Finite Group Databasebeta

← #14647113

Subgroups — #14647113

Order 2816.

830 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×#10622280C211yesmaximal, characteristic
2#13068525C212yesmaximal
3#13066459C211yesmaximal, characteristic, complemented
4#13066458C212yesmaximal, complemented
5C11×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D11C2211yescharacteristic
7C22×(C2×D11)⋊C4C412yes—
8C22×Dic11⋊C4C412yes—
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#95C2211yescharacteristic
11C2×C11⋊#95C2211yescharacteristic
12C2×C22⋊(C11⋊C8)C2212yes—
13C2×(C2×D11)⋊C8—22no—
14C2×(C2×D11)⋊C8—22no—
15#10622280—22no—
16#10622280—22no—
17C24×D11C2×C411yescharacteristic
18C23×C4×C11C2×C412yes—
19C23×C4×C11C2311yescharacteristic
20C23×Dic11C2×C411yescharacteristic
21C23×Dic11C2×C412yes—
22C22×C4×D11—22no—
23C22×C4×D11—21no—
24C22×C4×D11—21no—
25C22×C4×D11—44no—
26C22×C4×D11D412yes—
27C22×C4×D11D412yes—
28C22×C8×C11—22no—
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—44no—
32C2×Dic11⋊C4—22no—
33C2×Dic11⋊C4—22no—
34C2×Dic11⋊C4—44no—
35C22×C11⋊C8—22no—
36C11×C22⋊C8—22no—
37C11×C22⋊C8—22no—
38C11×#95—22no—
39C11⋊#95—22no—
40C22⋊(C11⋊C8)—22no—
41C22⋊(C11⋊C8)—22no—
42(C2×D11)⋊C8—44no—
43(C2×D11)⋊C8—44no—
44#8704—111nomaximal, Sylow
45C24×C11C22×C411yescharacteristic
46C23×D11—21no—
47C23×D11—21no—
48C23×D11—22no—
49C23×D11—22no—
50C23×D11—22no—
51C23×D11—22no—
52C23×D11—42no—
53C23×D11C22⋊C411yescharacteristic
54C23×D11C22⋊C411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C2×D412yes—
62C22×C4×C11#4112yes—
63C22×C4×C11#4111yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×Dic11—24no—
66C22×Dic11—22no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—42no—
72C22×Dic11—42no—
73C22×Dic11C22⋊C412yes—
74C2×C4×D11—24no—
75C2×C4×D11—24no—
76C2×C4×D11—22no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C2×C4×D11—48no—
83C2×C4×D11—44no—
84C2×C4×D11—44no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88(C2×D11)⋊C4—44no—
89(C2×D11)⋊C4—44no—
90Dic11⋊C4—44no—
91Dic11⋊C4—44no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8—42no—
95C2×#380—111no—
96#1779—112no—
97#1280—112no—
98#1280—111no—
99#1280D1111yescharacteristic, complemented
100C23×C11—22no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#11711yescharacteristic
105C23×C11#11711yescharacteristic
106C23×C11#13112yes—
107C23×C11#13112yes—
108C22×D11—24no—
109C22×D11—24no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—22no—
113C22×D11—22no—
114C22×D11—22no—
115C22×D11—22no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—44no—
119C22×D11—44no—
120C22×D11—44no—
121C22×D11—44no—
122C22×D11—42no—
123C22×D11—42no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—42no—
127C22×D11#10012yes—
128C22×D11#10112yes—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—82no—
138C2×C4×C11—82no—
139C2×C4×C11#12312yes—
140C2×C4×C11#12312yes—
141C2×Dic11—24no—
142C2×Dic11—24no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150C2×Dic11#9914yes—
151C4×D11—44no—
152C4×D11—44no—
153C4×D11—44no—
154C4×D11—44no—
155C8×C11—82no—
156C11⋊C8—82no—
157C24×C4—111no—
158C22×C4⋊C4—112no—
159C22×C22⋊C4—112no—
160C2×C22⋊C8—112no—
161C2×C22⋊C8—222no—
162C2×C22⋊C8—222no—
163C2×C22⋊C8C2×D1112yes—
164#380—222no—
165#380—222no—
166C2×#95—111no—
167C2×#95C2×D1111yescharacteristic
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11#38111yescharacteristic
177C22×C11#40812yes—
178C22×C11C2×#9912yes—
179C22×C11C2×#10011yescharacteristic
180C22×C11C2×#10111yescharacteristic
181C22×C11#43311yescharacteristic
182C22×C11#43311yescharacteristic
183C22×C11#43312yes—
184C2×D11—22no—
185C2×D11—22no—
186C2×D11—24no—
187C2×D11—24no—
188C2×D11—44no—
189C2×D11—44no—
190C2×D11—48no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—42no—
196C2×D11—42no—
197C4×C11—22no—
198C4×C11—22no—
199C4×C11—82no—
200Dic11—24no—
201Dic11—82no—
202C25—111no—
203C23×C4—111no—
204C23×C4—112no—
205C23×C4—112no—
206C23×C4—112no—
207C23×C4—222no—
208C23×C4—221no—
209C23×C4—221no—
210C23×C4—444no—
211C23×C4C4×D1112yes—
212C23×C4C22×D1111yescharacteristic
213C22×C8—22no—
214C22×C8—222no—
215C2×C4⋊C4—222no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—444no—
218C2×C22⋊C4—222no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4—444no—
221C22⋊C8—22no—
222C22⋊C8—22no—
223C22⋊C8—222no—
224C22⋊C8—222no—
225C22⋊C8—444no—
226C22⋊C8—444no—
227#95—22no—
228#95—222no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—22no—
232C2×C11#147112yes—
233C2×C11#147212yes—
234C2×C11#181811yescharacteristic
235C2×C11#181911yescharacteristic
236C2×C11#182111yescharacteristic
237D11—42no—
238D11—42no—
239C24—111no—
240C24—111no—
241C24—222no—
242C24—222no—
243C24—221no—
244C24—221no—
245C24—222no—
246C24—222no—
247C24—442no—
248C24C2×C4×D1111yescharacteristic
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—112no—
256C22×C4—224no—
257C22×C4—224no—
258C22×C4—224no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—222no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4—442no—
269C22×C4—442no—
270C22×C4—448no—
271C22×C4—444no—
272C22×C4—444no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4#433912yes—
276C22×C4D4×D1112yes—
277C22×C4#434111yescharacteristic
278C22×C4#434311yescharacteristic
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—442no—
283C2×C8—442no—
284C2×C8—442no—
285C4⋊C4—444no—
286C4⋊C4—444no—
287C22⋊C4—444no—
288C22⋊C4—444no—
289C11#870411yescharacteristic, complemented, Sylow
290C23—22no—
291C23—21no—
292C23—21no—
293C23—112no—
294C23—112no—
295C23—224no—
296C23—224no—
297C23—221no—
298C23—221no—
299C23—222no—
300C23—222no—
301C23—222no—
302C23—222no—
303C23—221no—
304C23—221no—
305C23—444no—
306C23—444no—
307C23—444no—
308C23—444no—
309C23—442no—
310C23—442no—
311C23—441no—
312C23—441no—
313C23—442no—
314C23#6692511yescharacteristic
315C23C22⋊C4×D1111yescharacteristic
316C23#6694511yescharacteristic
317C23#6695412yes—
318C23#6696012yes—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—114no—
330C2×C4—224no—
331C2×C4—224no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—882no—
342C2×C4—882no—
343C2×C4#6693612yes—
344C2×C4#6694712yes—
345C8—82no—
346C8—882no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—222no—
356C22—222no—
357C22—224no—
358C22—224no—
359C22—444no—
360C22—444no—
361C22—448no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—442no—
367C22—442no—
368C22#1062227711yescharacteristic
369C22#1062230311yescharacteristic
370C22#1062232211yescharacteristic
371C22#1062234012yes—
372C22D11×#9912yes—
373C22D11×#10011yescharacteristic
374C22D11×#10111yescharacteristic
375C22#1062245312yes—
376C4—22no—
377C4—22no—
378C4—82no—
379C4—224no—
380C4—882no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—442no—
385C2—442no—
386C2#1306697412yes—
387C2#1306697812yes—
388C2#1306868611yescharacteristic
389C2#1306868911yescharacteristic
390C2#1306869511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1280D11
hypocenterC11#8704
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #13066459C2semidirect
4. #13066458C2semidirect
5. C11×#1280C2semidirect
99. #1280D11semidirect
289. C11#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#106222802
#130685252
#130664592
#130664582
C11×#12802
#870411