Finite Group Databasebeta

← #14651601

Subgroups — #14651601

Order 2816.

614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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#13072892C211yesmaximal, characteristic
2#13071211C211yesmaximal, characteristic
3#13068716C211yesmaximal, characteristic, complemented
4#13068713C211yesmaximal, characteristic, complemented
5#13066942C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C22×(C2×D11)⋊C4C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622568—21no—
16#10622568—21no—
17#10622563—21no—
18#10622555—21no—
19#10622553—22no—
20#10622290C412yescomplemented
21#10622287C412yescomplemented
22#10622283—22no—
23#10622282—22no—
24#10622193—22no—
25#10622161—22no—
26#10622106—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11D412yes—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4C2×C412yes—
45C2×(C2×D11)⋊C4D412yes—
46#66979—21no—
47#66979—21no—
48#66979—21no—
49#66979—21no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—21no—
55C2×C4×Dic11D412yes—
56C2×#4318—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95C2×C412yes—
62C11⋊#95—22no—
63C11⋊#95—21no—
64C11⋊#95—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#9481—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—42no—
72C23×D11—42no—
73C23×D11—81no—
74C23×D11C22⋊C412yes—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—42no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—81no—
90C22×Dic11C22⋊C412yes—
91C11×M16—42no—
92C2×C8×C11—41no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—42no—
95C42×C11—42no—
96C22⋊Dic11—42no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—44no—
104(C2×D11)⋊C4—82no—
105(C2×D11)⋊C4—82no—
106(C2×D11)⋊C4—82no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—82no—
112Dic11⋊C4—82no—
113C4×Dic11—42no—
114C4×Dic11—41no—
115C4×Dic11—41no—
116#4318—42no—
117C2×C11⋊C8—41no—
118#2482—111no—
119#2312—111no—
120#1826—111no—
121#1826—111no—
122#1462—111no—
123#1284—111no—
124#1284D1111yescharacteristic, complemented
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—41no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12311yescharacteristic
131C22×D11—22no—
132C22×D11—22no—
133C22×D11—22no—
134C22×D11—42no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—81no—
141C22×D11—81no—
142C22×D11—88no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—81no—
170C8×C11—81no—
171C11⋊C8—81no—
172C2×#117—111no—
173C22×C22⋊C4—111no—
174#407—111no—
175#407C2×D1111yescharacteristic
176#399—112no—
177#397—112no—
178#388—222no—
179#388—222no—
180#388—222no—
181#385—221no—
182#381C2×D1111yescharacteristic
183#380—221no—
184#379—221no—
185#379—221no—
186C4×C22⋊C4—111no—
187C4×C22⋊C4C2×D1111yescharacteristic
188#339—222no—
189#339—222no—
190#323—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—44no—
199C22×C11#38611yescharacteristic
200C22×C11#42112yes—
201C22×C11#45812yes—
202C2×D11—44no—
203C2×D11—42no—
204C2×D11—42no—
205C2×D11—42no—
206C2×D11—84no—
207C2×D11—84no—
208C2×D11—82no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—82no—
214C4×C11—82no—
215Dic11—42no—
216Dic11—82no—
217Dic11—81no—
218Dic11—81no—
219C25—111no—
220C23×C4—111no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—21no—
223C2×M16—221no—
224#117—221no—
225#117—221no—
226#117—221no—
227#117—221no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—222no—
231C2×C4⋊C4—222no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—112no—
235C2×C22⋊C4—112no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—222no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—222no—
246C2×C42—112no—
247C2×C42—221no—
248C2×C42D4412yes—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#95—21no—
254#95—21no—
255#95—222no—
256#95—222no—
257#95—221no—
258#95C4×D1112yes—
259C2×C11—22no—
260C2×C11—22no—
261C2×C11—41no—
262C2×C11#189011yescharacteristic
263C2×C11#189711yescharacteristic
264C2×C11#191111yescharacteristic
265D11—82no—
266C24—112no—
267C24—221no—
268C24—221no—
269C24—442no—
270C24—442no—
271C24—881no—
272C24D4×D1111yescharacteristic
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—112no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—881no—
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4C2×D4411yescharacteristic
285C22×C4#433911yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4#434311yescharacteristic
289M16—42no—
290M16—442no—
291C2×C8—41no—
292C2×C8—441no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—882no—
298C4⋊C4—882no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—444no—
306C22⋊C4—442no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—882no—
310C22⋊C4—882no—
311C22⋊C4—882no—
312C42—42no—
313C42—442no—
314C42—441no—
315C42—441no—
316C11#948111yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23—41no—
320C23—222no—
321C23—222no—
322C23—222no—
323C23—442no—
324C23—442no—
325C23—442no—
326C23—442no—
327C23—442no—
328C23—442no—
329C23—881no—
330C23—881no—
331C23—888no—
332C23C22⋊C4×D1111yescharacteristic
333C23#6693511yescharacteristic
334C23#6694711yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—222no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—881no—
358C2×C4C4×D4411yescharacteristic
359C2×C4#6693711yescharacteristic
360C2×C4#6694611yescharacteristic
361C2×C4#6694811yescharacteristic
362C8—81no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22—444no—
373C22—442no—
374C22—442no—
375C22—442no—
376C22—882no—
377C22—884no—
378C22—884no—
379C22#1062227811yescharacteristic
380C22#1062235512yes—
381C22#1062243412yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—442no—
389C4—882no—
390C4—881no—
391C4—881no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—882no—
396C2#1306902811yescharacteristic
397C2#1306906311yescharacteristic
398C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9481
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
3. #13068716C2semidirect
4. #13068713C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
20. #10622290C4semidirect
21. #10622287C4semidirect
124. #1284D11semidirect
316. C11#9481semidirect

Maximal subgroups

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

subgroupindex
#130728922
#130712112
#130687162
#130687132
#130669422
#130664682
C11×#12842
#948111