Finite Group Databasebeta

← #14650615

Subgroups — #14650615

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13068637C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic, complemented
5#13066519C211yesmaximal, characteristic, complemented
6#13066491C211yesmaximal, characteristic, complemented
7C11×#1987C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C4×#4339C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12C8×C22⋊D11—22no—
13#10622707C412yescomplemented
14#10622704—21no—
15#10622700C412yescomplemented
16#10622697—21no—
17#10622579—21no—
18#10622577—21no—
19C2×#66869—21no—
20#10622538C2211yescharacteristic
21#10622537C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622447—21no—
24#10622446—21no—
25D11×C4⋊C8—21no—
26#10622443—21no—
27C11×#340—22no—
28#10622184—21no—
29#10622184—21no—
30#10622161—21no—
31C22×Q8×C11—21no—
32C2×#4339D411yescharacteristic
33C22×C8×C11D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8C2×C412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45#66979D411yescharacteristic
46C2×#4318—21no—
47C2×#4318—21no—
48C2×C8×D11—22no—
49C4×D44C2×C411yescharacteristic
50C4×D44D411yescharacteristic
51#66925—21no—
52C42×D11—21no—
53C4×Dic22C2×C411yescharacteristic
54C4×Dic22D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#95—21no—
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—22no—
60Dic11⋊C8—22no—
61C8×Dic11—22no—
62#66874—22no—
63#66873—22no—
64#66872—22no—
65#66871—22no—
66#66869—42no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)C2×C412yes—
71C4⋊(C11⋊C8)D411yescharacteristic
72C4⋊(C11⋊C8)D411yescharacteristic
73C4×C11⋊C8—21no—
74#9315—111nomaximal, Sylow
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—21no—
84#4339—21no—
85#4339—21no—
86#4339SD1612yes—
87#4339Q1612yes—
88C2×D44C22⋊C411yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×Dic22C22⋊C411yescharacteristic
93C2×C8×C11—22no—
94C2×C8×C11—42no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11—41no—
102C42×C11—41no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C22⋊Dic11—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110C4⋊Dic11C22⋊C411yescharacteristic
111C4⋊Dic11C22⋊C411yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—41no—
118#4318—41no—
119#4318—41no—
120#4318—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—41no—
125C8×D11—82no—
126#3079—111no—
127#2988—111no—
128#1987D1111yescharacteristic, complemented
129#1806—111no—
130#1548—111no—
131#1303—111no—
132#1292—111no—
133C23×C11#12111yescharacteristic
134C22×D11—21no—
135Q8×C11—82no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—81no—
143C2×C4×C11—82no—
144C2×C4×C11—81no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11C2×Q1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C22⋊D11—22no—
156C22⋊D11—22no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160D44—21no—
161D44#10312yes—
162C4×D11—22no—
163C4×D11—22no—
164C4×D11—41no—
165C4×D11—41no—
166C4×D11—81no—
167Dic22—21no—
168Dic22#10312yes—
169C8×C11—42no—
170C11⋊C8—42no—
171C11⋊C8—41no—
172C11⋊C8—41no—
173C11⋊C8—81no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175C4×#41—111no—
176#477—221no—
177#476—221no—
178#475—112no—
179#474—112no—
180C8×Q8—221no—
181C8×D4—221no—
182C8×D4—222no—
183#431—111no—
184#431—221no—
185#428—221no—
186#423—111no—
187#423—111no—
188C2×C4⋊C8—221no—
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#104—221no—
191#417—221no—
192C4×C4⋊C4C2×D1111yescharacteristic
193#340—22no—
194#339—221no—
195#333—221no—
196#333—221no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11#38611yescharacteristic
200C22×C11#46511yescharacteristic
201C22×C11#46711yescharacteristic
202C2×D11—22no—
203C2×D11—41no—
204C2×D11—41no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—82no—
209C4×C11—82no—
210C4×C11C2×#10311yescharacteristic
211C4×C11#41611yescharacteristic
212C4×C11#45511yescharacteristic
213C4×C11#45611yescharacteristic
214C4×C11#46511yescharacteristic
215C4×C11#46711yescharacteristic
216Dic11—22no—
217Dic11—41no—
218Dic11—41no—
219C2×#41—111no—
220C22×Q8—21no—
221C2×M16—221no—
222C2×M16—221no—
223C22×C8—222no—
224C22×C8C22⋊D1112yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C4×D1112yes—
229C4×Q8—111no—
230C4×Q8—111no—
231C4×D4—111no—
232C4×D4—111no—
233C4×D4—221no—
234C4×D4—221no—
235#117—111no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—222no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—111no—
249C4⋊C8—111no—
250C4⋊C8—222no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254#104—442no—
255#103—222no—
256#102—222no—
257C22⋊C8—222no—
258C22⋊C8—221no—
259C4×C8—222no—
260C4×C8—221no—
261#95—21no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11#188211yescharacteristic
265C2×C11#189211yescharacteristic
266C2×C11#190311yescharacteristic
267D11—42no—
268#41—112no—
269#41—112no—
270#41—221no—
271#41—221no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×Q8—111no—
276C2×D4—111no—
277C2×D4—221no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4D4×D1111yescharacteristic
284C22×C4#434111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286M16—441no—
287M16—441no—
288M16—441no—
289M16—441no—
290C2×C8—22no—
291C2×C8—42no—
292C2×C8—222no—
293C2×C8—221no—
294C2×C8—221no—
295C2×C8—441no—
296C2×C8—882no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—111no—
304C4⋊C4—111no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C42—41no—
311C42—41no—
312C42—221no—
313C42—221no—
314C42—221no—
315C42C2×C4×D1111yescharacteristic
316C42#433911yescharacteristic
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C11#931511yescharacteristic, complemented, Sylow
320C23—221no—
321C23#6699111yescharacteristic
322Q8—82no—
323Q8—82no—
324Q8—112no—
325Q8—221no—
326D4—112no—
327D4—222no—
328D4—222no—
329D4—221no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—221no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4C22⋊C4×D1111yescharacteristic
347C2×C4(C22⋊D11)⋊C411yescharacteristic
348C2×C4#6693611yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4SD16×D1111yescharacteristic
351C2×C4#6696911yescharacteristic
352C2×C4Q16×D1111yescharacteristic
353C2×C4#6697211yescharacteristic
354C2×C4C4×C22⋊D1111yescharacteristic
355C2×C4#6699011yescharacteristic
356C8—42no—
357C8—442no—
358C8—441no—
359C8—441no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—222no—
364C22—441no—
365C22—441no—
366C22#1062256911yescharacteristic
367C22#1062278411yescharacteristic
368C22#1062280111yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—222no—
375C4—441no—
376C4—441no—
377C4D11×#10311yescharacteristic
378C4#1062241711yescharacteristic
379C4#1062242011yescharacteristic
380C4#1062242611yescharacteristic
381C4#1062267411yescharacteristic
382C4#1062270811yescharacteristic
383C2—21no—
384C2—21no—
385C2—442no—
386C2#1306898811yescharacteristic
387C2#1306903611yescharacteristic
388C2#1306909311yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1987C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1987D11
hypocenterC11#9315
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. #13067297C2semidirect
5. #13066519C2semidirect
6. #13066491C2semidirect
7. C11×#1987C2semidirect
13. #10622707C4semidirect
15. #10622700C4semidirect
128. #1987D11semidirect
319. C11#9315semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130777252
#130686372
#130672972
#130665192
#130664912
C11×#19872
#931511