Finite Group Databasebeta

← #16022363

Subgroups — #16022363

Order 3328.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D13C211yesmaximal, characteristic
2#13117806C212yesmaximal, complemented
3#13117775C212yesmaximal, complemented
4#13117774C212yesmaximal, complemented
5#13117742C212yesmaximal, complemented
6#13117710C212yesmaximal, complemented
7#13117684C212yesmaximal, complemented
8#13117683C212yesmaximal, complemented
9#13117654C212yesmaximal
10#13117299C211yesmaximal, characteristic, complemented
11#13117295C211yesmaximal, characteristic, complemented
12#13117281C211yesmaximal, characteristic, complemented
13#13117280C211yesmaximal, characteristic, complemented
14#13117277C211yesmaximal, characteristic, complemented
15#13117228C211yesmaximal, characteristic, complemented
16#13117217C211yesmaximal, characteristic, complemented
17#13117215C211yesmaximal, characteristic, complemented
18C42×C22⋊D13C211yesmaximal, characteristic, complemented
19C4×#88135C211yesmaximal, characteristic, complemented
20C4×#88146C211yesmaximal, characteristic, complemented
21C2×C4×#6103C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic, complemented
23C13×#2290C211yesmaximal, characteristic, complemented
24C22×D4×D13C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C23×C4×D13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic, complemented
29C22×C42×C13C2211yescharacteristic, complemented
30C2×D4×Dic13C2211yescharacteristic
31C2×C4×C22⋊D13C2212yes—
32C2×C4×C22⋊D13C2211yescharacteristic
33C2×C4×C22⋊D13C2211yescharacteristic
34C22×#6103C2212yes—
35C2×#88180C2211yescharacteristic, complemented
36C22×C4×Dic13C2211yescharacteristic, complemented
37C4×D4×D13C4116yescomplemented
38C2×#88147C2211yescharacteristic
39C2×#88146C2212yes—
40C2×C4⋊C4×D13C2211yescharacteristic
41C2×#88135C2212yes—
42C2×#88135C2211yescharacteristic
43C2×#88135C2211yescharacteristic
44C2×C22⋊C4×D13C2212yes—
45C2×C22⋊C4×D13C2211yescharacteristic
46C2×C22⋊C4×D13C2211yescharacteristic
47C2×C4×D52C2211yescharacteristic
48C2×#88126C2211yescharacteristic, complemented
49C2×#88126C2211yescharacteristic, complemented
50C2×C42×D13C2211yescharacteristic
51C2×C42×D13C2211yescharacteristic, complemented
52C2×C42×D13C2211yescharacteristic, complemented
53C13×#388C2212yescomplemented
54C13×#387C2212yescomplemented
55C13×#386C2212yes—
56C13×#385C2212yescomplemented
57C4×C13×C4⋊C4C2211yescharacteristic, complemented
58C4×C13×C22⋊C4C2211yescharacteristic, complemented
59C4×C13×C22⋊C4C2211yescharacteristic, complemented
60C13×#376C2211yescharacteristic, complemented
61#11718881C2212yes—
62C4×C22⋊Dic13C2211yescharacteristic, complemented
63C4×C22⋊Dic13C2212yescomplemented
64C4×C22⋊Dic13C2211yescharacteristic, complemented
65C2×#88071C2212yescomplemented
66#11718651C2212yescomplemented
67#11718651C2212yescomplemented
68#11718650C2212yescomplemented
69#11718648C2212yes—
70#11718648C2212yescomplemented
71#11718642C2212yescomplemented
72C4⋊C4×Dic13C2212yescomplemented
73#11718633C2212yescomplemented
74#11718618C2212yes—
75#11718618C2212yes—
76#11718616C2212yes—
77#11718616C2212yes—
78#11718612C2212yescomplemented
79#11718611C2212yescomplemented
80#11718606C2212yescomplemented
81#11718605C2212yescomplemented
82#11718604C2212yescomplemented
83#11718603C2212yescomplemented
84C22⋊C4×Dic13C2212yescomplemented
85C22⋊C4×Dic13C2212yescomplemented
86C4×#6103C2212yes—
87C4×#6103C2211yescharacteristic
88C4×#6103C2211yescharacteristic
89C4×#6103C2211yescharacteristic
90C4×#6103C2211yescharacteristic
91C4×#6103C2211yescharacteristic, complemented
92C4×#6103C2211yescharacteristic, complemented
93C4×#6103C2212yescomplemented
94C4×#6103C2212yescomplemented
95C4×#6103C2211yescharacteristic, complemented
96C4×#6103C2211yescharacteristic, complemented
97C4×C4⋊Dic13C2211yescharacteristic, complemented
98#11718593C2211yescharacteristic, complemented
99C4×#6101C2212yescomplemented
100C4×#6101C2211yescharacteristic, complemented
101C4×#6101C2211yescharacteristic, complemented
102C42×Dic13C2211yescharacteristic, complemented
103C42×Dic13C2211yescharacteristic, complemented
104#11718331C2212yescomplemented
105#11718331C2212yescomplemented
106#11718329C2212yescomplemented
107#11718328C2212yes—
108#11718328C2212yes—
109#11718327C2212yes—
110#11718327C2212yes—
111#11718327C2212yescomplemented
112#11718326C2212yes—
113#11718326C2212yes—
114#11718325C2212yes—
115#11718325C2212yescomplemented
116D13×#95C2212yescomplemented
117#11718315C2212yescomplemented
118#11718314C2212yescomplemented
119#11718312C2212yescomplemented
120#11718311C2212yescomplemented
121#11718310C2212yescomplemented
122#11718309C2212yescomplemented
123#11718308C2212yescomplemented
124C24×D13C2311yescharacteristic
125C24×D13C2311yescharacteristic
126C22×D4×C13C2311yescharacteristic
127C23×C4×C13C2312yes—
128C23×C4×C13C2311yescharacteristic
129C23×C4×C13C2311yescharacteristic
130C22×C22⋊D13C2311yescharacteristic
131C22×C22⋊D13C2311yescharacteristic
132C23×Dic13C2312yes—
133C23×Dic13C2311yescharacteristic
134C23×Dic13C2311yescharacteristic
135C2×D4×D13—28no—
136C2×D4×D13C2×C418yes—
137C22×D52C2311yescharacteristic
138C22×C4×D13—42no—
139C22×C4×D13—42no—
140C22×C4×D13—42no—
141C22×C4×D13—42no—
142C22×C4×D13C2×C418yescomplemented
143C22×C4×D13C2×C418yescomplemented
144C22×C4×D13C2312yes—
145C22×C4×D13C2312yes—
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×C4×D13C2311yescharacteristic
151C22×C4×D13C2311yescharacteristic
152C22×C4×D13C2311yescharacteristic
153C22×C4×D13C2311yescharacteristic
154C22×C4×D13C2311yescharacteristic
155C4×D4×C13C2×C418yescomplemented
156C13×#117—42no—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2312yes—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2311yescharacteristic
164C2×C13×C22⋊C4C2311yescharacteristic
165C2×C42×C13—42no—
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2311yescharacteristic
169C2×C42×C13C2311yescharacteristic
170C2×C42×C13C2312yes—
171C2×C42×C13C2311yescharacteristic
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2311yescharacteristic
176C2×C22⋊Dic13C2311yescharacteristic
177D4×Dic13C2×C418yescomplemented
178C4×C22⋊D13—28no—
179C4×C22⋊D13C2×C418yes—
180C4×C22⋊D13C2×C418yescomplemented
181C2×#6103—28no—
182C2×#6103C2312yes—
183C2×#6103C2312yes—
184C2×#6103C2312yes—
185C2×#6103C2312yes—
186C2×#6103C2312yes—
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2311yescharacteristic
192C2×#6103C2311yescharacteristic
193C2×#6103C2311yescharacteristic
194C2×#6103C2311yescharacteristic
195C2×#6103C2312yes—
196#88180—42no—
197C2×C4⋊Dic13C2312yes—
198C2×C4⋊Dic13C2312yes—
199C2×C4⋊Dic13C2311yescharacteristic
200C2×#6101C2312yes—
201C2×#6101C2312yes—
202C2×#6101C2312yes—
203C2×#6101C2312yes—
204C2×#6101C2311yescharacteristic
205C2×#6101C2311yescharacteristic
206C2×C4×Dic13—42no—
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2311yescharacteristic
209C2×C4×Dic13C2311yescharacteristic
210C2×C4×Dic13C2312yes—
211C2×C4×Dic13C2312yes—
212C2×C4×Dic13C2312yes—
213C2×C4×Dic13C2311yescharacteristic
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2312yes—
216C2×C4×Dic13C2312yes—
217C2×C4×Dic13C2312yes—
218C2×C4×Dic13C2311yescharacteristic
219C2×C4×Dic13C2311yescharacteristic
220C2×C4×Dic13C2311yescharacteristic
221#88147C2×C418yescomplemented
222#88146—28no—
223C4⋊C4×D13C2×C418yescomplemented
224#88135—28no—
225#88135C2×C418yes—
226#88135C2×C418yescomplemented
227C22⋊C4×D13—28no—
228C22⋊C4×D13C2×C418yescomplemented
229C22⋊C4×D13C2×C418yescomplemented
230C4×D52C2×C418yescomplemented
231#88126—42no—
232#88126—42no—
233C42×D13—42no—
234C42×D13—42no—
235C42×D13C2×C418yescomplemented
236C13×#95C2312yes—
237C13×#95C2312yes—
238C13×#95C2312yes—
239C13×#95C2312yes—
240C13×#95C2312yes—
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#88071C2312yes—
254#88071C2312yes—
255#88071C2312yes—
256#34126—131nomaximal, Sylow
257C24×C13C2411yescharacteristic
258C24×C13C2411yescharacteristic
259C23×D13—24no—
260C23×D13—24no—
261C23×D13—24no—
262C23×D13—24no—
263C23×D13—41no—
264C23×D13—41no—
265C23×D13—41no—
266C23×D13—41no—
267C23×D13C22×C414yes—
268C23×D13C22×C414yes—
269C23×D13C2411yescharacteristic
270C23×D13C2411yescharacteristic
271C23×D13C2411yescharacteristic
272C2×D4×C13—24no—
273C2×D4×C13C22×C414yes—
274C22×C4×C13—22no—
275C22×C4×C13—22no—
276C22×C4×C13—22no—
277C22×C4×C13—22no—
278C22×C4×C13—24no—
279C22×C4×C13—24no—
280C22×C4×C13—42no—
281C22×C4×C13C22×C414yes—
282C22×C4×C13C22×C414yes—
283C22×C4×C13C2412yes—
284C22×C4×C13C2412yes—
285C22×C4×C13C2412yes—
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2411yescharacteristic
288C22×C4×C13C2411yescharacteristic
289C22×C4×C13C2411yescharacteristic
290C22×C4×C13C2412yes—
291C22×C4×C13C2411yescharacteristic
292C2×C22⋊D13—24no—
293C2×C22⋊D13C22×C414yes—
294C2×C22⋊D13C22×C414yes—
295C2×C22⋊D13#4118yes—
296C22×Dic13—24no—
297C22×Dic13—24no—
298C22×Dic13—42no—
299C22×Dic13—41no—
300C22×Dic13—41no—
301C22×Dic13—41no—
302C22×Dic13—41no—
303C22×Dic13C22×C414yes—
304C22×Dic13C22×C414yes—
305C22×Dic13C2412yes—
306C22×Dic13C2412yes—
307C22×Dic13C2412yes—
308C22×Dic13C2411yescharacteristic
309C22×Dic13C2411yescharacteristic
310C22×Dic13C2411yescharacteristic
311C22×Dic13C2411yescharacteristic
312C22×Dic13C2412yes—
313C22×Dic13C2411yescharacteristic
314D4×D13—232no—
315C2×D52—24no—
316C2×D52C22×C414yes—
317C2×C4×D13—24no—
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—24no—
327C2×C4×D13—24no—
328C2×C4×D13—24no—
329C2×C4×D13—416no—
330C2×C4×D13—416no—
331C2×C4×D13—42no—
332C2×C4×D13—42no—
333C2×C4×D13—41no—
334C2×C4×D13—41no—
335C2×C4×D13—41no—
336C2×C4×D13—41no—
337C2×C4×D13—41no—
338C2×C4×D13—41no—
339C2×C4×D13—41no—
340C2×C4×D13—41no—
341C2×C4×D13C22×C414yes—
342C2×C4×D13C22×C414yes—
343C2×C4×D13C22×C414yes—
344C2×C4×D13C22×C414yes—
345C2×C4×D13C22×C414yes—
346C2×C4×D13C22×C414yes—
347C2×C4×D13C22×C414yes—
348C2×C4×D13C22×C414yes—
349C2×C4×D13C22×C414yes—
350C13×C4⋊C4—24no—
351C13×C4⋊C4—42no—
352C13×C4⋊C4C22×C414yes—
353C13×C22⋊C4—24no—
354C13×C22⋊C4—24no—
355C13×C22⋊C4—42no—
356C13×C22⋊C4C22×C414yes—
357C13×C22⋊C4C22×C414yes—
358C42×C13—22no—
359C42×C13—22no—
360C42×C13—22no—
361C42×C13—22no—
362C42×C13—42no—
363C42×C13C22×C414yes—
364C22⋊Dic13—24no—
365C22⋊Dic13—24no—
366C22⋊Dic13—42no—
367C22⋊Dic13C22×C414yes—
368C22⋊Dic13C22×C414yes—
369#6103—24no—
370#6103—24no—
371#6103—24no—
372#6103—24no—
373#6103—24no—
374#6103—24no—
375#6103—24no—
376#6103—42no—
377#6103—42no—
378#6103C22×C414yes—
379#6103C22×C414yes—
380#6103C22×C414yes—
381#6103C22×C414yes—
382#6103#4118yes—
383C4⋊Dic13—24no—
384C4⋊Dic13—42no—
385C4⋊Dic13C22×C414yes—
386#6101—24no—
387#6101—24no—
388#6101—42no—
389#6101—42no—
390#6101C22×C414yes—
391#6101C22×C414yes—
392C4×Dic13—24no—
393C4×Dic13—22no—
394C4×Dic13—22no—
395C4×Dic13—22no—
396C4×Dic13—22no—
397C4×Dic13—24no—
398C4×Dic13—24no—
399C4×Dic13—24no—
400C4×Dic13—42no—
401C4×Dic13—42no—
402C4×Dic13—42no—
403C4×Dic13C22×C414yes—
404C4×Dic13C22×C414yes—
405C4×Dic13C22×C414yes—
406C22×C4×D4—131no—
407#2357—132no—
408#2353—132no—
409#2353—132no—
410#2349—132no—
411#2345—132no—
412#2342—132no—
413#2342—132no—
414D4×C22⋊C4—132no—
415#2293—131no—
416#2293—131no—
417#2290—131no—
418#2290—131no—
419#2290—131no—
420#2290D1311yescharacteristic, complemented
421#2283—131no—
422#2280—131no—
423#2280—131no—
424C42×D4—131no—
425C42×D4—131no—
426C4×#117—131no—
427C2×C4×C22⋊C4—131no—
428C2×C4×C22⋊C4—131no—
429C23×C13—22no—
430C23×C13—21no—
431C23×C13—21no—
432C23×C13—22no—
433C23×C13—22no—
434C23×C13—21no—
435C23×C13—21no—
436C23×C13C23×C412yes—
437C23×C13C23×C412yes—
438C23×C13C2×#4114yes—
439C23×C13C2511yescharacteristic
440C22×D13—22no—
441C22×D13—22no—
442C22×D13—21no—
443C22×D13—21no—
444C22×D13—21no—
445C22×D13—21no—
446C22×D13—28no—
447C22×D13—22no—
448C22×D13—22no—
449C22×D13—21no—
450C22×D13—21no—
451C22×D13—28no—
452C22×D13—28no—
453C22×D13—28no—
454C22×D13—44no—
455C22×D13—44no—
456C22×D13—48no—
457C22×D13—48no—
458C22×D13—48no—
459C22×D13—48no—
460C22×D13C23×C412yes—
461C22×D13C23×C412yes—
462C22×D13C23×C412yes—
463C22×D13C2×#4114yes—
464C22×D13C2×#4114yes—
465D4×C13—28no—
466C2×C4×C13—22no—
467C2×C4×C13—22no—
468C2×C4×C13—22no—
469C2×C4×C13—21no—
470C2×C4×C13—22no—
471C2×C4×C13—21no—
472C2×C4×C13—21no—
473C2×C4×C13—21no—
474C2×C4×C13—28no—
475C2×C4×C13—28no—
476C2×C4×C13—22no—
477C2×C4×C13—22no—
478C2×C4×C13—22no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—22no—
485C2×C4×C13—48no—
486C2×C4×C13C23×C412yes—
487C2×C4×C13C23×C412yes—
488C2×C4×C13C23×C412yes—
489C2×C4×C13C23×C412yes—
490C2×C4×C13C23×C412yes—
491C2×C4×C13C2×#4114yes—
492C2×C4×C13H(5,𝔽2)12yes—
493C2×C4×C13H(5,𝔽2)12yes—
494C22⋊D13—28no—
495C22⋊D13#117116yescomplemented
496C2×Dic13—22no—
497C2×Dic13—22no—
498C2×Dic13—22no—
499C2×Dic13—21no—
500C2×Dic13—21no—
501C2×Dic13—21no—
502C2×Dic13—21no—
503C2×Dic13—21no—
504C2×Dic13—21no—
505C2×Dic13—22no—
506C2×Dic13—22no—
507C2×Dic13—22no—
508C2×Dic13—22no—
509C2×Dic13—22no—
510C2×Dic13—22no—
511C2×Dic13—22no—
512C2×Dic13—22no—
513C2×Dic13—22no—
514C2×Dic13—44no—
515C2×Dic13—44no—
516C2×Dic13—48no—
517C2×Dic13C23×C412yes—
518C2×Dic13C23×C412yes—
519C2×Dic13C23×C412yes—
520C2×Dic13C23×C412yes—
521C2×Dic13C23×C412yes—
522C2×Dic13C2×#4114yes—
523C2×Dic13C2×#4114yes—
524D52—28no—
525C4×D13—28no—
526C4×D13—28no—
527C4×D13—28no—
528C4×D13—28no—
529C4×D13—28no—
530C4×D13—44no—
531C4×D13—44no—
532C4×D13—44no—
533C4×D13—44no—
534C4×D13—48no—
535C4×D13—48no—
536C23×D4—131no—
537C24×C4—131no—
538C24×C4—131no—
539C2×C4×D4—131no—
540C2×C4×D4—131no—
541C2×C4×D4—131no—
542C2×C4×D4—1316no—
543C2×C4×D4—132no—
544C2×C4×D4—131no—
545C2×C4×D4—131no—
546C2×C4×D4—131no—
547C2×C4×D4—132no—
548C2×C4×D4—131no—
549C2×C4×D4C2×D1311yescharacteristic
550C2×#117—131no—
551C2×#117—132no—
552C2×#117—131no—
553C2×#117—131no—
554C2×#117C2×D1311yescharacteristic, complemented
555C22×C4⋊C4—131no—
556C22×C22⋊C4—131no—
557C22×C22⋊C4—131no—
558C22×C22⋊C4—132no—
559C22×C22⋊C4—132no—
560C22×C42—131no—
561C22×C42—131no—
562C22×C42—131no—
563C22×C42—131no—
564C22×C42C2×D1311yescharacteristic, complemented
565#390—132no—
566#390—132no—
567#389—132no—
568#389—132no—
569#388—132no—
570#388—132no—
571#388—132no—
572#388—132no—
573#388—132no—
574#388—132no—
575#388—132no—
576#388C2×D1312yescomplemented
577#387—132no—
578#387—132no—
579#387—132no—
580#387C2×D1312yescomplemented
581#386—132no—
582#386—132no—
583#386—132no—
584#386C2×D1312yes—
585#385—132no—
586#385—132no—
587#385—132no—
588#385C2×D1312yescomplemented
589#383—132no—
590#382—132no—
591#381—132no—
592#381—132no—
593#381—132no—
594#380—132no—
595#380—132no—
596#380—132no—
597#380—132no—
598#380—132no—
599#379—132no—
600#379—132no—
601C4×C4⋊C4—132no—
602C4×C4⋊C4—132no—
603C4×C4⋊C4—131no—
604C4×C4⋊C4—131no—
605C4×C4⋊C4—131no—
606C4×C4⋊C4—132no—
607C4×C4⋊C4C2×D1311yescharacteristic, complemented
608C4×C22⋊C4—132no—
609C4×C22⋊C4—131no—
610C4×C22⋊C4—131no—
611C4×C22⋊C4—132no—
612C4×C22⋊C4—132no—
613C4×C22⋊C4—132no—
614C4×C22⋊C4—132no—
615C4×C22⋊C4—132no—
616C4×C22⋊C4—131no—
617C4×C22⋊C4—131no—
618C4×C22⋊C4—131no—
619C4×C22⋊C4—131no—
620C4×C22⋊C4—131no—
621C4×C22⋊C4—131no—
622C4×C22⋊C4—131no—
623C4×C22⋊C4—131no—
624C4×C22⋊C4—132no—
625C4×C22⋊C4—132no—
626C4×C22⋊C4—132no—
627C4×C22⋊C4C2×D1311yescharacteristic, complemented
628C4×C22⋊C4C2×D1311yescharacteristic, complemented
629#376—131no—
630#376—132no—
631#376C2×D1311yescharacteristic, complemented
632C2×#95—132no—
633C2×#95—132no—
634C43—131no—
635C43—131no—
636C22×C13—22no—
637C22×C13—22no—
638C22×C13—24no—
639C22×C13—24no—
640C22×C13—22no—
641C22×C13—22no—
642C22×C13—22no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13C2×#11714yes—
646C22×C13C24×C411yescharacteristic
647C22×C13C22×#4112yes—
648C22×C13C22×#4112yes—
649C22×C13C2×H(5,𝔽2)11yescharacteristic
650C22×C13C2×H(5,𝔽2)11yescharacteristic
651C2×D13—22no—
652C2×D13—22no—
653C2×D13—22no—
654C2×D13—22no—
655C2×D13—24no—
656C2×D13—24no—
657C2×D13—24no—
658C2×D13—24no—
659C2×D13—22no—
660C2×D13—22no—
661C2×D13—22no—
662C2×D13—416no—
663C2×D13—416no—
664C2×D13—42no—
665C2×D13—42no—
666C2×D13C2×#11714yes—
667C2×D13C4×#4114yes—
668C4×C13—22no—
669C4×C13—22no—
670C4×C13—22no—
671C4×C13—22no—
672C4×C13—24no—
673C4×C13—42no—
674C4×C13—42no—
675C4×C13—42no—
676C4×C13#51814yes—
677Dic13—22no—
678Dic13—22no—
679Dic13—22no—
680Dic13—22no—
681Dic13—24no—
682Dic13—42no—
683Dic13—42no—
684Dic13—42no—
685Dic13C2×#11714yes—
686C25—131no—
687C25—131no—
688C22×D4—131no—
689C22×D4—131no—
690C22×D4—138no—
691C22×D4—131no—
692C22×D4—268no—
693C22×D4C22×D1311yescharacteristic
694C23×C4—131no—
695C23×C4—131no—
696C23×C4—131no—
697C23×C4—131no—
698C23×C4—131no—
699C23×C4—131no—
700C23×C4—131no—
701C23×C4—138no—
702C23×C4—138no—
703C23×C4—131no—
704C23×C4—131no—
705C23×C4—131no—
706C23×C4—131no—
707C23×C4—132no—
708C23×C4—132no—
709C23×C4—132no—
710C23×C4—522no—
711C23×C4—522no—
712C23×C4—522no—
713C23×C4—522no—
714C23×C4C22×D1312yes—
715C23×C4C22×D1311yescharacteristic
716C23×C4C22×D1311yescharacteristic
717C4×D4—138no—
718C4×D4—138no—
719C4×D4—138no—
720C4×D4—138no—
721C4×D4—138no—
722C4×D4—138no—
723C4×D4—138no—
724C4×D4—268no—
725C4×D4—268no—
726C4×D4C4×D1318yescomplemented
727#117—42no—
728#117—268no—
729#117—522no—
730#117—522no—
731#117—522no—
732C2×C4⋊C4—131no—
733C2×C4⋊C4—131no—
734C2×C4⋊C4—131no—
735C2×C4⋊C4—138no—
736C2×C4⋊C4—132no—
737C2×C4⋊C4—132no—
738C2×C4⋊C4—132no—
739C2×C4⋊C4—132no—
740C2×C4⋊C4—132no—
741C2×C4⋊C4—132no—
742C2×C4⋊C4C22×D1312yes—
743C2×C4⋊C4C22×D1312yes—
744C2×C4⋊C4C22×D1311yescharacteristic
745C2×C22⋊C4—131no—
746C2×C22⋊C4—131no—
747C2×C22⋊C4—132no—
748C2×C22⋊C4—131no—
749C2×C22⋊C4—131no—
750C2×C22⋊C4—131no—
751C2×C22⋊C4—131no—
752C2×C22⋊C4—138no—
753C2×C22⋊C4—138no—
754C2×C22⋊C4—132no—
755C2×C22⋊C4—132no—
756C2×C22⋊C4—132no—
757C2×C22⋊C4—132no—
758C2×C22⋊C4—132no—
759C2×C22⋊C4—132no—
760C2×C22⋊C4—132no—
761C2×C22⋊C4—132no—
762C2×C22⋊C4—132no—
763C2×C22⋊C4—132no—
764C2×C22⋊C4—132no—
765C2×C22⋊C4—132no—
766C2×C22⋊C4—268no—
767C2×C22⋊C4—268no—
768C2×C22⋊C4C22×D1312yes—
769C2×C22⋊C4C22×D1312yes—
770C2×C22⋊C4C22×D1312yes—
771C2×C22⋊C4C22×D1311yescharacteristic
772C2×C22⋊C4C22×D1311yescharacteristic
773C2×C42—42no—
774C2×C42—131no—
775C2×C42—131no—
776C2×C42—131no—
777C2×C42—138no—
778C2×C42—132no—
779C2×C42—132no—
780C2×C42—132no—
781C2×C42—132no—
782C2×C42—131no—
783C2×C42—131no—
784C2×C42—131no—
785C2×C42—131no—
786C2×C42—132no—
787C2×C42—132no—
788C2×C42—132no—
789C2×C42—522no—
790C2×C42—522no—
791C2×C42—522no—
792C2×C42C22×D1311yescharacteristic
793C2×C42C22×D1311yescharacteristic
794C2×C42C22×D1311yescharacteristic
795C2×C42C22×D1311yescharacteristic
796C2×C42C22×D1312yes—
797C2×C42C22×D1311yescharacteristic
798#95—132no—
799#95—132no—
800#95—132no—
801#95—132no—
802#95—132no—
803#95—132no—
804#95—132no—
805#95—132no—
806#95—132no—
807#95—132no—
808#95—132no—
809#95—132no—
810#95—132no—
811#95—132no—
812#95—132no—
813#95C22×D1312yes—
814#95C22×D1312yes—
815#95C22×D1312yes—
816#95C22×D1312yes—
817#95C22×D1312yes—
818C2×C13—24no—
819C2×C13—42no—
820C2×C13C22×#11711yescharacteristic
821C2×C13C2×C4×#4111yescharacteristic
822C2×C13C2×#51811yescharacteristic
823C2×C13#348112yes—
824C2×C13#348112yes—
825D13—24no—
826D13—24no—
827D13—42no—
828C24—131no—
829C24—131no—
830C24—131no—
831C24—134no—
832C24—134no—
833C24—264no—
834C24—264no—
835C24—264no—
836C24—264no—
837C24—521no—
838C24—521no—
839C24—521no—
840C24—521no—
841C24C23×D1311yescharacteristic
842C24C23×D1311yescharacteristic
843C2×D4—24no—
844C2×D4—134no—
845C2×D4—138no—
846C2×D4—134no—
847C2×D4—134no—
848C2×D4—264no—
849C2×D4—264no—
850C2×D4—2632no—
851C2×D4C2×C4×D1314yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—42no—
859C22×C4—131no—
860C22×C4—131no—
861C22×C4—131no—
862C22×C4—132no—
863C22×C4—131no—
864C22×C4—131no—
865C22×C4—134no—
866C22×C4—134no—
867C22×C4—134no—
868C22×C4—134no—
869C22×C4—134no—
870C22×C4—134no—
871C22×C4—134no—
872C22×C4—134no—
873C22×C4—134no—
874C22×C4—134no—
875C22×C4—134no—
876C22×C4—132no—
877C22×C4—132no—
878C22×C4—132no—
879C22×C4—264no—
880C22×C4—264no—
881C22×C4—264no—
882C22×C4—264no—
883C22×C4—264no—
884C22×C4—264no—
885C22×C4—262no—
886C22×C4—262no—
887C22×C4—262no—
888C22×C4—262no—
889C22×C4—262no—
890C22×C4—262no—
891C22×C4—264no—
892C22×C4—264no—
893C22×C4—5216no—
894C22×C4—5216no—
895C22×C4—522no—
896C22×C4—522no—
897C22×C4—521no—
898C22×C4—521no—
899C22×C4—521no—
900C22×C4—521no—
901C22×C4—521no—
902C22×C4—521no—
903C22×C4—521no—
904C22×C4—521no—
905C22×C4—522no—
906C22×C4—521no—
907C22×C4—521no—
908C22×C4—521no—
909C22×C4—521no—
910C22×C4C2×C4×D1314yes—
911C22×C4C2×C4×D1314yes—
912C22×C4C23×D1312yes—
913C22×C4C23×D1312yes—
914C22×C4C23×D1312yes—
915C22×C4C23×D1311yescharacteristic
916C22×C4C23×D1311yescharacteristic
917C22×C4C23×D1311yescharacteristic
918C22×C4C23×D1311yescharacteristic
919C22×C4C23×D1312yes—
920C22×C4C23×D1311yescharacteristic
921C4⋊C4—24no—
922C4⋊C4—42no—
923C4⋊C4—134no—
924C4⋊C4—134no—
925C4⋊C4—134no—
926C4⋊C4—264no—
927C4⋊C4—264no—
928C4⋊C4—264no—
929C4⋊C4—522no—
930C4⋊C4—522no—
931C4⋊C4—522no—
932C4⋊C4C2×C4×D1314yes—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—42no—
936C22⋊C4—134no—
937C22⋊C4—134no—
938C22⋊C4—134no—
939C22⋊C4—134no—
940C22⋊C4—134no—
941C22⋊C4—134no—
942C22⋊C4—138no—
943C22⋊C4—264no—
944C22⋊C4—264no—
945C22⋊C4—264no—
946C22⋊C4—264no—
947C22⋊C4—264no—
948C22⋊C4—264no—
949C22⋊C4—264no—
950C22⋊C4—264no—
951C22⋊C4—264no—
952C22⋊C4—522no—
953C22⋊C4—522no—
954C22⋊C4—522no—
955C22⋊C4C2×C4×D1314yes—
956C22⋊C4C2×C4×D1314yes—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—42no—
962C42—134no—
963C42—134no—
964C42—134no—
965C42—264no—
966C42—264no—
967C42—264no—
968C42—262no—
969C42—264no—
970C42—262no—
971C42—262no—
972C42—262no—
973C42—522no—
974C42—522no—
975C42—522no—
976C42C2×C4×D1314yes—
977C13#3412611yescharacteristic, complemented, Sylow
978C23—21no—
979C23—22no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—21no—
985C23—132no—
986C23—132no—
987C23—134no—
988C23—134no—
989C23—132no—
990C23—268no—
991C23—268no—
992C23—268no—
993C23—261no—
994C23—261no—
995C23—262no—
996C23—262no—
997C23—261no—
998C23—261no—
999C23—268no—
1000C23—261no—
1001C23—262no—
1002C23—262no—
1003C23—261no—
1004C23—524no—
1005C23—524no—
1006C23—528no—
1007C23—528no—
1008C23—528no—
1009C23—528no—
1010C23C22×C4×D1312yes—
1011C23C22×C4×D1312yes—
1012C23#41×D1314yes—
1013C23C24×D1311yescharacteristic
1014D4—28no—
1015D4—1316no—
1016D4—268no—
1017D4—268no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—48no—
1038C2×C4—132no—
1039C2×C4—134no—
1040C2×C4—132no—
1041C2×C4—132no—
1042C2×C4—132no—
1043C2×C4—132no—
1044C2×C4—134no—
1045C2×C4—268no—
1046C2×C4—268no—
1047C2×C4—261no—
1048C2×C4—261no—
1049C2×C4—261no—
1050C2×C4—262no—
1051C2×C4—262no—
1052C2×C4—262no—
1053C2×C4—261no—
1054C2×C4—261no—
1055C2×C4—261no—
1056C2×C4—268no—
1057C2×C4—268no—
1058C2×C4—268no—
1059C2×C4—262no—
1060C2×C4—262no—
1061C2×C4—262no—
1062C2×C4—262no—
1063C2×C4—262no—
1064C2×C4—262no—
1065C2×C4—262no—
1066C2×C4—262no—
1067C2×C4—262no—
1068C2×C4—524no—
1069C2×C4—524no—
1070C2×C4—524no—
1071C2×C4—524no—
1072C2×C4—528no—
1073C2×C4—528no—
1074C2×C4—524no—
1075C2×C4—524no—
1076C2×C4—528no—
1077C2×C4C22×C4×D1312yes—
1078C2×C4C22×C4×D1312yes—
1079C2×C4C22×C4×D1312yes—
1080C2×C4C22×C4×D1312yes—
1081C2×C4C22×C4×D1312yes—
1082C2×C4#8825112yes—
1083C2×C4#41×D1314yes—
1084C2×C4#8825612yes—
1085C22—22no—
1086C22—22no—
1087C22—24no—
1088C22—24no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—42no—
1093C22—42no—
1094C22—134no—
1095C22—134no—
1096C22—262no—
1097C22—262no—
1098C22—262no—
1099C22—262no—
1100C22—264no—
1101C22—264no—
1102C22—264no—
1103C22—264no—
1104C22—262no—
1105C22—262no—
1106C22—262no—
1107C22—5216no—
1108C22—5216no—
1109C22—522no—
1110C22—522no—
1111C22D13×#11714yes—
1112C22C23×C4×D1311yescharacteristic
1113C22C2×#8825111yescharacteristic
1114C22C2×#41×D1312yes—
1115C22C2×#41×D1312yes—
1116C22C2×#8825611yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—24no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—134no—
1126C4—262no—
1127C4—262no—
1128C4—262no—
1129C4—262no—
1130C4—264no—
1131C4—522no—
1132C4—522no—
1133C4—522no—
1134C4#1171925014yes—
1135C2—24no—
1136C2—42no—
1137C2—264no—
1138C2—264no—
1139C2—522no—
1140C2C2×D13×#11711yescharacteristic
1141C2C4×#41×D1311yescharacteristic
1142C2C2×#1171925011yescharacteristic
1143C2#1312843812yes—
1144C2#1312844212yes—
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC13×#2290C2
socle, cosocleC23×C13C25
prime radicalC22×D4×D13C22
hypercenter#2290D13
hypocenterC13#34126
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #13117806C2semidirect
3. #13117775C2semidirect
4. #13117774C2semidirect
5. #13117742C2semidirect
6. #13117710C2semidirect
7. #13117684C2semidirect
8. #13117683C2semidirect
10. #13117299C2semidirect
11. #13117295C2semidirect
12. #13117281C2semidirect
13. #13117280C2semidirect
14. #13117277C2semidirect
15. #13117228C2semidirect
16. #13117217C2semidirect
17. #13117215C2semidirect
18. C42×C22⋊D13C2semidirect
19. C4×#88135C2semidirect
20. C4×#88146C2semidirect
21. C2×C4×#6103C2semidirect
22. C4×C22⋊C4×D13C2semidirect
23. C13×#2290C2semidirect
28. C2×C13×#117C22semidirect
29. C22×C42×C13C22semidirect
35. C2×#88180C22semidirect
36. C22×C4×Dic13C22semidirect
37. C4×D4×D13C4semidirect
48. C2×#88126C22semidirect
49. C2×#88126C22semidirect
51. C2×C42×D13C22semidirect
52. C2×C42×D13C22semidirect
53. C13×#388C22semidirect
54. C13×#387C22semidirect
56. C13×#385C22semidirect
57. C4×C13×C4⋊C4C22semidirect
58. C4×C13×C22⋊C4C22semidirect
59. C4×C13×C22⋊C4C22semidirect
60. C13×#376C22semidirect
62. C4×C22⋊Dic13C22semidirect
63. C4×C22⋊Dic13C22semidirect
64. C4×C22⋊Dic13C22semidirect
65. C2×#88071C22semidirect
66. #11718651C22semidirect
67. #11718651C22semidirect
68. #11718650C22semidirect
70. #11718648C22semidirect
71. #11718642C22semidirect
72. C4⋊C4×Dic13C22semidirect
73. #11718633C22semidirect
78. #11718612C22semidirect
79. #11718611C22semidirect
80. #11718606C22semidirect
81. #11718605C22semidirect
82. #11718604C22semidirect
83. #11718603C22semidirect
84. C22⋊C4×Dic13C22semidirect
85. C22⋊C4×Dic13C22semidirect
91. C4×#6103C22semidirect
92. C4×#6103C22semidirect
93. C4×#6103C22semidirect
94. C4×#6103C22semidirect
95. C4×#6103C22semidirect
96. C4×#6103C22semidirect
97. C4×C4⋊Dic13C22semidirect
98. #11718593C22semidirect
99. C4×#6101C22semidirect
100. C4×#6101C22semidirect
101. C4×#6101C22semidirect
102. C42×Dic13C22semidirect
103. C42×Dic13C22semidirect
104. #11718331C22semidirect
105. #11718331C22semidirect
106. #11718329C22semidirect
111. #11718327C22semidirect
115. #11718325C22semidirect
116. D13×#95C22semidirect
117. #11718315C22semidirect
118. #11718314C22semidirect
119. #11718312C22semidirect
120. #11718311C22semidirect
121. #11718310C22semidirect
122. #11718309C22semidirect
123. #11718308C22semidirect
142. C22×C4×D13C2×C4semidirect
143. C22×C4×D13C2×C4semidirect
155. C4×D4×C13C2×C4semidirect
177. D4×Dic13C2×C4semidirect
180. C4×C22⋊D13C2×C4semidirect
221. #88147C2×C4semidirect
223. C4⋊C4×D13C2×C4semidirect
226. #88135C2×C4semidirect
228. C22⋊C4×D13C2×C4semidirect
229. C22⋊C4×D13C2×C4semidirect
230. C4×D52C2×C4semidirect
235. C42×D13C2×C4semidirect
420. #2290D13semidirect
495. C22⋊D13#117semidirect
554. C2×#117C2×D13semidirect
564. C22×C42C2×D13semidirect
576. #388C2×D13semidirect
580. #387C2×D13semidirect
588. #385C2×D13semidirect
607. C4×C4⋊C4C2×D13semidirect
627. C4×C22⋊C4C2×D13semidirect
628. C4×C22⋊C4C2×D13semidirect
631. #376C2×D13semidirect
726. C4×D4C4×D13semidirect
977. C13#34126semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D132
#131178062
#131177752
#131177742
#131177422
#131177102
#131176842
#131176832
#131176542
#131172992
#131172952
#131172812
#131172802
#131172772
#131172282
#131172172
#131172152
C42×C22⋊D132
C4×#881352
C4×#881462
C2×C4×#61032
C4×C22⋊C4×D132
C13×#22902
#3412613