Finite Group Databasebeta

← #14666191

Subgroups — #14666191

Order 2816.

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

normal subgroups only

This group has 458 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#13069845C211yesmaximal, characteristic, complemented
2#13067618C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic
4#13066622C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066560C211yesmaximal, characteristic, complemented
7C11×#2609C211yesmaximal, characteristic, complemented
8C2×C11×#117—21no—
9#10623041C2211yescharacteristic
10C11×#398C2211yescharacteristic
11C11×#396—21no—
12C11×#394C2211yescharacteristic
13C11×#388—21no—
14C11×#387—21no—
15C11×#386—21no—
16C11×#385—21no—
17C11×#382C2211yescharacteristic
18#10622830—21no—
19#10622580—21no—
20#10622579—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C2×#4339—21no—
30C11×#117—42no—
31C11×#117—42no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11D411yescharacteristic
45C2×#4323—41no—
46#66983—21no—
47#66983—21no—
48C2×#4318—21no—
49#66950—41no—
50#66948—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57#66896—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66873—41no—
62#66873—41no—
63#66871—41no—
64#66869—42no—
65#12154—111nomaximal, Sylow
66C24×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—81no—
103C42×C11—21no—
104C42×C11—42no—
105C42×C11D812yescomplemented
106#4323—82no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111#4318—41no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2609D1111yescharacteristic, complemented
117#2040—111no—
118#1610—111no—
119#1598—111no—
120#1346—111no—
121#1345—111no—
122#1324—111no—
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C22×D11—41no—
132D4×C11—42no—
133D4×C11—81no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—48no—
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×C11C2×D811yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C22⋊D11—81no—
159C22⋊D11—81no—
160C2×Dic11—41no—
161D44—41no—
162D44—41no—
163D44—81no—
164D44—81no—
165C4×D11—81no—
166C4×D11—81no—
167Dic22—41no—
168Dic22—41no—
169C11⋊C8—81no—
170C11⋊C8—81no—
171C11⋊C8—81no—
172#537—111no—
173C2×#117—21no—
174#480—221no—
175#447—221no—
176C2×#104—221no—
177#417—221no—
178#398C2×D1111yescharacteristic
179#396—21no—
180#394C2×D1111yescharacteristic
181#388—21no—
182#387—21no—
183#386—21no—
184#385—21no—
185#382C2×D1111yescharacteristic
186#343—111no—
187#327—221no—
188#327—221no—
189#324—111no—
190#324—111no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#44711yescharacteristic
201C22×C11#45411yescharacteristic
202C22×C11B(4,𝔽2)11yescharacteristic
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215Dic11—81no—
216C2×#41—221no—
217C22×D4C22⋊D1111yescharacteristic
218C23×C4—21no—
219C2×D8—441no—
220C2×M16—221no—
221C22⋊Q8—441no—
222#121—221no—
223#121—221no—
224#121—441no—
225#117—42no—
226#117—42no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D1111yescharacteristic
231C2×C4⋊C4C22⋊D1111yescharacteristic
232C2×C4⋊C4C22×D1111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C42—21no—
239C2×C42C22⋊D1111yescharacteristic
240#107—441no—
241#104—442no—
242#103—441no—
243#102—441no—
244#102—441no—
245#102—441no—
246C22⋊C8—221no—
247C22⋊C8—221no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C22⋊D1111yescharacteristic
253#95C22⋊D1111yescharacteristic
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—82no—
257C2×C11#159811yescharacteristic
258C2×C11#219711yescharacteristic
259C2×C11#220411yescharacteristic
260D11—161no—
261C24—21no—
262#41—441no—
263#41—441no—
264#41—441no—
265#41—441no—
266C2×Q8—221no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—441no—
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285D8—882no—
286M16—441no—
287M16—441no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—21no—
309C42—42no—
310C42#432312yescomplemented
311C11#1215411yescharacteristic, complemented, Sylow
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—441no—
320C23#6700611yescharacteristic
321Q8—441no—
322Q8—441no—
323D4—42no—
324D4—81no—
325D4—441no—
326D4—441no—
327D4—881no—
328D4—881no—
329D4—881no—
330D4—881no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—48no—
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—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—441no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4C2×#432311yescharacteristic
357C2×C4#6698511yescharacteristic
358C8—881no—
359C8—881no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22#1062283011yescharacteristic
374C22#1062285711yescharacteristic
375C22#1062285811yescharacteristic
376C4—21no—
377C4—21no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—881no—
386C2—21no—
387C2—21no—
388C2—82no—
389C2—1761no—
390C2#1306755111yescharacteristic
391C2#1307060611yescharacteristic
392C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2609C2
socleC22×C11B(4,𝔽2)
prime radical#13067550C2
hypercenter#2609D11
hypocenterC11#12154
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2609

Complements

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

NH ≅ G/Ntype
1. #13069845C2semidirect
2. #13067618C2semidirect
4. #13066622C2semidirect
5. #13066619C2semidirect
6. #13066560C2semidirect
7. C11×#2609C2semidirect
105. C42×C11D8semidirect
116. #2609D11semidirect
310. C42#4323semidirect
311. C11#12154semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130676182
#130675502
#130666222
#130666192
#130665602
C11×#26092
#1215411