Finite Group Databasebeta

← #14666746

Subgroups — #14666746

Order 2816.

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

normal subgroups only

This group has 464 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#13069969C211yesmaximal, characteristic, complemented
2#13067606C211yesmaximal, characteristic, complemented
3#13067538C211yesmaximal, characteristic
4#13066616C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2693C211yesmaximal, characteristic
8C2×C11×#123—21no—
9#10623014C2211yescharacteristic
10C11×#400—21no—
11C11×#397C2211yescharacteristic
12C11×#396—21no—
13C11×#392C2211yescharacteristic
14C11×#386—21no—
15C11×#386—21no—
16C11×#385C2211yescharacteristic
17C11×#380—21no—
18#10622831—21no—
19#10622823—21no—
20#10622584—21no—
21#10622165—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622090—21no—
26#10622090—21no—
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C11×#123—42no—
32C11×#123—42no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×#4324—41no—
47#66977—21no—
48#66977—21no—
49C2×Dic11⋊C4—41no—
50#66931—41no—
51#66931—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58#66896—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—41no—
63#66872—41no—
64#12243—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×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—42no—
79C22×C4×C11—41no—
80C22×C4×C11—42no—
81C22×C4×C11—81no—
82C22×C4×C11—81no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—41no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—42no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—81no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4SD1612yescomplemented
103C22⋊Dic11—22no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107#4324—82no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—82no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2693D1111yescharacteristic
116#2062—111no—
117#1608—111no—
118#1596—111no—
119#1344—111no—
120#1343—111no—
121#1326—111no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—22no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11#12011yescharacteristic
134C23×C11C2×SD1611yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136D4×C11—42no—
137D4×C11—81no—
138D4×C11—82no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
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—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—84no—
161C2×C4×C11—81no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169Dic22—81no—
170Dic22—81no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173#543—111no—
174C2×#123—21no—
175#483—221no—
176#450—221no—
177#400—21no—
178#397C2×D1111yescharacteristic
179#396—21no—
180#392C2×D1111yescharacteristic
181#386—21no—
182#386—21no—
183#385—221no—
184#385C2×D1111yescharacteristic
185#380—21no—
186#342—111no—
187#342—221no—
188#328—221no—
189#328—221no—
190#323—111no—
191#323—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—42no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#45011yescharacteristic
209C22×C11#45611yescharacteristic
210C22×C11B(4,𝔽2)11yescharacteristic
211C4×C11—42no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218Dic11—82no—
219Dic11—81no—
220Dic11—81no—
221C22×D4—21no—
222C22×D4C22⋊D1111yescharacteristic
223C23×C4—21no—
224C23×C4C22⋊D1111yescharacteristic
225C2×SD16—441no—
226#123—42no—
227#123—42no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C22⋊Q8—441no—
231C22⋊Q8—441no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—441no—
236C2×C4⋊C4C22⋊D1111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4C22⋊D1111yescharacteristic
245C2×C22⋊C4C22×D1111yescharacteristic
246#106—441no—
247#103—441no—
248#102—441no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—441no—
256#95C22⋊D1111yescharacteristic
257#95C22⋊D1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—41no—
261C2×C11—41no—
262C2×C11—82no—
263C2×C11#160411yescharacteristic
264C2×C11#219711yescharacteristic
265C2×C11#220011yescharacteristic
266C24—21no—
267C24C2×C22⋊D1111yescharacteristic
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4C2×C22⋊D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291SD16—882no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—81no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—882no—
303C22⋊C4—21no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—222no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4#432412yescomplemented
316C11#1224311yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23#6698511yescharacteristic
329C23C2×#432411yescharacteristic
330C23#6700611yescharacteristic
331Q8—881no—
332Q8—881no—
333D4—42no—
334D4—81no—
335D4—82no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—84no—
358C2×C4—81no—
359C2×C4—442no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4—881no—
365C2×C4—881no—
366C8—881no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22#1062283111yescharacteristic
385C22#1062285711yescharacteristic
386C22#1062285911yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—882no—
395C4—881no—
396C4—881no—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—82no—
402C2#1306758511yescharacteristic
403C2#1307060611yescharacteristic
404C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2693C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#392C22
hypercenter#2693D11
hypocenterC11#12243
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2693

Complements

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

NH ≅ G/Ntype
1. #13069969C2semidirect
2. #13067606C2semidirect
4. #13066616C2semidirect
6. #13066564C2semidirect
102. C11×C22⋊C4SD16semidirect
315. C22⋊C4#4324semidirect
316. C11#12243semidirect

Maximal subgroups

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

subgroupindex
#130699692
#130676062
#130675382
#130666162
#130666132
#130665642
C11×#26932
#1224311