Finite Group Databasebeta

← #14656941

Subgroups — #14656941

Order 2816.

422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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#13073841C211yesmaximal, characteristic
2#13069600C211yesmaximal, characteristic
3#13067187C211yesmaximal, characteristic
4C2×#10622105C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic
6#13066462C211yesmaximal, characteristic
7C11×#1289C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C11×#380C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C4×C22⋊Dic11C2211yescharacteristic
13C2×C11⋊#95C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15#10622599—21no—
16#10622597—21no—
17#10622563—21no—
18#10622555—21no—
19#10622268—21no—
20#10622267—21no—
21#10622165—21no—
22#10622165—21no—
23#10622105—21no—
24#10622105—21no—
25#10622090—21no—
26#10622090—21no—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—21no—
29C22×Dic22Q811yescharacteristic
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11D411yescharacteristic
37C2×C22⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11Q811yescharacteristic
41#66977—21no—
42#66977—21no—
43#66977—21no—
44#66977—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#10377—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—81no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×Q811yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—42no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86C22×Dic11—81no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—81no—
90C2×C8×C11—41no—
91C2×C8×C11—81no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—42no—
107C4⋊Dic11—81no—
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—81no—
112C4×Dic11—81no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—81no—
115#2569—111no—
116#1996—111no—
117#1520—111no—
118C2×#328—111no—
119#1294—111no—
120#1289D1111yescharacteristic
121#1282—111no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11#12011yescharacteristic
125C23×C11C22⋊Q811yescharacteristic
126C23×C11#12411yescharacteristic
127C23×C11#13511yescharacteristic
128C23×C11#13511yescharacteristic
129C23×C11#13711yescharacteristic
130C23×C11#13711yescharacteristic
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11#12411yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—82no—
165C2×Dic11—82no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168Dic22—81no—
169Dic22—81no—
170C8×C11—81no—
171C11⋊C8—81no—
172C2×C22⋊Q8—111no—
173C2×C22⋊C8—111no—
174C2×C22⋊C8C2×D1111yescharacteristic
175#400—221no—
176#398—221no—
177#387—221no—
178#387—221no—
179#385—221no—
180#380—221no—
181#380C2×D1111yescharacteristic
182#380C2×D1111yescharacteristic
183C4×C22⋊C4—111no—
184C2×#95—111no—
185#342—221no—
186#342—221no—
187#328—221no—
188#328—221no—
189#328—221no—
190#328—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11#39311yescharacteristic
202C22×C11#45211yescharacteristic
203C22×C11#45211yescharacteristic
204C22×C11#47911yescharacteristic
205C22×C11#47911yescharacteristic
206C22×C11#48811yescharacteristic
207C22×C11#49111yescharacteristic
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—161no—
215Dic11—42no—
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219Dic11—81no—
220Dic11—81no—
221C22×Q8—111no—
222C23×C4—221no—
223C23×C4C22×D1111yescharacteristic
224C22×C8—21no—
225C22×C8—221no—
226C22⋊Q8—221no—
227C22⋊Q8—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—221no—
243C2×C42—221no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—221no—
247C22⋊C8—221no—
248#95—21no—
249#95—111no—
250#95—111no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95D4411yescharacteristic
258#95D4411yescharacteristic
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11#202611yescharacteristic
266C2×C11#203111yescharacteristic
267C2×C11#203211yescharacteristic
268C24D4×D1111yescharacteristic
269C2×Q8—221no—
270C2×Q8—221no—
271C2×Q8—881no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—442no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—881no—
286C22×C4C2×D4411yescharacteristic
287C22×C4#433911yescharacteristic
288C22×C4#433911yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4#434111yescharacteristic
291C22×C4Q8×D1111yescharacteristic
292C2×C8—41no—
293C2×C8—81no—
294C2×C8—441no—
295C2×C8—881no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—442no—
301C4⋊C4—442no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—881no—
305C4⋊C4—881no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C42—881no—
317C11#1037711yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23#6693511yescharacteristic
321C23#6693811yescharacteristic
322C23#6694911yescharacteristic
323C23#6696511yescharacteristic
324C23#6696811yescharacteristic
325C23#6696911yescharacteristic
326C23#6697111yescharacteristic
327Q8—881no—
328Q8—881no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—222no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—882no—
359C2×C4—882no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4#6692811yescharacteristic
363C2×C4#6693811yescharacteristic
364C2×C4#6694911yescharacteristic
365C2×C4#6695011yescharacteristic
366C8—81no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1062228611yescharacteristic
379C22#1062238111yescharacteristic
380C22#1062239611yescharacteristic
381C22#1062241011yescharacteristic
382C22#1062242311yescharacteristic
383C22#1062247011yescharacteristic
384C22#1062249011yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—81no—
390C4—81no—
391C4—161no—
392C4—442no—
393C4—881no—
394C4—881no—
395C4—881no—
396C4—881no—
397C4—881no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1306976611yescharacteristic
405C2#1306978711yescharacteristic
406C2#1306979411yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#393
prime radicalC24×C11C2×D4
hypercenter#1289D11
hypocenterC11#10377
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
317. C11#10377semidirect

Maximal subgroups

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

subgroupindex
#130738412
#130696002
#130671872
C2×#106221052
#130664942
#130664622
C11×#12892
#1037711