
241C4×C11#46511yescharacteristic
242C4×C11#46811yescharacteristic
243Dic11—81no—
244Dic11—81no—
245C22×D4—24no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4C22⋊D1111yescharacteristic
249C22×D4C22⋊D1112yes—
250C23×C4—21no—
251C2×SD16—224no—
252C2×M16—221no—
253C4⋊Q8—111no—
254C4⋊Q8—111no—
255#127—21no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127—42no—
260#127—42no—
261#125—221no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264#121—48no—
265C4×Q8—221no—
266C4×Q8—221no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271#117—221no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4—24no—
275C2×C22⋊C4—21no—
276C2×C42—21no—
277C2×C42C22×D1111yescharacteristic
278#107—222no—
279#106—222no—
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#102—222no—
285#102—222no—
286#102—224no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C4×C8—221no—
290C4×C8—221no—
291#95C22⋊D1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11—162no—
296C2×C11#200011yescharacteristic
297C2×C11#200211yescharacteristic
298C2×C11#200811yescharacteristic
299C24—21no—
300C24—22no—
301C2×Q8—221no—
302C2×Q8—221no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—44no—
311C2×D4—48no—
312C2×D4—48no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—82no—
322C2×D4—84no—
323C2×D4#432412yescomplemented
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—44no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332SD16—884no—
333M16—441no—
334M16—441no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—24no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C22⋊C4—48no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—441no—
351C42—41no—
352C42—41no—
353C42—441no—
354C42D4×D1111yescharacteristic
355C42D4×D1111yescharacteristic
356C42D4×D1111yescharacteristic
357C42#434111yescharacteristic
358C11#1024611yescharacteristic, complemented, Sylow
359C23—22no—
360C23—42no—
361C23—42no—
362C23—44no—
363C23—44no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#6700611yescharacteristic
370Q8—442no—
371Q8—881no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—41no—
376D4—44no—
377D4—82no—
378D4—82no—
379D4—82no—
380D4—816no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4#6698511yescharacteristic
397C2×C4C2×#432411yescharacteristic
398C2×C4#6699011yescharacteristic
399C2×C4#6699011yescharacteristic
400C2×C4#6699111yescharacteristic
401C2×C4#6699211yescharacteristic
402C2×C4#6699211yescharacteristic
403C2×C4#6699311yescharacteristic
404C2×C4#6700311yescharacteristic
405C2×C4#6700411yescharacteristic
406C8—442no—
407C8—442no—
408C8—881no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—84no—
415C22—84no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22#1062283111yescharacteristic
422C22#1062283611yescharacteristic
423C22#1062285211yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—44no—
428C4—81no—
429C4—881no—
430C4—881no—
431C4#1062265011yescharacteristic
432C4#1062265311yescharacteristic
433C4#1062265411yescharacteristic
434C4#1062265511yescharacteristic
435C4#1062269012yes—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—162no—
440C2#1306961911yescharacteristic
441C2#1306963111yescharacteristic
442C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2541C2
socleC22×C11#392
hypercenter#2541D11
hypocenterC11#10246
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078413C2semidirect
3. #13067284C2semidirect
4. #13067114C2semidirect
5. #13067007C2semidirect
6. #13066519C2semidirect
60. #66922D4semidirect
61. #66922D4semidirect
74. C4⋊(C11⋊C8)D4semidirect
75. C4⋊(C11⋊C8)D4semidirect
101. C2×D4×C11SD16semidirect
323. C2×D4#4324semidirect
358. C11#10246semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784132
#130672842
#130671142
#130670072
#130665192
C11×#25412
#1024611