Finite Group Databasebeta

← #14650613

Subgroups — #14650613

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#13078432C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic
3#13069564C211yesmaximal, characteristic, complemented
4#13068637C211yesmaximal, characteristic
5#13067296C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C4×#4339C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622746—21no—
14#10622734—21no—
15C2×#66869—21no—
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622464C412yescomplemented
19#10622463—21no—
20#10622459C412yescomplemented
21#10622455—21no—
22#10622446—21no—
23D11×C4⋊C8—21no—
24(C22⋊D11)⋊C8—22no—
25C8×D44—21no—
26C8×Dic22—21no—
27#10622167—22no—
28#10622161—21no—
29#10622119—21no—
30#10622119—21no—
31C2×#4339D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39#66979D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×#4318—21no—
43C22×C11⋊C8D412yes—
44C2×C8×D11—22no—
45C4×D44C2×C411yescharacteristic
46C4×D44D411yescharacteristic
47#66925—21no—
48C42×D11—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922C2×C412yes—
53C4×Dic22C2×C411yescharacteristic
54C4×Dic22D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8C2×C412yes—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×C22⋊C8—21no—
60C4×C8×C11—21no—
61C11×#95—21no—
62#66885—22no—
63(C2×D11)⋊C8—22no—
64#66882—22no—
65#66881—22no—
66#66880—22no—
67Dic11⋊C8—22no—
68C8×Dic11—22no—
69#66869—42no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#9315—111nomaximal, Sylow
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—21no—
80C22×Dic11—41no—
81#4339—21no—
82#4339—21no—
83#4339SD1612yes—
84#4339Q1612yes—
85C2×D44C22⋊C411yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×Dic22—22no—
90C2×Dic22—41no—
91C2×Dic22—82no—
92C2×Dic22C22⋊C411yescharacteristic
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—22no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11C22⋊C411yescharacteristic
114C4⋊Dic11C22⋊C411yescharacteristic
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120#4318—41no—
121#4318—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—42no—
124C2×C11⋊C8—41no—
125C8×D11—82no—
126#3079—111no—
127#2988—111no—
128#1987—111no—
129#1806—111no—
130#1548—111no—
131#1303D1111yescharacteristic, complemented
132#1292—111no—
133C23×C11#12111yescharacteristic
134C22×D11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11C2×SD1611yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C22⋊D11—22no—
152C22⋊D11—22no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—42no—
157C2×Dic11—82no—
158D44—21no—
159D44#10312yes—
160C4×D11—22no—
161C4×D11—22no—
162C4×D11—41no—
163C4×D11—41no—
164C4×D11—81no—
165Dic22—21no—
166Dic22—82no—
167Dic22—82no—
168Dic22#10312yes—
169C8×C11—42no—
170C8×C11—41no—
171C8×C11—41no—
172C11⋊C8—42no—
173C11⋊C8—81no—
174C2×C4⋊Q8—111no—
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—221no—
184#431C2×D1111yescharacteristic
185#428—221no—
186#423—111no—
187#423C2×D1111yescharacteristic
188C2×C4⋊C8—111no—
189C2×C4⋊C8—221no—
190C2×#104—221no—
191#417—221no—
192C4×C4⋊C4C2×D1111yescharacteristic
193#340—222no—
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×C11C2×#10311yescharacteristic
210C4×C11#41611yescharacteristic
211C4×C11#45511yescharacteristic
212C4×C11#45611yescharacteristic
213C4×C11#46511yescharacteristic
214C4×C11#46711yescharacteristic
215Dic11—22no—
216Dic11—41no—
217Dic11—41no—
218Dic11—82no—
219C2×#41—111no—
220C22×Q8—221no—
221C2×M16—21no—
222C2×M16—221no—
223C22×C8—112no—
224C22×C8—222no—
225C4⋊Q8—112no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
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—221no—
239C2×C4⋊C4—221no—
240C2×C42—21no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—222no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—222no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8C4×D1112yes—
252C4⋊C8D4411yescharacteristic
253C4⋊C8D4411yescharacteristic
254#104—442no—
255#103—222no—
256#102—222no—
257C22⋊C8—21no—
258C22⋊C8—222no—
259C4×C8—21no—
260C4×C8—222no—
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—111no—
273C2×Q8—222no—
274C2×Q8—441no—
275C2×Q8—882no—
276C2×D4—111no—
277C2×D4—221no—
278C22×C4—41no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—441no—
283C22×C4#433911yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286M16—41no—
287M16—41no—
288M16—441no—
289M16—441no—
290C2×C8—22no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—222no—
294C2×C8—442no—
295C2×C8—441no—
296C2×C8—882no—
297C4⋊C4—22no—
298C4⋊C4—41no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—222no—
304C4⋊C4—222no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C42—41no—
311C42—41no—
312C42—221no—
313C42—221no—
314C42—221no—
315C42C2×C4×D1111yescharacteristic
316C42C2×D4411yescharacteristic
317C42D4×D1111yescharacteristic
318C42#434311yescharacteristic
319C11#931511yescharacteristic, complemented, Sylow
320C23—221no—
321C23#6693711yescharacteristic
322Q8—112no—
323Q8—221no—
324Q8—882no—
325Q8—882no—
326D4—112no—
327D4—222no—
328D4—222no—
329D4—221no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—221no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—442no—
344C2×C4—881no—
345C2×C4—882no—
346C2×C4C4×D4411yescharacteristic
347C2×C4C22⋊C4×D1111yescharacteristic
348C2×C4#6693511yescharacteristic
349C2×C4#6694611yescharacteristic
350C2×C4#6694711yescharacteristic
351C2×C4#6694811yescharacteristic
352C2×C4#6696511yescharacteristic
353C2×C4SD16×D1111yescharacteristic
354C2×C4#6696911yescharacteristic
355C2×C4Q16×D1111yescharacteristic
356C8—42no—
357C8—41no—
358C8—41no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—222no—
364C22—441no—
365C22—441no—
366C22#1062227811yescharacteristic
367C22#1062239111yescharacteristic
368C22#1062242611yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—222no—
374C4—441no—
375C4—441no—
376C4—882no—
377C4#1062238511yescharacteristic
378C4D11×#10311yescharacteristic
379C4#1062243811yescharacteristic
380C4#1062243911yescharacteristic
381C4#1062247711yescharacteristic
382C4#1062250011yescharacteristic
383C2—21no—
384C2—21no—
385C2—442no—
386C2#1306898611yescharacteristic
387C2#1306903811yescharacteristic
388C2#1306909511yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9315
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #13069564C2semidirect
5. #13067296C2semidirect
6. #13066490C2semidirect
7. C11×#1303C2semidirect
18. #10622464C4semidirect
20. #10622459C4semidirect
131. #1303D11semidirect
319. C11#9315semidirect

Maximal subgroups

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

subgroupindex
#130784322
#130777242
#130695642
#130686372
#130672962
#130664902
C11×#13032
#931511