Finite Group Databasebeta

← #14655747

Subgroups — #14655747

Order 2816.

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

normal subgroups only

This group has 592 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, complemented
2#13078413C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic
4#13067283C211yesmaximal, characteristic, complemented
5#13067020C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4323—21no—
10C2×#66927C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622828—21no—
15#10622628—22no—
16#10622628—22no—
17#10622622—22no—
18#10622621—21no—
19#10622620—21no—
20C2×#66873—21no—
21#10622577—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622461—22no—
25#10622344—22no—
26#10622307—21no—
27#10622306—21no—
28C11×#323—22no—
29#10622123—22no—
30#10622094—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4323—24no—
44C2×#4323—42no—
45C2×#4323—42no—
46#66979—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51C2×#4314—24no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927D412yes—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66896—22no—
68#66896—22no—
69#66885—24no—
70#66873—24no—
71#66872—22no—
72#66871—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10178—111nomaximal, Sylow
78C24×C11—21no—
79C23×D11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11SD1612yescomplemented
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—82no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—82no—
104C2×D44—82no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C22⋊Dic11—41no—
118#4323—48no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—41no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#4314—84no—
133#3208—111no—
134#3077—111no—
135C2×#459—111no—
136#1545—111no—
137#1481—111no—
138#1460D1111yescharacteristic, complemented
139#1301—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146C22×D11—42no—
147C22×D11—82no—
148C22×D11—82no—
149C22×D11—81no—
150C22×D11—81no—
151D4×C11—22no—
152D4×C11—22no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×SD1611yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C2×Dic11—41no—
172C2×Dic11—41no—
173D44—44no—
174D44—42no—
175D44—42no—
176D44—82no—
177D44—82no—
178D44—81no—
179D44—81no—
180D44—82no—
181Dic22—42no—
182Dic22—42no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C22×D8—221no—
188#533—111no—
189C2×#127—111no—
190C2×C4×D4C2×D1111yescharacteristic
191#492—221no—
192#486—221no—
193#478—222no—
194#476—221no—
195#474—221no—
196#460—222no—
197#459—222no—
198#459—222no—
199#450—222no—
200#431C2×D1111yescharacteristic
201#431C2×D1111yescharacteristic
202#428—221no—
203#423—111no—
204C2×C4⋊C8—111no—
205#418—221no—
206C2×#102—221no—
207#331—222no—
208Q8⋊C8—222no—
209#323—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—42no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#39211yescharacteristic
218C22×C11#46511yescharacteristic
219C22×C11#46811yescharacteristic
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—162no—
224C2×D11—162no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11#44811yescharacteristic
230C4×C11#44911yescharacteristic
231C4×C11#45011yescharacteristic
232C4×C11#45211yescharacteristic
233C4×C11#47212yes—
234Dic11—81no—
235Dic11—81no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4—221no—
239C22×D4D4411yescharacteristic
240C23×C4—21no—
241C2×SD16—224no—
242C2×D8—224no—
243C2×D8—442no—
244C2×D8—442no—
245C2×M16—221no—
246C22×C8—221no—
247C4⋊Q8—111no—
248C4⋊Q8—111no—
249#127—112no—
250#127—221no—
251#127—221no—
252#127—221no—
253#125—221no—
254C22⋊Q8—221no—
255C22⋊Q8—221no—
256C4×Q8—221no—
257C4×Q8—221no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262#117—221no—
263C2×C4⋊C4D4411yescharacteristic
264C2×C22⋊C4—21no—
265C2×C42C22×D1111yescharacteristic
266#107—222no—
267#106—222no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274#102—224no—
275#102—224no—
276#102—222no—
277#102—222no—
278C22⋊C8—21no—
279C22⋊C8C22⋊D1112yes—
280C4×C8—21no—
281C4×C8—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—82no—
285C2×C11#200011yescharacteristic
286C2×C11#200811yescharacteristic
287C2×C11#201811yescharacteristic
288D11—162no—
289C24—21no—
290C24—441no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—222no—
299C2×D4—222no—
300C2×D4—222no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—882no—
309C2×D4—882no—
310C2×D4#431412yescomplemented
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4C2×D4411yescharacteristic
316C22×C4#433911yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318SD16—884no—
319D8—448no—
320M16—441no—
321M16—441no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—441no—
327C2×C8—441no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—441no—
339C42—441no—
340C42D4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42D4×D1111yescharacteristic
343C42D4×D1111yescharacteristic
344C11#1017811yescharacteristic, complemented, Sylow
345C23—22no—
346C23—41no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23—442no—
351C23—882no—
352C23—882no—
353C23—881no—
354C23—881no—
355C23#6698311yescharacteristic
356Q8—442no—
357Q8—442no—
358D4—22no—
359D4—22no—
360D4—41no—
361D4—41no—
362D4—444no—
363D4—442no—
364D4—442no—
365D4—882no—
366D4—882no—
367D4—881no—
368D4—881no—
369D4—882no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—81no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4#6693511yescharacteristic
379C2×C4#6693511yescharacteristic
380C2×C4#6693711yescharacteristic
381C2×C4#6693711yescharacteristic
382C2×C4C2×#431411yescharacteristic
383C2×C4#6695711yescharacteristic
384C2×C4#6696111yescharacteristic
385C2×C4#6696211yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699311yescharacteristic
388C8—42no—
389C8—81no—
390C8—442no—
391C8—442no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—82no—
396C22—82no—
397C22—81no—
398C22—81no—
399C22—882no—
400C22—882no—
401C22—882no—
402C22—1762no—
403C22—1762no—
404C22#1062257311yescharacteristic
405C22#1062272711yescharacteristic
406C22#1062274711yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—881no—
412C4—881no—
413C4#1062234411yescharacteristic
414C4#1062234611yescharacteristic
415C4#1062234711yescharacteristic
416C4#1062235111yescharacteristic
417C4#1062236212yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—1762no—
422C2#1306962111yescharacteristic
423C2#1306966811yescharacteristic
424C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radicalC2×#10622628C2
hypercenter#1460D11
hypocenterC11#10178
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #13079559C2semidirect
2. #13078413C2semidirect
4. #13067283C2semidirect
5. #13067020C2semidirect
6. #13066512C2semidirect
7. C11×#1460C2semidirect
85. C2×D4×C11SD16semidirect
138. #1460D11semidirect
310. C2×D4#4314semidirect
344. C11#10178semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784132
C2×#106226282
#130672832
#130670202
#130665122
C11×#14602
#1017811