Finite Group Databasebeta

← #14650208

Subgroups — #14650208

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13068706C211yesmaximal, characteristic
4#13067188C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic
7C2×C11×#484C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C11×#484—21no—
11C11×#484—21no—
12C11×#484—22no—
13C2×C11×#107C412yescomplemented
14C2×C11×#103C412yescomplemented
15C2×C11×C22⋊C8C2211yescharacteristic
16#10622825—21no—
17#10622825C2211yescharacteristic
18#10622825C2211yescharacteristic
19C4×C22⋊Dic11—21no—
20C4×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622598—21no—
23#10622594—22no—
24C4⋊C4×Dic11—21no—
25#10622176—22no—
26#10622167—22no—
27#10622164—21no—
28#10622164—21no—
29C22×Q8×C11C2×C411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11C2×C412yes—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4C2×C412yes—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D412yes—
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11D411yescharacteristic
50C2×C22⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—22no—
54C2×C4×Dic11—21no—
55C2×C4×Dic11—22no—
56C22×C11⋊C8—21no—
57C11×#107—22no—
58C11×#107—22no—
59C11×#103—22no—
60C11×#103—22no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#9257—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—42no—
82C22×C4×C11—82no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—22no—
92C22×Dic11—41no—
93C2×C8×C11—22no—
94C2×C8×C11—42no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4C22⋊C412yes—
104C11×C4⋊C4C22⋊C412yes—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C22⋊Dic11—21no—
108C22⋊Dic11—21no—
109C22⋊Dic11—21no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11Q1612yes—
115C4⋊Dic11—42no—
116C4⋊Dic11—42no—
117C4⋊Dic11—82no—
118C4×Dic11—42no—
119C4×Dic11—82no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—41no—
122C2×#484D1111yescharacteristic
123#2345—111no—
124#1996—111no—
125#1824—111no—
126#1520—111no—
127#1289—111no—
128#1282—111no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C4×D411yescharacteristic
132C23×C11#12011yescharacteristic
133C23×C11#12111yescharacteristic
134C23×C11C2×Q1611yescharacteristic
135C23×C11#13511yescharacteristic
136C23×C11#13711yescharacteristic
137C23×C11#13711yescharacteristic
138Q8×C11—42no—
139Q8×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C8×C11—42no—
173C11⋊C8—81no—
174C2×C22⋊Q8C2×D1111yescharacteristic
175C22×C4⋊C4C2×D1111yescharacteristic
176#484—22no—
177#484—21no—
178#484—21no—
179C2×#107Dic1112yescomplemented
180C2×#103Dic1112yescomplemented
181C2×C22⋊C8—111no—
182C2×C22⋊C8C2×D1111yescharacteristic
183#389—221no—
184#387—222no—
185#380—111no—
186#380—111no—
187#380—221no—
188C4×C4⋊C4—221no—
189C4×C22⋊C4—111no—
190C4×C22⋊C4—221no—
191#342—221no—
192#342—221no—
193#340—222no—
194#328—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11#38611yescharacteristic
206C22×C11C4×Q1611yescharacteristic
207C22×C11#44111yescharacteristic
208C22×C11#45111yescharacteristic
209C22×C11#45211yescharacteristic
210C22×C11#46211yescharacteristic
211C22×C11#46411yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11#41012yes—
220Dic11—42no—
221Dic11—81no—
222Dic11—82no—
223Dic11—161no—
224C22×Q8C2×Dic1111yescharacteristic
225C23×C4—21no—
226C23×C4C22×D1111yescharacteristic
227C22×C8—221no—
228C22×C8C2×Dic1112yes—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4C2×Dic1111yescharacteristic
241C2×C4⋊C4C2×Dic1112yes—
242C2×C4⋊C4C22⋊D1112yes—
243C2×C4⋊C4C22⋊D1111yescharacteristic
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42—221no—
251C2×C42—222no—
252#107—22no—
253#107—22no—
254#103—22no—
255#103—22no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260#95—112no—
261#95—222no—
262#95—222no—
263#95—221no—
264#95—221no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11#187811yescharacteristic
272C2×C11#189911yescharacteristic
273C2×C11#190411yescharacteristic
274C24D4×D1111yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—82no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4#434111yescharacteristic
293C22×C4C22×Dic1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—442no—
299C2×C8—441no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C4⋊C4—882no—
311C4⋊C4C22⋊Dic1112yes—
312C4⋊C4C22⋊Dic1112yes—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—112no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—442no—
324C42—882no—
325C11#925711yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23Q16×D1111yescharacteristic
329C23#6697111yescharacteristic
330C23#6697111yescharacteristic
331C23#6697211yescharacteristic
332C23D4×Dic1111yescharacteristic
333C23#6699011yescharacteristic
334C23#6699211yescharacteristic
335Q8—42no—
336Q8—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—222no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4D4×Dic1111yescharacteristic
366C2×C4#6698811yescharacteristic
367C2×C4#6699211yescharacteristic
368C2×C4C2×C22⋊Dic1111yescharacteristic
369C8—42no—
370C8—881no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22#1062279511yescharacteristic
382C22Q16×Dic1111yescharacteristic
383C22#1062279711yescharacteristic
384C22#1062279811yescharacteristic
385C22#1062279911yescharacteristic
386C22#1062280011yescharacteristic
387C22#1062283311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—42no—
393C4—81no—
394C4—81no—
395C4—442no—
396C4—881no—
397C4—882no—
398C4—1761no—
399C4#1062285312yes—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1306895911yescharacteristic
407C2#1306907511yescharacteristic
408C2#1306910511yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#484C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#484D11
hypocenterC11#9257
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
13. C2×C11×#107C4semidirect
14. C2×C11×#103C4semidirect
179. C2×#107Dic11semidirect
180. C2×#103Dic11semidirect
325. C11#9257semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130696022
#130687062
#130671882
#130664842
#130664632
C2×C11×#4842
#925711