Finite Group Databasebeta

← #14795289

Subgroups — #14795289

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078438C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13077282C211yesmaximal, characteristic
4#13070064C211yesmaximal, characteristic
5#13070059C211yesmaximal, characteristic
6#13069912C211yesmaximal, characteristic
7#13069912C211yesmaximal, characteristic
8#13069609C211yesmaximal, characteristic, complemented
9#13069398C211yesmaximal, characteristic, complemented
10#13069393C211yesmaximal, characteristic, complemented
11#13069391C211yesmaximal, characteristic, complemented
12#13069274C211yesmaximal, characteristic, complemented
13#13069274C211yesmaximal, characteristic, complemented
14#13068612C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C11×#441—21no—
21C11×#440—21no—
22C4×C11×Q16—21no—
23C4×C11×SD16—21no—
24C11×#428C2211yescharacteristic
25C11×#419C2211yescharacteristic
26C11×#417C2211yescharacteristic
27C4×C11×M16C2211yescharacteristic
28#10622847C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622845C2211yescharacteristic
31#10622845C2211yescharacteristic
32C2×#66900C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66886C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38#10622635—21no—
39#10622635—21no—
40#10622635—21no—
41#10622635—21no—
42#10622635—21no—
43#10622635—21no—
44#10622622—21no—
45#10622622—21no—
46#10622613—21no—
47#10622613—21no—
48#10622610C2211yescharacteristic
49#10622610C2211yescharacteristic
50#10622608C2211yescharacteristic
51#10622608C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622539—21no—
55#10622538—21no—
56#10622537C2211yescharacteristic
57#10622537C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C11×#137—22no—
70C11×#137—22no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×M16C2311yescharacteristic
74C2×C11×M16C2311yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11D411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C11×#117—21no—
86C11×#117C2311yescharacteristic
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66923—21no—
103#66923—21no—
104#66923—21no—
105#66923—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#97—21no—
113C4×C8×C11—21no—
114#66900—22no—
115#66900—22no—
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128#66886—22no—
129#66886—22no—
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66872—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)D411yescharacteristic
143C4⋊(C11⋊C8)D411yescharacteristic
144C4⋊(C11⋊C8)D411yescharacteristic
145C4⋊(C11⋊C8)D411yescharacteristic
146#66867—21no—
147#66867—21no—
148C4×C11⋊C8—21no—
149C4×C11⋊C8—21no—
150#24725—111nomaximal, Sylow
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C2×D411yescharacteristic
161C2×Q8×C11#4112yes—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11#4111yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C11×Q16—24no—
175C11×SD16—24no—
176C11×M16—21no—
177C11×M16—21no—
178C11×M16—21no—
179C11×M16#4112yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—41no—
197C42×C11—41no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208Dic11⋊C4—41no—
209Dic11⋊C4—41no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C2×D411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230#3080—111no—
231C2×#479—111no—
232C4×#137D1111yescharacteristic
233#2925—111no—
234#2079—111no—
235#2078—111no—
236#2052—111no—
237#2052—111no—
238#1998—111no—
239#1952—111no—
240#1951—111no—
241#1950—111no—
242#1930—111no—
243#1930—111no—
244#1801—111no—
245C23×C11—21no—
246C23×C11C2×#4111yescharacteristic
247Q8×C11—22no—
248Q8×C11—21no—
249Q8×C11—21no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—41no—
256D4×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—81no—
270C2×C4×C11—81no—
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11#12111yescharacteristic
274C2×C4×C11#12111yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—81no—
284C2×Dic11—81no—
285C8×C11—22no—
286C8×C11—41no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#137C2×D1111yescharacteristic
296C2×#125—111no—
297C4×#41C2×D1111yescharacteristic
298C2×C4×Q8C2×D1111yescharacteristic
299#479—221no—
300#479—221no—
301#479—221no—
302#479—221no—
303#479—221no—
304#479—221no—
305#478—221no—
306#478—221no—
307#441—21no—
308#440—21no—
309C4×Q16—21no—
310C4×SD16—21no—
311#433—221no—
312#433—221no—
313#432—221no—
314#431—221no—
315C2×#108—111no—
316C2×#108—111no—
317#428—111no—
318#428—111no—
319#428C2×D1111yescharacteristic
320C2×#107—111no—
321C2×#106—111no—
322#423—111no—
323#423—111no—
324C2×C4⋊C8—111no—
325#419C2×D1111yescharacteristic
326#417—111no—
327#417—111no—
328#417C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#101—111no—
332C2×#101—111no—
333#408—111no—
334#408—111no—
335#405—111no—
336#405—111no—
337C4×M16C2×D1111yescharacteristic
338#343—111no—
339#343—111no—
340#343—111no—
341#343—111no—
342#343—111no—
343#343—111no—
344#341—111no—
345#341—111no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×#12111yescharacteristic
352C22×C11#55211yescharacteristic
353C22×C11#55611yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11#52511yescharacteristic
364C4×C11#53611yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#54811yescharacteristic
367Dic11—81no—
368Dic11—81no—
369C2×#41C22×D1111yescharacteristic
370C22×Q8C22×D1111yescharacteristic
371#137—22no—
372#137—22no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×M16—111no—
376C2×M16—111no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16C22×D1111yescharacteristic
380C2×M16C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#125—221no—
384#125—221no—
385#125—221no—
386#125—221no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C22⋊D1111yescharacteristic
392C4×Q8C22⋊D1111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C22⋊D1111yescharacteristic
396C4×D4C22⋊D1111yescharacteristic
397#117—21no—
398#117C22×D1111yescharacteristic
399C2×C4⋊C4—21no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C22×D1111yescharacteristic
408#108—222no—
409#108—222no—
410#107—21no—
411#107—221no—
412#107—221no—
413#107—221no—
414#107—221no—
415#106—21no—
416#106—221no—
417#106—221no—
418#106—221no—
419#106—221no—
420C4⋊C8—111no—
421C4⋊C8—111no—
422C4⋊C8—111no—
423C4⋊C8—111no—
424C4⋊C8—221no—
425C4⋊C8—221no—
426C4⋊C8—221no—
427C4⋊C8—221no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—221no—
432#103—221no—
433#103—221no—
434#103—221no—
435#103—221no—
436#103—221no—
437#102—21no—
438#102—221no—
439#102—221no—
440#101—222no—
441#101—222no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446#97—21no—
447#97—221no—
448#97—221no—
449C4×C8—21no—
450C4×C8—221no—
451C4×C8—221no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—81no—
455C2×C11#241511yescharacteristic
456C2×C11#306711yescharacteristic
457C2×C11#306911yescharacteristic
458#41—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#433912yes—
468C2×Q8C2×C22⋊D1111yescharacteristic
469C2×D4—21no—
470C2×D4C2×C22⋊D1111yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4#434111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—24no—
482SD16—24no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—221no—
487M16—221no—
488M16—221no—
489M16—221no—
490M16—221no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16#433912yes—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—441no—
520C4⋊C4—441no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4C2×C22⋊D1111yescharacteristic
524C4⋊C4C2×C22⋊D1111yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—41no—
532C42—41no—
533C42D4×D1111yescharacteristic
534C42D4×D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C11#2472511yescharacteristic, complemented, Sylow
538C23—21no—
539C23C2×#434111yescharacteristic
540Q8—22no—
541Q8—21no—
542Q8—22no—
543Q8—21no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—881no—
567C2×C4—881no—
568C2×C4#6699211yescharacteristic
569C2×C4#6699211yescharacteristic
570C2×C4#6699211yescharacteristic
571C2×C4#6699211yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C2×C4#6704311yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—22no—
579C8—41no—
580C8—221no—
581C8—221no—
582C8—221no—
583C8—221no—
584C8—441no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1062307211yescharacteristic
594C22#1062307311yescharacteristic
595C22C2×#6699211yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—42no—
604C4—81no—
605C4—881no—
606C4—881no—
607C4#1062308211yescharacteristic
608C4#1062308311yescharacteristic
609C4#1062332211yescharacteristic
610C4#1062335611yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1307204511yescharacteristic
615C2#1307833311yescharacteristic
616C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×#121
prime radicalC2×C11×#41C23
hypercenterC4×#137D11
hypocenterC11#24725
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
8. #13069609C2semidirect
9. #13069398C2semidirect
10. #13069393C2semidirect
11. #13069391C2semidirect
12. #13069274C2semidirect
13. #13069274C2semidirect
14. #13068612C2semidirect
537. C11#24725semidirect

Maximal subgroups

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

subgroupindex
#130784382
C2×#106226352
#130772822
#130700642
#130700592
#130699122
#130696092
#130693982
#130693932
#130693912
#130692742
#130686122
C4×C11×#1372
#2472511