Finite Group Databasebeta

← #14911502

Subgroups — #14911502

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081604C211yesmaximal, characteristic, complemented
2D8×Dic22C211yesmaximal, characteristic, complemented
3#13070854C211yesmaximal, characteristic, complemented
4#13070853C211yesmaximal, characteristic, complemented
5#13070842C211yesmaximal, characteristic, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070767C211yesmaximal, characteristic, complemented
8#13070752C211yesmaximal, characteristic, complemented
9#13070673C211yesmaximal, characteristic
10#13070671C211yesmaximal, characteristic
11#13070659C211yesmaximal, characteristic, complemented
12#13070522C211yesmaximal, characteristic, complemented
13#13070477C211yesmaximal, characteristic, complemented
14#13070460C211yesmaximal, characteristic
15C11×#2175C211yesmaximal, characteristic, complemented
16#10623099—21no—
17D4×Dic22—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622804C2211yescharacteristic
22#10622794C2211yescharacteristic
23D8×Dic11C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27#10622641—21no—
28#10622620—21no—
29#10622487C2211yescharacteristic
30#10622487C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622485C2211yescharacteristic
33#10622431—21no—
34#10622411—21no—
35#10622372—21no—
36#10622372—21no—
37#10622309C2211yescharacteristic
38#10622295C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622140C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C22×Dic22—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C4×Q8×C11—21no—
63C4×D4×C11—21no—
64#67000—21no—
65#66997—21no—
66C2×#4326—21no—
67C2×#4325—21no—
68D4×Dic11—21no—
69D4×Dic11—21no—
70#66977—41no—
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4314—21no—
74#66951—41no—
75#66949—41no—
76#66946—21no—
77#66941—21no—
78#66941—21no—
79#66940—21no—
80#66931—41no—
81#66931—41no—
82#66929—41no—
83#66928—21no—
84#66925—41no—
85#66922—21no—
86C4×Dic22D411yescharacteristic
87C11×SD32—22no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#103—21no—
93C11×#102—21no—
94C4×C8×C11C2311yescharacteristic
95#66896—21no—
96#66896—21no—
97#66891—22no—
98#66890—22no—
99#66882—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102Dic11⋊C8D411yescharacteristic
103Dic11⋊C8D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66871—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33934—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C22×C4×C11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22—41no—
124C2×Dic22—41no—
125C2×Dic22—84no—
126C2×Dic22D811yescharacteristic
127C11×Q16—21no—
128C11×Q16—21no—
129C11×D8—21no—
130C11×D8#4112yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141#4326—81no—
142#4325—81no—
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—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11D811yescharacteristic
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164Dic44—21no—
165Dic44—21no—
166D88—21no—
167D88—21no—
168#4314—81no—
169C11×C16—21no—
170C11×C16—21no—
171C11⋊C16—21no—
172C11⋊C16—21no—
173#3393—111no—
174Q8×D8—111no—
175#2243—111no—
176#2243—111no—
177#2241—111no—
178#2227—111no—
179#2227—111no—
180#2224—111no—
181#2210—111no—
182#2210—111no—
183#2208—111no—
184#2183—111no—
185#2175—111no—
186#2175D1111yescharacteristic, complemented
187C4×D16—111no—
188C23×C11—41no—
189C22×D11—41no—
190Q8×C11—41no—
191Q8×C11—41no—
192D4×C11—22no—
193D4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—82no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205C2×Dic11—82no—
206C2×Dic11C2×D811yescharacteristic
207C2×Dic11C2×D811yescharacteristic
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210D44—41no—
211D44—41no—
212C4×D11—82no—
213Dic22—22no—
214Dic22—41no—
215Dic22—41no—
216Dic22—82no—
217Dic22—82no—
218Dic22—82no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#556—221no—
225D4×Q8—221no—
226C2×SD32—111no—
227C2×SD32C2×D1111yescharacteristic
228C2×D16—111no—
229#500—111no—
230#500—111no—
231#500—111no—
232#495—111no—
233#495—111no—
234#494—111no—
235#474—221no—
236#474—221no—
237#474—221no—
238#464—221no—
239#464—221no—
240#461—221no—
241C8×Q8—111no—
242C4×Q16—111no—
243C4×Q16C2×D1111yescharacteristic
244C4×D8—111no—
245C4×D8—111no—
246C4×D8—111no—
247C4×D8C2×D1111yescharacteristic
248#366—111no—
249#366—111no—
250#366C2×D1111yescharacteristic
251C4⋊C16—111no—
252C4⋊C16—111no—
253C4⋊C16—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#358—111no—
258#358—111no—
259#358C2×D1111yescharacteristic
260#357—111no—
261#357—111no—
262#357—111no—
263#357C2×D1111yescharacteristic
264#346—111no—
265#346C2×D1111yescharacteristic
266C4×C16—111no—
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11C22×D811yescharacteristic
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#54811yescharacteristic
280C4×C11#57711yescharacteristic
281Dic11—21no—
282Dic11—21no—
283Dic11—21no—
284Dic11—81no—
285Dic11—81no—
286Dic11—81no—
287Dic11#50912yes—
288C22×Q8—441no—
289C2×Q16—111no—
290C2×Q16—221no—
291C2×Q16C22×D1111yescharacteristic
292C2×SD16—221no—
293C2×SD16—221no—
294C2×D8—111no—
295C2×D8C22×D1111yescharacteristic
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299C4⋊Q8—221no—
300#126—441no—
301#126—441no—
302#124—221no—
303#124—221no—
304C22⋊Q8—441no—
305C22⋊Q8—441no—
306C22⋊Q8—441no—
307C22⋊Q8—441no—
308C4×Q8—21no—
309C4×Q8—111no—
310C4×Q8—221no—
311C4×D4—21no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315#117—441no—
316SD32—22no—
317SD32—222no—
318D16—222no—
319C2×C16—111no—
320C2×C16—111no—
321C2×C16C22×D1111yescharacteristic
322C2×C16C22×D1111yescharacteristic
323#107—111no—
324#107—111no—
325#107—221no—
326#107—221no—
327#107—221no—
328#107C22×D1111yescharacteristic
329#107C22×D1111yescharacteristic
330C4⋊C8—111no—
331C4⋊C8—111no—
332C4⋊C8—111no—
333#103—21no—
334#103—221no—
335#102—21no—
336#102—221no—
337#102—221no—
338#102—221no—
339C4×C8—111no—
340C4×C8—111no—
341C4×C8C22×D1111yescharacteristic
342C2×C11—82no—
343C2×C11#335811yescharacteristic
344C2×C11C2×#50911yescharacteristic
345C2×C11#341711yescharacteristic
346D11—161no—
347C2×Q8—21no—
348C2×Q8—111no—
349C2×Q8—221no—
350C2×Q8—441no—
351C2×Q8—441no—
352C2×Q8—441no—
353C2×Q8—884no—
354C2×D4—21no—
355C2×D4—221no—
356C22×C4—41no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360Q16—21no—
361Q16—21no—
362Q16—221no—
363Q16—221no—
364Q16—881no—
365SD16—881no—
366SD16—881no—
367D8—21no—
368D8—221no—
369D8—221no—
370D8#433912yes—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8D4×D1111yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—111no—
379C4⋊C4—111no—
380C4⋊C4—111no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C22⋊C4—41no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C42—41no—
398C42—111no—
399C42—111no—
400C42—441no—
401C42D4×D1111yescharacteristic
402C16—21no—
403C16—21no—
404C16—221no—
405C16—221no—
406C11#3393411yescharacteristic, complemented, Sylow
407C23—41no—
408C23—441no—
409Q8—41no—
410Q8—41no—
411Q8—222no—
412Q8—441no—
413Q8—441no—
414Q8—882no—
415Q8—882no—
416Q8—882no—
417D4—22no—
418D4—41no—
419D4—441no—
420D4—441no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—111no—
426C2×C4—111no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—882no—
433C2×C4—882no—
434C2×C4—882no—
435C2×C4D8×D1111yescharacteristic
436C2×C4D8×D1111yescharacteristic
437C2×C4C2×D4×D1111yescharacteristic
438C8—21no—
439C8—221no—
440C8—221no—
441C8C2×#433911yescharacteristic
442C8#6704311yescharacteristic
443C22—42no—
444C22—81no—
445C22—81no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22C2×D8×D1111yescharacteristic
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—112no—
456C4—221no—
457C4—221no—
458C4—221no—
459C4—881no—
460C4—881no—
461C4—881no—
462C4#1062308311yescharacteristic
463C4#1062330111yescharacteristic
464C2—82no—
465C2—1761no—
466C2#1308124911yescharacteristic
467C2D11×#50911yescharacteristic
468C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#2175D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #13081604C2semidirect
2. D8×Dic22C2semidirect
3. #13070854C2semidirect
4. #13070853C2semidirect
5. #13070842C2semidirect
6. #13070768C2semidirect
7. #13070767C2semidirect
8. #13070752C2semidirect
11. #13070659C2semidirect
12. #13070522C2semidirect
13. #13070477C2semidirect
15. C11×#2175C2semidirect
186. #2175D11semidirect
406. C11#33934semidirect

Maximal subgroups

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

subgroupindex
#130816042
D8×Dic222
#130708542
#130708532
#130708422
#130707682
#130707672
#130707522
#130706732
#130706712
#130706592
#130705222
#130704772
#130704602
C11×#21752
#3393411