Finite Group Databasebeta

← #15830533

Subgroups — #15830533

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128571C211yesmaximal, characteristic
2#13117696C211yesmaximal, characteristic, complemented
3#13113414C211yesmaximal, characteristic, complemented
4#13113397C211yesmaximal, characteristic, complemented
5#13113393C211yesmaximal, characteristic, complemented
6#13113384C211yesmaximal, characteristic, complemented
7#13113375C211yesmaximal, characteristic, complemented
8#13113366C211yesmaximal, characteristic, complemented
9#13113362C211yesmaximal, characteristic, complemented
10#13113345C211yesmaximal, characteristic, complemented
11#13113341C211yesmaximal, characteristic, complemented
12#13113332C211yesmaximal, characteristic, complemented
13#13113323C211yesmaximal, characteristic, complemented
14C2×#11718062C211yesmaximal, characteristic, complemented
15C13×#2924C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17#11719496C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19#11719240C411yescharacteristic, complemented
20#11719240C411yescharacteristic, complemented
21#11719239C411yescharacteristic, complemented
22#11719239C411yescharacteristic, complemented
23#11719237—21no—
24#11719235—21no—
25#11719232—21no—
26#11719232—21no—
27#11719230C411yescharacteristic, complemented
28#11719228C411yescharacteristic, complemented
29#11719226C411yescharacteristic, complemented
30#11719224C411yescharacteristic, complemented
31#11719219—21no—
32#11719212—21no—
33#11719195—21no—
34#11719195—21no—
35#11719184C2211yescharacteristic
36#11719184C2211yescharacteristic
37#11719182C2211yescharacteristic
38#11719182C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#432C2211yescharacteristic, complemented
42C13×#432C2211yescharacteristic, complemented
43C13×#431C2211yescharacteristic, complemented
44C13×#431C2211yescharacteristic, complemented
45C13×#424—21no—
46C13×#407C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C13×#405—21no—
49#11718872C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718642—21no—
52#11718642—21no—
53#11718611—21no—
54C22⋊C4×Dic13—21no—
55#11718598C2211yescharacteristic, complemented
56#11718597C2211yescharacteristic, complemented
57C4×C4⋊Dic13C2211yescharacteristic, complemented
58#11718593C2211yescharacteristic, complemented
59#11718062C2211yescharacteristic
60#11718062C2211yescharacteristic
61#11718062C2211yescharacteristic
62#11718062C2211yescharacteristic
63#11718062C2211yescharacteristic
64#11718062C2211yescharacteristic
65#11718062C2211yescharacteristic
66#11718062C2211yescharacteristic
67#11718062C2211yescharacteristic, complemented
68#11718062C2211yescharacteristic, complemented
69#11718062C2211yescharacteristic, complemented
70#11718062C2211yescharacteristic, complemented
71#11718059C2211yescharacteristic, complemented
72#11718059C2211yescharacteristic, complemented
73#11718059C2211yescharacteristic, complemented
74#11718059C2211yescharacteristic, complemented
75C23×C4×C13C2311yescharacteristic
76C22×C22⋊D13—21no—
77C23×Dic13—21no—
78C2×#6127—21no—
79C2×#6127—21no—
80C2×#6127C2×C411yescharacteristic
81C22×D52C2×C411yescharacteristic
82C2×C13×M16—21no—
83C22×C8×C13—21no—
84C13×#117C2×C411yescharacteristic
85C13×#117C2×C411yescharacteristic
86C13×#117C2×C411yescharacteristic
87C13×#117C2×C411yescharacteristic
88C13×#117D411yescharacteristic
89C13×#117D411yescharacteristic
90C13×#117D411yescharacteristic
91C13×#117D411yescharacteristic
92C2×C13×C4⋊C4D411yescharacteristic
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98#88207—21no—
99C2×C22⋊Dic13—21no—
100#88184—21no—
101#88184—21no—
102#88184—21no—
103#88184—21no—
104#88184C2×C411yescharacteristic
105#88184C2×C411yescharacteristic
106#88184C2×C411yescharacteristic
107#88184C2311yescharacteristic
108#88184C2311yescharacteristic
109#88184C2311yescharacteristic
110#88183—21no—
111#88183—21no—
112#88183—21no—
113C4×C22⋊D13—21no—
114C4×C22⋊D13—21no—
115C4×C22⋊D13—21no—
116C4×C22⋊D13—21no—
117C2×#6103—21no—
118#88180C2×C411yescharacteristic
119C2×C4⋊Dic13—21no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13C2×C411yescharacteristic
122#88178C2×C411yescharacteristic
123#88178C2311yescharacteristic
124C2×C4×Dic13—21no—
125C2×C4×Dic13—21no—
126#88152—21no—
127#88152—21no—
128#88150—21no—
129#88150—21no—
130#88149—21no—
131#88149—21no—
132#88148—21no—
133#88148—21no—
134#88148—21no—
135#88148—21no—
136#88147—21no—
137#88147—21no—
138#88146—21no—
139C4⋊C4×D13—21no—
140#88144—21no—
141#88142—21no—
142#88139—21no—
143#88139—21no—
144#88138—21no—
145#88138—21no—
146#88138—21no—
147#88138—21no—
148#88137—21no—
149#88137—21no—
150#88136—21no—
151#88136—21no—
152#88135—21no—
153#88135—21no—
154C22⋊C4×D13—21no—
155C22⋊C4×D13—21no—
156#88132—21no—
157#88132—21no—
158#88130—21no—
159#88130—21no—
160#88129—21no—
161#88129—21no—
162#88129C2×C411yescharacteristic, complemented
163#88129C2×C411yescharacteristic, complemented
164#88128C2×C411yescharacteristic, complemented
165#88128C2×C411yescharacteristic, complemented
166C4×D52—21no—
167C4×D52—21no—
168C4×D52C2×C411yescharacteristic, complemented
169C4×D52C2×C411yescharacteristic, complemented
170C4×D52C2×C411yescharacteristic, complemented
171C4×D52C2×C411yescharacteristic, complemented
172C4×D52C2×C411yescharacteristic, complemented
173C4×D52C2×C411yescharacteristic, complemented
174#88126—21no—
175#88126—21no—
176#88124C2×C411yescharacteristic, complemented
177#88124C2×C411yescharacteristic, complemented
178#88123C2×C411yescharacteristic, complemented
179#88123C2×C411yescharacteristic, complemented
180C4×Dic26C2×C411yescharacteristic, complemented
181C4×Dic26C2×C411yescharacteristic, complemented
182C13×C4⋊C8—21no—
183C13×C4⋊C8—21no—
184C13×C4⋊C8—21no—
185C13×C4⋊C8—21no—
186C13×C22⋊C8—21no—
187C13×C22⋊C8—21no—
188C13×C22⋊C8C2311yescharacteristic
189C13×C22⋊C8C2311yescharacteristic
190C13×C22⋊C8C2311yescharacteristic
191C13×C22⋊C8C2311yescharacteristic
192C13×#97—21no—
193C13×#97—21no—
194C4×C8×C13—21no—
195C4×C8×C13—21no—
196#88071—21no—
197#88071—21no—
198#88071—21no—
199#88071—21no—
200#88071—21no—
201#88071—21no—
202#88071C2311yescharacteristic
203#88071C2311yescharacteristic
204#88071C2311yescharacteristic
205#88071C2311yescharacteristic
206#17604—131nomaximal, Sylow
207C24×C13C2×D411yescharacteristic
208C23×D13—21no—
209C22×C4×C13—42no—
210C22×C4×C13C22×C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2411yescharacteristic
220C2×C22⋊D13—21no—
221C2×C22⋊D13—21no—
222C2×C22⋊D13—21no—
223C2×C22⋊D13—21no—
224C2×C22⋊D13—21no—
225C2×C22⋊D13—21no—
226C2×C22⋊D13—21no—
227C2×C22⋊D13—81no—
228C2×C22⋊D13—81no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—42no—
235C22×Dic13—42no—
236C22×Dic13—81no—
237#6127—42no—
238#6127—81no—
239#6127—81no—
240#6127—81no—
241#6127—81no—
242C2×D52—21no—
243C2×D52—21no—
244C2×D52—21no—
245C2×D52—21no—
246C2×D52—21no—
247C2×D52—42no—
248C2×D52C22×C411yescharacteristic
249C2×D52C22×C411yescharacteristic
250C2×D52C22×C411yescharacteristic
251C2×C4×D13—21no—
252C2×C4×D13—21no—
253C2×C4×D13—21no—
254C2×C4×D13—21no—
255C2×C4×D13—21no—
256C2×C4×D13—21no—
257C2×C4×D13—21no—
258C2×Dic26—21no—
259C2×Dic26—21no—
260C2×Dic26C22×C411yescharacteristic
261C13×M16—42no—
262C2×C8×C13—21no—
263C2×C8×C13—21no—
264C2×C8×C13—21no—
265C2×C8×C13—21no—
266C2×C8×C13—42no—
267C13×C4⋊C4C22⋊C411yescharacteristic
268C13×C4⋊C4C22⋊C411yescharacteristic
269C13×C4⋊C4C22⋊C411yescharacteristic
270C13×C4⋊C4C22⋊C411yescharacteristic
271C13×C4⋊C4C22⋊C411yescharacteristic
272C13×C4⋊C4C22⋊C411yescharacteristic
273C13×C4⋊C4C22⋊C411yescharacteristic
274C13×C4⋊C4C22⋊C411yescharacteristic
275C13×C22⋊C4C22⋊C411yescharacteristic
276C13×C22⋊C4C22⋊C411yescharacteristic
277C13×C22⋊C4C22⋊C411yescharacteristic
278C13×C22⋊C4C22⋊C411yescharacteristic
279C13×C22⋊C4C22⋊C411yescharacteristic
280C13×C22⋊C4C22⋊C411yescharacteristic
281C13×C22⋊C4C22⋊C411yescharacteristic
282C13×C22⋊C4C22⋊C411yescharacteristic
283C42×C13C22×C411yescharacteristic
284C42×C13C22×C411yescharacteristic
285C42×C13C22×C411yescharacteristic
286C42×C13C22×C411yescharacteristic
287C42×C13C2×D411yescharacteristic
288C42×C13C2×D411yescharacteristic
289C42×C13C2×D411yescharacteristic
290C42×C13C2×D411yescharacteristic
291C22⋊Dic13—21no—
292C22⋊Dic13—21no—
293C22⋊Dic13—21no—
294C22⋊Dic13—42no—
295#6103—21no—
296#6103—21no—
297#6103—21no—
298#6103—21no—
299#6103—21no—
300#6103—21no—
301#6103—21no—
302#6103—21no—
303#6103—21no—
304#6103—21no—
305#6103—21no—
306#6103—21no—
307#6103—21no—
308#6103—21no—
309#6103—21no—
310#6103—21no—
311C4⋊Dic13—21no—
312C4⋊Dic13—21no—
313C4⋊Dic13—21no—
314C4⋊Dic13—42no—
315C4⋊Dic13—81no—
316C4⋊Dic13C22×C411yescharacteristic
317C4⋊Dic13C22×C411yescharacteristic
318C4⋊Dic13C22×C411yescharacteristic
319C4⋊Dic13C22×C411yescharacteristic
320#6101—21no—
321#6101—21no—
322#6101—21no—
323#6101—21no—
324#6101—21no—
325#6101—21no—
326#6101—21no—
327#6101—21no—
328C4×Dic13—21no—
329C4×Dic13—21no—
330C4×Dic13—21no—
331C4×Dic13—42no—
332C4×Dic13—81no—
333#3494—131no—
334#2924D1311yescharacteristic, complemented
335#2343—131no—
336#1521—131no—
337#1517—131no—
338#1516—131no—
339#1514—131no—
340#1512—131no—
341#1510—131no—
342#1509—131no—
343#1505—131no—
344#1504—131no—
345#1502—131no—
346#1500—131no—
347C2×#327—131no—
348C23×C13—21no—
349C23×C13—21no—
350C23×C13—22no—
351C23×C13—41no—
352C23×C13C2×C22⋊C411yescharacteristic
353C23×C13C2×C22⋊C411yescharacteristic
354C23×C13C22×D411yescharacteristic
355C22×D13—21no—
356C22×D13—21no—
357C22×D13—21no—
358C22×D13—42no—
359C22×D13—81no—
360C22×D13—81no—
361C2×C4×C13—21no—
362C2×C4×C13—21no—
363C2×C4×C13—21no—
364C2×C4×C13—21no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13C2×C22⋊C411yescharacteristic
374C2×C4×C13C2×C22⋊C411yescharacteristic
375C2×C4×C13C2×C22⋊C411yescharacteristic
376C2×C4×C13C2×C22⋊C411yescharacteristic
377C2×C4×C13C2×C22⋊C411yescharacteristic
378C2×C4×C13C2×C22⋊C411yescharacteristic
379C2×C4×C13C2×C22⋊C411yescharacteristic
380C2×C4×C13C2×C22⋊C411yescharacteristic
381C2×C4×C13C2×C22⋊C411yescharacteristic
382C2×C4×C13C2×C22⋊C411yescharacteristic
383C2×C4×C13C23×C411yescharacteristic
384C2×C4×C13C22×D411yescharacteristic
385C22⋊D13—41no—
386C22⋊D13—41no—
387C22⋊D13—41no—
388C22⋊D13—41no—
389C22⋊D13—41no—
390C22⋊D13—41no—
391C22⋊D13—42no—
392C22⋊D13—81no—
393C22⋊D13—81no—
394C22⋊D13—81no—
395C2×Dic13—22no—
396C2×Dic13—21no—
397C2×Dic13—21no—
398C2×Dic13—21no—
399C2×Dic13—21no—
400C2×Dic13—21no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—81no—
413C2×Dic13—84no—
414D52—42no—
415D52—41no—
416D52—41no—
417D52—41no—
418D52—81no—
419D52—81no—
420D52—81no—
421D52—81no—
422C4×D13—42no—
423C4×D13—81no—
424C4×D13—81no—
425C4×D13—81no—
426C4×D13—81no—
427C4×D13—81no—
428C4×D13—81no—
429Dic26—41no—
430Dic26—81no—
431Dic26—81no—
432C8×C13—41no—
433C8×C13—41no—
434C8×C13—41no—
435C8×C13—41no—
436#555—261no—
437#553—261no—
438#553—261no—
439#551—261no—
440#551—261no—
441#547—261no—
442#546—261no—
443#546—261no—
444#544—131no—
445#542—131no—
446#542—131no—
447#540—131no—
448#540—131no—
449#535—131no—
450#532—131no—
451#532—131no—
452#529—131no—
453#529—131no—
454#525—131no—
455C2×#121—131no—
456#520—131no—
457#518—131no—
458C2×#117C2×D1311yescharacteristic
459#433—21no—
460#433—21no—
461#432C2×D1311yescharacteristic, complemented
462#432C2×D1311yescharacteristic, complemented
463#431C2×D1311yescharacteristic, complemented
464#431C2×D1311yescharacteristic, complemented
465#424—21no—
466#407C2×D1311yescharacteristic
467C2×C22⋊C8C2×D1311yescharacteristic
468#405—21no—
469#387—261no—
470#387—261no—
471#385—261no—
472#383—131no—
473#382—131no—
474#381—131no—
475C4×C4⋊C4—131no—
476C4×C22⋊C4—261no—
477#376—131no—
478C2×#95—131no—
479#328—131no—
480#328—131no—
481#328—131no—
482#328—131no—
483#327—131no—
484#327—131no—
485#327—131no—
486#327—131no—
487#327—131no—
488#327—131no—
489#327—131no—
490#327—131no—
491#327—131no—
492#327—131no—
493#327—131no—
494#327—131no—
495C22×C13—21no—
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13#41012yes—
505C22×C13C22×C22⋊C411yescharacteristic
506C22×C13#57611yescharacteristic
507C22×C13#57711yescharacteristic
508C2×D13—41no—
509C2×D13—41no—
510C2×D13—41no—
511C2×D13—41no—
512C2×D13—41no—
513C2×D13—41no—
514C2×D13—41no—
515C2×D13—41no—
516C2×D13—41no—
517C2×D13—162no—
518C4×C13—21no—
519C4×C13—21no—
520C4×C13—21no—
521C4×C13—21no—
522C4×C13—21no—
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—21no—
529C4×C13—21no—
530Dic13—42no—
531Dic13—41no—
532Dic13—41no—
533Dic13—41no—
534Dic13—41no—
535Dic13—41no—
536Dic13—81no—
537Dic13—81no—
538Dic13—81no—
539C2×#41—131no—
540C2×#41—261no—
541C2×#41—261no—
542C22×D4—131no—
543C22×D4—261no—
544C23×C4—261no—
545C23×C4C22×D1311yescharacteristic
546C2×M16—21no—
547C22×C8—21no—
548C4⋊Q8—131no—
549C4⋊Q8—131no—
550C4⋊Q8—261no—
551#127—131no—
552#127—131no—
553#126—261no—
554#126—261no—
555#126—261no—
556#126—261no—
557#125—131no—
558#125—131no—
559#125—261no—
560#124—131no—
561#124—131no—
562#124—261no—
563#124—261no—
564#124—261no—
565#124—261no—
566#123—261no—
567#123—261no—
568#123—261no—
569#123—261no—
570#123—261no—
571#123—261no—
572#123—261no—
573#123—261no—
574#123—261no—
575C22⋊Q8—131no—
576C22⋊Q8—131no—
577C22⋊Q8—261no—
578C22⋊Q8—261no—
579C22⋊Q8—261no—
580C22⋊Q8—261no—
581#121—131no—
582#121—131no—
583#121—131no—
584#121—131no—
585#121—131no—
586#121—131no—
587#121—261no—
588#121—261no—
589#121—261no—
590#121—261no—
591#121—261no—
592#121—261no—
593#121—261no—
594#121—261no—
595#121—261no—
596#121—261no—
597#120—261no—
598#120—261no—
599#120—261no—
600C4×Q8—131no—
601C4×Q8—131no—
602C4×D4—131no—
603C4×D4—131no—
604C4×D4—131no—
605C4×D4—131no—
606C4×D4—131no—
607C4×D4—131no—
608C4×D4—261no—
609C4×D4—261no—
610C4×D4—261no—
611C4×D4—261no—
612C4×D4—261no—
613C4×D4—261no—
614C4×D4—261no—
615C4×D4—261no—
616C4×D4—261no—
617C4×D4—261no—
618#117—131no—
619#117—261no—
620#117—261no—
621#117—261no—
622#117C4×D1311yescharacteristic
623#117C4×D1311yescharacteristic
624#117C4×D1311yescharacteristic
625#117C4×D1311yescharacteristic
626#117C22⋊D1311yescharacteristic
627#117C22⋊D1311yescharacteristic
628#117C22⋊D1311yescharacteristic
629#117C22⋊D1311yescharacteristic
630C2×C4⋊C4—131no—
631C2×C4⋊C4—261no—
632C2×C4⋊C4—261no—
633C2×C4⋊C4—261no—
634C2×C4⋊C4D5211yescharacteristic
635C2×C4⋊C4D5211yescharacteristic
636C2×C22⋊C4—261no—
637C2×C22⋊C4—261no—
638C2×C22⋊C4—261no—
639C2×C22⋊C4—261no—
640C2×C22⋊C4D5211yescharacteristic
641C2×C22⋊C4D5211yescharacteristic
642C2×C42—261no—
643C2×C42—261no—
644C2×C42C22×D1311yescharacteristic
645C2×C42C22×D1311yescharacteristic
646C4⋊C8—21no—
647C4⋊C8—21no—
648C4⋊C8—21no—
649C4⋊C8—21no—
650C22⋊C8—21no—
651C22⋊C8—21no—
652C22⋊C8C22×D1311yescharacteristic
653C22⋊C8C22×D1311yescharacteristic
654C22⋊C8C22×D1311yescharacteristic
655C22⋊C8C22×D1311yescharacteristic
656#97—21no—
657#97—21no—
658C4×C8—21no—
659C4×C8—21no—
660#95—131no—
661#95—131no—
662#95—131no—
663#95—131no—
664#95—261no—
665#95—261no—
666#95—261no—
667#95—261no—
668#95—261no—
669#95—261no—
670C2×C13—21no—
671C2×C13—21no—
672C2×C13—22no—
673C2×C13—41no—
674C2×C13C2×#41011yescharacteristic
675C2×C13#289711yescharacteristic
676C2×C13#290111yescharacteristic
677D13—81no—
678D13—81no—
679D13—81no—
680C24—261no—
681C24C2×D5211yescharacteristic
682#41—522no—
683#41—1041no—
684#41—1041no—
685#41—1041no—
686#41—1041no—
687C2×Q8—131no—
688C2×Q8—261no—
689C2×Q8—261no—
690C2×D4—131no—
691C2×D4—131no—
692C2×D4—131no—
693C2×D4—261no—
694C2×D4—261no—
695C2×D4—261no—
696C2×D4—261no—
697C2×D4—261no—
698C2×D4—261no—
699C2×D4—261no—
700C2×D4—261no—
701C2×D4—261no—
702C2×D4—261no—
703C2×D4—261no—
704C2×D4—261no—
705C2×D4—522no—
706C2×D4—1041no—
707C2×D4—1041no—
708C22×C4—42no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—522no—
722C22×C4—522no—
723C22×C4—1041no—
724C22×C4C2×C4×D1311yescharacteristic
725C22×C4C2×C4×D1311yescharacteristic
726C22×C4C2×D5211yescharacteristic
727C22×C4C2×D5211yescharacteristic
728C22×C4C2×D5211yescharacteristic
729C22×C4C2×D5211yescharacteristic
730C22×C4C2×D5211yescharacteristic
731C22×C4C2×C22⋊D1311yescharacteristic
732C22×C4C2×C22⋊D1311yescharacteristic
733C22×C4C23×D1311yescharacteristic
734M16—42no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—42no—
740C4⋊C4—131no—
741C4⋊C4—131no—
742C4⋊C4—131no—
743C4⋊C4—131no—
744C4⋊C4—261no—
745C4⋊C4—261no—
746C4⋊C4—261no—
747C4⋊C4—261no—
748C4⋊C4—261no—
749C4⋊C4—261no—
750C4⋊C4—261no—
751C4⋊C4—261no—
752C4⋊C4—261no—
753C4⋊C4—261no—
754C4⋊C4—261no—
755C4⋊C4—522no—
756C4⋊C4—1041no—
757C4⋊C4#610311yescharacteristic
758C4⋊C4#610311yescharacteristic
759C4⋊C4#610311yescharacteristic
760C4⋊C4#610311yescharacteristic
761C4⋊C4#610311yescharacteristic
762C4⋊C4#610311yescharacteristic
763C4⋊C4#610311yescharacteristic
764C4⋊C4#610311yescharacteristic
765C22⋊C4—261no—
766C22⋊C4—261no—
767C22⋊C4—261no—
768C22⋊C4—261no—
769C22⋊C4—261no—
770C22⋊C4—261no—
771C22⋊C4—261no—
772C22⋊C4—261no—
773C22⋊C4—261no—
774C22⋊C4—261no—
775C22⋊C4—261no—
776C22⋊C4—261no—
777C22⋊C4—261no—
778C22⋊C4—261no—
779C22⋊C4—261no—
780C22⋊C4—261no—
781C22⋊C4—261no—
782C22⋊C4—261no—
783C22⋊C4—261no—
784C22⋊C4—522no—
785C22⋊C4#610311yescharacteristic
786C22⋊C4#610311yescharacteristic
787C22⋊C4#610311yescharacteristic
788C22⋊C4#610311yescharacteristic
789C22⋊C4#610311yescharacteristic
790C22⋊C4#610311yescharacteristic
791C22⋊C4#610311yescharacteristic
792C22⋊C4#610311yescharacteristic
793C42—261no—
794C42—261no—
795C42—261no—
796C42—522no—
797C42—1041no—
798C42C2×C4×D1311yescharacteristic
799C42C2×C4×D1311yescharacteristic
800C42C2×C4×D1311yescharacteristic
801C42C2×C4×D1311yescharacteristic
802C42C2×C22⋊D1311yescharacteristic
803C42C2×C22⋊D1311yescharacteristic
804C42C2×C22⋊D1311yescharacteristic
805C42C2×C22⋊D1311yescharacteristic
806C13#1760411yescharacteristic, complemented, Sylow
807C23—22no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—261no—
812C23—261no—
813C23—261no—
814C23—522no—
815C23—1041no—
816C23—1041no—
817C23C2×#610311yescharacteristic
818C23C2×#610311yescharacteristic
819C23C22×D5211yescharacteristic
820Q8—521no—
821Q8—1041no—
822Q8—1041no—
823D4—521no—
824D4—521no—
825D4—521no—
826D4—522no—
827D4—522no—
828D4—521no—
829D4—521no—
830D4—521no—
831D4—521no—
832D4—521no—
833D4—521no—
834D4—1041no—
835D4—1041no—
836D4—1041no—
837D4—1041no—
838D4—1041no—
839D4—1041no—
840D4—1041no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—262no—
854C2×C4—261no—
855C2×C4—261no—
856C2×C4—261no—
857C2×C4—261no—
858C2×C4—261no—
859C2×C4—522no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—1041no—
872C2×C4—1041no—
873C2×C4—1041no—
874C2×C4—1041no—
875C2×C4—1041no—
876C2×C4—1041no—
877C2×C4—1041no—
878C2×C4—1044no—
879C2×C4C2×#610311yescharacteristic
880C2×C4C2×#610311yescharacteristic
881C2×C4C2×#610311yescharacteristic
882C2×C4C2×#610311yescharacteristic
883C2×C4C2×#610311yescharacteristic
884C2×C4C2×#610311yescharacteristic
885C2×C4C2×#610311yescharacteristic
886C2×C4C2×#610311yescharacteristic
887C2×C4C2×#610311yescharacteristic
888C2×C4C2×#610311yescharacteristic
889C2×C4C22×C4×D1311yescharacteristic
890C2×C4C22×C22⋊D1311yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—521no—
905C22—521no—
906C22—521no—
907C22—521no—
908C22—521no—
909C22—521no—
910C22—521no—
911C22—521no—
912C22—521no—
913C22—2082no—
914C22#1171866712yes—
915C22#1171945611yescharacteristic
916C22#1171945711yescharacteristic
917C22C22×#610311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—522no—
931C4—521no—
932C4—521no—
933C4—521no—
934C4—521no—
935C4—521no—
936C4—1041no—
937C4—1041no—
938C4—1041no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—1041no—
944C2—1041no—
945C2—1041no—
946C2C2×#1171866711yescharacteristic
947C2#1312336311yescharacteristic
948C2#1312338111yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C22×C22⋊C4
prime radical#13128571C2
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#17604
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13117696C2semidirect
3. #13113414C2semidirect
4. #13113397C2semidirect
5. #13113393C2semidirect
6. #13113384C2semidirect
7. #13113375C2semidirect
8. #13113366C2semidirect
9. #13113362C2semidirect
10. #13113345C2semidirect
11. #13113341C2semidirect
12. #13113332C2semidirect
13. #13113323C2semidirect
14. C2×#11718062C2semidirect
15. C13×#2924C2semidirect
19. #11719240C4semidirect
20. #11719240C4semidirect
21. #11719239C4semidirect
22. #11719239C4semidirect
27. #11719230C4semidirect
28. #11719228C4semidirect
29. #11719226C4semidirect
30. #11719224C4semidirect
41. C13×#432C22semidirect
42. C13×#432C22semidirect
43. C13×#431C22semidirect
44. C13×#431C22semidirect
55. #11718598C22semidirect
56. #11718597C22semidirect
57. C4×C4⋊Dic13C22semidirect
58. #11718593C22semidirect
67. #11718062C22semidirect
68. #11718062C22semidirect
69. #11718062C22semidirect
70. #11718062C22semidirect
71. #11718059C22semidirect
72. #11718059C22semidirect
73. #11718059C22semidirect
74. #11718059C22semidirect
162. #88129C2×C4semidirect
163. #88129C2×C4semidirect
164. #88128C2×C4semidirect
165. #88128C2×C4semidirect
168. C4×D52C2×C4semidirect
169. C4×D52C2×C4semidirect
170. C4×D52C2×C4semidirect
171. C4×D52C2×C4semidirect
172. C4×D52C2×C4semidirect
173. C4×D52C2×C4semidirect
176. #88124C2×C4semidirect
177. #88124C2×C4semidirect
178. #88123C2×C4semidirect
179. #88123C2×C4semidirect
180. C4×Dic26C2×C4semidirect
181. C4×Dic26C2×C4semidirect
334. #2924D13semidirect
461. #432C2×D13semidirect
462. #432C2×D13semidirect
463. #431C2×D13semidirect
464. #431C2×D13semidirect
806. C13#17604semidirect

Maximal subgroups

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

subgroupindex
#131285712
#131176962
#131134142
#131133972
#131133932
#131133842
#131133752
#131133662
#131133622
#131133452
#131133412
#131133322
#131133232
C2×#117180622
C13×#29242
#1760413