Finite Group Databasebeta

← #14650970

Subgroups — #14650970

Order 2816.

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

normal subgroups only

This group has 542 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#13078557C211yesmaximal, characteristic
2#13071507C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic
4#13068716C211yesmaximal, characteristic, complemented
5#13067131C211yesmaximal, characteristic
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1297C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622825C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622744C412yescomplemented
16#10622734C412yescomplemented
17C2×#66870—22no—
18#10622558—22no—
19C4×C4⋊Dic11—21no—
20#10622541—21no—
21#10622350—22no—
22#10622349—21no—
23#10622348—21no—
24#10622264—21no—
25#10622262—21no—
26#10622161—22no—
27#10622089—21no—
28#10622089—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C22×D44C2×C411yescharacteristic
32C2×C11×M16C2×C412yes—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11—21no—
36C2×C42×C11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11D412yes—
39#66983—21no—
40#66983—21no—
41#66983—21no—
42#66983—21no—
43C2×(C2×D11)⋊C4—21no—
44#66979—21no—
45#66979—21no—
46#66979C2×C412yes—
47#66979D412yes—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—22no—
55C2×#4318—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95D411yescharacteristic
60C11×#95D411yescharacteristic
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66885—22no—
67#66885—22no—
68#66882—22no—
69#66881—22no—
70#66870—44no—
71#9366—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—22no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—42no—
95C11×M16—42no—
96C2×C8×C11—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—41no—
100C42×C11—42no—
101C42×C11—42no—
102C22⋊Dic11—22no—
103C22⋊Dic11—22no—
104C22⋊Dic11—42no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4⋊Dic11C22⋊C412yes—
113C4⋊Dic11C22⋊C412yes—
114Dic11⋊C4—44no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—82no—
118#4318—42no—
119C2×C11⋊C8—41no—
120#3094—111no—
121#2347—111no—
122#1964—111no—
123#1826—111no—
124#1507—111no—
125#1305—111no—
126#1297D1111yescharacteristic, complemented
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C4×D411yescharacteristic
132C23×C11#12011yescharacteristic
133C23×C11#12111yescharacteristic
134C22×D11—41no—
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
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—81no—
152C2×C4×C11—81no—
153C2×C4×C11C2×C22⋊C411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C22⋊D11—82no—
158C22⋊D11—81no—
159C22⋊D11—81no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170D44—42no—
171D44—81no—
172C8×C11—42no—
173C11⋊C8—81no—
174C2×#121—111no—
175C2×#117—111no—
176#482—222no—
177#481—221no—
178#480—221no—
179#428—112no—
180#418—112no—
181C2×#99—222no—
182#407—111no—
183#407C2×D1111yescharacteristic
184#389—221no—
185#388—222no—
186#383—221no—
187#380—111no—
188C4×C4⋊C4—221no—
189C4×C4⋊C4—221no—
190C4×C22⋊C4C2×D1111yescharacteristic
191C4×C22⋊C4C2×D1111yescharacteristic
192#339—222no—
193#327—221no—
194#327—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#38611yescharacteristic
206C22×C11#45311yescharacteristic
207C22×C11#45411yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—162no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—82no—
218C4×C11#41012yes—
219Dic11—42no—
220Dic11—42no—
221Dic11—82no—
222Dic11—81no—
223C22×D4—111no—
224C22×D4—221no—
225C23×C4C22×D1111yescharacteristic
226C2×M16—221no—
227C2×M16C4×D1112yes—
228#121—221no—
229#121—221no—
230#121—221no—
231#121—221no—
232#117—112no—
233#117—112no—
234#117—221no—
235#117—221no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—221no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—112no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—221no—
249C2×C42—222no—
250#107—222no—
251#106—222no—
252#102—222no—
253#102—222no—
254#99—444no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259#95—21no—
260#95—222no—
261#95—222no—
262#95—221no—
263#95D4411yescharacteristic
264#95D4411yescharacteristic
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—41no—
268C2×C11—41no—
269C2×C11#188311yescharacteristic
270C2×C11#189911yescharacteristic
271C2×C11#190611yescharacteristic
272D11—161no—
273C24—221no—
274C24D4×D1111yescharacteristic
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—441no—
281C2×D4—441no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—222no—
289C22×C4—221no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×D4411yescharacteristic
292C22×C4#433911yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4#434311yescharacteristic
296M16—42no—
297M16—442no—
298C2×C8—22no—
299C2×C8—441no—
300C4⋊C4—112no—
301C4⋊C4—112no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—444no—
307C4⋊C4—442no—
308C22⋊C4—22no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—222no—
312C22⋊C4—222no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—442no—
316C42—42no—
317C42—42no—
318C42—222no—
319C42—222no—
320C42—882no—
321C11#936611yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—442no—
327C23—441no—
328C23—881no—
329C23—881no—
330C23#6693511yescharacteristic
331C23#6693711yescharacteristic
332C23#6694611yescharacteristic
333D4—442no—
334D4—881no—
335D4—882no—
336D4—881no—
337D4—881no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—442no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4C4×D4411yescharacteristic
364C2×C4C22⋊C4×D1111yescharacteristic
365C2×C4#6694711yescharacteristic
366C2×C4#6694811yescharacteristic
367C8—42no—
368C8—881no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—1762no—
383C22#1062227811yescharacteristic
384C22#1062243511yescharacteristic
385C22#1062244011yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—82no—
392C4—442no—
393C4—442no—
394C4—882no—
395C4—881no—
396C4#1062235312yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—1761no—
402C2#1306899311yescharacteristic
403C2#1306907311yescharacteristic
404C2#1306911611yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1297C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1297D11
hypocenterC11#9366
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #13071507C2semidirect
4. #13068716C2semidirect
6. #13066521C2semidirect
7. C11×#1297C2semidirect
15. #10622744C4semidirect
16. #10622734C4semidirect
126. #1297D11semidirect
321. C11#9366semidirect

Maximal subgroups

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

subgroupindex
#130785572
#130715072
#130694522
#130687162
#130671312
#130665212
C11×#12972
#936611