Finite Group Databasebeta

← #14737282

Subgroups — #14737282

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3#13079163C211yesmaximal, characteristic, complemented
4#13077359C211yesmaximal, characteristic
5#13068128C212yesmaximal, complemented
6#13068118C212yesmaximal, complemented
7#13068004C212yesmaximal, complemented
8#13067994C212yesmaximal, complemented
9#13067369C211yesmaximal, characteristic, complemented
10C2×#10622124C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66954—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622723—21no—
19#10622697C2212yes—
20#10622696C2212yes—
21#10622692C2212yes—
22#10622691C2212yes—
23#10622678—22no—
24#10622661—22no—
25#10622640—21no—
26#10622633—21no—
27#10622608—21no—
28#10622608—21no—
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622454C2212yes—
32#10622454C2212yes—
33#10622451C2212yes—
34#10622449—22no—
35#10622447C2212yes—
36#10622351—22no—
37#10622306—21no—
38#10622294—21no—
39C11×#333C2211yescharacteristic
40C11×#333C2211yescharacteristic
41C11×#332C2211yescharacteristic
42C11×#332C2211yescharacteristic
43#10622124C2212yes—
44#10622124C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47C2×#4339—21no—
48C22×Dic22—21no—
49C22×C8×C11—21no—
50C11×C4⋊Q8C2311yescharacteristic
51C11×C4⋊Q8C2311yescharacteristic
52C11×#125—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C11×#117—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4325—22no—
60#66983—21no—
61#66983D412yes—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×#4318D411yescharacteristic
65C2×#4318D411yescharacteristic
66C22×C11⋊C8—21no—
67C2×#4314—22no—
68C2×#4314—22no—
69#66954—44no—
70C2×#4313—22no—
71C2×C8×D11—22no—
72#66928—21no—
73#66927D411yescharacteristic
74C4×D44—21no—
75C4×D44C2312yes—
76#66922—21no—
77#66922—21no—
78#66922—21no—
79#66922D411yescharacteristic
80#66922C2312yes—
81C11×C4⋊C8—21no—
82C11×C4⋊C8C2311yescharacteristic
83C11×C4⋊C8C2311yescharacteristic
84C11×C4⋊C8C2311yescharacteristic
85C11×C4⋊C8C2311yescharacteristic
86C11×C22⋊C8—21no—
87C4×C8×C11—21no—
88#66899—22no—
89(C2×D11)⋊C8—22no—
90(C2×D11)⋊C8—22no—
91#66880—22no—
92#66880—22no—
93#66873—22no—
94#66872—22no—
95#66872—22no—
96#66872—22no—
97#66871—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103#19232—111nomaximal, Sylow
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—22no—
110C22×Dic11—41no—
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C2×D412yes—
116C2×C4×D11—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—81no—
121C2×Dic22—81no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—42no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139#4325—82no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147C4⋊Dic11C2×D412yes—
148#4318—22no—
149#4318SD1614yescomplemented
150C2×C11⋊C8—22no—
151C2×C11⋊C8—81no—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×D412yes—
154#4314—82no—
155#4314—82no—
156#4313—44no—
157C8×D11—44no—
158#3246—111no—
159#3206—111no—
160#3165—111no—
161#2935—111no—
162#1693—112no—
163#1691—112no—
164#1673—112no—
165#1671—112no—
166#1565—111no—
167#1542D1111yescharacteristic, complemented
168C2×#332—111no—
169C23×C11#12111yescharacteristic
170C22×D11—22no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—81no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11C2×SD1612yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C22⋊D11—44no—
188C2×Dic11—22no—
189C2×Dic11—42no—
190C2×Dic11—82no—
191D44—22no—
192D44—22no—
193D44—42no—
194D44—81no—
195C4×D11—42no—
196C4×D11—42no—
197Dic22—42no—
198Dic22—42no—
199Dic22—42no—
200Dic22—82no—
201C8×C11—41no—
202C8×C11—41no—
203C8×C11—41no—
204C8×C11—41no—
205C11⋊C8—22no—
206C11⋊C8—42no—
207C11⋊C8C2×SD1614yes—
208C2×#131—221no—
209#533C2×D1111yescharacteristic
210#532—111no—
211C2×C4⋊Q8—111no—
212#501—222no—
213#500—112no—
214#498—112no—
215#492—221no—
216#487—221no—
217#476—112no—
218#475—221no—
219#465—222no—
220#461—112no—
221#461—112no—
222#461—112no—
223#460—221no—
224#448—222no—
225#436—112no—
226#435—222no—
227C8×D4—112no—
228#431C2×D1111yescharacteristic
229#428—221no—
230#428—221no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8C2×D1111yescharacteristic
233#408—221no—
234C4×M16—111no—
235#335—112no—
236#334—112no—
237#333C2×D1111yescharacteristic
238#333C2×D1111yescharacteristic
239#332—112no—
240#332—112no—
241#332C2×D1111yescharacteristic
242#332C2×D1111yescharacteristic
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#46112yes—
246C22×C11C2×#12111yescharacteristic
247C2×D11—42no—
248C2×D11—42no—
249C2×D11—42no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—81no—
254C4×C11—81no—
255C4×C11#46112yes—
256C4×C11C22×SD1611yescharacteristic
257C4×C11C2×#13711yescharacteristic
258C4×C11#57611yescharacteristic
259C4×C11#57711yescharacteristic
260Dic11—42no—
261Dic11—82no—
262C2×#41—221no—
263C22×Q8—221no—
264C2×SD16—222no—
265C2×SD16—222no—
266C2×SD16—222no—
267#131—444no—
268C2×M16—111no—
269C2×M16—111no—
270C2×M16—222no—
271C22×C8—21no—
272C22×C8—222no—
273C22×C8—221no—
274C4⋊Q8—111no—
275C4⋊Q8—112no—
276C4⋊Q8—221no—
277C4⋊Q8—221no—
278C4⋊Q8—221no—
279C4⋊Q8C22×D1111yescharacteristic
280C4⋊Q8C22×D1111yescharacteristic
281#127—111no—
282#125—21no—
283#124—221no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286#121—112no—
287#121—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×D4—112no—
291C4×D4—221no—
292#117—21no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C42C22×D1111yescharacteristic
296#107—222no—
297#107—222no—
298#106—222no—
299#106—222no—
300#106—222no—
301C4⋊C8—21no—
302C4⋊C8—112no—
303C4⋊C8—221no—
304C4⋊C8C22×D1111yescharacteristic
305C4⋊C8C22×D1111yescharacteristic
306C4⋊C8C22×D1111yescharacteristic
307C4⋊C8C22×D1111yescharacteristic
308#103—222no—
309#103—222no—
310#103—222no—
311#102—222no—
312C22⋊C8—21no—
313C22⋊C8—222no—
314C22⋊C8—222no—
315#97—112no—
316C4×C8—21no—
317C4×C8—112no—
318C2×C11—22no—
319C2×C11C2×#46111yescharacteristic
320C2×C11#306211yescharacteristic
321C2×C11#306911yescharacteristic
322D11—82no—
323#41—442no—
324#41—442no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—221no—
328C2×Q8—222no—
329C2×Q8—441no—
330C2×Q8—881no—
331C2×Q8—881no—
332C2×D4—112no—
333C2×D4—222no—
334C2×D4—221no—
335C2×D4—221no—
336C22×C4—222no—
337C22×C4—441no—
338C22×C4#433911yescharacteristic
339C22×C4D4×D1111yescharacteristic
340C22×C4D4×D1111yescharacteristic
341SD16—882no—
342SD16—882no—
343SD16—882no—
344M16—114no—
345M16—222no—
346M16—444no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—42no—
352C2×C8—112no—
353C2×C8—112no—
354C2×C8—222no—
355C2×C8—444no—
356C2×C8—881no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C22⋊C4—41no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C42—41no—
373C42#433911yescharacteristic
374C42D4×D1111yescharacteristic
375C42D4×D1111yescharacteristic
376C42C23×D1111yescharacteristic
377C11#1923211yescharacteristic, complemented, Sylow
378C23—222no—
379C23#6693711yescharacteristic
380Q8—41no—
381Q8—41no—
382Q8—81no—
383Q8—442no—
384Q8—442no—
385Q8—442no—
386Q8—882no—
387D4—222no—
388D4—222no—
389D4—444no—
390D4—442no—
391D4—881no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—222no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—882no—
402C2×C4#6693711yescharacteristic
403C2×C4#6693711yescharacteristic
404C2×C4#6693711yescharacteristic
405C2×C4SD16×D1112yes—
406C2×C4#6697112yes—
407C2×C4C2×#433911yescharacteristic
408C2×C4C2×D4×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—114no—
415C8—222no—
416C8—442no—
417C22—21no—
418C22—21no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22#1062243112yes—
423C22C2×#6693711yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—442no—
430C4—882no—
431C4#1062243112yes—
432C4C2×SD16×D1111yescharacteristic
433C4C2×#6697111yescharacteristic
434C4#1062330011yescharacteristic
435C4#1062330111yescharacteristic
436C2—22no—
437C2—882no—
438C2C2×#1062243111yescharacteristic
439C2#1307829911yescharacteristic
440C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1542D11
hypocenterC11#19232
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #13079163C2semidirect
5. #13068128C2semidirect
6. #13068118C2semidirect
7. #13068004C2semidirect
8. #13067994C2semidirect
9. #13067369C2semidirect
10. C2×#10622124C2semidirect
11. C11×#1542C2semidirect
149. #4318SD16semidirect
167. #1542D11semidirect
377. C11#19232semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130795432
#130791632
#130773592
#130681282
#130681182
#130680042
#130679942
#130673692
C2×#106221242
C11×#15422
#1923211