Finite Group Databasebeta

← #14656315

Subgroups — #14656315

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic, complemented
5C2×#10622120C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4324—22no—
10C22×#4323—21no—
11C2×C4×D44C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×#66896—21no—
16C2×#66885—21no—
17C2×(C2×D11)⋊C8—22no—
18C2×#66882—21no—
19#10622689—22no—
20#10622689—22no—
21#10622685—22no—
22#10622685—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622459—22no—
26#10622459—22no—
27C11×#331—22no—
28#10622120—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127D412yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—28no—
43C2×#4324—44no—
44C2×#4324—44no—
45C2×#4323—24no—
46C2×#4323—42no—
47C2×#4323—42no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8D412yes—
54C4×D44—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66#66896—24no—
67#66885—24no—
68(C2×D11)⋊C8—44no—
69#66882—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#10266—111nomaximal, Sylow
75C24×C11—41no—
76C23×D11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—82no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—41no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44SD1612yescomplemented
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—42no—
108C2×Dic22—42no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—42no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#4324—416no—
119#4323—48no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8D814yescomplemented
134C2×#492—111no—
135C2×#474—111no—
136C2×#459—111no—
137#1954—111no—
138C2×#332—111no—
139C2×#331D1111yescharacteristic, complemented
140#1277—111no—
141C23×C11—42no—
142C23×C11—82no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11—82no—
146C23×C11#12111yescharacteristic
147C22×D11—22no—
148C22×D11—41no—
149C22×D11—42no—
150C22×D11—41no—
151C22×D11—42no—
152D4×C11—44no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12711yescharacteristic
168C2×C4×C11C2×D812yes—
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11#13511yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—82no—
178D44—22no—
179D44—22no—
180D44—41no—
181D44—41no—
182C4×D11—82no—
183C4×D11—81no—
184C4×D11—81no—
185Dic22—44no—
186Dic22—81no—
187Dic22—81no—
188C8×C11—42no—
189C8×C11—81no—
190C11⋊C8—24no—
191C11⋊C8—42no—
192C22×SD16—222no—
193C22×D8—221no—
194C2×C4⋊Q8—111no—
195C2×#127C2×D1111yescharacteristic
196C2×C4×D4—111no—
197#492—222no—
198#492—222no—
199#474—222no—
200#474—222no—
201#459—222no—
202#459—222no—
203C2×#107—221no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8C2×D1111yescharacteristic
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×#102—221no—
208C2×#102—221no—
209C2×C22⋊C8—222no—
210C2×C4×C8—111no—
211#332—222no—
212#331—22no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—162no—
217C22×C11—162no—
218C22×C11#39211yescharacteristic
219C22×C11#45912yes—
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C22×C11#47112yes—
223C2×D11—44no—
224C2×D11—42no—
225C2×D11—82no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11#44712yes—
231C4×C11#44811yescharacteristic
232C4×C11#44911yescharacteristic
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#49311yescharacteristic
236C4×C11#49611yescharacteristic
237Dic11—82no—
238Dic11—81no—
239C22×Q8—221no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—111no—
244C23×C4—221no—
245C2×SD16—228no—
246C2×SD16—444no—
247C2×SD16—444no—
248C2×D8—224no—
249C2×D8—442no—
250C2×D8—442no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—112no—
254C22×C8—221no—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259#127—21no—
260#127—21no—
261#127—21no—
262#127D4412yes—
263C4×D4—221no—
264C4×D4—221no—
265C4×D4—221no—
266C4×D4—221no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C42C22×D1111yescharacteristic
272#107—224no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8C22⋊D1112yes—
279#102—224no—
280#102—224no—
281C22⋊C8—444no—
282C4×C8—221no—
283C4×C8—221no—
284C2×C11—162no—
285C2×C11#166512yes—
286C2×C11#168512yes—
287C2×C11#200011yescharacteristic
288C2×C11#201111yescharacteristic
289C2×C11#201911yescharacteristic
290D11—82no—
291C24—41no—
292C24—221no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—82no—
310C2×D4—112no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C2×D4—221no—
315C2×D4—221no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—441no—
322C22×C4#433911yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4D4×D1111yescharacteristic
325SD16—4416no—
326D8—448no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8—41no—
332C2×C8—114no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—221no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—221no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42C2×D4411yescharacteristic
347C42D4×D1111yescharacteristic
348C42D4×D1111yescharacteristic
349C42C2×C22⋊D1111yescharacteristic
350C11#1026611yescharacteristic, complemented, Sylow
351C23—42no—
352C23—82no—
353C23—81no—
354C23—81no—
355C23—82no—
356C23—222no—
357C23—441no—
358C23—442no—
359C23—441no—
360C23—442no—
361C23#6693711yescharacteristic
362Q8—444no—
363Q8—881no—
364Q8—881no—
365D4—44no—
366D4—42no—
367D4—42no—
368D4—82no—
369D4—82no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—222no—
375D4—222no—
376D4—441no—
377D4—441no—
378C2×C4—22no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—882no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4—882no—
386C2×C4#6693511yescharacteristic
387C2×C4#6693511yescharacteristic
388C2×C4#6693711yescharacteristic
389C2×C4D8×D1112yes—
390C2×C4#6696411yescharacteristic
391C2×C4#6696511yescharacteristic
392C2×C4SD16×D1111yescharacteristic
393C2×C4#6696712yes—
394C2×C4#6696811yescharacteristic
395C2×C4#6698311yescharacteristic
396C2×C4#6699011yescharacteristic
397C2×C4#6699311yescharacteristic
398C8—42no—
399C8—81no—
400C8—224no—
401C8—442no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—162no—
406C22—162no—
407C22—442no—
408C22—444no—
409C22—882no—
410C22—881no—
411C22—881no—
412C22#1062236112yes—
413C22#1062239111yescharacteristic
414C22#1062239311yescharacteristic
415C22#1062239912yes—
416C22#1062257311yescharacteristic
417C4—21no—
418C4—21no—
419C4—881no—
420C4—882no—
421C4#1062238612yes—
422C4#1062238911yescharacteristic
423C4#1062239611yescharacteristic
424C4#1062276411yescharacteristic
425C4#1062277111yescharacteristic
426C4#1062278311yescharacteristic
427C4#1062278911yescharacteristic
428C2—162no—
429C2—882no—
430C2#1306795612yes—
431C2#1306808012yes—
432C2#1306962011yescharacteristic
433C2#1306968811yescharacteristic
434C2#1306973211yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#121
prime radicalC2×#10622685C2
hypercenterC2×#331D11
hypocenterC11#10266
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622459C2semidirect
4. #13069409C2semidirect
5. C2×#10622120C2semidirect
6. #13066450C2semidirect
7. C2×C11×#331C2semidirect
100. C2×D44SD16semidirect
133. C2×C11⋊C8D8semidirect
139. C2×#331D11semidirect
350. C11#10266semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106224592
C2×#106226852
#130694092
C2×#106221202
#130664502
C2×C11×#3312
#1026611