Finite Group Databasebeta

← #14666081

Subgroups — #14666081

Order 2816.

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

normal subgroups only

This group has 394 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#13076799C211yesmaximal, characteristic, complemented
2#13067636C211yesmaximal, characteristic
3#13067602C211yesmaximal, characteristic
4#13066639C211yesmaximal, characteristic, complemented
5#13066615C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2044C211yesmaximal, characteristic
8C11×#534C2211yescharacteristic
9C2×C11×#99—21no—
10C11×#386—21no—
11C11×#385C2211yescharacteristic
12#10622823—21no—
13#10622647—21no—
14#10622646—21no—
15#10622597—21no—
16#10622593—21no—
17#10622566C2211yescharacteristic
18#10622565—21no—
19#10622562C2211yescharacteristic
20C11⋊#401—21no—
21#10622270—21no—
22C11×#342C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×D4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C11×#123—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#120—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C11×#99—42no—
47C11×#95—21no—
48C11×#95—41no—
49#66896—41no—
50#66896—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61#66872—41no—
62#66871—41no—
63#12138—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—82no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—81no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2834—111no—
109#2044D1111yescharacteristic
110#1613—111no—
111#1607—111no—
112#1352—111no—
113#1344—111no—
114#1326—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—81no—
123C23×C11—81no—
124C23×C11#12011yescharacteristic
125C23×C11#13511yescharacteristic
126C23×C11AGL(1,ℤ/8)11yescharacteristic
127D4×C11—81no—
128D4×C11—81no—
129D4×C11—81no—
130D4×C11—81no—
131D4×C11—81no—
132D4×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C11⋊C8—81no—
164C11⋊C8—81no—
165#534C2×D1111yescharacteristic
166#481—221no—
167#480—221no—
168C2×#99—21no—
169#401—221no—
170#399—111no—
171#398—221no—
172#398—221no—
173#398—221no—
174#397—111no—
175#397—221no—
176#386—21no—
177#385—221no—
178#385C2×D1111yescharacteristic
179#342C2×D1111yescharacteristic
180#327—221no—
181#327—221no—
182#323—111no—
183#323—111no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—81no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—161no—
198C22×C11#44911yescharacteristic
199C22×C11#45411yescharacteristic
200C22×C11B(4,𝔽2)11yescharacteristic
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—161no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210Dic11—81no—
211C22×D4—21no—
212C23×C4C22⋊D1111yescharacteristic
213#123—41no—
214#121—21no—
215#121—21no—
216#120—41no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4C22⋊D1111yescharacteristic
229C2×C22⋊C4C22×D1111yescharacteristic
230#107—441no—
231#106—441no—
232#102—441no—
233#102—441no—
234#99—42no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237#95—21no—
238#95—41no—
239#95—111no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11—161no—
252C2×C11#159711yescharacteristic
253C2×C11#220011yescharacteristic
254C2×C11#220111yescharacteristic
255C24—21no—
256C24C2×C22⋊D1111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—81no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—81no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—881no—
285C4⋊C4—881no—
286C4⋊C4—881no—
287C4⋊C4—881no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—82no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—881no—
299C11#1213811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—81no—
308C23—81no—
309C23#6698511yescharacteristic
310C23#6699011yescharacteristic
311C23#6700311yescharacteristic
312D4—81no—
313D4—81no—
314D4—81no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C8—881no—
349C8—881no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—82no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—161no—
364C22#1062264511yescharacteristic
365C22#1062265011yescharacteristic
366C22#1062267511yescharacteristic
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4—881no—
374C4—881no—
375C4—881no—
376C4—881no—
377C2—21no—
378C2—21no—
379C2—41no—
380C2—41no—
381C2—161no—
382C2#1306754311yescharacteristic
383C2#1307062111yescharacteristic
384C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2044C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#534C22
hypercenter#2044D11
hypocenterC11#12138
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2044

Complements

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

NH ≅ G/Ntype
1. #13076799C2semidirect
4. #13066639C2semidirect
5. #13066615C2semidirect
6. #13066564C2semidirect
299. C11#12138semidirect

Maximal subgroups

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

subgroupindex
#130767992
#130676362
#130676022
#130666392
#130666152
#130665642
C11×#20442
#1213811