Finite Group Databasebeta

← #14911538

Subgroups — #14911538

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081629C211yesmaximal, characteristic, complemented
2#13081484C211yesmaximal, characteristic, complemented
3#13070858C211yesmaximal, characteristic, complemented
4#13070853C211yesmaximal, characteristic, complemented
5#13070848C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070774C211yesmaximal, characteristic, complemented
8#13070754C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070672C211yesmaximal, characteristic, complemented
11#13070652C211yesmaximal, characteristic
12#13070493C211yesmaximal, characteristic, complemented
13#13070482C211yesmaximal, characteristic, complemented
14C4×D176C211yesmaximal, characteristic, complemented
15C11×#2183C211yesmaximal, characteristic, complemented
16#10623116—21no—
17#10623110—21no—
18C8×Q8×C11C2211yescharacteristic
19C2×#66864C2211yescharacteristic
20C2×D176C2211yescharacteristic
21C2×D176C2211yescharacteristic
22#10622461—21no—
23#10622460—21no—
24#10622460—21no—
25#10622457—21no—
26#10622457—21no—
27#10622455—21no—
28C4×Dic44C2211yescharacteristic
29#10622309C2211yescharacteristic
30#10622309C2211yescharacteristic
31#10622308C2211yescharacteristic
32C4×D88C2211yescharacteristic
33C4×D88C2211yescharacteristic
34C4×D88C2211yescharacteristic
35C4×D88C2211yescharacteristic
36C4×D88C2211yescharacteristic
37#10622296C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44C11×#346C2211yescharacteristic
45C4×C11×C16C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C4×Q8×C11D411yescharacteristic
60#67000—41no—
61#66999—41no—
62C2×Dic44C2311yescharacteristic
63C2×D88—21no—
64C2×D88C2311yescharacteristic
65C2×D88C2311yescharacteristic
66C2×D88C2311yescharacteristic
67C2×#4314—21no—
68C2×#4314—21no—
69#66949—41no—
70#66949—41no—
71#66947—41no—
72#66947—41no—
73#66946—41no—
74C4⋊C4×D11—41no—
75#66928—21no—
76#66928—21no—
77#66927—21no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44—21no—
82C4×D44—21no—
83#66923—21no—
84#66923—21no—
85#66922—21no—
86C4×Dic22—21no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×C4⋊C8D411yescharacteristic
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8D411yescharacteristic
94C4×C8×C11C2311yescharacteristic
95C4×C8×C11C2311yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66885—21no—
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66885—21no—
102#66882—21no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66881—21no—
109#66880—21no—
110#66864—22no—
111D176—22no—
112D176—22no—
113#33937—111nomaximal, Sylow
114C2×Q8×C11D811yescharacteristic
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—41no—
119C2×D44—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×Dic22—21no—
126C2×Dic22—41no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4D811yescharacteristic
132C11×C4⋊C4D811yescharacteristic
133C11×C4⋊C4D811yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157Dic44—21no—
158Dic44—21no—
159D88—21no—
160D88—21no—
161D88—21no—
162D88—21no—
163D88—21no—
164D88—81no—
165D88#4112yes—
166#4314—81no—
167#4314—81no—
168C11×C16—21no—
169C11×C16—21no—
170C11×C16—21no—
171C11×C16—21no—
172#3396—111no—
173#3380—111no—
174#2244—111no—
175#2243—111no—
176#2242—111no—
177#2229—111no—
178#2228—111no—
179#2224—111no—
180#2210—111no—
181#2210—111no—
182#2206—111no—
183#2183D1111yescharacteristic, complemented
184#2177—111no—
185#2175—111no—
186C4×D16—111no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190Q8×C11—41no—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—22no—
204D44—41no—
205D44—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—82no—
210D44—161no—
211C4×D11—82no—
212C4×D11—161no—
213C4×D11—161no—
214C4×D11—161no—
215C4×D11—161no—
216Dic22—41no—
217Dic22—41no—
218Dic22—161no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11C2×#4111yescharacteristic
223C8×C112−1+411yescharacteristic
224#559—221no—
225#554—221no—
226C2×SD32—111no—
227C2×D16—111no—
228C2×D16—111no—
229#500—111no—
230#499—111no—
231#499—111no—
232#495—111no—
233#495—111no—
234#493—111no—
235#478—221no—
236#478—221no—
237#476—221no—
238#463—221no—
239#463—221no—
240#460—221no—
241C8×Q8C2×D1111yescharacteristic
242C4×Q16—111no—
243C4×D8—111no—
244C4×D8—111no—
245C4×D8—111no—
246C4×D8—111no—
247C4×D8—111no—
248#367—111no—
249#366—111no—
250#366—111no—
251C4⋊C16C2×D1111yescharacteristic
252C4⋊C16C2×D1111yescharacteristic
253C4⋊C16C2×D1111yescharacteristic
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#346C2×D1111yescharacteristic
265#346C2×D1111yescharacteristic
266C4×C16C2×D1111yescharacteristic
267C22×C11C22×D811yescharacteristic
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11#54811yescharacteristic
284C4×C11#57711yescharacteristic
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290C2×Q16—111no—
291C2×SD16—221no—
292C2×SD16—221no—
293C2×D8—111no—
294C2×D8—111no—
295C2×D8—111no—
296C2×D8—221no—
297C4⋊Q8—221no—
298#127—221no—
299#125—221no—
300#125—221no—
301#124—221no—
302#124—221no—
303#124—441no—
304#123—441no—
305#123—441no—
306C22⋊Q8—441no—
307C22⋊Q8—441no—
308C22⋊Q8—441no—
309C4×Q8—221no—
310C4×Q8D4411yescharacteristic
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—441no—
317C2×C4⋊C4—441no—
318SD32—222no—
319D16—222no—
320D16—222no—
321C2×C16C22×D1111yescharacteristic
322C2×C16C22×D1111yescharacteristic
323C2×C16C22×D1111yescharacteristic
324C2×C16C22×D1111yescharacteristic
325#107—111no—
326#107—111no—
327#107—111no—
328#107—111no—
329#107—221no—
330#106—221no—
331#106—221no—
332C4⋊C8D4411yescharacteristic
333C4⋊C8D4411yescharacteristic
334C4⋊C8D4411yescharacteristic
335#103—221no—
336#102—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340#102—221no—
341C4×C8C22×D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C4×C8C22×D1111yescharacteristic
344C2×C11#335811yescharacteristic
345C2×C11#341411yescharacteristic
346C2×C11#341511yescharacteristic
347D11—82no—
348D11—161no—
349D11—161no—
350C2×Q8—221no—
351C2×Q8—441no—
352C2×Q8D8811yescharacteristic
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C2×D4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363Q16—221no—
364Q16—221no—
365SD16—881no—
366SD16—881no—
367D8—112no—
368D8—221no—
369D8—221no—
370D8—221no—
371D8—221no—
372D8—221no—
373D8—881no—
374C2×C8C2×D4411yescharacteristic
375C2×C8C2×D4411yescharacteristic
376C2×C8C2×D4411yescharacteristic
377C2×C8C23×D1111yescharacteristic
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4D8811yescharacteristic
389C4⋊C4D8811yescharacteristic
390C4⋊C4D8811yescharacteristic
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C42—441no—
401C42C2×D4411yescharacteristic
402C42C2×D4411yescharacteristic
403C42C2×D4411yescharacteristic
404C16—21no—
405C16—21no—
406C16—21no—
407C16—21no—
408C11#3393711yescharacteristic, complemented, Sylow
409C23—441no—
410C23—441no—
411C23—441no—
412Q8—41no—
413Q8—441no—
414Q8—441no—
415Q8—1761no—
416D4—222no—
417D4—441no—
418D4—441no—
419D4—441no—
420D4—441no—
421D4—441no—
422D4—882no—
423D4—1761no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—882no—
430C2×C4—1761no—
431C2×C4—1761no—
432C2×C4—1761no—
433C2×C4—1761no—
434C2×C4C2×D8811yescharacteristic
435C2×C4C2×D8811yescharacteristic
436C2×C4C2×D8811yescharacteristic
437C2×C4C2×D8811yescharacteristic
438C2×C4C2×D8811yescharacteristic
439C2×C4C2×D8811yescharacteristic
440C2×C4C22×D4411yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8#6704011yescharacteristic
445C8#41×D1111yescharacteristic
446C22—442no—
447C22—881no—
448C22—881no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C22×D8811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4—881no—
466C4—881no—
467C4#1062310711yescharacteristic
468C4#1062328211yescharacteristic
469C2—882no—
470C2—1761no—
471C2—1761no—
472C2#1308125211yescharacteristic
473C2#1308175211yescharacteristic
474C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2183C2
socleC22×C11C22×D8
prime radical#13070652C2
hypercenter#2183D11
hypocenterC11#33937
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
1. #13081629C2semidirect
2. #13081484C2semidirect
3. #13070858C2semidirect
4. #13070853C2semidirect
5. #13070848C2semidirect
6. #13070781C2semidirect
7. #13070774C2semidirect
8. #13070754C2semidirect
9. #13070672C2semidirect
10. #13070672C2semidirect
12. #13070493C2semidirect
13. #13070482C2semidirect
14. C4×D176C2semidirect
15. C11×#2183C2semidirect
183. #2183D11semidirect
408. C11#33937semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130814842
#130708582
#130708532
#130708482
#130707812
#130707742
#130707542
#130706722
#130706522
#130704932
#130704822
C4×D1762
C11×#21832
#3393711