Finite Group Databasebeta

← #14803544

Subgroups — #14803544

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13069973C212yesmaximal, complemented
5#13069871C212yesmaximal, complemented
6#13069525C212yesmaximal, complemented
7#13069455C211yesmaximal, characteristic, complemented
8#13069389C211yesmaximal, characteristic, complemented
9#13069277C212yesmaximal, complemented
10C4×#66897C211yesmaximal, characteristic, complemented
11C11×#3077C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323C2212yes—
15C2×#66927C2211yescharacteristic
16C11×#478—22no—
17C11×#476—21no—
18C11×#474—21no—
19C11×#428C2212yes—
20C11×#423C2211yescharacteristic
21C11×#418C2212yes—
22C2×#66897C2211yescharacteristic
23C2×#66897C2211yescharacteristic
24C2×#66887C2212yes—
25C2×#66887C2212yes—
26C2×#66886C2212yes—
27#10622701—21no—
28#10622701—21no—
29#10622680—22no—
30#10622637—21no—
31#10622637—22no—
32Q8×C11⋊C8—21no—
33#10622628—21no—
34#10622628—22no—
35#10622628—21no—
36#10622614C2212yes—
37#10622614C2212yes—
38#10622612C2212yes—
39#10622610C2212yes—
40C2×#66873C2212yes—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44#10622196C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44C2312yes—
52C2×C11×M16C2312yes—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#125D412yes—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C11×#117C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—24no—
69C2×#4323—22no—
70C2×#4323—22no—
71C2×#4323—42no—
72C2×#4318C2311yescharacteristic
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927—21no—
81C11×#107—22no—
82C11×#106—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8—21no—
85C11×#102—22no—
86C11×#102—22no—
87#66897—22no—
88#66897—22no—
89#66887—24no—
90#66887—42no—
91#66886—42no—
92#66873—22no—
93#66873—22no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)D411yescharacteristic
101C4⋊(C11⋊C8)D412yes—
102C4⋊(C11⋊C8)D411yescharacteristic
103#66867—21no—
104#66867—21no—
105#66867—22no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—22no—
109#25312—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—82no—
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—82no—
138C2×D44—82no—
139C11×M16—22no—
140C11×M16—22no—
141C2×C8×C11—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C42×C11—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158#4323—44no—
159#4323—44no—
160#4318—21no—
161#4318—21no—
162#4318—21no—
163#4318—21no—
164#4318—21no—
165#4318—21no—
166#4318—21no—
167#4318#4112yes—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8C2×D412yes—
175C2×C11⋊C8C2×D412yes—
176#3138—111no—
177#3077D1111yescharacteristic, complemented
178C2×#459—111no—
179#2962—111no—
180#2063—112no—
181#2045—112no—
182#1978—112no—
183#1965—111no—
184#1950—111no—
185#1931—112no—
186C4×#100—111no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—81no—
191C23×C11—81no—
192C23×C11C2×#4111yescharacteristic
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—82no—
197C22×D11—82no—
198Q8×C11—42no—
199Q8×C11—81no—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—41no—
203D4×C11—41no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11—81no—
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222D44—42no—
223D44—42no—
224D44—42no—
225D44—42no—
226D44—82no—
227D44—82no—
228D44—82no—
229D44—82no—
230C8×C11—42no—
231C11⋊C8—22no—
232C11⋊C8—22no—
233C11⋊C8—22no—
234C11⋊C8—41no—
235C11⋊C8—41no—
236C11⋊C8—41no—
237C22×D8—112no—
238#533C2×D1111yescharacteristic
239C2×#127—111no—
240C2×C4×D4C2×D1111yescharacteristic
241#490—222no—
242#486—221no—
243#486—221no—
244#478—22no—
245#476—21no—
246#474—21no—
247#459—221no—
248#459—222no—
249#459—221no—
250#446—222no—
251#446—221no—
252C8×Q8—221no—
253C2×#108—112no—
254#428C2×D1112yes—
255#424—112no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258#418—112no—
259#418—112no—
260#418C2×D1112yes—
261C2×#102—112no—
262C2×#100—111no—
263C2×#100—111no—
264C2×#100—112no—
265C2×#100—112no—
266#405—112no—
267C4×M16—111no—
268C4×M16—111no—
269#343—111no—
270#343—111no—
271#341—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11C2×#12111yescharacteristic
280C22×C11#52911yescharacteristic
281C22×C11#54211yescharacteristic
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—162no—
286C2×D11—162no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—81no—
293C4×C11#47212yes—
294C4×C11#54611yescharacteristic
295C4×C11#54811yescharacteristic
296C4×C11#54811yescharacteristic
297C4×C11#55011yescharacteristic
298C22×D4—112no—
299C22×D4—221no—
300C22×D4—221no—
301C22×D4C22×D1111yescharacteristic
302C23×C4—21no—
303C2×D8—222no—
304C2×D8—222no—
305C2×D8—224no—
306C2×D8—442no—
307C2×M16—111no—
308C2×M16—111no—
309C2×M16—111no—
310C2×M16—111no—
311C2×M16C22×D1112yes—
312C22×C8—112no—
313C4⋊Q8C22⋊D1111yescharacteristic
314C4⋊Q8C22⋊D1111yescharacteristic
315#127—221no—
316#127—221no—
317#127—221no—
318#127—221no—
319#125C22⋊D1112yes—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328#117C22×D1112yes—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C22⋊C4—21no—
331C2×C42C22×D1111yescharacteristic
332#108—442no—
333#107—22no—
334#106—22no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8—111no—
338C4⋊C8—111no—
339C4⋊C8—112no—
340C4⋊C8—222no—
341C4⋊C8—222no—
342#102—22no—
343#102—22no—
344#102—222no—
345#102—222no—
346#102—222no—
347#102—222no—
348#102—222no—
349#102—222no—
350#100—224no—
351#100—222no—
352#100—222no—
353#100—442no—
354#97—222no—
355#97—221no—
356#97—221no—
357C4×C8—222no—
358C4×C8—221no—
359C4×C8—221no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—82no—
363C2×C11#242611yescharacteristic
364C2×C11C2×#47211yescharacteristic
365C2×C11#306811yescharacteristic
366D11—162no—
367C24—21no—
368C24—222no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—441no—
385C2×D4—441no—
386C2×D4—882no—
387C2×D4—882no—
388C2×D4#434312yes—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—82no—
393C22×C4#434111yescharacteristic
394C22×C4#434111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396D8—444no—
397D8—444no—
398M16—22no—
399M16—22no—
400M16—112no—
401M16—221no—
402M16—221no—
403M16—221no—
404M16—221no—
405M16—221no—
406M16—221no—
407M16—221no—
408C2×C8—22no—
409C2×C8—112no—
410C2×C8—112no—
411C2×C8—221no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—221no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4C2×C22⋊D1112yes—
424C4⋊C4C2×C22⋊D1112yes—
425C22⋊C4—22no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C42—22no—
429C42D4×D1111yescharacteristic
430C42D4×D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C11#2531211yescharacteristic, complemented, Sylow
434C23—22no—
435C23—41no—
436C23—41no—
437C23—81no—
438C23—81no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—882no—
443C23—882no—
444C23C2×#434111yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—442no—
452D4—442no—
453D4—442no—
454D4—442no—
455D4—882no—
456D4—882no—
457D4—882no—
458D4—882no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—81no—
467C2×C4#6699211yescharacteristic
468C2×C4#6699211yescharacteristic
469C2×C4#6699211yescharacteristic
470C2×C4#6699211yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×#434311yescharacteristic
473C2×C4#6704011yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C2×C4#6704211yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—42no—
478C8—222no—
479C8—222no—
480C8—222no—
481C8—441no—
482C8—441no—
483C8—441no—
484C22—21no—
485C22—21no—
486C22—42no—
487C22—82no—
488C22—82no—
489C22—81no—
490C22—81no—
491C22—882no—
492C22—882no—
493C22—882no—
494C22—1762no—
495C22—1762no—
496C22#1062315511yescharacteristic
497C22#1062317411yescharacteristic
498C22C2×#6699211yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4#1062281212yes—
506C4#1062316111yescharacteristic
507C4#1062316411yescharacteristic
508C4#1062334811yescharacteristic
509C4#1062336511yescharacteristic
510C2—21no—
511C2—21no—
512C2—82no—
513C2—1762no—
514C2#1307218411yescharacteristic
515C2C2×#1062281211yescharacteristic
516C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3077C2
socleC22×C11C2×#121
prime radicalC2×#10622628C2
hypercenter#3077D11
hypocenterC11#25312
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13078992C2semidirect
3. #13077565C2semidirect
4. #13069973C2semidirect
5. #13069871C2semidirect
6. #13069525C2semidirect
7. #13069455C2semidirect
8. #13069389C2semidirect
9. #13069277C2semidirect
10. C4×#66897C2semidirect
11. C11×#3077C2semidirect
177. #3077D11semidirect
433. C11#25312semidirect

Maximal subgroups

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

subgroupindex
#130789922
C2×#106226282
#130775652
#130699732
#130698712
#130695252
#130694552
#130693892
#130692772
C4×#668972
C11×#30772
#2531211