Finite Group Databasebeta

← #14666655

Subgroups — #14666655

Order 2816.

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

normal subgroups only

This group has 422 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#13069969C211yesmaximal, characteristic, complemented
2#13067572C211yesmaximal, characteristic, complemented
3#13067538C211yesmaximal, characteristic
4#13066637C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2824C211yesmaximal, characteristic
8#10623014C2211yescharacteristic
9C11×#400—21no—
10C11×#397—21no—
11C11×#394—21no—
12C11×#394—21no—
13C11×#393—21no—
14C11×#393C2211yescharacteristic
15C11×#392C2211yescharacteristic
16C11×#386—21no—
17C11×#385C2211yescharacteristic
18#10622841—21no—
19#10622831—21no—
20#10622823—21no—
21#10622165—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622090—21no—
26#10622090—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×#4326—41no—
44C2×#4324—41no—
45#66977—21no—
46#66977—21no—
47C2×Dic11⋊C4—41no—
48#66931—41no—
49#66931—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57#66899—41no—
58#66896—41no—
59C11⋊#95—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#12230—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11C2×D411yescharacteristic
65C2×Q8×C11—41no—
66C2×Q8×C11—81no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
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—41no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C11×C4⋊C4—81no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—81no—
93C11×C22⋊C4—81no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C22⋊Dic11—22no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102#4326—82no—
103#4324—82no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—82no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2824D1111yescharacteristic
112#2062—111no—
113#1602—111no—
114#1596—111no—
115#1351—111no—
116#1343—111no—
117#1326—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11#12011yescharacteristic
130C23×C11#13511yescharacteristic
131C23×C11#13711yescharacteristic
132Q8×C11—42no—
133Q8×C11—81no—
134D4×C11—42no—
135D4×C11—81no—
136D4×C11—82no—
137D4×C11—82no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
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—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166Dic22—81no—
167Dic22—81no—
168C11⋊C8—81no—
169C11⋊C8—81no—
170#543—111no—
171#451—221no—
172#450—221no—
173#400—21no—
174#397—21no—
175#394—21no—
176#394—21no—
177#393—21no—
178#393C2×D1111yescharacteristic
179#392C2×D1111yescharacteristic
180#386—21no—
181#385—221no—
182#385C2×D1111yescharacteristic
183#342—111no—
184#342—221no—
185#328—221no—
186#328—221no—
187#323—111no—
188#323—111no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#45211yescharacteristic
206C22×C11#45611yescharacteristic
207C22×C11B(4,𝔽2)11yescharacteristic
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215Dic11—82no—
216Dic11—81no—
217Dic11—81no—
218C22×Q8C22⋊D1111yescharacteristic
219C22×D4—21no—
220C22×D4C22⋊D1111yescharacteristic
221C23×C4C22⋊D1111yescharacteristic
222C2×Q16—441no—
223C2×SD16—441no—
224C22⋊Q8—221no—
225C22⋊Q8—221no—
226C22⋊Q8—441no—
227C22⋊Q8—441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—441no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4C22⋊D1111yescharacteristic
240C2×C22⋊C4C22×D1111yescharacteristic
241#103—441no—
242#102—441no—
243C22⋊C8—221no—
244C22⋊C8—221no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—441no—
251#95C22⋊D1111yescharacteristic
252#95C22⋊D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11—161no—
258C2×C11#160311yescharacteristic
259C2×C11#219911yescharacteristic
260C2×C11#220011yescharacteristic
261C24—21no—
262C24C2×C22⋊D1111yescharacteristic
263C2×Q8—41no—
264C2×Q8—81no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—81no—
271C2×D4—81no—
272C2×D4—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—81no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—441no—
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—882no—
286SD16—882no—
287C2×C8—441no—
288C2×C8—441no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—882no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—222no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C11#1223011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#6700311yescharacteristic
322C23#6700411yescharacteristic
323C23#6700611yescharacteristic
324Q8—42no—
325Q8—81no—
326Q8—881no—
327Q8—881no—
328D4—42no—
329D4—81no—
330D4—82no—
331D4—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C8—881no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1062285211yescharacteristic
379C22#1062285711yescharacteristic
380C22#1062285911yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—882no—
389C4—881no—
390C4—881no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2#1306757911yescharacteristic
397C2#1307061711yescharacteristic
398C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2824C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#392C22
hypercenter#2824D11
hypocenterC11#12230
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2824

Complements

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

NH ≅ G/Ntype
1. #13069969C2semidirect
2. #13067572C2semidirect
4. #13066637C2semidirect
6. #13066564C2semidirect
309. C11#12230semidirect

Maximal subgroups

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

subgroupindex
#130699692
#130675722
#130675382
#130666372
#130666132
#130665642
C11×#28242
#1223011