Finite Group Databasebeta

← #14666426

Subgroups — #14666426

Order 2816.

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

normal subgroups only

This group has 442 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#13076039C211yesmaximal, characteristic, complemented
2#13067602C211yesmaximal, characteristic
3#13067568C211yesmaximal, characteristic
4#13066636C211yesmaximal, characteristic, complemented
5#13066615C211yesmaximal, characteristic, complemented
6#13066546C211yesmaximal, characteristic, complemented
7C11×#2022C211yesmaximal, characteristic
8C11×#534C2211yescharacteristic
9C2×C11×#123—21no—
10C2×C11×#99—21no—
11C11×#381C2211yescharacteristic
12#10622823—21no—
13#10622653—21no—
14#10622646—21no—
15#10622566C2211yescharacteristic
16#10622560C2211yescharacteristic
17#10622558—21no—
18#10622271—21no—
19#10622270—21no—
20#10622264—21no—
21#10622259—21no—
22C11×#342C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×D4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C11×#123—42no—
31C11×#123—41no—
32C11×#123—42no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#120—41no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×#4324—41no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C11×#99—42no—
50C11×#95—21no—
51C11×#95—21no—
52#66896—41no—
53C11⋊#95—21no—
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#12193—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C2×Dic22—41no—
91C2×Dic22—42no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—44no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C22⋊Dic11—42no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105#4324—82no—
106C4⋊Dic11—41no—
107Dic11⋊C4—81no—
108Dic11⋊C4—81no—
109Dic11⋊C4—81no—
110C4×Dic11—42no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2764—111no—
114#2022D1111yescharacteristic
115#1607—111no—
116#1601—111no—
117#1351—111no—
118#1344—111no—
119#1317—111no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11#12011yescharacteristic
130C23×C11#13511yescharacteristic
131C23×C11AGL(1,ℤ/8)11yescharacteristic
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
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—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×Dic11—22no—
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—
170C11⋊C8—81no—
171C11⋊C8—81no—
172#534C2×D1111yescharacteristic
173C2×#123—21no—
174#480—221no—
175#448—221no—
176C2×#99—21no—
177#400—221no—
178#398—221no—
179#397—111no—
180#393—111no—
181#391—221no—
182#388—221no—
183#385—221no—
184#383—221no—
185#381C2×D1111yescharacteristic
186#342C2×D1111yescharacteristic
187#327—221no—
188#327—221no—
189#323—111no—
190#323—111no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—161no—
205C22×C11#44911yescharacteristic
206C22×C11#45311yescharacteristic
207C22×C11B(4,𝔽2)11yescharacteristic
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11—81no—
213C4×C11—81no—
214Dic11—42no—
215Dic11—81no—
216Dic11—81no—
217Dic11—81no—
218C22×Q8—111no—
219C22×D4—21no—
220C23×C4C22⋊D1111yescharacteristic
221C2×SD16—441no—
222#123—42no—
223#123—41no—
224#123—42no—
225#121—21no—
226#121—21no—
227#120—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—41no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4C22⋊D1111yescharacteristic
238C2×C22⋊C4C22×D1111yescharacteristic
239C2×C42—221no—
240#107—441no—
241#103—441no—
242#102—441no—
243#99—42no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#95—21no—
247#95—21no—
248#95—111no—
249#95—111no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—41no—
259C2×C11—41no—
260C2×C11—161no—
261C2×C11#160011yescharacteristic
262C2×C11#219711yescharacteristic
263C2×C11#220111yescharacteristic
264C24—21no—
265C24C2×C22⋊D1111yescharacteristic
266C2×Q8—441no—
267C2×Q8—442no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290SD16—882no—
291C2×C8—441no—
292C2×C8—441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—44no—
296C4⋊C4—441no—
297C4⋊C4—881no—
298C4⋊C4—881no—
299C4⋊C4—881no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—44no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—442no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C42—442no—
311C11#1219311yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—81no—
320C23—81no—
321C23#6698511yescharacteristic
322C23#6699011yescharacteristic
323C23#6700311yescharacteristic
324Q8—442no—
325Q8—881no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—222no—
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—441no—
360C2×C4—441no—
361C2×C4—441no—
362C8—881no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22#1062264511yescharacteristic
379C22#1062265011yescharacteristic
380C22#1062269011yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—442no—
388C4—881no—
389C4—881no—
390C4—881no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2#1306756011yescharacteristic
397C2#1307060311yescharacteristic
398C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2022C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#534C22
hypercenter#2022D11
hypocenterC11#12193
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13076039C2semidirect
4. #13066636C2semidirect
5. #13066615C2semidirect
6. #13066546C2semidirect
311. C11#12193semidirect

Maximal subgroups

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

subgroupindex
#130760392
#130676022
#130675682
#130666362
#130666152
#130665462
C11×#20222
#1219311