Finite Group Databasebeta

← #16023630

Subgroups — #16023630

Order 3328.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719311C211yesmaximal, characteristic
2#13117856C211yesmaximal, characteristic, complemented
3#13117841C211yesmaximal, characteristic, complemented
4#13117839C211yesmaximal, characteristic, complemented
5#13117816C212yesmaximal, complemented
6#13117813C212yesmaximal, complemented
7#13117771C212yesmaximal, complemented
8#13117742C212yesmaximal, complemented
9#13117728C211yesmaximal, characteristic, complemented
10#13117717C211yesmaximal, characteristic, complemented
11#13117675C211yesmaximal, characteristic, complemented
12#13117661C211yesmaximal, characteristic, complemented
13#13117633C212yesmaximal, complemented
14#13117621C212yesmaximal, complemented
15#13117462C212yesmaximal, complemented
16C4×#88151C211yesmaximal, characteristic, complemented
17#13117366C211yesmaximal, characteristic, complemented
18#13117352C211yesmaximal, characteristic, complemented
19C4×#88192C211yesmaximal, characteristic, complemented
20C2×#11718648C211yesmaximal, characteristic, complemented
21#13117197C212yesmaximal, complemented
22C4×C22⋊C4×D13C211yesmaximal, characteristic, complemented
23C13×#2361C211yesmaximal, characteristic, complemented
24C22×#6129C2211yescharacteristic
25C23×C4×D13C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13C2212yes—
28C2×C4×D4×C13C2211yescharacteristic, complemented
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88192C2211yescharacteristic
31C2×#88191C2212yes—
32C2×D4×Dic13C2212yes—
33C2×D4×Dic13C2212yes—
34C2×D4×Dic13C2211yescharacteristic, complemented
35C2×C4×C22⋊D13C2212yes—
36C22×#6103C2212yes—
37C22×C4⋊Dic13C2211yescharacteristic
38C2×#88178C2211yescharacteristic
39#11719311C4116yescomplemented
40C2×#88151C2211yescharacteristic
41C2×#88146C2211yescharacteristic
42C2×#88141C2211yescharacteristic, complemented
43C2×#88137C2212yes—
44C2×#88135C2212yes—
45C2×#88135C2212yes—
46C2×C22⋊C4×D13C2211yescharacteristic
47C2×C22⋊C4×D13C2211yescharacteristic
48C2×C42×D13C2211yescharacteristic
49C2×C42×D13C2211yescharacteristic
50C2×C4×Dic26C2211yescharacteristic, complemented
51C13×#390C2211yescharacteristic, complemented
52C13×#389C2211yescharacteristic, complemented
53C13×#388C2212yescomplemented
54C13×#386C2212yes—
55C13×#385C2212yescomplemented
56C4×C13×C4⋊C4C2211yescharacteristic, complemented
57C4×C13×C22⋊C4C2211yescharacteristic
58#11718882C2211yescharacteristic, complemented
59#11718881C2212yes—
60#11718874C2212yes—
61#11718871C2212yes—
62C4×C22⋊Dic13C2212yes—
63C4×C22⋊Dic13C2211yescharacteristic
64C4×C22⋊Dic13C2212yescomplemented
65C2×#88071C2212yes—
66C2×#88071C2212yescomplemented
67#11718651C2212yes—
68#11718650C2212yes—
69#11718648C2211yescharacteristic
70#11718648C2211yescharacteristic
71#11718648C2212yes—
72#11718648C2211yescharacteristic
73#11718648C2211yescharacteristic
74#11718648C2212yes—
75#11718646C2211yescharacteristic, complemented
76#11718639C2212yescomplemented
77C4⋊C4×Dic13C2212yescomplemented
78C4⋊C4×Dic13C2212yescomplemented
79C4⋊C4×Dic13C2211yescharacteristic, complemented
80C4⋊C4×Dic13C2211yescharacteristic, complemented
81#11718635C2211yescharacteristic, complemented
82#11718634C2211yescharacteristic, complemented
83#11718633C2212yescomplemented
84#11718619C2212yes—
85#11718618C2212yes—
86#11718618C2212yes—
87#11718617C2212yes—
88#11718617C2212yes—
89#11718612C2212yescomplemented
90#11718611C2212yescomplemented
91#11718607C2212yes—
92#11718606C2212yescomplemented
93#11718605C2212yescomplemented
94#11718604C2212yescomplemented
95#11718603C2212yescomplemented
96C22⋊C4×Dic13C2211yescharacteristic
97C22⋊C4×Dic13C2212yes—
98C22⋊C4×Dic13C2211yescharacteristic
99C22⋊C4×Dic13C2212yescomplemented
100C22⋊C4×Dic13C2212yescomplemented
101#11718601C2212yes—
102C4×#6103C2211yescharacteristic
103C4×#6103C2211yescharacteristic
104C4×#6103C2212yes—
105C4×C4⋊Dic13C2212yescomplemented
106C4×C4⋊Dic13C2211yescharacteristic, complemented
107#11718593C2212yescomplemented
108#11718590C2211yescharacteristic, complemented
109#11718589C2211yescharacteristic, complemented
110#11718331C2212yes—
111#11718330C2212yes—
112#11718329C2212yes—
113#11718327C2212yes—
114#11718327C2211yescharacteristic
115#11718327C2211yescharacteristic
116D13×#95C2211yescharacteristic
117D13×#95C2211yescharacteristic
118#11718316C2212yescomplemented
119#11718315C2212yescomplemented
120#11718314C2212yescomplemented
121#11718312C2212yescomplemented
122#11718311C2212yescomplemented
123#11718308C2212yescomplemented
124C24×D13C2311yescharacteristic
125C22×D4×C13C2312yes—
126C22×D4×C13C2311yescharacteristic
127C23×C4×C13C2311yescharacteristic
128C23×C4×C13C2312yes—
129C23×C4×C13C2312yes—
130C22×C22⋊D13C2312yes—
131C22×C22⋊D13C2312yes—
132C23×Dic13C2312yes—
133C23×Dic13C2312yes—
134C23×Dic13C2312yes—
135C23×Dic13C2311yescharacteristic
136C2×#6129—42no—
137C2×#6129—42no—
138C2×#6129C2×C418yescomplemented
139C22×C4×D13—42no—
140C22×C4×D13—42no—
141C22×C4×D13C2×C418yescomplemented
142C22×C4×D13C2311yescharacteristic
143C22×C4×D13C2311yescharacteristic
144C22×C4×D13C2311yescharacteristic
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2311yescharacteristic
147C22×C4×D13C2311yescharacteristic
148C22×C4×D13C2311yescharacteristic
149C22×C4×D13C2311yescharacteristic
150C22×Dic26C2311yescharacteristic
151C13×#121C2×C418yescomplemented
152C4×D4×C13—28no—
153C4×D4×C13—42no—
154C2×C13×C4⋊C4—42no—
155C2×C13×C4⋊C4C2311yescharacteristic
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2311yescharacteristic
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C22⋊C4C2311yescharacteristic
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2311yescharacteristic
166C2×C42×C13C2311yescharacteristic
167C2×C42×C13C2311yescharacteristic
168C2×C42×C13C2312yes—
169C2×C22⋊Dic13C2311yescharacteristic
170C2×C22⋊Dic13C2312yes—
171C2×C22⋊Dic13C2312yes—
172C2×C22⋊Dic13C2312yes—
173C2×C22⋊Dic13C2312yes—
174C2×C22⋊Dic13C2312yes—
175C2×C22⋊Dic13C2311yescharacteristic
176#88192C2×C418yescomplemented
177#88191C2×C4116yescomplemented
178D4×Dic13—28no—
179D4×Dic13—42no—
180D4×Dic13C2×C4116yescomplemented
181C4×C22⋊D13—44no—
182C2×#6103—44no—
183C2×#6103C2311yescharacteristic
184C2×#6103C2311yescharacteristic
185C2×#6103C2311yescharacteristic
186C2×#6103C2311yescharacteristic
187C2×#6103C2312yes—
188C2×#6103C2312yes—
189C2×#6103C2312yes—
190C2×#6103C2312yes—
191C2×#6103C2312yes—
192C2×#6103C2312yes—
193C2×C4⋊Dic13—42no—
194C2×C4⋊Dic13C2311yescharacteristic
195C2×C4⋊Dic13C2311yescharacteristic
196C2×C4⋊Dic13C2312yes—
197C2×C4⋊Dic13C2312yes—
198C2×C4⋊Dic13C2312yes—
199C2×C4⋊Dic13C2311yescharacteristic
200#88178C2×C418yescomplemented
201C2×#6101C2312yes—
202C2×#6101C2312yes—
203C2×#6101C2312yes—
204C2×#6101C2312yes—
205C2×#6101C2312yes—
206C2×C4×Dic13C2311yescharacteristic
207C2×C4×Dic13C2311yescharacteristic
208C2×C4×Dic13C2312yes—
209C2×C4×Dic13C2312yes—
210C2×C4×Dic13C2311yescharacteristic
211C2×C4×Dic13C2311yescharacteristic
212C2×C4×Dic13C2311yescharacteristic
213C2×C4×Dic13C2311yescharacteristic
214C2×C4×Dic13C2312yes—
215C2×C4×Dic13C2312yes—
216C2×C4×Dic13C2312yes—
217C2×C4×Dic13C2312yes—
218#88151C2×C418yescomplemented
219#88146C2×C418yescomplemented
220#88141—42no—
221#88137C2×C4116yescomplemented
222#88135—44no—
223#88135C2×C4116yescomplemented
224C22⋊C4×D13—24no—
225C22⋊C4×D13—24no—
226C42×D13—42no—
227C42×D13—42no—
228C4×Dic26—42no—
229C13×#95C2311yescharacteristic
230C13×#95C2311yescharacteristic
231C13×#95C2312yes—
232C13×#95C2312yes—
233#88071C2312yes—
234#88071C2311yescharacteristic
235#88071C2312yes—
236#88071C2312yes—
237#88071C2311yescharacteristic
238#88071C2312yes—
239#88071C2312yes—
240#88071C2312yes—
241#88071C2312yes—
242#88071C2312yes—
243#88071C2312yes—
244#88071C2312yes—
245#88071C2312yes—
246#88071C2312yes—
247#88071C2311yescharacteristic
248#88071C2311yescharacteristic
249#88071C2311yescharacteristic
250#88071C2311yescharacteristic
251#88071C2312yes—
252#88071C2312yes—
253#34233—131nomaximal, Sylow
254C24×C13C2412yes—
255C24×C13C2411yescharacteristic
256C23×D13—22no—
257C23×D13—22no—
258C23×D13—22no—
259C23×D13—22no—
260C23×D13—41no—
261C23×D13—41no—
262C23×D13C22×C414yes—
263C23×D13C2411yescharacteristic
264C23×D13C2411yescharacteristic
265C2×D4×C13—24no—
266C2×D4×C13—24no—
267C2×D4×C13—22no—
268C2×D4×C13—22no—
269C2×D4×C13C22×C418yes—
270C2×D4×C13C22×C414yes—
271C22×C4×C13—22no—
272C22×C4×C13—22no—
273C22×C4×C13—24no—
274C22×C4×C13—24no—
275C22×C4×C13—42no—
276C22×C4×C13—42no—
277C22×C4×C13—42no—
278C22×C4×C13—42no—
279C22×C4×C13C22×C414yes—
280C22×C4×C13C2411yescharacteristic
281C22×C4×C13C2412yes—
282C22×C4×C13C2412yes—
283C22×C4×C13C2411yescharacteristic
284C22×C4×C13C2412yes—
285C22×C4×C13C2411yescharacteristic
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2411yescharacteristic
288C22×C4×C13C2411yescharacteristic
289C2×C22⋊D13—24no—
290C2×C22⋊D13—24no—
291C2×C22⋊D13—42no—
292C2×C22⋊D13—42no—
293C2×C22⋊D13C22×C418yes—
294C2×C22⋊D13C22×C418yes—
295C22×Dic13—24no—
296C22×Dic13—24no—
297C22×Dic13—41no—
298C22×Dic13—41no—
299C22×Dic13—42no—
300C22×Dic13—42no—
301C22×Dic13—42no—
302C22×Dic13—42no—
303C22×Dic13—42no—
304C22×Dic13—42no—
305C22×Dic13C22×C418yes—
306C22×Dic13C22×C414yes—
307C22×Dic13C2411yescharacteristic
308C22×Dic13C2412yes—
309C22×Dic13C2411yescharacteristic
310C22×Dic13C2412yes—
311C22×Dic13C2411yescharacteristic
312C22×Dic13C2411yescharacteristic
313C22×Dic13C2412yes—
314C22×Dic13C2412yes—
315C22×Dic13C2411yescharacteristic
316C22×Dic13C2411yescharacteristic
317#6129—416no—
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—22no—
325C2×C4×D13—22no—
326C2×C4×D13—22no—
327C2×C4×D13—22no—
328C2×C4×D13—22no—
329C2×C4×D13—22no—
330C2×C4×D13—416no—
331C2×C4×D13—41no—
332C2×C4×D13—41no—
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×D13C22×C414yes—
340C2×C4×D13C22×C414yes—
341C2×C4×D13C22×C414yes—
342C2×C4×D13C22×C414yes—
343C2×Dic26—22no—
344C2×Dic26—22no—
345C2×Dic26C22×C414yes—
346C13×C4⋊C4—24no—
347C13×C4⋊C4—22no—
348C13×C4⋊C4—22no—
349C13×C4⋊C4—42no—
350C13×C4⋊C4C22×C414yes—
351C13×C22⋊C4—22no—
352C13×C22⋊C4—24no—
353C13×C22⋊C4—42no—
354C13×C22⋊C4—42no—
355C13×C22⋊C4C22×C418yes—
356C13×C22⋊C4#4114yescomplemented
357C42×C13—24no—
358C42×C13—22no—
359C42×C13—22no—
360C22⋊Dic13—22no—
361C22⋊Dic13—24no—
362C22⋊Dic13—42no—
363C22⋊Dic13—42no—
364C22⋊Dic13C22×C418yes—
365C22⋊Dic13C22×C418yes—
366C22⋊Dic13#4114yescomplemented
367#6103—24no—
368#6103—24no—
369#6103—22no—
370#6103—22no—
371#6103—22no—
372#6103—22no—
373#6103—42no—
374#6103—42no—
375#6103C22×C418yes—
376#6103C22×C418yes—
377C4⋊Dic13—22no—
378C4⋊Dic13—22no—
379C4⋊Dic13—24no—
380C4⋊Dic13—42no—
381C4⋊Dic13C22×C418yes—
382C4⋊Dic13C22×C414yes—
383#6101—42no—
384#6101—42no—
385#6101—42no—
386#6101—42no—
387#6101C22×C418yes—
388C4×Dic13—22no—
389C4×Dic13—22no—
390C4×Dic13—24no—
391C4×Dic13—42no—
392C4×Dic13—41no—
393C4×Dic13—41no—
394C4×Dic13—41no—
395C4×Dic13—41no—
396C4×Dic13—42no—
397C4×Dic13—42no—
398C4×Dic13—42no—
399C4×Dic13C22×C418yes—
400C2×#525—131no—
401#2361—131no—
402#2361D1311yescharacteristic, complemented
403#2360—131no—
404#2360—131no—
405#2358—132no—
406#2358—132no—
407#2353—132no—
408#2349—132no—
409#2347—131no—
410#2346—131no—
411#2341—131no—
412#2339—131no—
413#2335—132no—
414#2335—132no—
415#2318—132no—
416C4×C22⋊Q8—131no—
417C4×C22⋊Q8—131no—
418C4×#121—131no—
419C4×#121—131no—
420C2×#380—131no—
421#2275—132no—
422C2×C4×C22⋊C4—131no—
423C23×C13—21no—
424C23×C13—21no—
425C23×C13—21no—
426C23×C13—21no—
427C23×C13—22no—
428C23×C13—22no—
429C23×C13—22no—
430C23×C13—22no—
431C23×C13—22no—
432C23×C13—22no—
433C23×C13C23×C414yes—
434C23×C13C23×C412yes—
435C23×C13C2×#4112yes—
436C23×C13C2×#4112yes—
437C23×C13C2511yescharacteristic
438C22×D13—21no—
439C22×D13—21no—
440C22×D13—21no—
441C22×D13—21no—
442C22×D13—28no—
443C22×D13—21no—
444C22×D13—21no—
445C22×D13—21no—
446C22×D13—21no—
447C22×D13—21no—
448C22×D13—21no—
449C22×D13—28no—
450C22×D13—44no—
451C22×D13—44no—
452C22×D13—44no—
453C22×D13—44no—
454C22×D13—44no—
455C22×D13C23×C412yes—
456C22×D13C23×C412yes—
457C22×D13H(5,𝔽2)12yes—
458C22×D132−1+412yes—
459D4×C13—216no—
460D4×C13—28no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13—21no—
464C2×C4×C13—21no—
465C2×C4×C13—21no—
466C2×C4×C13—21no—
467C2×C4×C13—21no—
468C2×C4×C13—21no—
469C2×C4×C13—28no—
470C2×C4×C13—21no—
471C2×C4×C13—21no—
472C2×C4×C13—22no—
473C2×C4×C13—22no—
474C2×C4×C13—21no—
475C2×C4×C13—22no—
476C2×C4×C13—22no—
477C2×C4×C13—21no—
478C2×C4×C13—21no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—21no—
482C2×C4×C13—84no—
483C2×C4×C13—84no—
484C2×C4×C13C23×C414yes—
485C2×C4×C13C23×C412yes—
486C2×C4×C13C23×C412yes—
487C2×C4×C13C2×#4112yes—
488C2×C4×C13C2×#4112yes—
489C2×C4×C13H(5,𝔽2)12yes—
490C2×C4×C13H(5,𝔽2)12yes—
491C22⋊D13—216no—
492C22⋊D13—48no—
493C2×Dic13—21no—
494C2×Dic13—21no—
495C2×Dic13—22no—
496C2×Dic13—21no—
497C2×Dic13—21no—
498C2×Dic13—21no—
499C2×Dic13—22no—
500C2×Dic13—22no—
501C2×Dic13—21no—
502C2×Dic13—21no—
503C2×Dic13—21no—
504C2×Dic13—22no—
505C2×Dic13—22no—
506C2×Dic13—22no—
507C2×Dic13—21no—
508C2×Dic13—21no—
509C2×Dic13—21no—
510C2×Dic13—21no—
511C2×Dic13—22no—
512C2×Dic13—22no—
513C2×Dic13—21no—
514C2×Dic13—22no—
515C2×Dic13—22no—
516C2×Dic13—21no—
517C2×Dic13—44no—
518C2×Dic13—48no—
519C2×Dic13—84no—
520C2×Dic13—84no—
521C2×Dic13C23×C412yes—
522C2×Dic13C23×C414yes—
523C2×Dic13C23×C414yes—
524C2×Dic13C23×C412yes—
525C2×Dic13C2×#4112yes—
526C2×Dic13C2×#4112yes—
527C4×D13—28no—
528C4×D13—28no—
529C4×D13—44no—
530C4×D13—44no—
531C4×D13—44no—
532C4×D13—44no—
533C4×D13—44no—
534C4×D13—44no—
535Dic26—28no—
536C22×#41—131no—
537C24×C4—131no—
538#525—1316no—
539C2×#123—132no—
540C2×C22⋊Q8—131no—
541C2×C22⋊Q8—131no—
542C2×#121—131no—
543C2×#121C2×D1311yescharacteristic
544C2×#120—132no—
545C2×C4×Q8—131no—
546C2×C4×Q8—131no—
547C2×C4×D4—132no—
548C2×C4×D4—132no—
549C2×C4×D4—131no—
550C2×C4×D4—132no—
551C2×C4×D4—132no—
552C2×C4×D4—132no—
553C2×C4×D4C2×D1312yes—
554C2×C4×D4C2×D1311yescharacteristic, complemented
555C2×#117—131no—
556C22×C4⋊C4—131no—
557C22×C4⋊C4C2×D1311yescharacteristic
558C22×C22⋊C4—132no—
559C22×C22⋊C4—131no—
560C22×C22⋊C4—131no—
561C22×C42—131no—
562C22×C42—131no—
563#391—131no—
564#391—131no—
565#390—131no—
566#390—132no—
567#390—132no—
568#390C2×D1311yescharacteristic, complemented
569#389—132no—
570#389—131no—
571#389—131no—
572#389—131no—
573#389—132no—
574#389C2×D1311yescharacteristic, complemented
575#388—132no—
576#388—132no—
577#388—132no—
578#388—132no—
579#388—132no—
580#388—132no—
581#388—132no—
582#388C2×D1312yescomplemented
583#387—132no—
584#387—132no—
585#387—132no—
586#387—132no—
587#386—132no—
588#386—132no—
589#386—132no—
590#386—132no—
591#386—132no—
592#386C2×D1312yes—
593#385—132no—
594#385—132no—
595#385—132no—
596#385—132no—
597#385—132no—
598#385C2×D1312yescomplemented
599#383—132no—
600#382—132no—
601#381—132no—
602#380—132no—
603#380—131no—
604#380—131no—
605#380—132no—
606#380—131no—
607#380—131no—
608#380—132no—
609C4×C4⋊C4—132no—
610C4×C4⋊C4—131no—
611C4×C4⋊C4—132no—
612C4×C4⋊C4—131no—
613C4×C4⋊C4—132no—
614C4×C4⋊C4—131no—
615C4×C4⋊C4C2×D1311yescharacteristic, complemented
616C4×C22⋊C4—132no—
617C4×C22⋊C4—132no—
618C4×C22⋊C4—131no—
619C4×C22⋊C4—131no—
620C4×C22⋊C4—132no—
621C4×C22⋊C4—132no—
622C4×C22⋊C4—132no—
623C4×C22⋊C4—131no—
624C4×C22⋊C4—131no—
625C4×C22⋊C4—131no—
626C4×C22⋊C4—132no—
627C4×C22⋊C4—131no—
628C4×C22⋊C4—131no—
629C4×C22⋊C4—132no—
630C4×C22⋊C4C2×D1311yescharacteristic
631#376—132no—
632C2×#95—132no—
633C2×#95—132no—
634C2×#95—131no—
635C2×#95—131no—
636C22×C13—22no—
637C22×C13—22no—
638C22×C13—22no—
639C22×C13—22no—
640C22×C13—22no—
641C22×C13—22no—
642C22×C13—24no—
643C22×C13—24no—
644C22×C13—24no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13C4×#4114yes—
650C22×C13C24×C411yescharacteristic
651C22×C13C22×#4111yescharacteristic
652C22×C13C22×#4111yescharacteristic
653C22×C13C2×H(5,𝔽2)11yescharacteristic
654C22×C13C2×H(5,𝔽2)11yescharacteristic
655C22×C13C2×H(5,𝔽2)11yescharacteristic
656C22×C13C2×2−1+411yescharacteristic
657C2×D13—22no—
658C2×D13—22no—
659C2×D13—22no—
660C2×D13—22no—
661C2×D13—22no—
662C2×D13—22no—
663C2×D13—22no—
664C2×D13—22no—
665C2×D13—22no—
666C2×D13—416no—
667C2×D13—41no—
668C2×D13—41no—
669C2×D13—41no—
670C2×D13—41no—
671C2×D13#52014yes—
672C4×C13—24no—
673C4×C13—22no—
674C4×C13—22no—
675C4×C13—22no—
676C4×C13—41no—
677C4×C13—42no—
678C4×C13—42no—
679C4×C13—41no—
680C4×C13#51814yes—
681Dic13—24no—
682Dic13—22no—
683Dic13—22no—
684Dic13—24no—
685Dic13—22no—
686Dic13—22no—
687Dic13—41no—
688Dic13—42no—
689Dic13—42no—
690Dic13—41no—
691C25—131no—
692C2×#41—138no—
693C2×#41—522no—
694C2×#41—522no—
695C22×Q8—131no—
696C22×D4—132no—
697C22×D4—132no—
698C22×D4C22×D1312yes—
699C22×D4C22×D1311yescharacteristic
700C23×C4—131no—
701C23×C4—132no—
702C23×C4—131no—
703C23×C4—131no—
704C23×C4—138no—
705C23×C4—131no—
706C23×C4—131no—
707C23×C4—132no—
708C23×C4—132no—
709C23×C4—131no—
710C23×C4—131no—
711C23×C4—131no—
712C23×C4—131no—
713C23×C4—522no—
714C23×C4—522no—
715C23×C4C22×D1311yescharacteristic
716C23×C4C22×D1312yes—
717C23×C4C22×D1312yes—
718#123—1316no—
719C22⋊Q8—138no—
720C22⋊Q8—138no—
721#121—138no—
722#121C4×D1318yescomplemented
723#120—1316no—
724C4×Q8—522no—
725C4×Q8—522no—
726C4×D4—28no—
727C4×D4—42no—
728C4×D4—1316no—
729C4×D4—1316no—
730C4×D4—268no—
731C4×D4—522no—
732C4×D4—524no—
733C4×D4—524no—
734#117—138no—
735C2×C4⋊C4—42no—
736C2×C4⋊C4—131no—
737C2×C4⋊C4—132no—
738C2×C4⋊C4—132no—
739C2×C4⋊C4—131no—
740C2×C4⋊C4—131no—
741C2×C4⋊C4—132no—
742C2×C4⋊C4—132no—
743C2×C4⋊C4—132no—
744C2×C4⋊C4—132no—
745C2×C4⋊C4—132no—
746C2×C4⋊C4—132no—
747C2×C4⋊C4—522no—
748C2×C4⋊C4C22×D1311yescharacteristic
749C2×C4⋊C4C22×D1311yescharacteristic
750C2×C4⋊C4C22×D1312yes—
751C2×C4⋊C4C22×D1312yes—
752C2×C4⋊C4C22×D1311yescharacteristic
753C2×C22⋊C4—131no—
754C2×C22⋊C4—132no—
755C2×C22⋊C4—132no—
756C2×C22⋊C4—132no—
757C2×C22⋊C4—132no—
758C2×C22⋊C4—131no—
759C2×C22⋊C4—132no—
760C2×C22⋊C4—132no—
761C2×C22⋊C4—132no—
762C2×C22⋊C4—131no—
763C2×C22⋊C4—131no—
764C2×C22⋊C4—131no—
765C2×C22⋊C4—131no—
766C2×C22⋊C4—132no—
767C2×C22⋊C4—132no—
768C2×C22⋊C4—132no—
769C2×C22⋊C4—132no—
770C2×C22⋊C4—264no—
771C2×C22⋊C4—264no—
772C2×C22⋊C4—524no—
773C2×C22⋊C4C22×D1311yescharacteristic
774C2×C22⋊C4C22×D1312yes—
775C2×C22⋊C4C22×D1312yes—
776C2×C22⋊C4C22×D1312yes—
777C2×C22⋊C4C22×D1312yes—
778C2×C22⋊C4C22×D1311yescharacteristic
779C2×C42—132no—
780C2×C42—132no—
781C2×C42—131no—
782C2×C42—131no—
783C2×C42—132no—
784C2×C42—132no—
785C2×C42—132no—
786C2×C42—132no—
787C2×C42—131no—
788C2×C42—131no—
789C2×C42—131no—
790C2×C42—131no—
791C2×C42—522no—
792C2×C42—522no—
793C2×C42C22×D1312yes—
794C2×C42C22×D1311yescharacteristic
795C2×C42C22×D1311yescharacteristic
796#95—131no—
797#95—132no—
798#95—131no—
799#95—131no—
800#95—131no—
801#95—131no—
802#95—131no—
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#95—132no—
814#95—132no—
815#95—132no—
816#95C22×D1311yescharacteristic
817#95C22×D1311yescharacteristic
818#95C22×D1312yes—
819#95C22×D1312yes—
820C2×C13—24no—
821C2×C13—44no—
822C2×C13C2×C4×#4111yescharacteristic
823C2×C13C2×#51811yescharacteristic
824C2×C13C2×#52011yescharacteristic
825C2×C13#351911yescharacteristic
826C2×C13#351911yescharacteristic
827C2×C13#352011yescharacteristic
828C2×C13#352011yescharacteristic
829D13—24no—
830D13—42no—
831C24—131no—
832C24—131no—
833C24—134no—
834C24—262no—
835C24—262no—
836C24—262no—
837C24—262no—
838C24—521no—
839C24—521no—
840C24C23×D1312yes—
841C24C23×D1311yescharacteristic
842#41—5216no—
843C2×Q8—134no—
844C2×Q8—262no—
845C2×Q8—262no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—138no—
851C2×D4—138no—
852C2×D4—264no—
853C2×D4—264no—
854C2×D4—522no—
855C2×D4—522no—
856C2×D4C2×C4×D1318yes—
857C2×D4C2×C4×D1314yes—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—131no—
867C22×C4—131no—
868C22×C4—131no—
869C22×C4—131no—
870C22×C4—132no—
871C22×C4—132no—
872C22×C4—134no—
873C22×C4—138no—
874C22×C4—134no—
875C22×C4—134no—
876C22×C4—134no—
877C22×C4—134no—
878C22×C4—131no—
879C22×C4—132no—
880C22×C4—131no—
881C22×C4—132no—
882C22×C4—262no—
883C22×C4—262no—
884C22×C4—262no—
885C22×C4—262no—
886C22×C4—262no—
887C22×C4—262no—
888C22×C4—264no—
889C22×C4—262no—
890C22×C4—262no—
891C22×C4—262no—
892C22×C4—262no—
893C22×C4—264no—
894C22×C4—262no—
895C22×C4—262no—
896C22×C4—5216no—
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—521no—
906C22×C4—521no—
907C22×C4—522no—
908C22×C4—522no—
909C22×C4—522no—
910C22×C4—522no—
911C22×C4—522no—
912C22×C4—522no—
913C22×C4C2×C4×D1314yes—
914C22×C4C23×D1311yescharacteristic
915C22×C4C23×D1312yes—
916C22×C4C23×D1312yes—
917C22×C4C23×D1311yescharacteristic
918C22×C4C23×D1312yes—
919C22×C4C23×D1311yescharacteristic
920C22×C4C23×D1311yescharacteristic
921C22×C4C23×D1311yescharacteristic
922C22×C4C23×D1311yescharacteristic
923C4⋊C4—24no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—134no—
928C4⋊C4—138no—
929C4⋊C4—138no—
930C4⋊C4—264no—
931C4⋊C4—262no—
932C4⋊C4—262no—
933C4⋊C4—522no—
934C4⋊C4—522no—
935C4⋊C4—522no—
936C4⋊C4—522no—
937C4⋊C4—522no—
938C4⋊C4C2×C4×D1314yes—
939C22⋊C4—22no—
940C22⋊C4—24no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—138no—
944C22⋊C4—138no—
945C22⋊C4—134no—
946C22⋊C4—138no—
947C22⋊C4—138no—
948C22⋊C4—262no—
949C22⋊C4—262no—
950C22⋊C4—264no—
951C22⋊C4—264no—
952C22⋊C4—264no—
953C22⋊C4—262no—
954C22⋊C4—262no—
955C22⋊C4—262no—
956C22⋊C4—522no—
957C22⋊C4—522no—
958C22⋊C4—522no—
959C22⋊C4—522no—
960C22⋊C4C2×C4×D1318yes—
961C22⋊C4#612914yescomplemented
962C42—24no—
963C42—22no—
964C42—22no—
965C42—138no—
966C42—264no—
967C42—262no—
968C42—262no—
969C42—521no—
970C42—521no—
971C42—521no—
972C42—521no—
973C42—522no—
974C42—522no—
975C42—522no—
976C42—522no—
977C13#3423311yescharacteristic, complemented, Sylow
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—132no—
989C23—132no—
990C23—132no—
991C23—132no—
992C23—268no—
993C23—261no—
994C23—261no—
995C23—261no—
996C23—261no—
997C23—268no—
998C23—261no—
999C23—261no—
1000C23—261no—
1001C23—261no—
1002C23—261no—
1003C23—261no—
1004C23—524no—
1005C23—524no—
1006C23—524no—
1007C23—524no—
1008C23—524no—
1009C23C22×C4×D1314yes—
1010C23C22×C4×D1312yes—
1011C23C2×#612912yes—
1012C23#41×D1312yes—
1013C23C24×D1311yescharacteristic
1014Q8—268no—
1015D4—216no—
1016D4—28no—
1017D4—2616no—
1018D4—528no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—132no—
1043C2×C4—134no—
1044C2×C4—132no—
1045C2×C4—134no—
1046C2×C4—132no—
1047C2×C4—132no—
1048C2×C4—261no—
1049C2×C4—261no—
1050C2×C4—262no—
1051C2×C4—261no—
1052C2×C4—261no—
1053C2×C4—261no—
1054C2×C4—262no—
1055C2×C4—261no—
1056C2×C4—262no—
1057C2×C4—261no—
1058C2×C4—261no—
1059C2×C4—262no—
1060C2×C4—268no—
1061C2×C4—268no—
1062C2×C4—261no—
1063C2×C4—261no—
1064C2×C4—261no—
1065C2×C4—262no—
1066C2×C4—262no—
1067C2×C4—261no—
1068C2×C4—262no—
1069C2×C4—262no—
1070C2×C4—262no—
1071C2×C4—262no—
1072C2×C4—261no—
1073C2×C4—261no—
1074C2×C4—524no—
1075C2×C4—524no—
1076C2×C4—524no—
1077C2×C4—524no—
1078C2×C4—524no—
1079C2×C4—524no—
1080C2×C4—524no—
1081C2×C4—528no—
1082C2×C4—1044no—
1083C2×C4—1044no—
1084C2×C4C22×C4×D1314yes—
1085C2×C4C22×C4×D1312yes—
1086C2×C4C22×C4×D1312yes—
1087C2×C4C2×#612912yes—
1088C2×C4C2×#612912yes—
1089C2×C4#8825112yes—
1090C2×C4#8825612yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—134no—
1105C22—262no—
1106C22—262no—
1107C22—262no—
1108C22—262no—
1109C22—262no—
1110C22—262no—
1111C22—262no—
1112C22—262no—
1113C22—262no—
1114C22—5216no—
1115C22—521no—
1116C22—521no—
1117C22—521no—
1118C22—521no—
1119C22C4×#612914yes—
1120C22C23×C4×D1311yescharacteristic
1121C22C22×#612911yescharacteristic
1122C22C2×#8825111yescharacteristic
1123C22C2×#41×D1311yescharacteristic
1124C22C2×#8825611yescharacteristic
1125C22D13×H(5,𝔽2)11yescharacteristic
1126C22D13×2−1+411yescharacteristic
1127C4—24no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—42no—
1132C4—42no—
1133C4—41no—
1134C4—41no—
1135C4—262no—
1136C4—262no—
1137C4—264no—
1138C4—264no—
1139C4—262no—
1140C4—262no—
1141C4—521no—
1142C4—522no—
1143C4—522no—
1144C4—521no—
1145C4#1171925014yes—
1146C2—24no—
1147C2—44no—
1148C2—264no—
1149C2—522no—
1150C2C2×C4×#612911yescharacteristic
1151C2C2×#1171925011yescharacteristic
1152C2D13×#52011yescharacteristic
1153C2#1312885911yescharacteristic
1154C2#1312886111yescharacteristic
1155C2#1312887611yescharacteristic
1156C2#1312887811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2361C2
socle, cosocleC23×C13C25
prime radicalC2×#11719311C2
hypercenter#2361D13
hypocenterC13#34233
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #13117856C2semidirect
3. #13117841C2semidirect
4. #13117839C2semidirect
5. #13117816C2semidirect
6. #13117813C2semidirect
7. #13117771C2semidirect
8. #13117742C2semidirect
9. #13117728C2semidirect
10. #13117717C2semidirect
11. #13117675C2semidirect
12. #13117661C2semidirect
13. #13117633C2semidirect
14. #13117621C2semidirect
15. #13117462C2semidirect
16. C4×#88151C2semidirect
17. #13117366C2semidirect
18. #13117352C2semidirect
19. C4×#88192C2semidirect
20. C2×#11718648C2semidirect
21. #13117197C2semidirect
22. C4×C22⋊C4×D13C2semidirect
23. C13×#2361C2semidirect
28. C2×C4×D4×C13C22semidirect
34. C2×D4×Dic13C22semidirect
39. #11719311C4semidirect
42. C2×#88141C22semidirect
50. C2×C4×Dic26C22semidirect
51. C13×#390C22semidirect
52. C13×#389C22semidirect
53. C13×#388C22semidirect
55. C13×#385C22semidirect
56. C4×C13×C4⋊C4C22semidirect
58. #11718882C22semidirect
64. C4×C22⋊Dic13C22semidirect
66. C2×#88071C22semidirect
75. #11718646C22semidirect
76. #11718639C22semidirect
77. C4⋊C4×Dic13C22semidirect
78. C4⋊C4×Dic13C22semidirect
79. C4⋊C4×Dic13C22semidirect
80. C4⋊C4×Dic13C22semidirect
81. #11718635C22semidirect
82. #11718634C22semidirect
83. #11718633C22semidirect
89. #11718612C22semidirect
90. #11718611C22semidirect
92. #11718606C22semidirect
93. #11718605C22semidirect
94. #11718604C22semidirect
95. #11718603C22semidirect
99. C22⋊C4×Dic13C22semidirect
100. C22⋊C4×Dic13C22semidirect
105. C4×C4⋊Dic13C22semidirect
106. C4×C4⋊Dic13C22semidirect
107. #11718593C22semidirect
108. #11718590C22semidirect
109. #11718589C22semidirect
118. #11718316C22semidirect
119. #11718315C22semidirect
120. #11718314C22semidirect
121. #11718312C22semidirect
122. #11718311C22semidirect
123. #11718308C22semidirect
138. C2×#6129C2×C4semidirect
141. C22×C4×D13C2×C4semidirect
151. C13×#121C2×C4semidirect
176. #88192C2×C4semidirect
177. #88191C2×C4semidirect
180. D4×Dic13C2×C4semidirect
200. #88178C2×C4semidirect
218. #88151C2×C4semidirect
219. #88146C2×C4semidirect
221. #88137C2×C4semidirect
223. #88135C2×C4semidirect
356. C13×C22⋊C4#41semidirect
366. C22⋊Dic13#41semidirect
402. #2361D13semidirect
554. C2×C4×D4C2×D13semidirect
568. #390C2×D13semidirect
574. #389C2×D13semidirect
582. #388C2×D13semidirect
598. #385C2×D13semidirect
615. C4×C4⋊C4C2×D13semidirect
722. #121C4×D13semidirect
961. C22⋊C4#6129semidirect
977. C13#34233semidirect

Maximal subgroups

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

subgroupindex
C2×#117193112
#131178562
#131178412
#131178392
#131178162
#131178132
#131177712
#131177422
#131177282
#131177172
#131176752
#131176612
#131176332
#131176212
#131174622
C4×#881512
#131173662
#131173522
C4×#881922
C2×#117186482
#131171972
C4×C22⋊C4×D132
C13×#23612
#3423313