Finite Group Databasebeta

← #14666475

Subgroups — #14666475

Order 2816.

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

normal subgroups only

This group has 424 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#13076759C211yesmaximal, characteristic, complemented
2#13067619C211yesmaximal, characteristic, complemented
3#13067585C211yesmaximal, characteristic, complemented
4#13066645C211yesmaximal, 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#10622653—21no—
14#10622646—21no—
15#10622596C2211yescharacteristic
16#10622592C2211yescharacteristic
17#10622565—21no—
18#10622565—21no—
19#10622561—21no—
20#10622560—21no—
21#10622546—21no—
22C11×#343C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C11×AGL(1,ℤ/8)—42no—
31C11×AGL(1,ℤ/8)—42no—
32C2×C11×SD16—41no—
33C2×C11×D8—41no—
34C2×C11×M16—21no—
35C11×C22⋊Q8—41no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—41no—
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C42×C11D411yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×#4324—41no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C11×#104—42no—
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#66874—41no—
64#66871—41no—
65#12200—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—
89C2×Dic22—41no—
90C2×Dic22—81no—
91C11×SD16—44no—
92C11×D8—44no—
93C11×M16—22no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C42×C11—41no—
104C22⋊Dic11—81no—
105C22⋊Dic11—81no—
106C22⋊Dic11—81no—
107C22⋊Dic11—81no—
108#4324—82no—
109C4⋊Dic11—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—81no—
113Dic11⋊C4—81no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116#2830—111no—
117#2006D1111yescharacteristic
118#1610—111no—
119#1604—111no—
120#1354—111no—
121#1346—111no—
122#1318—111no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
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—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
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—
167C2×Dic11—41no—
168Dic22—42no—
169Dic22—81no—
170C8×C11—42no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173C2×AGL(1,ℤ/8)—21no—
174#537C2×D1111yescharacteristic
175#480—221no—
176#448—221no—
177C2×#104—21no—
178#398—111no—
179#397—221no—
180#397—221no—
181#396—221no—
182#395—111no—
183#394—221no—
184#393—221no—
185#390C2×D1111yescharacteristic
186#387—221no—
187#343C2×D1111yescharacteristic
188#327—221no—
189#327—221no—
190#324—111no—
191#324—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
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
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—81no—
212C4×C11—81no—
213Dic11—81no—
214Dic11—81no—
215Dic11—81no—
216Dic11—81no—
217C2×#41—21no—
218C22×Q8—111no—
219C22×D4C22⋊D1111yescharacteristic
220AGL(1,ℤ/8)—42no—
221AGL(1,ℤ/8)—42no—
222C2×SD16—41no—
223C2×SD16—441no—
224C2×D8—41no—
225C2×M16—21no—
226C22⋊Q8—41no—
227#121—21no—
228#121—21no—
229#121—41no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C42C22⋊D1111yescharacteristic
242#107—441no—
243#104—42no—
244#103—441no—
245#102—441no—
246C22⋊C8—221no—
247C22⋊C8—221no—
248#95—111no—
249#95—111no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—161no—
258C2×C11—161no—
259C2×C11#160011yescharacteristic
260C2×C11#220011yescharacteristic
261C2×C11#220311yescharacteristic
262C24—21no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—441no—
269C2×Q8—881no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—44no—
288SD16—882no—
289D8—44no—
290M16—22no—
291M16—41no—
292C2×C8—41no—
293C2×C8—441no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—881no—
302C4⋊C4—881no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C22⋊C4—881no—
310C22⋊C4—881no—
311C42—41no—
312C11#1220011yescharacteristic, complemented, Sylow
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#6699011yescharacteristic
322Q8—41no—
323Q8—41no—
324Q8—442no—
325Q8—881no—
326D4—41no—
327D4—42no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
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#6698511yescharacteristic
359C2×C4#6700311yescharacteristic
360C8—42no—
361C8—881no—
362C8—881no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22#1062264511yescharacteristic
376C22#1062265011yescharacteristic
377C22#1062269011yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—881no—
385C4—881no—
386C4—881no—
387C4—881no—
388C2—21no—
389C2—21no—
390C2—161no—
391C2—161no—
392C2#1306756011yescharacteristic
393C2#1307062211yescharacteristic
394C2#1307063611yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#2006C2
socleC22×C11B(4,𝔽2)
hypercenter#2006D11
hypocenterC11#12200
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. #13076759C2semidirect
2. #13067619C2semidirect
3. #13067585C2semidirect
4. #13066645C2semidirect
5. #13066621C2semidirect
6. #13066548C2semidirect
312. C11#12200semidirect

Maximal subgroups

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

subgroupindex
#130767592
#130676192
#130675852
#130666452
#130666212
#130665482
C11×#20062
#1220011