Finite Group Databasebeta

← #14666470

Subgroups — #14666470

Order 2816.

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

normal subgroups only

This group has 434 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#13069662C211yesmaximal, characteristic, complemented
2#13067584C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2832C211yesmaximal, characteristic, complemented
8C2×#66995—21no—
9#10623041C2211yescharacteristic
10C11×#400—21no—
11C11×#397—21no—
12C11×#395C2211yescharacteristic
13C11×#394—21no—
14C11×#394C2211yescharacteristic
15C11×#393—21no—
16C11×#393—21no—
17C11×#391C2211yescharacteristic
18C11×#388—21no—
19#10622840—21no—
20#10622830—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C2×#4339—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
40C2×C42×C11D411yescharacteristic
41C2×#4326—41no—
42#66995—42no—
43#66995—42no—
44C2×#4325—41no—
45C2×#4325—41no—
46C2×#4323—41no—
47#66983—21no—
48#66983—21no—
49C2×#4318—21no—
50#66950—41no—
51#66948—41no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95D411yescharacteristic
59C11×#95D411yescharacteristic
60#66899—41no—
61#66896—41no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66869—42no—
65#12199—111nomaximal, Sylow
66C24×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—81no—
73C2×D4×C11—41no—
74C2×D4×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84#4339—41no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—81no—
99C11×C22⋊C4—81no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C42×C11—41no—
104#4326—44no—
105#4325—44no—
106#4325—82no—
107#4323—82no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112#4318—22no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#2832D1111yescharacteristic, complemented
118#2007—111no—
119#1604—111no—
120#1598—111no—
121#1354—111no—
122#1345—111no—
123#1319—111no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132C22×D11—41no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—81no—
136Q8×C11—81no—
137D4×C11—42no—
138D4×C11—81no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
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—41no—
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#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C22⋊D11—81no—
163C22⋊D11—81no—
164C2×Dic11—41no—
165D44—41no—
166D44—41no—
167D44—81no—
168D44—81no—
169C4×D11—81no—
170C4×D11—81no—
171Dic22—41no—
172Dic22—41no—
173C11⋊C8—42no—
174C11⋊C8—81no—
175C11⋊C8—81no—
176C2×#137—221no—
177#537—111no—
178#448—221no—
179#447—221no—
180C2×#104—221no—
181#400—21no—
182#397—21no—
183#395C2×D1111yescharacteristic
184#394—21no—
185#394C2×D1111yescharacteristic
186#393—21no—
187#393—21no—
188#391C2×D1111yescharacteristic
189#388—21no—
190#343—111no—
191#327—221no—
192#327—221no—
193#324—111no—
194#324—111no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11#44911yescharacteristic
205C22×C11#45311yescharacteristic
206C22×C11B(4,𝔽2)11yescharacteristic
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—81no—
219Dic11—81no—
220C2×#41—221no—
221C22×Q8C22⋊D1111yescharacteristic
222C22×Q8C22⋊D1111yescharacteristic
223C22×D4C22⋊D1111yescharacteristic
224#137—442no—
225#137—442no—
226C2×Q16—441no—
227C2×SD16—441no—
228C2×SD16—441no—
229C2×D8—441no—
230C2×M16—221no—
231C22⋊Q8—441no—
232#121—221no—
233#121—221no—
234#121—441no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C22×D1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42C22⋊D1111yescharacteristic
245#104—442no—
246#103—441no—
247#102—441no—
248C22⋊C8—221no—
249C22⋊C8—221no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95C22⋊D1111yescharacteristic
257#95C22⋊D1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—161no—
261C2×C11#160011yescharacteristic
262C2×C11#219911yescharacteristic
263C2×C11#220311yescharacteristic
264D11—161no—
265C24—21no—
266#41—441no—
267#41—441no—
268#41—441no—
269#41—441no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—81no—
276C2×Q8—221no—
277C2×D4—41no—
278C2×D4—81no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—441no—
289C22×C4C2×C22⋊D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292Q16—444no—
293SD16—444no—
294SD16—882no—
295D8—882no—
296M16—222no—
297M16—441no—
298C2×C8—441no—
299C2×C8—441no—
300C2×C8—441no—
301C4⋊C4—41no—
302C4⋊C4—81no—
303C4⋊C4—81no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—81no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—41no—
316C11#1219911yescharacteristic, complemented, Sylow
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—441no—
325C23#6700611yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—441no—
331Q8—441no—
332D4—42no—
333D4—81no—
334D4—441no—
335D4—441no—
336D4—881no—
337D4—881no—
338D4—881no—
339D4—881no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
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—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—441no—
362C2×C4—881no—
363C2×C4—881no—
364C2×C4#6700211yescharacteristic
365C2×C4#6700311yescharacteristic
366C8—442no—
367C8—881no—
368C8—881no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—881no—
379C22—881no—
380C22—881no—
381C22#1062285111yescharacteristic
382C22#1062285411yescharacteristic
383C22#1062285711yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—881no—
394C2—21no—
395C2—21no—
396C2—161no—
397C2—1761no—
398C2#1306756211yescharacteristic
399C2#1307061711yescharacteristic
400C2#1307063711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2832C2
socleC22×C11B(4,𝔽2)
prime radical#13067550C2
hypercenter#2832D11
hypocenterC11#12199
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2832

Complements

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

NH ≅ G/Ntype
1. #13069662C2semidirect
2. #13067584C2semidirect
4. #13066646C2semidirect
5. #13066619C2semidirect
6. #13066550C2semidirect
7. C11×#2832C2semidirect
117. #2832D11semidirect
316. C11#12199semidirect

Maximal subgroups

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

subgroupindex
#130696622
#130675842
#130675502
#130666462
#130666192
#130665502
C11×#28322
#1219911