Finite Group Databasebeta

← C2×#13129177 #16770602

Subgroups — C2×#13129177 #16770602

Order 3328.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129177C2132yesmaximal, direct product factor
2C2×#11719351C214yesmaximal, complemented
3C2×Q8×Dic26C211yesmaximal, characteristic, complemented
4C2×#11719268C211yesmaximal, characteristic, complemented
5C2×#11719435C211yesmaximal, characteristic, complemented
6C2×#11719399C212yesmaximal, complemented
7C2×#11719344C212yesmaximal, complemented
8C2×#11719256C212yesmaximal, complemented
9C2×#11719212C212yesmaximal, complemented
10C2×#11719205C212yesmaximal, complemented
11C2×#11719394C212yesmaximal, complemented
12C2×#11719348C212yesmaximal, complemented
13C2×#11719266C212yesmaximal, complemented
14C2×#11719333C214yesmaximal, complemented
15C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#11719285C211yesmaximal, characteristic, complemented
17C2×#11719262C211yesmaximal, characteristic, complemented
18C2×C13×#554C211yesmaximal, characteristic, complemented
19C22×Q8×D13C2212yes—
20C22×#6127C2214yes—
21C13×#554C22116yescomplemented
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×#125C2212yes—
24C2×C13×C22⋊Q8C2214yes—
25C2×C13×C22⋊Q8C2212yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13C2212yes—
28C2×C4×D4×C13C2211yescharacteristic
29C22×C13×C4⋊C4C2212yes—
30C2×#88201C2211yescharacteristic
31C2×#88200C2214yes—
32C2×#88200C2211yescharacteristic
33C2×Q8×Dic13C2212yes—
34C2×#88198C2212yes—
35C2×#88192C2212yes—
36C2×#88192C2211yescharacteristic
37C2×#88190C2211yescharacteristic
38C2×#88184C2212yes—
39C2×#88183C2214yes—
40C2×C4×C22⋊D13C2212yes—
41C2×#88180C2212yes—
42C2×#88180C2212yes—
43C2×#88178C2214yes—
44C2×#88178C2214yes—
45#11719435C22116yescomplemented
46D13×C4⋊Q8C22116yescomplemented
47#11719399C22132yescomplemented
48#11719394C22132yescomplemented
49#11719351C22164yescomplemented
50#11719348C22132yescomplemented
51#11719344C22132yescomplemented
52#11719333C22164yescomplemented
53#11719285C22116yescomplemented
54Q8×Dic26C22116yescomplemented
55#11719268C22116yescomplemented
56#11719266C22132yescomplemented
57#11719262C22116yescomplemented
58#11719256C22132yescomplemented
59C2×#88152C2212yes—
60C2×#88152C2214yes—
61C2×#88151C2212yes—
62C2×#88151C2214yes—
63C2×#88151C2211yescharacteristic
64C2×#88150C2214yes—
65#11719212C22132yescomplemented
66C2×#88149C2211yescharacteristic
67C2×#88148C2214yes—
68C2×#88148C2212yes—
69C2×#88147C2212yes—
70C2×#88146C2212yes—
71C2×#88146C2214yes—
72C2×C4⋊C4×D13C2212yes—
73C2×C4⋊C4×D13C2212yes—
74C2×C4⋊C4×D13C2212yes—
75#11719205C22132yescomplemented
76C2×#88144C2214yes—
77C2×#88144C2211yescharacteristic
78C2×#88144C2211yescharacteristic
79C2×#88144C2212yes—
80C2×#88143C2214yes—
81C2×#88142C2214yes—
82C2×#88142C2212yes—
83C2×#88142C2212yes—
84C2×#88142C2214yes—
85C2×#88142C2212yes—
86C2×#88139C2214yes—
87C2×#88139C2214yes—
88C2×#88137C2214yes—
89C2×#88137C2214yes—
90C2×#88137C2212yes—
91C2×#88133C2212yes—
92C2×#88133C2214yes—
93C2×C4×D52C2212yes—
94C2×C4×D52C2211yescharacteristic
95C2×#88126C2212yes—
96C2×C42×D13C2211yescharacteristic
97C2×#88123C2212yes—
98C2×#88123C2211yescharacteristic
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2312yes—
103C22×D4×C13C2311yescharacteristic
104C23×C4×C13C2312yes—
105C23×C4×C13C2314yes—
106C22×C22⋊D13C2312yes—
107C22×C22⋊D13C2314yes—
108C2×Q8×D13—48no—
109C2×Q8×D13C23116yes—
110C2×#6127—416no—
111C2×#6127C23132yes—
112C22×D52C2311yescharacteristic
113C22×D52C2312yes—
114C22×C4×D13C2311yescharacteristic
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2312yes—
118C22×C4×D13C2314yes—
119C22×C4×D13C2314yes—
120C22×Dic26C2311yescharacteristic
121C22×Dic26C2312yes—
122C22×Dic26C2314yes—
123C22×Dic26C2314yes—
124C13×C4⋊Q8C2318yes—
125C13×#125C23116yes—
126C13×C22⋊Q8C23132yes—
127C13×C22⋊Q8C23116yes—
128C4×Q8×C13C2318yes—
129C4×D4×C13C23116yes—
130C4×D4×C13C2318yes—
131C2×C13×C4⋊C4C2311yescharacteristic
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C4⋊C4C2314yes—
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2314yes—
137C2×C13×C4⋊C4C2311yescharacteristic
138C2×C13×C4⋊C4C23116yes—
139C2×C13×C22⋊C4C2314yes—
140C2×C13×C22⋊C4C2312yes—
141C2×C42×C13C2311yescharacteristic
142C2×C42×C13C2312yes—
143C2×C22⋊Dic13C2312yes—
144C2×C22⋊Dic13C2312yes—
145C2×C22⋊Dic13C2314yes—
146C2×C22⋊Dic13C2312yes—
147#88201C2318yes—
148#88200C23132yes—
149#88200C2318yes—
150Q8×Dic13C23116yes—
151#88198C23116yes—
152#88192C2318yes—
153#88192C23116yes—
154#88190C2318yes—
155#88184C23116yes—
156#88183C23132yes—
157C4×C22⋊D13C23116yes—
158C2×#6103C2312yes—
159C2×#6103C2312yes—
160C2×#6103C2312yes—
161C2×#6103C2312yes—
162C2×#6103C2312yes—
163C2×#6103C2312yes—
164C2×#6103C2314yes—
165C2×#6103C2314yes—
166#88180C23116yes—
167#88180C23116yes—
168C2×C4⋊Dic13C2312yes—
169C2×C4⋊Dic13C2311yescharacteristic
170C2×C4⋊Dic13C2314yes—
171C2×C4⋊Dic13C2312yes—
172C2×C4⋊Dic13C2312yes—
173C2×C4⋊Dic13C2311yescharacteristic
174C2×C4⋊Dic13C2314yes—
175C2×C4⋊Dic13C2312yes—
176C2×C4⋊Dic13C2312yes—
177#88178C23132yes—
178#88178C23132yes—
179C2×#6101C2312yes—
180C2×#6101C2314yes—
181C2×#6101C2312yes—
182C2×#6101C2312yes—
183C2×#6101C2314yes—
184C2×#6101C2312yes—
185C2×#6101C2314yes—
186C2×#6101C2314yes—
187C2×C4×Dic13C2314yes—
188C2×C4×Dic13C2312yes—
189C2×C4×Dic13C2311yescharacteristic
190C2×C4×Dic13C2311yescharacteristic
191C2×C4×Dic13C2311yescharacteristic
192C2×C4×Dic13C2314yes—
193#88152C23116yes—
194#88152C23132yes—
195#88151C23116yes—
196#88151C2318yes—
197#88151C23132yes—
198#88150C23132yes—
199#88149C2318yes—
200#88148C23132yes—
201#88148C23116yes—
202#88147C23116yes—
203#88146C23116yes—
204#88146C23132yes—
205C4⋊C4×D13C23116yes—
206C4⋊C4×D13C23116yes—
207C4⋊C4×D13C23116yes—
208#88144C23116yes—
209#88144C2318yes—
210#88144C23132yes—
211#88144C2318yes—
212#88143C23132yes—
213#88142C23116yes—
214#88142C23116yes—
215#88142C23116yes—
216#88142C23132yes—
217#88142C23132yes—
218#88139C23132yes—
219#88139C23132yes—
220#88137C23132yes—
221#88137C23132yes—
222#88137C23116yes—
223#88133C23116yes—
224#88133C23132yes—
225C4×D52C2318yes—
226C4×D52C23116yes—
227#88126C23116yes—
228C42×D13C2318yes—
229#88123C2318yes—
230#88123C23116yes—
231C4×Dic26C2318yes—
232C4×Dic26C23116yes—
233C2×#3544—131nomaximal, Sylow
234C24×C13C2412yes—
235C23×D13C2412yes—
236C23×D13C2411yescharacteristic
237C2×Q8×C13—24no—
238C2×Q8×C13—44no—
239C2×Q8×C13C2414yes—
240C2×Q8×C13C2418yes—
241C2×D4×C13—24no—
242C2×D4×C13C2414yes—
243C22×C4×C13—28no—
244C22×C4×C13—48no—
245C22×C4×C13C2412yes—
246C22×C4×C13C2412yes—
247C22×C4×C13C2411yescharacteristic
248C22×C4×C13C2412yes—
249C22×C4×C13C2414yes—
250C22×C4×C13C2418yes—
251C22×C4×C13C24116yes—
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C2×C22⋊D13—28no—
255C2×C22⋊D13—48no—
256C2×C22⋊D13C2418yes—
257C2×C22⋊D13C24116yes—
258C22×Dic13C2412yes—
259C22×Dic13C2411yescharacteristic
260C22×Dic13C2411yescharacteristic
261C22×Dic13C2412yes—
262C22×Dic13C2414yes—
263C22×Dic13C2411yescharacteristic
264C22×Dic13C2412yes—
265Q8×D13—432no—
266#6127—464no—
267C2×D52—28no—
268C2×D52—24no—
269C2×D52C2414yes—
270C2×D52C2418yes—
271C2×C4×D13—216no—
272C2×C4×D13—24no—
273C2×C4×D13—24no—
274C2×C4×D13—28no—
275C2×C4×D13—24no—
276C2×C4×D13—48no—
277C2×C4×D13C2414yes—
278C2×C4×D13C2414yes—
279C2×C4×D13C2414yes—
280C2×C4×D13C2418yes—
281C2×C4×D13C24116yes—
282C2×C4×D13C24116yes—
283C2×Dic26—24no—
284C2×Dic26—48no—
285C2×Dic26—48no—
286C2×Dic26—44no—
287C2×Dic26C2414yes—
288C2×Dic26C2418yes—
289C2×Dic26C24116yes—
290C2×Dic26C24116yes—
291C13×C4⋊C4C2414yes—
292C13×C4⋊C4C2418yes—
293C13×C4⋊C4C2418yes—
294C13×C4⋊C4C24116yes—
295C13×C4⋊C4C2418yes—
296C13×C4⋊C4C24116yes—
297C13×C4⋊C4C2414yes—
298C13×C22⋊C4C24116yes—
299C13×C22⋊C4C2418yes—
300C42×C13C2414yes—
301C42×C13C2418yes—
302C22⋊Dic13C2418yes—
303C22⋊Dic13C2418yes—
304C22⋊Dic13C24116yes—
305C22⋊Dic13C2418yes—
306#6103C2418yes—
307#6103C2418yes—
308#6103C2418yes—
309#6103C2418yes—
310#6103C2418yes—
311#6103C2418yes—
312#6103C24116yes—
313#6103C24116yes—
314C4⋊Dic13C2418yes—
315C4⋊Dic13C2414yes—
316C4⋊Dic13C24116yes—
317C4⋊Dic13C2418yes—
318C4⋊Dic13C2418yes—
319C4⋊Dic13C2414yes—
320C4⋊Dic13C24116yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C2418yes—
323#6101C2418yes—
324#6101C24116yes—
325#6101C2418yes—
326#6101C2418yes—
327#6101C24116yes—
328#6101C2418yes—
329#6101C24116yes—
330#6101C24116yes—
331C4×Dic13C24116yes—
332C4×Dic13C2418yes—
333C4×Dic13C2414yes—
334C4×Dic13C2414yes—
335C4×Dic13C2414yes—
336C4×Dic13C24116yes—
337#3544—1332no—
338C2×#563—134no—
339C2×Q82—131no—
340C2×#555—131no—
341C2×#554—131no—
342C2×#554D1311yescharacteristic, complemented
343C2×#552—132no—
344C2×#552—132no—
345C2×#547—132no—
346C2×#547—132no—
347C2×#544—132no—
348C2×#544—132no—
349C2×#542—132no—
350C2×#542—132no—
351C2×#536—134no—
352C22×C4⋊Q8—131no—
353C2×#529—131no—
354C2×#529—131no—
355C23×C13—24no—
356C23×C13—24no—
357C23×C13—24no—
358C23×C13C2514yes—
359C23×C13C2511yescharacteristic
360C22×D13—22no—
361C22×D13—22no—
362C22×D13—24no—
363C22×D13—24no—
364C22×D13—24no—
365C22×D13H(5,𝔽2)14yes—
366C22×D13C2514yes—
367C22×D13C2512yes—
368Q8×C13—28no—
369Q8×C13—48no—
370D4×C13—28no—
371C2×C4×C13—22no—
372C2×C4×C13—24no—
373C2×C4×C13—28no—
374C2×C4×C13—24no—
375C2×C4×C13—24no—
376C2×C4×C13—216no—
377C2×C4×C13—416no—
378C2×C4×C132−1+414yes—
379C2×C4×C132−1+414yes—
380C2×C4×C13C2514yes—
381C2×C4×C13C2514yes—
382C2×C4×C13C2512yes—
383C2×C4×C13C2514yes—
384C2×C4×C13C2518yes—
385C2×C4×C13C2512yes—
386C2×C4×C13C2512yes—
387C22⋊D13—216no—
388C22⋊D13—416no—
389C2×Dic13—22no—
390C2×Dic13—28no—
391C2×Dic13—24no—
392C2×Dic13—24no—
393C2×Dic13—22no—
394C2×Dic13—24no—
395C2×Dic13—22no—
396C2×Dic13C2514yes—
397C2×Dic13C2512yes—
398C2×Dic13C2512yes—
399C2×Dic13C2514yes—
400C2×Dic13C2518yes—
401C2×Dic13C2512yes—
402C2×Dic13C2514yes—
403D52—216no—
404D52—28no—
405C4×D13—232no—
406C4×D13—28no—
407C4×D13—28no—
408C4×D13—216no—
409C4×D13—28no—
410C4×D13—416no—
411Dic26—28no—
412Dic26—416no—
413Dic26—416no—
414Dic26—48no—
415C22×#41—134no—
416C23×Q8—132no—
417#563—1364no—
418Q82—1316no—
419#555—1316no—
420#554—1316no—
421#554C2×D13116yescomplemented
422#552—1332no—
423#552—1332no—
424#547—1332no—
425#547—1332no—
426#544—1332no—
427#544—1332no—
428#542—1332no—
429#542—1332no—
430#536—1364no—
431C2×C4⋊Q8—132no—
432C2×C4⋊Q8—1316no—
433C2×C4⋊Q8—132no—
434C2×C4⋊Q8—132no—
435C2×C4⋊Q8—134no—
436C2×C4⋊Q8—134no—
437C2×C4⋊Q8—132no—
438C2×C4⋊Q8—131no—
439C2×C4⋊Q8—132no—
440C2×C4⋊Q8C2×D1311yescharacteristic
441#529—1316no—
442#529—1316no—
443C2×#126—132no—
444C2×#126—134no—
445C2×#126—132no—
446C2×#126—134no—
447C2×#125—134no—
448C2×#125—131no—
449C2×#125—131no—
450C2×#125—132no—
451C2×#125—134no—
452C2×#125C2×D1312yes—
453C2×#124—131no—
454C2×#124—131no—
455C2×#124—134no—
456C2×#124—134no—
457C2×#123—134no—
458C2×#123—132no—
459C2×#123—134no—
460C2×#123—132no—
461C2×#123—134no—
462C2×#123—134no—
463C2×C22⋊Q8—131no—
464C2×C22⋊Q8—134no—
465C2×C22⋊Q8—134no—
466C2×C22⋊Q8—134no—
467C2×C22⋊Q8—134no—
468C2×C22⋊Q8—131no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—132no—
471C2×C22⋊Q8C2×D1314yes—
472C2×C22⋊Q8C2×D1312yes—
473C2×#121—131no—
474C2×#121—132no—
475C2×#121—132no—
476C2×#121—131no—
477C2×C4×Q8—132no—
478C2×C4×Q8—131no—
479C2×C4×Q8—132no—
480C2×C4×Q8C2×D1311yescharacteristic
481C2×C4×D4—132no—
482C2×C4×D4—132no—
483C2×C4×D4—132no—
484C2×C4×D4—131no—
485C2×C4×D4C2×D1311yescharacteristic
486C2×C4×D4C2×D1312yes—
487C2×#117—132no—
488C2×#117—132no—
489C2×#117—134no—
490C2×#117—132no—
491C2×#117—132no—
492C22×C4⋊C4—132no—
493C22×C4⋊C4—132no—
494C22×C4⋊C4—132no—
495C22×C4⋊C4C2×D1312yes—
496C22×C42—131no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—24no—
500C22×C13—48no—
501C22×C13C2×H(5,𝔽2)12yes—
502C22×C13C2×2−1+412yes—
503C22×C13C2×2−1+412yes—
504C22×C13C2611yescharacteristic
505C2×D13—22no—
506C2×D13—22no—
507C2×D13—28no—
508C2×D13—24no—
509C2×D13—24no—
510C2×D13—24no—
511C2×D13—48no—
512C2×D13C2×H(5,𝔽2)14yes—
513C4×C13—22no—
514C4×C13—24no—
515C4×C13—28no—
516C4×C13—24no—
517C4×C13—24no—
518C4×C13C2×2−1+414yes—
519C4×C13C2×2−1+414yes—
520Dic13—22no—
521Dic13—28no—
522Dic13—24no—
523Dic13—24no—
524Dic13—22no—
525Dic13—22no—
526Dic13—24no—
527C2×#41—1332no—
528C2×#41—5216no—
529C22×Q8—1316no—
530C22×Q8—131no—
531C22×Q8—134no—
532C22×Q8—134no—
533C22×Q8—132no—
534C22×Q8—528no—
535C22×Q8C22×D1311yescharacteristic
536C22×Q8C22×D1312yes—
537C22×D4—132no—
538C22×D4—134no—
539C22×D4—131no—
540C22×D4—132no—
541C22×D4C22×D1311yescharacteristic
542C23×C4—134no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—132no—
546C23×C4—131no—
547C23×C4—134no—
548C23×C4C22×D1312yes—
549C23×C4C22×D1314yes—
550C4⋊Q8—1316no—
551C4⋊Q8—1316no—
552C4⋊Q8—1316no—
553C4⋊Q8—1332no—
554C4⋊Q8—1332no—
555C4⋊Q8—1316no—
556C4⋊Q8—138no—
557C4⋊Q8—1316no—
558C4⋊Q8C22×D1318yes—
559#126—1316no—
560#126—1332no—
561#126—1316no—
562#126—1332no—
563#125—138no—
564#125—138no—
565#125—1316no—
566#125—1332no—
567#125—1332no—
568#125C22×D13116yes—
569#124—138no—
570#124—138no—
571#124—1332no—
572#124—1332no—
573#123—1332no—
574#123—1316no—
575#123—1332no—
576#123—1316no—
577#123—1332no—
578#123—1332no—
579C22⋊Q8—138no—
580C22⋊Q8—1332no—
581C22⋊Q8—1332no—
582C22⋊Q8—1332no—
583C22⋊Q8—138no—
584C22⋊Q8—1332no—
585C22⋊Q8—1316no—
586C22⋊Q8—1332no—
587C22⋊Q8C22×D13132yes—
588C22⋊Q8C22×D13116yes—
589#121—138no—
590#121—1316no—
591#121—1316no—
592#121—138no—
593C4×Q8—1316no—
594C4×Q8—138no—
595C4×Q8—1316no—
596C4×Q8C22×D1318yes—
597C4×D4—1316no—
598C4×D4—1316no—
599C4×D4—1316no—
600C4×D4—138no—
601C4×D4C22×D1318yes—
602C4×D4C22×D13116yes—
603#117—1316no—
604#117—1316no—
605#117—1332no—
606#117—1316no—
607#117—1316no—
608C2×C4⋊C4—131no—
609C2×C4⋊C4—132no—
610C2×C4⋊C4—132no—
611C2×C4⋊C4—134no—
612C2×C4⋊C4—134no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—131no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—132no—
617C2×C4⋊C4—132no—
618C2×C4⋊C4—132no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4—132no—
621C2×C4⋊C4—132no—
622C2×C4⋊C4—132no—
623C2×C4⋊C4—134no—
624C2×C4⋊C4—134no—
625C2×C4⋊C4—1316no—
626C2×C4⋊C4—1316no—
627C2×C4⋊C4—1316no—
628C2×C4⋊C4C22×D1312yes—
629C2×C4⋊C4C22×D1312yes—
630C2×C4⋊C4C22×D1311yescharacteristic
631C2×C4⋊C4C22×D1314yes—
632C2×C4⋊C4C22×D13116yes—
633C2×C4⋊C4C22×D1311yescharacteristic
634C2×C4⋊C4C22×D1314yes—
635C2×C4⋊C4C22×D1312yes—
636C2×C22⋊C4—132no—
637C2×C22⋊C4—134no—
638C2×C22⋊C4—132no—
639C2×C22⋊C4—132no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—132no—
642C2×C22⋊C4—132no—
643C2×C22⋊C4—134no—
644C2×C22⋊C4—132no—
645C2×C22⋊C4—134no—
646C2×C22⋊C4—132no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4C22×D1314yes—
649C2×C22⋊C4C22×D1312yes—
650C2×C42—134no—
651C2×C42—131no—
652C2×C42—131no—
653C2×C42—132no—
654C2×C42—134no—
655C2×C42—131no—
656C2×C42—138no—
657C2×C42C22×D1312yes—
658C2×C42C22×D1311yescharacteristic
659C2×C13—44no—
660C2×C13#354414yescomplemented
661C2×C13C22×H(5,𝔽2)11yescharacteristic
662C2×C13C22×2−1+411yescharacteristic
663C2×C13C22×2−1+411yescharacteristic
664D13—24no—
665D13—44no—
666C24—131no—
667C24—132no—
668C24C23×D1312yes—
669#41—5264no—
670C2×Q8—24no—
671C2×Q8—44no—
672C2×Q8—134no—
673C2×Q8—1316no—
674C2×Q8—1316no—
675C2×Q8—138no—
676C2×Q8—264no—
677C2×Q8—528no—
678C2×Q8—524no—
679C2×Q8—528no—
680C2×Q8—5232no—
681C2×Q8C23×D1314yes—
682C2×Q8C23×D1318yes—
683C2×D4—24no—
684C2×D4—138no—
685C2×D4—1316no—
686C2×D4—134no—
687C2×D4—138no—
688C2×D4—268no—
689C2×D4—268no—
690C2×D4—264no—
691C2×D4—528no—
692C2×D4C23×D1314yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—131no—
698C22×C4—131no—
699C22×C4—131no—
700C22×C4—134no—
701C22×C4—132no—
702C22×C4—134no—
703C22×C4—134no—
704C22×C4—134no—
705C22×C4—1316no—
706C22×C4—138no—
707C22×C4—1316no—
708C22×C4—264no—
709C22×C4—2616no—
710C22×C4—264no—
711C22×C4—268no—
712C22×C4—264no—
713C22×C4—528no—
714C22×C4C23×D1318yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1311yescharacteristic
718C22×C4C23×D1312yes—
719C22×C4C23×D1314yes—
720C22×C4C23×D13116yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1311yescharacteristic
723C4⋊C4—134no—
724C4⋊C4—138no—
725C4⋊C4—138no—
726C4⋊C4—1316no—
727C4⋊C4—1316no—
728C4⋊C4—1316no—
729C4⋊C4—134no—
730C4⋊C4—1316no—
731C4⋊C4—138no—
732C4⋊C4—138no—
733C4⋊C4—138no—
734C4⋊C4—138no—
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—138no—
738C4⋊C4—1316no—
739C4⋊C4—1316no—
740C4⋊C4C23×D1318yes—
741C4⋊C4C23×D1318yes—
742C4⋊C4C23×D1314yes—
743C4⋊C4C23×D13116yes—
744C4⋊C4C23×D1314yes—
745C4⋊C4C23×D13116yes—
746C4⋊C4C23×D1318yes—
747C22⋊C4—138no—
748C22⋊C4—1316no—
749C22⋊C4—138no—
750C22⋊C4—138no—
751C22⋊C4—138no—
752C22⋊C4—138no—
753C22⋊C4—138no—
754C22⋊C4—1316no—
755C22⋊C4—138no—
756C22⋊C4—1316no—
757C22⋊C4—138no—
758C22⋊C4—138no—
759C22⋊C4C23×D13116yes—
760C22⋊C4C23×D1318yes—
761C42—134no—
762C42—134no—
763C42—134no—
764C42—1316no—
765C42—138no—
766C42—1316no—
767C42C23×D1314yes—
768C42C23×D1318yes—
769C13C2×#354411yescharacteristic, complemented, Sylow
770C23—24no—
771C23—24no—
772C23—24no—
773C23—134no—
774C23—132no—
775C23—134no—
776C23—262no—
777C23—262no—
778C23—264no—
779C23—264no—
780C23—264no—
781C23C24×D1314yes—
782C23C24×D1311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—268no—
786Q8—5216no—
787Q8—528no—
788Q8—5216no—
789D4—28no—
790D4—2616no—
791D4—2616no—
792D4—268no—
793D4—5216no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—134no—
802C2×C4—132no—
803C2×C4—132no—
804C2×C4—134no—
805C2×C4—132no—
806C2×C4—138no—
807C2×C4—134no—
808C2×C4—268no—
809C2×C4—2632no—
810C2×C4—264no—
811C2×C4—262no—
812C2×C4—264no—
813C2×C4—262no—
814C2×C4—268no—
815C2×C4—262no—
816C2×C4—264no—
817C2×C4—268no—
818C2×C4—2616no—
819C2×C4—268no—
820C2×C4—5216no—
821C2×C4#8825414yes—
822C2×C4#8825714yes—
823C2×C4C24×D1314yes—
824C2×C4C24×D1314yes—
825C2×C4C24×D1312yes—
826C2×C4C24×D1314yes—
827C2×C4C24×D1318yes—
828C2×C4C24×D1312yes—
829C2×C4C24×D1312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—134no—
835C22—262no—
836C22—262no—
837C22—268no—
838C22—264no—
839C22—264no—
840C22—264no—
841C22—528no—
842C22C2×#8825412yes—
843C22C2×#8825712yes—
844C22D13×H(5,𝔽2)12yes—
845C22C25×D1311yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—268no—
852C4—262no—
853C4—264no—
854C4—262no—
855C4—262no—
856C4—264no—
857C4—264no—
858C4C2×#8825414yes—
859C4C2×#8825714yes—
860C2—44no—
861C2—264no—
862C2—524no—
863C2#1312917714yesdirect product factor
864C2C2×D13×H(5,𝔽2)11yescharacteristic
865C2C22×#8825711yescharacteristic
866C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#554C2
socleC23×C13C25
hypercenterC2×#554D13
hypocenterC13C2×#3544
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13129177C2direct (N × H)
2. C2×#11719351C2semidirect
3. C2×Q8×Dic26C2semidirect
4. C2×#11719268C2semidirect
5. C2×#11719435C2semidirect
6. C2×#11719399C2semidirect
7. C2×#11719344C2semidirect
8. C2×#11719256C2semidirect
9. C2×#11719212C2semidirect
10. C2×#11719205C2semidirect
11. C2×#11719394C2semidirect
12. C2×#11719348C2semidirect
13. C2×#11719266C2semidirect
14. C2×#11719333C2semidirect
15. C2×D13×C4⋊Q8C2semidirect
16. C2×#11719285C2semidirect
17. C2×#11719262C2semidirect
18. C2×C13×#554C2semidirect
21. C13×#554C22semidirect
45. #11719435C22semidirect
46. D13×C4⋊Q8C22semidirect
47. #11719399C22semidirect
48. #11719394C22semidirect
49. #11719351C22semidirect
50. #11719348C22semidirect
51. #11719344C22semidirect
52. #11719333C22semidirect
53. #11719285C22semidirect
54. Q8×Dic26C22semidirect
55. #11719268C22semidirect
56. #11719266C22semidirect
57. #11719262C22semidirect
58. #11719256C22semidirect
65. #11719212C22semidirect
75. #11719205C22semidirect
342. C2×#554D13semidirect
421. #554C2×D13semidirect
660. C2×C13#3544semidirect
769. C13C2×#3544semidirect
863. C2#13129177direct (N × H)

Maximal subgroups

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

subgroupindex
#131291772
C2×#117193512
C2×Q8×Dic262
C2×#117192682
C2×#117194352
C2×#117193992
C2×#117193442
C2×#117192562
C2×#117192122
C2×#117192052
C2×#117193942
C2×#117193482
C2×#117192662
C2×#117193332
C2×D13×C4⋊Q82
C2×#117192852
C2×#117192622
C2×C13×#5542
C2×#354413