Finite Group Databasebeta

← #14666317

Subgroups — #14666317

Order 2816.

486 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 63 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#13067635C211yesmaximal, characteristic
3#13067567C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2677C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8—21no—
9C2×C11×C22⋊Q8—21no—
10#10623024C2211yescharacteristic
11C11×#399C2211yescharacteristic
12C11×#398—21no—
13C11×#395—21no—
14C11×#393C2211yescharacteristic
15C11×#388—21no—
16C11×#387—21no—
17C11×#385C2211yescharacteristic
18#10622840—21no—
19#10622826—21no—
20#10622581—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11—21no—
28C22×Q8×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C11×C4⋊Q8—44no—
32C11×C22⋊Q8—44no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C42×C11—21no—
45C2×C22⋊Dic11—21no—
46C2×#4325—41no—
47#66983—21no—
48#66983—21no—
49C2×(C2×D11)⋊C4—41no—
50#66939—41no—
51#66935—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58#66899—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#66870—42no—
65#12176—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C2×Q8×C11—41no—
72C2×Q8×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—42no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C2×D44—21no—
92C2×D44—21no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4SD1612yescomplemented
105C42×C11—42no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108#4325—82no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—82no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2677D1111yescharacteristic, complemented
117#2044—111no—
118#1613—111no—
119#1601—111no—
120#1352—111no—
121#1351—111no—
122#1326—111no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11#12011yescharacteristic
128C23×C11C2×SD1611yescharacteristic
129C23×C11#13711yescharacteristic
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—81no—
134C22×D11—81no—
135Q8×C11—42no—
136Q8×C11—81no—
137Q8×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
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—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C22⋊D11—81no—
163C22⋊D11—81no—
164C22⋊D11—81no—
165C22⋊D11—81no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172D44—81no—
173D44—81no—
174C11⋊C8—81no—
175C11⋊C8—81no—
176#534—111no—
177C2×C4⋊Q8—21no—
178C2×C22⋊Q8—21no—
179#481—221no—
180#448—221no—
181C2×#99—221no—
182#399C2×D1111yescharacteristic
183#398—21no—
184#395—21no—
185#393C2×D1111yescharacteristic
186#388—21no—
187#387—21no—
188#386—221no—
189#385C2×D1111yescharacteristic
190#342—111no—
191#327—221no—
192#327—221no—
193#323—111no—
194#323—111no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—81no—
204C22×C11#44811yescharacteristic
205C22×C11#45411yescharacteristic
206C22×C11B(4,𝔽2)11yescharacteristic
207C2×D11—82no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—161no—
212C4×C11—42no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—81no—
219C4×C11—81no—
220Dic11—81no—
221Dic11—161no—
222C22×Q8—21no—
223C22×Q8C22⋊D1111yescharacteristic
224C22×D4—221no—
225C23×C4C22⋊D1111yescharacteristic
226C2×SD16—441no—
227C4⋊Q8—44no—
228#123—441no—
229C22⋊Q8—44no—
230#121—221no—
231#121—221no—
232#120—441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4C22⋊D1111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—441no—
244C2×C22⋊C4C22⋊D1111yescharacteristic
245C2×C22⋊C4C22×D1111yescharacteristic
246C2×C42—21no—
247#106—441no—
248#103—441no—
249#102—441no—
250#99—442no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—441no—
258#95C22⋊D1111yescharacteristic
259#95C22⋊D1111yescharacteristic
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—41no—
263C2×C11—41no—
264C2×C11#159911yescharacteristic
265C2×C11#219611yescharacteristic
266C2×C11#220111yescharacteristic
267D11—161no—
268C24—221no—
269C24C2×C22⋊D1111yescharacteristic
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—81no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—221no—
292C22×C4—441no—
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295SD16—882no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—24no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C22⋊C4—21no—
308C22⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—441no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—882no—
316C22⋊C4#432512yescomplemented
317C42—42no—
318C11#1217611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—881no—
327C23—881no—
328C23C2×#432511yescharacteristic
329C23#6699511yescharacteristic
330C23#6700611yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—84no—
334D4—881no—
335D4—881no—
336D4—881no—
337D4—881no—
338D4—881no—
339D4—881no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C8—881no—
371C8—881no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—882no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—1761no—
386C22#1062284011yescharacteristic
387C22#1062285711yescharacteristic
388C22#1062285811yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—881no—
398C4—1761no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—1761no—
404C2#1306755611yescharacteristic
405C2#1307060011yescharacteristic
406C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2677C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2677D11
hypocenterC11#12176
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2677

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066637C2semidirect
6. #13066564C2semidirect
7. C11×#2677C2semidirect
104. C11×C22⋊C4SD16semidirect
116. #2677D11semidirect
316. C22⋊C4#4325semidirect
318. C11#12176semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130676352
#130675672
#130666402
#130666372
#130665642
C11×#26772
#1217611