Finite Group Databasebeta

← #16033827

Subgroups — #16033827

Order 3328.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120541C211yesmaximal, characteristic, complemented
2#13120533C211yesmaximal, characteristic, complemented
3#13120532C211yesmaximal, characteristic, complemented
4#13120515C211yesmaximal, characteristic
5#13120238C211yesmaximal, characteristic, complemented
6#13120101C211yesmaximal, characteristic, complemented
7#13119925C211yesmaximal, characteristic, complemented
8#13119887C211yesmaximal, characteristic
9#13119717C211yesmaximal, characteristic, complemented
10#13119667C211yesmaximal, characteristic, complemented
11#13119635C211yesmaximal, characteristic, complemented
12#13119629C211yesmaximal, characteristic, complemented
13#13119056C211yesmaximal, characteristic, complemented
14#13119044C211yesmaximal, characteristic
15#13119012C211yesmaximal, characteristic, complemented
16#13118938C211yesmaximal, characteristic
17#13118141C211yesmaximal, characteristic, complemented
18#13118134C211yesmaximal, characteristic, complemented
19#13118106C211yesmaximal, characteristic, complemented
20#13118099C211yesmaximal, characteristic
21C4×#88143C211yesmaximal, characteristic, complemented
22C4×#88143C211yesmaximal, characteristic, complemented
23C4×#88130C211yesmaximal, characteristic, complemented
24C4×#88200C211yesmaximal, characteristic, complemented
25C4×#88148C211yesmaximal, characteristic
26#13117331C211yesmaximal, characteristic, complemented
27#13117316C211yesmaximal, characteristic, complemented
28#13117280C211yesmaximal, characteristic
29C4×#88126C211yesmaximal, characteristic, complemented
30C4×#88146C211yesmaximal, characteristic, complemented
31C13×#2295C211yesmaximal, characteristic, complemented
32C2×C4×Q8×C13C2211yescharacteristic
33C2×#88200C2211yescharacteristic
34C2×#88148C2211yescharacteristic
35C2×#88146C2211yescharacteristic
36C2×#88146C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88143C2211yescharacteristic
39C2×#88130C2211yescharacteristic
40C2×C4×D52C2211yescharacteristic
41C2×#88126C2211yescharacteristic
42C2×#88126C2211yescharacteristic
43C2×#88126C2211yescharacteristic
44C2×#88126C2211yescharacteristic
45C2×C42×D13C2211yescharacteristic
46C2×C42×D13C2211yescharacteristic
47C13×#391C2211yescharacteristic
48C13×#391C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C4×C13×C4⋊C4C2211yescharacteristic
56C4×C13×C4⋊C4C2211yescharacteristic
57C4×C13×C4⋊C4C2211yescharacteristic
58C13×#376C2211yescharacteristic
59C13×#376C2211yescharacteristic
60C43×C13C2211yescharacteristic
61#11718892C2211yescharacteristic
62#11718891C2211yescharacteristic
63#11718890C2211yescharacteristic
64#11718655C2211yescharacteristic
65#11718655C2211yescharacteristic
66#11718654C2211yescharacteristic
67#11718653C2211yescharacteristic
68#11718653C2211yescharacteristic
69#11718652C2211yescharacteristic
70#11718651C2211yescharacteristic
71#11718650C2211yescharacteristic
72#11718650C2211yescharacteristic
73#11718650C2211yescharacteristic
74#11718650C2211yescharacteristic
75#11718650C2211yescharacteristic
76#11718648C2211yescharacteristic
77#11718645C2211yescharacteristic
78#11718645C2211yescharacteristic
79#11718645C2211yescharacteristic
80#11718643C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718642C2211yescharacteristic
84#11718639C2211yescharacteristic
85#11718639C2211yescharacteristic
86#11718639C2211yescharacteristic
87#11718639C2211yescharacteristic
88C4⋊C4×Dic13C2211yescharacteristic
89C4⋊C4×Dic13C2211yescharacteristic
90#11718634C2211yescharacteristic
91#11718633C2211yescharacteristic
92#11718633C2211yescharacteristic
93#11718633C2211yescharacteristic
94#11718633C2211yescharacteristic
95#11718601C2211yescharacteristic
96#11718601C2211yescharacteristic
97#11718601C2211yescharacteristic
98C4×#6103C2211yescharacteristic
99C4×#6103C2211yescharacteristic
100C4×#6103C2211yescharacteristic
101C4×#6103C2211yescharacteristic
102C4×#6103C2211yescharacteristic
103C4×#6103C2211yescharacteristic
104C4×#6103C2211yescharacteristic
105C4×#6103C2211yescharacteristic
106C4×#6103C2211yescharacteristic
107C4×#6103C2211yescharacteristic
108#11718598C2211yescharacteristic
109C4×C4⋊Dic13C2211yescharacteristic
110C4×C4⋊Dic13C2211yescharacteristic
111C4×C4⋊Dic13C2211yescharacteristic
112#11718594C2211yescharacteristic
113#11718594C2211yescharacteristic
114#11718594C2211yescharacteristic
115#11718593C2211yescharacteristic
116#11718593C2211yescharacteristic
117C4×#6101C2211yescharacteristic
118C4×#6101C2211yescharacteristic
119C4×#6101C2211yescharacteristic
120C4×#6101C2211yescharacteristic
121C4×#6101C2211yescharacteristic
122C4×#6101C2211yescharacteristic
123C4×#6101C2211yescharacteristic
124C4×#6101C2211yescharacteristic
125C4×#6101C2211yescharacteristic
126C4×#6101C2211yescharacteristic
127C4×#6101C2211yescharacteristic
128C4×#6101C2211yescharacteristic
129C42×Dic13C2211yescharacteristic
130C42×Dic13C2211yescharacteristic
131#11718337C2211yescharacteristic
132#11718336C2211yescharacteristic
133#11718336C2211yescharacteristic
134#11718336C2211yescharacteristic
135#11718336C2211yescharacteristic
136#11718336C2211yescharacteristic
137#11718333C2211yescharacteristic
138#11718331C2211yescharacteristic
139#11718331C2211yescharacteristic
140#11718330C2211yescharacteristic
141#11718330C2211yescharacteristic
142#11718330C2211yescharacteristic
143#11718330C2211yescharacteristic
144#11718330C2211yescharacteristic
145#11718329C2211yescharacteristic
146#11718329C2211yescharacteristic
147#11718329C2211yescharacteristic
148#11718329C2211yescharacteristic
149#11718327C2211yescharacteristic
150#11718327C2211yescharacteristic
151#11718326C2211yescharacteristic
152#11718326C2211yescharacteristic
153#11718326C2211yescharacteristic
154#11718325C2211yescharacteristic
155C13⋊#401C2211yescharacteristic
156#11718321C2211yescharacteristic
157#11718321C2211yescharacteristic
158#11718321C2211yescharacteristic
159#11718321C2211yescharacteristic
160#11718321C2211yescharacteristic
161#11718319C2211yescharacteristic
162#11718319C2211yescharacteristic
163#11718319C2211yescharacteristic
164#11718318C2211yescharacteristic
165#11718318C2211yescharacteristic
166#11718318C2211yescharacteristic
167#11718318C2211yescharacteristic
168#11718316C2211yescharacteristic
169#11718314C2211yescharacteristic
170#11718314C2211yescharacteristic
171#11718314C2211yescharacteristic
172#11718314C2211yescharacteristic
173#11718313C2211yescharacteristic
174#11718313C2211yescharacteristic
175#11718313C2211yescharacteristic
176#11718313C2211yescharacteristic
177#11718313C2211yescharacteristic
178#11718313C2211yescharacteristic
179#11718311C2211yescharacteristic
180#11718311C2211yescharacteristic
181#11718309C2211yescharacteristic
182#11718309C2211yescharacteristic
183#11718308C2211yescharacteristic
184#11718308C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718308C2211yescharacteristic
187C22×Q8×C13C2311yescharacteristic
188C22×D52C2311yescharacteristic
189C22×C4×D13C2311yescharacteristic
190C22×C4×D13C2311yescharacteristic
191C22×C4×D13C2311yescharacteristic
192C22×C4×D13C2311yescharacteristic
193C22×C4×D13C2311yescharacteristic
194C22×C4×D13C2311yescharacteristic
195C4×Q8×C13—24no—
196C2×C13×C4⋊C4C2311yescharacteristic
197C2×C13×C4⋊C4C2311yescharacteristic
198C2×C13×C4⋊C4C2311yescharacteristic
199C2×C13×C4⋊C4C2311yescharacteristic
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C13×C4⋊C4C2311yescharacteristic
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C13×C4⋊C4C2311yescharacteristic
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C42×C13C2311yescharacteristic
206C2×C42×C13C2311yescharacteristic
207C2×C42×C13C2311yescharacteristic
208C2×C42×C13C2311yescharacteristic
209C2×C42×C13C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C42×C13C2311yescharacteristic
213C2×C42×C13C2311yescharacteristic
214C2×C42×C13C2311yescharacteristic
215C2×C42×C13C2311yescharacteristic
216#88200—24no—
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
219C2×#6103C2311yescharacteristic
220C2×#6103C2311yescharacteristic
221C2×#6103C2311yescharacteristic
222C2×#6103C2311yescharacteristic
223C2×#6103C2311yescharacteristic
224C2×#6103C2311yescharacteristic
225C2×#6103C2311yescharacteristic
226C2×#6103C2311yescharacteristic
227C2×#6103C2311yescharacteristic
228C2×#6103C2311yescharacteristic
229C2×#6103C2311yescharacteristic
230C2×#6103C2311yescharacteristic
231C2×#6103C2311yescharacteristic
232C2×#6103C2311yescharacteristic
233C2×#6103C2311yescharacteristic
234C2×#6103C2311yescharacteristic
235C2×#6103C2311yescharacteristic
236C2×#6103C2311yescharacteristic
237C2×#6103C2311yescharacteristic
238C2×#6103C2311yescharacteristic
239C2×C4⋊Dic13C2311yescharacteristic
240C2×C4⋊Dic13C2311yescharacteristic
241C2×C4⋊Dic13C2311yescharacteristic
242C2×C4⋊Dic13C2311yescharacteristic
243C2×C4⋊Dic13C2311yescharacteristic
244C2×C4⋊Dic13C2311yescharacteristic
245C2×C4⋊Dic13C2311yescharacteristic
246C2×#6101C2311yescharacteristic
247C2×#6101C2311yescharacteristic
248C2×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×#6101C2311yescharacteristic
254C2×#6101C2311yescharacteristic
255C2×#6101C2311yescharacteristic
256C2×#6101C2311yescharacteristic
257C2×#6101C2311yescharacteristic
258C2×#6101C2311yescharacteristic
259C2×#6101C2311yescharacteristic
260C2×#6101C2311yescharacteristic
261C2×#6101C2311yescharacteristic
262C2×#6101C2311yescharacteristic
263C2×#6101C2311yescharacteristic
264C2×#6101C2311yescharacteristic
265C2×#6101C2311yescharacteristic
266C2×#6101C2311yescharacteristic
267C2×#6101C2311yescharacteristic
268C2×#6101C2311yescharacteristic
269C2×#6101C2311yescharacteristic
270C2×C4×Dic13C2311yescharacteristic
271C2×C4×Dic13C2311yescharacteristic
272C2×C4×Dic13C2311yescharacteristic
273C2×C4×Dic13C2311yescharacteristic
274C2×C4×Dic13C2311yescharacteristic
275C2×C4×Dic13C2311yescharacteristic
276C2×C4×Dic13C2311yescharacteristic
277C2×C4×Dic13C2311yescharacteristic
278C2×C4×Dic13C2311yescharacteristic
279C2×C4×Dic13C2311yescharacteristic
280C2×C4×Dic13C2311yescharacteristic
281C2×C4×Dic13C2311yescharacteristic
282C2×C4×Dic13C2311yescharacteristic
283C2×C4×Dic13C2311yescharacteristic
284C2×C4×Dic13C2311yescharacteristic
285C2×C4×Dic13C2311yescharacteristic
286C2×C4×Dic13C2311yescharacteristic
287C2×C4×Dic13C2311yescharacteristic
288#88148—24no—
289#88146—24no—
290#88146—24no—
291#88143—24no—
292#88143—24no—
293#88130—24no—
294C4×D52—24no—
295#88126—24no—
296#88126—24no—
297#88126—24no—
298#88126—24no—
299C42×D13—24no—
300C42×D13—24no—
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
305C13×#95C2311yescharacteristic
306C13×#95C2311yescharacteristic
307C13×#95C2311yescharacteristic
308C13×#95C2311yescharacteristic
309C13×#95C2311yescharacteristic
310C13×#95C2311yescharacteristic
311C13×#95C2311yescharacteristic
312C13×#95C2311yescharacteristic
313C13×#95C2311yescharacteristic
314C13×#95C2311yescharacteristic
315#88071C2311yescharacteristic
316#88071C2311yescharacteristic
317#88071C2311yescharacteristic
318#88071C2311yescharacteristic
319#88071C2311yescharacteristic
320#88071C2311yescharacteristic
321#88071C2311yescharacteristic
322#88071C2311yescharacteristic
323#88071C2311yescharacteristic
324#88071C2311yescharacteristic
325#88071C2311yescharacteristic
326#88071C2311yescharacteristic
327#88071C2311yescharacteristic
328#88071C2311yescharacteristic
329#88071C2311yescharacteristic
330#88071C2311yescharacteristic
331#88071C2311yescharacteristic
332#88071C2311yescharacteristic
333#88071C2311yescharacteristic
334#88071C2311yescharacteristic
335#88071C2311yescharacteristic
336#88071C2311yescharacteristic
337#88071C2311yescharacteristic
338#88071C2311yescharacteristic
339#88071C2311yescharacteristic
340#88071C2311yescharacteristic
341#88071C2311yescharacteristic
342#88071C2311yescharacteristic
343#88071C2311yescharacteristic
344#88071C2311yescharacteristic
345#88071C2311yescharacteristic
346#88071C2311yescharacteristic
347#88071C2311yescharacteristic
348#88071C2311yescharacteristic
349#88071C2311yescharacteristic
350#88071C2311yescharacteristic
351#88071C2311yescharacteristic
352#88071C2311yescharacteristic
353#88071C2311yescharacteristic
354#88071C2311yescharacteristic
355#88071C2311yescharacteristic
356#88071C2311yescharacteristic
357#34873—131nomaximal, Sylow
358C23×D13C2411yescharacteristic
359C23×D13C2411yescharacteristic
360C2×Q8×C13—22no—
361C2×Q8×C13—22no—
362C2×Q8×C13—41no—
363C22×C4×C13C2411yescharacteristic
364C22×C4×C13C2411yescharacteristic
365C22×C4×C13C2411yescharacteristic
366C22×C4×C13C2411yescharacteristic
367C22×C4×C13C2411yescharacteristic
368C22×C4×C13C2411yescharacteristic
369C22×C4×C13C2411yescharacteristic
370C22×C4×C13C2411yescharacteristic
371C22×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
374C22×C4×C13C2411yescharacteristic
375C22×C4×C13C2411yescharacteristic
376C22×C4×C13C2411yescharacteristic
377C22×C4×C13C2411yescharacteristic
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2411yescharacteristic
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2411yescharacteristic
382C22×Dic13C2411yescharacteristic
383C22×Dic13C2411yescharacteristic
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2411yescharacteristic
386C22×Dic13C2411yescharacteristic
387C22×Dic13C2411yescharacteristic
388C22×Dic13C2411yescharacteristic
389C22×Dic13C2411yescharacteristic
390C22×Dic13C2411yescharacteristic
391C22×Dic13C2411yescharacteristic
392C2×D52—22no—
393C2×D52—22no—
394C2×D52—41no—
395C2×C4×D13—22no—
396C2×C4×D13—22no—
397C2×C4×D13—22no—
398C2×C4×D13—22no—
399C2×C4×D13—22no—
400C2×C4×D13—22no—
401C2×C4×D13—22no—
402C2×C4×D13—22no—
403C2×C4×D13—22no—
404C2×C4×D13—22no—
405C2×C4×D13—22no—
406C2×C4×D13—22no—
407C2×C4×D13—22no—
408C2×C4×D13—22no—
409C2×C4×D13—22no—
410C2×C4×D13—41no—
411C2×C4×D13—41no—
412C2×C4×D13#4114yes—
413C13×C4⋊C4—22no—
414C13×C4⋊C4—22no—
415C13×C4⋊C4—22no—
416C13×C4⋊C4—22no—
417C13×C4⋊C4—22no—
418C13×C4⋊C4—22no—
419C13×C4⋊C4—22no—
420C13×C4⋊C4—22no—
421C13×C4⋊C4—41no—
422C42×C13—22no—
423C42×C13—22no—
424C42×C13—22no—
425C42×C13—22no—
426C42×C13—22no—
427C42×C13—22no—
428C42×C13—22no—
429C42×C13—22no—
430C42×C13—22no—
431C42×C13—41no—
432C42×C13#4114yes—
433#6103—22no—
434#6103—22no—
435#6103—22no—
436#6103—22no—
437#6103—22no—
438#6103—22no—
439#6103—22no—
440#6103—22no—
441#6103—22no—
442#6103—22no—
443#6103—22no—
444#6103—22no—
445#6103—22no—
446#6103—22no—
447#6103—22no—
448#6103—22no—
449#6103—22no—
450#6103—22no—
451#6103—22no—
452#6103—41no—
453#6103—41no—
454#6103#4114yes—
455C4⋊Dic13—22no—
456C4⋊Dic13—22no—
457C4⋊Dic13—22no—
458C4⋊Dic13—22no—
459C4⋊Dic13—22no—
460C4⋊Dic13—22no—
461C4⋊Dic13—41no—
462#6101—22no—
463#6101—22no—
464#6101—22no—
465#6101—22no—
466#6101—22no—
467#6101—22no—
468#6101—22no—
469#6101—22no—
470#6101—22no—
471#6101—22no—
472#6101—22no—
473#6101—22no—
474#6101—22no—
475#6101—22no—
476#6101—22no—
477#6101—22no—
478#6101—22no—
479#6101—22no—
480#6101—22no—
481#6101—41no—
482#6101—41no—
483#6101—41no—
484#6101—41no—
485#6101#4114yes—
486C4×Dic13—22no—
487C4×Dic13—22no—
488C4×Dic13—22no—
489C4×Dic13—22no—
490C4×Dic13—22no—
491C4×Dic13—22no—
492C4×Dic13—22no—
493C4×Dic13—22no—
494C4×Dic13—22no—
495C4×Dic13—22no—
496C4×Dic13—22no—
497C4×Dic13—22no—
498C4×Dic13—22no—
499C4×Dic13—22no—
500C4×Dic13—22no—
501C4×Dic13—41no—
502C4×Dic13—41no—
503C4×Dic13#4114yes—
504#2612—131no—
505#2611—131no—
506#2611—131no—
507#2609—131no—
508#2585—131no—
509#2573—131no—
510#2556—131no—
511#2553—131no—
512#2533—131no—
513#2530—131no—
514#2528—131no—
515#2527—131no—
516#2478—131no—
517#2477—131no—
518#2475—131no—
519#2470—131no—
520#2402—131no—
521#2401—131no—
522#2396—131no—
523#2395—131no—
524C4×#125—131no—
525C4×#125—131no—
526C4×#126—131no—
527C4×C22⋊Q8—131no—
528C4×#123—131no—
529#2298—131no—
530#2296—131no—
531#2295D1311yescharacteristic, complemented
532#2290—131no—
533C4×#117—131no—
534C4×#117—131no—
535C23×C13C2511yescharacteristic
536C22×D13—21no—
537C22×D13—21no—
538C22×D13—21no—
539C22×D13—21no—
540C22×D13—21no—
541C22×D13—21no—
542C22×D13—21no—
543C22×D13—21no—
544C22×D13—21no—
545C22×D13—21no—
546C22×D13—21no—
547C22×D13—21no—
548C22×D13C2×#4112yes—
549C22×D13C2×#4112yes—
550Q8×C13—44no—
551C2×C4×C13—21no—
552C2×C4×C13—21no—
553C2×C4×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—21no—
556C2×C4×C13—21no—
557C2×C4×C13—21no—
558C2×C4×C13—21no—
559C2×C4×C13—21no—
560C2×C4×C13—21no—
561C2×C4×C13—21no—
562C2×C4×C13—21no—
563C2×C4×C13—21no—
564C2×C4×C13—21no—
565C2×C4×C13—21no—
566C2×C4×C13—21no—
567C2×C4×C13—21no—
568C2×C4×C13—21no—
569C2×C4×C13—21no—
570C2×C4×C13—21no—
571C2×C4×C13—21no—
572C2×C4×C13—21no—
573C2×C4×C13—21no—
574C2×C4×C13—21no—
575C2×C4×C13—21no—
576C2×C4×C13—21no—
577C2×C4×C13—21no—
578C2×C4×C13—21no—
579C2×C4×C13—21no—
580C2×C4×C13—21no—
581C2×C4×C13—21no—
582C2×C4×C13—21no—
583C2×C4×C13—21no—
584C2×C4×C13—21no—
585C2×C4×C13—21no—
586C2×C4×C13—21no—
587C2×C4×C13—21no—
588C2×C4×C13C2×#4112yes—
589C2×C4×C13C2×#4112yes—
590C2×C4×C13C2×#4112yes—
591C2×C4×C13C2×#4112yes—
592C2×C4×C13C2×#4112yes—
593C2×C4×C13C2×#4112yes—
594C2×C4×C13C2×#4112yes—
595C2×C4×C132−1+412yes—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13—21no—
602C2×Dic13—21no—
603C2×Dic13—21no—
604C2×Dic13—21no—
605C2×Dic13—21no—
606C2×Dic13—21no—
607C2×Dic13—21no—
608C2×Dic13—21no—
609C2×Dic13—21no—
610C2×Dic13—21no—
611C2×Dic13—21no—
612C2×Dic13—21no—
613C2×Dic13—21no—
614C2×Dic13—21no—
615C2×Dic13—21no—
616C2×Dic13—21no—
617C2×Dic13—21no—
618C2×Dic13—21no—
619C2×Dic13—21no—
620C2×Dic13—21no—
621C2×Dic13—21no—
622C2×Dic13—21no—
623C2×Dic13—21no—
624C2×Dic13—21no—
625C2×Dic13—21no—
626C2×Dic13—21no—
627C2×Dic13—21no—
628C2×Dic13—21no—
629C2×Dic13—21no—
630C2×Dic13—21no—
631C2×Dic13—21no—
632C2×Dic13C2×#4112yes—
633C2×Dic13C2×#4112yes—
634C2×Dic13C2×#4112yes—
635C2×Dic13C2×#4112yes—
636C2×Dic13C2×#4112yes—
637C2×Dic13C2×#4112yes—
638D52—44no—
639C4×D13—28no—
640C4×D13—28no—
641C4×D13—28no—
642C4×D13—44no—
643C4×D13—44no—
644C4×D13—44no—
645C2×#126—131no—
646C2×#125—131no—
647C2×#125—131no—
648C2×#123—131no—
649C2×C22⋊Q8—131no—
650C2×C4×Q8C2×D1311yescharacteristic
651C2×C4×D4—131no—
652C2×#117—131no—
653C2×#117—131no—
654C2×#117—131no—
655C2×#117—131no—
656C2×#117—131no—
657C2×#117—131no—
658C22×C42—131no—
659C22×C42—131no—
660#401—131no—
661#400—131no—
662#400—131no—
663#400—131no—
664#400—131no—
665#400—131no—
666#400—131no—
667#400—131no—
668#400—131no—
669#400—131no—
670#399—131no—
671#399—131no—
672#398—131no—
673#398—131no—
674#398—131no—
675#398—131no—
676#398—131no—
677#398—131no—
678#398—131no—
679#397—131no—
680#397—131no—
681#397—131no—
682#397—131no—
683#397—131no—
684#397—131no—
685#396—131no—
686#396—131no—
687#396—131no—
688#395—131no—
689#394—131no—
690#394—131no—
691#393—131no—
692#391—131no—
693#391C2×D1311yescharacteristic
694#391C2×D1311yescharacteristic
695#389—131no—
696#389—131no—
697#389—131no—
698#389—131no—
699#389—131no—
700#389—131no—
701#389—131no—
702#389—131no—
703#389—131no—
704#389C2×D1311yescharacteristic
705#389C2×D1311yescharacteristic
706#388—131no—
707#388—131no—
708#388—131no—
709#388—131no—
710#388—131no—
711#388—131no—
712#388—131no—
713#388—131no—
714#388—131no—
715#388—131no—
716#388—131no—
717#387—131no—
718#387—131no—
719#387—131no—
720#387—131no—
721#387—131no—
722#387—131no—
723#387—131no—
724#387—131no—
725#387—131no—
726#387—131no—
727#387—131no—
728#387—131no—
729#387—131no—
730#387—131no—
731#387—131no—
732#387—131no—
733#387—131no—
734#387—131no—
735#387—131no—
736#387—131no—
737#387—131no—
738#387C2×D1311yescharacteristic
739#387C2×D1311yescharacteristic
740#387C2×D1311yescharacteristic
741#387C2×D1311yescharacteristic
742#386—131no—
743#386—131no—
744#386—131no—
745#385—131no—
746#385—131no—
747#385—131no—
748#385—131no—
749#385—131no—
750#385—131no—
751#385—131no—
752#385—131no—
753#385—131no—
754#383—131no—
755#382—131no—
756#382—131no—
757#381—131no—
758#380—131no—
759C4×C4⋊C4—131no—
760C4×C4⋊C4—131no—
761C4×C4⋊C4—131no—
762C4×C4⋊C4—131no—
763C4×C4⋊C4—131no—
764C4×C4⋊C4—131no—
765C4×C4⋊C4—131no—
766C4×C4⋊C4—131no—
767C4×C4⋊C4—131no—
768C4×C4⋊C4—131no—
769C4×C4⋊C4—131no—
770C4×C4⋊C4—131no—
771C4×C4⋊C4—131no—
772C4×C4⋊C4—131no—
773C4×C4⋊C4—131no—
774C4×C4⋊C4—131no—
775C4×C4⋊C4—131no—
776C4×C4⋊C4C2×D1311yescharacteristic
777C4×C4⋊C4C2×D1311yescharacteristic
778C4×C4⋊C4C2×D1311yescharacteristic
779C4×C22⋊C4—131no—
780C4×C22⋊C4—131no—
781C4×C22⋊C4—131no—
782C4×C22⋊C4—131no—
783C4×C22⋊C4—131no—
784C4×C22⋊C4—131no—
785C4×C22⋊C4—131no—
786C4×C22⋊C4—131no—
787C4×C22⋊C4—131no—
788C4×C22⋊C4—131no—
789C4×C22⋊C4—131no—
790C4×C22⋊C4—131no—
791#376—131no—
792#376—131no—
793#376—131no—
794#376—131no—
795#376C2×D1311yescharacteristic
796#376C2×D1311yescharacteristic
797C43—131no—
798C43—131no—
799C43C2×D1311yescharacteristic
800C22×C13C22×#4111yescharacteristic
801C22×C13C22×#4111yescharacteristic
802C22×C13C22×#4111yescharacteristic
803C22×C13C22×#4111yescharacteristic
804C22×C13C22×#4111yescharacteristic
805C22×C13C2×2−1+411yescharacteristic
806C22×C13#58511yescharacteristic
807C2×D13—22no—
808C2×D13—22no—
809C2×D13—22no—
810C2×D13—22no—
811C2×D13—22no—
812C2×D13—22no—
813C2×D13—41no—
814C2×D13—41no—
815C2×D13—41no—
816C2×D13—41no—
817C2×D13—41no—
818C2×D13—41no—
819C2×D13—41no—
820C2×D13—41no—
821C4×C13—22no—
822C4×C13—22no—
823C4×C13—22no—
824C4×C13—22no—
825C4×C13—22no—
826C4×C13—41no—
827C4×C13—41no—
828C4×C13—41no—
829C4×C13—41no—
830C4×C13—41no—
831C4×C13—41no—
832C4×C13—41no—
833C4×C13—41no—
834C4×C13—41no—
835C4×C13#55214yes—
836Dic13—22no—
837Dic13—22no—
838Dic13—22no—
839Dic13—22no—
840Dic13—22no—
841Dic13—22no—
842Dic13—41no—
843Dic13—41no—
844Dic13—41no—
845Dic13—41no—
846Dic13—41no—
847Dic13—41no—
848Dic13—41no—
849Dic13—41no—
850C22×Q8C22×D1311yescharacteristic
851C22×D4—131no—
852C23×C4—131no—
853C23×C4—131no—
854C23×C4—131no—
855C23×C4—131no—
856C23×C4—131no—
857C23×C4—131no—
858#126—264no—
859#125—264no—
860#125—264no—
861#123—264no—
862C22⋊Q8—264no—
863C4×Q8—24no—
864C4×D4—264no—
865#117—264no—
866#117—264no—
867#117—264no—
868#117—264no—
869#117—264no—
870#117—264no—
871C2×C4⋊C4—131no—
872C2×C4⋊C4—131no—
873C2×C4⋊C4—131no—
874C2×C4⋊C4—131no—
875C2×C4⋊C4—131no—
876C2×C4⋊C4—131no—
877C2×C4⋊C4—131no—
878C2×C4⋊C4—131no—
879C2×C4⋊C4—131no—
880C2×C4⋊C4—131no—
881C2×C4⋊C4—131no—
882C2×C4⋊C4—131no—
883C2×C4⋊C4—131no—
884C2×C4⋊C4—131no—
885C2×C4⋊C4—131no—
886C2×C4⋊C4—131no—
887C2×C4⋊C4—131no—
888C2×C4⋊C4—131no—
889C2×C4⋊C4—131no—
890C2×C4⋊C4—131no—
891C2×C4⋊C4—131no—
892C2×C4⋊C4—131no—
893C2×C4⋊C4—131no—
894C2×C4⋊C4—131no—
895C2×C4⋊C4—131no—
896C2×C4⋊C4—131no—
897C2×C4⋊C4—131no—
898C2×C4⋊C4—131no—
899C2×C4⋊C4—131no—
900C2×C4⋊C4—131no—
901C2×C4⋊C4—131no—
902C2×C4⋊C4C22×D1311yescharacteristic
903C2×C4⋊C4C22×D1311yescharacteristic
904C2×C4⋊C4C22×D1311yescharacteristic
905C2×C4⋊C4C22×D1311yescharacteristic
906C2×C4⋊C4C22×D1311yescharacteristic
907C2×C4⋊C4C22×D1311yescharacteristic
908C2×C4⋊C4C22×D1311yescharacteristic
909C2×C4⋊C4C22×D1311yescharacteristic
910C2×C4⋊C4C22×D1311yescharacteristic
911C2×C22⋊C4—131no—
912C2×C22⋊C4—131no—
913C2×C22⋊C4—131no—
914C2×C22⋊C4—131no—
915C2×C22⋊C4—131no—
916C2×C22⋊C4—131no—
917C2×C22⋊C4—131no—
918C2×C22⋊C4—131no—
919C2×C22⋊C4—131no—
920C2×C22⋊C4—131no—
921C2×C22⋊C4—131no—
922C2×C22⋊C4—131no—
923C2×C22⋊C4—131no—
924C2×C22⋊C4—131no—
925C2×C22⋊C4—131no—
926C2×C22⋊C4—131no—
927C2×C22⋊C4—131no—
928C2×C22⋊C4—131no—
929C2×C22⋊C4—131no—
930C2×C22⋊C4—131no—
931C2×C22⋊C4—131no—
932C2×C22⋊C4—131no—
933C2×C42—131no—
934C2×C42—131no—
935C2×C42—131no—
936C2×C42—131no—
937C2×C42—131no—
938C2×C42—131no—
939C2×C42—131no—
940C2×C42—131no—
941C2×C42—131no—
942C2×C42—131no—
943C2×C42—131no—
944C2×C42—131no—
945C2×C42—131no—
946C2×C42—131no—
947C2×C42—131no—
948C2×C42—131no—
949C2×C42—131no—
950C2×C42—131no—
951C2×C42—264no—
952C2×C42—264no—
953C2×C42C22×D1311yescharacteristic
954C2×C42C22×D1311yescharacteristic
955C2×C42C22×D1311yescharacteristic
956C2×C42C22×D1311yescharacteristic
957C2×C42C22×D1311yescharacteristic
958C2×C42C22×D1311yescharacteristic
959C2×C42C22×D1311yescharacteristic
960C2×C42C22×D1311yescharacteristic
961C2×C42C22×D1311yescharacteristic
962C2×C42C22×D1311yescharacteristic
963C2×C42C22×D1311yescharacteristic
964#95—131no—
965#95—131no—
966#95—131no—
967#95—131no—
968#95—131no—
969#95—131no—
970#95—131no—
971#95—131no—
972#95—131no—
973#95—131no—
974#95—131no—
975#95—131no—
976#95—131no—
977#95—131no—
978#95—131no—
979#95—131no—
980#95—131no—
981#95—131no—
982#95—131no—
983#95—131no—
984#95—131no—
985#95—131no—
986#95—131no—
987#95—131no—
988#95—131no—
989#95—131no—
990#95—131no—
991#95—131no—
992#95—131no—
993#95—131no—
994#95—131no—
995#95—131no—
996#95—131no—
997#95—131no—
998#95—131no—
999#95—131no—
1000#95—131no—
1001#95—131no—
1002#95—131no—
1003#95—131no—
1004#95—131no—
1005#95—131no—
1006#95C22×D1311yescharacteristic
1007#95C22×D1311yescharacteristic
1008#95C22×D1311yescharacteristic
1009#95C22×D1311yescharacteristic
1010#95C22×D1311yescharacteristic
1011#95C22×D1311yescharacteristic
1012#95C22×D1311yescharacteristic
1013#95C22×D1311yescharacteristic
1014#95C22×D1311yescharacteristic
1015#95C22×D1311yescharacteristic
1016#95C22×D1311yescharacteristic
1017#95C22×D1311yescharacteristic
1018#95C22×D1311yescharacteristic
1019#95C22×D1311yescharacteristic
1020C2×C13#344411yescharacteristic
1021C2×C13#344411yescharacteristic
1022C2×C13#346111yescharacteristic
1023C2×C13C2×#55211yescharacteristic
1024C2×C13#347511yescharacteristic
1025C2×C13#347511yescharacteristic
1026C2×C13#348211yescharacteristic
1027D13—42no—
1028D13—42no—
1029C24—131no—
1030C24—131no—
1031C2×Q8—22no—
1032C2×Q8—22no—
1033C2×Q8—41no—
1034C2×D4—262no—
1035C2×D4—262no—
1036C2×D4—521no—
1037C22×C4—131no—
1038C22×C4—131no—
1039C22×C4—131no—
1040C22×C4—131no—
1041C22×C4—131no—
1042C22×C4—131no—
1043C22×C4—134no—
1044C22×C4—131no—
1045C22×C4—131no—
1046C22×C4—131no—
1047C22×C4—131no—
1048C22×C4—131no—
1049C22×C4—131no—
1050C22×C4—131no—
1051C22×C4—131no—
1052C22×C4—262no—
1053C22×C4—262no—
1054C22×C4—262no—
1055C22×C4—262no—
1056C22×C4—262no—
1057C22×C4—262no—
1058C22×C4—262no—
1059C22×C4—262no—
1060C22×C4—262no—
1061C22×C4—262no—
1062C22×C4—262no—
1063C22×C4—262no—
1064C22×C4—262no—
1065C22×C4—262no—
1066C22×C4—262no—
1067C22×C4—521no—
1068C22×C4—521no—
1069C22×C4C23×D1311yescharacteristic
1070C22×C4C23×D1311yescharacteristic
1071C22×C4C23×D1311yescharacteristic
1072C22×C4C23×D1311yescharacteristic
1073C22×C4C23×D1311yescharacteristic
1074C22×C4C23×D1311yescharacteristic
1075C22×C4C23×D1311yescharacteristic
1076C22×C4C23×D1311yescharacteristic
1077C22×C4C23×D1311yescharacteristic
1078C22×C4C23×D1311yescharacteristic
1079C22×C4C23×D1311yescharacteristic
1080C22×C4C23×D1311yescharacteristic
1081C22×C4C23×D1311yescharacteristic
1082C22×C4C23×D1311yescharacteristic
1083C22×C4C23×D1311yescharacteristic
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—22no—
1092C4⋊C4—41no—
1093C4⋊C4—134no—
1094C4⋊C4—262no—
1095C4⋊C4—262no—
1096C4⋊C4—262no—
1097C4⋊C4—262no—
1098C4⋊C4—262no—
1099C4⋊C4—262no—
1100C4⋊C4—262no—
1101C4⋊C4—262no—
1102C4⋊C4—262no—
1103C4⋊C4—262no—
1104C4⋊C4—262no—
1105C4⋊C4—262no—
1106C4⋊C4—262no—
1107C4⋊C4—262no—
1108C4⋊C4—262no—
1109C4⋊C4—262no—
1110C4⋊C4—262no—
1111C4⋊C4—262no—
1112C4⋊C4—262no—
1113C4⋊C4—262no—
1114C4⋊C4—262no—
1115C4⋊C4—262no—
1116C4⋊C4—262no—
1117C4⋊C4—262no—
1118C4⋊C4—262no—
1119C4⋊C4—521no—
1120C4⋊C4—521no—
1121C4⋊C4—521no—
1122C4⋊C4—521no—
1123C4⋊C4—521no—
1124C22⋊C4—134no—
1125C22⋊C4—262no—
1126C22⋊C4—262no—
1127C22⋊C4—262no—
1128C22⋊C4—262no—
1129C22⋊C4—262no—
1130C22⋊C4—262no—
1131C22⋊C4—262no—
1132C22⋊C4—262no—
1133C22⋊C4—262no—
1134C22⋊C4—262no—
1135C22⋊C4—262no—
1136C22⋊C4—262no—
1137C22⋊C4—262no—
1138C22⋊C4—262no—
1139C22⋊C4—262no—
1140C22⋊C4—262no—
1141C22⋊C4—262no—
1142C22⋊C4—262no—
1143C22⋊C4—262no—
1144C22⋊C4—521no—
1145C22⋊C4—521no—
1146C42—22no—
1147C42—22no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—41no—
1156C42—134no—
1157C42—262no—
1158C42—262no—
1159C42—262no—
1160C42—262no—
1161C42—262no—
1162C42—262no—
1163C42—262no—
1164C42—262no—
1165C42—262no—
1166C42—262no—
1167C42—262no—
1168C42—262no—
1169C42—262no—
1170C42—262no—
1171C42—262no—
1172C42—521no—
1173C42—521no—
1174C42#612714yes—
1175C13#3487311yescharacteristic, complemented, Sylow
1176C23—132no—
1177C23—132no—
1178C23—261no—
1179C23—261no—
1180C23—261no—
1181C23—261no—
1182C23—261no—
1183C23—261no—
1184C23—261no—
1185C23—261no—
1186C23—261no—
1187C23—261no—
1188C23—261no—
1189C23—261no—
1190C23C24×D1311yescharacteristic
1191Q8—44no—
1192D4—524no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—132no—
1231C2×C4—132no—
1232C2×C4—132no—
1233C2×C4—132no—
1234C2×C4—132no—
1235C2×C4—132no—
1236C2×C4—268no—
1237C2×C4—268no—
1238C2×C4—261no—
1239C2×C4—261no—
1240C2×C4—261no—
1241C2×C4—261no—
1242C2×C4—261no—
1243C2×C4—261no—
1244C2×C4—261no—
1245C2×C4—261no—
1246C2×C4—261no—
1247C2×C4—261no—
1248C2×C4—261no—
1249C2×C4—261no—
1250C2×C4—268no—
1251C2×C4—261no—
1252C2×C4—261no—
1253C2×C4—261no—
1254C2×C4—261no—
1255C2×C4—261no—
1256C2×C4—261no—
1257C2×C4—261no—
1258C2×C4—261no—
1259C2×C4—261no—
1260C2×C4—261no—
1261C2×C4—261no—
1262C2×C4—261no—
1263C2×C4—261no—
1264C2×C4—261no—
1265C2×C4—261no—
1266C2×C4—261no—
1267C2×C4—261no—
1268C2×C4—261no—
1269C2×C4—261no—
1270C2×C4—261no—
1271C2×C4—261no—
1272C2×C4—261no—
1273C2×C4—261no—
1274C2×C4—261no—
1275C2×C4—524no—
1276C2×C4—524no—
1277C2×C4—524no—
1278C2×C4C2×#612712yes—
1279C2×C4C2×#612712yes—
1280C2×C4C2×#612712yes—
1281C2×C4#8825412yes—
1282C2×C4#41×D1312yes—
1283C2×C4#41×D1312yes—
1284C2×C4#41×D1312yes—
1285C2×C4#41×D1312yes—
1286C22—262no—
1287C22—262no—
1288C22—262no—
1289C22—262no—
1290C22—262no—
1291C22—262no—
1292C22—521no—
1293C22—521no—
1294C22—521no—
1295C22—521no—
1296C22—521no—
1297C22—521no—
1298C22—521no—
1299C22—521no—
1300C22C22×#612711yescharacteristic
1301C22C2×#8825411yescharacteristic
1302C22C2×#41×D1311yescharacteristic
1303C22C2×#41×D1311yescharacteristic
1304C22C2×#41×D1311yescharacteristic
1305C22C2×#41×D1311yescharacteristic
1306C22#1171964811yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—22no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—262no—
1322C4—262no—
1323C4—262no—
1324C4—262no—
1325C4—262no—
1326C4—262no—
1327C4—521no—
1328C4—521no—
1329C4—521no—
1330C4—521no—
1331C4—521no—
1332C4—521no—
1333C4—521no—
1334C4—521no—
1335C4#1171928614yes—
1336C2—522no—
1337C2—522no—
1338C2#1312812911yescharacteristic
1339C2#1312813011yescharacteristic
1340C2#1312826711yescharacteristic
1341C2C2×#1171928611yescharacteristic
1342C2#1312838811yescharacteristic
1343C2#1312839011yescharacteristic
1344C2#1312845411yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC13×#2295C2
prime radicalC22×D52C23
hypercenter#2295D13
hypocenterC13#34873
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #2295

Complements

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

NH ≅ G/Ntype
1. #13120541C2semidirect
2. #13120533C2semidirect
3. #13120532C2semidirect
5. #13120238C2semidirect
6. #13120101C2semidirect
7. #13119925C2semidirect
9. #13119717C2semidirect
10. #13119667C2semidirect
11. #13119635C2semidirect
12. #13119629C2semidirect
13. #13119056C2semidirect
15. #13119012C2semidirect
17. #13118141C2semidirect
18. #13118134C2semidirect
19. #13118106C2semidirect
21. C4×#88143C2semidirect
22. C4×#88143C2semidirect
23. C4×#88130C2semidirect
24. C4×#88200C2semidirect
26. #13117331C2semidirect
27. #13117316C2semidirect
29. C4×#88126C2semidirect
30. C4×#88146C2semidirect
31. C13×#2295C2semidirect
531. #2295D13semidirect
1175. C13#34873semidirect

Maximal subgroups

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

subgroupindex
#131205412
#131205332
#131205322
#131205152
#131202382
#131201012
#131199252
#131198872
#131197172
#131196672
#131196352
#131196292
#131190562
#131190442
#131190122
#131189382
#131181412
#131181342
#131181062
#131180992
C4×#881432
C4×#881302
C4×#882002
C4×#881482
#131173312
#131173162
#131172802
C4×#881262
C4×#881462
C13×#22952
#3487313