Finite Group Databasebeta

← #14650201

Subgroups — #14650201

Order 2816.

552 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071485C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13068702C211yesmaximal, characteristic
4#13067188C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic
7C2×C11×#483C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66979—21no—
11C11×#483—21no—
12C11×#483—21no—
13C11×#483—22no—
14C2×C11×#106C412yescomplemented
15C2×C11×#103C412yescomplemented
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622825C2211yescharacteristic
18#10622825C2211yescharacteristic
19#10622824—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
51#66979—42no—
52#66979—42no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—21no—
59C11×#106—22no—
60C11×#106—22no—
61C11×#103—22no—
62C11×#103—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#9256—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—42no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11—41no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4C22⋊C412yes—
109C11×C4⋊C4C22⋊C412yes—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11SD1612yes—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122C4⋊Dic11—44no—
123C4×Dic11—42no—
124C4×Dic11—44no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—41no—
127C2×#483D1111yescharacteristic
128#2344—111no—
129#1996—111no—
130#1823—111no—
131#1520—111no—
132#1289—111no—
133#1282—111no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11C4×D411yescharacteristic
137C23×C11#12011yescharacteristic
138C23×C11#12111yescharacteristic
139C23×C11C2×SD1611yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11#13711yescharacteristic
143Q8×C11—42no—
144Q8×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C8×C11—42no—
182C11⋊C8—81no—
183C2×C22⋊Q8C2×D1111yescharacteristic
184C2×#117—221no—
185C22×C4⋊C4C2×D1111yescharacteristic
186#483—22no—
187#483—21no—
188#483—21no—
189C2×#106Dic1112yescomplemented
190C2×#103Dic1112yescomplemented
191C2×C22⋊C8—111no—
192C2×C22⋊C8C2×D1111yescharacteristic
193#389—221no—
194#387—222no—
195#381—221no—
196#380—111no—
197#380—111no—
198C4×C4⋊C4—221no—
199C4×C22⋊C4—111no—
200#342—221no—
201#342—221no—
202#340—222no—
203#328—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11#38611yescharacteristic
215C22×C11C4×SD1611yescharacteristic
216C22×C11#44011yescharacteristic
217C22×C11#45011yescharacteristic
218C22×C11#45211yescharacteristic
219C22×C11#46111yescharacteristic
220C22×C11#46311yescharacteristic
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11#41012yes—
229Dic11—42no—
230Dic11—82no—
231Dic11—81no—
232Dic11—161no—
233C22×Q8C2×Dic1111yescharacteristic
234C23×C4—21no—
235C23×C4C22×D1111yescharacteristic
236C22×C8—221no—
237C22×C8C2×Dic1112yes—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242#117—442no—
243#117—442no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4C2×Dic1111yescharacteristic
252C2×C4⋊C4C2×Dic1112yes—
253C2×C4⋊C4C22⋊D1112yes—
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C42—222no—
262C2×C42—221no—
263#106—22no—
264#106—22no—
265#103—22no—
266#103—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—221no—
270C22⋊C8—221no—
271#95—112no—
272#95—222no—
273#95—222no—
274#95—221no—
275#95—221no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11#187711yescharacteristic
283C2×C11#189911yescharacteristic
284C2×C11#190511yescharacteristic
285C24D4×D1111yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—42no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—221no—
301C22×C4—222no—
302C22×C4—221no—
303C22×C4—441no—
304C22×C4D4×D1111yescharacteristic
305C22×C4#434111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C22×Dic1111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C2×C8—22no—
311C2×C8—42no—
312C2×C8—442no—
313C2×C8—441no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—444no—
325C4⋊C4C22⋊Dic1112yes—
326C4⋊C4C22⋊Dic1112yes—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—112no—
330C22⋊C4—221no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42—442no—
338C42—444no—
339C11#925611yescharacteristic, complemented, Sylow
340C23—41no—
341C23—41no—
342C23SD16×D1111yescharacteristic
343C23#6696711yescharacteristic
344C23#6696811yescharacteristic
345C23#6696911yescharacteristic
346C23D4×Dic1111yescharacteristic
347C23#6699011yescharacteristic
348C23#6699211yescharacteristic
349Q8—42no—
350Q8—81no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—441no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4D4×Dic1111yescharacteristic
384C2×C4#6698811yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4C2×C22⋊Dic1111yescharacteristic
387C8—42no—
388C8—881no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22SD16×Dic1111yescharacteristic
400C22#1062277511yescharacteristic
401C22#1062277711yescharacteristic
402C22#1062277811yescharacteristic
403C22#1062278211yescharacteristic
404C22#1062278611yescharacteristic
405C22#1062283311yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—42no—
411C4—81no—
412C4—81no—
413C4—442no—
414C4—882no—
415C4—881no—
416C4—1761no—
417C4#1062285312yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2#1306895211yescharacteristic
425C2#1306907511yescharacteristic
426C2#1306911211yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#483C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#483D11
hypocenterC11#9256
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
14. C2×C11×#106C4semidirect
15. C2×C11×#103C4semidirect
189. C2×#106Dic11semidirect
190. C2×#103Dic11semidirect
339. C11#9256semidirect

Maximal subgroups

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

subgroupindex
#130714852
#130696022
#130687022
#130671882
#130664842
#130664632
C2×C11×#4832
#925611