Finite Group Databasebeta

← #16022484

Subgroups — #16022484

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719332C211yesmaximal, characteristic
2C2×C4×#6131C211yesmaximal, characteristic, complemented
3C2×D13×#117C211yesmaximal, characteristic, complemented
4#13117874C211yesmaximal, characteristic, complemented
5#13117872C211yesmaximal, characteristic, complemented
6#13117867C211yesmaximal, characteristic, complemented
7#13117854C211yesmaximal, characteristic, complemented
8#13117851C211yesmaximal, characteristic, complemented
9#13117846C211yesmaximal, characteristic, complemented
10#13117837C211yesmaximal, characteristic, complemented
11#13117833C212yesmaximal, complemented
12#13117821C212yesmaximal, complemented
13#13117814C212yesmaximal, complemented
14#13117814C212yesmaximal, complemented
15#13117325C211yesmaximal, characteristic, complemented
16#13117317C211yesmaximal, characteristic, complemented
17#13117296C212yesmaximal, complemented
18#13117278C212yesmaximal, complemented
19#13117274C212yesmaximal, complemented
20C4×#88147C212yesmaximal, complemented
21C4×#88146C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic, complemented
23C13×#2362C211yesmaximal, characteristic, complemented
24C22×#6131C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic, complemented
28C2×C13×#117C2211yescharacteristic
29C2×#88200C2211yescharacteristic
30C2×Q8×Dic13C2211yescharacteristic, complemented
31C2×#88184C2211yescharacteristic
32C2×#88180C2211yescharacteristic
33#11719332C4116yescomplemented
34C4×#6131—28no—
35D13×#117—28no—
36C2×#88149C2211yescharacteristic
37C2×#88148C2212yes—
38C2×#88147C2212yes—
39C2×#88147C2212yes—
40C2×#88147C2212yes—
41C2×#88147C2211yescharacteristic, complemented
42C2×#88146C2211yescharacteristic
43C2×#88146C2211yescharacteristic
44C2×#88146C2211yescharacteristic
45C2×#88146C2212yescomplemented
46C2×C4⋊C4×D13C2211yescharacteristic
47C2×C4⋊C4×D13C2211yescharacteristic
48C2×#88136C2212yes—
49C2×#88135C2212yes—
50C2×C22⋊C4×D13C2212yes—
51C2×C22⋊C4×D13C2211yescharacteristic
52C2×C22⋊C4×D13C2211yescharacteristic
53C2×#88131C2212yes—
54C2×C4×D52C2212yes—
55C2×C4×D52C2212yes—
56C2×C4×D52C2211yescharacteristic, complemented
57C2×#88126C2212yes—
58C2×C42×D13C2212yes—
59C2×C42×D13C2211yescharacteristic
60C2×C42×D13C2211yescharacteristic
61C2×C42×D13C2212yescomplemented
62C13×#391C2211yescharacteristic, complemented
63C13×#389C2211yescharacteristic, complemented
64C13×#388C2212yes—
65C13×#388C2212yes—
66C13×#387C2212yescomplemented
67C4×C13×C4⋊C4C2212yescomplemented
68C4×C13×C4⋊C4C2211yescharacteristic, complemented
69C4×C13×C22⋊C4C2211yescharacteristic
70#11718891C2211yescharacteristic, complemented
71C4×C22⋊Dic13C2211yescharacteristic
72#11718650C2212yes—
73#11718650C2212yes—
74#11718650C2212yescomplemented
75#11718649C2211yescharacteristic, complemented
76#11718646C2211yescharacteristic, complemented
77#11718642C2212yescomplemented
78C4⋊C4×Dic13C2212yescomplemented
79C4⋊C4×Dic13C2212yescomplemented
80C4⋊C4×Dic13C2211yescharacteristic, complemented
81C4⋊C4×Dic13C2211yescharacteristic, complemented
82#11718634C2211yescharacteristic, complemented
83#11718633C2212yescomplemented
84#11718618C2212yes—
85#11718618C2212yes—
86#11718617C2212yes—
87#11718617C2212yes—
88#11718612C2212yes—
89#11718612C2212yes—
90C22⋊C4×Dic13C2211yescharacteristic
91C22⋊C4×Dic13C2211yescharacteristic
92#11718601C2212yescomplemented
93#11718601C2212yescomplemented
94#11718600C2211yescharacteristic, complemented
95C4×#6103C2212yes—
96C4×#6103C2212yes—
97C4×#6103C2211yescharacteristic
98C4×#6103C2211yescharacteristic
99C4×#6103C2212yescomplemented
100C4×C4⋊Dic13C2211yescharacteristic, complemented
101#11718594C2212yescomplemented
102C42×Dic13C2212yescomplemented
103#11718589C2211yescharacteristic, complemented
104#11718330C2212yescomplemented
105#11718330C2212yescomplemented
106#11718329C2212yes—
107#11718329C2212yes—
108#11718329C2212yescomplemented
109#11718327C2211yescharacteristic
110#11718327C2212yes—
111#11718327C2212yes—
112#11718327C2211yescharacteristic
113#11718327C2212yescomplemented
114#11718327C2212yescomplemented
115#11718327C2212yescomplemented
116#11718326C2212yes—
117#11718326C2212yes—
118#11718326C2212yes—
119#11718326C2212yes—
120D13×#95C2211yescharacteristic
121D13×#95C2211yescharacteristic
122#11718313C2212yescomplemented
123#11718310C2212yescomplemented
124#11718309C2212yescomplemented
125#11718308C2212yescomplemented
126C24×D13C2311yescharacteristic
127C22×Q8×C13C2311yescharacteristic
128C23×C4×C13C2311yescharacteristic
129C22×C22⋊D13C2312yes—
130C23×Dic13C2311yescharacteristic
131C2×#6131—24no—
132C2×#6131—24no—
133C2×#6131C2×C418yescomplemented
134C22×D52C2312yes—
135C22×D52C2312yes—
136C22×D52C2311yescharacteristic
137C22×C4×D13—24no—
138C22×C4×D13—24no—
139C22×C4×D13C2×C418yescomplemented
140C22×C4×D13C2311yescharacteristic
141C22×C4×D13C2312yes—
142C22×C4×D13C2312yes—
143C22×C4×D13C2311yescharacteristic
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2312yes—
147C22×C4×D13C2312yes—
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2312yes—
150C22×C4×D13C2311yescharacteristic
151C22×C4×D13C2311yescharacteristic
152C22×C4×D13C2311yescharacteristic
153C13×C22⋊Q8C2×C418yescomplemented
154C4×Q8×C13—24no—
155C13×#117—24no—
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2311yescharacteristic
159C2×C13×C4⋊C4C2312yes—
160C2×C13×C4⋊C4C2311yescharacteristic
161C2×C13×C4⋊C4C2311yescharacteristic
162C2×C13×C22⋊C4C2311yescharacteristic
163C2×C13×C22⋊C4C2311yescharacteristic
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2312yes—
169C2×C42×C13C2312yes—
170C2×C42×C13C2312yes—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2311yescharacteristic
173C2×C22⋊Dic13C2311yescharacteristic
174#88200C2×C418yescomplemented
175Q8×Dic13—24no—
176#88184C2×C418yescomplemented
177C2×#6103C2312yes—
178C2×#6103C2312yes—
179C2×#6103C2312yes—
180C2×#6103C2312yes—
181C2×#6103C2311yescharacteristic
182C2×#6103C2311yescharacteristic
183C2×#6103C2312yes—
184C2×#6103C2312yes—
185C2×#6103C2312yes—
186C2×#6103C2312yes—
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2311yescharacteristic
192C2×#6103C2311yescharacteristic
193#88180—24no—
194C2×C4⋊Dic13C2312yes—
195C2×C4⋊Dic13C2312yes—
196C2×C4⋊Dic13C2311yescharacteristic
197C2×C4⋊Dic13C2311yescharacteristic
198C2×C4⋊Dic13C2311yescharacteristic
199C2×#6101C2312yes—
200C2×#6101C2312yes—
201C2×#6101C2312yes—
202C2×#6101C2312yes—
203C2×#6101C2312yes—
204C2×C4×Dic13C2311yescharacteristic
205C2×C4×Dic13C2312yes—
206C2×C4×Dic13C2312yes—
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2311yescharacteristic
209C2×C4×Dic13C2311yescharacteristic
210C2×C4×Dic13C2311yescharacteristic
211C2×C4×Dic13C2311yescharacteristic
212C2×C4×Dic13C2312yes—
213C2×C4×Dic13C2312yes—
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2312yes—
216C2×C4×Dic13C2312yes—
217C2×C4×Dic13C2312yes—
218#88149C2×C418yescomplemented
219#88148C2×C4116yescomplemented
220#88147—24no—
221#88147—28no—
222#88147—28no—
223#88147C2×C4116yescomplemented
224#88146—24no—
225#88146—28no—
226#88146C2×C418yescomplemented
227#88146D418yescomplemented
228C4⋊C4×D13—24no—
229C4⋊C4×D13—24no—
230#88136C2×C4116yescomplemented
231#88135C2×C4116yescomplemented
232C22⋊C4×D13—28no—
233C22⋊C4×D13—24no—
234C22⋊C4×D13—24no—
235#88131—28no—
236C4×D52—28no—
237C4×D52—28no—
238C4×D52—24no—
239#88126—28no—
240C42×D13—24no—
241C42×D13—24no—
242C42×D13—28no—
243C42×D13—28no—
244C13×#95C2311yescharacteristic
245C13×#95C2311yescharacteristic
246C13×#95C2312yes—
247C13×#95C2312yes—
248C13×#95C2312yes—
249C13×#95C2312yes—
250#88071C2311yescharacteristic
251#88071C2312yes—
252#88071C2312yes—
253#88071C2312yes—
254#88071C2312yes—
255#88071C2311yescharacteristic
256#88071C2312yes—
257#88071C2311yescharacteristic
258#88071C2311yescharacteristic
259#88071C2311yescharacteristic
260#88071C2311yescharacteristic
261#88071C2312yes—
262#88071C2312yes—
263#88071C2312yes—
264#34136—131nomaximal, Sylow
265C24×C13C2411yescharacteristic
266C23×D13—22no—
267C23×D13—22no—
268C23×D13—22no—
269C23×D13—22no—
270C23×D13—41no—
271C23×D13—41no—
272C23×D13C22×C414yes—
273C23×D13C2412yes—
274C23×D13C2411yescharacteristic
275C23×D13C2411yescharacteristic
276C2×Q8×C13—22no—
277C2×Q8×C13—22no—
278C2×Q8×C13C22×C414yes—
279C22×C4×C13—22no—
280C22×C4×C13—22no—
281C22×C4×C13C22×C414yes—
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2412yes—
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2412yes—
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2412yes—
288C22×C4×C13C2412yes—
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2411yescharacteristic
291C22×C4×C13C2411yescharacteristic
292C2×C22⋊D13—42no—
293C2×C22⋊D13—42no—
294C2×C22⋊D13C22×C418yes—
295C22×Dic13—22no—
296C22×Dic13—22no—
297C22×Dic13C22×C414yes—
298C22×Dic13C2411yescharacteristic
299C22×Dic13C2412yes—
300C22×Dic13C2411yescharacteristic
301C22×Dic13C2412yes—
302C22×Dic13C2411yescharacteristic
303C22×Dic13C2412yes—
304C22×Dic13C2411yescharacteristic
305C22×Dic13C2411yescharacteristic
306C22×Dic13C2411yescharacteristic
307#6131—232no—
308C2×D52—24no—
309C2×D52—24no—
310C2×D52—24no—
311C2×D52—24no—
312C2×D52—22no—
313C2×D52—22no—
314C2×D52C22×C418yes—
315C2×D52C22×C418yes—
316C2×D52C22×C414yes—
317C2×C4×D13—22no—
318C2×C4×D13—22no—
319C2×C4×D13—22no—
320C2×C4×D13—22no—
321C2×C4×D13—22no—
322C2×C4×D13—24no—
323C2×C4×D13—22no—
324C2×C4×D13—24no—
325C2×C4×D13—232no—
326C2×C4×D13—22no—
327C2×C4×D13—22no—
328C2×C4×D13—22no—
329C2×C4×D13—22no—
330C2×C4×D13—24no—
331C2×C4×D13—24no—
332C2×C4×D13—24no—
333C2×C4×D13—24no—
334C2×C4×D13—22no—
335C2×C4×D13—22no—
336C2×C4×D13—24no—
337C2×C4×D13—24no—
338C2×C4×D13—24no—
339C2×C4×D13—24no—
340C2×C4×D13—22no—
341C2×C4×D13—22no—
342C2×C4×D13—42no—
343C2×C4×D13—42no—
344C2×C4×D13—41no—
345C2×C4×D13—42no—
346C2×C4×D13—41no—
347C2×C4×D13—41no—
348C2×C4×D13—42no—
349C2×C4×D13—41no—
350C2×C4×D13C22×C418yes—
351C2×C4×D13C22×C414yes—
352C2×C4×D13C22×C414yes—
353C2×C4×D13C22×C414yes—
354C2×C4×D13C22×C414yes—
355C2×C4×D13C2×D414yes—
356C2×C4×D13#4114yes—
357C13×C4⋊C4—22no—
358C13×C4⋊C4—24no—
359C13×C4⋊C4—24no—
360C13×C4⋊C4C22×C414yes—
361C13×C4⋊C4C22×C418yes—
362C13×C4⋊C4C2×D414yes—
363C13×C22⋊C4—24no—
364C13×C22⋊C4—22no—
365C13×C22⋊C4—22no—
366C13×C22⋊C4C22×C418yes—
367C42×C13—24no—
368C42×C13—24no—
369C42×C13—22no—
370C42×C13—22no—
371C42×C13—24no—
372C22⋊Dic13—24no—
373C22⋊Dic13—22no—
374C22⋊Dic13—22no—
375#6103—24no—
376#6103—22no—
377#6103—22no—
378#6103—24no—
379#6103—24no—
380#6103—24no—
381#6103—24no—
382#6103—42no—
383#6103—42no—
384#6103C22×C418yes—
385#6103C22×C418yes—
386#6103C22×C418yes—
387#6103C22×C418yes—
388#6103C2×D418yes—
389#6103#4114yescomplemented
390#6103#4114yescomplemented
391C4⋊Dic13—22no—
392C4⋊Dic13—24no—
393C4⋊Dic13—24no—
394C4⋊Dic13C22×C414yes—
395C4⋊Dic13C2×D414yes—
396#6101—24no—
397#6101—24no—
398#6101—42no—
399#6101—42no—
400#6101C22×C418yes—
401C4×Dic13—22no—
402C4×Dic13—22no—
403C4×Dic13—22no—
404C4×Dic13—24no—
405C4×Dic13—24no—
406C4×Dic13—22no—
407C4×Dic13—24no—
408C4×Dic13—22no—
409C4×Dic13—22no—
410C4×Dic13—24no—
411C4×Dic13—42no—
412C4×Dic13—42no—
413C4×Dic13C22×C418yes—
414C4×Dic13C2×D418yes—
415C2×#525—131no—
416C2×C4×#41—131no—
417C22×#117—131no—
418#2363—131no—
419#2363—131no—
420#2362—131no—
421#2362D1311yescharacteristic, complemented
422#2361—131no—
423#2361—131no—
424#2360—131no—
425#2360—131no—
426#2359—132no—
427#2359—132no—
428#2358—132no—
429#2358—132no—
430#2297—131no—
431#2296—131no—
432#2293—132no—
433#2290—132no—
434#2290—132no—
435C42×D4—132no—
436C4×#117—131no—
437C2×C4×C22⋊C4—131no—
438C23×C13—21no—
439C23×C13—21no—
440C23×C13—21no—
441C23×C13—21no—
442C23×C13—21no—
443C23×C13—21no—
444C23×C13C23×C412yes—
445C23×C13C2511yescharacteristic
446C22×D13—21no—
447C22×D13—21no—
448C22×D13—21no—
449C22×D13—21no—
450C22×D13—21no—
451C22×D13—21no—
452C22×D13—21no—
453C22×D13—21no—
454C22×D13—22no—
455C22×D13—22no—
456C22×D13—22no—
457C22×D13—22no—
458C22×D13—22no—
459C22×D13—22no—
460C22×D13—28no—
461C22×D13—28no—
462C22×D13—44no—
463C22×D13—44no—
464C22×D13—44no—
465C22×D13—44no—
466C22×D13—44no—
467C22×D13C23×C414yes—
468C22×D13C23×C412yes—
469C22×D13C23×C412yes—
470C22×D13C22×D412yes—
471C22×D13C2×#4112yes—
472C22×D13C2×#4112yes—
473C22×D13C2×#4112yes—
474Q8×C13—28no—
475C2×C4×C13—21no—
476C2×C4×C13—22no—
477C2×C4×C13—21no—
478C2×C4×C13—21no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—21no—
483C2×C4×C13—22no—
484C2×C4×C13—21no—
485C2×C4×C13—22no—
486C2×C4×C13—21no—
487C2×C4×C13—28no—
488C2×C4×C13—22no—
489C2×C4×C13—21no—
490C2×C4×C13—21no—
491C2×C4×C13—21no—
492C2×C4×C13—21no—
493C2×C4×C13—22no—
494C2×C4×C13—21no—
495C2×C4×C13—22no—
496C2×C4×C13—21no—
497C2×C4×C13C23×C414yes—
498C2×C4×C13C23×C414yes—
499C2×C4×C13C23×C412yes—
500C2×C4×C13C23×C412yes—
501C2×C4×C13C22×D414yes—
502C2×C4×C13C22×D412yes—
503C2×C4×C13C2×#4112yes—
504C2×C4×C13C2×#4112yes—
505C2×C4×C13C2×#4112yes—
506C22⋊D13—48no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—21no—
510C2×Dic13—22no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—22no—
514C2×Dic13—22no—
515C2×Dic13—22no—
516C2×Dic13—21no—
517C2×Dic13—28no—
518C2×Dic13—22no—
519C2×Dic13—21no—
520C2×Dic13—21no—
521C2×Dic13—22no—
522C2×Dic13—21no—
523C2×Dic13—21no—
524C2×Dic13—21no—
525C2×Dic13—22no—
526C2×Dic13—21no—
527C2×Dic13C23×C414yes—
528C2×Dic13C23×C412yes—
529C2×Dic13C23×C412yes—
530C2×Dic13C22×D414yes—
531C2×Dic13C22×D412yes—
532C2×Dic13C2×#4112yes—
533C2×Dic13C2×#4112yes—
534C2×Dic13C2×#4112yes—
535D52—216no—
536D52—216no—
537D52—28no—
538C4×D13—28no—
539C4×D13—28no—
540C4×D13—28no—
541C4×D13—216no—
542C4×D13—48no—
543C4×D13—48no—
544C4×D13—44no—
545C4×D13—48no—
546C4×D13—44no—
547C4×D13—44no—
548C4×D13—48no—
549C4×D13—44no—
550C4×D13C4×D4116yescomplemented
551C22×#41—131no—
552C24×C4—131no—
553#525—1316no—
554C2×#123—132no—
555C2×C22⋊Q8—131no—
556C2×C22⋊Q8C2×D1311yescharacteristic
557C2×#121—131no—
558C2×#121—131no—
559C2×#120—132no—
560C4×#41—268no—
561C2×C4×Q8—131no—
562C2×C4×Q8C2×D1311yescharacteristic, complemented
563C2×C4×D4—132no—
564C2×C4×D4—132no—
565C2×C4×D4—132no—
566C2×C4×D4—131no—
567C2×C4×D4—132no—
568C2×C4×D4—132no—
569C2×C4×D4—132no—
570C2×C4×D4—131no—
571C2×#117—131no—
572C2×#117—131no—
573C2×#117—131no—
574C2×#117—131no—
575C2×#117—132no—
576C2×#117—132no—
577C2×#117—132no—
578C2×#117—268no—
579C2×#117C2×D1311yescharacteristic
580C22×C4⋊C4—131no—
581C22×C4⋊C4—131no—
582C22×C22⋊C4—132no—
583C22×C22⋊C4—131no—
584C22×C22⋊C4—131no—
585C22×C42—132no—
586C22×C42—131no—
587C22×C42—131no—
588C22×C42—132no—
589#391—131no—
590#391C2×D1311yescharacteristic, complemented
591#390—131no—
592#390—132no—
593#390—132no—
594#390—131no—
595#389—132no—
596#389—131no—
597#389—131no—
598#389—131no—
599#389—132no—
600#389C2×D1311yescharacteristic, complemented
601#388—132no—
602#388—132no—
603#388—132no—
604#388—132no—
605#388—132no—
606#388—132no—
607#388C2×D1312yes—
608#388C2×D1312yes—
609#387—132no—
610#387—132no—
611#387—132no—
612#387C2×D1312yescomplemented
613#386—132no—
614#386—132no—
615#386—132no—
616#386—132no—
617#386—132no—
618#386—132no—
619#385—132no—
620#385—132no—
621#385—132no—
622#385—132no—
623#385—132no—
624#385—132no—
625C4×C4⋊C4—132no—
626C4×C4⋊C4—131no—
627C4×C4⋊C4—131no—
628C4×C4⋊C4—132no—
629C4×C4⋊C4—131no—
630C4×C4⋊C4—132no—
631C4×C4⋊C4C2×D1312yescomplemented
632C4×C4⋊C4C2×D1311yescharacteristic, complemented
633C4×C22⋊C4—131no—
634C4×C22⋊C4—131no—
635C4×C22⋊C4—131no—
636C4×C22⋊C4—132no—
637C4×C22⋊C4—132no—
638C4×C22⋊C4—132no—
639C4×C22⋊C4—131no—
640C4×C22⋊C4—131no—
641C4×C22⋊C4—132no—
642C4×C22⋊C4—132no—
643C4×C22⋊C4—132no—
644C4×C22⋊C4—131no—
645C4×C22⋊C4—131no—
646C4×C22⋊C4—132no—
647C4×C22⋊C4—132no—
648C4×C22⋊C4C2×D1311yescharacteristic
649#376—132no—
650C2×#95—131no—
651C2×#95—131no—
652C43—132no—
653C22×C13—22no—
654C22×C13—22no—
655C22×C13—22no—
656C22×C13—41no—
657C22×C13—41no—
658C22×C13—41no—
659C22×C13—41no—
660C22×C13C24×C411yescharacteristic
661C22×C13C23×D411yescharacteristic
662C22×C13C22×#4111yescharacteristic
663C22×C13C22×#4111yescharacteristic
664C22×C13C22×#4111yescharacteristic
665C22×C13#58511yescharacteristic
666C22×C13#58511yescharacteristic
667C2×D13—22no—
668C2×D13—22no—
669C2×D13—22no—
670C2×D13—22no—
671C2×D13—22no—
672C2×D13—22no—
673C2×D13—22no—
674C2×D13—22no—
675C2×D13—22no—
676C2×D13—22no—
677C2×D13—22no—
678C2×D13—22no—
679C2×D13—24no—
680C2×D13—24no—
681C2×D13—24no—
682C2×D13—416no—
683C2×D13—42no—
684C2×D13—42no—
685C2×D13—42no—
686C2×D13—42no—
687C2×D13C2×C4×D414yes—
688C2×D13C4×#4114yescomplemented
689C4×C13—22no—
690C4×C13—24no—
691C4×C13—24no—
692C4×C13—22no—
693C4×C13—24no—
694C4×C13—22no—
695C4×C13—41no—
696C4×C13—42no—
697C4×C13—41no—
698C4×C13C2×C4×D414yes—
699Dic13—22no—
700Dic13—24no—
701Dic13—22no—
702Dic13—24no—
703Dic13—22no—
704Dic13—42no—
705Dic13—41no—
706Dic13—41no—
707Dic13C2×C4×D414yes—
708C25—131no—
709C2×#41—138no—
710C2×#41—264no—
711C2×#41—264no—
712C22×Q8C22×D1311yescharacteristic
713C22×D4—132no—
714C22×D4—132no—
715C22×D4—132no—
716C22×D4—131no—
717C23×C4—131no—
718C23×C4—131no—
719C23×C4—138no—
720C23×C4—131no—
721C23×C4—131no—
722C23×C4—132no—
723C23×C4—131no—
724C23×C4—132no—
725C23×C4—132no—
726C23×C4—131no—
727C23×C4—131no—
728C23×C4—131no—
729C23×C4—131no—
730C23×C4—132no—
731C23×C4—132no—
732C23×C4—264no—
733C23×C4—264no—
734C23×C4C22×D1311yescharacteristic
735#123—1316no—
736C22⋊Q8—138no—
737C22⋊Q8C4×D1318yescomplemented
738#121—138no—
739#121—138no—
740#120—1316no—
741C4×Q8—24no—
742C4×Q8—264no—
743C4×D4—1316no—
744C4×D4—1316no—
745C4×D4—268no—
746C4×D4—268no—
747C4×D4—264no—
748C4×D4—268no—
749C4×D4—268no—
750C4×D4—264no—
751#117—24no—
752#117—138no—
753#117—138no—
754#117—268no—
755#117—268no—
756#117—268no—
757#117—264no—
758#117—264no—
759C2×C4⋊C4—131no—
760C2×C4⋊C4—131no—
761C2×C4⋊C4—132no—
762C2×C4⋊C4—132no—
763C2×C4⋊C4—132no—
764C2×C4⋊C4—131no—
765C2×C4⋊C4—132no—
766C2×C4⋊C4—132no—
767C2×C4⋊C4—132no—
768C2×C4⋊C4—132no—
769C2×C4⋊C4—264no—
770C2×C4⋊C4—264no—
771C2×C4⋊C4C22×D1311yescharacteristic
772C2×C4⋊C4C22×D1312yes—
773C2×C4⋊C4C22×D1312yes—
774C2×C4⋊C4C22×D1311yescharacteristic
775C2×C4⋊C4C22×D1312yes—
776C2×C4⋊C4C22×D1311yescharacteristic
777C2×C22⋊C4—132no—
778C2×C22⋊C4—131no—
779C2×C22⋊C4—131no—
780C2×C22⋊C4—132no—
781C2×C22⋊C4—132no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—131no—
786C2×C22⋊C4—131no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—131no—
789C2×C22⋊C4—131no—
790C2×C22⋊C4—132no—
791C2×C22⋊C4—132no—
792C2×C22⋊C4—132no—
793C2×C22⋊C4—132no—
794C2×C22⋊C4—132no—
795C2×C22⋊C4—132no—
796C2×C22⋊C4—268no—
797C2×C22⋊C4—264no—
798C2×C22⋊C4—264no—
799C2×C22⋊C4C22×D1312yes—
800C2×C22⋊C4C22×D1311yescharacteristic
801C2×C22⋊C4C22×D1311yescharacteristic
802C2×C22⋊C4C22×D1312yes—
803C2×C42—132no—
804C2×C42—132no—
805C2×C42—132no—
806C2×C42—131no—
807C2×C42—132no—
808C2×C42—131no—
809C2×C42—132no—
810C2×C42—132no—
811C2×C42—131no—
812C2×C42—131no—
813C2×C42—131no—
814C2×C42—131no—
815C2×C42—132no—
816C2×C42—132no—
817C2×C42—268no—
818C2×C42—268no—
819C2×C42—264no—
820C2×C42—264no—
821C2×C42C22×D1312yes—
822C2×C42C22×D1311yescharacteristic
823C2×C42C22×D1312yes—
824C2×C42C22×D1312yes—
825C2×C42C22×D1311yescharacteristic
826#95—131no—
827#95—131no—
828#95—131no—
829#95—131no—
830#95—131no—
831#95—131no—
832#95—132no—
833#95—132no—
834#95—132no—
835#95—132no—
836#95—132no—
837#95—132no—
838#95—132no—
839#95—132no—
840#95C22×D1311yescharacteristic
841#95C22×D1311yescharacteristic
842#95C22×D1312yes—
843#95C22×D1312yes—
844#95C22×D1312yes—
845#95C22×D1312yes—
846C2×C13—42no—
847C2×C13C22×C4×D411yescharacteristic
848C2×C13C2×C4×#4111yescharacteristic
849C2×C13#342811yescharacteristic
850C2×C13D4×#4111yescharacteristic
851C2×C13D4×#4111yescharacteristic
852C2×C13#347511yescharacteristic
853C2×C13#347511yescharacteristic
854D13—24no—
855D13—24no—
856D13—44no—
857C24—131no—
858C24—131no—
859C24—132no—
860C24—134no—
861C24—262no—
862C24—262no—
863C24—262no—
864C24—262no—
865C24—521no—
866C24—521no—
867C24C23×D1311yescharacteristic
868#41—2632no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8C2×C4×D1314yes—
872C2×D4—138no—
873C2×D4—138no—
874C2×D4—138no—
875C2×D4—134no—
876C2×D4—264no—
877C2×D4—264no—
878C2×D4—264no—
879C2×D4—264no—
880C2×D4—262no—
881C2×D4—262no—
882C2×D4—522no—
883C2×D4—522no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—131no—
887C22×C4—134no—
888C22×C4—134no—
889C22×C4—134no—
890C22×C4—134no—
891C22×C4—131no—
892C22×C4—131no—
893C22×C4—132no—
894C22×C4—131no—
895C22×C4—132no—
896C22×C4—134no—
897C22×C4—138no—
898C22×C4—134no—
899C22×C4—134no—
900C22×C4—131no—
901C22×C4—131no—
902C22×C4—132no—
903C22×C4—262no—
904C22×C4—264no—
905C22×C4—262no—
906C22×C4—2632no—
907C22×C4—264no—
908C22×C4—264no—
909C22×C4—264no—
910C22×C4—262no—
911C22×C4—262no—
912C22×C4—264no—
913C22×C4—262no—
914C22×C4—262no—
915C22×C4—262no—
916C22×C4—262no—
917C22×C4—262no—
918C22×C4—262no—
919C22×C4—264no—
920C22×C4—264no—
921C22×C4—262no—
922C22×C4—262no—
923C22×C4—262no—
924C22×C4—262no—
925C22×C4—264no—
926C22×C4—264no—
927C22×C4—262no—
928C22×C4—262no—
929C22×C4—264no—
930C22×C4—521no—
931C22×C4—522no—
932C22×C4—522no—
933C22×C4—522no—
934C22×C4—521no—
935C22×C4—521no—
936C22×C4—522no—
937C22×C4—521no—
938C22×C4C2×C4×D1314yes—
939C22×C4C23×D1311yescharacteristic
940C22×C4C23×D1312yes—
941C22×C4C23×D1311yescharacteristic
942C22×C4C23×D1311yescharacteristic
943C22×C4C23×D1312yes—
944C22×C4C23×D1312yes—
945C22×C4C23×D1312yes—
946C22×C4C23×D1311yescharacteristic
947C22×C4C23×D1311yescharacteristic
948C22×C4C23×D1311yescharacteristic
949C4⋊C4—22no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—134no—
953C4⋊C4—138no—
954C4⋊C4—134no—
955C4⋊C4—264no—
956C4⋊C4—264no—
957C4⋊C4—264no—
958C4⋊C4—264no—
959C4⋊C4—262no—
960C4⋊C4—522no—
961C4⋊C4—522no—
962C4⋊C4C2×C4×D1314yes—
963C4⋊C4C2×C4×D1318yes—
964C4⋊C4D4×D1314yes—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—138no—
969C22⋊C4—138no—
970C22⋊C4—138no—
971C22⋊C4—138no—
972C22⋊C4—138no—
973C22⋊C4—134no—
974C22⋊C4—134no—
975C22⋊C4—264no—
976C22⋊C4—264no—
977C22⋊C4—264no—
978C22⋊C4—262no—
979C22⋊C4—262no—
980C22⋊C4—264no—
981C22⋊C4—262no—
982C22⋊C4—262no—
983C22⋊C4—264no—
984C22⋊C4—264no—
985C22⋊C4—522no—
986C22⋊C4—522no—
987C22⋊C4C2×C4×D1318yes—
988C42—24no—
989C42—24no—
990C42—22no—
991C42—22no—
992C42—24no—
993C42—138no—
994C42—138no—
995C42—262no—
996C42—264no—
997C42—264no—
998C42—262no—
999C42—264no—
1000C42—262no—
1001C42—262no—
1002C42—264no—
1003C42—262no—
1004C42—262no—
1005C42—522no—
1006C42—522no—
1007C13#3413611yescharacteristic, complemented, Sylow
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—132no—
1015C23—132no—
1016C23—132no—
1017C23—132no—
1018C23—132no—
1019C23—132no—
1020C23—134no—
1021C23—268no—
1022C23—268no—
1023C23—261no—
1024C23—261no—
1025C23—261no—
1026C23—261no—
1027C23—261no—
1028C23—261no—
1029C23—261no—
1030C23—261no—
1031C23—262no—
1032C23—262no—
1033C23—262no—
1034C23—262no—
1035C23—262no—
1036C23—262no—
1037C23—524no—
1038C23—524no—
1039C23—524no—
1040C23—524no—
1041C23—524no—
1042C23C22×C4×D1312yes—
1043C23C24×D1311yescharacteristic
1044Q8—28no—
1045D4—2616no—
1046D4—2616no—
1047D4—268no—
1048D4—528no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—132no—
1072C2×C4—132no—
1073C2×C4—132no—
1074C2×C4—1316no—
1075C2×C4—134no—
1076C2×C4—132no—
1077C2×C4—134no—
1078C2×C4—132no—
1079C2×C4—132no—
1080C2×C4—268no—
1081C2×C4—2616no—
1082C2×C4—268no—
1083C2×C4—268no—
1084C2×C4—261no—
1085C2×C4—261no—
1086C2×C4—261no—
1087C2×C4—262no—
1088C2×C4—261no—
1089C2×C4—261no—
1090C2×C4—262no—
1091C2×C4—262no—
1092C2×C4—262no—
1093C2×C4—261no—
1094C2×C4—268no—
1095C2×C4—262no—
1096C2×C4—261no—
1097C2×C4—261no—
1098C2×C4—261no—
1099C2×C4—261no—
1100C2×C4—262no—
1101C2×C4—261no—
1102C2×C4—262no—
1103C2×C4—261no—
1104C2×C4—528no—
1105C2×C4—528no—
1106C2×C4—528no—
1107C2×C4—524no—
1108C2×C4—524no—
1109C2×C4—524no—
1110C2×C4—528no—
1111C2×C4—524no—
1112C2×C4C22×C4×D1314yes—
1113C2×C4C22×C4×D1312yes—
1114C2×C4C22×C4×D1314yes—
1115C2×C4C22×C4×D1312yes—
1116C2×C4C2×D4×D1314yes—
1117C2×C4C2×D4×D1312yes—
1118C2×C4#41×D1312yes—
1119C2×C4#41×D1312yes—
1120C2×C4#41×D1312yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—134no—
1129C22—134no—
1130C22—262no—
1131C22—262no—
1132C22—262no—
1133C22—262no—
1134C22—262no—
1135C22—262no—
1136C22—262no—
1137C22—262no—
1138C22—262no—
1139C22—262no—
1140C22—262no—
1141C22—262no—
1142C22—264no—
1143C22—264no—
1144C22—264no—
1145C22—5216no—
1146C22—522no—
1147C22—522no—
1148C22—522no—
1149C22—522no—
1150C22C23×C4×D1311yescharacteristic
1151C22C22×D4×D1311yescharacteristic
1152C22C2×#41×D1311yescharacteristic
1153C22C2×#41×D1311yescharacteristic
1154C22C2×#41×D1311yescharacteristic
1155C22#1171965211yescharacteristic
1156C22#1171965211yescharacteristic
1157C4—22no—
1158C4—24no—
1159C4—24no—
1160C4—24no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—134no—
1167C4—262no—
1168C4—264no—
1169C4—262no—
1170C4—264no—
1171C4—262no—
1172C4—522no—
1173C4—521no—
1174C4—521no—
1175C4C4×D4×D1314yes—
1176C2—42no—
1177C2—264no—
1178C2—264no—
1179C2—524no—
1180C2C2×C4×D4×D1311yescharacteristic
1181C2C4×#41×D1311yescharacteristic
1182C2#1312803811yescharacteristic
1183C2#1312832311yescharacteristic
1184C2#1312832511yescharacteristic
1185C2#1312838911yescharacteristic
1186C2#1312839711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2362C2
socle, cosocleC23×C13C25
prime radicalC2×#11719332C2
hypercenter#2362D13
hypocenterC13#34136
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6131C2semidirect
3. C2×D13×#117C2semidirect
4. #13117874C2semidirect
5. #13117872C2semidirect
6. #13117867C2semidirect
7. #13117854C2semidirect
8. #13117851C2semidirect
9. #13117846C2semidirect
10. #13117837C2semidirect
11. #13117833C2semidirect
12. #13117821C2semidirect
13. #13117814C2semidirect
14. #13117814C2semidirect
15. #13117325C2semidirect
16. #13117317C2semidirect
17. #13117296C2semidirect
18. #13117278C2semidirect
19. #13117274C2semidirect
20. C4×#88147C2semidirect
21. C4×#88146C2semidirect
22. C4×C22⋊C4×D13C2semidirect
23. C13×#2362C2semidirect
27. C2×C4×Q8×C13C22semidirect
30. C2×Q8×Dic13C22semidirect
33. #11719332C4semidirect
41. C2×#88147C22semidirect
45. C2×#88146C22semidirect
56. C2×C4×D52C22semidirect
61. C2×C42×D13C22semidirect
62. C13×#391C22semidirect
63. C13×#389C22semidirect
66. C13×#387C22semidirect
67. C4×C13×C4⋊C4C22semidirect
68. C4×C13×C4⋊C4C22semidirect
70. #11718891C22semidirect
74. #11718650C22semidirect
75. #11718649C22semidirect
76. #11718646C22semidirect
77. #11718642C22semidirect
78. C4⋊C4×Dic13C22semidirect
79. C4⋊C4×Dic13C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. C4⋊C4×Dic13C22semidirect
82. #11718634C22semidirect
83. #11718633C22semidirect
92. #11718601C22semidirect
93. #11718601C22semidirect
94. #11718600C22semidirect
99. C4×#6103C22semidirect
100. C4×C4⋊Dic13C22semidirect
101. #11718594C22semidirect
102. C42×Dic13C22semidirect
103. #11718589C22semidirect
104. #11718330C22semidirect
105. #11718330C22semidirect
108. #11718329C22semidirect
113. #11718327C22semidirect
114. #11718327C22semidirect
115. #11718327C22semidirect
122. #11718313C22semidirect
123. #11718310C22semidirect
124. #11718309C22semidirect
125. #11718308C22semidirect
133. C2×#6131C2×C4semidirect
139. C22×C4×D13C2×C4semidirect
153. C13×C22⋊Q8C2×C4semidirect
174. #88200C2×C4semidirect
176. #88184C2×C4semidirect
218. #88149C2×C4semidirect
219. #88148C2×C4semidirect
223. #88147C2×C4semidirect
226. #88146C2×C4semidirect
227. #88146D4semidirect
230. #88136C2×C4semidirect
231. #88135C2×C4semidirect
389. #6103#41semidirect
390. #6103#41semidirect
421. #2362D13semidirect
550. C4×D13C4×D4semidirect
562. C2×C4×Q8C2×D13semidirect
590. #391C2×D13semidirect
600. #389C2×D13semidirect
612. #387C2×D13semidirect
631. C4×C4⋊C4C2×D13semidirect
632. C4×C4⋊C4C2×D13semidirect
688. C2×D13C4×#41semidirect
737. C22⋊Q8C4×D13semidirect
1007. C13#34136semidirect

Maximal subgroups

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

subgroupindex
C2×#117193322
C2×C4×#61312
C2×D13×#1172
#131178742
#131178722
#131178672
#131178542
#131178512
#131178462
#131178372
#131178332
#131178212
#131178142
#131173252
#131173172
#131172962
#131172782
#131172742
C4×#881472
C4×#881462
C4×C22⋊C4×D132
C13×#23622
#3413613