Finite Group Databasebeta

← C2×#13129307 #16770548

Subgroups — C2×#13129307 #16770548

Order 3328.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129307C2132yesmaximal, direct product factor
2C2×#11719352C214yesmaximal, complemented
3C2×#11719290C212yesmaximal, complemented
4C2×#11719290C211yesmaximal, characteristic, complemented
5C2×#11719272C211yesmaximal, characteristic, complemented
6C2×#11719284C212yesmaximal, complemented
7C2×#11719282C211yesmaximal, characteristic, complemented
8C2×Q8×D52C211yesmaximal, characteristic, complemented
9C2×#11719338C212yesmaximal, complemented
10C2×#11719336C212yesmaximal, complemented
11C2×#11719438C212yesmaximal, complemented
12C2×#11719239C212yesmaximal, complemented
13C2×#11719240C212yesmaximal, complemented
14C2×#11719397C214yesmaximal, complemented
15C2×#11719429C212yesmaximal, complemented
16C2×#11719182C211yesmaximal, characteristic, complemented
17C2×#11719184C211yesmaximal, characteristic, complemented
18C2×C13×#533C211yesmaximal, characteristic, complemented
19C22×#6131C2212yes—
20C22×Q8×D13C2212yes—
21C22×#6127C2212yes—
22C13×#533C22116yescomplemented
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×C4⋊Q8C2211yescharacteristic
25C2×C13×#125C2212yes—
26C2×C13×C22⋊Q8C2212yes—
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×C22⋊Q8C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31C2×C4×Q8×C13C2212yes—
32C2×C13×#117C2212yes—
33C22×C42×C13C2211yescharacteristic
34C2×#88201C2214yes—
35C2×#88201C2212yes—
36C2×#88200C2214yes—
37C2×#88198C2212yes—
38C2×#88184C2212yes—
39C2×#88184C2211yescharacteristic
40C2×#88184C2212yes—
41C2×#88183C2212yes—
42C2×C4×C22⋊D13C2212yes—
43C2×#88178C2211yescharacteristic
44#11719438C22132yescomplemented
45#11719429C22132yescomplemented
46#11719397C22164yescomplemented
47#11719352C22164yescomplemented
48#11719338C22132yescomplemented
49#11719336C22132yescomplemented
50#11719290C22116yescomplemented
51#11719290C22132yescomplemented
52#11719284C22132yescomplemented
53#11719282C22116yescomplemented
54Q8×D52C22116yescomplemented
55#11719272C22116yescomplemented
56#11719240C22132yescomplemented
57#11719239C22132yescomplemented
58C2×#88152C2214yes—
59C2×#88151C2214yes—
60C2×#88151C2212yes—
61C2×#88150C2214yes—
62C2×#88150C2214yes—
63C2×#88150C2214yes—
64C2×#88149C2214yes—
65C2×#88149C2212yes—
66C2×#88148C2214yes—
67C2×#88148C2214yes—
68C2×#88148C2214yes—
69C2×#88148C2214yes—
70C2×#88148C2214yes—
71C2×#88147C2212yes—
72C2×#88147C2214yes—
73C2×C4⋊C4×D13C2214yes—
74C2×#88143C2214yes—
75C2×#88141C2212yes—
76C2×#88139C2214yes—
77C2×#88138C2214yes—
78C2×#88138C2214yes—
79C2×#88137C2214yes—
80#11719184C22116yescomplemented
81C2×#88130C2212yes—
82#11719182C22116yescomplemented
83C2×#88129C2212yes—
84C2×#88129C2212yes—
85C2×#88129C2211yescharacteristic
86C2×#88128C2212yes—
87C2×#88128C2211yescharacteristic
88C2×C4×D52C2212yes—
89C2×C4×D52C2212yes—
90C2×C4×D52C2212yes—
91C2×C4×D52C2211yescharacteristic
92C2×C4×D52C2212yes—
93C2×C4×D52C2212yes—
94C2×#88126C2212yes—
95C2×#88124C2212yes—
96C2×#88124C2211yescharacteristic
97C2×#88123C2212yes—
98C2×#88123C2211yescharacteristic
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2311yescharacteristic
103C22×Q8×C13C2312yes—
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C22×C22⋊D13C2314yes—
108C22×C22⋊D13C2312yes—
109C2×#6131—48no—
110C2×#6131C23116yes—
111C2×Q8×D13—48no—
112C2×Q8×D13C23116yes—
113C2×#6127—48no—
114C2×#6127C23116yes—
115C22×D52C2311yescharacteristic
116C22×D52C2312yes—
117C22×D52C2312yes—
118C22×D52C2312yes—
119C22×D52C2314yes—
120C22×D52C2314yes—
121C22×C4×D13C2312yes—
122C22×C4×D13C2314yes—
123C22×C4×D13C2314yes—
124C22×C4×D13C2314yes—
125C22×C4×D13C2314yes—
126C22×Dic26C2311yescharacteristic
127C22×Dic26C2312yes—
128C22×Dic26C2314yes—
129C13×C4⋊Q8C2318yes—
130C13×C4⋊Q8C2318yes—
131C13×#125C23116yes—
132C13×C22⋊Q8C2318yes—
133C13×C22⋊Q8C2318yes—
134C13×C22⋊Q8C23116yes—
135C4×Q8×C13C2318yes—
136C4×Q8×C13C2318yes—
137C4×Q8×C13C23116yes—
138C13×#117C23116yes—
139C2×C13×C4⋊C4C2311yescharacteristic
140C2×C13×C4⋊C4C2312yes—
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C13×C4⋊C4C2311yescharacteristic
144C2×C13×C4⋊C4C2312yes—
145C2×C13×C4⋊C4C2312yes—
146C2×C13×C4⋊C4C2312yes—
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C22⋊C4C2312yes—
149C2×C13×C22⋊C4C2312yes—
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2312yes—
152C2×C42×C13C2312yes—
153C2×C42×C13C2311yescharacteristic
154C2×C42×C13C2311yescharacteristic
155C2×C42×C13C2311yescharacteristic
156C2×C42×C13C2318yes—
157C2×C22⋊Dic13C2312yes—
158#88201C23116yes—
159#88201C23132yes—
160#88200C23132yes—
161#88198C23116yes—
162#88184C23116yes—
163#88184C23116yes—
164#88184C2318yes—
165#88183C23116yes—
166C4×C22⋊D13C23116yes—
167C2×#6103C2312yes—
168C2×#6103C2312yes—
169C2×#6103C2314yes—
170C2×#6103C2314yes—
171C2×#6103C2312yes—
172C2×#6103C2314yes—
173C2×#6103C2314yes—
174C2×#6103C2314yes—
175C2×#6103C2312yes—
176C2×#6103C2314yes—
177C2×#6103C2314yes—
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2311yescharacteristic
180C2×C4⋊Dic13C2311yescharacteristic
181C2×C4⋊Dic13C2312yes—
182C2×C4⋊Dic13C2314yes—
183#88178C2318yes—
184C2×#6101C2312yes—
185C2×#6101C2314yes—
186C2×#6101C2312yes—
187C2×#6101C2312yes—
188C2×#6101C2314yes—
189C2×#6101C2314yes—
190C2×#6101C2312yes—
191C2×C4×Dic13C2312yes—
192C2×C4×Dic13C2314yes—
193#88152C23132yes—
194#88151C23116yes—
195#88151C23132yes—
196#88150C23132yes—
197#88150C23132yes—
198#88150C23132yes—
199#88149C23116yes—
200#88149C23132yes—
201#88148C23132yes—
202#88148C23132yes—
203#88148C23132yes—
204#88148C23132yes—
205#88148C23132yes—
206#88147C23116yes—
207#88147C23132yes—
208C4⋊C4×D13C23132yes—
209#88143C23132yes—
210#88141C23116yes—
211#88139C23132yes—
212#88138C23132yes—
213#88138C23132yes—
214#88137C23132yes—
215#88130C23116yes—
216#88129C23116yes—
217#88129C2318yes—
218#88129C23116yes—
219#88128C2318yes—
220#88128C23116yes—
221C4×D52C23116yes—
222C4×D52C23116yes—
223C4×D52C2318yes—
224C4×D52C23116yes—
225C4×D52C23116yes—
226C4×D52C23116yes—
227#88126C23116yes—
228#88124C2318yes—
229#88124C23116yes—
230#88123C2318yes—
231#88123C23116yes—
232C4×Dic26C2318yes—
233C4×Dic26C23116yes—
234C2×#3554—131nomaximal, Sylow
235C24×C13C2411yescharacteristic
236C23×D13C2412yes—
237C23×D13C2414yes—
238C2×Q8×C13—24no—
239C2×Q8×C13—24no—
240C2×Q8×C13—44no—
241C2×Q8×C13C2414yes—
242C2×Q8×C13C2414yes—
243C2×Q8×C13C2418yes—
244C22×C4×C13—24no—
245C22×C4×C13—24no—
246C22×C4×C13—42no—
247C22×C4×C13C2412yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2411yescharacteristic
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2414yes—
254C22×C4×C13C2412yes—
255C22×C4×C13C2412yes—
256C22×C4×C13C2414yes—
257C22×C4×C13C2414yes—
258C22×C4×C13C2411yescharacteristic
259C22×C4×C13C2411yescharacteristic
260C2×C22⋊D13—48no—
261C2×C22⋊D13—44no—
262C2×C22⋊D13C24116yes—
263C2×C22⋊D13C2418yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2414yes—
267C22×Dic13C2412yes—
268#6131—432no—
269Q8×D13—432no—
270#6127—432no—
271C2×D52—28no—
272C2×D52—24no—
273C2×D52—28no—
274C2×D52—44no—
275C2×D52—48no—
276C2×D52—48no—
277C2×D52C2418yes—
278C2×D52C2414yes—
279C2×D52C2418yes—
280C2×D52C2418yes—
281C2×D52C24116yes—
282C2×D52C24116yes—
283C2×C4×D13—28no—
284C2×C4×D13—48no—
285C2×C4×D13—48no—
286C2×C4×D13—48no—
287C2×C4×D13—48no—
288C2×C4×D13C2418yes—
289C2×C4×D13C24116yes—
290C2×C4×D13C24116yes—
291C2×C4×D13C24116yes—
292C2×C4×D13C24116yes—
293C2×Dic26—28no—
294C2×Dic26—24no—
295C2×Dic26—48no—
296C2×Dic26C2414yes—
297C2×Dic26C2418yes—
298C2×Dic26C24116yes—
299C13×C4⋊C4C2414yes—
300C13×C4⋊C4C2418yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C2418yes—
303C13×C4⋊C4C2414yes—
304C13×C4⋊C4C2418yes—
305C13×C4⋊C4C2418yes—
306C13×C4⋊C4C2418yes—
307C13×C4⋊C4C2418yes—
308C13×C22⋊C4C2418yes—
309C13×C22⋊C4C2418yes—
310C42×C13C2414yes—
311C42×C13C2418yes—
312C42×C13C2418yes—
313C42×C13C2414yes—
314C42×C13C2414yes—
315C42×C13C2414yes—
316C22⋊Dic13C2418yes—
317#6103C2418yes—
318#6103C2418yes—
319#6103C24116yes—
320#6103C24116yes—
321#6103C2418yes—
322#6103C24116yes—
323#6103C24116yes—
324#6103C24116yes—
325#6103C2418yes—
326#6103C24116yes—
327#6103C24116yes—
328C4⋊Dic13C2418yes—
329C4⋊Dic13C2414yes—
330C4⋊Dic13C2414yes—
331C4⋊Dic13C2418yes—
332C4⋊Dic13C24116yes—
333#6101C2418yes—
334#6101C24116yes—
335#6101C2418yes—
336#6101C2418yes—
337#6101C24116yes—
338#6101C24116yes—
339#6101C2418yes—
340C4×Dic13C2418yes—
341C4×Dic13C24116yes—
342#3554—1332no—
343C2×#562—134no—
344C2×#559—132no—
345C2×#559—131no—
346C2×#557—131no—
347C2×#554—132no—
348C2×#550—131no—
349C2×D4×Q8—131no—
350C2×#548—132no—
351C2×#547—132no—
352C2×#542—132no—
353C2×#542—132no—
354C2×#540—132no—
355C2×#539—134no—
356C2×#536—132no—
357C2×#533D1311yescharacteristic, complemented
358C2×#532—131no—
359C2×#529—131no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13C2512yes—
364C23×C13C2511yescharacteristic
365C22×D13—24no—
366C22×D13—28no—
367C22×D13—24no—
368C22×D13—28no—
369C22×D13—28no—
370C22×D13—24no—
371C22×D13C2514yes—
372C22×D13C2518yes—
373Q8×C13—28no—
374Q8×C13—28no—
375Q8×C13—48no—
376C2×C4×C13—24no—
377C2×C4×C13—22no—
378C2×C4×C13—24no—
379C2×C4×C13—22no—
380C2×C4×C13—24no—
381C2×C4×C13—22no—
382C2×C4×C13—24no—
383C2×C4×C13—22no—
384C2×C4×C13—28no—
385C2×C4×C13—28no—
386C2×C4×C13—44no—
387C2×C4×C13H(5,𝔽2)14yes—
388C2×C4×C132−1+414yes—
389C2×C4×C13C2514yes—
390C2×C4×C13C2514yes—
391C2×C4×C13C2512yes—
392C2×C4×C13C2512yes—
393C2×C4×C13C2512yes—
394C2×C4×C13C2512yes—
395C2×C4×C13C2514yes—
396C2×C4×C13C2514yes—
397C2×C4×C13C2512yes—
398C2×C4×C13C2512yes—
399C22⋊D13—416no—
400C22⋊D13—48no—
401C2×Dic13—28no—
402C2×Dic13—24no—
403C2×Dic13—24no—
404C2×Dic13—24no—
405C2×Dic13C2514yes—
406C2×Dic13C2514yes—
407C2×Dic13C2518yes—
408C2×Dic13C2514yes—
409D52—216no—
410D52—216no—
411D52—28no—
412D52—48no—
413D52—416no—
414D52—416no—
415C4×D13—216no—
416C4×D13—416no—
417C4×D13—416no—
418C4×D13—416no—
419C4×D13—416no—
420Dic26—216no—
421Dic26—28no—
422Dic26—416no—
423C22×#41—132no—
424C22×#41—132no—
425C23×Q8—132no—
426#562—1364no—
427#559—1332no—
428#559—1316no—
429#557—1316no—
430#554—1332no—
431#550—1316no—
432D4×Q8—1316no—
433#548—1332no—
434#547—1332no—
435#542—1332no—
436#542—1332no—
437#540—1332no—
438#539—1364no—
439#536—1332no—
440#533C2×D13116yescomplemented
441#532—1316no—
442C2×C4⋊Q8—132no—
443C2×C4⋊Q8—131no—
444C2×C4⋊Q8—132no—
445C2×C4⋊Q8C2×D1311yescharacteristic
446C2×C4⋊Q8C2×D1311yescharacteristic
447C2×#127—131no—
448C2×#127—132no—
449#529—1316no—
450C2×#126—134no—
451C2×#126—132no—
452C2×#125—134no—
453C2×#125—131no—
454C2×#125—132no—
455C2×#125C2×D1312yes—
456C2×#124—132no—
457C2×#124—134no—
458C2×#124—134no—
459C2×#124—131no—
460C2×#124—132no—
461C2×#124—132no—
462C2×#123—132no—
463C2×#123—134no—
464C2×#123—134no—
465C2×#123—134no—
466C2×#123—134no—
467C2×#123—134no—
468C2×#123—134no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—131no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8—134no—
473C2×C22⋊Q8—134no—
474C2×C22⋊Q8—134no—
475C2×C22⋊Q8—132no—
476C2×C22⋊Q8C2×D1311yescharacteristic
477C2×C22⋊Q8C2×D1311yescharacteristic
478C2×C22⋊Q8C2×D1312yes—
479C2×#121—131no—
480C2×#121—132no—
481C2×#121—132no—
482C2×#121—134no—
483C2×#121—132no—
484C2×#121—134no—
485C2×#121—134no—
486C2×C4×Q8—132no—
487C2×C4×Q8—131no—
488C2×C4×Q8—132no—
489C2×C4×Q8C2×D1311yescharacteristic
490C2×C4×Q8C2×D1311yescharacteristic
491C2×C4×Q8C2×D1312yes—
492C2×C4×D4—132no—
493C2×C4×D4—134no—
494C2×C4×D4—132no—
495C2×C4×D4—131no—
496C2×C4×D4—132no—
497C2×C4×D4—132no—
498C2×C4×D4—132no—
499C2×C4×D4—132no—
500C2×C4×D4—132no—
501C2×#117—132no—
502C2×#117C2×D1312yes—
503C22×C4⋊C4—134no—
504C22×C42C2×D1311yescharacteristic
505C22×C13—22no—
506C22×C13—22no—
507C22×C13—22no—
508C22×C13—44no—
509C22×C13C2×H(5,𝔽2)12yes—
510C22×C13C2×2−1+412yes—
511C22×C13#58512yes—
512C22×C13C2611yescharacteristic
513C2×D13—24no—
514C2×D13—28no—
515C2×D13—24no—
516C2×D13—28no—
517C2×D13—28no—
518C2×D13—24no—
519C2×D13—48no—
520C2×D13—416no—
521C4×C13—24no—
522C4×C13—22no—
523C4×C13—24no—
524C4×C13—22no—
525C4×C13—24no—
526C4×C13—22no—
527C4×C13—24no—
528C4×C13—22no—
529C4×C13C2×H(5,𝔽2)14yes—
530C4×C13C2×2−1+414yes—
531Dic13—28no—
532Dic13—24no—
533Dic13—24no—
534Dic13—24no—
535C2×#41—1316no—
536C2×#41—1316no—
537C2×#41—528no—
538C2×#41—528no—
539C22×Q8—1316no—
540C22×Q8—131no—
541C22×Q8—132no—
542C22×Q8—134no—
543C22×Q8—528no—
544C22×Q8C22×D1311yescharacteristic
545C22×Q8C22×D1311yescharacteristic
546C22×Q8C22×D1312yes—
547C22×D4—132no—
548C22×D4—134no—
549C22×D4—131no—
550C22×D4—132no—
551C22×D4—132no—
552C22×D4—132no—
553C22×D4—134no—
554C22×D4—134no—
555C23×C4—132no—
556C23×C4—134no—
557C23×C4—134no—
558C23×C4—134no—
559C23×C4—134no—
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C4⋊Q8—1316no—
564C4⋊Q8—138no—
565C4⋊Q8—1316no—
566C4⋊Q8C22×D1318yes—
567C4⋊Q8C22×D1318yes—
568#127—138no—
569#127—1316no—
570#126—1332no—
571#126—1316no—
572#125—1332no—
573#125—138no—
574#125—1316no—
575#125C22×D13116yes—
576#124—1316no—
577#124—1332no—
578#124—1332no—
579#124—138no—
580#124—1316no—
581#124—1316no—
582#123—1316no—
583#123—1332no—
584#123—1332no—
585#123—1332no—
586#123—1332no—
587#123—1332no—
588#123—1332no—
589C22⋊Q8—1332no—
590C22⋊Q8—138no—
591C22⋊Q8—1332no—
592C22⋊Q8—1332no—
593C22⋊Q8—1332no—
594C22⋊Q8—1332no—
595C22⋊Q8—1316no—
596C22⋊Q8C22×D1318yes—
597C22⋊Q8C22×D1318yes—
598C22⋊Q8C22×D13116yes—
599#121—138no—
600#121—1316no—
601#121—1316no—
602#121—1332no—
603#121—1316no—
604#121—1332no—
605#121—1332no—
606C4×Q8—1316no—
607C4×Q8—138no—
608C4×Q8—1316no—
609C4×Q8C22×D1318yes—
610C4×Q8C22×D1318yes—
611C4×Q8C22×D13116yes—
612C4×D4—1316no—
613C4×D4—1332no—
614C4×D4—1316no—
615C4×D4—138no—
616C4×D4—1316no—
617C4×D4—1316no—
618C4×D4—1316no—
619C4×D4—1316no—
620C4×D4—1316no—
621#117—1316no—
622#117C22×D13116yes—
623C2×C4⋊C4—132no—
624C2×C4⋊C4—134no—
625C2×C4⋊C4—134no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—131no—
629C2×C4⋊C4—131no—
630C2×C4⋊C4—132no—
631C2×C4⋊C4—132no—
632C2×C4⋊C4—134no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4—132no—
635C2×C4⋊C4—1332no—
636C2×C4⋊C4C22×D1312yes—
637C2×C4⋊C4C22×D1312yes—
638C2×C4⋊C4C22×D1312yes—
639C2×C4⋊C4C22×D1312yes—
640C2×C4⋊C4C22×D1311yescharacteristic
641C2×C4⋊C4C22×D1311yescharacteristic
642C2×C4⋊C4C22×D1312yes—
643C2×C4⋊C4C22×D1312yes—
644C2×C4⋊C4C22×D1312yes—
645C2×C22⋊C4—132no—
646C2×C22⋊C4—132no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4—132no—
649C2×C22⋊C4—132no—
650C2×C22⋊C4—134no—
651C2×C22⋊C4—134no—
652C2×C22⋊C4—134no—
653C2×C22⋊C4—134no—
654C2×C22⋊C4—134no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—134no—
657C2×C22⋊C4C22×D1312yes—
658C2×C22⋊C4C22×D1312yes—
659C2×C42—132no—
660C2×C42—134no—
661C2×C42C22×D1311yescharacteristic
662C2×C42C22×D1312yes—
663C2×C42C22×D1312yes—
664C2×C42C22×D1311yescharacteristic
665C2×C42C22×D1311yescharacteristic
666C2×C42C22×D1311yescharacteristic
667C2×C42C22×D1318yes—
668C2×C13—42no—
669C2×C13#355414yescomplemented
670C2×C13C22×H(5,𝔽2)11yescharacteristic
671C2×C13C22×2−1+411yescharacteristic
672C2×C13C2×#58511yescharacteristic
673D13—44no—
674D13—48no—
675C24—132no—
676C24—134no—
677C24C23×D1311yescharacteristic
678#41—5232no—
679#41—5232no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—44no—
683C2×Q8—134no—
684C2×Q8—138no—
685C2×Q8—1316no—
686C2×Q8—264no—
687C2×Q8—268no—
688C2×Q8—528no—
689C2×Q8—5232no—
690C2×Q8C23×D1314yes—
691C2×Q8C23×D1314yes—
692C2×Q8C23×D1318yes—
693C2×D4—138no—
694C2×D4—1316no—
695C2×D4—134no—
696C2×D4—138no—
697C2×D4—138no—
698C2×D4—138no—
699C2×D4—1316no—
700C2×D4—1316no—
701C2×D4—264no—
702C2×D4—268no—
703C2×D4—268no—
704C2×D4—528no—
705C2×D4—524no—
706C2×D4—528no—
707C2×D4—528no—
708C2×D4—524no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—42no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—134no—
715C22×C4—132no—
716C22×C4—138no—
717C22×C4—1316no—
718C22×C4—1316no—
719C22×C4—1316no—
720C22×C4—1316no—
721C22×C4—268no—
722C22×C4—528no—
723C22×C4—528no—
724C22×C4—528no—
725C22×C4—528no—
726C22×C4C23×D1314yes—
727C22×C4C23×D1314yes—
728C22×C4C23×D1312yes—
729C22×C4C23×D1311yescharacteristic
730C22×C4C23×D1311yescharacteristic
731C22×C4C23×D1311yescharacteristic
732C22×C4C23×D1311yescharacteristic
733C22×C4C23×D1312yes—
734C22×C4C23×D1312yes—
735C22×C4C23×D1312yes—
736C22×C4C23×D1314yes—
737C22×C4C23×D1311yescharacteristic
738C22×C4C23×D1311yescharacteristic
739C4⋊C4—138no—
740C4⋊C4—1316no—
741C4⋊C4—1316no—
742C4⋊C4—138no—
743C4⋊C4—138no—
744C4⋊C4—134no—
745C4⋊C4—134no—
746C4⋊C4—138no—
747C4⋊C4—138no—
748C4⋊C4—1316no—
749C4⋊C4—1316no—
750C4⋊C4—138no—
751C4⋊C4C23×D1318yes—
752C4⋊C4C23×D1318yes—
753C4⋊C4C23×D1318yes—
754C4⋊C4C23×D1318yes—
755C4⋊C4C23×D1314yes—
756C4⋊C4C23×D1314yes—
757C4⋊C4C23×D1318yes—
758C4⋊C4C23×D1318yes—
759C4⋊C4C23×D1318yes—
760C22⋊C4—138no—
761C22⋊C4—138no—
762C22⋊C4—138no—
763C22⋊C4—138no—
764C22⋊C4—138no—
765C22⋊C4—1316no—
766C22⋊C4—1316no—
767C22⋊C4—1316no—
768C22⋊C4—1316no—
769C22⋊C4—1316no—
770C22⋊C4—1316no—
771C22⋊C4—1316no—
772C22⋊C4C23×D1318yes—
773C22⋊C4C23×D1318yes—
774C42—138no—
775C42—1316no—
776C42C23×D1314yes—
777C42C23×D1314yes—
778C42C23×D1314yes—
779C42C23×D1314yes—
780C42C23×D1318yes—
781C42C23×D1318yes—
782C13C2×#355411yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—134no—
787C23—138no—
788C23—264no—
789C23—268no—
790C23—264no—
791C23—268no—
792C23—268no—
793C23—264no—
794C23C24×D1312yes—
795C23C24×D1311yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—268no—
800Q8—2616no—
801Q8—5216no—
802D4—268no—
803D4—2616no—
804D4—2616no—
805D4—528no—
806D4—5216no—
807D4—5216no—
808D4—528no—
809D4—5216no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—134no—
822C2×C4—134no—
823C2×C4—138no—
824C2×C4—134no—
825C2×C4—264no—
826C2×C4—264no—
827C2×C4—268no—
828C2×C4—264no—
829C2×C4—2616no—
830C2×C4—5216no—
831C2×C4—5216no—
832C2×C4—5216no—
833C2×C4—5216no—
834C2×C4#8825414yes—
835C2×C4#8825614yes—
836C2×C4C24×D1314yes—
837C2×C4C24×D1312yes—
838C2×C4C24×D1312yes—
839C2×C4C24×D1312yes—
840C2×C4C24×D1312yes—
841C2×C4C24×D1314yes—
842C2×C4C24×D1314yes—
843C2×C4C24×D1314yes—
844C2×C4C24×D1312yes—
845C2×C4C24×D1312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—264no—
851C22—268no—
852C22—264no—
853C22—268no—
854C22—268no—
855C22—264no—
856C22—528no—
857C22—5216no—
858C22C2×#8825412yes—
859C22C2×#8825612yes—
860C22#1171964812yes—
861C22C25×D1311yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—264no—
871C4—268no—
872C4—264no—
873C4—264no—
874C4C2×#8825414yes—
875C4C2×#8825614yes—
876C2—42no—
877C2—524no—
878C2—528no—
879C2#1312930714yesdirect product factor
880C2C22×#8825611yescharacteristic
881C2C22×#8825411yescharacteristic
882C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#533C2
socleC23×C13C25
hypercenterC2×#533D13
hypocenterC13C2×#3554
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13129307C2direct (N × H)
2. C2×#11719352C2semidirect
3. C2×#11719290C2semidirect
4. C2×#11719290C2semidirect
5. C2×#11719272C2semidirect
6. C2×#11719284C2semidirect
7. C2×#11719282C2semidirect
8. C2×Q8×D52C2semidirect
9. C2×#11719338C2semidirect
10. C2×#11719336C2semidirect
11. C2×#11719438C2semidirect
12. C2×#11719239C2semidirect
13. C2×#11719240C2semidirect
14. C2×#11719397C2semidirect
15. C2×#11719429C2semidirect
16. C2×#11719182C2semidirect
17. C2×#11719184C2semidirect
18. C2×C13×#533C2semidirect
22. C13×#533C22semidirect
44. #11719438C22semidirect
45. #11719429C22semidirect
46. #11719397C22semidirect
47. #11719352C22semidirect
48. #11719338C22semidirect
49. #11719336C22semidirect
50. #11719290C22semidirect
51. #11719290C22semidirect
52. #11719284C22semidirect
53. #11719282C22semidirect
54. Q8×D52C22semidirect
55. #11719272C22semidirect
56. #11719240C22semidirect
57. #11719239C22semidirect
80. #11719184C22semidirect
82. #11719182C22semidirect
357. C2×#533D13semidirect
440. #533C2×D13semidirect
669. C2×C13#3554semidirect
782. C13C2×#3554semidirect
879. C2#13129307direct (N × H)

Maximal subgroups

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

subgroupindex
#131293072
C2×#117193522
C2×#117192902
C2×#117192722
C2×#117192842
C2×#117192822
C2×Q8×D522
C2×#117193382
C2×#117193362
C2×#117194382
C2×#117192392
C2×#117192402
C2×#117193972
C2×#117194292
C2×#117191822
C2×#117191842
C2×C13×#5332
C2×#355413