Finite Group Databasebeta

← #14663410

Subgroups — #14663410

Order 2816.

462 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073620C211yesmaximal, characteristic
2#13066958C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066548C211yesmaximal, characteristic, complemented
5#13066547C211yesmaximal, characteristic, complemented
6#13066547C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×#66993C411yescharacteristic
9C2×#66989C411yescharacteristic
10C2×#66940C2211yescharacteristic
11C2×#66928C411yescharacteristic
12C11×#390C2211yescharacteristic
13#10622601C2211yescharacteristic
14#10622572—21no—
15#10622572—21no—
16#10622570—21no—
17#10622570—21no—
18C4×Dic11⋊C4C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66993—41no—
39#66993—41no—
40#66989—42no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×Dic11⋊C4D411yescharacteristic
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52#66940—41no—
53#66940—41no—
54#66928—42no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66879—41no—
61Dic11⋊C8—41no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#11567—111nomaximal, Sylow
65C24×C11—21no—
66C23×D11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44—41no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—81no—
99C11×C22⋊C4—81no—
100C42×C11—41no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—42no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#2548—111no—
120#1467—111no—
121#1461—111no—
122#1318—111no—
123#1318—111no—
124#1318—111no—
125#1318D1111yescharacteristic, complemented
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11#13111yescharacteristic
153C2×C4×C11#13111yescharacteristic
154C22⋊D11—82no—
155C22⋊D11—84no—
156C22⋊D11—82no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—22no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11#9911yescharacteristic
169C2×Dic11#9911yescharacteristic
170C2×Dic11#10012yes—
171D44—81no—
172D44—81no—
173Dic22—42no—
174Dic22—42no—
175C8×C11—81no—
176C8×C11—81no—
177C11⋊C8—81no—
178C11⋊C8—81no—
179C2×#127—111no—
180C2×#124—111no—
181C2×#124—111no—
182C2×C4×Q8—111no—
183#432—221no—
184#431—221no—
185#394—221no—
186#394—221no—
187#390—111no—
188#390—221no—
189#390—221no—
190#390C2×D1111yescharacteristic
191C4×C4⋊C4—111no—
192#324—111no—
193#324—111no—
194#324—221no—
195#324—221no—
196#324C2×D1111yescharacteristic
197#324C2×D1111yescharacteristic
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11#40811yescharacteristic
208C22×C11C2×#9911yescharacteristic
209C22×C11C2×#10011yescharacteristic
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—81no—
222Dic11—21no—
223Dic11—22no—
224Dic11—41no—
225Dic11—41no—
226Dic11—81no—
227Dic11#35512yes—
228C22×Q8—111no—
229C22×D4—111no—
230C22×D4—221no—
231C22×D4—221no—
232C22×D4C4×D1111yescharacteristic
233#127—441no—
234#127—441no—
235#124—442no—
236#124—442no—
237C4×Q8—441no—
238C4×Q8—441no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C22×D1111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C42—111no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42C4×D1111yescharacteristic
256C4⋊C8—441no—
257C4⋊C8—441no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—221no—
261C22⋊C8—221no—
262#97—441no—
263C4×C8—441no—
264#95—221no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—161no—
268C2×C11#147111yescharacteristic
269C2×C11#212811yescharacteristic
270C2×C11C2×#35511yescharacteristic
271D11—161no—
272C24—21no—
273C24—221no—
274C2×Q8—222no—
275C2×Q8—221no—
276C2×Q8—221no—
277C2×Q8—441no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—221no—
283C2×D4—221no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—881no—
292C2×D4—881no—
293C22×C4—21no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—221no—
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4D4×D1111yescharacteristic
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—441no—
305C2×C8—441no—
306C4⋊C4—41no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C22⋊C4—442no—
315C22⋊C4—442no—
316C22⋊C4—881no—
317C22⋊C4—881no—
318C42—41no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42—221no—
323C42—221no—
324C42—221no—
325C42—441no—
326C11#1156711yescharacteristic, complemented, Sylow
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23C22⋊C4×D1111yescharacteristic
342Q8—442no—
343Q8—442no—
344D4—81no—
345D4—81no—
346D4—881no—
347D4—881no—
348D4—882no—
349D4—882no—
350D4—884no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—111no—
361C2×C4—111no—
362C2×C4—112no—
363C2×C4—222no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4#6695411yescharacteristic
375C2×C4#6696011yescharacteristic
376C8—81no—
377C8—81no—
378C8—881no—
379C8—881no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22#1062234011yescharacteristic
397C22D11×#9911yescharacteristic
398C22D11×#10011yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—112no—
405C4—221no—
406C4—222no—
407C4—441no—
408C4—441no—
409C4—881no—
410C2—21no—
411C2—21no—
412C2—161no—
413C2—1761no—
414C2#1306697411yescharacteristic
415C2#1307028611yescharacteristic
416C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11567
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066958C2semidirect
3. #13066938C2semidirect
4. #13066548C2semidirect
5. #13066547C2semidirect
6. #13066547C2semidirect
7. C11×#1318C2semidirect
125. #1318D11semidirect
326. C11#11567semidirect

Maximal subgroups

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

subgroupindex
#130736202
#130669582
#130669382
#130665482
#130665472
C11×#13182
#1156711