Finite Group Databasebeta

← #14663155

Subgroups — #14663155

Order 2816.

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

normal subgroups only

This group has 586 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
1#13071104C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic, complemented
3#13066549C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C22×C4×Dic11C411yescharacteristic
9C11×#432—21no—
10#10622601C411yescharacteristic
11#10622601C2211yescharacteristic
12#10622587C411yescharacteristic
13#10622587C2211yescharacteristic
14#10622571—21no—
15#10622571—21no—
16C4×(C2×D11)⋊C4—21no—
17C4×(C2×D11)⋊C4—21no—
18#10622539—21no—
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11C2×C411yescharacteristic
24C22×C22⋊D11—21no—
25C23×Dic11—21no—
26C2×#4339—22no—
27C2×#4339—22no—
28C2×#4339—42no—
29C2×#4339—41no—
30C2×#4339—41no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22C2×C411yescharacteristic
34C11×#117—41no—
35C11×#117—41no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—42no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11C2×C411yescharacteristic
50C11×C4⋊C8—41no—
51C11×C22⋊C8—22no—
52C11×#97—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—41no—
59#66867—41no—
60#11507—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—24no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—42no—
81C22×Dic11—42no—
82C22×Dic11—42no—
83#4339—44no—
84#4339—44no—
85#4339—44no—
86#4339—44no—
87C2×D44—21no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44M1612yes—
91C2×C4×D11—24no—
92C2×C4×D11—42no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×Dic22—21no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22M1612yes—
99C2×C8×C11—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—21no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112C4×Dic11—41no—
113C4×Dic11—41no—
114C4×Dic11—42no—
115C2×C11⋊C8—42no—
116#2297—111no—
117#1464—111no—
118#1464D1111yescharacteristic, complemented
119#1319—112no—
120#1318—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#10012yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—22no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11#9911yescharacteristic
151C2×C4×C11#9911yescharacteristic
152C2×C4×C11C2×M1611yescharacteristic
153C2×C4×C11C2×M1611yescharacteristic
154C22⋊D11—48no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—48no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165D44—42no—
166D44—42no—
167C4×D11—44no—
168C4×D11—44no—
169Dic22—42no—
170Dic22—42no—
171C8×C11—82no—
172C11⋊C8—82no—
173C22×#41—111no—
174C2×#117C2×D1111yescharacteristic
175C22×C42—111no—
176#432—21no—
177#432—221no—
178#391—111no—
179#391—111no—
180#390—111no—
181#390—111no—
182#386—221no—
183#386—221no—
184C4×C22⋊C4—221no—
185C4×C22⋊C4—221no—
186#324—112no—
187#324C2×D1112yes—
188#323—21no—
189#323—221no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11#40711yescharacteristic
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#10011yescharacteristic
200C2×D11—42no—
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—41no—
215Dic11—42no—
216Dic11—42no—
217Dic11—42no—
218C2×#41—222no—
219C2×#41—222no—
220C2×#41—442no—
221C2×#41—441no—
222C2×#41—441no—
223C22×Q8—111no—
224C22×D4—111no—
225C22×D4—221no—
226C23×C4—221no—
227C23×C4—221no—
228C23×C4C4×D1111yescharacteristic
229#117—41no—
230#117—41no—
231C2×C4⋊C4C4×D1111yescharacteristic
232C2×C4⋊C4C22×D1111yescharacteristic
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4D4411yescharacteristic
238C2×C22⋊C4C22⋊D1111yescharacteristic
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—221no—
242C2×C42—442no—
243C2×C42D4411yescharacteristic
244C2×C42C22⋊D1111yescharacteristic
245C4⋊C8—41no—
246C4⋊C8—441no—
247C22⋊C8—22no—
248C22⋊C8—222no—
249#97—41no—
250#97—441no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—42no—
258C2×C11#146211yescharacteristic
259C2×C11#212611yescharacteristic
260C2×C11#213211yescharacteristic
261D11—82no—
262C24—221no—
263C24(C2×D11)⋊C411yescharacteristic
264#41—444no—
265#41—444no—
266#41—444no—
267#41—444no—
268C2×Q8—112no—
269C2×Q8—221no—
270C2×Q8—441no—
271C2×Q8—441no—
272C2×D4—112no—
273C2×D4—224no—
274C2×D4—221no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—442no—
278C2×D4—442no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—224no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4(C2×D11)⋊C411yescharacteristic
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C2×C8—42no—
301C2×C8—442no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—441no—
315C42—441no—
316C42—442no—
317C11#1150711yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23—222no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23#6688712yes—
330C23C2×(C2×D11)⋊C411yescharacteristic
331Q8—442no—
332Q8—442no—
333D4—442no—
334D4—442no—
335D4—448no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—444no—
356C2×C4—444no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—448no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4#6687011yescharacteristic
365C2×C4#6687011yescharacteristic
366C2×C4M16×D1111yescharacteristic
367C2×C4M16×D1111yescharacteristic
368C8—82no—
369C8—882no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—442no—
378C22—442no—
379C22—442no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22C2×#6687011yescharacteristic
385C22#1062273911yescharacteristic
386C22C2×#6688711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—442no—
396C4—442no—
397C4—442no—
398C2—21no—
399C2—21no—
400C2—42no—
401C2—882no—
402C2#1306694211yescharacteristic
403C2#1307027911yescharacteristic
404C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC22×#4339C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11507
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13066950C2semidirect
3. #13066549C2semidirect
4. #13066547C2semidirect
5. C11×#1464C2semidirect
118. #1464D11semidirect
317. C11#11507semidirect

Maximal subgroups

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

subgroupindex
#130711042
#130669502
#130665492
#130665472
C11×#14642
#1150711