Finite Group Databasebeta

← #14911485

Subgroups — #14911485

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081589C211yesmaximal, characteristic, complemented
2#13081483C211yesmaximal, characteristic, complemented
3#13070857C211yesmaximal, characteristic, complemented
4#13070856C211yesmaximal, characteristic, complemented
5#13070838C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070771C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070649C211yesmaximal, characteristic, complemented
10#13070649C211yesmaximal, characteristic, complemented
11#13070523C211yesmaximal, characteristic, complemented
12#13070492C211yesmaximal, characteristic, complemented
13#13070490C211yesmaximal, characteristic, complemented
14D16×Dic11C211yesmaximal, characteristic, complemented
15C11×#2206C211yesmaximal, characteristic, complemented
16#10623249—21no—
17#10623070—21no—
18C2×C11×D16C2211yescharacteristic
19C2×C11×D16C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C4×C11×D8C2211yescharacteristic
22#10622764C2211yescharacteristic
23#10622764C2211yescharacteristic
24#10622763—21no—
25#10622763—21no—
26D8×Dic11C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622685—21no—
32#10622622—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622376—21no—
36#10622374—21no—
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622140C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×D8—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C11×#127—21no—
65C4×D4×C11—21no—
66#66993—21no—
67#66993—21no—
68#66992—41no—
69#66992—41no—
70#66991—41no—
71D4×Dic11—21no—
72D4×Dic11—21no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75C2×#4323—21no—
76C2×#4323—21no—
77#66977—41no—
78C2×Dic11⋊C4—41no—
79C2×D88C2311yescharacteristic
80#66943—21no—
81#66941—21no—
82#66931—41no—
83#66931—41no—
84C4×D44—21no—
85#66923—21no—
86C4×Dic22D411yescharacteristic
87C11×D16—22no—
88C11×D16—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#102—21no—
93C4×C8×C11C2311yescharacteristic
94#66896—21no—
95#66896—21no—
96#66896—21no—
97#66896—21no—
98#66890—22no—
99#66885—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33933—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128#4341—84no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—41no—
132C2×Dic22D811yescharacteristic
133C11×D8—21no—
134C11×D8—21no—
135C11×D8—21no—
136C11×D8—21no—
137C11×D8—21no—
138C11×D8—81no—
139C11×D8#4112yescomplemented
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C22⋊C4—41no—
144C42×C11C2×D411yescharacteristic
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4323—81no—
150#4323—81no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156C4⋊Dic11D811yescharacteristic
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4D811yescharacteristic
162Dic11⋊C4D811yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167D88—21no—
168D88—21no—
169C11×C16—21no—
170C11×C16—21no—
171C11⋊C16—21no—
172C11⋊C16—21no—
173#3391—111no—
174#3380—111no—
175#2244—111no—
176#2244—111no—
177#2240—111no—
178#2228—111no—
179#2228—111no—
180#2226—111no—
181#2206—111no—
182#2206—111no—
183#2206D1111yescharacteristic, complemented
184#2183—111no—
185#2177—111no—
186#2177—111no—
187C4×D16—111no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C22×D11—41no—
192D4×C11—22no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—82no—
199D4×C11—161no—
200C2×C4×C11—41no—
201C2×C4×C11—161no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—82no—
206C22⋊D11—82no—
207C22⋊D11—161no—
208C22⋊D11—161no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—82no—
213C2×Dic11—82no—
214C2×Dic11—82no—
215C2×Dic11—161no—
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—41no—
221D44—41no—
222C4×D11—82no—
223Dic22—22no—
224Dic22—161no—
225C8×C11—21no—
226C8×C11C2×#4111yescharacteristic
227C8×C112−1+411yescharacteristic
228C11⋊C8—21no—
229C11⋊C8—21no—
230#554—221no—
231#550—221no—
232C2×D16—111no—
233C2×D16C2×D1111yescharacteristic
234C2×D16C2×D1111yescharacteristic
235#500—111no—
236#499—111no—
237#499—111no—
238#493—111no—
239#493—111no—
240#493C2×D1111yescharacteristic
241#478—221no—
242#478—221no—
243#476—221no—
244#459—221no—
245#459—221no—
246#459—221no—
247C8×Q8—111no—
248C4×D8—111no—
249C4×D8—111no—
250C4×D8—111no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254#367—111no—
255#367—111no—
256#366—111no—
257C4⋊C16—111no—
258C4⋊C16—111no—
259C4⋊C16C2×D1111yescharacteristic
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#357—111no—
265#357—111no—
266#357—111no—
267#357—111no—
268#357C2×D1111yescharacteristic
269#357C2×D1111yescharacteristic
270#346—111no—
271#346—111no—
272C4×C16—111no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11C22×D811yescharacteristic
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—81no—
289C4×C11#54811yescharacteristic
290C4×C11#57711yescharacteristic
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297Dic11#50912yes—
298C2×#41—441no—
299C2×D8—21no—
300C2×D8—111no—
301C2×D8—221no—
302C2×D8—221no—
303C2×D8C22×D1111yescharacteristic
304C2×D8C22×D1111yescharacteristic
305C2×D8C22×D1111yescharacteristic
306C4⋊Q8—221no—
307#127—21no—
308#127—221no—
309#127—221no—
310#125—221no—
311#125—221no—
312C22⋊Q8—441no—
313C22⋊Q8—441no—
314C22⋊Q8—441no—
315#121—441no—
316#121—441no—
317#121—441no—
318C4×Q8—111no—
319C4×D4—21no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—221no—
324C4×D4—221no—
325C2×C4⋊C4—441no—
326D16—22no—
327D16—22no—
328D16—222no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107—111no—
336#107—221no—
337#107C22×D1111yescharacteristic
338#106—221no—
339#106—221no—
340C4⋊C8—111no—
341C4⋊C8—111no—
342C4⋊C8—111no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347#102—221no—
348#102—221no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8C22×D1111yescharacteristic
352C2×C11—82no—
353C2×C11—161no—
354C2×C11—161no—
355C2×C11#335811yescharacteristic
356C2×C11C2×#50911yescharacteristic
357C2×C11#341511yescharacteristic
358D11—161no—
359#41—884no—
360C2×Q8—111no—
361C2×Q8—441no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—221no—
368C2×D4—441no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C22×C4—41no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4—441no—
378D8—21no—
379D8—21no—
380D8—21no—
381D8—21no—
382D8—21no—
383D8—81no—
384D8—221no—
385D8—221no—
386D8—881no—
387D8—881no—
388D8#434112yescomplemented
389C2×C8—111no—
390C2×C8—111no—
391C2×C8D4×D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—111no—
395C4⋊C4—111no—
396C4⋊C4—111no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C22⋊C4—41no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42—111no—
412C42—111no—
413C42D4×D1111yescharacteristic
414C16—21no—
415C16—21no—
416C16—221no—
417C16—221no—
418C11#3393311yescharacteristic, complemented, Sylow
419C23—41no—
420C23—41no—
421C23—41no—
422C23—441no—
423Q8—222no—
424Q8—1761no—
425D4—22no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—82no—
432D4—161no—
433D4—441no—
434D4—441no—
435D4—882no—
436D4—882no—
437D4—1761no—
438D4—1761no—
439C2×C4—41no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—111no—
443C2×C4—111no—
444C2×C4—161no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4—882no—
450C2×C4—882no—
451C2×C4—882no—
452C2×C4—1761no—
453C2×C4D8×D1111yescharacteristic
454C2×C4D8×D1111yescharacteristic
455C2×C4C2×D4×D1111yescharacteristic
456C8—21no—
457C8—221no—
458C8—221no—
459C8C2×#434111yescharacteristic
460C8#6704311yescharacteristic
461C22—42no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—112no—
478C4—221no—
479C4—221no—
480C4—221no—
481C4—881no—
482C4—881no—
483C4—881no—
484C4#1062312911yescharacteristic
485C4#1062330611yescharacteristic
486C2—82no—
487C2—161no—
488C2—161no—
489C2—1761no—
490C2#1308124611yescharacteristic
491C2D11×#50911yescharacteristic
492C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081589C2semidirect
2. #13081483C2semidirect
3. #13070857C2semidirect
4. #13070856C2semidirect
5. #13070838C2semidirect
6. #13070774C2semidirect
7. #13070771C2semidirect
8. #13070761C2semidirect
9. #13070649C2semidirect
10. #13070649C2semidirect
11. #13070523C2semidirect
12. #13070492C2semidirect
13. #13070490C2semidirect
14. D16×Dic11C2semidirect
15. C11×#2206C2semidirect
139. C11×D8#41semidirect
183. #2206D11semidirect
388. D8#4341semidirect
418. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130815892
#130814832
#130708572
#130708562
#130708382
#130707742
#130707712
#130707612
#130706492
#130705232
#130704922
#130704902
D16×Dic112
C11×#22062
#3393311