Finite Group Databasebeta

← #14663239

Subgroups — #14663239

Order 2816.

596 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C4×#66993C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066561C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C411yescharacteristic
8C2×C4×C22⋊D11—21no—
9C2×C4×C22⋊D11—21no—
10C2×C4×D44C411yescharacteristic
11C11×#407—21no—
12#10622834C411yescharacteristic
13#10622820—21no—
14#10622601C2211yescharacteristic
15#10622589C2211yescharacteristic
16#10622570—21no—
17#10622570—21no—
18C42×Dic11C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×M16—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66993—22no—
40#66993—22no—
41C4×C22⋊D11—44no—
42C4×C22⋊D11—44no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11C2×C411yescharacteristic
53C2×#4318—41no—
54C4×D44—41no—
55C4×D44—41no—
56C11×C22⋊C8—22no—
57C11×C22⋊C8—41no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11529—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C24×C11C22⋊C411yescharacteristic
63C23×D11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—24no—
80C2×C22⋊D11—24no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44M1612yescomplemented
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C11×M16—82no—
97C2×C8×C11—42no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—21no—
102C42×C11—21no—
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108C4⋊Dic11—41no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111C4×Dic11—24no—
112C4×Dic11—21no—
113C4×Dic11—41no—
114C4×Dic11—42no—
115C4×Dic11M1612yescomplemented
116#4318—82no—
117C2×C11⋊C8—42no—
118C4×#127—111no—
119#1465—111no—
120#1465D1111yescharacteristic, complemented
121#1325—112no—
122#1318—112no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C22×D11—22no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141D4×C11—42no—
142D4×C11—42no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11#9911yescharacteristic
157C2×C4×C11#9911yescharacteristic
158C2×C4×C11C2×M1611yescharacteristic
159C2×C4×C11C2×M1611yescharacteristic
160C22⋊D11—48no—
161C22⋊D11—48no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171D44—42no—
172D44—42no—
173C4×D11—82no—
174C4×D11—82no—
175C8×C11—82no—
176C11⋊C8—82no—
177C2×#127—111no—
178C2×C4×D4—111no—
179C2×C4×D4—221no—
180C2×C4×D4—221no—
181C2×C4×D4C2×D1111yescharacteristic
182#407—21no—
183#407—221no—
184#390—111no—
185#390—111no—
186#390—221no—
187#390—221no—
188#384—111no—
189C43—111no—
190#324—112no—
191#324C2×D1112yes—
192#323—21no—
193#323—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#40711yescharacteristic
207C22×C11C2×#9911yescharacteristic
208C22×C11#41311yescharacteristic
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11#35312yes—
223Dic11—24no—
224Dic11—42no—
225Dic11—81no—
226C22×D4—111no—
227C22×D4—221no—
228C22×D4—221no—
229C22×D4C4×D1111yescharacteristic
230C23×C4—221no—
231C23×C4D4411yescharacteristic
232C23×C4C22⋊D1111yescharacteristic
233C2×M16—41no—
234C2×M16—441no—
235#127—222no—
236#127—222no—
237C4×D4—41no—
238C4×D4—41no—
239C4×D4—441no—
240C4×D4—441no—
241C4×D4—444no—
242C4×D4—444no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4C22×D1111yescharacteristic
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4D4411yescharacteristic
253C2×C22⋊C4C22⋊D1111yescharacteristic
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—221no—
257C2×C42—221no—
258C2×C42C4×D1111yescharacteristic
259C22⋊C8—22no—
260C22⋊C8—41no—
261C22⋊C8—222no—
262C22⋊C8—441no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—81no—
266C2×C11—81no—
267C2×C11#146511yescharacteristic
268C2×C11C2×#35311yescharacteristic
269C2×C11#213211yescharacteristic
270D11—82no—
271C24—221no—
272C24(C2×D11)⋊C411yescharacteristic
273C24(C2×D11)⋊C411yescharacteristic
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—112no—
279C2×D4—224no—
280C2×D4—224no—
281C2×D4—221no—
282C2×D4—441no—
283C2×D4—441no—
284C2×D4—442no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—442no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4(C2×D11)⋊C411yescharacteristic
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4C2×D4411yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306M16—82no—
307M16—882no—
308C2×C8—42no—
309C2×C8—442no—
310C4⋊C4—41no—
311C4⋊C4—441no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C42—21no—
322C42—21no—
323C42—112no—
324C42—224no—
325C42—221no—
326C42—441no—
327C42—442no—
328C11#1152911yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—222no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23C2×(C2×D11)⋊C411yescharacteristic
347D4—42no—
348D4—42no—
349D4—442no—
350D4—442no—
351D4—448no—
352D4—448no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—882no—
376C2×C4—882no—
377C2×C4#6687011yescharacteristic
378C2×C4#6687011yescharacteristic
379C2×C4M16×D1111yescharacteristic
380C2×C4M16×D1111yescharacteristic
381C8—82no—
382C8—882no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—442no—
396C22—442no—
397C22—442no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22—881no—
402C22C2×#6687011yescharacteristic
403C22#1062273911yescharacteristic
404C22#1062274511yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—224no—
412C4—442no—
413C4—881no—
414C4#1062211212yes—
415C2—21no—
416C2—21no—
417C2—81no—
418C2—81no—
419C2—882no—
420C2#1306695211yescharacteristic
421C2C2×#1062211211yescharacteristic
422C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11529
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066561C2semidirect
4. #13066547C2semidirect
5. C11×#1465C2semidirect
91. C2×D44M16semidirect
115. C4×Dic11M16semidirect
120. #1465D11semidirect
328. C11#11529semidirect

Maximal subgroups

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

subgroupindex
C4×#669932
#130669542
#130665612
#130665472
C11×#14652
#1152911