Finite Group Databasebeta

← #14647255

Subgroups — #14647255

Order 2816.

418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071112C211yesmaximal, characteristic
2#13068697C211yesmaximal, characteristic
3#13068691C211yesmaximal, characteristic
4#13066470C211yesmaximal, characteristic
5#13066469C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic
7C11×#1284C211yesmaximal, characteristic
8C2×#66979C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C11×#381C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12#10622824C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622558—21no—
16#10622557—21no—
17#10622545C411yescharacteristic, complemented
18C4×Dic11⋊C4C411yescharacteristic, complemented
19C4×Dic11⋊C4C411yescharacteristic, complemented
20C42×Dic11C411yescharacteristic, complemented
21#10622267—21no—
22#10622266—21no—
23#10622192—21no—
24#10622192—21no—
25#10622165—21no—
26#10622165—21no—
27C23×C4×C11C2311yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—21no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C22⋊Dic11D411yescharacteristic
37#66979—21no—
38#66979—21no—
39#66979—21no—
40#66979—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11C2×C411yescharacteristic
51C2×#4318—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#8741—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—41no—
93C42×C11—41no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—42no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—41no—
112C4×Dic11—41no—
113C4×Dic11—42no—
114C4×Dic11—42no—
115#4318—41no—
116#4318—41no—
117C2×C11⋊C8—41no—
118#2298—111no—
119#1822—111no—
120#1820—111no—
121#1284—111no—
122#1284—111no—
123#1284—111no—
124#1284D1111yescharacteristic
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11#12311yescharacteristic
131C23×C11#12311yescharacteristic
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
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—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#11711yescharacteristic
150C2×C4×C11#11711yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C8×C11—81no—
171C11⋊C8—81no—
172C2×#117—111no—
173#407—111no—
174#407C2×D1111yescharacteristic
175#388—221no—
176#388—221no—
177#387—221no—
178#387—221no—
179#381—111no—
180#381C2×D1111yescharacteristic
181C4×C4⋊C4—111no—
182C4×C4⋊C4—111no—
183C4×C22⋊C4—111no—
184C4×C22⋊C4C2×D1111yescharacteristic
185#376—111no—
186C43—111no—
187#343—221no—
188#343—221no—
189#342—221no—
190#342—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11#38111yescharacteristic
202C22×C11#41011yescharacteristic
203C22×C11#41011yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11—81no—
210C4×C11—161no—
211Dic11—42no—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216Dic11—81no—
217Dic11—161no—
218C23×C4C22×D1111yescharacteristic
219C2×M16—21no—
220C2×M16—221no—
221#117—221no—
222#117—221no—
223#117—221no—
224#117—221no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—221no—
240C2×C42—221no—
241C2×C42C4×D1111yescharacteristic
242C2×C42C4×D1111yescharacteristic
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—41no—
260C2×C11—41no—
261C2×C11#182011yescharacteristic
262C2×C11#182711yescharacteristic
263C2×C11#182711yescharacteristic
264C24D4×D1111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—441no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4#433911yescharacteristic
279C22×C4#433911yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4#434111yescharacteristic
282C22×C4#434311yescharacteristic
283M16—41no—
284M16—41no—
285M16—441no—
286M16—441no—
287C2×C8—41no—
288C2×C8—441no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—442no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—41no—
306C42—41no—
307C42—221no—
308C42—221no—
309C42—221no—
310C42—221no—
311C42—441no—
312C42—441no—
313C42—442no—
314C42—442no—
315C11#874111yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23C22⋊C4×D1111yescharacteristic
321C23#6693611yescharacteristic
322C23#6694711yescharacteristic
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
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—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—222no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
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—881no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4#6692511yescharacteristic
358C2×C4#6693611yescharacteristic
359C2×C4#6694511yescharacteristic
360C2×C4#6694711yescharacteristic
361C8—81no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22#1062227711yescharacteristic
374C22#1062235311yescharacteristic
375C22#1062235311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—81no—
382C4—161no—
383C4—442no—
384C4—441no—
385C4—441no—
386C4—441no—
387C4—441no—
388C4—881no—
389C4—1761no—
390C2—21no—
391C2—21no—
392C2—41no—
393C2—41no—
394C2#1306869211yescharacteristic
395C2#1306871811yescharacteristic
396C2#1306871911yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#381
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#8741
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
17. #10622545C4semidirect
18. C4×Dic11⋊C4C4semidirect
19. C4×Dic11⋊C4C4semidirect
20. C42×Dic11C4semidirect
315. C11#8741semidirect

Maximal subgroups

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

subgroupindex
#130711122
#130686972
#130686912
#130664702
#130664692
#130664682
C11×#12842
#874111