Finite Group Databasebeta

← #16036224

Subgroups — #16036224

Order 3328.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123220C211yesmaximal, characteristic, complemented
2#13123216C211yesmaximal, characteristic, complemented
3#13123171C211yesmaximal, characteristic, complemented
4#13123143C211yesmaximal, characteristic, complemented
5#13120936C211yesmaximal, characteristic, complemented
6#13120934C211yesmaximal, characteristic, complemented
7#13120891C211yesmaximal, characteristic, complemented
8#13120889C211yesmaximal, characteristic, complemented
9#13120239C211yesmaximal, characteristic, complemented
10#13120231C211yesmaximal, characteristic, complemented
11#13120101C211yesmaximal, characteristic, complemented
12#13120093C211yesmaximal, characteristic, complemented
13#13119378C211yesmaximal, characteristic, complemented
14#13119319C211yesmaximal, characteristic, complemented
15#13119231C211yesmaximal, characteristic, complemented
16#13119215C211yesmaximal, characteristic, complemented
17#13119143C211yesmaximal, characteristic
18#13118690C211yesmaximal, characteristic, complemented
19#13118559C211yesmaximal, characteristic, complemented
20#13118334C211yesmaximal, characteristic, complemented
21#13118315C211yesmaximal, characteristic
22#13118313C211yesmaximal, characteristic
23#13118286C211yesmaximal, characteristic
24#13117504C211yesmaximal, characteristic
25#13117502C211yesmaximal, characteristic
26#13117438C211yesmaximal, characteristic, complemented
27#13117437C211yesmaximal, characteristic, complemented
28#13117368C211yesmaximal, characteristic, complemented
29C2×#11718308C211yesmaximal, characteristic, complemented
30C4×#88135C211yesmaximal, characteristic
31C13×#2493C211yesmaximal, characteristic, complemented
32C2×#88183C2211yescharacteristic
33C2×C4×C22⋊D13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C2×#88150C2211yescharacteristic
40C2×#88143C2211yescharacteristic
41C2×#88141C2211yescharacteristic
42C2×#88140C2211yescharacteristic
43C2×#88135C2211yescharacteristic
44C2×#88135C2211yescharacteristic
45C2×#88132C2211yescharacteristic
46C2×C42×D13C2211yescharacteristic
47C13×#401C2211yescharacteristic
48C13×#400C2211yescharacteristic
49C13×#400C2211yescharacteristic
50C13×#400C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#385C2211yescharacteristic
55C13×#385C2211yescharacteristic
56C13×#383C2211yescharacteristic
57C13×#381C2211yescharacteristic
58C13×#381C2211yescharacteristic
59C13×#380C2211yescharacteristic
60C4×C13×C22⋊C4C2211yescharacteristic
61C2×C13×#95C2211yescharacteristic
62#11718874C2211yescharacteristic
63#11718873C2211yescharacteristic
64#11718872C2211yescharacteristic
65#11718871C2211yescharacteristic
66C2×#88071C2211yescharacteristic
67#11718655C2211yescharacteristic
68#11718654C2211yescharacteristic
69#11718650C2211yescharacteristic
70#11718650C2211yescharacteristic
71#11718650C2211yescharacteristic
72#11718645C2211yescharacteristic
73#11718645C2211yescharacteristic
74#11718642C2211yescharacteristic
75#11718641C2211yescharacteristic
76#11718641C2211yescharacteristic
77#11718639C2211yescharacteristic
78#11718639C2211yescharacteristic
79#11718639C2211yescharacteristic
80#11718639C2211yescharacteristic
81#11718639C2211yescharacteristic
82C4⋊C4×Dic13C2211yescharacteristic
83#11718634C2211yescharacteristic
84#11718634C2211yescharacteristic
85#11718633C2211yescharacteristic
86#11718633C2211yescharacteristic
87#11718633C2211yescharacteristic
88#11718619C2211yescharacteristic
89#11718607C2211yescharacteristic
90#11718604C2211yescharacteristic
91#11718604C2211yescharacteristic
92#11718604C2211yescharacteristic
93#11718603C2211yescharacteristic
94#11718603C2211yescharacteristic
95#11718603C2211yescharacteristic
96C22⋊C4×Dic13C2211yescharacteristic
97C22⋊C4×Dic13C2211yescharacteristic
98C22⋊C4×Dic13C2211yescharacteristic
99C22⋊C4×Dic13C2211yescharacteristic
100C4×#6103C2211yescharacteristic
101#11718598C2211yescharacteristic
102#11718594C2211yescharacteristic
103#11718594C2211yescharacteristic
104#11718594C2211yescharacteristic
105C4×#6101C2211yescharacteristic
106C42×Dic13C2211yescharacteristic
107#11718337C2211yescharacteristic
108#11718336C2211yescharacteristic
109#11718336C2211yescharacteristic
110#11718336C2211yescharacteristic
111#11718336C2211yescharacteristic
112#11718335C2211yescharacteristic
113#11718331C2211yescharacteristic
114#11718331C2211yescharacteristic
115#11718330C2211yescharacteristic
116#11718330C2211yescharacteristic
117#11718329C2211yescharacteristic
118#11718329C2211yescharacteristic
119#11718329C2211yescharacteristic
120#11718328C2211yescharacteristic
121#11718328C2211yescharacteristic
122#11718328C2211yescharacteristic
123#11718327C2211yescharacteristic
124#11718327C2211yescharacteristic
125#11718325C2211yescharacteristic
126#11718325C2211yescharacteristic
127C13⋊#401C2211yescharacteristic
128#11718321C2211yescharacteristic
129#11718321C2211yescharacteristic
130#11718321C2211yescharacteristic
131#11718320C2211yescharacteristic
132#11718319C2211yescharacteristic
133#11718319C2211yescharacteristic
134#11718319C2211yescharacteristic
135#11718319C2211yescharacteristic
136#11718319C2211yescharacteristic
137#11718319C2211yescharacteristic
138#11718319C2211yescharacteristic
139#11718318C2211yescharacteristic
140#11718318C2211yescharacteristic
141#11718318C2211yescharacteristic
142#11718318C2211yescharacteristic
143#11718316C2211yescharacteristic
144#11718316C2211yescharacteristic
145#11718316C2211yescharacteristic
146#11718316C2211yescharacteristic
147#11718316C2211yescharacteristic
148#11718316C2211yescharacteristic
149#11718316C2211yescharacteristic
150#11718315C2211yescharacteristic
151#11718315C2211yescharacteristic
152#11718315C2211yescharacteristic
153#11718315C2211yescharacteristic
154#11718315C2211yescharacteristic
155#11718315C2211yescharacteristic
156#11718315C2211yescharacteristic
157#11718314C2211yescharacteristic
158#11718314C2211yescharacteristic
159#11718314C2211yescharacteristic
160#11718314C2211yescharacteristic
161#11718314C2211yescharacteristic
162#11718313C2211yescharacteristic
163#11718311C2211yescharacteristic
164#11718311C2211yescharacteristic
165#11718311C2211yescharacteristic
166#11718310C2211yescharacteristic
167#11718310C2211yescharacteristic
168#11718310C2211yescharacteristic
169#11718310C2211yescharacteristic
170#11718308C2211yescharacteristic
171#11718308C2211yescharacteristic
172#11718308C2211yescharacteristic
173#11718308C2211yescharacteristic
174#11718308C2211yescharacteristic
175#11718308C2211yescharacteristic
176#11718308C2211yescharacteristic
177#11718308C2211yescharacteristic
178#11718308C2211yescharacteristic
179#11718308C2211yescharacteristic
180#11718308C2211yescharacteristic
181#11718308C2211yescharacteristic
182#11718308C2211yescharacteristic
183#11718307C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C23×C4×C13C2311yescharacteristic
188C23×C4×C13C2311yescharacteristic
189C23×C4×C13C2311yescharacteristic
190C22×C22⋊D13C2311yescharacteristic
191C23×Dic13C2311yescharacteristic
192C23×Dic13C2311yescharacteristic
193C23×Dic13C2311yescharacteristic
194C23×Dic13C2311yescharacteristic
195C22×C4×D13C2311yescharacteristic
196C22×C4×D13C2311yescharacteristic
197C22×C4×D13C2311yescharacteristic
198C22×Dic26C2311yescharacteristic
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×C13×C22⋊C4C2311yescharacteristic
206C2×C13×C22⋊C4C2311yescharacteristic
207C2×C13×C22⋊C4C2311yescharacteristic
208C2×C13×C22⋊C4C2311yescharacteristic
209C2×C42×C13C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C22⋊Dic13C2311yescharacteristic
212C2×C22⋊Dic13C2311yescharacteristic
213C2×C22⋊Dic13C2311yescharacteristic
214#88183—24no—
215C4×C22⋊D13—24no—
216C2×#6103C2311yescharacteristic
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
219C2×#6103C2311yescharacteristic
220C2×#6103C2311yescharacteristic
221C2×#6103C2311yescharacteristic
222C2×#6103C2311yescharacteristic
223C2×#6103C2311yescharacteristic
224C2×#6103C2311yescharacteristic
225C2×#6103C2311yescharacteristic
226C2×#6103C2311yescharacteristic
227C2×C4⋊Dic13—24no—
228C2×C4⋊Dic13C2311yescharacteristic
229C2×C4⋊Dic13C2311yescharacteristic
230C2×C4⋊Dic13C2311yescharacteristic
231C2×C4⋊Dic13C2311yescharacteristic
232C2×C4⋊Dic13C2311yescharacteristic
233C2×C4⋊Dic13C2311yescharacteristic
234C2×C4⋊Dic13C2311yescharacteristic
235C2×C4⋊Dic13C2311yescharacteristic
236C2×C4⋊Dic13C2311yescharacteristic
237C2×#6101—24no—
238C2×#6101—24no—
239C2×#6101—42no—
240C2×#6101C2311yescharacteristic
241C2×#6101C2311yescharacteristic
242C2×#6101C2311yescharacteristic
243C2×#6101C2311yescharacteristic
244C2×#6101C2311yescharacteristic
245C2×#6101C2311yescharacteristic
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×C4×Dic13—42no—
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
285#88150—42no—
286#88143—42no—
287#88141—42no—
288#88140—24no—
289#88135—24no—
290#88135—24no—
291#88132—24no—
292C42×D13—42no—
293C13×#95C2311yescharacteristic
294C13×#95C2311yescharacteristic
295C13×#95C2311yescharacteristic
296C13×#95C2311yescharacteristic
297C13×#95C2311yescharacteristic
298C13×#95C2311yescharacteristic
299C13×#95C2311yescharacteristic
300C13×#95C2311yescharacteristic
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
305C13×#95C2311yescharacteristic
306C13×#95C2311yescharacteristic
307C13×#95C2311yescharacteristic
308C13×#95C2311yescharacteristic
309C13×#95C2311yescharacteristic
310C13×#95C2311yescharacteristic
311C13×#95C2311yescharacteristic
312C13×#95C2311yescharacteristic
313#88071C2311yescharacteristic
314#88071C2311yescharacteristic
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#35026—131nomaximal, Sylow
358C24×C13C2411yescharacteristic
359C23×D13C2411yescharacteristic
360C22×C4×C13—22no—
361C22×C4×C13—22no—
362C22×C4×C13—22no—
363C22×C4×C13—22no—
364C22×C4×C13—22no—
365C22×C4×C13—22no—
366C22×C4×C13—41no—
367C22×C4×C13—41no—
368C22×C4×C13—41no—
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×C4×C13C2411yescharacteristic
379C22×C4×C13C2411yescharacteristic
380C22×C4×C13C2411yescharacteristic
381C22×C4×C13C2411yescharacteristic
382C22×C4×C13C2411yescharacteristic
383C2×C22⋊D13—22no—
384C2×C22⋊D13—22no—
385C2×C22⋊D13#4114yes—
386C22×Dic13—22no—
387C22×Dic13—22no—
388C22×Dic13—22no—
389C22×Dic13—22no—
390C22×Dic13—22no—
391C22×Dic13—22no—
392C22×Dic13—41no—
393C22×Dic13—41no—
394C22×Dic13—41no—
395C22×Dic13—41no—
396C22×Dic13#4114yes—
397C22×Dic13#4114yes—
398C22×Dic13C2411yescharacteristic
399C22×Dic13C2411yescharacteristic
400C22×Dic13C2411yescharacteristic
401C22×Dic13C2411yescharacteristic
402C22×Dic13C2411yescharacteristic
403C22×Dic13C2411yescharacteristic
404C22×Dic13C2411yescharacteristic
405C22×Dic13C2411yescharacteristic
406C22×Dic13C2411yescharacteristic
407C22×Dic13C2411yescharacteristic
408C22×Dic13C2411yescharacteristic
409C22×Dic13C2411yescharacteristic
410C22×Dic13C2411yescharacteristic
411C22×Dic13C2411yescharacteristic
412C22×Dic13C2411yescharacteristic
413C2×C4×D13—22no—
414C2×C4×D13—22no—
415C2×C4×D13—22no—
416C2×C4×D13—22no—
417C2×C4×D13—22no—
418C2×C4×D13—22no—
419C2×C4×D13—41no—
420C2×C4×D13—41no—
421C2×C4×D13—41no—
422C2×Dic26—22no—
423C2×Dic26—22no—
424C2×Dic26—22no—
425C13×C4⋊C4—22no—
426C13×C4⋊C4—41no—
427C13×C4⋊C4—41no—
428C13×C4⋊C4—41no—
429C13×C4⋊C4—41no—
430C13×C4⋊C4—41no—
431C13×C22⋊C4—22no—
432C13×C22⋊C4—22no—
433C13×C22⋊C4—22no—
434C13×C22⋊C4—22no—
435C42×C13—22no—
436C42×C13—41no—
437C22⋊Dic13—22no—
438C22⋊Dic13—22no—
439C22⋊Dic13—22no—
440#6103—22no—
441#6103—22no—
442#6103—22no—
443#6103—22no—
444#6103—22no—
445#6103—22no—
446#6103—22no—
447#6103—41no—
448#6103—41no—
449#6103—41no—
450#6103—41no—
451C4⋊Dic13—22no—
452C4⋊Dic13—22no—
453C4⋊Dic13—22no—
454C4⋊Dic13—22no—
455C4⋊Dic13—22no—
456C4⋊Dic13—22no—
457C4⋊Dic13—22no—
458C4⋊Dic13—41no—
459C4⋊Dic13—41no—
460#6101—22no—
461#6101—22no—
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—41no—
481#6101—41no—
482#6101—41no—
483#6101—41no—
484#6101—41no—
485#6101—41no—
486#6101—41no—
487#6101—41no—
488#6101—41no—
489C4×Dic13—22no—
490C4×Dic13—22no—
491C4×Dic13—22no—
492C4×Dic13—22no—
493C4×Dic13—22no—
494C4×Dic13—22no—
495C4×Dic13—22no—
496C4×Dic13—41no—
497C4×Dic13—41no—
498C4×Dic13—41no—
499C4×Dic13—41no—
500C4×Dic13—41no—
501C4×Dic13—41no—
502C4×Dic13—41no—
503C4×Dic13—41no—
504#2864—131no—
505#2863—131no—
506#2855—131no—
507#2851—131no—
508#2655—131no—
509#2655—131no—
510#2652—131no—
511#2652—131no—
512#2585—131no—
513#2585—131no—
514#2573—131no—
515#2573—131no—
516#2509—131no—
517#2503—131no—
518#2494—131no—
519#2493—131no—
520#2493D1311yescharacteristic, complemented
521#2486—131no—
522#2453—131no—
523#2442—131no—
524#2421—131no—
525#2419—131no—
526#2419—131no—
527#2417—131no—
528#2322—131no—
529#2322—131no—
530#2313—131no—
531#2313—131no—
532C4×C22⋊Q8—131no—
533C2×#389—131no—
534C42×D4—131no—
535C23×C13—21no—
536C23×C13—21no—
537C23×C13—21no—
538C23×C13—21no—
539C23×C13C2×#4112yes—
540C23×C13C2×#4112yes—
541C23×C13C2×#4112yes—
542C23×C13C2511yescharacteristic
543C22×D13—21no—
544C22×D13—21no—
545C22×D13—21no—
546C22×D13—21no—
547C22×D13—21no—
548C22×D13—21no—
549C22×D13C2×#4112yes—
550C2×C4×C13—21no—
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×C13—21no—
589C2×C4×C13—21no—
590C2×C4×C13—21no—
591C2×C4×C13—44no—
592C2×C4×C13—44no—
593C2×C4×C13—82no—
594C2×C4×C132−1+412yes—
595C22⋊D13—28no—
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—28no—
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×Dic13—21no—
633C2×Dic13—21no—
634C2×Dic13—21no—
635C2×Dic13—44no—
636C2×Dic13—44no—
637C2×Dic13—82no—
638C2×Dic13C2×#4112yes—
639C2×Dic13C2×#4112yes—
640C2×Dic13C2×#4112yes—
641C2×Dic13C2×#4112yes—
642C2×Dic13C2×#4112yes—
643C2×Dic13H(5,𝔽2)12yes—
644C2×Dic132−1+412yes—
645C4×D13—44no—
646C4×D13—44no—
647C4×D13—44no—
648Dic26—44no—
649C2×#125—131no—
650C2×#123—131no—
651C2×#123—131no—
652C2×C22⋊Q8—131no—
653C2×C22⋊Q8—131no—
654C2×C4×Q8—131no—
655C2×C4×D4—131no—
656C2×C4×D4—131no—
657C2×C4×D4—131no—
658C22×C4⋊C4—131no—
659C22×C4⋊C4—131no—
660C22×C4⋊C4—131no—
661C22×C4⋊C4—131no—
662C22×C42—131no—
663C22×C42—131no—
664#401—131no—
665#401C2×D1311yescharacteristic
666#400—131no—
667#400—131no—
668#400—131no—
669#400—131no—
670#400—131no—
671#400—131no—
672#400—131no—
673#400—131no—
674#400—131no—
675#400—131no—
676#400—131no—
677#400C2×D1311yescharacteristic
678#400C2×D1311yescharacteristic
679#400C2×D1311yescharacteristic
680#398—131no—
681#398—131no—
682#398—131no—
683#398—131no—
684#398—131no—
685#398—131no—
686#398—131no—
687#398—131no—
688#397—131no—
689#397—131no—
690#397—131no—
691#397—131no—
692#397—131no—
693#397—131no—
694#396—131no—
695#396—131no—
696#391—131no—
697#391—131no—
698#391—131no—
699#391—131no—
700#389—131no—
701#389—131no—
702#389—131no—
703#389—131no—
704#389—131no—
705#389—131no—
706#389—131no—
707#389—131no—
708#389—131no—
709#389—131no—
710#389—131no—
711#389—131no—
712#389—131no—
713#389—131no—
714#389—131no—
715#389—131no—
716#389—131no—
717#389—131no—
718#388—131no—
719#388—131no—
720#388—131no—
721#388—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#387—131no—
739#387—131no—
740#387—131no—
741#387—131no—
742#387—131no—
743#387—131no—
744#387—131no—
745#387—131no—
746#387—131no—
747#387—131no—
748#387—131no—
749#387—131no—
750#387—131no—
751#387C2×D1311yescharacteristic
752#387C2×D1311yescharacteristic
753#387C2×D1311yescharacteristic
754#386—131no—
755#386—131no—
756#385—131no—
757#385—131no—
758#385—131no—
759#385—131no—
760#385—131no—
761#385—131no—
762#385—131no—
763#385—131no—
764#385C2×D1311yescharacteristic
765#385C2×D1311yescharacteristic
766#383—131no—
767#383C2×D1311yescharacteristic
768#382—131no—
769#382—131no—
770#382—131no—
771#381—131no—
772#381—131no—
773#381—131no—
774#381—131no—
775#381—131no—
776#381—131no—
777#381C2×D1311yescharacteristic
778#381C2×D1311yescharacteristic
779#380—131no—
780#380—131no—
781#380—131no—
782#380—131no—
783#380—131no—
784#380—131no—
785#380—131no—
786#380C2×D1311yescharacteristic
787C4×C4⋊C4—131no—
788C4×C4⋊C4—131no—
789C4×C4⋊C4—131no—
790C4×C4⋊C4—131no—
791C4×C4⋊C4—131no—
792C4×C4⋊C4—131no—
793C4×C22⋊C4—131no—
794C4×C22⋊C4—131no—
795C4×C22⋊C4—131no—
796C4×C22⋊C4—131no—
797C4×C22⋊C4—131no—
798C4×C22⋊C4—131no—
799C4×C22⋊C4—131no—
800C4×C22⋊C4C2×D1311yescharacteristic
801C2×#95—131no—
802C2×#95C2×D1311yescharacteristic
803C43—131no—
804C22×C13—22no—
805C22×C13—22no—
806C22×C13—22no—
807C22×C13—22no—
808C22×C13—22no—
809C22×C13—22no—
810C22×C13#52914yes—
811C22×C13C22×#4111yescharacteristic
812C22×C13C22×#4111yescharacteristic
813C22×C13C22×#4111yescharacteristic
814C22×C13C2×H(5,𝔽2)11yescharacteristic
815C22×C13C2×2−1+411yescharacteristic
816C22×C13C2×2−1+411yescharacteristic
817C22×C13#58511yescharacteristic
818C2×D13—22no—
819C2×D13—22no—
820C2×D13—22no—
821C2×D13—41no—
822C2×D13—41no—
823C2×D13—41no—
824C2×D13—41no—
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—41no—
836C4×C13—41no—
837C4×C13—41no—
838C4×C13—41no—
839Dic13—22no—
840Dic13—22no—
841Dic13—22no—
842Dic13—22no—
843Dic13—41no—
844Dic13—41no—
845Dic13—41no—
846Dic13—41no—
847Dic13—41no—
848Dic13—41no—
849Dic13—41no—
850Dic13—41no—
851Dic13—41no—
852Dic13—41no—
853Dic13#53914yes—
854C22×Q8—131no—
855C22×D4—131no—
856C23×C4—131no—
857C23×C4—131no—
858C23×C4—131no—
859C23×C4—131no—
860C23×C4—131no—
861C23×C4—131no—
862C23×C4—131no—
863C23×C4C22×D1311yescharacteristic
864C23×C4C22×D1311yescharacteristic
865C23×C4C22×D1311yescharacteristic
866#125—522no—
867#123—264no—
868#123—264no—
869C22⋊Q8—264no—
870C22⋊Q8—522no—
871C4×Q8—522no—
872C4×D4—264no—
873C4×D4—264no—
874C4×D4—264no—
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⋊C4—131no—
903C2×C4⋊C4—131no—
904C2×C4⋊C4—131no—
905C2×C4⋊C4—131no—
906C2×C4⋊C4—131no—
907C2×C4⋊C4—131no—
908C2×C4⋊C4—131no—
909C2×C4⋊C4—131no—
910C2×C4⋊C4—131no—
911C2×C4⋊C4—131no—
912C2×C4⋊C4—131no—
913C2×C4⋊C4—264no—
914C2×C4⋊C4—264no—
915C2×C4⋊C4—264no—
916C2×C4⋊C4—522no—
917C2×C4⋊C4C22×D1311yescharacteristic
918C2×C4⋊C4C22×D1311yescharacteristic
919C2×C4⋊C4C22×D1311yescharacteristic
920C2×C4⋊C4C22×D1311yescharacteristic
921C2×C4⋊C4C22×D1311yescharacteristic
922C2×C4⋊C4C22×D1311yescharacteristic
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×C22⋊C4—131no—
934C2×C22⋊C4—131no—
935C2×C22⋊C4—131no—
936C2×C22⋊C4—131no—
937C2×C22⋊C4C22×D1311yescharacteristic
938C2×C22⋊C4C22×D1311yescharacteristic
939C2×C22⋊C4C22×D1311yescharacteristic
940C2×C22⋊C4C22×D1311yescharacteristic
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—131no—
952C2×C42—131no—
953C2×C42—131no—
954C2×C42—131no—
955C2×C42—131no—
956C2×C42—522no—
957C2×C42—522no—
958C2×C42C22×D1311yescharacteristic
959C2×C42C22×D1311yescharacteristic
960#95—131no—
961#95—131no—
962#95—131no—
963#95—131no—
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#95C22×D1311yescharacteristic
1005#95C22×D1311yescharacteristic
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
1020#95C22×D1311yescharacteristic
1021#95C22×D1311yescharacteristic
1022#95C22×D1311yescharacteristic
1023#95C22×D1311yescharacteristic
1024C2×C13—24no—
1025C2×C13C2×#52911yescharacteristic
1026C2×C13C2×#53911yescharacteristic
1027C2×C13#346111yescharacteristic
1028C2×C13#350511yescharacteristic
1029C2×C13#350911yescharacteristic
1030C2×C13#351511yescharacteristic
1031C2×C13#352011yescharacteristic
1032D13—42no—
1033C24—131no—
1034C24C23×D1311yescharacteristic
1035C2×Q8—262no—
1036C2×Q8—262no—
1037C2×Q8—262no—
1038C2×D4—134no—
1039C2×D4—262no—
1040C2×D4—262no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—131no—
1051C22×C4—134no—
1052C22×C4—131no—
1053C22×C4—131no—
1054C22×C4—131no—
1055C22×C4—131no—
1056C22×C4—134no—
1057C22×C4—131no—
1058C22×C4—131no—
1059C22×C4—131no—
1060C22×C4—131no—
1061C22×C4—131no—
1062C22×C4—131no—
1063C22×C4—131no—
1064C22×C4—131no—
1065C22×C4—131no—
1066C22×C4—131no—
1067C22×C4—262no—
1068C22×C4—262no—
1069C22×C4—262no—
1070C22×C4—262no—
1071C22×C4—262no—
1072C22×C4—262no—
1073C22×C4—262no—
1074C22×C4—262no—
1075C22×C4—262no—
1076C22×C4—262no—
1077C22×C4—262no—
1078C22×C4—262no—
1079C22×C4—521no—
1080C22×C4—521no—
1081C22×C4—521no—
1082C22×C4—521no—
1083C22×C4—521no—
1084C22×C4—521no—
1085C22×C4—521no—
1086C22×C4C23×D1311yescharacteristic
1087C22×C4C23×D1311yescharacteristic
1088C22×C4C23×D1311yescharacteristic
1089C22×C4C23×D1311yescharacteristic
1090C22×C4C23×D1311yescharacteristic
1091C22×C4C23×D1311yescharacteristic
1092C22×C4C23×D1311yescharacteristic
1093C22×C4C23×D1311yescharacteristic
1094C22×C4C23×D1311yescharacteristic
1095C22×C4C23×D1311yescharacteristic
1096C22×C4C23×D1311yescharacteristic
1097C22×C4C23×D1311yescharacteristic
1098C22×C4C23×D1311yescharacteristic
1099C22×C4C23×D1311yescharacteristic
1100C4⋊C4—22no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
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—262no—
1120C4⋊C4—262no—
1121C4⋊C4—262no—
1122C4⋊C4—262no—
1123C4⋊C4—262no—
1124C4⋊C4—262no—
1125C4⋊C4—262no—
1126C4⋊C4—262no—
1127C4⋊C4—262no—
1128C4⋊C4—262no—
1129C4⋊C4—262no—
1130C4⋊C4—262no—
1131C4⋊C4—262no—
1132C4⋊C4—262no—
1133C4⋊C4—521no—
1134C4⋊C4—521no—
1135C4⋊C4—521no—
1136C4⋊C4—521no—
1137C4⋊C4—521no—
1138C4⋊C4—521no—
1139C4⋊C4—521no—
1140C4⋊C4—521no—
1141C4⋊C4—521no—
1142C4⋊C4—521no—
1143C4⋊C4—521no—
1144C22⋊C4—22no—
1145C22⋊C4—22no—
1146C22⋊C4—22no—
1147C22⋊C4—22no—
1148C22⋊C4—262no—
1149C22⋊C4—262no—
1150C22⋊C4—262no—
1151C22⋊C4—262no—
1152C22⋊C4—262no—
1153C22⋊C4—262no—
1154C22⋊C4—262no—
1155C22⋊C4—262no—
1156C22⋊C4—262no—
1157C22⋊C4—262no—
1158C22⋊C4—521no—
1159C22⋊C4—521no—
1160C22⋊C4—521no—
1161C22⋊C4—521no—
1162C42—22no—
1163C42—41no—
1164C42—262no—
1165C42—262no—
1166C42—262no—
1167C42—262no—
1168C42—262no—
1169C42—262no—
1170C42—262no—
1171C42—521no—
1172C42—521no—
1173C42—521no—
1174C42—521no—
1175C42—521no—
1176C42—521no—
1177C42—521no—
1178C42—521no—
1179C13#3502611yescharacteristic, complemented, Sylow
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—132no—
1185C23—261no—
1186C23—261no—
1187C23—261no—
1188C23—261no—
1189C23—261no—
1190C23—261no—
1191C23#41×D1312yes—
1192C23#41×D1312yes—
1193C23#41×D1312yes—
1194C23C24×D1311yescharacteristic
1195Q8—524no—
1196D4—268no—
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—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—82no—
1241C2×C4—132no—
1242C2×C4—132no—
1243C2×C4—132no—
1244C2×C4—132no—
1245C2×C4—132no—
1246C2×C4—132no—
1247C2×C4—132no—
1248C2×C4—268no—
1249C2×C4—261no—
1250C2×C4—261no—
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—261no—
1276C2×C4—261no—
1277C2×C4—261no—
1278C2×C4—261no—
1279C2×C4—261no—
1280C2×C4—261no—
1281C2×C4—261no—
1282C2×C4—261no—
1283C2×C4—261no—
1284C2×C4—261no—
1285C2×C4—261no—
1286C2×C4—261no—
1287C2×C4—524no—
1288C2×C4—524no—
1289C2×C4—524no—
1290C2×C4—524no—
1291C2×C4—524no—
1292C2×C4—1042no—
1293C2×C4#8825712yes—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—262no—
1301C22—262no—
1302C22—262no—
1303C22—521no—
1304C22—521no—
1305C22—521no—
1306C22—521no—
1307C22#1171941114yes—
1308C22C2×#41×D1311yescharacteristic
1309C22C2×#41×D1311yescharacteristic
1310C22C2×#41×D1311yescharacteristic
1311C22C2×#8825711yescharacteristic
1312C22#1171964811yescharacteristic
1313C22D13×H(5,𝔽2)11yescharacteristic
1314C22D13×2−1+411yescharacteristic
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—134no—
1330C4—262no—
1331C4—262no—
1332C4—262no—
1333C4—262no—
1334C4—521no—
1335C4—521no—
1336C4—521no—
1337C4—521no—
1338C4—521no—
1339C4—521no—
1340C4—521no—
1341C4—521no—
1342C4—521no—
1343C4—521no—
1344C2—24no—
1345C2—522no—
1346C2C2×#1171941111yescharacteristic
1347C2D13×#53911yescharacteristic
1348C2#1312826511yescharacteristic
1349C2#1312866711yescharacteristic
1350C2#1312871411yescharacteristic
1351C2#1312880311yescharacteristic
1352C2#1312887411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2493C2
prime radicalC22×C22⋊D13C23
hypercenter#2493D13
hypocenterC13#35026
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2493

Complements

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

NH ≅ G/Ntype
1. #13123220C2semidirect
2. #13123216C2semidirect
3. #13123171C2semidirect
4. #13123143C2semidirect
5. #13120936C2semidirect
6. #13120934C2semidirect
7. #13120891C2semidirect
8. #13120889C2semidirect
9. #13120239C2semidirect
10. #13120231C2semidirect
11. #13120101C2semidirect
12. #13120093C2semidirect
13. #13119378C2semidirect
14. #13119319C2semidirect
15. #13119231C2semidirect
16. #13119215C2semidirect
18. #13118690C2semidirect
19. #13118559C2semidirect
20. #13118334C2semidirect
26. #13117438C2semidirect
27. #13117437C2semidirect
28. #13117368C2semidirect
29. C2×#11718308C2semidirect
31. C13×#2493C2semidirect
520. #2493D13semidirect
1179. C13#35026semidirect

Maximal subgroups

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

subgroupindex
#131232202
#131232162
#131231712
#131231432
#131209362
#131209342
#131208912
#131208892
#131202392
#131202312
#131201012
#131200932
#131193782
#131193192
#131192312
#131192152
#131191432
#131186902
#131185592
#131183342
#131183152
#131183132
#131182862
#131175042
#131175022
#131174382
#131174372
#131173682
C2×#117183082
C4×#881352
C13×#24932
#3502613