Finite Group Databasebeta

← #14657618

Subgroups — #14657618

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2#13069410C211yesmaximal, characteristic
3#13068613C211yesmaximal, characteristic
4C2×#10622095C211yesmaximal, characteristic, complemented
5C2×#10622184C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×(C2×D11)⋊C8—21no—
14#10622697—22no—
15#10622697—22no—
16C2×#66873—21no—
17C2×#66873—21no—
18C2×#66872—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24#10622184—22no—
25#10622167—21no—
26#10622095—22no—
27C22×Q8×C11—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D412yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×C8×C11—21no—
52C4×C8×C11—21no—
53(C2×D11)⋊C8—42no—
54(C2×D11)⋊C8—42no—
55#66873—24no—
56#66873—42no—
57#66872—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)D412yes—
64#10480—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C2×Q8×C11—81no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44SD1612yes—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11SD1612yes—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—81no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×#476—111no—
121#1990D1111yescharacteristic, complemented
122#1954—111no—
123#1802—111no—
124C2×#334—111no—
125C2×#333—111no—
126#1296—111no—
127C23×C11#12111yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135Q8×C11—82no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11C2×SD1611yescharacteristic
152C2×C4×C11C2×SD1611yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162D44—22no—
163D44—22no—
164D44—41no—
165D44—41no—
166C4×D11—81no—
167C4×D11—81no—
168C4×D11—81no—
169C4×D11—81no—
170C8×C11—22no—
171C8×C11—41no—
172C11⋊C8—42no—
173C11⋊C8—81no—
174C11⋊C8—81no—
175C2×C4⋊Q8C2×D1111yescharacteristic
176C2×C4×D4—111no—
177#476—222no—
178#476—222no—
179C2×#106—221no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8—111no—
182C2×C4⋊C8—111no—
183C2×#102—221no—
184C2×#102—221no—
185C2×C22⋊C8—221no—
186C2×C22⋊C8—221no—
187C2×C4×C8C2×D1111yescharacteristic
188#384C2×D1111yescharacteristic
189#340—21no—
190#340—21no—
191#340—221no—
192#334—222no—
193#333—222no—
194C22×C11#39411yescharacteristic
195C22×C11#46111yescharacteristic
196C22×C11#46311yescharacteristic
197C22×C11#46511yescharacteristic
198C22×C11#47011yescharacteristic
199C22×C11#47111yescharacteristic
200C22×C11#47211yescharacteristic
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—82no—
211C4×C11—161no—
212C4×C11#44811yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#46011yescharacteristic
215C4×C11#46411yescharacteristic
216C4×C11#46511yescharacteristic
217C4×C11#46811yescharacteristic
218C4×C11#48311yescharacteristic
219C4×C11#48511yescharacteristic
220Dic11—81no—
221C22×Q8—21no—
222C22×D4—111no—
223C23×C4—221no—
224C22×C8—221no—
225C22×C8—221no—
226C22×C8—221no—
227C22×C8C22⋊D1111yescharacteristic
228C22×C8C22⋊D1111yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D4412yes—
233C4×D4—221no—
234C4×D4—221no—
235C4×D4—221no—
236C4×D4—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—111no—
243C2×C22⋊C4—221no—
244C2×C42C22×D1111yescharacteristic
245#106—224no—
246C4⋊C8—112no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8—221no—
252#102—224no—
253#102—442no—
254C22⋊C8—442no—
255C22⋊C8—442no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11#167111yescharacteristic
259C2×C11#167711yescharacteristic
260C2×C11#169511yescharacteristic
261C2×C11#170311yescharacteristic
262C2×C11#203511yescharacteristic
263C2×C11#205111yescharacteristic
264C2×C11#205511yescharacteristic
265D11—82no—
266C24—221no—
267C2×Q8—22no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×Q8—81no—
271C2×D4—112no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—221no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4D4×D1111yescharacteristic
287C22×C4#434111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—222no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C2×C8—441no—
299C2×C8—441no—
300C2×C8—441no—
301C2×C8—441no—
302C2×C8—441no—
303C2×C8#432512yes—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—81no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C42C2×D4411yescharacteristic
318C42#433911yescharacteristic
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C11#1048011yescharacteristic, complemented, Sylow
322C23—222no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23#6699111yescharacteristic
330Q8—82no—
331Q8—82no—
332D4—222no—
333D4—222no—
334D4—441no—
335D4—441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—881no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4#6693511yescharacteristic
352C2×C4#6693611yescharacteristic
353C2×C4#6693811yescharacteristic
354C2×C4#6693911yescharacteristic
355C2×C4SD16×D1111yescharacteristic
356C2×C4#6696911yescharacteristic
357C2×C4#6697111yescharacteristic
358C2×C4#6697111yescharacteristic
359C2×C4#6698311yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4C2×#432511yescharacteristic
362C2×C4#6699511yescharacteristic
363C2×C4#6700211yescharacteristic
364C2×C4#6700311yescharacteristic
365C8—22no—
366C8—41no—
367C8—442no—
368C8—881no—
369C8—881no—
370C22—442no—
371C22—442no—
372C22—442no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22#1062257411yescharacteristic
378C22#1062267011yescharacteristic
379C22#1062269611yescharacteristic
380C22#1062277311yescharacteristic
381C22#1062278411yescharacteristic
382C22#1062279011yescharacteristic
383C22#1062280211yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—161no—
388C4—881no—
389C4#1062241811yescharacteristic
390C4#1062241911yescharacteristic
391C4#1062242311yescharacteristic
392C4#1062242811yescharacteristic
393C4#1062264011yescharacteristic
394C4#1062264111yescharacteristic
395C4#1062266111yescharacteristic
396C4#1062266211yescharacteristic
397C2—882no—
398C2#1306798811yescharacteristic
399C2#1306802211yescharacteristic
400C2#1306813611yescharacteristic
401C2#1306818811yescharacteristic
402C2#1306981111yescharacteristic
403C2#1306990911yescharacteristic
404C2#1306993111yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#10480
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#10622095C2semidirect
5. C2×#10622184C2semidirect
6. #13066499C2semidirect
7. C11×#1990C2semidirect
121. #1990D11semidirect
321. C11#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130694102
#130686132
C2×#106220952
C2×#106221842
#130664992
C11×#19902
#1048011