Finite Group Databasebeta

← #14666447

Subgroups — #14666447

Order 2816.

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

normal subgroups only

This group has 434 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#13074112C211yesmaximal, characteristic, complemented
2#13067653C211yesmaximal, characteristic, complemented
3#13067619C211yesmaximal, characteristic, complemented
4#13066642C211yesmaximal, characteristic, complemented
5#13066621C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#2006C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#537C2211yescharacteristic
10C2×C11×#104—21no—
11C11×#390C2211yescharacteristic
12#10622835—21no—
13#10622647—21no—
14#10622646—21no—
15#10622599C2211yescharacteristic
16#10622596C2211yescharacteristic
17#10622564—21no—
18#10622564—21no—
19#10622558—21no—
20#10622558—21no—
21C4×Dic11⋊C4—21no—
22C11×#343C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C11×AGL(1,ℤ/8)—42no—
30C11×AGL(1,ℤ/8)—42no—
31C2×C11×SD16—41no—
32C2×C11×D8—41no—
33C2×C11×M16—21no—
34C11×C22⋊Q8—41no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#121—41no—
38C2×C11×C4⋊C4C2311yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11D411yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C11×#104—42no—
53#66896—41no—
54#66896—41no—
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#66872—41no—
64#66871—41no—
65#12196—111nomaximal, Sylow
66C24×C11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C11×SD16—44no—
90C11×D8—44no—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—81no—
105C22⋊Dic11—81no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111C4×Dic11—42no—
112C4×Dic11—81no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2593—111no—
116#2006D1111yescharacteristic
117#1616—111no—
118#1610—111no—
119#1353—111no—
120#1346—111no—
121#1318—111no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131Q8×C11—41no—
132Q8×C11—41no—
133D4×C11—41no—
134D4×C11—42no—
135D4×C11—41no—
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×Dic11—22no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C8×C11—42no—
168C11⋊C8—81no—
169C11⋊C8—81no—
170C2×AGL(1,ℤ/8)—21no—
171#537C2×D1111yescharacteristic
172#481—221no—
173#480—221no—
174C2×#104—21no—
175#400—111no—
176#398—111no—
177#394—221no—
178#390C2×D1111yescharacteristic
179#388—221no—
180#388—221no—
181#388—221no—
182#388—221no—
183C4×C4⋊C4—221no—
184#343C2×D1111yescharacteristic
185#327—221no—
186#327—221no—
187#324—111no—
188#324—111no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11#44911yescharacteristic
202C22×C11#45311yescharacteristic
203C22×C11B(4,𝔽2)11yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210Dic11—42no—
211Dic11—81no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—21no—
215C22×D4C22⋊D1111yescharacteristic
216AGL(1,ℤ/8)—42no—
217AGL(1,ℤ/8)—42no—
218C2×SD16—41no—
219C2×D8—41no—
220C2×M16—21no—
221C22⋊Q8—41no—
222#121—21no—
223#121—21no—
224#121—41no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42—221no—
237C2×C42—221no—
238C2×C42C22⋊D1111yescharacteristic
239#107—441no—
240#106—441no—
241#104—42no—
242#102—441no—
243#102—441no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#95—111no—
247#95—111no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252C2×C11—21no—
253C2×C11—21no—
254C2×C11—161no—
255C2×C11—161no—
256C2×C11#160011yescharacteristic
257C2×C11#219811yescharacteristic
258C2×C11#220411yescharacteristic
259C24—21no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4D4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—44no—
283D8—44no—
284M16—22no—
285M16—41no—
286C2×C8—41no—
287C2×C8—441no—
288C2×C8—441no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C42—41no—
306C42—442no—
307C42—881no—
308C11#1219611yescharacteristic, complemented, Sylow
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#6699011yescharacteristic
318Q8—41no—
319Q8—41no—
320D4—41no—
321D4—42no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—222no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4#6698511yescharacteristic
353C2×C4#6700311yescharacteristic
354C8—42no—
355C8—881no—
356C8—881no—
357C22—21no—
358C22—21no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22#1062264511yescharacteristic
370C22#1062265011yescharacteristic
371C22#1062269011yescharacteristic
372C4—21no—
373C4—21no—
374C4—42no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—442no—
379C4—881no—
380C4—881no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2—161no—
385C2—161no—
386C2#1306756011yescharacteristic
387C2#1307061111yescharacteristic
388C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2006C2
socleC22×C11B(4,𝔽2)
hypercenter#2006D11
hypocenterC11#12196
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2006

Complements

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

NH ≅ G/Ntype
1. #13074112C2semidirect
2. #13067653C2semidirect
3. #13067619C2semidirect
4. #13066642C2semidirect
5. #13066621C2semidirect
6. #13066548C2semidirect
308. C11#12196semidirect

Maximal subgroups

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

subgroupindex
#130741122
#130676532
#130676192
#130666422
#130666212
#130665482
C11×#20062
#1219611