Finite Group Databasebeta

← #14662037

Subgroups — #14662037

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622549C211yesmaximal, characteristic
2C2×#10622189C212yesmaximal
3C2×#10622189C212yesmaximal
4#13066846C211yesmaximal, characteristic
5C2×C11×#336C211yesmaximal, characteristic
6C23×C8×C11C2212yes—
7C22×C42×C11C2211yescharacteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C22×C4⋊Dic11C2212yes—
10C22×C4⋊Dic11C2211yescharacteristic
11C2×C11⋊#95—22no—
12C2×C11⋊#95—22no—
13#10622549—24no—
14C11×#336C414yescomplemented
15#10622189—24no—
16#10622189—24no—
17C23×C4×C11D412yes—
18C23×C4×C11C2311yescharacteristic
19C23×Dic11—22no—
20C23×Dic11—21no—
21C23×Dic11—21no—
22C22×C8×C11—22no—
23C22×C8×C11—22no—
24C22×C8×C11—22no—
25C22×C8×C11—22no—
26C22×C8×C11—22no—
27C22×C8×C11—22no—
28C22×C8×C11C2×C414yes—
29C2×C42×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11C2×C412yes—
32C2×C42×C11Q812yes—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D414yes—
45C2×C4⋊Dic11D412yes—
46C2×C4⋊Dic11Q812yes—
47C11⋊#95—28no—
48C11⋊#95—44no—
49#11268—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C4⋊C414yes—
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×Q811yescharacteristic
62C22×C4×C11C2×Q811yescharacteristic
63C22×C4×C11#4112yes—
64C22×C4×C11#4112yes—
65C22×C4×C11#4112yes—
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—24no—
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—41no—
72C22×Dic11—42no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C22×Dic11—42no—
81C22×Dic11—42no—
82C22×Dic11—42no—
83C22×Dic11—42no—
84C22×Dic11—42no—
85C2×C8×C11—24no—
86C2×C8×C11—24no—
87C2×C8×C11—24no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C42×C11—24no—
93C42×C11—24no—
94C4⋊Dic11—24no—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—24no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100C4⋊Dic11—42no—
101C4⋊Dic11—42no—
102C2×#382—111no—
103C2×#340—112no—
104C2×#340—112no—
105C2×#336D1111yescharacteristic
106C4⋊#95—111no—
107C23×C11C2×C4⋊C411yescharacteristic
108C23×C11#12011yescharacteristic
109C23×C11#12111yescharacteristic
110C23×C11C22⋊Q811yescharacteristic
111C23×C11#12311yescharacteristic
112C23×C11#12411yescharacteristic
113C23×C11#12411yescharacteristic
114C23×C11#13512yes—
115C23×C11#13512yes—
116C23×C11AGL(1,ℤ/8)12yes—
117C23×C11#13712yes—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11#11712yes—
126C2×C4×C11C4×D412yes—
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×Q811yescharacteristic
129C2×C4×C11#12112yes—
130C2×C4×C11C22⋊Q812yes—
131C2×C4×C11C22⋊Q812yes—
132C2×C4×C11#12312yes—
133C2×C4×C11#12312yes—
134C2×C4×C11#12412yes—
135C2×C4×C11#12512yes—
136C2×C4×C11#12512yes—
137C2×C4×C11#12511yescharacteristic
138C2×C4×C11#12612yes—
139C2×C4×C11#12612yes—
140C2×C4×C11C4⋊Q811yescharacteristic
141C2×Dic11—42no—
142C2×Dic11—44no—
143C2×Dic11—42no—
144C2×Dic11—44no—
145C2×Dic11—44no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151C2×Dic11—82no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—82no—
155C2×Dic11—82no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C8×C11—44no—
159C23×C8C2×D1112yes—
160C22×C4⋊C4—111no—
161C22×C4⋊C4—111no—
162C22×C4⋊C4—112no—
163C22×C42C2×D1111yescharacteristic
164#382—224no—
165C2×#95—222no—
166C2×#95—222no—
167#340—224no—
168#340—224no—
169#336Dic1114yescomplemented
170C22×C11#38211yescharacteristic
171C22×C11#38511yescharacteristic
172C22×C11#38911yescharacteristic
173C22×C11#39311yescharacteristic
174C22×C11#39411yescharacteristic
175C22×C11#39711yescharacteristic
176C22×C11#40011yescharacteristic
177C22×C11#42712yes—
178C22×C11#42812yes—
179C22×C11#44912yes—
180C22×C11#45212yes—
181C22×C11#46312yes—
182C22×C11#46412yes—
183C22×C11#47812yes—
184C22×C11#47912yes—
185C22×C11#48212yes—
186C22×C11#48512yes—
187C22×C11#48811yescharacteristic
188C22×C11#48811yescharacteristic
189C22×C11#48812yes—
190C22×C11#48912yes—
191C22×C11#49011yescharacteristic
192C22×C11#49111yescharacteristic
193C4×C11—44no—
194C4×C11#38712yes—
195C4×C11#38812yes—
196C4×C11#39812yes—
197C4×C11#40012yes—
198Dic11—82no—
199Dic11—82no—
200Dic11—84no—
201C23×C4—222no—
202C23×C4—221no—
203C23×C4—221no—
204C23×C4D4412yes—
205C23×C4C22×D1111yescharacteristic
206C22×C8—22no—
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8C2×Dic1114yes—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—114no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4—222no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42Dic2212yes—
230C2×C42C2×Dic1112yes—
231#95—228no—
232#95—444no—
233C2×C11#144211yescharacteristic
234C2×C11#183511yescharacteristic
235C2×C11#183611yescharacteristic
236C2×C11#185412yes—
237C2×C11#194912yes—
238C2×C11#202511yescharacteristic
239C2×C11#202611yescharacteristic
240C2×C11#204212yes—
241C2×C11#207311yescharacteristic
242C2×C11#207411yescharacteristic
243C2×C11#210112yes—
244C24C2×D4411yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—224no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4—442no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4—442no—
260C22×C4—442no—
261C22×C4—442no—
262C22×C4—442no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4—442no—
266C22×C4—442no—
267C22×C4—442no—
268C22×C4C4⋊Dic1114yes—
269C22×C4C2×Dic2211yescharacteristic
270C22×C4#433912yes—
271C22×C4#433912yes—
272C22×C4D4×D1112yes—
273C22×C4D4×D1111yescharacteristic
274C22×C4#434112yes—
275C22×C4#434111yescharacteristic
276C22×C4Q8×D1111yescharacteristic
277C22×C4#434311yescharacteristic
278C22×C4C22×Dic1111yescharacteristic
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C4⋊C4—224no—
287C4⋊C4—224no—
288C4⋊C4—224no—
289C4⋊C4—224no—
290C4⋊C4—442no—
291C4⋊C4—442no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C42—24no—
295C42—24no—
296C11#1126811yescharacteristic, complemented, Sylow
297C23#6692811yescharacteristic
298C23#6692811yescharacteristic
299C23#6693511yescharacteristic
300C23#6693911yescharacteristic
301C23#6694811yescharacteristic
302C23#6695011yescharacteristic
303C23#6695712yes—
304C23#6695712yes—
305C23#6696112yes—
306C23#6696212yes—
307C23C2×C4⋊Dic1111yescharacteristic
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—444no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—444no—
319C2×C4—444no—
320C2×C4—444no—
321C2×C4—444no—
322C2×C4—882no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—882no—
328C2×C4—882no—
329C2×C4—882no—
330C2×C4—882no—
331C2×C4—882no—
332C2×C4#6692312yes—
333C2×C4#6693112yes—
334C2×C4#6693212yes—
335C2×C4#6693612yes—
336C2×C4#6693712yes—
337C2×C4#6693812yes—
338C2×C4#6694111yescharacteristic
339C2×C4#6694212yes—
340C2×C4#6694311yescharacteristic
341C2×C4#6694712yes—
342C2×C4#6694912yes—
343C2×C4#6695112yes—
344C2×C4#6697912yes—
345C2×C4D4×Dic1111yescharacteristic
346C2×C4D4×Dic1112yes—
347C2×C4Q8×Dic1111yescharacteristic
348C8—44no—
349C22#1062227211yescharacteristic
350C22#1062228511yescharacteristic
351C22#1062228611yescharacteristic
352C22#1062228711yescharacteristic
353C22#1062231012yes—
354C22#1062231011yescharacteristic
355C22#1062231011yescharacteristic
356C22#1062231611yescharacteristic
357C22#1062232611yescharacteristic
358C22#1062232712yes—
359C22#1062233612yes—
360C22#1062234612yes—
361C22#1062234712yes—
362C22#1062235012yes—
363C22#1062244212yes—
364C22#1062245712yes—
365C22#1062245812yes—
366C22#1062246012yes—
367C22#1062254911yescharacteristic
368C22#1062256311yescharacteristic
369C22#1062259811yescharacteristic
370C22#1062271912yes—
371C22#1062273412yes—
372C4—44no—
373C4—884no—
374C4—882no—
375C4—882no—
376C4#1062227012yes—
377C4#1062227312yes—
378C4#1062256412yes—
379C4#1062259412yes—
380C2#1306687311yescharacteristic
381C2#1306874711yescharacteristic
382C2#1306875011yescharacteristic
383C2#1306881712yes—
384C2#1306938612yes—
385C2#1306976311yescharacteristic
386C2#1306976811yescharacteristic
387C2#1306985812yes—
388C2#1307003111yescharacteristic
389C2#1307003611yescharacteristic
390C2#1307018512yes—
subgroupG/H
centerC24C2×D44
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#336C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#336D11
hypocenterC11#11268
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
14. C11×#336C4semidirect
169. #336Dic11semidirect
296. C11#11268semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
C2×#106221892
#130668462
C2×C11×#3362
#1126811