Finite Group Databasebeta

← C2×#13128263 #16769745

Subgroups — C2×#13128263 #16769745

Order 3328.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128263C2132yesmaximal, direct product factor
2C2×#11719224C211yesmaximal, characteristic, complemented
3C2×#11719239C212yesmaximal, complemented
4C2×#11719266C212yesmaximal, complemented
5C2×#11719223C212yesmaximal, complemented
6C2×#11719288C212yesmaximal, complemented
7C2×#11719269C214yesmaximal, complemented
8C2×#11719538C211yesmaximal, characteristic
9C2×#11719231C211yesmaximal, characteristic, complemented
10C2×#11719530C211yesmaximal, characteristic, complemented
11C2×#11719175C212yesmaximal, complemented
12C2×#11719283C212yesmaximal, complemented
13C2×#11719184C212yesmaximal, complemented
14C2×#11719262C212yesmaximal, complemented
15C2×#11719243C214yesmaximal, complemented
16C2×C4×#6127C211yesmaximal, characteristic, complemented
17C22×C4×Dic26C211yesmaximal, characteristic, complemented
18C2×C4×C13×#41C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C22×#6127C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C4×C13×#41C22116yescomplemented
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2212yes—
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2212yes—
29C2×C13×#117C2212yes—
30C2×C13×#117C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2212yes—
33#11719538C22116yes—
34#11719530C22116yescomplemented
35C2×#88200C2212yes—
36C2×#88198C2212yes—
37C2×#88193C2214yes—
38C2×#88192C2212yes—
39C2×#88190C2212yes—
40C2×#88189C2214yes—
41C2×#88184C2212yes—
42C2×#88183C2214yes—
43C2×C4×C22⋊D13C2212yes—
44C2×C4×C22⋊D13C2212yes—
45C2×C4×C22⋊D13C2214yes—
46C2×#88180C2211yescharacteristic
47C2×#88180C2214yes—
48C22×C4⋊Dic13C2211yescharacteristic
49C2×#88178C2212yes—
50C2×#88178C2212yes—
51C2×#88178C2214yes—
52C2×#88178C2212yes—
53C22×#6101C2212yes—
54C22×C4×Dic13C2212yes—
55#11719288C22132yescomplemented
56#11719283C22132yescomplemented
57#11719269C22164yescomplemented
58#11719266C22132yescomplemented
59#11719262C22132yescomplemented
60#11719243C22164yescomplemented
61#11719239C22132yescomplemented
62#11719231C22116yescomplemented
63#11719224C22116yescomplemented
64#11719223C22132yescomplemented
65C2×#88152C2214yes—
66C2×#88151C2212yes—
67C2×#88151C2212yes—
68C2×#88150C2214yes—
69C2×#88144C2212yes—
70C2×#88143C2214yes—
71C2×#88143C2214yes—
72C2×#88142C2212yes—
73C2×#88140C2214yes—
74C2×#88139C2214yes—
75C2×#88137C2214yes—
76C2×#88133C2214yes—
77C2×#88133C2214yes—
78C2×#88132C2214yes—
79#11719184C22132yescomplemented
80C2×#88130C2214yes—
81C2×#88129C2212yes—
82C4×#6127C22116yescomplemented
83C2×C4×D52C2211yescharacteristic
84C2×C4×D52C2211yescharacteristic
85C2×#88126C2212yes—
86C2×#88126C2214yes—
87C2×C42×D13C2212yes—
88#11719175C22132yescomplemented
89C2×#88124C2214yes—
90C2×#88124C2212yes—
91C2×#88123C2212yes—
92C2×#88123C2212yes—
93C2×C4×Dic26C2212yes—
94C2×C4×Dic26C2211yescharacteristic
95C2×C4×Dic26C2212yes—
96C2×C4×Dic26C2212yes—
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2211yescharacteristic
99C2×C4×Dic26C2214yes—
100C2×C4×Dic26C22116yescomplemented
101C2×C13×#41—28no—
102C2×C13×#41C2318yes—
103C22×Q8×C13C2311yescharacteristic
104C22×D4×C13C2312yes—
105C22×D4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2312yes—
108C23×C4×C13C2312yes—
109C23×C4×C13C2311yescharacteristic
110C23×C4×C13C2312yes—
111C23×C4×C13C2311yescharacteristic
112C22×C22⋊D13C2312yes—
113C22×C22⋊D13C2314yes—
114C23×Dic13C2312yes—
115C23×Dic13C2312yes—
116C2×#6127—28no—
117C2×#6127C2318yes—
118C22×D52C2311yescharacteristic
119C22×C4×D13C2312yes—
120C22×C4×D13C2312yes—
121C22×C4×D13C2312yes—
122C22×Dic26—28no—
123C22×Dic26C2311yescharacteristic
124C22×Dic26C2312yes—
125C22×Dic26C2312yes—
126C22×Dic26C2318yes—
127C22×Dic26C2314yes—
128C4×Q8×C13C2318yes—
129C4×Q8×C13C2318yes—
130C4×D4×C13C23116yes—
131C4×D4×C13C2318yes—
132C4×D4×C13C2318yes—
133C4×D4×C13C23116yes—
134C13×#117C23116yes—
135C13×#117C2318yes—
136C2×C13×C4⋊C4C2311yescharacteristic
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2312yes—
139C2×C13×C4⋊C4C2311yescharacteristic
140C2×C13×C22⋊C4C2312yes—
141C2×C13×C22⋊C4C2312yes—
142C2×C13×C22⋊C4C2312yes—
143C2×C42×C13C2311yescharacteristic
144C2×C42×C13C2311yescharacteristic
145C2×C42×C13C2311yescharacteristic
146C2×C42×C13C2311yescharacteristic
147C2×C42×C13C2312yes—
148C2×C42×C13C2318yes—
149C2×C42×C13C2312yes—
150C2×C42×C13C2312yes—
151C2×C42×C13C23116yes—
152C2×C22⋊Dic13C2312yes—
153C2×C22⋊Dic13C2314yes—
154C2×C22⋊Dic13C2314yes—
155C2×C22⋊Dic13C2314yes—
156#88200C23116yes—
157#88198C23116yes—
158#88193C23132yes—
159#88192C23116yes—
160#88190C23116yes—
161#88189C23132yes—
162#88184C23116yes—
163#88183C23132yes—
164C4×C22⋊D13C23116yes—
165C4×C22⋊D13C23116yes—
166C4×C22⋊D13C23132yes—
167C2×#6103C2312yes—
168C2×#6103C2312yes—
169C2×#6103C2314yes—
170C2×#6103C2314yes—
171C2×#6103C2314yes—
172#88180C23132yes—
173#88180C2318yes—
174C2×C4⋊Dic13C2312yes—
175C2×C4⋊Dic13C2312yes—
176C2×C4⋊Dic13C2311yescharacteristic
177C2×C4⋊Dic13C2314yes—
178C2×C4⋊Dic13C2311yescharacteristic
179C2×C4⋊Dic13C2318yes—
180C2×C4⋊Dic13C2314yes—
181C2×C4⋊Dic13C2314yes—
182#88178C23116yes—
183#88178C23116yes—
184#88178C23132yes—
185#88178C23116yes—
186C2×#6101C2314yes—
187C2×#6101C2314yes—
188C2×#6101C2312yes—
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2312yes—
192C2×#6101C23116yes—
193C2×#6101C2314yes—
194C2×#6101C2314yes—
195C2×#6101C2314yes—
196C2×C4×Dic13C2312yes—
197C2×C4×Dic13C2314yes—
198C2×C4×Dic13C2314yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C23116yes—
201C2×C4×Dic13C2312yes—
202#88152C23132yes—
203#88151C23116yes—
204#88151C23116yes—
205#88150C23132yes—
206#88144C23116yes—
207#88143C23132yes—
208#88143C23132yes—
209#88142C23116yes—
210#88140C23132yes—
211#88139C23132yes—
212#88137C23132yes—
213#88133C23132yes—
214#88133C23132yes—
215#88132C23132yes—
216#88130C23132yes—
217#88129C23116yes—
218C4×D52C2318yes—
219C4×D52C2318yes—
220#88126C23116yes—
221#88126C23132yes—
222C42×D13C23116yes—
223#88124C23132yes—
224#88124C23116yes—
225#88123C23116yes—
226#88123C23116yes—
227C4×Dic26C23116yes—
228C4×Dic26C23116yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C4×Dic26C2318yes—
232C4×Dic26C23132yes—
233C4×Dic26C2318yes—
234C2×#3461—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2411yescharacteristic
237C23×D13C2412yes—
238C13×#41—232no—
239C2×Q8×C13—24no—
240C2×Q8×C13C2414yes—
241C2×D4×C13—28no—
242C2×D4×C13—24no—
243C2×D4×C13C2418yes—
244C2×D4×C13C2414yes—
245C22×C4×C13—28no—
246C22×C4×C13—24no—
247C22×C4×C13—28no—
248C22×C4×C13—44no—
249C22×C4×C13—42no—
250C22×C4×C13#4118yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2414yes—
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2411yescharacteristic
255C22×C4×C13C2412yes—
256C22×C4×C13C2412yes—
257C22×C4×C13C2412yes—
258C22×C4×C13C2418yes—
259C22×C4×C13C2418yes—
260C22×C4×C13C2414yes—
261C22×C4×C13C2418yes—
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2411yescharacteristic
264C22×C4×C13C2414yes—
265C22×C4×C13C2411yescharacteristic
266C2×C22⋊D13—28no—
267C2×C22⋊D13—48no—
268C2×C22⋊D13C2418yes—
269C2×C22⋊D13C24116yes—
270C22×Dic13—28no—
271C22×Dic13—44no—
272C22×Dic13C2418yes—
273C22×Dic13C2412yes—
274C22×Dic13C2414yes—
275C22×Dic13C2412yes—
276C22×Dic13C2414yes—
277C22×Dic13C2412yes—
278C22×Dic13C2418yes—
279#6127—232no—
280C2×D52—24no—
281C2×D52C2414yes—
282C2×C4×D13—28no—
283C2×C4×D13—28no—
284C2×C4×D13—44no—
285C2×C4×D13C2418yes—
286C2×C4×D13C2418yes—
287C2×C4×D13C2418yes—
288C2×Dic26—28no—
289C2×Dic26—28no—
290C2×Dic26—232no—
291C2×Dic26—24no—
292C2×Dic26—48no—
293C2×Dic26C2414yes—
294C2×Dic26C2418yes—
295C2×Dic26C2418yes—
296C2×Dic26C24116yes—
297C13×C4⋊C4C2414yes—
298C13×C4⋊C4C2418yes—
299C13×C4⋊C4C2418yes—
300C13×C4⋊C4C2414yes—
301C13×C22⋊C4C2418yes—
302C13×C22⋊C4C2418yes—
303C13×C22⋊C4C2418yes—
304C42×C13C2414yes—
305C42×C13C2414yes—
306C42×C13C2414yes—
307C42×C13C2414yes—
308C42×C13C2418yes—
309C42×C13C2418yes—
310C42×C13C2418yes—
311C22⋊Dic13C2418yes—
312C22⋊Dic13C24116yes—
313C22⋊Dic13C24116yes—
314C22⋊Dic13C24116yes—
315#6103C2418yes—
316#6103C2418yes—
317#6103C24116yes—
318#6103C24116yes—
319#6103C24116yes—
320C4⋊Dic13C2418yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C2414yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C2414yes—
325C4⋊Dic13C24116yes—
326C4⋊Dic13C24116yes—
327#6101C24116yes—
328#6101C24116yes—
329#6101C2418yes—
330#6101C24116yes—
331#6101C24116yes—
332#6101C2418yes—
333#6101C24116yes—
334#6101C24116yes—
335#6101C24116yes—
336C4×Dic13C2418yes—
337C4×Dic13C24116yes—
338C4×Dic13C24116yes—
339C4×Dic13C2418yes—
340C4×Dic13C2418yes—
341#3461—1332no—
342C2×#544—131no—
343C2×#542—132no—
344C2×#542—132no—
345C2×#541—132no—
346C2×#541—132no—
347C2×#539—134no—
348C2×#537—131no—
349C2×#536—131no—
350C2×#536—131no—
351C2×#533—132no—
352C2×#533—132no—
353C2×#529—132no—
354C2×#529—134no—
355C2×#529—132no—
356C2×C4×#41—131no—
357C2×C4×#41D1311yescharacteristic, complemented
358C22×C4×Q8—131no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—24no—
362C23×C13—24no—
363C23×C13—24no—
364C23×C13C2×#4114yes—
365C23×C13C2514yes—
366C23×C13C2512yes—
367C23×C13C2511yescharacteristic
368C22×D13—24no—
369C22×D13—24no—
370C22×D13—24no—
371C22×D13C2514yes—
372Q8×C13—28no—
373D4×C13—216no—
374D4×C13—28no—
375C2×C4×C13—24no—
376C2×C4×C13—22no—
377C2×C4×C13—24no—
378C2×C4×C13—24no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—216no—
382C2×C4×C13—28no—
383C2×C4×C13—216no—
384C2×C4×C13—48no—
385C2×C4×C13—44no—
386C2×C4×C13C2×#4114yes—
387C2×C4×C13C2×#4114yes—
388C2×C4×C13C2×#41116yes—
389C2×C4×C132−1+414yes—
390C2×C4×C13C2512yes—
391C2×C4×C13C2512yes—
392C2×C4×C13C2512yes—
393C2×C4×C13C2514yes—
394C2×C4×C13C2514yes—
395C2×C4×C13C2514yes—
396C2×C4×C13C2512yes—
397C2×C4×C13C2512yes—
398C2×C4×C13C2512yes—
399C22⋊D13—216no—
400C22⋊D13—416no—
401C2×Dic13—216no—
402C2×Dic13—28no—
403C2×Dic13—24no—
404C2×Dic13—24no—
405C2×Dic13—24no—
406C2×Dic13—28no—
407C2×Dic13—48no—
408C2×Dic13C2514yes—
409C2×Dic13C2518yes—
410C2×Dic13C2514yes—
411C2×Dic13C2518yes—
412C2×Dic13C2514yes—
413D52—28no—
414C4×D13—216no—
415C4×D13—216no—
416C4×D13—48no—
417Dic26—216no—
418Dic26—216no—
419Dic26—28no—
420Dic26—416no—
421C22×#41—131no—
422C22×#41C2×D1311yescharacteristic
423C23×Q8—131no—
424#544—1316no—
425#542—1332no—
426#542—1332no—
427#541—1332no—
428#541—1332no—
429#539—1364no—
430#537—1316no—
431#536—1316no—
432#536—1316no—
433#533—1332no—
434#533—1332no—
435C2×C4⋊Q8—132no—
436C2×C4⋊Q8—132no—
437C2×C4⋊Q8—132no—
438C2×C4⋊Q8—132no—
439#529—1364no—
440#529—1332no—
441#529—1332no—
442C2×#126—134no—
443C2×#126—134no—
444C2×#126—134no—
445C2×#126—134no—
446C2×#125—134no—
447C2×#125—134no—
448C2×#125—132no—
449C2×#125—132no—
450C2×#125—134no—
451C2×#124—132no—
452C2×#124—134no—
453C2×#124—132no—
454C2×#123—134no—
455C2×#123—134no—
456C2×#123—134no—
457C2×#123—134no—
458C2×C22⋊Q8—132no—
459C2×C22⋊Q8—132no—
460C2×C22⋊Q8—132no—
461C2×C22⋊Q8—132no—
462C2×C22⋊Q8—134no—
463C2×C22⋊Q8—134no—
464C2×C22⋊Q8—132no—
465C2×C22⋊Q8—132no—
466C2×C22⋊Q8—134no—
467C2×#121—132no—
468C2×#121—134no—
469C2×#121—132no—
470C4×#41—1316no—
471C4×#41C2×D13116yescomplemented
472C2×C4×Q8—132no—
473C2×C4×Q8—132no—
474C2×C4×Q8—132no—
475C2×C4×Q8—132no—
476C2×C4×Q8—131no—
477C2×C4×Q8—131no—
478C2×C4×Q8—134no—
479C2×C4×Q8—1316no—
480C2×C4×Q8C2×D1311yescharacteristic
481C2×C4×Q8C2×D1311yescharacteristic
482C2×C4×D4—132no—
483C2×C4×D4—132no—
484C2×C4×D4—134no—
485C2×C4×D4—131no—
486C2×C4×D4—131no—
487C2×C4×D4C2×D1312yes—
488C2×C4×D4C2×D1311yescharacteristic
489C2×C4×D4C2×D1312yes—
490C2×C4×D4C2×D1311yescharacteristic
491C2×#117—131no—
492C2×#117—134no—
493C2×#117—132no—
494C2×#117—134no—
495C2×#117C2×D1311yescharacteristic
496C2×#117C2×D1312yes—
497C22×C4⋊C4—132no—
498C22×C4⋊C4—131no—
499C22×C42—132no—
500C22×C42—132no—
501C22×C42C2×D1311yescharacteristic
502C22×C42C2×D1312yes—
503C22×C13—22no—
504C22×C13—22no—
505C22×C13—28no—
506C22×C13—24no—
507C22×C13—24no—
508C22×C13—24no—
509C22×C13—48no—
510C22×C13C22×#4114yes—
511C22×C13C22×#4112yes—
512C22×C13C2×2−1+412yes—
513C22×C13#58512yes—
514C22×C13C2611yescharacteristic
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—48no—
519C4×C13—24no—
520C4×C13—22no—
521C4×C13—24no—
522C4×C13—24no—
523C4×C13—22no—
524C4×C13—22no—
525C4×C13C22×#4114yes—
526C4×C13C22×#4114yes—
527C4×C13C2×2−1+414yes—
528Dic13—28no—
529Dic13—24no—
530Dic13—24no—
531Dic13—24no—
532Dic13—28no—
533C2×#41—28no—
534C2×#41—138no—
535C2×#41—268no—
536C2×#41C22×D1318yes—
537C22×Q8—132no—
538C22×Q8—132no—
539C22×Q8—131no—
540C22×Q8—138no—
541C22×Q8—134no—
542C22×Q8—268no—
543C22×Q8C22×D1311yescharacteristic
544C22×D4—132no—
545C22×D4—134no—
546C22×D4—131no—
547C22×D4C22×D1312yes—
548C22×D4C22×D1311yescharacteristic
549C23×C4—132no—
550C23×C4—132no—
551C23×C4—132no—
552C23×C4—132no—
553C23×C4—132no—
554C23×C4C22×D1312yes—
555C23×C4C22×D1312yes—
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1312yes—
559C23×C4C22×D1311yescharacteristic
560C4⋊Q8—1316no—
561C4⋊Q8—1316no—
562C4⋊Q8—1316no—
563C4⋊Q8—1316no—
564#126—1332no—
565#126—1332no—
566#126—1332no—
567#126—1332no—
568#125—1332no—
569#125—1316no—
570#125—1332no—
571#125—1316no—
572#125—1332no—
573#124—1316no—
574#124—1332no—
575#124—1316no—
576#123—1332no—
577#123—1332no—
578#123—1332no—
579#123—1332no—
580C22⋊Q8—1316no—
581C22⋊Q8—1316no—
582C22⋊Q8—1316no—
583C22⋊Q8—1316no—
584C22⋊Q8—1332no—
585C22⋊Q8—1316no—
586C22⋊Q8—1316no—
587C22⋊Q8—1332no—
588C22⋊Q8—1332no—
589#121—1332no—
590#121—1316no—
591#121—1316no—
592C4×Q8—1316no—
593C4×Q8—1316no—
594C4×Q8—1316no—
595C4×Q8—1316no—
596C4×Q8—138no—
597C4×Q8—138no—
598C4×Q8—1332no—
599C4×Q8C22×D1318yes—
600C4×Q8C22×D1318yes—
601C4×D4—1316no—
602C4×D4—1316no—
603C4×D4—1332no—
604C4×D4—138no—
605C4×D4—138no—
606C4×D4C22×D1318yes—
607C4×D4C22×D13116yes—
608C4×D4C22×D13116yes—
609C4×D4C22×D1318yes—
610#117—138no—
611#117—1332no—
612#117—1316no—
613#117—1332no—
614#117C22×D1318yes—
615#117C22×D13116yes—
616C2×C4⋊C4—132no—
617C2×C4⋊C4—132no—
618C2×C4⋊C4—134no—
619C2×C4⋊C4—134no—
620C2×C4⋊C4—138no—
621C2×C4⋊C4—1316no—
622C2×C4⋊C4—132no—
623C2×C4⋊C4—131no—
624C2×C4⋊C4—131no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—134no—
627C2×C4⋊C4—134no—
628C2×C4⋊C4—134no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—134no—
632C2×C4⋊C4—134no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4C22×D1312yes—
635C2×C4⋊C4C22×D1311yescharacteristic
636C2×C4⋊C4C22×D1311yescharacteristic
637C2×C4⋊C4C22×D1312yes—
638C2×C22⋊C4—132no—
639C2×C22⋊C4—134no—
640C2×C22⋊C4—134no—
641C2×C22⋊C4—134no—
642C2×C22⋊C4—132no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4—134no—
645C2×C22⋊C4—134no—
646C2×C22⋊C4—134no—
647C2×C22⋊C4C22×D1312yes—
648C2×C22⋊C4C22×D1312yes—
649C2×C22⋊C4C22×D1312yes—
650C2×C42—132no—
651C2×C42—132no—
652C2×C42—134no—
653C2×C42—1316no—
654C2×C42—132no—
655C2×C42—134no—
656C2×C42—1316no—
657C2×C42C22×D1311yescharacteristic
658C2×C42C22×D1311yescharacteristic
659C2×C42C22×D1312yes—
660C2×C42C22×D1312yes—
661C2×C42C22×D1318yes—
662C2×C42C22×D13116yes—
663C2×C42C22×D1312yes—
664C2×C42C22×D1311yescharacteristic
665C2×C42C22×D1311yescharacteristic
666C2×C13—24no—
667C2×C13—44no—
668C2×C13#346114yescomplemented
669C2×C13C23×#4111yescharacteristic
670C2×C13C22×2−1+411yescharacteristic
671C2×C13C2×#58511yescharacteristic
672D13—44no—
673C24—132no—
674C24C23×D1312yes—
675C24C23×D1311yescharacteristic
676#41—232no—
677#41—2632no—
678C2×Q8—24no—
679C2×Q8—138no—
680C2×Q8—138no—
681C2×Q8—134no—
682C2×Q8—1316no—
683C2×Q8—268no—
684C2×Q8—268no—
685C2×Q8—2632no—
686C2×Q8—264no—
687C2×Q8—528no—
688C2×Q8C23×D1314yes—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—138no—
692C2×D4—1316no—
693C2×D4—134no—
694C2×D4—268no—
695C2×D4—264no—
696C2×D4—528no—
697C2×D4C23×D1318yes—
698C2×D4C23×D1314yes—
699C22×C4—28no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—42no—
703C22×C4—44no—
704C22×C4—132no—
705C22×C4—134no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—134no—
709C22×C4—138no—
710C22×C4—138no—
711C22×C4—138no—
712C22×C4—138no—
713C22×C4—138no—
714C22×C4—268no—
715C22×C4—268no—
716C22×C4—268no—
717C22×C4—524no—
718C22×C4—524no—
719C22×C4#612718yes—
720C22×C4C23×D1311yescharacteristic
721C22×C4C23×D1314yes—
722C22×C4C23×D1311yescharacteristic
723C22×C4C23×D1311yescharacteristic
724C22×C4C23×D1312yes—
725C22×C4C23×D1312yes—
726C22×C4C23×D1312yes—
727C22×C4C23×D1318yes—
728C22×C4C23×D1318yes—
729C22×C4C23×D1314yes—
730C22×C4C23×D1318yes—
731C22×C4C23×D1311yescharacteristic
732C22×C4C23×D1311yescharacteristic
733C22×C4C23×D1314yes—
734C22×C4C23×D1311yescharacteristic
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—1316no—
738C4⋊C4—1316no—
739C4⋊C4—138no—
740C4⋊C4—134no—
741C4⋊C4—134no—
742C4⋊C4—138no—
743C4⋊C4—1316no—
744C4⋊C4—1316no—
745C4⋊C4—1316no—
746C4⋊C4—1316no—
747C4⋊C4—1316no—
748C4⋊C4—1316no—
749C4⋊C4—1316no—
750C4⋊C4—1316no—
751C4⋊C4C23×D1318yes—
752C4⋊C4C23×D1314yes—
753C4⋊C4C23×D1314yes—
754C4⋊C4C23×D1318yes—
755C22⋊C4—138no—
756C22⋊C4—1316no—
757C22⋊C4—1316no—
758C22⋊C4—1316no—
759C22⋊C4—138no—
760C22⋊C4—138no—
761C22⋊C4—1316no—
762C22⋊C4—1316no—
763C22⋊C4—1316no—
764C22⋊C4C23×D1318yes—
765C22⋊C4C23×D1318yes—
766C22⋊C4C23×D1318yes—
767C42—1316no—
768C42—138no—
769C42—138no—
770C42—138no—
771C42—1316no—
772C42C23×D1314yes—
773C42C23×D1314yes—
774C42C23×D1314yes—
775C42C23×D1318yes—
776C42C23×D1314yes—
777C42C23×D1318yes—
778C42C23×D1318yes—
779C13C2×#346111yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—134no—
786C23—264no—
787C23—264no—
788C23—264no—
789C23C2×#612714yes—
790C23C24×D1314yes—
791C23C24×D1312yes—
792C23C24×D1311yescharacteristic
793Q8—28no—
794Q8—2616no—
795Q8—2616no—
796Q8—268no—
797Q8—5216no—
798D4—216no—
799D4—28no—
800D4—2616no—
801D4—268no—
802D4—5216no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—28no—
811C2×C4—216no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—134no—
815C2×C4—138no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—138no—
819C2×C4—264no—
820C2×C4—2616no—
821C2×C4—268no—
822C2×C4—264no—
823C2×C4—268no—
824C2×C4—264no—
825C2×C4—2616no—
826C2×C4—2616no—
827C2×C4—528no—
828C2×C4—528no—
829C2×C4C2×#612714yes—
830C2×C4C2×#612714yes—
831C2×C4C2×#6127116yes—
832C2×C4#8825714yes—
833C2×C4C24×D1312yes—
834C2×C4C24×D1312yes—
835C2×C4C24×D1312yes—
836C2×C4C24×D1314yes—
837C2×C4C24×D1314yes—
838C2×C4C24×D1314yes—
839C2×C4C24×D1312yes—
840C2×C4C24×D1312yes—
841C2×C4C24×D1312yes—
842C22—28no—
843C22—22no—
844C22—22no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—528no—
853C22C22×#612714yes—
854C22C22×#612712yes—
855C22C2×#8825712yes—
856C22#1171964812yes—
857C22C25×D1311yescharacteristic
858C4—24no—
859C4—22no—
860C4—24no—
861C4—22no—
862C4—22no—
863C4—24no—
864C4—264no—
865C4—268no—
866C4—264no—
867C4—268no—
868C4—264no—
869C4C22×#612714yes—
870C4C22×#612714yes—
871C4C2×#8825714yes—
872C2—24no—
873C2—44no—
874C2—524no—
875C2#1312826314yesdirect product factor
876C2C23×#612711yescharacteristic
877C2C22×#8825711yescharacteristic
878C2C2×#1171964811yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C4×C13×#41C2
socleC23×C13C25
prime radicalC2×#11719538C2
hypercenterC2×C4×#41D13
hypocenterC13C2×#3461
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13128263C2direct (N × H)
2. C2×#11719224C2semidirect
3. C2×#11719239C2semidirect
4. C2×#11719266C2semidirect
5. C2×#11719223C2semidirect
6. C2×#11719288C2semidirect
7. C2×#11719269C2semidirect
9. C2×#11719231C2semidirect
10. C2×#11719530C2semidirect
11. C2×#11719175C2semidirect
12. C2×#11719283C2semidirect
13. C2×#11719184C2semidirect
14. C2×#11719262C2semidirect
15. C2×#11719243C2semidirect
16. C2×C4×#6127C2semidirect
17. C22×C4×Dic26C2semidirect
18. C2×C4×C13×#41C2semidirect
22. C4×C13×#41C22semidirect
34. #11719530C22semidirect
55. #11719288C22semidirect
56. #11719283C22semidirect
57. #11719269C22semidirect
58. #11719266C22semidirect
59. #11719262C22semidirect
60. #11719243C22semidirect
61. #11719239C22semidirect
62. #11719231C22semidirect
63. #11719224C22semidirect
64. #11719223C22semidirect
79. #11719184C22semidirect
82. C4×#6127C22semidirect
88. #11719175C22semidirect
100. C2×C4×Dic26C22semidirect
357. C2×C4×#41D13semidirect
471. C4×#41C2×D13semidirect
668. C2×C13#3461semidirect
779. C13C2×#3461semidirect
875. C2#13128263direct (N × H)

Maximal subgroups

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

subgroupindex
#131282632
C2×#117192242
C2×#117192392
C2×#117192662
C2×#117192232
C2×#117192882
C2×#117192692
C2×#117195382
C2×#117192312
C2×#117195302
C2×#117191752
C2×#117192832
C2×#117191842
C2×#117192622
C2×#117192432
C2×C4×#61272
C22×C4×Dic262
C2×C4×C13×#412
C2×#346113