Finite Group Databasebeta

← #14649694

Subgroups — #14649694

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078413C211yesmaximal, characteristic
2#13067179C211yesmaximal, characteristic, complemented
3#13067114C211yesmaximal, characteristic, complemented
4#13067007C211yesmaximal, characteristic
5#13066519C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2357C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#390—21no—
11C11×#388—22no—
12C11×#382C2211yescharacteristic
13C11×#381—21no—
14C4×C11×C4⋊C4—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16C4×C11×C22⋊C4—21no—
17#10622828—21no—
18#10622622—22no—
19#10622621C412yescomplemented
20#10622620C412yescomplemented
21#10622577—21no—
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25D4⋊(C11⋊C8)—22no—
26#10622090—21no—
27#10622090—21no—
28#10622090—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11C2×C412yes—
34C4×D4×C11D412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C42×C11—21no—
42C2×C42×C11—22no—
43C2×C42×C11C2311yescharacteristic
44#66979—21no—
45#66977—21no—
46#66977—21no—
47C2×#4318—21no—
48#66923—21no—
49#66922C2×C411yescharacteristic
50#66922C2×C411yescharacteristic
51C4×Dic22—21no—
52C4×Dic22—21no—
53C11×#95—22no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57C11×#95D412yes—
58#66896—22no—
59#66896—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66872—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)C2×C412yes—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#9177—111nomaximal, Sylow
71C24×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11C22⋊C412yes—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—82no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×Dic22—21no—
89C2×Dic22—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4C22⋊C412yes—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—44no—
98C11×C22⋊C4—82no—
99C42×C11—41no—
100C42×C11—41no—
101C42×C11—82no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C4×Dic11—41no—
114#4318—41no—
115#4318—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#3077—111no—
120#2357D1111yescharacteristic
121#1518—111no—
122#1503—111no—
123#1478—111no—
124#1303—111no—
125#1286—111no—
126C23×C11—22no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132D4×C11—22no—
133D4×C11—22no—
134D4×C11—41no—
135D4×C11—41no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
151C2×C4×C11C2×C22⋊C411yescharacteristic
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163Dic22—81no—
164Dic22—81no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168#533—111no—
169C2×C4×D4C2×D1111yescharacteristic
170#478—222no—
171#476—112no—
172#474—112no—
173#431—111no—
174#431—111no—
175#428—221no—
176#423—111no—
177#418—221no—
178#390—21no—
179#388—22no—
180#382C2×D1111yescharacteristic
181#381—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4C2×D1111yescharacteristic
184C4×C22⋊C4—21no—
185#328—221no—
186#328—221no—
187#328—222no—
188D4⋊C8—222no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11#38611yescharacteristic
197C22×C11#45211yescharacteristic
198C22×C11#45211yescharacteristic
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—42no—
205C4×C11—81no—
206C4×C11—82no—
207C4×C11#41611yescharacteristic
208C4×C11#41911yescharacteristic
209C4×C11#48511yescharacteristic
210C4×C11#48511yescharacteristic
211Dic11—81no—
212Dic11—81no—
213C22×D4C22⋊D1111yescharacteristic
214C23×C4—21no—
215C2×M16—221no—
216C4⋊Q8—111no—
217C4⋊Q8—111no—
218#125—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4C4×D1112yes—
226C4×D4D4412yes—
227#117—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C42—21no—
235C2×C42—22no—
236C2×C42C22×D1111yescharacteristic
237#107—222no—
238#106—222no—
239C4⋊C8—112no—
240C4⋊C8—221no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243#102—222no—
244#102—222no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247C4×C8—221no—
248C4×C8—221no—
249#95—22no—
250#95—21no—
251#95C22⋊D1111yescharacteristic
252#95C22⋊D1111yescharacteristic
253#95C22⋊D1112yes—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—82no—
257C2×C11#187311yescharacteristic
258C2×C11#190411yescharacteristic
259C2×C11#190611yescharacteristic
260C24—21no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4(C2×D11)⋊C412yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—82no—
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279M16—441no—
280M16—441no—
281C2×C8—222no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4(C2×D11)⋊C412yes—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—44no—
298C22⋊C4—82no—
299C22⋊C4—441no—
300C42—41no—
301C42—41no—
302C42—82no—
303C42—441no—
304C42C2×C4×D1111yescharacteristic
305C42C2×D4411yescharacteristic
306C42#433911yescharacteristic
307C42#433911yescharacteristic
308C11#917711yescharacteristic, complemented, Sylow
309C23—22no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23#6700611yescharacteristic
315Q8—881no—
316Q8—881no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4C2×(C2×D11)⋊C411yescharacteristic
339C2×C4C4×C22⋊D1111yescharacteristic
340C2×C4C4×C22⋊D1111yescharacteristic
341C2×C4#6698211yescharacteristic
342C2×C4#6698311yescharacteristic
343C2×C4#6698311yescharacteristic
344C2×C4#6700311yescharacteristic
345C2×C4#6700311yescharacteristic
346C2×C4#6700411yescharacteristic
347C2×C4#6700411yescharacteristic
348C8—442no—
349C8—881no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22#1062282611yescharacteristic
359C22#1062285211yescharacteristic
360C22#1062285211yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—82no—
369C4—881no—
370C4—881no—
371C4#1062260911yescharacteristic
372C4#1062260911yescharacteristic
373C4#1062261511yescharacteristic
374C4#1062261711yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2#1306892811yescharacteristic
379C2#1306910311yescharacteristic
380C2#1306911711yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2357C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2357D11
hypocenterC11#9177
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13067179C2semidirect
3. #13067114C2semidirect
5. #13066519C2semidirect
6. #13066474C2semidirect
19. #10622621C4semidirect
20. #10622620C4semidirect
308. C11#9177semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130671792
#130671142
#130670072
#130665192
#130664742
C11×#23572
#917711