Finite Group Databasebeta

← #14647407

Subgroups — #14647407

Order 2816.

466 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 85 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#13071584C211yesmaximal, characteristic
2C4×#66870C211yesmaximal, characteristic
3#13066952C211yesmaximal, characteristic
4#13066502C211yesmaximal, characteristic, complemented
5#13066501C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C11×#381C2211yescharacteristic
11C4×C11×C22⋊C4C2211yescharacteristic
12C4×C22⋊Dic11C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622570—21no—
16C2×#66870—21no—
17#10622557—21no—
18#10622282—21no—
19#10622279C411yescharacteristic, complemented
20#10622277C411yescharacteristic, complemented
21#10622263C411yescharacteristic, complemented
22#10622262—21no—
23#10622262C411yescharacteristic, complemented
24#10622165—21no—
25#10622107—21no—
26#10622106—21no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11D411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11D411yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39C4×C22⋊D11—21no—
40C4×C22⋊D11—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11C2×C411yescharacteristic
52C2×#4318—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11×#95C2×C411yescharacteristic
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95C2×C411yescharacteristic
63C11⋊#95C2×C411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66870—24no—
67#8778—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C23×D11C22⋊C411yescharacteristic
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—81no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—22no—
81C2×C22⋊D11—21no—
82C2×C22⋊D11—21no—
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—41no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—81no—
93C11×M16—81no—
94C2×C8×C11—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—81no—
98C42×C11—81no—
99C22⋊Dic11—22no—
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102C22⋊Dic11—41no—
103C22⋊Dic11—42no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—81no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—42no—
115C4×Dic11—81no—
116C4×Dic11—81no—
117C4×Dic11—81no—
118#4318—81no—
119C2×C11⋊C8—41no—
120#2357—111no—
121C4×#99—111no—
122#1465—111no—
123#1297—111no—
124#1297—111no—
125#1284—111no—
126#1284D1111yescharacteristic, complemented
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11#12311yescharacteristic
133C23×C11#12311yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—41no—
138C22×D11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
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—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C2×C4×C11#11711yescharacteristic
155C2×C4×C11#11711yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12311yescharacteristic
158C22⋊D11—42no—
159C22⋊D11—42no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—22no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11#10412yes—
176C4×D11—81no—
177C4×D11—81no—
178C8×C11—81no—
179C11⋊C8—81no—
180C2×C4×D4—111no—
181C2×#99—221no—
182#407—111no—
183#407C2×D1111yescharacteristic
184#390—221no—
185#388—221no—
186#388—221no—
187#382—111no—
188#381—111no—
189#381C2×D1111yescharacteristic
190C4×C4⋊C4—111no—
191C4×C4⋊C4—221no—
192C4×C22⋊C4—111no—
193C4×C22⋊C4—111no—
194C4×C22⋊C4—111no—
195C4×C22⋊C4C2×D1111yescharacteristic
196#342—221no—
197#324—221no—
198#323—221no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#38111yescharacteristic
210C22×C11C2×#10411yescharacteristic
211C22×C11#42111yescharacteristic
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—81no—
216C2×D11—81no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11—82no—
224Dic11—22no—
225Dic11—42no—
226Dic11—41no—
227Dic11—41no—
228Dic11—81no—
229Dic11—82no—
230C22×D4—111no—
231C23×C4—111no—
232C23×C4C22×D1111yescharacteristic
233C2×M16—21no—
234C2×M16—221no—
235C4×D4—221no—
236C4×D4—221no—
237C4×D4—221no—
238C4×D4—221no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C42—21no—
251C2×C42—111no—
252C2×C42—221no—
253C2×C42—221no—
254C2×C42—221no—
255C2×C42—221no—
256#99—224no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—221no—
260C22⋊C8—221no—
261#95—21no—
262#95—21no—
263#95—111no—
264#95—111no—
265#95—221no—
266#95—221no—
267#95—221no—
268#95C4×D1111yescharacteristic
269#95C4×D1111yescharacteristic
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—41no—
273C2×C11—41no—
274C2×C11#182611yescharacteristic
275C2×C11#182711yescharacteristic
276C2×C11#182811yescharacteristic
277D11—81no—
278C24—111no—
279C24D4×D1111yescharacteristic
280C2×D4—222no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—81no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—441no—
296C22×C4—881no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4#433911yescharacteristic
299C22×C4#433911yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4#434111yescharacteristic
302C22×C4#434311yescharacteristic
303M16—81no—
304M16—881no—
305C2×C8—41no—
306C2×C8—441no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—81no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—222no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C22⋊C4—881no—
323C42—81no—
324C42—221no—
325C42—221no—
326C42—442no—
327C42—881no—
328C42—881no—
329C42—881no—
330C11#877811yescharacteristic, complemented, Sylow
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—441no—
339C23—441no—
340C23C22⋊C4×D1111yescharacteristic
341C23#6693611yescharacteristic
342C23#6694711yescharacteristic
343D4—442no—
344D4—442no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—112no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—222no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4—881no—
377C2×C4—881no—
378C2×C4#6692511yescharacteristic
379C2×C4#6693611yescharacteristic
380C2×C4#6694511yescharacteristic
381C2×C4#6694711yescharacteristic
382C8—81no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—81no—
393C22—81no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22—881no—
398C22—881no—
399C22#1062227711yescharacteristic
400C22D11×#10411yescharacteristic
401C22#1062243411yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—81no—
407C4—81no—
408C4—82no—
409C4—222no—
410C4—442no—
411C4—441no—
412C4—441no—
413C4—881no—
414C4—882no—
415C2—21no—
416C2—21no—
417C2—41no—
418C2—41no—
419C2—881no—
420C2#1306871411yescharacteristic
421C2#1306871811yescharacteristic
422C2#1306872311yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#381
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#8778
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
4. #13066502C2semidirect
5. #13066501C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
19. #10622279C4semidirect
20. #10622277C4semidirect
21. #10622263C4semidirect
23. #10622262C4semidirect
126. #1284D11semidirect
330. C11#8778semidirect

Maximal subgroups

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

subgroupindex
#130715842
C4×#668702
#130669522
#130665022
#130665012
#130664682
C11×#12842
#877811