Finite Group Databasebeta

← #14911250

Subgroups — #14911250

Order 2816.

516 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#13081017C211yesmaximal, characteristic, complemented
2#13080965C211yesmaximal, characteristic, complemented
3#13070903C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070798C211yesmaximal, characteristic, complemented
8#13070764C211yesmaximal, characteristic, complemented
9#13070718C211yesmaximal, characteristic, complemented
10#13070701C211yesmaximal, characteristic, complemented
11#13070490C211yesmaximal, characteristic, complemented
12#13070440C211yesmaximal, characteristic, complemented
13#13070401C211yesmaximal, characteristic, complemented
14D11×#367C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16#10623226—21no—
17#10623082—21no—
18C11×#499C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20#10622770C2211yescharacteristic
21#10622770C2211yescharacteristic
22C2×#66890C2211yescharacteristic
23#10622679—21no—
24#10622620—21no—
25C2×#66862C2211yescharacteristic
26C2×C16×D11C2211yescharacteristic
27#10622496C2211yescharacteristic
28#10622496C2211yescharacteristic
29#10622493C2211yescharacteristic
30D11×#107C2211yescharacteristic
31D11×#107C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622479—21no—
34#10622476—21no—
35#10622387—21no—
36#10622387—21no—
37C4×D88C2211yescharacteristic
38C8×D44C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×#367C2211yescharacteristic
41C11×#366C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622128C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4339—41no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63#66991—21no—
64#66991—21no—
65#66977—41no—
66C2×D88C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66951—41no—
70#66948—21no—
71#66948—21no—
72#66948—41no—
73#66947—41no—
74#66946—41no—
75#66945—21no—
76C4⋊C4×D11—21no—
77C4⋊C4×D11—21no—
78C4⋊C4×D11—21no—
79#66936—41no—
80#66936—41no—
81C4×D44—21no—
82C4×D44D411yescharacteristic
83#66922—21no—
84C2×C11×C16C2311yescharacteristic
85C2×C11×C16C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#106—21no—
90C11×#102—21no—
91C4×C8×C11C2311yescharacteristic
92#66896—21no—
93#66896—21no—
94#66890—22no—
95#66885—21no—
96(C2×D11)⋊C8D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104#66873—21no—
105#66873—21no—
106#66872—21no—
107#66871—21no—
108#66871—21no—
109#66871—21no—
110C4⋊(C11⋊C8)D411yescharacteristic
111#66862—22no—
112C16×D11—22no—
113#33912—111nomaximal, Sylow
114C2×D4×C11—21no—
115C22×C4×C11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118#4339—84no—
119C2×D44—21no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44D811yescharacteristic
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×C4×D11C2×D411yescharacteristic
129C2×Dic22—41no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11C2×D411yescharacteristic
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4D811yescharacteristic
148(C2×D11)⋊C4D811yescharacteristic
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153C4⋊Dic11D811yescharacteristic
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160D88—21no—
161D88—21no—
162C8×D11—21no—
163C8×D11—21no—
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11⋊C16—21no—
169C11⋊C16#4112yescomplemented
170#3339—111no—
171#3334—111no—
172#2255—111no—
173#2234—111no—
174#2233—111no—
175#2233—111no—
176#2232—111no—
177#2228D1111yescharacteristic, complemented
178#2226—111no—
179#2218—111no—
180#2215—111no—
181#2177—111no—
182#2168—111no—
183#2159—111no—
184C2×#367—111no—
185C23×C11—41no—
186C22×D11—41no—
187C22×D11C2×D811yescharacteristic
188C22×D11C2×D811yescharacteristic
189D4×C11—41no—
190D4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—82no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—82no—
199C22⋊D11—82no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—22no—
206D44—41no—
207D44—41no—
208D44—82no—
209D44—161no—
210C4×D11—21no—
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—82no—
215C4×D11—82no—
216C4×D11—161no—
217C4×D11—161no—
218Dic22—82no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#553—221no—
225#547—221no—
226C2×D16—111no—
227C2×M32—111no—
228C22×C16—111no—
229#500—111no—
230#499C2×D1111yescharacteristic
231#482—221no—
232#481—221no—
233#480—221no—
234#480—221no—
235#478—221no—
236#474—221no—
237#466—111no—
238#466—111no—
239#466—111no—
240#466—111no—
241C4×D8—111no—
242C4×D8C2×D1111yescharacteristic
243C8×D4—111no—
244#427—111no—
245C2×#107—111no—
246C2×#107—111no—
247C2×#107—111no—
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367—111no—
253#367C2×D1111yescharacteristic
254#366—111no—
255#366—111no—
256#366C2×D1111yescharacteristic
257C4⋊C16C2×D1111yescharacteristic
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264C22⋊C16—111no—
265C22⋊C16—111no—
266#346—111no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C2×D11—21no—
272C2×D11—21no—
273C2×D11—21no—
274C2×D11—21no—
275C2×D11—21no—
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11#50912yes—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#54711yescharacteristic
286C4×C11#57811yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—81no—
290Dic11—81no—
291Dic11—81no—
292C2×#41—441no—
293C2×D8—111no—
294C2×D8C22×D1111yescharacteristic
295C22×C8—111no—
296C22×C8—111no—
297C4⋊Q8—221no—
298#126—441no—
299#125—21no—
300#123—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—21no—
310C4×D4—111no—
311C4×D4—221no—
312C4×D4—441no—
313#117—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317D16—222no—
318M32—222no—
319C2×C16—111no—
320C2×C16—111no—
321C2×C16—222no—
322C2×C16C22×D1111yescharacteristic
323C2×C16C22×D1111yescharacteristic
324#107—111no—
325#107—111no—
326#107—111no—
327#107—221no—
328#107—221no—
329#107—221no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#107C22×D1111yescharacteristic
334#106—21no—
335#106—221no—
336C4⋊C8—111no—
337#102—21no—
338#102—221no—
339#102—221no—
340#102—221no—
341#102—221no—
342#102—221no—
343C22⋊C8—111no—
344C22⋊C8—111no—
345C4×C8C22×D1111yescharacteristic
346C2×C11—161no—
347C2×C11#333411yescharacteristic
348C2×C11C2×#50911yescharacteristic
349C2×C11#341611yescharacteristic
350D11—22no—
351D11—41no—
352D11—161no—
353#41—884no—
354C2×Q8—441no—
355C2×D4—21no—
356C2×D4—111no—
357C2×D4—221no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—441no—
362C22×C4—41no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4—441no—
369D8—21no—
370D8—21no—
371D8—221no—
372D8—221no—
373C2×C8—111no—
374C2×C8—111no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8D4×D1111yescharacteristic
380C2×C8C23×D1111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—111no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C22⋊C4—41no—
395C22⋊C4—111no—
396C22⋊C4—111no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C42—441no—
404C42D4×D1111yescharacteristic
405C16—21no—
406C16—21no—
407C16—112no—
408C16—221no—
409C11#3391211yescharacteristic, complemented, Sylow
410C23—41no—
411C23—111no—
412C23—111no—
413C23—441no—
414Q8—882no—
415D4—41no—
416D4—41no—
417D4—222no—
418D4—441no—
419D4—441no—
420D4—882no—
421D4—882no—
422D4—882no—
423D4—1761no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—882no—
438C2×C4—882no—
439C2×C4—1761no—
440C2×C4—1761no—
441C2×C4D8×D1111yescharacteristic
442C2×C4D8×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C8—21no—
445C8—221no—
446C8—221no—
447C8#6704011yescharacteristic
448C8#41×D1111yescharacteristic
449C22—81no—
450C22—81no—
451C22—81no—
452C22—112no—
453C22—221no—
454C22—221no—
455C22—221no—
456C22—221no—
457C22—221no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×D8×D1111yescharacteristic
462C4—21no—
463C4—21no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—221no—
468C4—221no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062316211yescharacteristic
473C4#1062331011yescharacteristic
474C2—161no—
475C2—222no—
476C2—441no—
477C2—1761no—
478C2#1308096211yescharacteristic
479C2D11×#50911yescharacteristic
480C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
hypercenter#2228D11
hypocenterC11#33912
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13081017C2semidirect
2. #13080965C2semidirect
3. #13070903C2semidirect
4. #13070806C2semidirect
5. #13070803C2semidirect
6. #13070800C2semidirect
7. #13070798C2semidirect
8. #13070764C2semidirect
9. #13070718C2semidirect
10. #13070701C2semidirect
11. #13070490C2semidirect
12. #13070440C2semidirect
13. #13070401C2semidirect
14. D11×#367C2semidirect
15. C11×#2228C2semidirect
169. C11⋊C16#41semidirect
177. #2228D11semidirect
409. C11#33912semidirect

Maximal subgroups

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

subgroupindex
#130810172
#130809652
#130709032
#130708062
#130708032
#130708002
#130707982
#130707642
#130707182
#130707012
#130704902
#130704402
#130704012
D11×#3672
C11×#22282
#3391211