Finite Group Databasebeta

← #14648037

Subgroups — #14648037

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071563C211yesmaximal, characteristic
2#13068743C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×#10622121C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1947C211yesmaximal, characteristic, complemented
8C2×#66945—21no—
9C2×C4×D44C2211yescharacteristic
10C2×C11×#107—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622600—21no—
15C2×#66873—21no—
16#10622552—21no—
17#10622548C2211yescharacteristic
18C4×C4⋊Dic11—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622283—22no—
22C11×#340—21no—
23#10622167—21no—
24#10622167—22no—
25#10622121C414yescomplemented
26C22×D44D411yescharacteristic
27C22×C4×D11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D412yes—
43C2×C4×Dic11—22no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66945—42no—
47#66945—42no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44C2×C412yes—
51C4×D44Q812yes—
52C11×#107—42no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8C2×C412yes—
55C11×#95—21no—
56C11⋊#95—22no—
57#66873—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4×C11⋊C8—21no—
61C4×C11⋊C8C2×C412yes—
62#8897—111nomaximal, Sylow
63C23×D11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—22no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C4⋊C412yes—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4D812yes—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11C22×C411yescharacteristic
99C42×C11C2×Q811yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—44no—
105(C2×D11)⋊C4—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—42no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11C4⋊C412yes—
113C4×Dic11—44no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2354—111no—
121#1947D1111yescharacteristic, complemented
122#1834—111no—
123#1802—111no—
124C2×D4⋊C8—111no—
125#1296—111no—
126#1279—111no—
127C23×C11#12011yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11C2×C4⋊C411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C22⋊Q811yescharacteristic
150C2×C4×C11C22⋊Q811yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166D44—22no—
167D44—22no—
168D44—41no—
169D44—41no—
170C4×D11—42no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—42no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×C4×D4—111no—
178C2×#117—221no—
179C2×#107—21no—
180C2×C4⋊C8—111no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×#102—221no—
183C2×C4×C8—111no—
184#390—221no—
185#388—222no—
186#384—111no—
187#384C2×D1111yescharacteristic
188#380—221no—
189C4×C4⋊C4—221no—
190C4×C4⋊C4C2×D1111yescharacteristic
191#340—21no—
192#340—221no—
193#340—222no—
194D4⋊C8—114no—
195C22×C11#38511yescharacteristic
196C22×C11#44711yescharacteristic
197C22×C11#44911yescharacteristic
198C22×C11#45211yescharacteristic
199C22×C11#45211yescharacteristic
200C22×C11#45411yescharacteristic
201C22×C11#45511yescharacteristic
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—81no—
213C4×C11—161no—
214C4×C11#42711yescharacteristic
215C4×C11#42811yescharacteristic
216C4×C11C4×D811yescharacteristic
217C4×C11#44011yescharacteristic
218C4×C11#47411yescharacteristic
219C4×C11#47811yescharacteristic
220C4×C11#48211yescharacteristic
221C4×C11#48511yescharacteristic
222Dic11—42no—
223Dic11—82no—
224C22×D4—111no—
225C23×C4—221no—
226C22×C8—21no—
227C22×C8—221no—
228C22×C8—221no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—221no—
232C4×D4—221no—
233#117—442no—
234#117—442no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C22⋊D1111yescharacteristic
243C2×C4⋊C4C22⋊D1111yescharacteristic
244C2×C22⋊C4—221no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—222no—
247C2×C42—21no—
248C2×C42—222no—
249C2×C42C22×D1111yescharacteristic
250#107—42no—
251C4⋊C8—21no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8C4×D1112yes—
255#102—442no—
256C4×C8—112no—
257C4×C8—221no—
258#95—21no—
259#95—222no—
260C2×C11#162511yescharacteristic
261C2×C11#163811yescharacteristic
262C2×C11#164111yescharacteristic
263C2×C11#164611yescharacteristic
264C2×C11#185411yescharacteristic
265C2×C11#186011yescharacteristic
266C2×C11#186211yescharacteristic
267D11—82no—
268C24—221no—
269C2×D4—112no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—221no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—222no—
293C2×C8—441no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—112no—
307C4⋊C4—221no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4#432312yes—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—444no—
317C22⋊C4—882no—
318C42—41no—
319C42—41no—
320C42—444no—
321C42C2×C4×D1111yescharacteristic
322C42#433911yescharacteristic
323C42Q8×D1111yescharacteristic
324C42#434311yescharacteristic
325C11#889711yescharacteristic, complemented, Sylow
326C23—222no—
327C23—441no—
328C23—441no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23#6699011yescharacteristic
334D4—222no—
335D4—222no—
336D4—441no—
337D4—441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—222no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4C4⋊C4×D1111yescharacteristic
360C2×C4#6694611yescharacteristic
361C2×C4#6694711yescharacteristic
362C2×C4#6694911yescharacteristic
363C2×C4#6696411yescharacteristic
364C2×C4#6696511yescharacteristic
365C2×C4#6697111yescharacteristic
366C2×C4#6697211yescharacteristic
367C2×C4C4×C22⋊D1111yescharacteristic
368C2×C4C2×#432311yescharacteristic
369C2×C4#6699511yescharacteristic
370C2×C4#6699911yescharacteristic
371C2×C4#6700211yescharacteristic
372C2×C4#6700311yescharacteristic
373C8—42no—
374C8—442no—
375C8—881no—
376C22—442no—
377C22—442no—
378C22—442no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22#1062260211yescharacteristic
384C22#1062264911yescharacteristic
385C22#1062266011yescharacteristic
386C22#1062277111yescharacteristic
387C22#1062280011yescharacteristic
388C22#1062281411yescharacteristic
389C22#1062281511yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—161no—
395C4—442no—
396C4—882no—
397C4#1062249311yescharacteristic
398C4#1062249411yescharacteristic
399C4#1062249811yescharacteristic
400C4#1062250111yescharacteristic
401C4C4×#432311yescharacteristic
402C4#1062263911yescharacteristic
403C4#1062267911yescharacteristic
404C4#1062270011yescharacteristic
405C2—882no—
406C2#1306770311yescharacteristic
407C2#1306778711yescharacteristic
408C2#1306780711yescharacteristic
409C2#1306784311yescharacteristic
410C2#1306881211yescharacteristic
411C2#1306884611yescharacteristic
412C2#1306886211yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socleC23×C11#120
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1947D11
hypocenterC11#8897
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #13068743C2semidirect
5. #13066500C2semidirect
6. #13066457C2semidirect
7. C11×#1947C2semidirect
25. #10622121C4semidirect
121. #1947D11semidirect
325. C11#8897semidirect

Maximal subgroups

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

subgroupindex
#130715632
#130687432
#130686132
C2×#106221212
#130665002
#130664572
C11×#19472
#889711