Finite Group Databasebeta

← #14911374

Subgroups — #14911374

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081036C211yesmaximal, characteristic, complemented
2#13080961C211yesmaximal, characteristic, complemented
3#13070897C211yesmaximal, characteristic, complemented
4#13070810C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070803C211yesmaximal, characteristic, complemented
7#13070801C211yesmaximal, characteristic, complemented
8#13070762C211yesmaximal, characteristic, complemented
9#13070752C211yesmaximal, characteristic, complemented
10#13070720C211yesmaximal, characteristic, complemented
11#13070719C211yesmaximal, characteristic, complemented
12#13070462C211yesmaximal, characteristic, complemented
13#13070446C211yesmaximal, characteristic, complemented
14#13070401C211yesmaximal, characteristic, complemented
15C11×#2159C211yesmaximal, characteristic, complemented
16#10623063—21no—
17#10623038—21no—
18C2×C11×M32C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622728C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622616—21no—
25#10622580—21no—
26C2×D176C2211yescharacteristic
27C2×#66862C2211yescharacteristic
28#10622503—21no—
29#10622496C2211yescharacteristic
30#10622496C2211yescharacteristic
31#10622495—21no—
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622483—21no—
39#10622479—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46#10622147C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622143C2211yescharacteristic
49Dic11⋊C16C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4339—41no—
60C22×C8×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C11×C4⋊C4—21no—
63#66983—21no—
64#66983—21no—
65#66982—41no—
66C4×C22⋊D11D411yescharacteristic
67C2×D88C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66949—41no—
71#66948—21no—
72#66948—21no—
73#66947—41no—
74#66946—21no—
75#66946—21no—
76#66945—21no—
77C4⋊C4×D11—21no—
78#66941—21no—
79#66941—21no—
80#66938—41no—
81#66937—41no—
82#66928—41no—
83#66925—41no—
84C11×M32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66885—21no—
95#66885—21no—
96(C2×D11)⋊C8D411yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66873—21no—
104#66873—21no—
105#66873—21no—
106#66873—21no—
107#66872—21no—
108#66871—21no—
109#66871—21no—
110#66871—21no—
111D176—22no—
112#66862—22no—
113#33921—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11D811yescharacteristic
119#4339—84no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—41no—
123C2×D44—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—41no—
129C2×Dic22—41no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11—41no—
141C22⋊Dic11D811yescharacteristic
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4D811yescharacteristic
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4D811yescharacteristic
156C4×Dic11—41no—
157C4×Dic11C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160D88—21no—
161D88—21no—
162D88—21no—
163D88—21no—
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3341—111no—
171#3334—111no—
172#2254—111no—
173#2234—111no—
174#2234—111no—
175#2233—111no—
176#2233—111no—
177#2226—111no—
178#2224—111no—
179#2218—111no—
180#2218—111no—
181C4×D16—111no—
182#2169—111no—
183#2159—111no—
184#2159D1111yescharacteristic, complemented
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187C22×D11—41no—
188C22×D11C2×D811yescharacteristic
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—22no—
199C22⋊D11—82no—
200C22⋊D11—161no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206D44—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—82no—
211D44—161no—
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—82no—
215C4×D11—82no—
216C4×D11—82no—
217Dic22—82no—
218Dic22—161no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#555—221no—
225#547—221no—
226C2×D16—111no—
227C2×M32—111no—
228C2×M32C2×D1111yescharacteristic
229#500—111no—
230#500—111no—
231#482—221no—
232#482—221no—
233#480—221no—
234#480—221no—
235#476—221no—
236#474—221no—
237#466—111no—
238#466—111no—
239#466—111no—
240#466—111no—
241C4×D8—111no—
242C4×D8—111no—
243C8×D4—111no—
244#427—111no—
245#427C2×D1111yescharacteristic
246C2×#107—111no—
247C2×#107C2×D1111yescharacteristic
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367C2×D1111yescharacteristic
253#367C2×D1111yescharacteristic
254#366—111no—
255#366C2×D1111yescharacteristic
256#366C2×D1111yescharacteristic
257C4⋊C16—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264C22⋊C16—111no—
265C22⋊C16—111no—
266C4×C16—111no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11C22×D811yescharacteristic
271C2×D11—21no—
272C2×D11—21no—
273C2×D11—21no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#54711yescharacteristic
286C4×C11#57811yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—81no—
290Dic11—81no—
291Dic11#50912yes—
292C2×#41—441no—
293C2×D8—111no—
294C2×D8—111no—
295C22×C8—111no—
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#124—441no—
300#124—441no—
301#123—441no—
302#123—441no—
303C22⋊Q8—441no—
304#121—221no—
305#121—221no—
306#121—221no—
307#121—221no—
308#121—441no—
309C4×D4—111no—
310C4×D4—221no—
311C4×D4—221no—
312#117—21no—
313#117—221no—
314#117—441no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—221no—
317D16—222no—
318M32—22no—
319M32—222no—
320C2×C16—111no—
321C2×C16—111no—
322C2×C16C22×D1111yescharacteristic
323C2×C16C22×D1111yescharacteristic
324#107—21no—
325#107—111no—
326#107—111no—
327#107—221no—
328#107—221no—
329#107—221no—
330#107C22×D1111yescharacteristic
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#107C22×D1111yescharacteristic
334#106—21no—
335#106—221no—
336C4⋊C8—111no—
337#102—221no—
338#102—221no—
339#102—221no—
340#102—221no—
341#102—221no—
342#102—221no—
343C22⋊C8—111no—
344C22⋊C8—111no—
345C4×C8—111no—
346C2×C11—41no—
347C2×C11#333411yescharacteristic
348C2×C11C2×#50911yescharacteristic
349C2×C11#341611yescharacteristic
350D11—41no—
351D11—161no—
352D11—161no—
353#41—884no—
354C2×Q8—441no—
355C2×Q8—441no—
356C2×D4—111no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—441no—
362C2×D4—441no—
363C22×C4—41no—
364C22×C4—111no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4D4×D1111yescharacteristic
369D8—221no—
370D8—221no—
371D8—221no—
372D8—221no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—111no—
376C2×C8—111no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8D4×D1111yescharacteristic
380C2×C8C23×D1111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—111no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C22⋊C4—41no—
393C22⋊C4—111no—
394C22⋊C4—111no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—41no—
403C42—111no—
404C42—441no—
405C16—21no—
406C16—221no—
407C16—221no—
408C16#433912yescomplemented
409C11#3392111yescharacteristic, complemented, Sylow
410C23—111no—
411C23—441no—
412C23—441no—
413C23D8×D1111yescharacteristic
414Q8—882no—
415Q8—1761no—
416D4—222no—
417D4—441no—
418D4—441no—
419D4—441no—
420D4—441no—
421D4—882no—
422D4—882no—
423D4—1761no—
424D4—1761no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—111no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—882no—
440C2×C4—882no—
441C2×C4—882no—
442C2×C4D8×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C8—21no—
445C8—221no—
446C8—221no—
447C8C2×#433911yescharacteristic
448C8#6704011yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—221no—
453C22—221no—
454C22—221no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×D8×D1111yescharacteristic
462C4—21no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—112no—
468C4—221no—
469C4—221no—
470C4—881no—
471C4—881no—
472C4#1062303811yescharacteristic
473C4#1062329711yescharacteristic
474C2—41no—
475C2—441no—
476C2—1761no—
477C2—1761no—
478C2#1308096111yescharacteristic
479C2D11×#50911yescharacteristic
480C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
hypercenter#2159D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. #13081036C2semidirect
2. #13080961C2semidirect
3. #13070897C2semidirect
4. #13070810C2semidirect
5. #13070807C2semidirect
6. #13070803C2semidirect
7. #13070801C2semidirect
8. #13070762C2semidirect
9. #13070752C2semidirect
10. #13070720C2semidirect
11. #13070719C2semidirect
12. #13070462C2semidirect
13. #13070446C2semidirect
14. #13070401C2semidirect
15. C11×#2159C2semidirect
167. C11×C16#41semidirect
184. #2159D11semidirect
408. C16#4339semidirect
409. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810362
#130809612
#130708972
#130708102
#130708072
#130708032
#130708012
#130707622
#130707522
#130707202
#130707192
#130704622
#130704462
#130704012
C11×#21592
#3392111