Finite Group Databasebeta

← C2×#13129225 #16770621

Subgroups — C2×#13129225 #16770621

Order 3328.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129225C2132yesmaximal, direct product factor
2C2×#11719326C214yesmaximal, complemented
3C2×#11719268C211yesmaximal, characteristic, complemented
4C2×#11719321C212yesmaximal, complemented
5C2×#11719248C211yesmaximal, characteristic, complemented
6C2×#11719319C212yesmaximal, complemented
7C2×#11719246C212yesmaximal, complemented
8C2×D4×Dic26C211yesmaximal, characteristic, complemented
9C2×#11719257C212yesmaximal, complemented
10C2×#11719256C211yesmaximal, characteristic, complemented
11C2×#11719434C212yesmaximal, complemented
12C2×#11719374C214yesmaximal, complemented
13C2×#11719424C212yesmaximal, complemented
14C2×#11719538C212yesmaximal, complemented
15C2×#11719530C212yesmaximal, complemented
16C2×#11719175C211yesmaximal, characteristic, complemented
17C2×#11719184C211yesmaximal, characteristic, complemented
18C2×C13×#532C211yesmaximal, characteristic, complemented
19C22×C13×#41C2212yes—
20C22×#6127C2212yes—
21C23×Dic26C2212yes—
22C13×#532C22116yescomplemented
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×#127C2211yescharacteristic
25C2×C13×#124C2212yes—
26C2×C13×#121C2212yes—
27C2×C13×#121C2211yescharacteristic
28C2×C13×#121C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C4×D4×C13C2212yes—
31C2×C4×D4×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33#11719538C22132yescomplemented
34#11719530C22132yescomplemented
35C2×#88200C2214yes—
36C2×#88198C2214yes—
37C2×#88193C2214yes—
38C2×#88193C2214yes—
39C2×#88193C2214yes—
40C2×#88192C2214yes—
41C2×#88192C2212yes—
42C2×#88192C2212yes—
43C2×#88190C2214yes—
44C2×#88189C2214yes—
45C2×#88189C2214yes—
46C2×#88189C2214yes—
47C2×D4×Dic13C2212yes—
48C2×D4×Dic13C2212yes—
49C2×#88184C2212yes—
50C2×#88184C2211yescharacteristic
51C2×#88183C2212yes—
52C2×C4×C22⋊D13C2212yes—
53C2×#88180C2212yes—
54C2×#88180C2212yes—
55C22×C4⋊Dic13C2212yes—
56C2×#88178C2212yes—
57C2×#88178C2212yes—
58C2×#88178C2212yes—
59C2×#88178C2212yes—
60C2×#88178C2211yescharacteristic
61C2×#88178C2212yes—
62#11719434C22132yescomplemented
63#11719424C22132yescomplemented
64#11719374C22164yescomplemented
65#11719326C22164yescomplemented
66#11719321C22132yescomplemented
67#11719319C22132yescomplemented
68#11719268C22116yescomplemented
69#11719257C22132yescomplemented
70#11719256C22116yescomplemented
71#11719248C22116yescomplemented
72#11719246C22132yescomplemented
73D4×Dic26C22116yescomplemented
74C2×#88150C2214yes—
75C2×#88146C2212yes—
76C2×C4⋊C4×D13C2212yes—
77C2×#88144C2212yes—
78C2×#88143C2214yes—
79C2×#88142C2212yes—
80C2×#88139C2214yes—
81C2×#88139C2214yes—
82C2×#88137C2214yes—
83C2×#88135C2214yes—
84C2×#88133C2214yes—
85C2×#88132C2214yes—
86C2×#88132C2214yes—
87C2×#88131C2214yes—
88#11719184C22116yescomplemented
89C2×#88130C2212yes—
90C2×#88129C2211yescharacteristic
91C2×C4×D52C2211yescharacteristic
92C2×#88126C2212yes—
93#11719175C22116yescomplemented
94C2×#88124C2212yes—
95C2×#88124C2211yescharacteristic
96C2×#88123C2211yescharacteristic
97C2×#88123C2211yescharacteristic
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C2×C13×#41—48no—
102C2×C13×#41C23116yes—
103C22×Q8×C13C2312yes—
104C22×D4×C13C2311yescharacteristic
105C22×D4×C13C2311yescharacteristic
106C22×D4×C13C2312yes—
107C22×D4×C13C2312yes—
108C22×D4×C13C2312yes—
109C22×D4×C13C2312yes—
110C23×C4×C13C2311yescharacteristic
111C23×C4×C13C2312yes—
112C23×C4×C13C2312yes—
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2311yescharacteristic
115C22×C22⋊D13C2314yes—
116C22×C22⋊D13C2314yes—
117C22×C22⋊D13C2312yes—
118C23×Dic13C2314yes—
119C23×Dic13C2314yes—
120C2×#6127—48no—
121C2×#6127C23116yes—
122C22×D52C2311yescharacteristic
123C22×C4×D13C2312yes—
124C22×C4×D13C2314yes—
125C22×Dic26—48no—
126C22×Dic26C2312yes—
127C22×Dic26C2311yescharacteristic
128C22×Dic26C2312yes—
129C22×Dic26C2314yes—
130C22×Dic26C23116yes—
131C13×C4⋊Q8C2318yes—
132C13×#127C2318yes—
133C13×#124C23116yes—
134C13×#121C2318yes—
135C13×#121C2318yes—
136C13×#121C23116yes—
137C4×D4×C13C2318yes—
138C4×D4×C13C23116yes—
139C4×D4×C13C2318yes—
140C2×C13×C4⋊C4C2311yescharacteristic
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2311yescharacteristic
143C2×C13×C22⋊C4C2312yes—
144C2×C13×C22⋊C4C2312yes—
145C2×C13×C22⋊C4C2312yes—
146C2×C13×C22⋊C4C2312yes—
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2311yescharacteristic
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2318yes—
152C2×C22⋊Dic13C2314yes—
153C2×C22⋊Dic13C2314yes—
154C2×C22⋊Dic13C2314yes—
155C2×C22⋊Dic13C2314yes—
156C2×C22⋊Dic13C2314yes—
157C2×C22⋊Dic13C2312yes—
158#88200C23132yes—
159#88198C23132yes—
160#88193C23132yes—
161#88193C23132yes—
162#88193C23132yes—
163#88192C23116yes—
164#88192C23116yes—
165#88192C23132yes—
166#88190C23132yes—
167#88189C23132yes—
168#88189C23132yes—
169#88189C23132yes—
170D4×Dic13C23116yes—
171D4×Dic13C23116yes—
172#88184C2318yes—
173#88184C23116yes—
174#88183C23116yes—
175C4×C22⋊D13C23116yes—
176C2×#6103C2312yes—
177C2×#6103C2312yes—
178C2×#6103C2312yes—
179C2×#6103C2312yes—
180C2×#6103C2314yes—
181#88180C23116yes—
182#88180C23116yes—
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2312yes—
185C2×C4⋊Dic13C2311yescharacteristic
186C2×C4⋊Dic13C2312yes—
187C2×C4⋊Dic13C2312yes—
188C2×C4⋊Dic13C2311yescharacteristic
189C2×C4⋊Dic13C2314yes—
190C2×C4⋊Dic13C23116yes—
191#88178C23116yes—
192#88178C23116yes—
193#88178C2318yes—
194#88178C23116yes—
195#88178C23116yes—
196#88178C23116yes—
197C2×#6101C2314yes—
198C2×#6101C2314yes—
199C2×#6101C2312yes—
200C2×#6101C2312yes—
201C2×#6101C2312yes—
202C2×#6101C2312yes—
203C2×#6101C2314yes—
204C2×#6101C2314yes—
205C2×#6101C2314yes—
206C2×C4×Dic13C2314yes—
207C2×C4×Dic13C2312yes—
208C2×C4×Dic13C2314yes—
209#88150C23132yes—
210#88146C23116yes—
211C4⋊C4×D13C23116yes—
212#88144C23116yes—
213#88143C23132yes—
214#88142C23116yes—
215#88139C23132yes—
216#88139C23132yes—
217#88137C23132yes—
218#88135C23132yes—
219#88133C23132yes—
220#88132C23132yes—
221#88132C23132yes—
222#88131C23132yes—
223#88130C23116yes—
224#88129C2318yes—
225C4×D52C2318yes—
226#88126C23116yes—
227#88124C23116yes—
228#88124C2318yes—
229#88123C2318yes—
230#88123C2318yes—
231C4×Dic26C23116yes—
232C4×Dic26C23116yes—
233C4×Dic26C2318yes—
234C2×#3547—131nomaximal, Sylow
235C24×C13C2411yescharacteristic
236C24×C13C2412yes—
237C24×C13C2412yes—
238C23×D13C2412yes—
239C13×#41—432no—
240C2×Q8×C13—44no—
241C2×Q8×C13C2418yes—
242C2×D4×C13—24no—
243C2×D4×C13—24no—
244C2×D4×C13—44no—
245C2×D4×C13—44no—
246C2×D4×C13—44no—
247C2×D4×C13—44no—
248C2×D4×C13C2414yes—
249C2×D4×C13C2414yes—
250C2×D4×C13C2418yes—
251C2×D4×C13C2418yes—
252C2×D4×C13C2418yes—
253C2×D4×C13C2418yes—
254C22×C4×C13—28no—
255C22×C4×C13—28no—
256C22×C4×C13—24no—
257C22×C4×C13—24no—
258C22×C4×C13—42no—
259C22×C4×C13C2411yescharacteristic
260C22×C4×C13C2412yes—
261C22×C4×C13C2411yescharacteristic
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2412yes—
264C22×C4×C13C2411yescharacteristic
265C22×C4×C13C2414yes—
266C22×C4×C13C2418yes—
267C22×C4×C13C2418yes—
268C22×C4×C13C2414yes—
269C22×C4×C13C2414yes—
270C22×C4×C13C2411yescharacteristic
271C22×C4×C13C2411yescharacteristic
272C2×C22⋊D13—48no—
273C2×C22⋊D13—48no—
274C2×C22⋊D13—44no—
275C2×C22⋊D13C24116yes—
276C2×C22⋊D13C24116yes—
277C2×C22⋊D13C2418yes—
278C22×Dic13—48no—
279C22×Dic13—48no—
280C22×Dic13C2412yes—
281C22×Dic13C2414yes—
282C22×Dic13C2412yes—
283C22×Dic13C2414yes—
284C22×Dic13C2412yes—
285C22×Dic13C24116yes—
286C22×Dic13C24116yes—
287#6127—432no—
288C2×D52—24no—
289C2×D52C2414yes—
290C2×C4×D13—28no—
291C2×C4×D13—48no—
292C2×C4×D13C2418yes—
293C2×C4×D13C24116yes—
294C2×Dic26—24no—
295C2×Dic26—28no—
296C2×Dic26—432no—
297C2×Dic26—48no—
298C2×Dic26—44no—
299C2×Dic26C2418yes—
300C2×Dic26C2414yes—
301C2×Dic26C2418yes—
302C2×Dic26C24116yes—
303C13×C4⋊C4C2414yes—
304C13×C4⋊C4C2418yes—
305C13×C4⋊C4C2414yes—
306C13×C22⋊C4C2418yes—
307C13×C22⋊C4C2418yes—
308C13×C22⋊C4C2418yes—
309C13×C22⋊C4C2418yes—
310C42×C13C2414yes—
311C42×C13C2414yes—
312C42×C13C2414yes—
313C42×C13C2414yes—
314C22⋊Dic13C24116yes—
315C22⋊Dic13C24116yes—
316C22⋊Dic13C24116yes—
317C22⋊Dic13C24116yes—
318C22⋊Dic13C24116yes—
319C22⋊Dic13C2418yes—
320#6103C2418yes—
321#6103C2418yes—
322#6103C2418yes—
323#6103C2418yes—
324#6103C24116yes—
325C4⋊Dic13C2418yes—
326C4⋊Dic13C2418yes—
327C4⋊Dic13C2414yes—
328C4⋊Dic13C2418yes—
329C4⋊Dic13C2418yes—
330C4⋊Dic13C2414yes—
331C4⋊Dic13C24116yes—
332#6101C24116yes—
333#6101C24116yes—
334#6101C2418yes—
335#6101C2418yes—
336#6101C2418yes—
337#6101C2418yes—
338#6101C24116yes—
339#6101C24116yes—
340#6101C24116yes—
341C4×Dic13C24116yes—
342C4×Dic13C2418yes—
343C4×Dic13C24116yes—
344#3547—1332no—
345C2×#562—134no—
346C2×#555—132no—
347C2×#555—131no—
348C2×#554—131no—
349C2×#553—132no—
350C2×#552—132no—
351C2×D4×Q8—131no—
352C2×#548—132no—
353C2×#547—131no—
354C2×#544—132no—
355C2×#542—134no—
356C2×#540—132no—
357C2×#537—132no—
358C2×#536—132no—
359C2×#533—131no—
360C2×#532D1311yescharacteristic, complemented
361C2×#529—131no—
362C23×C13—24no—
363C23×C13—24no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—24no—
367C23×C13—24no—
368C23×C13—24no—
369C23×C13—22no—
370C23×C13—24no—
371C23×C13C2512yes—
372C23×C13C2514yes—
373C23×C13C2514yes—
374C23×C13C2511yescharacteristic
375C22×D13—24no—
376C22×D13—24no—
377C22×D13—24no—
378C22×D13C2514yes—
379Q8×C13—48no—
380D4×C13—28no—
381D4×C13—28no—
382D4×C13—48no—
383D4×C13—48no—
384D4×C13—48no—
385D4×C13—48no—
386C2×C4×C13—24no—
387C2×C4×C13—24no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—216no—
393C2×C4×C13—216no—
394C2×C4×C13—28no—
395C2×C4×C13—28no—
396C2×C4×C13—44no—
397C2×C4×C13H(5,𝔽2)14yes—
398C2×C4×C132−1+414yes—
399C2×C4×C13C2512yes—
400C2×C4×C13C2514yes—
401C2×C4×C13C2512yes—
402C2×C4×C13C2512yes—
403C2×C4×C13C2514yes—
404C2×C4×C13C2512yes—
405C2×C4×C13C2512yes—
406C2×C4×C13C2512yes—
407C22⋊D13—416no—
408C22⋊D13—416no—
409C22⋊D13—48no—
410C2×Dic13—24no—
411C2×Dic13—28no—
412C2×Dic13—24no—
413C2×Dic13—28no—
414C2×Dic13—24no—
415C2×Dic13—416no—
416C2×Dic13—416no—
417C2×Dic13C2514yes—
418C2×Dic13C2518yes—
419C2×Dic13C2514yes—
420C2×Dic13C2518yes—
421C2×Dic13C2514yes—
422D52—28no—
423C4×D13—216no—
424C4×D13—416no—
425Dic26—28no—
426Dic26—216no—
427Dic26—416no—
428Dic26—48no—
429C22×#41—132no—
430C22×#41C2×D1312yes—
431C23×Q8—132no—
432#562—1364no—
433#555—1332no—
434#555—1316no—
435#554—1316no—
436#553—1332no—
437#552—1332no—
438D4×Q8—1316no—
439#548—1332no—
440#547—1316no—
441#544—1332no—
442#542—1364no—
443#540—1332no—
444#537—1332no—
445#536—1332no—
446#533—1316no—
447#532C2×D13116yescomplemented
448C2×C4⋊Q8—134no—
449C2×C4⋊Q8—132no—
450C2×C4⋊Q8—131no—
451C2×C4⋊Q8—131no—
452C2×C4⋊Q8C2×D1311yescharacteristic
453C2×#127C2×D1311yescharacteristic
454#529—1316no—
455C2×#126—134no—
456C2×#126—132no—
457C2×#125—134no—
458C2×#125—132no—
459C2×#125—131no—
460C2×#125—132no—
461C2×#124—134no—
462C2×#124—134no—
463C2×#124—134no—
464C2×#124—131no—
465C2×#124C2×D1312yes—
466C2×#123—134no—
467C2×#123—134no—
468C2×#123—134no—
469C2×#123—132no—
470C2×#123—134no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8—131no—
473C2×C22⋊Q8—132no—
474C2×C22⋊Q8—132no—
475C2×C22⋊Q8—132no—
476C2×C22⋊Q8—132no—
477C2×C22⋊Q8—132no—
478C2×C22⋊Q8—134no—
479C2×C22⋊Q8—134no—
480C2×C22⋊Q8—134no—
481C2×#121—134no—
482C2×#121—132no—
483C2×#121—132no—
484C2×#121—134no—
485C2×#121—134no—
486C2×#121—134no—
487C2×#121—131no—
488C2×#121—132no—
489C2×#121C2×D1311yescharacteristic
490C2×#121C2×D1311yescharacteristic
491C2×#121C2×D1312yes—
492C2×C4×Q8—131no—
493C2×C4×Q8—132no—
494C2×C4×Q8—132no—
495C2×C4×D4—132no—
496C2×C4×D4—132no—
497C2×C4×D4—132no—
498C2×C4×D4—134no—
499C2×C4×D4—131no—
500C2×C4×D4C2×D1311yescharacteristic
501C2×C4×D4C2×D1312yes—
502C2×C4×D4C2×D1311yescharacteristic
503C2×#117—132no—
504C2×#117—132no—
505C2×#117—132no—
506C2×#117—134no—
507C2×#117—132no—
508C22×C4⋊C4—132no—
509C22×C4⋊C4—132no—
510C22×C42C2×D1311yescharacteristic
511C22×C13—24no—
512C22×C13—24no—
513C22×C13—22no—
514C22×C13—22no—
515C22×C13—24no—
516C22×C13—24no—
517C22×C13—24no—
518C22×C13—22no—
519C22×C13—24no—
520C22×C13—48no—
521C22×C13—48no—
522C22×C13—44no—
523C22×C13C2×H(5,𝔽2)12yes—
524C22×C13C2×2−1+412yes—
525C22×C13#58512yes—
526C22×C13C2611yescharacteristic
527C2×D13—24no—
528C2×D13—24no—
529C2×D13—24no—
530C2×D13—48no—
531C4×C13—24no—
532C4×C13—24no—
533C4×C13—22no—
534C4×C13—22no—
535C4×C13—22no—
536C4×C13—22no—
537C4×C13C2×H(5,𝔽2)14yes—
538C4×C13C2×2−1+414yes—
539Dic13—24no—
540Dic13—28no—
541Dic13—24no—
542Dic13—28no—
543Dic13—24no—
544C2×#41—48no—
545C2×#41—1316no—
546C2×#41—528no—
547C2×#41C22×D13116yes—
548C22×Q8—131no—
549C22×Q8—132no—
550C22×Q8—132no—
551C22×Q8—134no—
552C22×Q8—1316no—
553C22×Q8—528no—
554C22×Q8C22×D1312yes—
555C22×D4—132no—
556C22×D4—134no—
557C22×D4—134no—
558C22×D4—131no—
559C22×D4C22×D1311yescharacteristic
560C22×D4C22×D1311yescharacteristic
561C22×D4C22×D1312yes—
562C22×D4C22×D1312yes—
563C22×D4C22×D1312yes—
564C22×D4C22×D1312yes—
565C23×C4—134no—
566C23×C4—134no—
567C23×C4—132no—
568C23×C4—134no—
569C23×C4C22×D1312yes—
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1312yes—
572C23×C4C22×D1311yescharacteristic
573C23×C4C22×D1311yescharacteristic
574C4⋊Q8—1332no—
575C4⋊Q8—1316no—
576C4⋊Q8—138no—
577C4⋊Q8—138no—
578C4⋊Q8C22×D1318yes—
579#127C22×D1318yes—
580#126—1332no—
581#126—1316no—
582#125—1332no—
583#125—1316no—
584#125—138no—
585#125—1316no—
586#124—1332no—
587#124—1332no—
588#124—1332no—
589#124—138no—
590#124C22×D13116yes—
591#123—1332no—
592#123—1332no—
593#123—1332no—
594#123—1316no—
595#123—1332no—
596C22⋊Q8—1332no—
597C22⋊Q8—138no—
598C22⋊Q8—1316no—
599C22⋊Q8—1316no—
600C22⋊Q8—1316no—
601C22⋊Q8—1316no—
602C22⋊Q8—1316no—
603C22⋊Q8—1332no—
604C22⋊Q8—1332no—
605C22⋊Q8—1332no—
606#121—1332no—
607#121—1332no—
608#121—1332no—
609#121—1316no—
610#121—1332no—
611#121—1316no—
612#121—138no—
613#121—1316no—
614#121C22×D1318yes—
615#121C22×D1318yes—
616#121C22×D13116yes—
617C4×Q8—138no—
618C4×Q8—1316no—
619C4×Q8—1316no—
620C4×D4—1316no—
621C4×D4—1316no—
622C4×D4—1316no—
623C4×D4—1332no—
624C4×D4—138no—
625C4×D4C22×D1318yes—
626C4×D4C22×D13116yes—
627C4×D4C22×D1318yes—
628#117—1316no—
629#117—1316no—
630#117—1316no—
631#117—1332no—
632#117—1316no—
633C2×C4⋊C4—131no—
634C2×C4⋊C4—132no—
635C2×C4⋊C4—132no—
636C2×C4⋊C4—134no—
637C2×C4⋊C4—134no—
638C2×C4⋊C4—1316no—
639C2×C4⋊C4—132no—
640C2×C4⋊C4—131no—
641C2×C4⋊C4—132no—
642C2×C4⋊C4—134no—
643C2×C4⋊C4—132no—
644C2×C4⋊C4—132no—
645C2×C4⋊C4—134no—
646C2×C4⋊C4—134no—
647C2×C4⋊C4—134no—
648C2×C4⋊C4—132no—
649C2×C4⋊C4—132no—
650C2×C4⋊C4—1316no—
651C2×C4⋊C4C22×D1311yescharacteristic
652C2×C4⋊C4C22×D1311yescharacteristic
653C2×C4⋊C4C22×D1312yes—
654C2×C22⋊C4—134no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—134no—
657C2×C22⋊C4—134no—
658C2×C22⋊C4—134no—
659C2×C22⋊C4—132no—
660C2×C22⋊C4—132no—
661C2×C22⋊C4—132no—
662C2×C22⋊C4—134no—
663C2×C22⋊C4—132no—
664C2×C22⋊C4—132no—
665C2×C22⋊C4C22×D1312yes—
666C2×C22⋊C4C22×D1312yes—
667C2×C22⋊C4C22×D1312yes—
668C2×C22⋊C4C22×D1312yes—
669C2×C42—134no—
670C2×C42—134no—
671C2×C42—132no—
672C2×C42C22×D1311yescharacteristic
673C2×C42C22×D1311yescharacteristic
674C2×C42C22×D1311yescharacteristic
675C2×C42C22×D1311yescharacteristic
676C2×C42C22×D1318yes—
677C2×C13—44no—
678C2×C13—44no—
679C2×C13—42no—
680C2×C13#354714yescomplemented
681C2×C13C22×H(5,𝔽2)11yescharacteristic
682C2×C13C22×2−1+411yescharacteristic
683C2×C13C2×#58511yescharacteristic
684D13—44no—
685C24—132no—
686C24C23×D1311yescharacteristic
687C24C23×D1312yes—
688C24C23×D1312yes—
689#41—432no—
690#41—5232no—
691C2×Q8—44no—
692C2×Q8—134no—
693C2×Q8—138no—
694C2×Q8—138no—
695C2×Q8—1316no—
696C2×Q8—264no—
697C2×Q8—268no—
698C2×Q8—528no—
699C2×Q8—524no—
700C2×Q8—5232no—
701C2×Q8C23×D1318yes—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—138no—
709C2×D4—1316no—
710C2×D4—1316no—
711C2×D4—134no—
712C2×D4—264no—
713C2×D4—528no—
714C2×D4—524no—
715C2×D4—528no—
716C2×D4C23×D1314yes—
717C2×D4C23×D1314yes—
718C2×D4C23×D1318yes—
719C2×D4C23×D1318yes—
720C2×D4C23×D1318yes—
721C2×D4C23×D1318yes—
722C22×C4—28no—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—132no—
728C22×C4—134no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—134no—
732C22×C4—1316no—
733C22×C4—1316no—
734C22×C4—138no—
735C22×C4—1316no—
736C22×C4—268no—
737C22×C4—528no—
738C22×C4—528no—
739C22×C4—528no—
740C22×C4C23×D1314yes—
741C22×C4C23×D1314yes—
742C22×C4C23×D1318yes—
743C22×C4C23×D1318yes—
744C22×C4C23×D1311yescharacteristic
745C22×C4C23×D1312yes—
746C22×C4C23×D1311yescharacteristic
747C22×C4C23×D1311yescharacteristic
748C22×C4C23×D1311yescharacteristic
749C22×C4C23×D1312yes—
750C22×C4C23×D1314yes—
751C22×C4C23×D1311yescharacteristic
752C22×C4C23×D1311yescharacteristic
753C4⋊C4—134no—
754C4⋊C4—138no—
755C4⋊C4—138no—
756C4⋊C4—1316no—
757C4⋊C4—1316no—
758C4⋊C4—138no—
759C4⋊C4—134no—
760C4⋊C4—138no—
761C4⋊C4—1316no—
762C4⋊C4—138no—
763C4⋊C4—138no—
764C4⋊C4—1316no—
765C4⋊C4—1316no—
766C4⋊C4—1316no—
767C4⋊C4—138no—
768C4⋊C4—138no—
769C4⋊C4C23×D1314yes—
770C4⋊C4C23×D1314yes—
771C4⋊C4C23×D1318yes—
772C22⋊C4—1316no—
773C22⋊C4—1316no—
774C22⋊C4—1316no—
775C22⋊C4—1316no—
776C22⋊C4—1316no—
777C22⋊C4—138no—
778C22⋊C4—138no—
779C22⋊C4—138no—
780C22⋊C4—1316no—
781C22⋊C4—138no—
782C22⋊C4—138no—
783C22⋊C4C23×D1318yes—
784C22⋊C4C23×D1318yes—
785C22⋊C4C23×D1318yes—
786C22⋊C4C23×D1318yes—
787C42—1316no—
788C42—1316no—
789C42—138no—
790C42C23×D1314yes—
791C42C23×D1314yes—
792C42C23×D1314yes—
793C42C23×D1314yes—
794C13C2×#354711yescharacteristic, complemented, Sylow
795C23—24no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—134no—
805C23—264no—
806C23—264no—
807C23—264no—
808C23C24×D1312yes—
809C23C24×D1314yes—
810C23C24×D1314yes—
811C23C24×D1311yescharacteristic
812Q8—48no—
813Q8—268no—
814Q8—2616no—
815Q8—528no—
816Q8—5216no—
817D4—28no—
818D4—28no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—48no—
823D4—268no—
824D4—528no—
825D4—5216no—
826D4—5216no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—216no—
834C2×C4—28no—
835C2×C4—216no—
836C2×C4—28no—
837C2×C4—44no—
838C2×C4—134no—
839C2×C4—138no—
840C2×C4—134no—
841C2×C4—134no—
842C2×C4—138no—
843C2×C4—268no—
844C2×C4—264no—
845C2×C4—264no—
846C2×C4—264no—
847C2×C4—268no—
848C2×C4—2616no—
849C2×C4—5216no—
850C2×C4—5216no—
851C2×C4—5216no—
852C2×C4#8825114yes—
853C2×C4#8825714yes—
854C2×C4C24×D1312yes—
855C2×C4C24×D1314yes—
856C2×C4C24×D1312yes—
857C2×C4C24×D1312yes—
858C2×C4C24×D1312yes—
859C2×C4C24×D1314yes—
860C2×C4C24×D1312yes—
861C2×C4C24×D1312yes—
862C22—24no—
863C22—22no—
864C22—24no—
865C22—22no—
866C22—24no—
867C22—24no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—48no—
872C22—44no—
873C22—48no—
874C22—264no—
875C22—264no—
876C22—264no—
877C22—528no—
878C22C2×#8825112yes—
879C22C2×#8825712yes—
880C22#1171964812yes—
881C22C25×D1311yescharacteristic
882C4—24no—
883C4—22no—
884C4—24no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—268no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—268no—
893C4C2×#8825114yes—
894C4C2×#8825714yes—
895C2—44no—
896C2—42no—
897C2—44no—
898C2—524no—
899C2#1312922514yesdirect product factor
900C2C22×#8825111yescharacteristic
901C2C22×#8825711yescharacteristic
902C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#532C2
socleC23×C13C25
hypercenterC2×#532D13
hypocenterC13C2×#3547
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13129225C2direct (N × H)
2. C2×#11719326C2semidirect
3. C2×#11719268C2semidirect
4. C2×#11719321C2semidirect
5. C2×#11719248C2semidirect
6. C2×#11719319C2semidirect
7. C2×#11719246C2semidirect
8. C2×D4×Dic26C2semidirect
9. C2×#11719257C2semidirect
10. C2×#11719256C2semidirect
11. C2×#11719434C2semidirect
12. C2×#11719374C2semidirect
13. C2×#11719424C2semidirect
14. C2×#11719538C2semidirect
15. C2×#11719530C2semidirect
16. C2×#11719175C2semidirect
17. C2×#11719184C2semidirect
18. C2×C13×#532C2semidirect
22. C13×#532C22semidirect
33. #11719538C22semidirect
34. #11719530C22semidirect
62. #11719434C22semidirect
63. #11719424C22semidirect
64. #11719374C22semidirect
65. #11719326C22semidirect
66. #11719321C22semidirect
67. #11719319C22semidirect
68. #11719268C22semidirect
69. #11719257C22semidirect
70. #11719256C22semidirect
71. #11719248C22semidirect
72. #11719246C22semidirect
73. D4×Dic26C22semidirect
88. #11719184C22semidirect
93. #11719175C22semidirect
360. C2×#532D13semidirect
447. #532C2×D13semidirect
680. C2×C13#3547semidirect
794. C13C2×#3547semidirect
899. C2#13129225direct (N × H)

Maximal subgroups

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

subgroupindex
#131292252
C2×#117193262
C2×#117192682
C2×#117193212
C2×#117192482
C2×#117193192
C2×#117192462
C2×D4×Dic262
C2×#117192572
C2×#117192562
C2×#117194342
C2×#117193742
C2×#117194242
C2×#117195382
C2×#117195302
C2×#117191752
C2×#117191842
C2×C13×#5322
C2×#354713