Finite Group Databasebeta

← #14666090

Subgroups — #14666090

Order 2816.

404 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069867C211yesmaximal, characteristic
2#13067601C211yesmaximal, characteristic
3#13067567C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066616C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2835C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#400—21no—
10C11×#400—21no—
11C11×#400—21no—
12C11×#397—21no—
13C11×#397C2211yescharacteristic
14C11×#395—21no—
15C11×#393C2211yescharacteristic
16C11×#385—21no—
17C11×#385C2211yescharacteristic
18#10622840—21no—
19#10622826—21no—
20#10622580—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×#4325—41no—
41#66983—21no—
42#66983—21no—
43C2×(C2×D11)⋊C4—41no—
44#66939—41no—
45#66935—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66899—41no—
57C11⋊#95—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—41no—
61#66871—41no—
62#66870—42no—
63#12139—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—81no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C2×D44—21no—
87C2×D44—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—81no—
92C11×C4⋊C4—81no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—81no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101#4325—82no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—82no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2835D1111yescharacteristic, complemented
110#2044—111no—
111#1607—111no—
112#1601—111no—
113#1351—111no—
114#1344—111no—
115#1326—111no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#12011yescharacteristic
121C23×C11#13511yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—81no—
127C22×D11—81no—
128Q8×C11—42no—
129Q8×C11—81no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C22⋊D11—81no—
155C22⋊D11—81no—
156C22⋊D11—81no—
157C22⋊D11—81no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164D44—81no—
165D44—81no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168#534—111no—
169#480—221no—
170#448—221no—
171C2×#99—221no—
172#400—21no—
173#400—21no—
174#400—21no—
175#397—21no—
176#397C2×D1111yescharacteristic
177#395—21no—
178#393C2×D1111yescharacteristic
179#386—221no—
180#385—21no—
181#385C2×D1111yescharacteristic
182#342—111no—
183#327—221no—
184#327—221no—
185#323—111no—
186#323—111no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11#44911yescharacteristic
197C22×C11#45411yescharacteristic
198C22×C11B(4,𝔽2)11yescharacteristic
199C2×D11—82no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—161no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—81no—
213Dic11—161no—
214C22×Q8C22⋊D1111yescharacteristic
215C22×D4—221no—
216C23×C4C22⋊D1111yescharacteristic
217C2×SD16—441no—
218#123—441no—
219#121—221no—
220#121—221no—
221#120—441no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—441no—
231C2×C22⋊C4C22⋊D1111yescharacteristic
232C2×C22⋊C4C22×D1111yescharacteristic
233#107—441no—
234#103—441no—
235#102—441no—
236#99—442no—
237C22⋊C8—221no—
238C22⋊C8—221no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—441no—
248#95C22⋊D1111yescharacteristic
249#95C22⋊D1111yescharacteristic
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—41no—
253C2×C11—41no—
254C2×C11#159711yescharacteristic
255C2×C11#219911yescharacteristic
256C2×C11#220111yescharacteristic
257D11—161no—
258C24—221no—
259C24C2×C22⋊D1111yescharacteristic
260C2×Q8—41no—
261C2×Q8—81no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—81no—
278C22×C4—221no—
279C22×C4—441no—
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—882no—
283C2×C8—441no—
284C2×C8—441no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—882no—
303C11#1213911yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—881no—
312C23—881no—
313C23#6700211yescharacteristic
314C23#6700311yescharacteristic
315C23#6700611yescharacteristic
316Q8—42no—
317Q8—81no—
318D4—881no—
319D4—881no—
320D4—881no—
321D4—881no—
322D4—881no—
323D4—881no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C8—881no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—882no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22—1761no—
370C22#1062285111yescharacteristic
371C22#1062285711yescharacteristic
372C22#1062285811yescharacteristic
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—881no—
382C4—1761no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—1761no—
388C2#1306754511yescharacteristic
389C2#1307061711yescharacteristic
390C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2835C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2835D11
hypocenterC11#12139
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2835

Complements

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

NH ≅ G/Ntype
4. #13066637C2semidirect
5. #13066616C2semidirect
6. #13066564C2semidirect
7. C11×#2835C2semidirect
109. #2835D11semidirect
303. C11#12139semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130676012
#130675672
#130666372
#130666162
#130665642
C11×#28352
#1213911