Finite Group Databasebeta

← #14666868

Subgroups — #14666868

Order 2816.

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

normal subgroups only

This group has 438 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#13075993C211yesmaximal, characteristic
2#13067573C211yesmaximal, characteristic, complemented
3#13067539C211yesmaximal, characteristic
4#13066636C211yesmaximal, characteristic, complemented
5#13066612C211yesmaximal, characteristic
6#13066546C211yesmaximal, characteristic, complemented
7C11×#2030C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C11×#381—21no—
10C11×#381C2211yescharacteristic
11#10622826—21no—
12#10622663—21no—
13#10622659—21no—
14#10622573C2211yescharacteristic
15#10622569—21no—
16#10622560C2211yescharacteristic
17#10622286—21no—
18#10622278—21no—
19#10622277—21no—
20C11⋊#401—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C22×Dic22D411yescharacteristic
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—41no—
35C11×C22⋊Q8—41no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×#4326—41no—
42C2×#4325—41no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—41no—
50C11×#95—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66873—41no—
62#12263—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—41no—
86C2×D44—42no—
87C2×C4×D11—42no—
88C2×C4×D11—81no—
89C2×C4×D11—81no—
90C2×Dic22—41no—
91C2×Dic22—81no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C22⋊Dic11—81no—
103#4326—82no—
104#4325—82no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107(C2×D11)⋊C4—81no—
108(C2×D11)⋊C4—81no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2760—111no—
112#2030D1111yescharacteristic, complemented
113#1602—111no—
114#1596—111no—
115#1351—111no—
116#1343—111no—
117#1317—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C23×C11#13511yescharacteristic
124C23×C11#13711yescharacteristic
125C22×D11—22no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132Q8×C11—81no—
133Q8×C11—81no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
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×C4×C11—81no—
152C2×C4×C11—81no—
153C22⋊D11—82no—
154C22⋊D11—82no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164D44—42no—
165D44—81no—
166C4×D11—84no—
167Dic22—42no—
168Dic22—81no—
169C11⋊C8—81no—
170C11⋊C8—81no—
171#543C2×D1111yescharacteristic
172#451—221no—
173#450—221no—
174#401—221no—
175#393—111no—
176#393—221no—
177#392—111no—
178#386—221no—
179#386—221no—
180#386—221no—
181#381—21no—
182#381—221no—
183#381C2×D1111yescharacteristic
184#342—21no—
185#342C2×D1111yescharacteristic
186#328—221no—
187#328—221no—
188#323—111no—
189#323—111no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—81no—
199C22×C11#45211yescharacteristic
200C22×C11#45511yescharacteristic
201C22×C11B(4,𝔽2)11yescharacteristic
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—161no—
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219C22×Q8—111no—
220C22×D4—111no—
221C22×D4—221no—
222C23×C4—221no—
223C23×C4C22⋊D1111yescharacteristic
224C2×Q16—441no—
225C2×SD16—441no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—41no—
229C22⋊Q8—41no—
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×C22⋊C4—221no—
237C2×C22⋊C4C22⋊D1111yescharacteristic
238C2×C22⋊C4C22×D1111yescharacteristic
239#103—441no—
240#102—441no—
241C22⋊C8—221no—
242C22⋊C8—221no—
243#95—21no—
244#95—21no—
245#95—41no—
246#95—41no—
247#95—111no—
248#95—111no—
249#95—221no—
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#160611yescharacteristic
259C2×C11#219711yescharacteristic
260C2×C11#220011yescharacteristic
261D11—82no—
262C24—221no—
263C24C2×C22⋊D1111yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—441no—
267C2×Q8—881no—
268C2×D4—441no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—881no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—442no—
287C22×C4—881no—
288C22×C4—881no—
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291Q16—882no—
292SD16—882no—
293C2×C8—441no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—881no—
306C22⋊C4—881no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C22⋊C4—881no—
310C11#1226311yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—222no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23#6699011yescharacteristic
323C23#6699511yescharacteristic
324C23#6700311yescharacteristic
325Q8—81no—
326Q8—81no—
327Q8—442no—
328Q8—881no—
329D4—442no—
330D4—881no—
331D4—882no—
332D4—882no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
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—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
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—884no—
362C8—881no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—442no—
374C22—442no—
375C22—442no—
376C22—881no—
377C22—881no—
378C22—881no—
379C22—881no—
380C22#1062264511yescharacteristic
381C22#1062266011yescharacteristic
382C22#1062267411yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—161no—
390C4—881no—
391C4—881no—
392C4—881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—882no—
398C2#1306759411yescharacteristic
399C2#1307060311yescharacteristic
400C2#1307062011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2030C2
socleC22×C11B(4,𝔽2)
prime radical#10622573C22
hypercenter#2030D11
hypocenterC11#12263
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
2. #13067573C2semidirect
4. #13066636C2semidirect
6. #13066546C2semidirect
7. C11×#2030C2semidirect
112. #2030D11semidirect
310. C11#12263semidirect

Maximal subgroups

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

subgroupindex
#130759932
#130675732
#130675392
#130666362
#130666122
#130665462
C11×#20302
#1226311