Finite Group Databasebeta

← #16025709

Subgroups — #16025709

Order 3328.

2586 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×#11719252C211yesmaximal, characteristic
2#13118003C212yesmaximal, complemented
3#13117987C212yesmaximal, complemented
4#13117920C212yesmaximal, complemented
5#13117880C212yesmaximal, complemented
6#13117780C211yesmaximal, characteristic, complemented
7#13117768C211yesmaximal, characteristic, complemented
8#13117766C211yesmaximal, characteristic, complemented
9#13117766C211yesmaximal, characteristic, complemented
10#13117765C211yesmaximal, characteristic, complemented
11#13117736C211yesmaximal, characteristic, complemented
12#13117732C211yesmaximal, characteristic, complemented
13#13117624C212yesmaximal, complemented
14#13117620C212yesmaximal, complemented
15#13117495C212yesmaximal, complemented
16#13117489C212yesmaximal, complemented
17#13117444C211yesmaximal, characteristic, complemented
18#13117441C211yesmaximal, characteristic, complemented
19#13117425C211yesmaximal, characteristic, complemented
20#13117424C211yesmaximal, characteristic, complemented
21#13117215C211yesmaximal, characteristic, complemented
22D13×#380C211yesmaximal, characteristic, complemented
23C13×#2354C211yesmaximal, characteristic, complemented
24C22×#6127C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic, complemented
29C2×#88193C2211yescharacteristic
30C2×#88191C2211yescharacteristic
31C2×C4×C22⋊D13C2211yescharacteristic
32C2×C4×C22⋊D13C2211yescharacteristic
33C2×#88180C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic, complemented
35#11719252C4116yescomplemented
36C2×#88150C2211yescharacteristic
37C2×#88148C2211yescharacteristic
38C2×#88147C2212yes—
39C2×#88146C2211yescharacteristic, complemented
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×C4⋊C4×D13C2211yescharacteristic
42C2×C4⋊C4×D13C2211yescharacteristic, complemented
43C2×#88138C2211yescharacteristic
44C2×#88137C2211yescharacteristic
45C2×#88136C2211yescharacteristic
46C2×#88135C2212yes—
47C2×C22⋊C4×D13C2212yes—
48C2×#88132C2211yescharacteristic
49C2×C4×D52C2211yescharacteristic
50C2×#88126C2211yescharacteristic
51C13×#390C2212yes—
52C13×#388C2212yes—
53C13×#388C2212yescomplemented
54C13×#384C2211yescharacteristic, complemented
55C13×#380C2211yescharacteristic
56C13×#380C2211yescharacteristic, complemented
57C4×C13×C4⋊C4C2211yescharacteristic, complemented
58C4×C13×C4⋊C4C2212yescomplemented
59#11718881C2212yes—
60#11718873C2211yescharacteristic
61#11718873C2211yescharacteristic, complemented
62#11718651C2212yes—
63#11718651C2212yes—
64#11718650C2212yes—
65#11718650C2212yescomplemented
66#11718648C2211yescharacteristic
67#11718648C2211yescharacteristic
68#11718648C2211yescharacteristic
69#11718648C2211yescharacteristic
70#11718648C2211yescharacteristic
71#11718648C2211yescharacteristic
72#11718648C2211yescharacteristic, complemented
73#11718648C2211yescharacteristic, complemented
74#11718642C2212yescomplemented
75#11718639C2212yescomplemented
76#11718639C2212yescomplemented
77#11718638C2211yescharacteristic, complemented
78#11718637C2211yescharacteristic, complemented
79C4⋊C4×Dic13C2211yescharacteristic, complemented
80C4⋊C4×Dic13C2211yescharacteristic, complemented
81#11718634C2212yescomplemented
82#11718619C2212yes—
83#11718619C2212yescomplemented
84#11718618C2212yes—
85#11718618C2212yes—
86#11718617C2212yes—
87#11718617C2212yes—
88#11718617C2212yescomplemented
89#11718616C2212yes—
90#11718612C2212yes—
91#11718607C2212yescomplemented
92#11718606C2212yes—
93#11718606C2212yes—
94#11718606C2212yescomplemented
95#11718604C2212yes—
96#11718603C2212yes—
97C22⋊C4×Dic13C2212yescomplemented
98#11718601C2212yes—
99#11718601C2212yescomplemented
100#11718600C2212yes—
101C4×#6103C2212yes—
102C4×#6103C2212yes—
103C4×#6103C2212yes—
104C4×#6103C2212yes—
105C4×#6103C2212yescomplemented
106#11718597C2211yescharacteristic, complemented
107C4×C4⋊Dic13C2211yescharacteristic, complemented
108#11718594C2212yescomplemented
109#11718594C2212yescomplemented
110#11718594C2212yescomplemented
111#11718590C2212yescomplemented
112#11718330C2212yes—
113#11718330C2212yescomplemented
114#11718329C2212yes—
115#11718328C2212yes—
116#11718326C2212yes—
117#11718326C2212yes—
118D13×#95C2212yes—
119#11718314C2212yescomplemented
120#11718313C2212yescomplemented
121#11718310C2212yescomplemented
122#11718308C2212yescomplemented
123#11718307C2212yescomplemented
124C24×D13C2311yescharacteristic
125C22×D4×C13C2311yescharacteristic
126C23×C4×C13C2311yescharacteristic
127C23×C4×C13C2311yescharacteristic
128C22×C22⋊D13C2311yescharacteristic
129C22×C22⋊D13C2311yescharacteristic
130C22×C22⋊D13C2311yescharacteristic
131C22×C22⋊D13C2311yescharacteristic
132C23×Dic13C2312yes—
133C23×Dic13C2311yescharacteristic
134C2×#6127—42no—
135C2×#6127—42no—
136C2×#6127C2×C418yescomplemented
137C22×D52C2311yescharacteristic
138C22×D52C2311yescharacteristic
139C22×C4×D13—42no—
140C22×C4×D13—42no—
141C22×C4×D13C2×C418yescomplemented
142C22×C4×D13C2311yescharacteristic
143C22×C4×D13C2311yescharacteristic
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2312yes—
146C22×C4×D13C2312yes—
147C22×C4×D13C2312yes—
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×Dic26C2311yescharacteristic
151C4×D4×C13C2×C418yescomplemented
152C13×#117—42no—
153C13×#117—42no—
154C2×C13×C4⋊C4C2311yescharacteristic
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2311yescharacteristic
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2312yes—
160C2×C13×C4⋊C4C2311yescharacteristic
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2311yescharacteristic
166C2×C13×C22⋊C4C2311yescharacteristic
167C2×C42×C13C2312yes—
168C2×C42×C13C2312yes—
169C2×C42×C13C2312yes—
170C2×C42×C13C2311yescharacteristic
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2311yescharacteristic
175C2×C22⋊Dic13C2311yescharacteristic
176#88193C2×C418yescomplemented
177#88191C2×C418yescomplemented
178C4×C22⋊D13C2×C418yescomplemented
179C4×C22⋊D13C2×C418yescomplemented
180C2×#6103C2312yes—
181C2×#6103C2312yes—
182C2×#6103C2312yes—
183C2×#6103C2312yes—
184C2×#6103C2312yes—
185C2×#6103C2312yes—
186C2×#6103C2312yes—
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2311yescharacteristic
190C2×#6103C2311yescharacteristic
191C2×#6103C2311yescharacteristic
192C2×#6103C2311yescharacteristic
193C2×#6103C2311yescharacteristic
194C2×#6103C2311yescharacteristic
195#88180—42no—
196C2×C4⋊Dic13—42no—
197C2×C4⋊Dic13C2311yescharacteristic
198C2×C4⋊Dic13C2311yescharacteristic
199C2×C4⋊Dic13C2311yescharacteristic
200C2×C4⋊Dic13C2311yescharacteristic
201C2×C4⋊Dic13C2312yes—
202C2×C4⋊Dic13C2311yescharacteristic
203C2×#6101C2312yes—
204C2×#6101C2312yes—
205C2×#6101C2312yes—
206C2×#6101C2312yes—
207C2×#6101C2312yes—
208C2×#6101C2311yescharacteristic
209C2×#6101C2311yescharacteristic
210C2×#6101C2311yescharacteristic
211C2×#6101C2311yescharacteristic
212C2×C4×Dic13C2312yes—
213C2×C4×Dic13C2312yes—
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2312yes—
216C2×C4×Dic13C2312yes—
217C2×C4×Dic13C2311yescharacteristic
218#88150C2×C418yescomplemented
219#88148C2×C418yescomplemented
220#88147—44no—
221#88146—42no—
222C4⋊C4×D13—42no—
223C4⋊C4×D13—42no—
224C4⋊C4×D13—42no—
225#88138C2×C418yes—
226#88137C2×C418yescomplemented
227#88136C2×C418yescomplemented
228#88135—44no—
229C22⋊C4×D13—44no—
230#88132C2×C418yescomplemented
231C4×D52C2×C418yescomplemented
232#88126C2×C418yescomplemented
233C13×#95C2312yes—
234C13×#95C2312yes—
235C13×#95C2312yes—
236#88071C2312yes—
237#88071C2312yes—
238#88071C2312yes—
239#88071C2312yes—
240#88071C2312yes—
241#88071C2312yes—
242#88071C2312yes—
243#88071C2312yes—
244#88071C2312yes—
245#88071C2312yes—
246#88071C2312yes—
247#88071C2312yes—
248#88071C2312yes—
249#88071C2312yes—
250#88071C2312yes—
251#88071C2312yes—
252#88071C2312yes—
253#34362—131nomaximal, Sylow
254C24×C13C2411yescharacteristic
255C24×C13C2411yescharacteristic
256C23×D13—22no—
257C23×D13—22no—
258C23×D13—41no—
259C23×D13—41no—
260C23×D13—41no—
261C23×D13—41no—
262C23×D13C22×C414yes—
263C23×D13C2411yescharacteristic
264C23×D13C2411yescharacteristic
265C23×D13C2411yescharacteristic
266C2×D4×C13—41no—
267C2×D4×C13—41no—
268C2×D4×C13C22×C414yes—
269C22×C4×C13—22no—
270C22×C4×C13—22no—
271C22×C4×C13—22no—
272C22×C4×C13—22no—
273C22×C4×C13C22×C414yes—
274C22×C4×C13C22×C414yes—
275C22×C4×C13C2412yes—
276C22×C4×C13C2412yes—
277C22×C4×C13C2412yes—
278C22×C4×C13C2412yes—
279C22×C4×C13C2411yescharacteristic
280C22×C4×C13C2411yescharacteristic
281C22×C4×C13C2411yescharacteristic
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2411yescharacteristic
284C2×C22⋊D13—22no—
285C2×C22⋊D13—22no—
286C2×C22⋊D13—41no—
287C2×C22⋊D13—41no—
288C2×C22⋊D13—41no—
289C2×C22⋊D13—41no—
290C2×C22⋊D13—41no—
291C2×C22⋊D13—41no—
292C2×C22⋊D13C22×C414yes—
293C2×C22⋊D13C22×C414yes—
294C2×C22⋊D13C22×C414yes—
295C2×C22⋊D13C22×C414yes—
296C22×Dic13—41no—
297C22×Dic13—41no—
298C22×Dic13—42no—
299C22×Dic13—42no—
300C22×Dic13—42no—
301C22×Dic13C22×C414yes—
302C22×Dic13C2412yes—
303C22×Dic13C2412yes—
304C22×Dic13C2412yes—
305C22×Dic13C2412yes—
306C22×Dic13C2411yescharacteristic
307C22×Dic13C2411yescharacteristic
308C22×Dic13C2411yescharacteristic
309C22×Dic13C2411yescharacteristic
310C22×Dic13C2411yescharacteristic
311#6127—416no—
312C2×D52—22no—
313C2×D52—22no—
314C2×D52—41no—
315C2×D52—41no—
316C2×D52C22×C414yes—
317C2×D52C22×C414yes—
318C2×C4×D13—22no—
319C2×C4×D13—22no—
320C2×C4×D13—22no—
321C2×C4×D13—22no—
322C2×C4×D13—22no—
323C2×C4×D13—22no—
324C2×C4×D13—24no—
325C2×C4×D13—24no—
326C2×C4×D13—416no—
327C2×C4×D13—41no—
328C2×C4×D13—41no—
329C2×C4×D13—41no—
330C2×C4×D13—41no—
331C2×C4×D13—42no—
332C2×C4×D13—42no—
333C2×C4×D13—42no—
334C2×C4×D13—42no—
335C2×C4×D13—42no—
336C2×C4×D13—42no—
337C2×C4×D13—42no—
338C2×C4×D13C22×C414yes—
339C2×C4×D13C22×C414yes—
340C2×C4×D13C22×C414yes—
341C2×C4×D13C22×C414yes—
342C2×C4×D13C22×C414yes—
343C2×Dic26—41no—
344C2×Dic26—41no—
345C2×Dic26C22×C414yes—
346C13×C4⋊C4—22no—
347C13×C4⋊C4—22no—
348C13×C4⋊C4—22no—
349C13×C4⋊C4—22no—
350C13×C4⋊C4—42no—
351C13×C4⋊C4—42no—
352C13×C4⋊C4C22×C414yes—
353C13×C22⋊C4—42no—
354C13×C22⋊C4—42no—
355C13×C22⋊C4—42no—
356C13×C22⋊C4—42no—
357C13×C22⋊C4C22×C414yes—
358C13×C22⋊C4C22×C414yes—
359C42×C13—42no—
360C42×C13—42no—
361C42×C13—42no—
362C42×C13C22×C414yes—
363C22⋊Dic13—42no—
364C22⋊Dic13—42no—
365C22⋊Dic13—42no—
366C22⋊Dic13C22×C414yes—
367C22⋊Dic13C22×C414yes—
368#6103—24no—
369#6103—24no—
370#6103—42no—
371#6103—42no—
372#6103—42no—
373#6103—42no—
374#6103—42no—
375#6103—42no—
376#6103—42no—
377#6103C22×C414yes—
378#6103C22×C414yes—
379#6103C22×C414yes—
380#6103C22×C414yes—
381#6103C22×C414yes—
382#6103C22×C414yes—
383C4⋊Dic13—22no—
384C4⋊Dic13—22no—
385C4⋊Dic13—22no—
386C4⋊Dic13—22no—
387C4⋊Dic13—42no—
388C4⋊Dic13C22×C414yes—
389#6101—42no—
390#6101—42no—
391#6101—42no—
392#6101—42no—
393#6101—42no—
394#6101C22×C414yes—
395#6101C22×C414yes—
396#6101C22×C414yes—
397#6101C22×C414yes—
398C4×Dic13—42no—
399C4×Dic13—42no—
400C4×Dic13—42no—
401C4×Dic13—42no—
402C4×Dic13—42no—
403C4×Dic13C22×C414yes—
404C2×#525—131no—
405#2378—132no—
406#2377—132no—
407#2368—132no—
408#2364—132no—
409#2354—131no—
410#2354D1311yescharacteristic, complemented
411#2352—131no—
412#2352—131no—
413#2352—131no—
414#2352—131no—
415D4×C4⋊C4—131no—
416D4×C4⋊C4—131no—
417#2335—132no—
418#2335—132no—
419#2321—132no—
420#2321—132no—
421#2314—131no—
422#2314—131no—
423#2311—131no—
424#2311—131no—
425#2280—131no—
426C2×#380—131no—
427C23×C13—21no—
428C23×C13—21no—
429C23×C13—21no—
430C23×C13—21no—
431C23×C13—21no—
432C23×C13—21no—
433C23×C13—21no—
434C23×C13—21no—
435C23×C13—21no—
436C23×C13—21no—
437C23×C13—21no—
438C23×C13—21no—
439C23×C13C23×C412yes—
440C23×C13C23×C412yes—
441C23×C13C2511yescharacteristic
442C22×D13—21no—
443C22×D13—21no—
444C22×D13—21no—
445C22×D13—21no—
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—21no—
455C22×D13—21no—
456C22×D13—21no—
457C22×D13—21no—
458C22×D13—28no—
459C22×D13—44no—
460C22×D13—44no—
461C22×D13—44no—
462C22×D13—44no—
463C22×D13—44no—
464C22×D13—44no—
465C22×D13C23×C412yes—
466C22×D13C23×C412yes—
467C22×D13C23×C412yes—
468C22×D13H(5,𝔽2)12yes—
469C22×D132−1+412yes—
470D4×C13—44no—
471C2×C4×C13—21no—
472C2×C4×C13—21no—
473C2×C4×C13—21no—
474C2×C4×C13—21no—
475C2×C4×C13—21no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—21no—
479C2×C4×C13—28no—
480C2×C4×C13—28no—
481C2×C4×C13—22no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—22no—
485C2×C4×C13—22no—
486C2×C4×C13—22no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—22no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13C23×C412yes—
494C2×C4×C13C23×C412yes—
495C2×C4×C13C23×C412yes—
496C2×C4×C13C23×C412yes—
497C2×C4×C13C23×C412yes—
498C2×C4×C13H(5,𝔽2)12yes—
499C2×C4×C13H(5,𝔽2)12yes—
500C22⋊D13—28no—
501C22⋊D13—44no—
502C22⋊D13—44no—
503C22⋊D13—44no—
504C2×Dic13—21no—
505C2×Dic13—21no—
506C2×Dic13—21no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—21no—
510C2×Dic13—21no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—21no—
514C2×Dic13—22no—
515C2×Dic13—22no—
516C2×Dic13—22no—
517C2×Dic13—22no—
518C2×Dic13—22no—
519C2×Dic13—22no—
520C2×Dic13—22no—
521C2×Dic13—22no—
522C2×Dic13—22no—
523C2×Dic13—22no—
524C2×Dic13—22no—
525C2×Dic13—22no—
526C2×Dic13—44no—
527C2×Dic13—84no—
528C2×Dic13C23×C412yes—
529C2×Dic13C23×C412yes—
530C2×Dic13C23×C412yes—
531C2×Dic13C23×C412yes—
532C2×Dic13C23×C412yes—
533D52—28no—
534D52—44no—
535C4×D13—28no—
536C4×D13—28no—
537C4×D13—28no—
538C4×D13—44no—
539C4×D13—44no—
540C4×D13—84no—
541C4×D13—84no—
542C4×D13—84no—
543Dic26—44no—
544C22×#41—131no—
545C24×C4—131no—
546#525—1316no—
547C2×#123—131no—
548C2×#123—131no—
549C2×C22⋊Q8—131no—
550C2×C22⋊Q8—131no—
551C2×#121—131no—
552C2×#121—131no—
553C2×#120—131no—
554C2×#120—131no—
555C2×C4×D4—131no—
556C2×C4×D4—131no—
557C2×C4×D4—132no—
558C2×C4×D4—132no—
559C2×C4×D4—131no—
560C2×C4×D4C2×D1311yescharacteristic
561C2×#117—131no—
562C2×#117—131no—
563C2×#117—131no—
564C2×#117C2×D1311yescharacteristic
565C2×#117C2×D1311yescharacteristic, complemented
566C22×C4⋊C4—131no—
567C22×C4⋊C4—131no—
568C22×C4⋊C4—131no—
569C22×C4⋊C4—131no—
570C22×C22⋊C4—132no—
571#391—132no—
572#391—132no—
573#390—132no—
574#390—132no—
575#390—132no—
576#390C2×D1312yes—
577#389—132no—
578#389—132no—
579#388—132no—
580#388—132no—
581#388—132no—
582#388—132no—
583#388—132no—
584#388—132no—
585#388—132no—
586#388—132no—
587#388—132no—
588#388—132no—
589#388C2×D1312yes—
590#388C2×D1312yescomplemented
591#387—132no—
592#387—132no—
593#387—132no—
594#387—132no—
595#387—132no—
596#387—132no—
597#387—132no—
598#387—132no—
599#386—132no—
600#386—132no—
601#386—132no—
602#386—132no—
603#386—132no—
604#386—132no—
605#386—132no—
606#386—132no—
607#385—132no—
608#385—132no—
609#385—132no—
610#385—132no—
611#384—131no—
612#384C2×D1311yescharacteristic, complemented
613#382—131no—
614#382—131no—
615#381—132no—
616#380—131no—
617#380—131no—
618#380—131no—
619#380—131no—
620#380—131no—
621#380—131no—
622#380—131no—
623#380—131no—
624#380—131no—
625#380—131no—
626#380—132no—
627#380—132no—
628#380C2×D1311yescharacteristic
629#380C2×D1311yescharacteristic, complemented
630#379—132no—
631C4×C4⋊C4—131no—
632C4×C4⋊C4—131no—
633C4×C4⋊C4—131no—
634C4×C4⋊C4—132no—
635C4×C4⋊C4C2×D1311yescharacteristic, complemented
636C4×C4⋊C4C2×D1312yescomplemented
637C4×C22⋊C4—132no—
638C4×C22⋊C4—132no—
639C4×C22⋊C4—132no—
640C4×C22⋊C4—132no—
641C4×C22⋊C4—132no—
642C4×C22⋊C4—132no—
643C2×#95—132no—
644C22×C13—22no—
645C22×C13—22no—
646C22×C13—22no—
647C22×C13—22no—
648C22×C13—22no—
649C22×C13—22no—
650C22×C13—41no—
651C22×C13—41no—
652C22×C13—41no—
653C22×C13—41no—
654C22×C13—41no—
655C22×C13—41no—
656C22×C13—41no—
657C22×C13—41no—
658C22×C13C24×C411yescharacteristic
659C22×C13C2×H(5,𝔽2)11yescharacteristic
660C22×C13C2×H(5,𝔽2)11yescharacteristic
661C22×C13C2×H(5,𝔽2)11yescharacteristic
662C22×C13C2×2−1+411yescharacteristic
663C22×C13#58511yescharacteristic
664C22×C13#58511yescharacteristic
665C2×D13—22no—
666C2×D13—22no—
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—416no—
678C2×D13—41no—
679C2×D13—41no—
680C2×D13—41no—
681C2×D13—41no—
682C2×D13—41no—
683C2×D13—41no—
684C2×D13—41no—
685C2×D13—41no—
686C2×D13#52014yes—
687C4×C13—22no—
688C4×C13—22no—
689C4×C13—22no—
690C4×C13—22no—
691C4×C13—42no—
692C4×C13—42no—
693C4×C13—42no—
694C4×C13—42no—
695C4×C13#51814yes—
696Dic13—22no—
697Dic13—22no—
698Dic13—22no—
699Dic13—22no—
700Dic13—22no—
701Dic13—42no—
702Dic13—42no—
703Dic13—42no—
704Dic13—42no—
705C25—131no—
706C2×#41—138no—
707C2×#41—522no—
708C2×#41—522no—
709C22×Q8—131no—
710C22×D4—131no—
711C22×D4—131no—
712C22×D4—131no—
713C22×D4—131no—
714C22×D4—131no—
715C22×D4—131no—
716C22×D4C22×D1311yescharacteristic
717C23×C4—131no—
718C23×C4—131no—
719C23×C4—131no—
720C23×C4—131no—
721C23×C4—138no—
722C23×C4—131no—
723C23×C4—131no—
724C23×C4—132no—
725C23×C4—132no—
726C23×C4—132no—
727C23×C4—132no—
728C23×C4—522no—
729C23×C4—522no—
730C23×C4C22×D1311yescharacteristic
731C23×C4C22×D1311yescharacteristic
732#123—138no—
733#123—138no—
734C22⋊Q8—138no—
735C22⋊Q8—138no—
736#121—138no—
737#121—138no—
738#120—138no—
739#120—138no—
740C4×D4—138no—
741C4×D4—138no—
742C4×D4—138no—
743C4×D4—524no—
744C4×D4—524no—
745C4×D4C4×D1318yescomplemented
746#117—42no—
747#117—42no—
748#117—138no—
749#117—522no—
750#117—522no—
751C2×C4⋊C4—131no—
752C2×C4⋊C4—131no—
753C2×C4⋊C4—131no—
754C2×C4⋊C4—131no—
755C2×C4⋊C4—131no—
756C2×C4⋊C4—131no—
757C2×C4⋊C4—131no—
758C2×C4⋊C4—131no—
759C2×C4⋊C4—131no—
760C2×C4⋊C4—132no—
761C2×C4⋊C4—132no—
762C2×C4⋊C4—132no—
763C2×C4⋊C4—132no—
764C2×C4⋊C4—132no—
765C2×C4⋊C4—132no—
766C2×C4⋊C4—522no—
767C2×C4⋊C4—522no—
768C2×C4⋊C4—522no—
769C2×C4⋊C4—522no—
770C2×C4⋊C4C22×D1311yescharacteristic
771C2×C4⋊C4C22×D1311yescharacteristic
772C2×C4⋊C4C22×D1311yescharacteristic
773C2×C4⋊C4C22×D1311yescharacteristic
774C2×C4⋊C4C22×D1312yes—
775C2×C4⋊C4C22×D1312yes—
776C2×C4⋊C4C22×D1311yescharacteristic
777C2×C22⋊C4—131no—
778C2×C22⋊C4—131no—
779C2×C22⋊C4—131no—
780C2×C22⋊C4—131no—
781C2×C22⋊C4—131no—
782C2×C22⋊C4—131no—
783C2×C22⋊C4—131no—
784C2×C22⋊C4—131no—
785C2×C22⋊C4—132no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—132no—
789C2×C22⋊C4—132no—
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—132no—
797C2×C22⋊C4—524no—
798C2×C22⋊C4C22×D1312yes—
799C2×C22⋊C4C22×D1312yes—
800C2×C22⋊C4C22×D1312yes—
801C2×C22⋊C4C22×D1312yes—
802C2×C22⋊C4C22×D1311yescharacteristic
803C2×C22⋊C4C22×D1311yescharacteristic
804C2×C42—131no—
805C2×C42—132no—
806C2×C42—132no—
807C2×C42—132no—
808C2×C42—132no—
809C2×C42—132no—
810C2×C42C22×D1312yes—
811C2×C42C22×D1312yes—
812C2×C42C22×D1312yes—
813C2×C42C22×D1311yescharacteristic
814#95—132no—
815#95—132no—
816#95—132no—
817#95—132no—
818#95—132no—
819#95—132no—
820#95—132no—
821#95—132no—
822#95—132no—
823#95—132no—
824#95—132no—
825#95—132no—
826#95—132no—
827#95—132no—
828#95—132no—
829#95—132no—
830#95—132no—
831#95C22×D1312yes—
832#95C22×D1312yes—
833#95C22×D1312yes—
834C2×C13—42no—
835C2×C13—42no—
836C2×C13C2×#51811yescharacteristic
837C2×C13C2×#52011yescharacteristic
838C2×C13#342811yescharacteristic
839C2×C13#354111yescharacteristic
840C2×C13#354111yescharacteristic
841C2×C13#354211yescharacteristic
842C2×C13#354211yescharacteristic
843D13—24no—
844D13—42no—
845D13—42no—
846C24—131no—
847C24—131no—
848C24—131no—
849C24—134no—
850C24—262no—
851C24—262no—
852C24—521no—
853C24—521no—
854C24—521no—
855C24—521no—
856C24C23×D1311yescharacteristic
857C24C23×D1311yescharacteristic
858#41—5216no—
859C2×Q8—134no—
860C2×Q8—521no—
861C2×Q8—521no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—134no—
865C2×D4—134no—
866C2×D4—134no—
867C2×D4—134no—
868C2×D4—134no—
869C2×D4—134no—
870C2×D4—262no—
871C2×D4—262no—
872C2×D4—262no—
873C2×D4—262no—
874C2×D4—521no—
875C2×D4—521no—
876C2×D4—521no—
877C2×D4—521no—
878C2×D4—521no—
879C2×D4—521no—
880C2×D4—521no—
881C2×D4—521no—
882C2×D4C2×C4×D1314yes—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—131no—
888C22×C4—131no—
889C22×C4—131no—
890C22×C4—131no—
891C22×C4—131no—
892C22×C4—134no—
893C22×C4—134no—
894C22×C4—134no—
895C22×C4—134no—
896C22×C4—134no—
897C22×C4—134no—
898C22×C4—132no—
899C22×C4—132no—
900C22×C4—132no—
901C22×C4—132no—
902C22×C4—264no—
903C22×C4—264no—
904C22×C4—262no—
905C22×C4—262no—
906C22×C4—262no—
907C22×C4—262no—
908C22×C4—262no—
909C22×C4—262no—
910C22×C4—5216no—
911C22×C4—521no—
912C22×C4—521no—
913C22×C4—521no—
914C22×C4—521no—
915C22×C4—522no—
916C22×C4—522no—
917C22×C4—522no—
918C22×C4—522no—
919C22×C4—522no—
920C22×C4—522no—
921C22×C4—522no—
922C22×C4—521no—
923C22×C4—521no—
924C22×C4—522no—
925C22×C4—522no—
926C22×C4—522no—
927C22×C4C2×C4×D1314yes—
928C22×C4C2×C4×D1314yes—
929C22×C4C23×D1312yes—
930C22×C4C23×D1312yes—
931C22×C4C23×D1312yes—
932C22×C4C23×D1312yes—
933C22×C4C23×D1311yescharacteristic
934C22×C4C23×D1311yescharacteristic
935C22×C4C23×D1311yescharacteristic
936C22×C4C23×D1311yescharacteristic
937C22×C4C23×D1311yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—134no—
945C4⋊C4—134no—
946C4⋊C4—134no—
947C4⋊C4—134no—
948C4⋊C4—134no—
949C4⋊C4—262no—
950C4⋊C4—262no—
951C4⋊C4—262no—
952C4⋊C4—262no—
953C4⋊C4—522no—
954C4⋊C4—522no—
955C4⋊C4—522no—
956C4⋊C4—522no—
957C4⋊C4—522no—
958C4⋊C4—522no—
959C4⋊C4C2×C4×D1314yes—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—134no—
965C22⋊C4—134no—
966C22⋊C4—134no—
967C22⋊C4—134no—
968C22⋊C4—134no—
969C22⋊C4—134no—
970C22⋊C4—134no—
971C22⋊C4—134no—
972C22⋊C4—264no—
973C22⋊C4—264no—
974C22⋊C4—522no—
975C22⋊C4—522no—
976C22⋊C4—522no—
977C22⋊C4—522no—
978C22⋊C4—522no—
979C22⋊C4—522no—
980C22⋊C4—522no—
981C22⋊C4—522no—
982C22⋊C4—522no—
983C22⋊C4—522no—
984C22⋊C4C2×C4×D1314yes—
985C22⋊C4C2×C4×D1314yes—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—134no—
990C42—522no—
991C42—522no—
992C42—522no—
993C42—522no—
994C42—522no—
995C42C2×C4×D1314yes—
996C13#3436211yescharacteristic, complemented, Sylow
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—132no—
1010C23—132no—
1011C23—132no—
1012C23—132no—
1013C23—132no—
1014C23—268no—
1015C23—261no—
1016C23—261no—
1017C23—261no—
1018C23—261no—
1019C23—261no—
1020C23—261no—
1021C23—261no—
1022C23—261no—
1023C23—261no—
1024C23—261no—
1025C23—261no—
1026C23—261no—
1027C23—261no—
1028C23—261no—
1029C23—261no—
1030C23—261no—
1031C23—524no—
1032C23—524no—
1033C23—524no—
1034C23—524no—
1035C23—524no—
1036C23—524no—
1037C23C22×C4×D1312yes—
1038C23C22×C4×D1312yes—
1039C23C24×D1311yescharacteristic
1040Q8—524no—
1041D4—44no—
1042D4—268no—
1043D4—268no—
1044D4—524no—
1045D4—524no—
1046D4—524no—
1047D4—524no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—132no—
1071C2×C4—132no—
1072C2×C4—132no—
1073C2×C4—132no—
1074C2×C4—132no—
1075C2×C4—261no—
1076C2×C4—261no—
1077C2×C4—261no—
1078C2×C4—261no—
1079C2×C4—261no—
1080C2×C4—261no—
1081C2×C4—261no—
1082C2×C4—261no—
1083C2×C4—261no—
1084C2×C4—261no—
1085C2×C4—268no—
1086C2×C4—268no—
1087C2×C4—268no—
1088C2×C4—262no—
1089C2×C4—262no—
1090C2×C4—262no—
1091C2×C4—262no—
1092C2×C4—262no—
1093C2×C4—262no—
1094C2×C4—262no—
1095C2×C4—262no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—262no—
1099C2×C4—262no—
1100C2×C4—524no—
1101C2×C4—524no—
1102C2×C4—524no—
1103C2×C4—1044no—
1104C2×C4—1044no—
1105C2×C4—1044no—
1106C2×C4—1044no—
1107C2×C4C22×C4×D1312yes—
1108C2×C4C22×C4×D1312yes—
1109C2×C4C22×C4×D1312yes—
1110C2×C4C22×C4×D1312yes—
1111C2×C4C22×C4×D1312yes—
1112C2×C4#8825112yes—
1113C2×C4#8825612yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—134no—
1129C22—262no—
1130C22—262no—
1131C22—262no—
1132C22—262no—
1133C22—262no—
1134C22—262no—
1135C22—262no—
1136C22—262no—
1137C22—262no—
1138C22—262no—
1139C22—262no—
1140C22—262no—
1141C22—5216no—
1142C22—521no—
1143C22—521no—
1144C22—521no—
1145C22—521no—
1146C22—521no—
1147C22—521no—
1148C22—521no—
1149C22—521no—
1150C22C23×C4×D1311yescharacteristic
1151C22C2×#8825111yescharacteristic
1152C22C2×#8825611yescharacteristic
1153C22#1171964811yescharacteristic
1154C22#1171964811yescharacteristic
1155C22D13×H(5,𝔽2)11yescharacteristic
1156C22D13×2−1+411yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—262no—
1166C4—262no—
1167C4—262no—
1168C4—262no—
1169C4—262no—
1170C4—522no—
1171C4—522no—
1172C4—522no—
1173C4—522no—
1174C4#1171925014yes—
1175C2—42no—
1176C2—42no—
1177C2—264no—
1178C2—522no—
1179C2—522no—
1180C2C2×#1171925011yescharacteristic
1181C2D13×#52011yescharacteristic
1182C2#1312803711yescharacteristic
1183C2#1312911911yescharacteristic
1184C2#1312913611yescharacteristic
1185C2#1312914211yescharacteristic
1186C2#1312915911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2354C2
socle, cosocleC23×C13C25
prime radicalC2×#11719252C2
hypercenter#2354D13
hypocenterC13#34362
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13118003C2semidirect
3. #13117987C2semidirect
4. #13117920C2semidirect
5. #13117880C2semidirect
6. #13117780C2semidirect
7. #13117768C2semidirect
8. #13117766C2semidirect
9. #13117766C2semidirect
10. #13117765C2semidirect
11. #13117736C2semidirect
12. #13117732C2semidirect
13. #13117624C2semidirect
14. #13117620C2semidirect
15. #13117495C2semidirect
16. #13117489C2semidirect
17. #13117444C2semidirect
18. #13117441C2semidirect
19. #13117425C2semidirect
20. #13117424C2semidirect
21. #13117215C2semidirect
22. D13×#380C2semidirect
23. C13×#2354C2semidirect
28. C2×C13×#117C22semidirect
34. C22×C4⋊Dic13C22semidirect
35. #11719252C4semidirect
39. C2×#88146C22semidirect
42. C2×C4⋊C4×D13C22semidirect
53. C13×#388C22semidirect
54. C13×#384C22semidirect
56. C13×#380C22semidirect
57. C4×C13×C4⋊C4C22semidirect
58. C4×C13×C4⋊C4C22semidirect
61. #11718873C22semidirect
65. #11718650C22semidirect
72. #11718648C22semidirect
73. #11718648C22semidirect
74. #11718642C22semidirect
75. #11718639C22semidirect
76. #11718639C22semidirect
77. #11718638C22semidirect
78. #11718637C22semidirect
79. C4⋊C4×Dic13C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. #11718634C22semidirect
83. #11718619C22semidirect
88. #11718617C22semidirect
91. #11718607C22semidirect
94. #11718606C22semidirect
97. C22⋊C4×Dic13C22semidirect
99. #11718601C22semidirect
105. C4×#6103C22semidirect
106. #11718597C22semidirect
107. C4×C4⋊Dic13C22semidirect
108. #11718594C22semidirect
109. #11718594C22semidirect
110. #11718594C22semidirect
111. #11718590C22semidirect
113. #11718330C22semidirect
119. #11718314C22semidirect
120. #11718313C22semidirect
121. #11718310C22semidirect
122. #11718308C22semidirect
123. #11718307C22semidirect
136. C2×#6127C2×C4semidirect
141. C22×C4×D13C2×C4semidirect
151. C4×D4×C13C2×C4semidirect
176. #88193C2×C4semidirect
177. #88191C2×C4semidirect
178. C4×C22⋊D13C2×C4semidirect
179. C4×C22⋊D13C2×C4semidirect
218. #88150C2×C4semidirect
219. #88148C2×C4semidirect
226. #88137C2×C4semidirect
227. #88136C2×C4semidirect
230. #88132C2×C4semidirect
231. C4×D52C2×C4semidirect
232. #88126C2×C4semidirect
410. #2354D13semidirect
565. C2×#117C2×D13semidirect
590. #388C2×D13semidirect
612. #384C2×D13semidirect
629. #380C2×D13semidirect
635. C4×C4⋊C4C2×D13semidirect
636. C4×C4⋊C4C2×D13semidirect
745. C4×D4C4×D13semidirect
996. C13#34362semidirect

Maximal subgroups

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

subgroupindex
C2×#117192522
#131180032
#131179872
#131179202
#131178802
#131177802
#131177682
#131177662
#131177652
#131177362
#131177322
#131176242
#131176202
#131174952
#131174892
#131174442
#131174412
#131174252
#131174242
#131172152
D13×#3802
C13×#23542
#3436213