Finite Group Databasebeta

← #14651471

Subgroups — #14651471

Order 2816.

554 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077644C211yesmaximal, characteristic
2#13073565C211yesmaximal, characteristic
3#13067334C211yesmaximal, characteristic, complemented
4#13067332C211yesmaximal, characteristic, complemented
5#13066956C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×#66950—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622552C412yes—
16#10622548C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622449—22no—
20#10622339—21no—
21D11×C22⋊C8—21no—
22#10622319—22no—
23#10622290—21no—
24#10622290—21no—
25#10622124—22no—
26#10622120—22no—
27#10622106—21no—
28#10622106—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11C2×C412yes—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×(C2×D11)⋊C4D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11C2×C412yes—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×#4313—22no—
46C2×C8×D11—22no—
47#66950—44no—
48#66950—44no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66(C2×D11)⋊C8—22no—
67(C2×D11)⋊C8—22no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70#66867—21no—
71#66867—21no—
72#9455—111nomaximal, Sylow
73C23×D11C22⋊C411yescharacteristic
74C23×D11C22⋊C411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—22no—
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×D44—22no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—41no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C11×C4⋊C4—24no—
99C42×C11—42no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—44no—
115C4⋊Dic11—44no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#4313—82no—
121C8×D11—82no—
122#2973—111no—
123#2542—111no—
124#1556—111no—
125#1556—111no—
126#1466—111no—
127#1285—111no—
128#1285D1111yescharacteristic, complemented
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11#10112yes—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160D44—42no—
161D44—42no—
162C4×D11—42no—
163C4×D11—42no—
164C4×D11—81no—
165C4×D11—81no—
166Dic22—82no—
167Dic22—82no—
168C8×C11—42no—
169C8×C11—81no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C2×C4⋊Q8—111no—
173C2×C22⋊Q8—221no—
174C2×C22⋊Q8—221no—
175C2×C4×D4—111no—
176#435—222no—
177#435—222no—
178#432—111no—
179#432—111no—
180#432C2×D1111yescharacteristic
181#432C2×D1111yescharacteristic
182#407—221no—
183C2×C22⋊C8—221no—
184#399—221no—
185#399—221no—
186#390—112no—
187#384—112no—
188C4×C4⋊C4C2×D1111yescharacteristic
189#332—222no—
190#332—222no—
191#323—221no—
192#323—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#38611yescharacteristic
196C22×C11C2×#10111yescharacteristic
197C22×C11#41311yescharacteristic
198C2×D11—22no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—44no—
214C4×C11#45312yes—
215Dic11—41no—
216Dic11—41no—
217Dic11—82no—
218C22×Q8—221no—
219C22×D4—111no—
220C23×C4—111no—
221C23×C4—111no—
222C2×M16—222no—
223C22×C8—222no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C22⋊Q8—444no—
229C22⋊Q8—444no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—222no—
243C2×C22⋊C4—222no—
244C2×C42C4×D1112yes—
245C2×C42C22×D1111yescharacteristic
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249C4⋊C8D4412yes—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—222no—
253C22⋊C8—222no—
254C22⋊C8—221no—
255C22⋊C8—221no—
256#97—21no—
257#97—21no—
258#97—221no—
259#97—221no—
260#95—21no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#188711yescharacteristic
264C2×C11#190111yescharacteristic
265C2×C11#190911yescharacteristic
266D11—42no—
267D11—81no—
268C24—111no—
269C24—111no—
270C2×Q8—442no—
271C2×Q8—442no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×D4—222no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—22no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—222no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4C2×C4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291M16—882no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—222no—
295C2×C8—441no—
296C2×C8—882no—
297C4⋊C4—24no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—444no—
303C4⋊C4—444no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—444no—
311C22⋊C4—444no—
312C42—42no—
313C42C2×D4411yescharacteristic
314C42#433911yescharacteristic
315C42D4×D1111yescharacteristic
316C42#434311yescharacteristic
317C11#945511yescharacteristic, complemented, Sylow
318C23—112no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23C22⋊C4×D1111yescharacteristic
329Q8—882no—
330Q8—882no—
331D4—442no—
332D4—442no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4C4×D4411yescharacteristic
352C2×C4#6693511yescharacteristic
353C2×C4#6693711yescharacteristic
354C2×C4#6694611yescharacteristic
355C2×C4#6694711yescharacteristic
356C2×C4#6694811yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—222no—
364C22—442no—
365C22—442no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22—881no—
372C22—881no—
373C22#1062227811yescharacteristic
374C22#1062235811yescharacteristic
375C22D11×#10111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—44no—
382C4—441no—
383C4—441no—
384C4—882no—
385C4#1062243512yes—
386C2—21no—
387C2—21no—
388C2—442no—
389C2—881no—
390C2#1306901311yescharacteristic
391C2#1306908311yescharacteristic
392C2#1306913711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#9455
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
3. #13067334C2semidirect
4. #13067332C2semidirect
6. #13066472C2semidirect
7. C11×#1285C2semidirect
128. #1285D11semidirect
317. C11#9455semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130735652
#130673342
#130673322
#130669562
#130664722
C11×#12852
#945511