Finite Group Databasebeta

← #16026372

Subgroups — #16026372

Order 3328.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719312C211yesmaximal, characteristic
2#13118011C212yesmaximal, complemented
3#13117973C212yesmaximal, complemented
4#13117897C212yesmaximal, complemented
5#13117873C211yesmaximal, characteristic, complemented
6#13117870C211yesmaximal, characteristic, complemented
7#13117857C211yesmaximal, characteristic, complemented
8#13117854C211yesmaximal, characteristic, complemented
9#13117816C212yesmaximal, complemented
10#13117728C211yesmaximal, characteristic, complemented
11#13117725C211yesmaximal, characteristic, complemented
12#13117657C211yesmaximal, characteristic, complemented
13D4×#6103C211yesmaximal, characteristic, complemented
14#13117650C212yesmaximal, complemented
15#13117647C212yesmaximal, complemented
16#13117529C211yesmaximal, characteristic, complemented
17#13117498C212yesmaximal, complemented
18#13117493C212yesmaximal, complemented
19#13117425C211yesmaximal, characteristic, complemented
20#121×Dic13C211yesmaximal, characteristic, complemented
21#13117342C211yesmaximal, characteristic, complemented
22#13117324C211yesmaximal, characteristic, complemented
23C13×#2324C211yesmaximal, characteristic, complemented
24C22×D4×D13C2211yescharacteristic
25C22×#6127C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic, complemented
29C2×#88194C2212yes—
30C2×#88192C2211yescharacteristic
31C2×#88191C2212yes—
32C2×D4×Dic13C2211yescharacteristic
33C2×D4×Dic13C2212yescomplemented
34C2×#88184C2211yescharacteristic
35C22×#6103C2212yes—
36C22×C4×Dic13C2211yescharacteristic, complemented
37#11719312C4116yescomplemented
38C2×#88149C2211yescharacteristic
39C2×#88147C2211yescharacteristic
40C2×#88146C2211yescharacteristic
41C2×#88146C2211yescharacteristic, complemented
42C2×C4⋊C4×D13C2211yescharacteristic, complemented
43C2×#88139C2212yes—
44C2×#88136C2212yes—
45C2×#88135C2212yescomplemented
46C2×#88135C2212yescomplemented
47C2×C22⋊C4×D13C2212yes—
48C2×C4×D52C2211yescharacteristic
49C2×C4×D52C2212yescomplemented
50C13×#390C2211yescharacteristic
51C13×#390C2212yescomplemented
52C13×#389C2211yescharacteristic, complemented
53C13×#388C2212yescomplemented
54C13×#386C2212yescomplemented
55C13×#385C2212yescomplemented
56C13×#380C2211yescharacteristic, complemented
57C4×C13×C4⋊C4C2211yescharacteristic, complemented
58#11718882C2211yescharacteristic
59#11718881C2212yescomplemented
60#11718874C2212yes—
61#11718874C2212yescomplemented
62#11718873C2211yescharacteristic, complemented
63C4×C22⋊Dic13C2212yescomplemented
64#11718651C2212yes—
65#11718651C2212yescomplemented
66#11718651C2212yescomplemented
67#11718650C2212yescomplemented
68#11718649C2211yescharacteristic
69#11718649C2211yescharacteristic
70#11718649C2211yescharacteristic
71#11718649C2212yescomplemented
72#11718648C2211yescharacteristic
73#11718648C2211yescharacteristic
74#11718646C2211yescharacteristic, complemented
75C4⋊C4×Dic13C2211yescharacteristic, complemented
76C4⋊C4×Dic13C2211yescharacteristic, complemented
77C4⋊C4×Dic13C2212yescomplemented
78#11718635C2211yescharacteristic, complemented
79#11718635C2211yescharacteristic, complemented
80#11718634C2211yescharacteristic, complemented
81#11718619C2211yescharacteristic
82#11718619C2211yescharacteristic
83#11718619C2212yes—
84#11718619C2212yescomplemented
85#11718619C2211yescharacteristic, complemented
86#11718619C2211yescharacteristic, complemented
87#11718618C2212yes—
88#11718618C2212yescomplemented
89#11718618C2212yescomplemented
90#11718617C2212yes—
91#11718617C2212yes—
92#11718617C2212yescomplemented
93#11718617C2212yescomplemented
94#11718617C2212yescomplemented
95#11718616C2212yes—
96#11718616C2212yes—
97#11718612C2212yescomplemented
98#11718607C2212yescomplemented
99#11718605C2212yescomplemented
100#11718605C2212yescomplemented
101C22⋊C4×Dic13C2212yescomplemented
102#11718601C2212yes—
103#11718601C2212yescomplemented
104#11718600C2211yescharacteristic
105C4×#6103C2211yescharacteristic
106C4×#6103C2211yescharacteristic
107C4×#6103C2211yescharacteristic, complemented
108C4×#6103C2211yescharacteristic, complemented
109C4×C4⋊Dic13C2211yescharacteristic, complemented
110C4×#6101C2212yescomplemented
111#11718589C2211yescharacteristic, complemented
112#11718331C2212yes—
113#11718330C2212yes—
114#11718330C2212yescomplemented
115#11718329C2212yescomplemented
116#11718327C2212yescomplemented
117#11718327C2212yescomplemented
118#11718326C2212yes—
119#11718326C2212yescomplemented
120#11718326C2212yescomplemented
121#11718312C2212yescomplemented
122#11718312C2212yescomplemented
123#11718307C2212yescomplemented
124C24×D13C2312yes—
125C22×D4×C13C2311yescharacteristic
126C22×D4×C13C2312yes—
127C23×C4×C13C2311yescharacteristic
128C23×C4×C13C2312yes—
129C22×C22⋊D13C2312yes—
130C22×C22⋊D13C2312yes—
131C22×C22⋊D13C2312yes—
132C22×C22⋊D13C2311yescharacteristic
133C22×C22⋊D13C2311yescharacteristic
134C23×Dic13C2311yescharacteristic
135C23×Dic13C2312yes—
136C23×Dic13C2311yescharacteristic
137C2×D4×D13—42no—
138C2×D4×D13—42no—
139C2×D4×D13C2×C418yescomplemented
140C2×#6127—42no—
141C2×#6127—42no—
142C2×#6127C2×C418yescomplemented
143C22×D52C2311yescharacteristic
144C22×D52C2312yes—
145C22×D52C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2312yes—
149C22×C4×D13C2312yes—
150C22×C4×D13C2312yes—
151C22×Dic26C2311yescharacteristic
152C13×#121C2×C418yescomplemented
153C4×D4×C13—42no—
154C13×#117—42no—
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2311yescharacteristic
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C4⋊C4C2311yescharacteristic
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2311yescharacteristic
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C13×C22⋊C4C2311yescharacteristic
167C2×C13×C22⋊C4C2312yes—
168C2×C42×C13C2311yescharacteristic
169C2×C42×C13C2311yescharacteristic
170C2×C42×C13C2312yes—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2312yes—
176#88194C2×C4116yescomplemented
177#88192C2×C418yescomplemented
178#88191C2×C4116yescomplemented
179D4×Dic13—42no—
180D4×Dic13—44no—
181#88184C2×C418yescomplemented
182C2×#6103—44no—
183C2×#6103C2311yescharacteristic
184C2×#6103C2311yescharacteristic
185C2×#6103C2311yescharacteristic
186C2×#6103C2312yes—
187C2×#6103C2311yescharacteristic
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2312yes—
192C2×#6103C2312yes—
193C2×#6103C2312yes—
194C2×#6103C2312yes—
195C2×#6103C2311yescharacteristic
196C2×#6103C2311yescharacteristic
197C2×#6103C2312yes—
198C2×#6103C2311yescharacteristic
199C2×#6103C2311yescharacteristic
200C2×#6103C2312yes—
201C2×#6103C2312yes—
202C2×#6103C2312yes—
203C2×C4⋊Dic13C2311yescharacteristic
204C2×C4⋊Dic13C2312yes—
205C2×C4⋊Dic13C2311yescharacteristic
206C2×C4⋊Dic13C2311yescharacteristic
207C2×#6101C2312yes—
208C2×#6101C2312yes—
209C2×#6101C2312yes—
210C2×C4×Dic13—42no—
211C2×C4×Dic13C2311yescharacteristic
212C2×C4×Dic13C2311yescharacteristic
213C2×C4×Dic13C2312yes—
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2312yes—
216C2×C4×Dic13C2311yescharacteristic
217C2×C4×Dic13C2311yescharacteristic
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220#88149C2×C418yescomplemented
221#88147—42no—
222#88146—42no—
223#88146C2×C418yescomplemented
224C4⋊C4×D13—42no—
225#88139C2×C4116yescomplemented
226#88136C2×C4116yescomplemented
227#88135—44no—
228#88135—44no—
229C22⋊C4×D13—44no—
230C4×D52—44no—
231C4×D52—42no—
232C13×#95C2312yes—
233C13×#95C2312yes—
234C13×#95C2312yes—
235#88071C2312yes—
236#88071C2312yes—
237#88071C2312yes—
238#88071C2311yescharacteristic
239#88071C2311yescharacteristic
240#88071C2312yes—
241#88071C2312yes—
242#88071C2312yes—
243#88071C2312yes—
244#88071C2312yes—
245#88071C2312yes—
246#88071C2311yescharacteristic
247#88071C2311yescharacteristic
248#88071C2311yescharacteristic
249#88071C2311yescharacteristic
250#88071C2311yescharacteristic
251#88071C2311yescharacteristic
252#34411—131nomaximal, Sylow
253C24×C13C2412yes—
254C24×C13C2411yescharacteristic
255C23×D13—42no—
256C23×D13—42no—
257C23×D13—42no—
258C23×D13—42no—
259C23×D13—42no—
260C23×D13—42no—
261C23×D13C22×C418yes—
262C23×D13C2411yescharacteristic
263C23×D13C2412yes—
264C23×D13C2411yescharacteristic
265C2×D4×C13—22no—
266C2×D4×C13—22no—
267C2×D4×C13—42no—
268C2×D4×C13—42no—
269C2×D4×C13C22×C414yes—
270C2×D4×C13C22×C418yes—
271C22×C4×C13—22no—
272C22×C4×C13—22no—
273C22×C4×C13—42no—
274C22×C4×C13—42no—
275C22×C4×C13—42no—
276C22×C4×C13C22×C414yes—
277C22×C4×C13C2411yescharacteristic
278C22×C4×C13C2411yescharacteristic
279C22×C4×C13C2412yes—
280C22×C4×C13C2412yes—
281C22×C4×C13C2411yescharacteristic
282C22×C4×C13C2411yescharacteristic
283C22×C4×C13C2412yes—
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2411yescharacteristic
286C2×C22⋊D13—42no—
287C2×C22⋊D13—42no—
288C2×C22⋊D13—41no—
289C2×C22⋊D13—41no—
290C2×C22⋊D13—41no—
291C2×C22⋊D13—41no—
292C2×C22⋊D13—42no—
293C2×C22⋊D13—42no—
294C2×C22⋊D13—42no—
295C2×C22⋊D13—42no—
296C2×C22⋊D13C22×C418yes—
297C2×C22⋊D13C22×C418yes—
298C2×C22⋊D13C22×C418yes—
299C2×C22⋊D13C22×C414yes—
300C2×C22⋊D13C22×C414yes—
301C22×Dic13—22no—
302C22×Dic13—22no—
303C22×Dic13—24no—
304C22×Dic13—41no—
305C22×Dic13—41no—
306C22×Dic13—41no—
307C22×Dic13—41no—
308C22×Dic13—42no—
309C22×Dic13—42no—
310C22×Dic13C2411yescharacteristic
311C22×Dic13C2411yescharacteristic
312C22×Dic13C2412yes—
313C22×Dic13C2412yes—
314C22×Dic13C2411yescharacteristic
315C22×Dic13C2412yes—
316C22×Dic13C2411yescharacteristic
317C22×Dic13C2411yescharacteristic
318C22×Dic13C2411yescharacteristic
319D4×D13—416no—
320#6127—416no—
321C2×D52—22no—
322C2×D52—22no—
323C2×D52—42no—
324C2×D52—42no—
325C2×D52—41no—
326C2×D52—41no—
327C2×D52C22×C414yes—
328C2×D52C22×C414yes—
329C2×D52C22×C418yes—
330C2×C4×D13—22no—
331C2×C4×D13—22no—
332C2×C4×D13—22no—
333C2×C4×D13—22no—
334C2×C4×D13—24no—
335C2×C4×D13—42no—
336C2×C4×D13—42no—
337C2×C4×D13—42no—
338C2×C4×D13—42no—
339C2×C4×D13—42no—
340C2×C4×D13—42no—
341C2×C4×D13—42no—
342C2×C4×D13—42no—
343C2×C4×D13C22×C414yes—
344C2×C4×D13C22×C414yes—
345C2×Dic26—41no—
346C2×Dic26—41no—
347C2×Dic26C22×C414yes—
348C13×C4⋊C4—22no—
349C13×C4⋊C4—22no—
350C13×C4⋊C4—42no—
351C13×C4⋊C4—41no—
352C13×C4⋊C4—41no—
353C13×C4⋊C4C22×C414yes—
354C13×C22⋊C4—42no—
355C13×C22⋊C4—42no—
356C13×C22⋊C4—42no—
357C13×C22⋊C4—41no—
358C13×C22⋊C4—41no—
359C13×C22⋊C4—42no—
360C13×C22⋊C4C22×C418yes—
361C42×C13—22no—
362C42×C13—22no—
363C42×C13—42no—
364C22⋊Dic13—24no—
365C22⋊Dic13—42no—
366C22⋊Dic13—42no—
367C22⋊Dic13—42no—
368C22⋊Dic13C22×C418yes—
369#6103—22no—
370#6103—22no—
371#6103—22no—
372#6103—24no—
373#6103—22no—
374#6103—42no—
375#6103—42no—
376#6103—42no—
377#6103—42no—
378#6103—42no—
379#6103—42no—
380#6103—42no—
381#6103—41no—
382#6103—41no—
383#6103—42no—
384#6103—41no—
385#6103—41no—
386#6103C22×C418yes—
387#6103C22×C418yes—
388#6103C22×C418yes—
389C4⋊Dic13—22no—
390C4⋊Dic13—22no—
391C4⋊Dic13—24no—
392C4⋊Dic13C22×C414yes—
393#6101—24no—
394#6101—42no—
395#6101—42no—
396C4×Dic13—22no—
397C4×Dic13—22no—
398C4×Dic13—42no—
399C4×Dic13—42no—
400C4×Dic13—42no—
401C4×Dic13—41no—
402C4×Dic13—41no—
403C4×Dic13—42no—
404C4×Dic13C22×C418yes—
405C2×#535—131no—
406#2380—132no—
407#2375—132no—
408#2366—132no—
409#2363—131no—
410#2363—131no—
411#2361—131no—
412#2361—131no—
413#2358—132no—
414#2347—131no—
415#2347—131no—
416D4×C22⋊C4—131no—
417D4×C22⋊C4—131no—
418#2337—132no—
419#2337—132no—
420#2324—131no—
421#2324D1311yescharacteristic, complemented
422#2321—132no—
423#2321—132no—
424#2311—131no—
425C4×#121—131no—
426C4×#121—131no—
427#2297—131no—
428C23×C13—22no—
429C23×C13—21no—
430C23×C13—22no—
431C23×C13—21no—
432C23×C13—21no—
433C23×C13—22no—
434C23×C13—22no—
435C23×C13—21no—
436C23×C13—22no—
437C23×C13—21no—
438C23×C13—21no—
439C23×C13—22no—
440C23×C13C23×C414yes—
441C23×C13C23×C412yes—
442C23×C13C2511yescharacteristic
443C22×D13—21no—
444C22×D13—21no—
445C22×D13—22no—
446C22×D13—21no—
447C22×D13—21no—
448C22×D13—21no—
449C22×D13—22no—
450C22×D13—22no—
451C22×D13—22no—
452C22×D13—21no—
453C22×D13—21no—
454C22×D13—21no—
455C22×D13—21no—
456C22×D13—22no—
457C22×D13—21no—
458C22×D13—21no—
459C22×D13—21no—
460C22×D13—22no—
461C22×D13—48no—
462C22×D13—48no—
463C22×D13—48no—
464C22×D13—84no—
465C22×D13—84no—
466C22×D13—84no—
467C22×D13—84no—
468C22×D13C23×C412yes—
469C22×D13C23×C414yes—
470C22×D13C23×C412yes—
471D4×C13—28no—
472D4×C13—48no—
473C2×C4×C13—21no—
474C2×C4×C13—22no—
475C2×C4×C13—21no—
476C2×C4×C13—22no—
477C2×C4×C13—28no—
478C2×C4×C13—21no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—22no—
483C2×C4×C13—21no—
484C2×C4×C13—21no—
485C2×C4×C13—21no—
486C2×C4×C13—21no—
487C2×C4×C13—22no—
488C2×C4×C13—21no—
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—21no—
496C2×C4×C13—84no—
497C2×C4×C13C23×C414yes—
498C2×C4×C13C23×C412yes—
499C2×C4×C13C23×C412yes—
500C2×C4×C13H(5,𝔽2)12yes—
501C2×C4×C13H(5,𝔽2)12yes—
502C22⋊D13—44no—
503C22⋊D13—44no—
504C22⋊D13—48no—
505C22⋊D13—48no—
506C22⋊D13—48no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—22no—
510C2×Dic13—21no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—21no—
514C2×Dic13—21no—
515C2×Dic13—21no—
516C2×Dic13—22no—
517C2×Dic13—21no—
518C2×Dic13—21no—
519C2×Dic13—22no—
520C2×Dic13—22no—
521C2×Dic13—22no—
522C2×Dic13—22no—
523C2×Dic13—22no—
524C2×Dic13—22no—
525C2×Dic13—21no—
526C2×Dic13—21no—
527C2×Dic13—21no—
528C2×Dic13—21no—
529C2×Dic13—44no—
530C2×Dic13—44no—
531C2×Dic13—84no—
532C2×Dic13C23×C412yes—
533C2×Dic13C23×C414yes—
534C2×Dic13C23×C412yes—
535C2×Dic13H(5,𝔽2)12yes—
536C2×Dic13H(5,𝔽2)12yes—
537D52—28no—
538D52—48no—
539D52—44no—
540C4×D13—28no—
541C4×D13—28no—
542C4×D13—84no—
543C4×D13—84no—
544C4×D13—84no—
545Dic26—44no—
546C22×#41—131no—
547C23×D4—131no—
548#535—1316no—
549C2×#127—132no—
550C2×#124—132no—
551C2×#121—131no—
552C2×#121—131no—
553C2×#121—131no—
554C2×#121C2×D1311yescharacteristic
555C2×#120—132no—
556C2×#120—132no—
557C2×C4×D4—131no—
558C2×C4×D4—132no—
559C2×C4×D4—131no—
560C2×C4×D4—132no—
561C2×C4×D4—132no—
562C2×C4×D4—131no—
563C2×C4×D4—132no—
564C2×C4×D4C2×D1311yescharacteristic
565C2×#117—131no—
566C2×#117—131no—
567C2×#117C2×D1311yescharacteristic, complemented
568C22×C4⋊C4—131no—
569C22×C22⋊C4—132no—
570C22×C22⋊C4—132no—
571C22×C42—131no—
572#391—131no—
573#391—131no—
574#391—132no—
575#390—131no—
576#390—131no—
577#390—131no—
578#390—132no—
579#390—131no—
580#390—132no—
581#390—132no—
582#390—132no—
583#390—131no—
584#390C2×D1311yescharacteristic
585#390C2×D1312yescomplemented
586#389—131no—
587#389—131no—
588#389—131no—
589#389C2×D1311yescharacteristic, complemented
590#388—132no—
591#388—132no—
592#388—132no—
593#388—132no—
594#388—132no—
595#388—132no—
596#388—132no—
597#388—132no—
598#388—132no—
599#388—132no—
600#388—132no—
601#388C2×D1312yescomplemented
602#386—132no—
603#386—132no—
604#386—132no—
605#386—132no—
606#386—132no—
607#386—132no—
608#386—132no—
609#386—132no—
610#386—132no—
611#386—131no—
612#386—131no—
613#386—131no—
614#386—132no—
615#386—131no—
616#386—132no—
617#386—132no—
618#386—132no—
619#386C2×D1312yescomplemented
620#385—132no—
621#385—132no—
622#385—132no—
623#385C2×D1312yescomplemented
624#383—132no—
625#383—132no—
626#380—131no—
627#380—131no—
628#380—131no—
629#380C2×D1311yescharacteristic, complemented
630#379—132no—
631#379—132no—
632C4×C4⋊C4—132no—
633C4×C4⋊C4—131no—
634C4×C4⋊C4—131no—
635C4×C4⋊C4—131no—
636C4×C4⋊C4—132no—
637C4×C4⋊C4C2×D1311yescharacteristic, complemented
638C4×C22⋊C4—132no—
639C4×C22⋊C4—132no—
640C4×C22⋊C4—131no—
641C4×C22⋊C4—131no—
642C4×C22⋊C4—131no—
643C4×C22⋊C4—131no—
644C4×C22⋊C4—132no—
645C4×C22⋊C4—132no—
646C22×C13—22no—
647C22×C13—24no—
648C22×C13—22no—
649C22×C13—24no—
650C22×C13—22no—
651C22×C13—24no—
652C22×C13—41no—
653C22×C13—42no—
654C22×C13—41no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—41no—
659C22×C13—41no—
660C22×C13C24×C411yescharacteristic
661C22×C13C2×H(5,𝔽2)11yescharacteristic
662C22×C13C2×H(5,𝔽2)11yescharacteristic
663C22×C13C2×H(5,𝔽2)11yescharacteristic
664C22×C13C2×H(5,𝔽2)11yescharacteristic
665C22×C13#58511yescharacteristic
666C22×C13#58511yescharacteristic
667C2×D13—22no—
668C2×D13—22no—
669C2×D13—24no—
670C2×D13—22no—
671C2×D13—24no—
672C2×D13—22no—
673C2×D13—24no—
674C2×D13—22no—
675C2×D13—22no—
676C2×D13—41no—
677C2×D13—42no—
678C2×D13—41no—
679C2×D13—41no—
680C2×D13—42no—
681C2×D13—41no—
682C2×D13—42no—
683C2×D13—41no—
684C2×D13—41no—
685C2×D13—42no—
686C2×D13—41no—
687C2×D13—41no—
688C2×D13—816no—
689C4×C13—22no—
690C4×C13—24no—
691C4×C13—42no—
692C4×C13—41no—
693C4×C13—41no—
694C4×C13—41no—
695C4×C13—42no—
696C4×C13—41no—
697C4×C13#51814yes—
698Dic13—22no—
699Dic13—22no—
700Dic13—24no—
701Dic13—22no—
702Dic13—22no—
703Dic13—42no—
704Dic13—41no—
705Dic13—41no—
706Dic13—42no—
707C25—132no—
708C2×#41—138no—
709C2×#41—522no—
710C2×#41—522no—
711C22×Q8—131no—
712C22×D4—132no—
713C22×D4—132no—
714C22×D4—131no—
715C22×D4—132no—
716C22×D4—131no—
717C22×D4—138no—
718C22×D4—131no—
719C22×D4—132no—
720C22×D4—131no—
721C22×D4—522no—
722C22×D4—522no—
723C22×D4C22×D1311yescharacteristic
724C22×D4C22×D1312yes—
725C23×C4—131no—
726C23×C4—131no—
727C23×C4—131no—
728C23×C4—132no—
729C23×C4—131no—
730C23×C4—132no—
731C23×C4—132no—
732C23×C4—132no—
733C23×C4C22×D1311yescharacteristic
734C23×C4C22×D1312yes—
735#127—1316no—
736#124—1316no—
737#121—138no—
738#121—138no—
739#121—138no—
740#121C4×D1318yescomplemented
741#120—1316no—
742#120—1316no—
743C4×D4—42no—
744C4×D4—522no—
745C4×D4—524no—
746C4×D4—522no—
747C4×D4—522no—
748C4×D4—524no—
749C4×D4—524no—
750C4×D4—524no—
751#117—42no—
752#117—138no—
753#117—522no—
754C2×C4⋊C4—131no—
755C2×C4⋊C4—131no—
756C2×C4⋊C4—131no—
757C2×C4⋊C4—132no—
758C2×C4⋊C4—132no—
759C2×C4⋊C4—132no—
760C2×C4⋊C4—132no—
761C2×C4⋊C4—522no—
762C2×C4⋊C4C22×D1311yescharacteristic
763C2×C4⋊C4C22×D1311yescharacteristic
764C2×C4⋊C4C22×D1311yescharacteristic
765C2×C4⋊C4C22×D1311yescharacteristic
766C2×C4⋊C4C22×D1312yes—
767C2×C4⋊C4C22×D1311yescharacteristic
768C2×C22⋊C4—132no—
769C2×C22⋊C4—132no—
770C2×C22⋊C4—132no—
771C2×C22⋊C4—132no—
772C2×C22⋊C4—132no—
773C2×C22⋊C4—131no—
774C2×C22⋊C4—131no—
775C2×C22⋊C4—132no—
776C2×C22⋊C4—131no—
777C2×C22⋊C4—131no—
778C2×C22⋊C4—132no—
779C2×C22⋊C4—132no—
780C2×C22⋊C4—132no—
781C2×C22⋊C4—132no—
782C2×C22⋊C4—132no—
783C2×C22⋊C4—132no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—132no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—132no—
788C2×C22⋊C4—131no—
789C2×C22⋊C4—131no—
790C2×C22⋊C4—132no—
791C2×C22⋊C4—131no—
792C2×C22⋊C4—131no—
793C2×C22⋊C4—524no—
794C2×C22⋊C4—524no—
795C2×C22⋊C4C22×D1312yes—
796C2×C22⋊C4C22×D1311yescharacteristic
797C2×C22⋊C4C22×D1311yescharacteristic
798C2×C22⋊C4C22×D1312yes—
799C2×C22⋊C4C22×D1312yes—
800C2×C22⋊C4C22×D1312yes—
801C2×C22⋊C4C22×D1312yes—
802C2×C42—132no—
803C2×C42—131no—
804C2×C42—131no—
805C2×C42—132no—
806C2×C42—132no—
807C2×C42—132no—
808C2×C42—132no—
809C2×C42—131no—
810C2×C42—131no—
811C2×C42—522no—
812C2×C42C22×D1311yescharacteristic
813C2×C42C22×D1311yescharacteristic
814C2×C42C22×D1312yes—
815#95—131no—
816#95—131no—
817#95—131no—
818#95—131no—
819#95—132no—
820#95—131no—
821#95—131no—
822#95—132no—
823#95—132no—
824#95—132no—
825#95—131no—
826#95—131no—
827#95—132no—
828#95—132no—
829#95—132no—
830#95—132no—
831#95—132no—
832#95C22×D1312yes—
833#95C22×D1312yes—
834#95C22×D1312yes—
835C2×C13—44no—
836C2×C13—42no—
837C2×C13C2×#51811yescharacteristic
838C2×C13C4×H(5,𝔽2)11yescharacteristic
839C2×C13C4×H(5,𝔽2)11yescharacteristic
840C2×C13#353711yescharacteristic
841C2×C13#354011yescharacteristic
842C2×C13#354611yescharacteristic
843C2×C13#354611yescharacteristic
844D13—42no—
845D13—44no—
846D13—42no—
847C24—131no—
848C24—132no—
849C24—131no—
850C24—138no—
851C24—522no—
852C24—522no—
853C24—522no—
854C24—522no—
855C24—522no—
856C24—522no—
857C24C23×D1312yes—
858C24C23×D1311yescharacteristic
859#41—5216no—
860C2×Q8—134no—
861C2×Q8—521no—
862C2×Q8—521no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—134no—
868C2×D4—138no—
869C2×D4—138no—
870C2×D4—138no—
871C2×D4—134no—
872C2×D4—134no—
873C2×D4—134no—
874C2×D4—138no—
875C2×D4—262no—
876C2×D4—262no—
877C2×D4—522no—
878C2×D4—521no—
879C2×D4—521no—
880C2×D4—522no—
881C2×D4—5216no—
882C2×D4—522no—
883C2×D4—522no—
884C2×D4—522no—
885C2×D4—522no—
886C2×D4—521no—
887C2×D4—521no—
888C2×D4—521no—
889C2×D4—521no—
890C2×D4—522no—
891C2×D4—522no—
892C2×D4C2×C4×D1314yes—
893C2×D4C2×C4×D1318yes—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—131no—
900C22×C4—132no—
901C22×C4—131no—
902C22×C4—131no—
903C22×C4—131no—
904C22×C4—134no—
905C22×C4—134no—
906C22×C4—131no—
907C22×C4—131no—
908C22×C4—132no—
909C22×C4—132no—
910C22×C4—264no—
911C22×C4—262no—
912C22×C4—262no—
913C22×C4—264no—
914C22×C4—262no—
915C22×C4—262no—
916C22×C4—262no—
917C22×C4—262no—
918C22×C4—522no—
919C22×C4—522no—
920C22×C4—522no—
921C22×C4—522no—
922C22×C4—522no—
923C22×C4—522no—
924C22×C4—522no—
925C22×C4—522no—
926C22×C4—521no—
927C22×C4—521no—
928C22×C4—521no—
929C22×C4—521no—
930C22×C4—522no—
931C22×C4—522no—
932C22×C4C2×C4×D1314yes—
933C22×C4C23×D1311yescharacteristic
934C22×C4C23×D1311yescharacteristic
935C22×C4C23×D1312yes—
936C22×C4C23×D1312yes—
937C22×C4C23×D1311yescharacteristic
938C22×C4C23×D1311yescharacteristic
939C22×C4C23×D1312yes—
940C22×C4C23×D1311yescharacteristic
941C22×C4C23×D1311yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—42no—
947C4⋊C4—134no—
948C4⋊C4—264no—
949C4⋊C4—264no—
950C4⋊C4—262no—
951C4⋊C4—262no—
952C4⋊C4—522no—
953C4⋊C4—522no—
954C4⋊C4C2×C4×D1314yes—
955C22⋊C4—42no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—138no—
962C22⋊C4—138no—
963C22⋊C4—138no—
964C22⋊C4—138no—
965C22⋊C4—262no—
966C22⋊C4—262no—
967C22⋊C4—264no—
968C22⋊C4—262no—
969C22⋊C4—262no—
970C22⋊C4—264no—
971C22⋊C4—522no—
972C22⋊C4—522no—
973C22⋊C4—522no—
974C22⋊C4—522no—
975C22⋊C4—522no—
976C22⋊C4—522no—
977C22⋊C4—522no—
978C22⋊C4—521no—
979C22⋊C4—522no—
980C22⋊C4—521no—
981C22⋊C4—521no—
982C22⋊C4—521no—
983C22⋊C4—522no—
984C22⋊C4—522no—
985C22⋊C4—522no—
986C22⋊C4C2×C4×D1318yes—
987C42—22no—
988C42—22no—
989C42—42no—
990C42—138no—
991C42—262no—
992C42—262no—
993C42—521no—
994C42—521no—
995C42—522no—
996C42—522no—
997C42—522no—
998C42—522no—
999C13#3441111yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—21no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—22no—
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—132no—
1013C23—134no—
1014C23—132no—
1015C23—261no—
1016C23—262no—
1017C23—261no—
1018C23—262no—
1019C23—261no—
1020C23—261no—
1021C23—261no—
1022C23—261no—
1023C23—262no—
1024C23—261no—
1025C23—261no—
1026C23—262no—
1027C23—261no—
1028C23—262no—
1029C23—261no—
1030C23—261no—
1031C23—261no—
1032C23—262no—
1033C23—528no—
1034C23—528no—
1035C23—528no—
1036C23—1044no—
1037C23—1044no—
1038C23—1044no—
1039C23—1044no—
1040C23C22×C4×D1314yes—
1041C23C22×C4×D1312yes—
1042C23C24×D1311yescharacteristic
1043Q8—524no—
1044D4—28no—
1045D4—48no—
1046D4—268no—
1047D4—528no—
1048D4—524no—
1049D4—528no—
1050D4—528no—
1051D4—528no—
1052D4—524no—
1053D4—524no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—84no—
1078C2×C4—132no—
1079C2×C4—134no—
1080C2×C4—132no—
1081C2×C4—132no—
1082C2×C4—132no—
1083C2×C4—261no—
1084C2×C4—261no—
1085C2×C4—261no—
1086C2×C4—261no—
1087C2×C4—261no—
1088C2×C4—261no—
1089C2×C4—262no—
1090C2×C4—261no—
1091C2×C4—261no—
1092C2×C4—262no—
1093C2×C4—268no—
1094C2×C4—268no—
1095C2×C4—262no—
1096C2×C4—261no—
1097C2×C4—261no—
1098C2×C4—262no—
1099C2×C4—262no—
1100C2×C4—262no—
1101C2×C4—262no—
1102C2×C4—261no—
1103C2×C4—261no—
1104C2×C4—261no—
1105C2×C4—261no—
1106C2×C4—262no—
1107C2×C4—524no—
1108C2×C4—524no—
1109C2×C4—1044no—
1110C2×C4—1044no—
1111C2×C4—1044no—
1112C2×C4—1044no—
1113C2×C4C22×C4×D1314yes—
1114C2×C4C22×C4×D1312yes—
1115C2×C4C22×C4×D1312yes—
1116C2×C4#8825112yes—
1117C2×C4#8825612yes—
1118C22—22no—
1119C22—24no—
1120C22—22no—
1121C22—24no—
1122C22—22no—
1123C22—24no—
1124C22—41no—
1125C22—42no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—262no—
1133C22—262no—
1134C22—264no—
1135C22—262no—
1136C22—264no—
1137C22—262no—
1138C22—262no—
1139C22—264no—
1140C22—262no—
1141C22—521no—
1142C22—522no—
1143C22—521no—
1144C22—521no—
1145C22—522no—
1146C22—521no—
1147C22—522no—
1148C22—521no—
1149C22—521no—
1150C22—521no—
1151C22—522no—
1152C22—521no—
1153C22—10416no—
1154C22C23×C4×D1311yescharacteristic
1155C22C2×#8825111yescharacteristic
1156C22C2×#8825611yescharacteristic
1157C22D13×H(5,𝔽2)11yescharacteristic
1158C22D13×H(5,𝔽2)11yescharacteristic
1159C22#1171965011yescharacteristic
1160C22#1171965211yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—42no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—262no—
1170C4—262no—
1171C4—264no—
1172C4—262no—
1173C4—262no—
1174C4—522no—
1175C4—521no—
1176C4—521no—
1177C4—522no—
1178C4#1171925014yes—
1179C2—44no—
1180C2—42no—
1181C2—522no—
1182C2—524no—
1183C2—522no—
1184C2C2×#1171925011yescharacteristic
1185C2#1312804011yescharacteristic
1186C2#1312804211yescharacteristic
1187C2#1312907411yescharacteristic
1188C2#1312910811yescharacteristic
1189C2#1312919811yescharacteristic
1190C2#1312920611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2324C2
socle, cosocleC23×C13C25
prime radicalC2×#11719312C2
hypercenter#2324D13
hypocenterC13#34411
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13118011C2semidirect
3. #13117973C2semidirect
4. #13117897C2semidirect
5. #13117873C2semidirect
6. #13117870C2semidirect
7. #13117857C2semidirect
8. #13117854C2semidirect
9. #13117816C2semidirect
10. #13117728C2semidirect
11. #13117725C2semidirect
12. #13117657C2semidirect
13. D4×#6103C2semidirect
14. #13117650C2semidirect
15. #13117647C2semidirect
16. #13117529C2semidirect
17. #13117498C2semidirect
18. #13117493C2semidirect
19. #13117425C2semidirect
20. #121×Dic13C2semidirect
21. #13117342C2semidirect
22. #13117324C2semidirect
23. C13×#2324C2semidirect
28. C2×C13×#117C22semidirect
33. C2×D4×Dic13C22semidirect
36. C22×C4×Dic13C22semidirect
37. #11719312C4semidirect
41. C2×#88146C22semidirect
42. C2×C4⋊C4×D13C22semidirect
45. C2×#88135C22semidirect
46. C2×#88135C22semidirect
49. C2×C4×D52C22semidirect
51. C13×#390C22semidirect
52. C13×#389C22semidirect
53. C13×#388C22semidirect
54. C13×#386C22semidirect
55. C13×#385C22semidirect
56. C13×#380C22semidirect
57. C4×C13×C4⋊C4C22semidirect
59. #11718881C22semidirect
61. #11718874C22semidirect
62. #11718873C22semidirect
63. C4×C22⋊Dic13C22semidirect
65. #11718651C22semidirect
66. #11718651C22semidirect
67. #11718650C22semidirect
71. #11718649C22semidirect
74. #11718646C22semidirect
75. C4⋊C4×Dic13C22semidirect
76. C4⋊C4×Dic13C22semidirect
77. C4⋊C4×Dic13C22semidirect
78. #11718635C22semidirect
79. #11718635C22semidirect
80. #11718634C22semidirect
84. #11718619C22semidirect
85. #11718619C22semidirect
86. #11718619C22semidirect
88. #11718618C22semidirect
89. #11718618C22semidirect
92. #11718617C22semidirect
93. #11718617C22semidirect
94. #11718617C22semidirect
97. #11718612C22semidirect
98. #11718607C22semidirect
99. #11718605C22semidirect
100. #11718605C22semidirect
101. C22⋊C4×Dic13C22semidirect
103. #11718601C22semidirect
107. C4×#6103C22semidirect
108. C4×#6103C22semidirect
109. C4×C4⋊Dic13C22semidirect
110. C4×#6101C22semidirect
111. #11718589C22semidirect
114. #11718330C22semidirect
115. #11718329C22semidirect
116. #11718327C22semidirect
117. #11718327C22semidirect
119. #11718326C22semidirect
120. #11718326C22semidirect
121. #11718312C22semidirect
122. #11718312C22semidirect
123. #11718307C22semidirect
139. C2×D4×D13C2×C4semidirect
142. C2×#6127C2×C4semidirect
152. C13×#121C2×C4semidirect
176. #88194C2×C4semidirect
177. #88192C2×C4semidirect
178. #88191C2×C4semidirect
181. #88184C2×C4semidirect
220. #88149C2×C4semidirect
223. #88146C2×C4semidirect
225. #88139C2×C4semidirect
226. #88136C2×C4semidirect
421. #2324D13semidirect
567. C2×#117C2×D13semidirect
585. #390C2×D13semidirect
589. #389C2×D13semidirect
601. #388C2×D13semidirect
619. #386C2×D13semidirect
623. #385C2×D13semidirect
629. #380C2×D13semidirect
637. C4×C4⋊C4C2×D13semidirect
740. #121C4×D13semidirect
999. C13#34411semidirect

Maximal subgroups

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

subgroupindex
C2×#117193122
#131180112
#131179732
#131178972
#131178732
#131178702
#131178572
#131178542
#131178162
#131177282
#131177252
#131176572
D4×#61032
#131176502
#131176472
#131175292
#131174982
#131174932
#131174252
#121×Dic132
#131173422
#131173242
C13×#23242
#3441113