Finite Group Databasebeta

← #14666165

Subgroups — #14666165

Order 2816.

432 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 59 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#13075522C211yesmaximal, characteristic, complemented
2#13067602C211yesmaximal, characteristic
3#13067602C211yesmaximal, characteristic
4#13066615C211yesmaximal, characteristic, complemented
5#13066615C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2044C211yesmaximal, characteristic
8C11×#534C2211yescharacteristic
9C2×#66932—21no—
10C2×C11×#99—21no—
11C11×#386—21no—
12C11×#385C2211yescharacteristic
13#10622825—21no—
14#10622646—21no—
15#10622646—21no—
16#10622598—21no—
17#10622596—21no—
18#10622566C2211yescharacteristic
19#10622566C2211yescharacteristic
20#10622274—21no—
21#10622266—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⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48#66932—42no—
49#66932—42no—
50C11×#99—42no—
51C11×#95—21no—
52C11×#95—41no—
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#66871—41no—
64#66871—41no—
65#12150—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—42no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—42no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—82no—
98C11×C22⋊C4D812yes—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—42no—
106C4⋊Dic11—42no—
107C4⋊Dic11—81no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110C4×Dic11—42no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2722—111no—
114#2044D1111yescharacteristic
115#1607—111no—
116#1607—111no—
117#1344—111no—
118#1344—111no—
119#1326—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×C11C2×D811yescharacteristic
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—22no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
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—
168C11⋊C8—81no—
169C11⋊C8—81no—
170#534C2×D1111yescharacteristic
171C2×#126—221no—
172#480—221no—
173#480—221no—
174C2×#99—21no—
175#398—221no—
176#398—221no—
177#397—111no—
178#397—111no—
179#389—221no—
180#387—221no—
181#386—21no—
182#385C2×D1111yescharacteristic
183#380—221no—
184#342C2×D1111yescharacteristic
185#327—221no—
186#327—221no—
187#323—111no—
188#323—111no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11—82no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—161no—
203C22×C11#44711yescharacteristic
204C22×C11#45411yescharacteristic
205C22×C11B(4,𝔽2)11yescharacteristic
206C4×C11—42no—
207C4×C11—42no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—81no—
211C4×C11—161no—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215Dic11—81no—
216C22×D4—21no—
217C23×C4C22⋊D1111yescharacteristic
218#126—442no—
219#126—442no—
220#123—41no—
221#121—21no—
222#121—21no—
223#120—41no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—41no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4C22⋊D1111yescharacteristic
237C2×C22⋊C4C22×D1111yescharacteristic
238C2×C42—221no—
239#107—441no—
240#107—441no—
241#102—441no—
242#102—441no—
243#99—42no—
244C22⋊C8—221no—
245C22⋊C8—221no—
246#95—21no—
247#95—41no—
248#95—111no—
249#95—111no—
250#95—221no—
251#95—221no—
252#95—221no—
253#95—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—41no—
257C2×C11—41no—
258C2×C11—161no—
259C2×C11#159811yescharacteristic
260C2×C11#219711yescharacteristic
261C2×C11#220111yescharacteristic
262C24—21no—
263C24C2×C22⋊D1111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4D4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C2×C8—441no—
285C2×C8—441no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—42no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—442no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C4⋊C4—881no—
296C22⋊C4—21no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4#432312yes—
308C42—442no—
309C11#1215011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23C2×#432311yescharacteristic
320C23#6699011yescharacteristic
321C23#6700211yescharacteristic
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
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—
358C8—881no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—82no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—161no—
374C22#1062264511yescharacteristic
375C22#1062264911yescharacteristic
376C22#1062267511yescharacteristic
377C4—42no—
378C4—41no—
379C4—42no—
380C4—41no—
381C4—81no—
382C4—161no—
383C4—881no—
384C4—881no—
385C4—881no—
386C4—881no—
387C2—21no—
388C2—21no—
389C2—41no—
390C2—41no—
391C2—161no—
392C2#1306755011yescharacteristic
393C2#1307060411yescharacteristic
394C2#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#12150
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. #13075522C2semidirect
4. #13066615C2semidirect
5. #13066615C2semidirect
6. #13066564C2semidirect
309. C11#12150semidirect

Maximal subgroups

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

subgroupindex
#130755222
#130676022
#130666152
#130665642
C11×#20442
#1215011