Finite Group Databasebeta

← #16026442

Subgroups — #16026442

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×#11719510C211yesmaximal, characteristic
2#13118006C212yesmaximal, complemented
3#13117975C212yesmaximal, complemented
4#13117945C212yesmaximal, complemented
5#13117879C211yesmaximal, characteristic, complemented
6#13117870C211yesmaximal, characteristic, complemented
7#13117857C211yesmaximal, characteristic, complemented
8#13117848C211yesmaximal, characteristic, complemented
9#13117815C212yesmaximal, complemented
10#13117723C211yesmaximal, characteristic, complemented
11#13117719C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic13C211yesmaximal, characteristic, complemented
13#13117557C212yesmaximal, complemented
14#13117557C212yesmaximal, complemented
15#13117532C211yesmaximal, characteristic, complemented
16#13117523C211yesmaximal, characteristic, complemented
17#13117494C212yesmaximal, complemented
18#13117491C212yesmaximal, complemented
19#13117425C211yesmaximal, characteristic, complemented
20#13117352C211yesmaximal, characteristic, complemented
21C4×#88192C211yesmaximal, characteristic, complemented
22#13117322C211yesmaximal, characteristic, complemented
23D4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
24C23×D4×C13C2211yescharacteristic
25C22×#6127C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C22×C13×C22⋊C4C2212yes—
29C2×#88207C2212yes—
30C2×#88207C2212yes—
31C22×C22⋊Dic13C2212yes—
32#11719510C4116yescomplemented
33C2×#88194C2212yes—
34C2×#88192C2211yescharacteristic
35C2×#88192C2211yescharacteristic
36C2×#88192C2211yescharacteristic
37C2×#88192C2211yescharacteristic
38C2×#88190C2212yes—
39C2×D4×Dic13C2211yescharacteristic
40C2×D4×Dic13C2211yescharacteristic
41C2×C4×C22⋊D13C2212yescomplemented
42C2×C4×C22⋊D13C2212yescomplemented
43C2×#88180C2211yescharacteristic
44C2×#88146C2211yescharacteristic, complemented
45C2×C4⋊C4×D13C2211yescharacteristic, complemented
46C2×#88135C2212yescomplemented
47C2×#88135C2212yescomplemented
48C2×#88126C2211yescharacteristic, complemented
49C2×C42×D13C2211yescharacteristic, complemented
50C13×#390C2211yescharacteristic
51C13×#390C2211yescharacteristic
52C13×#386C2212yes—
53C13×#386C2212yes—
54C13×#380C2211yescharacteristic
55C13×#379C2212yes—
56C4×C13×C22⋊C4C2211yescharacteristic
57#11718908C2212yes—
58#11718882C2211yescharacteristic
59#11718882C2211yescharacteristic
60#11718881C2212yes—
61#11718881C2212yes—
62#11718874C2212yescomplemented
63#11718874C2212yescomplemented
64#11718873C2211yescharacteristic
65#11718871C2212yescomplemented
66#11718871C2212yescomplemented
67C4×C22⋊Dic13C2211yescharacteristic
68C4×C22⋊Dic13C2212yescomplemented
69C4×C22⋊Dic13C2212yescomplemented
70#11718648C2211yescharacteristic, complemented
71#11718648C2211yescharacteristic, complemented
72C4⋊C4×Dic13C2211yescharacteristic, complemented
73C4⋊C4×Dic13C2211yescharacteristic, complemented
74#11718634C2211yescharacteristic, complemented
75#11718634C2211yescharacteristic, complemented
76#11718619C2212yescomplemented
77#11718619C2212yescomplemented
78#11718618C2211yescharacteristic
79#11718618C2212yes—
80#11718618C2211yescharacteristic
81#11718618C2212yescomplemented
82#11718618C2212yescomplemented
83#11718618C2212yescomplemented
84#11718618C2212yescomplemented
85#11718617C2212yes—
86#11718617C2211yescharacteristic
87#11718617C2211yescharacteristic
88#11718617C2212yescomplemented
89#11718617C2212yescomplemented
90#11718617C2212yescomplemented
91#11718617C2212yescomplemented
92#11718607C2212yescomplemented
93#11718607C2212yescomplemented
94#11718606C2212yes—
95#11718606C2212yes—
96#11718606C2212yescomplemented
97#11718606C2212yescomplemented
98#11718606C2212yescomplemented
99#11718606C2212yescomplemented
100#11718605C2212yes—
101#11718605C2212yes—
102#11718605C2212yescomplemented
103#11718605C2212yescomplemented
104#11718605C2212yescomplemented
105#11718605C2212yescomplemented
106C22⋊C4×Dic13C2212yescomplemented
107C22⋊C4×Dic13C2212yescomplemented
108C4×#6103C2211yescharacteristic, complemented
109C4×#6103C2211yescharacteristic, complemented
110C4×C4⋊Dic13C2211yescharacteristic, complemented
111C4×C4⋊Dic13C2211yescharacteristic, complemented
112#11718589C2211yescharacteristic, complemented
113#11718589C2211yescharacteristic, complemented
114#11718326C2211yescharacteristic, complemented
115#11718326C2211yescharacteristic, complemented
116#11718326C2212yescomplemented
117#11718311C2212yescomplemented
118#11718311C2212yescomplemented
119#11718309C2212yescomplemented
120#11718309C2212yescomplemented
121#11718307C2211yescharacteristic, complemented
122#11718307C2212yescomplemented
123#11718307C2211yescharacteristic, complemented
124C25×C13C2312yes—
125C22×D4×C13—42no—
126C22×D4×C13—42no—
127C22×D4×C13C2×C418yescomplemented
128C22×D4×C13C2311yescharacteristic
129C22×D4×C13C2311yescharacteristic
130C22×D4×C13C2312yes—
131C23×C4×C13C2311yescharacteristic
132C23×C4×C13C2312yes—
133C23×C4×C13C2312yes—
134C22×C22⋊D13C2312yes—
135C22×C22⋊D13C2312yes—
136C22×C22⋊D13C2312yes—
137C22×C22⋊D13C2312yes—
138C22×C22⋊D13C2311yescharacteristic
139C22×C22⋊D13C2311yescharacteristic
140C23×Dic13C2312yes—
141C23×Dic13C2312yes—
142C2×#6127—42no—
143C2×#6127—42no—
144C2×#6127C2×C418yescomplemented
145C22×D52C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×C4×D13C2312yes—
151C22×Dic26C2311yescharacteristic
152C4×D4×C13—42no—
153C4×D4×C13—42no—
154C2×C13×C4⋊C4C2311yescharacteristic
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C22⋊C4—44no—
157C2×C13×C22⋊C4C2311yescharacteristic
158C2×C13×C22⋊C4C2312yes—
159C2×C13×C22⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2312yes—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168#88207C2×C4116yescomplemented
169#88207C2×C4116yescomplemented
170C2×C22⋊Dic13—44no—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2311yescharacteristic
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2312yes—
176C2×C22⋊Dic13C2312yes—
177C2×C22⋊Dic13C2312yes—
178C2×C22⋊Dic13C2311yescharacteristic
179C2×C22⋊Dic13C2312yes—
180C2×C22⋊Dic13C2312yes—
181C2×C22⋊Dic13C2312yes—
182C2×C22⋊Dic13C2312yes—
183C2×C22⋊Dic13C2312yes—
184C2×C22⋊Dic13C2312yes—
185#88194C2×C4116yescomplemented
186#88192C2×C418yescomplemented
187#88192C2×C418yescomplemented
188#88192C2×C418yescomplemented
189#88192C2×C418yescomplemented
190#88190C2×C4116yescomplemented
191D4×Dic13—42no—
192D4×Dic13—42no—
193C4×C22⋊D13—44no—
194C4×C22⋊D13—44no—
195C2×#6103C2311yescharacteristic
196C2×#6103C2311yescharacteristic
197C2×#6103C2311yescharacteristic
198C2×#6103C2311yescharacteristic
199C2×#6103C2312yes—
200C2×#6103C2312yes—
201C2×#6103C2312yes—
202C2×#6103C2311yescharacteristic
203C2×#6103C2311yescharacteristic
204#88180C2×C418yescomplemented
205C2×C4⋊Dic13C2311yescharacteristic
206C2×C4⋊Dic13C2311yescharacteristic
207C2×C4⋊Dic13C2311yescharacteristic
208C2×C4⋊Dic13C2311yescharacteristic
209C2×#6101C2311yescharacteristic
210C2×#6101C2311yescharacteristic
211C2×#6101C2312yes—
212C2×#6101C2312yes—
213C2×#6101C2312yes—
214C2×#6101C2312yes—
215C2×#6101C2312yes—
216C2×C4×Dic13C2311yescharacteristic
217C2×C4×Dic13C2311yescharacteristic
218C2×C4×Dic13C2312yes—
219C2×C4×Dic13C2312yes—
220C2×C4×Dic13C2311yescharacteristic
221C2×C4×Dic13C2311yescharacteristic
222C2×C4×Dic13C2312yes—
223C2×C4×Dic13C2312yes—
224C2×C4×Dic13C2312yes—
225C2×C4×Dic13C2312yes—
226#88146—42no—
227C4⋊C4×D13—42no—
228#88135—44no—
229#88135—44no—
230#88126—42no—
231C42×D13—42no—
232C13×#95C2311yescharacteristic
233C13×#95C2311yescharacteristic
234C13×#95C2312yes—
235#88071C2311yescharacteristic
236#88071C2312yes—
237#88071C2311yescharacteristic
238#88071C2311yescharacteristic
239#88071C2311yescharacteristic
240#88071C2311yescharacteristic
241#88071C2311yescharacteristic
242#88071C2312yes—
243#88071C2312yes—
244#88071C2312yes—
245#88071C2312yes—
246#88071C2312yes—
247#88071C2312yes—
248#88071C2312yes—
249#88071C2312yes—
250#88071C2312yes—
251#88071C2312yes—
252#34415—131nomaximal, Sylow
253C24×C13—42no—
254C24×C13—42no—
255C24×C13—42no—
256C24×C13—42no—
257C24×C13—42no—
258C24×C13—42no—
259C24×C13C22×C418yes—
260C24×C13C2411yescharacteristic
261C24×C13C2412yes—
262C24×C13C2412yes—
263C23×D13C2411yescharacteristic
264C23×D13C2411yescharacteristic
265C2×D4×C13—22no—
266C2×D4×C13—22no—
267C2×D4×C13—22no—
268C2×D4×C13—22no—
269C2×D4×C13—416no—
270C2×D4×C13—42no—
271C2×D4×C13—42no—
272C2×D4×C13C22×C414yes—
273C2×D4×C13C22×C414yes—
274C2×D4×C13C22×C418yes—
275C22×C4×C13—22no—
276C22×C4×C13—22no—
277C22×C4×C13—24no—
278C22×C4×C13—42no—
279C22×C4×C13—42no—
280C22×C4×C13—42no—
281C22×C4×C13—42no—
282C22×C4×C13—42no—
283C22×C4×C13C22×C414yes—
284C22×C4×C13C2411yescharacteristic
285C22×C4×C13C2412yes—
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2412yes—
288C22×C4×C13C2411yescharacteristic
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2411yescharacteristic
291C22×C4×C13C2411yescharacteristic
292C2×C22⋊D13—42no—
293C2×C22⋊D13—42no—
294C2×C22⋊D13—42no—
295C2×C22⋊D13—42no—
296C2×C22⋊D13—41no—
297C2×C22⋊D13—41no—
298C2×C22⋊D13—41no—
299C2×C22⋊D13—41no—
300C2×C22⋊D13—42no—
301C2×C22⋊D13—42no—
302C2×C22⋊D13—42no—
303C2×C22⋊D13—42no—
304C2×C22⋊D13C22×C418yes—
305C2×C22⋊D13C22×C418yes—
306C2×C22⋊D13C22×C418yes—
307C2×C22⋊D13C22×C418yes—
308C2×C22⋊D13C22×C414yes—
309C2×C22⋊D13C22×C414yes—
310C22×Dic13—24no—
311C22×Dic13—42no—
312C22×Dic13—42no—
313C22×Dic13—42no—
314C22×Dic13—42no—
315C22×Dic13—42no—
316C22×Dic13C2411yescharacteristic
317C22×Dic13C2411yescharacteristic
318C22×Dic13C2412yes—
319C22×Dic13C2411yescharacteristic
320C22×Dic13C2412yes—
321C22×Dic13C2412yes—
322C22×Dic13C2412yes—
323C22×Dic13C2411yescharacteristic
324C22×Dic13C2411yescharacteristic
325C22×Dic13C2411yescharacteristic
326#6127—416no—
327C2×D52—41no—
328C2×D52—41no—
329C2×D52C22×C414yes—
330C2×C4×D13—22no—
331C2×C4×D13—22no—
332C2×C4×D13—22no—
333C2×C4×D13—22no—
334C2×C4×D13—22no—
335C2×C4×D13—22no—
336C2×C4×D13—41no—
337C2×C4×D13—41no—
338C2×C4×D13—41no—
339C2×C4×D13—41no—
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×C22⋊C4—24no—
351C13×C22⋊C4—22no—
352C13×C22⋊C4—42no—
353C13×C22⋊C4—42no—
354C13×C22⋊C4—42no—
355C13×C22⋊C4—41no—
356C13×C22⋊C4—42no—
357C13×C22⋊C4—42no—
358C13×C22⋊C4—42no—
359C42×C13—22no—
360C42×C13—22no—
361C22⋊Dic13—24no—
362C22⋊Dic13—22no—
363C22⋊Dic13—42no—
364C22⋊Dic13—42no—
365C22⋊Dic13—42no—
366C22⋊Dic13—42no—
367C22⋊Dic13—42no—
368C22⋊Dic13—41no—
369C22⋊Dic13—42no—
370C22⋊Dic13C22×C418yes—
371C22⋊Dic13C22×C418yes—
372C22⋊Dic13C22×C418yes—
373C22⋊Dic13C22×C418yes—
374C22⋊Dic13C22×C418yes—
375#6103—22no—
376#6103—22no—
377#6103—41no—
378#6103—41no—
379#6103—42no—
380#6103—42no—
381#6103—41no—
382#6103—41no—
383#6103—42no—
384C4⋊Dic13—22no—
385C4⋊Dic13—22no—
386C4⋊Dic13C22×C414yes—
387C4⋊Dic13C22×C414yes—
388#6101—41no—
389#6101—41no—
390#6101—42no—
391#6101—42no—
392#6101—42no—
393#6101—42no—
394#6101—42no—
395C4×Dic13—22no—
396C4×Dic13—22no—
397C4×Dic13—24no—
398C4×Dic13—24no—
399C4×Dic13—41no—
400C4×Dic13—41no—
401C4×Dic13—42no—
402C4×Dic13—42no—
403C4×Dic13—42no—
404C4×Dic13C22×C418yes—
405C2×#535—131no—
406#2379—132no—
407#2375—132no—
408#2372—132no—
409#2363—131no—
410#2363—131no—
411#2361—131no—
412#2361—131no—
413#2358—132no—
414#2346—131no—
415#2346—131no—
416D4×C22⋊C4—131no—
417D4×C22⋊C4D1311yescharacteristic, complemented
418#2328—132no—
419#2328—132no—
420#2324—131no—
421#2324—131no—
422#2321—132no—
423#2321—132no—
424#2311—131no—
425C4×#121—131no—
426C4×#121—131no—
427#2297—131no—
428C23×C13—21no—
429C23×C13—22no—
430C23×C13—22no—
431C23×C13—22no—
432C23×C13—22no—
433C23×C13—21no—
434C23×C13—22no—
435C23×C13—22no—
436C23×C13—22no—
437C23×C13—22no—
438C23×C13—21no—
439C23×C13—21no—
440C23×C13—22no—
441C23×C13—21no—
442C23×C13—22no—
443C23×C13—21no—
444C23×C13—22no—
445C23×C13—22no—
446C23×C13—48no—
447C23×C13—48no—
448C23×C13—48no—
449C23×C13—84no—
450C23×C13—84no—
451C23×C13—84no—
452C23×C13—84no—
453C23×C13C23×C412yes—
454C23×C13C23×C414yes—
455C23×C13C23×C414yes—
456C23×C13C2511yescharacteristic
457C22×D13—21no—
458C22×D13—21no—
459C22×D13—21no—
460C22×D13—21no—
461C22×D13—21no—
462C22×D13—21no—
463C22×D13—21no—
464C22×D13—21no—
465C22×D13—21no—
466C22×D13—21no—
467C22×D13—21no—
468C22×D13—21no—
469C22×D13C23×C412yes—
470C22×D13C23×C412yes—
471D4×C13—28no—
472D4×C13—28no—
473D4×C13—48no—
474C2×C4×C13—21no—
475C2×C4×C13—21no—
476C2×C4×C13—21no—
477C2×C4×C13—21no—
478C2×C4×C13—28no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—21no—
482C2×C4×C13—21no—
483C2×C4×C13—21no—
484C2×C4×C13—21no—
485C2×C4×C13—21no—
486C2×C4×C13—22no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—21no—
490C2×C4×C13—21no—
491C2×C4×C13—22no—
492C2×C4×C13—21no—
493C2×C4×C13—21no—
494C2×C4×C13—84no—
495C2×C4×C13—84no—
496C2×C4×C13C23×C412yes—
497C2×C4×C13C23×C412yes—
498C2×C4×C13H(5,𝔽2)12yes—
499C2×C4×C13H(5,𝔽2)12yes—
500C2×C4×C13H(5,𝔽2)12yes—
501C22⋊D13—44no—
502C22⋊D13—44no—
503C22⋊D13—48no—
504C22⋊D13—48no—
505C22⋊D13—48no—
506C22⋊D13—48no—
507C2×Dic13—21no—
508C2×Dic13—22no—
509C2×Dic13—22no—
510C2×Dic13—21no—
511C2×Dic13—21no—
512C2×Dic13—21no—
513C2×Dic13—21no—
514C2×Dic13—22no—
515C2×Dic13—22no—
516C2×Dic13—21no—
517C2×Dic13—21no—
518C2×Dic13—21no—
519C2×Dic13—21no—
520C2×Dic13—22no—
521C2×Dic13—22no—
522C2×Dic13—21no—
523C2×Dic13—21no—
524C2×Dic13—22no—
525C2×Dic13—22no—
526C2×Dic13—22no—
527C2×Dic13—21no—
528C2×Dic13—21no—
529C2×Dic13—22no—
530C2×Dic13—21no—
531C2×Dic13—21no—
532C2×Dic13—84no—
533C2×Dic13—84no—
534C2×Dic13C23×C414yes—
535C2×Dic13C23×C414yes—
536C2×Dic13C23×C412yes—
537C2×Dic13C23×C412yes—
538C2×Dic13H(5,𝔽2)12yes—
539D52—44no—
540C4×D13—28no—
541C4×D13—28no—
542C4×D13—44no—
543C4×D13—44no—
544C4×D13—84no—
545Dic26—44no—
546C22×#41—131no—
547C23×D4C2×D1311yescharacteristic
548#535—1316no—
549C2×#127—132no—
550C2×#124—132no—
551C2×#121—131no—
552C2×#121—131no—
553C2×#121—131no—
554C2×#121—131no—
555C2×#120—132no—
556C2×#120—132no—
557C2×C4×D4—131no—
558C2×C4×D4—131no—
559C2×C4×D4—132no—
560C2×C4×D4—132no—
561C2×C4×D4—132no—
562C2×C4×D4—132no—
563C2×C4×D4C2×D1311yescharacteristic
564C2×C4×D4C2×D1311yescharacteristic
565C2×#117—131no—
566C2×#117—131no—
567C2×#117—131no—
568C22×C4⋊C4—131no—
569C22×C22⋊C4—132no—
570C22×C22⋊C4C2×D1312yes—
571C22×C42—131no—
572#391—132no—
573#391—131no—
574#391—131no—
575#390—131no—
576#390—131no—
577#390—132no—
578#390—132no—
579#390—132no—
580#390—132no—
581#390—132no—
582#390—131no—
583#390—131no—
584#390C2×D1311yescharacteristic
585#390C2×D1311yescharacteristic
586#389—131no—
587#389—131no—
588#389—131no—
589#389—131no—
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#388—132no—
602#386—132no—
603#386—132no—
604#386—132no—
605#386—132no—
606#386—132no—
607#386—131no—
608#386—131no—
609#386—132no—
610#386—132no—
611#386—132no—
612#386—132no—
613#386—132no—
614#386—132no—
615#386—132no—
616#386—131no—
617#386—131no—
618#386C2×D1312yes—
619#386C2×D1312yes—
620#385—132no—
621#385—132no—
622#385—132no—
623#385—132no—
624#382—132no—
625#382—132no—
626#380—131no—
627#380—131no—
628#380—131no—
629#380C2×D1311yescharacteristic
630#379—132no—
631#379C2×D1312yes—
632C4×C4⋊C4—131no—
633C4×C4⋊C4—131no—
634C4×C4⋊C4—131no—
635C4×C4⋊C4—131no—
636C4×C22⋊C4—132no—
637C4×C22⋊C4—131no—
638C4×C22⋊C4—132no—
639C4×C22⋊C4—132no—
640C4×C22⋊C4—132no—
641C4×C22⋊C4—131no—
642C4×C22⋊C4—131no—
643C4×C22⋊C4C2×D1311yescharacteristic
644#376—132no—
645#376—132no—
646C22×C13—22no—
647C22×C13—24no—
648C22×C13—24no—
649C22×C13—24no—
650C22×C13—24no—
651C22×C13—24no—
652C22×C13—24no—
653C22×C13—22no—
654C22×C13—22no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—42no—
659C22×C13—41no—
660C22×C13—41no—
661C22×C13—42no—
662C22×C13—42no—
663C22×C13—41no—
664C22×C13—42no—
665C22×C13—42no—
666C22×C13—41no—
667C22×C13—816no—
668C22×C13C24×C411yescharacteristic
669C22×C13C2×H(5,𝔽2)11yescharacteristic
670C22×C13C2×H(5,𝔽2)11yescharacteristic
671C22×C13C2×H(5,𝔽2)11yescharacteristic
672C22×C13C2×H(5,𝔽2)11yescharacteristic
673C22×C13#58511yescharacteristic
674C22×C13#58511yescharacteristic
675C2×D13—22no—
676C2×D13—22no—
677C2×D13—22no—
678C2×D13—22no—
679C2×D13—22no—
680C2×D13—22no—
681C2×D13—41no—
682C2×D13—41no—
683C2×D13—41no—
684C2×D13—41no—
685C2×D13—41no—
686C2×D13—41no—
687C2×D13—41no—
688C2×D13—41no—
689C4×C13—22no—
690C4×C13—22no—
691C4×C13—41no—
692C4×C13—42no—
693C4×C13—42no—
694C4×C13—41no—
695C4×C13—41no—
696C4×C13#51814yes—
697Dic13—22no—
698Dic13—22no—
699Dic13—24no—
700Dic13—24no—
701Dic13—22no—
702Dic13—41no—
703Dic13—42no—
704Dic13—42no—
705Dic13—41no—
706Dic13—41no—
707C25C22×D1312yes—
708C2×#41—138no—
709C2×#41—522no—
710C2×#41—522no—
711C22×Q8—131no—
712C22×D4—42no—
713C22×D4—42no—
714C22×D4—132no—
715C22×D4—132no—
716C22×D4—132no—
717C22×D4—132no—
718C22×D4—131no—
719C22×D4—131no—
720C22×D4—131no—
721C22×D4C4×D1318yescomplemented
722C22×D4C22×D1311yescharacteristic
723C22×D4C22×D1311yescharacteristic
724C22×D4C22×D1312yes—
725C23×C4—131no—
726C23×C4—131no—
727C23×C4—132no—
728C23×C4—132no—
729C23×C4—131no—
730C23×C4—131no—
731C23×C4—132no—
732C23×C4C22×D1311yescharacteristic
733C23×C4C22×D1312yes—
734C23×C4C22×D1312yes—
735#127—1316no—
736#124—1316no—
737#121—138no—
738#121—138no—
739#121—138no—
740#121—138no—
741#120—1316no—
742#120—1316no—
743C4×D4—42no—
744C4×D4—42no—
745C4×D4—524no—
746C4×D4—524no—
747C4×D4—524no—
748C4×D4—522no—
749C4×D4—522no—
750C4×D4—524no—
751#117—138no—
752#117—522no—
753#117—522no—
754C2×C4⋊C4—131no—
755C2×C4⋊C4—131no—
756C2×C4⋊C4—131no—
757C2×C4⋊C4—131no—
758C2×C4⋊C4—132no—
759C2×C4⋊C4—131no—
760C2×C4⋊C4—131no—
761C2×C4⋊C4—132no—
762C2×C4⋊C4—132no—
763C2×C4⋊C4—132no—
764C2×C4⋊C4—132no—
765C2×C4⋊C4—522no—
766C2×C4⋊C4C22×D1311yescharacteristic
767C2×C4⋊C4C22×D1311yescharacteristic
768C2×C22⋊C4—44no—
769C2×C22⋊C4—132no—
770C2×C22⋊C4—132no—
771C2×C22⋊C4—132no—
772C2×C22⋊C4—132no—
773C2×C22⋊C4—132no—
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—131no—
784C2×C22⋊C4—132no—
785C2×C22⋊C4—131no—
786C2×C22⋊C4—132no—
787C2×C22⋊C4—131no—
788C2×C22⋊C4—132no—
789C2×C22⋊C4—132no—
790C2×C22⋊C4—131no—
791C2×C22⋊C4—131no—
792C2×C22⋊C4—524no—
793C2×C22⋊C4C22×D1311yescharacteristic
794C2×C22⋊C4C22×D1312yes—
795C2×C22⋊C4C22×D1312yes—
796C2×C22⋊C4C22×D1312yes—
797C2×C22⋊C4C22×D1312yes—
798C2×C22⋊C4C22×D1312yes—
799C2×C22⋊C4C22×D1312yes—
800C2×C22⋊C4C22×D1312yes—
801C2×C22⋊C4C22×D1311yescharacteristic
802C2×C42—132no—
803C2×C42—131no—
804C2×C42—132no—
805C2×C42—132no—
806C2×C42—131no—
807C2×C42—132no—
808C2×C42—132no—
809C2×C42—132no—
810C2×C42—131no—
811C2×C42—131no—
812C2×C42—522no—
813C2×C42C22×D1311yescharacteristic
814C2×C42C22×D1311yescharacteristic
815#95—131no—
816#95—132no—
817#95—132no—
818#95—132no—
819#95—132no—
820#95—132no—
821#95—131no—
822#95—131no—
823#95—132no—
824#95—132no—
825#95—131no—
826#95—131no—
827#95—131no—
828#95—132no—
829#95—132no—
830#95—132no—
831#95—132no—
832#95C22×D1311yescharacteristic
833#95C22×D1312yes—
834#95C22×D1311yescharacteristic
835C2×C13—44no—
836C2×C13—44no—
837C2×C13—42no—
838C2×C13C2×#51811yescharacteristic
839C2×C13C4×H(5,𝔽2)11yescharacteristic
840C2×C13C4×H(5,𝔽2)11yescharacteristic
841C2×C13#354211yescharacteristic
842C2×C13#354211yescharacteristic
843C2×C13#354911yescharacteristic
844C2×C13#355111yescharacteristic
845D13—42no—
846D13—42no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—131no—
854C24—131no—
855C24C2×C4×D1318yes—
856C24C23×D1311yescharacteristic
857C24C23×D1312yes—
858C24C23×D1312yes—
859#41—5216no—
860C2×Q8—134no—
861C2×Q8—521no—
862C2×Q8—521no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—416no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—134no—
871C2×D4—134no—
872C2×D4—138no—
873C2×D4—138no—
874C2×D4—138no—
875C2×D4—138no—
876C2×D4—134no—
877C2×D4—521no—
878C2×D4—521no—
879C2×D4—522no—
880C2×D4—522no—
881C2×D4—522no—
882C2×D4—522no—
883C2×D4—521no—
884C2×D4—521no—
885C2×D4—521no—
886C2×D4—521no—
887C2×D4—522no—
888C2×D4—522no—
889C2×D4—522no—
890C2×D4—522no—
891C2×D4C2×C4×D1314yes—
892C2×D4C2×C4×D1314yes—
893C2×D4C2×C4×D1318yes—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—131no—
903C22×C4—132no—
904C22×C4—132no—
905C22×C4—131no—
906C22×C4—131no—
907C22×C4—134no—
908C22×C4—134no—
909C22×C4—131no—
910C22×C4—131no—
911C22×C4—132no—
912C22×C4—132no—
913C22×C4—131no—
914C22×C4—262no—
915C22×C4—264no—
916C22×C4—262no—
917C22×C4—262no—
918C22×C4—262no—
919C22×C4—262no—
920C22×C4—262no—
921C22×C4—521no—
922C22×C4—521no—
923C22×C4—521no—
924C22×C4—521no—
925C22×C4—522no—
926C22×C4—522no—
927C22×C4—522no—
928C22×C4—522no—
929C22×C4—522no—
930C22×C4—522no—
931C22×C4—522no—
932C22×C4—522no—
933C22×C4C2×C4×D1314yes—
934C22×C4C23×D1311yescharacteristic
935C22×C4C23×D1312yes—
936C22×C4C23×D1311yescharacteristic
937C22×C4C23×D1312yes—
938C22×C4C23×D1311yescharacteristic
939C22×C4C23×D1311yescharacteristic
940C22×C4C23×D1311yescharacteristic
941C22×C4C23×D1311yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—134no—
945C4⋊C4—134no—
946C4⋊C4—262no—
947C4⋊C4—262no—
948C4⋊C4—522no—
949C4⋊C4—521no—
950C4⋊C4—521no—
951C4⋊C4—522no—
952C4⋊C4—522no—
953C4⋊C4—522no—
954C4⋊C4—522no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—41no—
963C22⋊C4—42no—
964C22⋊C4—138no—
965C22⋊C4—138no—
966C22⋊C4—138no—
967C22⋊C4—138no—
968C22⋊C4—138no—
969C22⋊C4—262no—
970C22⋊C4—262no—
971C22⋊C4—264no—
972C22⋊C4—262no—
973C22⋊C4—521no—
974C22⋊C4—521no—
975C22⋊C4—522no—
976C22⋊C4—522no—
977C22⋊C4—522no—
978C22⋊C4—521no—
979C22⋊C4—521no—
980C22⋊C4—522no—
981C22⋊C4—522no—
982C22⋊C4—522no—
983C22⋊C4—522no—
984C22⋊C4—522no—
985C22⋊C4—522no—
986C22⋊C4—521no—
987C42—22no—
988C42—22no—
989C42—138no—
990C42—264no—
991C42—262no—
992C42—262no—
993C42—264no—
994C42—521no—
995C42—521no—
996C42—522no—
997C42—522no—
998C42—522no—
999C13#3441511yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—21no—
1017C23—22no—
1018C23—48no—
1019C23—48no—
1020C23—48no—
1021C23—84no—
1022C23—84no—
1023C23—84no—
1024C23—84no—
1025C23—132no—
1026C23—132no—
1027C23—261no—
1028C23—261no—
1029C23—261no—
1030C23—261no—
1031C23—261no—
1032C23—261no—
1033C23—261no—
1034C23—261no—
1035C23—261no—
1036C23—261no—
1037C23—261no—
1038C23—261no—
1039C23C22×C4×D1312yes—
1040C23C22×C4×D1314yes—
1041C23C22×C4×D1314yes—
1042C23C24×D1311yescharacteristic
1043Q8—524no—
1044D4—28no—
1045D4—28no—
1046D4—48no—
1047D4—524no—
1048D4—528no—
1049D4—528no—
1050D4—528no—
1051D4—528no—
1052D4—524no—
1053D4—524no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—84no—
1075C2×C4—84no—
1076C2×C4—134no—
1077C2×C4—134no—
1078C2×C4—132no—
1079C2×C4—132no—
1080C2×C4—132no—
1081C2×C4—261no—
1082C2×C4—262no—
1083C2×C4—261no—
1084C2×C4—261no—
1085C2×C4—261no—
1086C2×C4—261no—
1087C2×C4—262no—
1088C2×C4—261no—
1089C2×C4—262no—
1090C2×C4—262no—
1091C2×C4—268no—
1092C2×C4—268no—
1093C2×C4—261no—
1094C2×C4—261no—
1095C2×C4—262no—
1096C2×C4—261no—
1097C2×C4—262no—
1098C2×C4—261no—
1099C2×C4—261no—
1100C2×C4—262no—
1101C2×C4—262no—
1102C2×C4—261no—
1103C2×C4—261no—
1104C2×C4—262no—
1105C2×C4—262no—
1106C2×C4—261no—
1107C2×C4—261no—
1108C2×C4—524no—
1109C2×C4—524no—
1110C2×C4—1044no—
1111C2×C4—1044no—
1112C2×C4—1044no—
1113C2×C4C22×C4×D1312yes—
1114C2×C4C22×C4×D1312yes—
1115C2×C4#8825112yes—
1116C2×C4#8825112yes—
1117C2×C4#8825112yes—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—22no—
1124C22—24no—
1125C22—24no—
1126C22—22no—
1127C22—42no—
1128C22—42no—
1129C22—41no—
1130C22—42no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—42no—
1135C22—41no—
1136C22—42no—
1137C22—42no—
1138C22—41no—
1139C22—816no—
1140C22—262no—
1141C22—262no—
1142C22—262no—
1143C22—262no—
1144C22—262no—
1145C22—262no—
1146C22—521no—
1147C22—521no—
1148C22—521no—
1149C22—521no—
1150C22—521no—
1151C22—521no—
1152C22—521no—
1153C22—521no—
1154C22C23×C4×D1311yescharacteristic
1155C22C2×#8825111yescharacteristic
1156C22C2×#8825111yescharacteristic
1157C22C2×#8825111yescharacteristic
1158C22#1171964811yescharacteristic
1159C22D13×H(5,𝔽2)11yescharacteristic
1160C22#1171965011yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—262no—
1169C4—262no—
1170C4—264no—
1171C4—264no—
1172C4—262no—
1173C4—522no—
1174C4—521no—
1175C4—521no—
1176C4—522no—
1177C4—521no—
1178C4#1171919114yes—
1179C2—42no—
1180C2—44no—
1181C2—44no—
1182C2—522no—
1183C2—522no—
1184C2C2×#1171919111yescharacteristic
1185C2#1312804011yescharacteristic
1186C2C4×#8825111yescharacteristic
1187C2#1312915011yescharacteristic
1188C2#1312915711yescharacteristic
1189C2#1312923811yescharacteristic
1190C2#1312925611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingD4×C13×C22⋊C4C2
socle, cosocleC23×C13C25
prime radicalC2×#11719510C2
hypercenterD4×C22⋊C4D13
hypocenterC13#34415
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13118006C2semidirect
3. #13117975C2semidirect
4. #13117945C2semidirect
5. #13117879C2semidirect
6. #13117870C2semidirect
7. #13117857C2semidirect
8. #13117848C2semidirect
9. #13117815C2semidirect
10. #13117723C2semidirect
11. #13117719C2semidirect
12. D4×C22⋊Dic13C2semidirect
13. #13117557C2semidirect
14. #13117557C2semidirect
15. #13117532C2semidirect
16. #13117523C2semidirect
17. #13117494C2semidirect
18. #13117491C2semidirect
19. #13117425C2semidirect
20. #13117352C2semidirect
21. C4×#88192C2semidirect
22. #13117322C2semidirect
23. D4×C13×C22⋊C4C2semidirect
32. #11719510C4semidirect
41. C2×C4×C22⋊D13C22semidirect
42. C2×C4×C22⋊D13C22semidirect
44. C2×#88146C22semidirect
45. C2×C4⋊C4×D13C22semidirect
46. C2×#88135C22semidirect
47. C2×#88135C22semidirect
48. C2×#88126C22semidirect
49. C2×C42×D13C22semidirect
62. #11718874C22semidirect
63. #11718874C22semidirect
65. #11718871C22semidirect
66. #11718871C22semidirect
68. C4×C22⋊Dic13C22semidirect
69. C4×C22⋊Dic13C22semidirect
70. #11718648C22semidirect
71. #11718648C22semidirect
72. C4⋊C4×Dic13C22semidirect
73. C4⋊C4×Dic13C22semidirect
74. #11718634C22semidirect
75. #11718634C22semidirect
76. #11718619C22semidirect
77. #11718619C22semidirect
81. #11718618C22semidirect
82. #11718618C22semidirect
83. #11718618C22semidirect
84. #11718618C22semidirect
88. #11718617C22semidirect
89. #11718617C22semidirect
90. #11718617C22semidirect
91. #11718617C22semidirect
92. #11718607C22semidirect
93. #11718607C22semidirect
96. #11718606C22semidirect
97. #11718606C22semidirect
98. #11718606C22semidirect
99. #11718606C22semidirect
102. #11718605C22semidirect
103. #11718605C22semidirect
104. #11718605C22semidirect
105. #11718605C22semidirect
106. C22⋊C4×Dic13C22semidirect
107. C22⋊C4×Dic13C22semidirect
108. C4×#6103C22semidirect
109. C4×#6103C22semidirect
110. C4×C4⋊Dic13C22semidirect
111. C4×C4⋊Dic13C22semidirect
112. #11718589C22semidirect
113. #11718589C22semidirect
114. #11718326C22semidirect
115. #11718326C22semidirect
116. #11718326C22semidirect
117. #11718311C22semidirect
118. #11718311C22semidirect
119. #11718309C22semidirect
120. #11718309C22semidirect
121. #11718307C22semidirect
122. #11718307C22semidirect
123. #11718307C22semidirect
127. C22×D4×C13C2×C4semidirect
144. C2×#6127C2×C4semidirect
168. #88207C2×C4semidirect
169. #88207C2×C4semidirect
185. #88194C2×C4semidirect
186. #88192C2×C4semidirect
187. #88192C2×C4semidirect
188. #88192C2×C4semidirect
189. #88192C2×C4semidirect
190. #88190C2×C4semidirect
204. #88180C2×C4semidirect
417. D4×C22⋊C4D13semidirect
721. C22×D4C4×D13semidirect
999. C13#34415semidirect

Maximal subgroups

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

subgroupindex
C2×#117195102
#131180062
#131179752
#131179452
#131178792
#131178702
#131178572
#131178482
#131178152
#131177232
#131177192
D4×C22⋊Dic132
#131175572
#131175322
#131175232
#131174942
#131174912
#131174252
#131173522
C4×#881922
#131173222
D4×C13×C22⋊C42
#3441513