Finite Group Databasebeta

← #14666440

Subgroups — #14666440

Order 2816.

458 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 55 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#13073865C211yesmaximal, characteristic, complemented
2#13067653C211yesmaximal, characteristic, complemented
3#13067551C211yesmaximal, characteristic
4#13066642C211yesmaximal, characteristic, complemented
5#13066618C211yesmaximal, characteristic, complemented
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2007C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#537C2211yescharacteristic
10C2×C11×#104—21no—
11C11×#391C2211yescharacteristic
12#10622844—21no—
13#10622649—21no—
14#10622647—21no—
15#10622604C2211yescharacteristic
16#10622599C2211yescharacteristic
17C4×(C2×D11)⋊C4—21no—
18#10622283—21no—
19#10622278—21no—
20#10622277—21no—
21#10622264—21no—
22C11×#343C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C11×#137—42no—
32C11×#137—42no—
33C2×C11×Q16—41no—
34C2×C11×SD16—41no—
35C2×C11×M16—21no—
36C11×C22⋊Q8—41no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—41no—
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×#4323—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4×Dic11—21no—
50C11×#104—42no—
51C11×#95—21no—
52C11×#95—21no—
53#66896—41no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66873—41no—
64#66872—41no—
65#12195—111nomaximal, Sylow
66C23×D11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×D44—41no—
90C2×D44—42no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—81no—
94C11×Q16—44no—
95C11×SD16—44no—
96C11×M16—22no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105#4323—82no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112C4⋊Dic11—41no—
113C4×Dic11—42no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2572—111no—
117#2007D1111yescharacteristic, complemented
118#1616—111no—
119#1598—111no—
120#1353—111no—
121#1345—111no—
122#1319—111no—
123C23×C11—41no—
124C23×C11#12011yescharacteristic
125C22×D11—22no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132Q8×C11—42no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—81no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
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—81no—
156C2×C4×C11—81no—
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168D44—42no—
169D44—81no—
170C4×D11—84no—
171C8×C11—42no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174C2×#137—21no—
175#537C2×D1111yescharacteristic
176#481—221no—
177#447—221no—
178C2×#104—21no—
179#400—111no—
180#394—111no—
181#393—221no—
182#391C2×D1111yescharacteristic
183#388—221no—
184#386—221no—
185#383—221no—
186#381—221no—
187C4×C22⋊C4—221no—
188#343C2×D1111yescharacteristic
189#327—221no—
190#327—221no—
191#324—111no—
192#324—111no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#44911yescharacteristic
199C22×C11#45311yescharacteristic
200C22×C11B(4,𝔽2)11yescharacteristic
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214C4×C11—81no—
215Dic11—81no—
216Dic11—81no—
217Dic11—81no—
218C2×#41—21no—
219C22×Q8C22⋊D1111yescharacteristic
220C22×D4—111no—
221C23×C4—221no—
222#137—42no—
223#137—42no—
224C2×Q16—41no—
225C2×SD16—41no—
226C2×D8—441no—
227C2×M16—21no—
228C22⋊Q8—41no—
229#121—21no—
230#121—21no—
231#121—41no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42—221no—
240C2×C42C22⋊D1111yescharacteristic
241#106—441no—
242#104—42no—
243#102—441no—
244#102—441no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#95—21no—
248#95—21no—
249#95—111no—
250#95—111no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—161no—
259C2×C11#160011yescharacteristic
260C2×C11#219711yescharacteristic
261C2×C11#220411yescharacteristic
262D11—82no—
263C24—221no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—441no—
278C2×D4—442no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—881no—
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291Q16—44no—
292SD16—44no—
293D8—882no—
294M16—22no—
295M16—41no—
296C2×C8—41no—
297C2×C8—441no—
298C2×C8—441no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—442no—
306C22⋊C4—442no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—881no—
310C22⋊C4—881no—
311C42—41no—
312C42—442no—
313C11#1219511yescharacteristic, complemented, Sylow
314C23—41no—
315C23—222no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23#6699011yescharacteristic
323Q8—42no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—442no—
334D4—881no—
335C2×C4—21no—
336C2×C4—21no—
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—81no—
349C2×C4—81no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—884no—
360C2×C4#6698511yescharacteristic
361C2×C4#6700311yescharacteristic
362C8—42no—
363C8—881no—
364C8—881no—
365C22—21no—
366C22—21no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—442no—
371C22—442no—
372C22—442no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22#1062264511yescharacteristic
378C22#1062265011yescharacteristic
379C22#1062269011yescharacteristic
380C4—21no—
381C4—21no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—881no—
388C4—881no—
389C4—881no—
390C2—21no—
391C2—21no—
392C2—161no—
393C2—882no—
394C2#1306756011yescharacteristic
395C2#1307060511yescharacteristic
396C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2007C2
socleC22×C11B(4,𝔽2)
prime radical#13067551C2
hypercenter#2007D11
hypocenterC11#12195
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2007

Complements

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

NH ≅ G/Ntype
1. #13073865C2semidirect
2. #13067653C2semidirect
4. #13066642C2semidirect
5. #13066618C2semidirect
6. #13066550C2semidirect
7. C11×#2007C2semidirect
117. #2007D11semidirect
313. C11#12195semidirect

Maximal subgroups

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

subgroupindex
#130738652
#130676532
#130675512
#130666422
#130666182
#130665502
C11×#20072
#1219511