Finite Group Databasebeta

← #14795078

Subgroups — #14795078

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622539C211yesmaximal, characteristic, complemented
3C4×#66983C211yesmaximal, characteristic
4#13070047C212yesmaximal, complemented
5#13069805C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069356C212yesmaximal, complemented
9#13069312C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2857C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C22×C42×C11C2211yescharacteristic
15C2×#66983C2211yescharacteristic
16C2×C4×C22⋊D11—21no—
17C2×C4×D44C2211yescharacteristic
18C11×#391—21no—
19C11×#389—21no—
20C11×#389C2212yes—
21C11×#384C2211yescharacteristic
22C11×#380—21no—
23C11×#380C2212yes—
24#10622826—21no—
25#10622825C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622700—24no—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C2×#66872C2212yes—
31C2×#66871C2212yes—
32#10622553—21no—
33#10622552C2211yescharacteristic
34C4×(C2×D11)⋊C4—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622541C2211yescharacteristic
37#10622539—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C22⋊Q8—44no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—21no—
69#66983—22no—
70#66983—22no—
71C4×C22⋊D11—44no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83C4×D44—22no—
84C4×D44—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C22⋊(C11⋊C8)—24no—
91#66873—24no—
92#66873—24no—
93#66872—24no—
94#66871—24no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)D414yescomplemented
97#66867—24no—
98#24709—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C23×D11—21no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44#4112yes—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—42no—
147C11×C22⋊C4—44no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C2×D412yes—
153C42×C11#4112yes—
154C22⋊Dic11—42no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—42no—
157(C2×D11)⋊C4—42no—
158(C2×D11)⋊C4—42no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11#4112yes—
165Dic11⋊C4—42no—
166C4×Dic11—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2×D414yes—
173C2×#474—111no—
174C2×#432—111no—
175#2857D1111yescharacteristic, complemented
176C4×#121—111no—
177#2076—112no—
178#2034—112no—
179#1988—111no—
180#1948—111no—
181#1944—112no—
182#1936—112no—
183#1802—111no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11#13712yes—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199Q8×C11—84no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11AGL(1,ℤ/8)12yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C22⋊D11—48no—
234C2×Dic11—22no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243D44—22no—
244D44—22no—
245D44—41no—
246D44—41no—
247C4×D11—84no—
248C11⋊C8—24no—
249C11⋊C8—42no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×C22⋊Q8—21no—
252C2×#121—111no—
253C2×C4×D4—111no—
254C2×C4×D4—221no—
255C22×C42C2×D1111yescharacteristic
256#474—224no—
257#432—224no—
258C2×#107—112no—
259C2×#106—112no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8—111no—
262C2×#102—112no—
263C2×#102—112no—
264C2×C22⋊C8—112no—
265C2×#97—112no—
266#391—21no—
267#390—111no—
268#389—21no—
269#389—111no—
270#389C2×D1112yes—
271#388—221no—
272#386—221no—
273#384C2×D1111yescharacteristic
274#380—21no—
275#380—111no—
276#380C2×D1112yes—
277C4×C4⋊C4—111no—
278C4×C22⋊C4—221no—
279#340—112no—
280#340—112no—
281#340—112no—
282#340—112no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11C2×#12111yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#53611yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57511yescharacteristic
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C4×C11—22no—
305C4×C11—41no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—82no—
309C4×C11—82no—
310C4×C11#46914yes—
311C4×C11#54711yescharacteristic
312C4×C11#54811yescharacteristic
313C4×C11#55211yescharacteristic
314C4×C11#55611yescharacteristic
315Dic11—42no—
316Dic11—81no—
317Dic11—81no—
318C22×Q8—21no—
319C22×D4—111no—
320C22×D4—221no—
321C23×C4—221no—
322C23×C4C22⋊D1111yescharacteristic
323C23×C4C22⋊D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C22×C8—112no—
326C22×C8—112no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C22⋊Q8—44no—
330#121—222no—
331#121—222no—
332C4×D4—222no—
333C4×D4—222no—
334C4×D4—444no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22×D1112yes—
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—221no—
354C2×C42C22⋊D1111yescharacteristic
355C2×C42C22⋊D1111yescharacteristic
356C2×C42C22×D1111yescharacteristic
357C2×C42C22×D1111yescharacteristic
358#107—224no—
359#106—224no—
360C4⋊C8—114no—
361C4⋊C8—222no—
362#102—224no—
363#102—224no—
364C22⋊C8—224no—
365#97—224no—
366#95—22no—
367#95—22no—
368#95—221no—
369#95—221no—
370#95—221no—
371C2×C11—42no—
372C2×C11#241511yescharacteristic
373C2×C11C2×#46911yescharacteristic
374C2×C11#305611yescharacteristic
375C2×C11#311011yescharacteristic
376C2×C11#311511yescharacteristic
377C2×C11#323511yescharacteristic
378C2×C11#323911yescharacteristic
379D11—82no—
380C24—221no—
381C24C2×C22⋊D1111yescharacteristic
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—112no—
386C2×D4—224no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—442no—
393C2×D4—442no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—442no—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420C2×C8—114no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—44no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—112no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—442no—
441C22⋊C4—44no—
442C22⋊C4—224no—
443C22⋊C4—442no—
444C22⋊C4—442no—
445C22⋊C4—442no—
446C22⋊C4—442no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—442no—
452C42D4×D1112yes—
453C42#434112yes—
454C11#2470911yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—222no—
462C23—441no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23#6699512yes—
469C23C22×C22⋊D1111yescharacteristic
470Q8—84no—
471D4—222no—
472D4—222no—
473D4—448no—
474D4—441no—
475D4—441no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—222no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—884no—
509C2×C4#6698512yes—
510C2×C4#6699212yes—
511C2×C4#6699212yes—
512C2×C4#6700212yes—
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C2×C4#6704011yescharacteristic
516C2×C4#6704011yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#41×D1111yescharacteristic
519C8—224no—
520C8—442no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—442no—
529C22—442no—
530C22—442no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22C2×#6698511yescharacteristic
536C22C2×#6699211yescharacteristic
537C22C2×#6699511yescharacteristic
538C22#1062334711yescharacteristic
539C22C2×#6700211yescharacteristic
540C22#1062335311yescharacteristic
541C22#1062335911yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—82no—
547C4—82no—
548C4—442no—
549C4—881no—
550C4—881no—
551C4#1062265214yes—
552C4#1062316211yescharacteristic
553C4#1062316411yescharacteristic
554C4#1062317011yescharacteristic
555C4#1062317211yescharacteristic
556C2—42no—
557C2—882no—
558C2#1307204611yescharacteristic
559C2C2×#1062265211yescharacteristic
560C2#1307824211yescharacteristic
561C2#1307871111yescharacteristic
562C2#1307876111yescharacteristic
563C2#1307981411yescharacteristic
564C2#1307984611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2857C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2857D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×#10622539C2semidirect
4. #13070047C2semidirect
6. #13069569C2semidirect
7. #13069377C2semidirect
8. #13069356C2semidirect
9. #13069312C2semidirect
10. #13068613C2semidirect
11. C11×#2857C2semidirect
96. C4⋊(C11⋊C8)D4semidirect
175. #2857D11semidirect
454. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106225392
C4×#669832
#130700472
#130698052
#130695692
#130693772
#130693562
#130693122
#130686132
C11×#28572
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