Finite Group Databasebeta

← #14666718

Subgroups — #14666718

Order 2816.

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

normal subgroups only

This group has 378 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#13069966C211yesmaximal, characteristic, complemented
2#13067589C211yesmaximal, characteristic, complemented
3#13067555C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic, complemented
7C11×#2785C211yesmaximal, characteristic
8#10623031C2211yescharacteristic
9C11×#395C2211yescharacteristic
10C11×#394—21no—
11C11×#394C2211yescharacteristic
12C11×#393—21no—
13C11×#388—21no—
14C11×#388—21no—
15C11×#388—21no—
16C11×#382—21no—
17C11×#382C2211yescharacteristic
18#10622841—21no—
19#10622831—21no—
20#10622577—21no—
21#10622168C2211yescharacteristic
22#10622166C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622161—21no—
25#10622090—21no—
26#10622090—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11—21no—
40C2×C42×C11D411yescharacteristic
41C2×#4326—41no—
42C2×#4324—41no—
43#66979—21no—
44#66977—21no—
45#66977—21no—
46C2×#4318—21no—
47#66943—41no—
48#66941—41no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66899—41no—
57#66896—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66872—41no—
61#66871—41no—
62#12239—111nomaximal, Sylow
63C24×C11—21no—
64C2×Q8×C11—41no—
65C2×Q8×C11—81no—
66C2×D4×C11—41no—
67C2×D4×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—81no—
81C11×C4⋊C4—81no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—81no—
87C11×C22⋊C4—81no—
88C11×C22⋊C4—81no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—42no—
92C22⋊Dic11—41no—
93#4326—82no—
94#4324—82no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102#4318—22no—
103#4318—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2785D1111yescharacteristic
108#2061—111no—
109#1605—111no—
110#1599—111no—
111#1354—111no—
112#1345—111no—
113#1324—111no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122Q8×C11—42no—
123Q8×C11—81no—
124D4×C11—42no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
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—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151Dic22—81no—
152Dic22—81no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156#544—111no—
157#451—221no—
158#450—221no—
159#428—221no—
160#395C2×D1111yescharacteristic
161#394—21no—
162#394C2×D1111yescharacteristic
163#393—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#382—21no—
168#382C2×D1111yescharacteristic
169#343—111no—
170#339—221no—
171#328—221no—
172#328—221no—
173#324—111no—
174#324—111no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#45211yescharacteristic
185C22×C11#45611yescharacteristic
186C22×C11B(4,𝔽2)11yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8C22⋊D1111yescharacteristic
199C22×D4C22⋊D1111yescharacteristic
200C2×Q16—441no—
201C2×SD16—441no—
202C2×M16—221no—
203C4⋊Q8—441no—
204#125—441no—
205C22⋊Q8—221no—
206C22⋊Q8—221no—
207#117—221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—21no—
219C2×C42C22⋊D1111yescharacteristic
220#107—441no—
221#106—441no—
222#103—441no—
223#102—441no—
224C22⋊C8—221no—
225C22⋊C8—221no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C22⋊D1111yescharacteristic
232#95C22⋊D1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—161no—
236C2×C11#160311yescharacteristic
237C2×C11#219911yescharacteristic
238C2×C11#220411yescharacteristic
239C24—21no—
240C2×Q8—41no—
241C2×Q8—81no—
242C2×Q8—221no—
243C2×Q8—221no—
244C2×D4—41no—
245C2×D4—81no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4C2×C22⋊D1111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254Q16—882no—
255SD16—882no—
256M16—222no—
257M16—441no—
258C2×C8—441no—
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C22⋊C4—81no—
278C22⋊C4—441no—
279C42—21no—
280C42—21no—
281C42—42no—
282C42—441no—
283C11#1223911yescharacteristic, complemented, Sylow
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#6700611yescharacteristic
292Q8—42no—
293Q8—81no—
294Q8—881no—
295Q8—881no—
296D4—42no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4#6700311yescharacteristic
322C2×C4#6700411yescharacteristic
323C8—442no—
324C8—881no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062285211yescharacteristic
336C22#1062285711yescharacteristic
337C22#1062285911yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—881no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2#1306757911yescharacteristic
353C2#1307061711yescharacteristic
354C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2785C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
hypercenter#2785D11
hypocenterC11#12239
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2785

Complements

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

NH ≅ G/Ntype
1. #13069966C2semidirect
2. #13067589C2semidirect
4. #13066646C2semidirect
6. #13066560C2semidirect
283. C11#12239semidirect

Maximal subgroups

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

subgroupindex
#130699662
#130675892
#130675552
#130666462
#130666192
#130665602
C11×#27852
#1223911