Finite Group Databasebeta

← #14910683

Subgroups — #14910683

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081014C211yesmaximal, characteristic, complemented
2#13080354C211yesmaximal, characteristic, complemented
3#13070846C211yesmaximal, characteristic, complemented
4#13070827C211yesmaximal, characteristic, complemented
5#13070783C211yesmaximal, characteristic, complemented
6#13070713C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic, complemented
9#13070540C211yesmaximal, characteristic, complemented
10#13070535C211yesmaximal, characteristic, complemented
11#13070467C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13#13070320C211yesmaximal, characteristic, complemented
14C2×#10622130C211yesmaximal, characteristic, complemented
15C11×#2233C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623129—21no—
19#10623045—21no—
20C11×#466C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622768C2211yescharacteristic
23C2×#66890C2211yescharacteristic
24#10622728C2211yescharacteristic
25C8×C22⋊D11C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622653—21no—
28#10622581—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic
32#10622504—21no—
33#10622500C2211yescharacteristic
34#10622498—21no—
35#10622496C2211yescharacteristic
36#10622493C2211yescharacteristic
37#10622491C2211yescharacteristic
38#10622486C2211yescharacteristic
39#10622485C2211yescharacteristic
40#10622396—21no—
41#10622380—21no—
42C11×#367C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×C22⋊C16C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—21no—
60C22×Dic22—21no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C2×C11×C4⋊C4—21no—
65#66992—41no—
66#66989—21no—
67D4×Dic11—41no—
68C2×#4324—21no—
69C2×#4324—21no—
70#66983—21no—
71#66983—41no—
72C4×C22⋊D11—41no—
73C4×C22⋊D11D411yescharacteristic
74#66965—22no—
75#66965—41no—
76C2×Dic44—22no—
77C2×Dic44—21no—
78C2×Dic44—41no—
79C2×Dic44C2311yescharacteristic
80C2×Dic44C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66951—41no—
84#66950—21no—
85#66948—21no—
86#66947—41no—
87#66946—21no—
88#66945—21no—
89#66943—21no—
90#66940—21no—
91#66938—41no—
92#66931—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100C22⋊(C11⋊C8)D411yescharacteristic
101#66890—41no—
102#66885—21no—
103(C2×D11)⋊C8D411yescharacteristic
104#66882C2311yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—41no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66874—21no—
112#66873—21no—
113#66873—21no—
114#66872—21no—
115#66872—21no—
116#66864—22no—
117#66864—41no—
118C16×D11—41no—
119#33868—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11D811yescharacteristic
127C22×Dic11—41no—
128C22×Dic11—41no—
129#4341—42no—
130#4341—81no—
131C2×D44—21no—
132C2×D44—41no—
133C2×C4×D11—41no—
134C2×C4×D11C2×D411yescharacteristic
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—42no—
138C2×Dic22—41no—
139C2×Dic22—81no—
140C11×D8—21no—
141C11×D8—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2411yescharacteristic
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C22⋊C4—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11D811yescharacteristic
154#4324—42no—
155#4324—81no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4D811yescharacteristic
162C4⋊Dic11—21no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4D811yescharacteristic
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—42no—
177Dic44#4112yes—
178D88—21no—
179D88—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2233D1111yescharacteristic, complemented
191#2229—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11C2×D811yescharacteristic
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—82no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—161no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—22no—
217C22⋊D11—82no—
218C22⋊D11—82no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—82no—
223C2×Dic11—82no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227D44—41no—
228D44—41no—
229D44—161no—
230C4×D11—21no—
231C4×D11—21no—
232C4×D11—161no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×Q16—111no—
245#553—221no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499—111no—
253#495—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#466—111no—
259#466—111no—
260#466C2×D1111yescharacteristic
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268C2×#107C2×D1111yescharacteristic
269#367C2×D1111yescharacteristic
270#367C2×D1111yescharacteristic
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357C2×D1111yescharacteristic
282#357C2×D1111yescharacteristic
283C22⋊C16—111no—
284C22⋊C16C2×D1111yescharacteristic
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11#50812yes—
292C22×C11C22×D811yescharacteristic
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—81no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—42no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—221no—
313#135—222no—
314#135—441no—
315C2×Q16—111no—
316C2×Q16—111no—
317C2×Q16—222no—
318C2×Q16—221no—
319C2×Q16—441no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8—111no—
325C22×C8C22×D1111yescharacteristic
326#126—441no—
327#125—221no—
328#124—221no—
329#124—441no—
330#123—441no—
331C22⋊Q8—221no—
332C22⋊Q8—441no—
333#121—21no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×Q8—221no—
339C4×D4—111no—
340C4×D4—221no—
341C4×D4—441no—
342C4×D4—441no—
343#117—221no—
344C2×C4⋊C4—21no—
345SD32—222no—
346SD32—441no—
347D16—441no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—441no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—21no—
355#107—111no—
356#107C22×D1111yescharacteristic
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8—111no—
362#103—221no—
363#103—221no—
364#102—21no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—22no—
372C2×C11—161no—
373C2×C11#329411yescharacteristic
374C2×C11C2×#50811yescharacteristic
375C2×C11#341611yescharacteristic
376D11—41no—
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—442no—
383C2×Q8—441no—
384C2×Q8—881no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4D4×D1111yescharacteristic
398Q16—112no—
399Q16—221no—
400Q16—221no—
401Q16—221no—
402Q16—442no—
403SD16—442no—
404SD16—881no—
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—111no—
412C2×C8—111no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8D4×D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—111no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C22⋊C4—41no—
428C22⋊C4—111no—
429C22⋊C4—111no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—111no—
438C42—441no—
439C42—441no—
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—41no—
446C23—111no—
447C23—441no—
448C23D8×D1111yescharacteristic
449Q8—222no—
450Q8—441no—
451Q8—441no—
452Q8—441no—
453Q8—882no—
454D4—41no—
455D4—41no—
456D4—82no—
457D4—222no—
458D4—441no—
459D4—441no—
460D4—882no—
461D4—882no—
462D4—1761no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—111no—
471C2×C4—161no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—1761no—
480C2×C4D8×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C8—21no—
483C8—221no—
484C8—221no—
485C8#41×D1111yescharacteristic
486C8#6704211yescharacteristic
487C22—21no—
488C22—21no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—221no—
493C22—221no—
494C22—221no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22#1062252912yes—
499C22C2×D8×D1111yescharacteristic
500C4—21no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—221no—
505C4—221no—
506C4—221no—
507C4—442no—
508C4—881no—
509C4—881no—
510C4#1062318511yescharacteristic
511C4#1062330911yescharacteristic
512C2—22no—
513C2—161no—
514C2—441no—
515C2—1761no—
516C2#1308042711yescharacteristic
517C2C2×#1062252911yescharacteristic
518C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
hypercenter#2233D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
1. #13081014C2semidirect
2. #13080354C2semidirect
3. #13070846C2semidirect
4. #13070827C2semidirect
5. #13070783C2semidirect
6. #13070713C2semidirect
7. #13070700C2semidirect
8. #13070670C2semidirect
9. #13070540C2semidirect
10. #13070535C2semidirect
11. #13070467C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. #13070320C2semidirect
14. C2×#10622130C2semidirect
15. C11×#2233C2semidirect
190. #2233D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810142
#130803542
#130708462
#130708272
#130707832
#130707132
#130707002
#130706702
#130705402
#130705352
#130704672
(C22⋊D11)⋊C162
#130703202
C2×#106221302
C11×#22332
#3386811