Finite Group Databasebeta

← C2×#13128659 #16771399

Subgroups — C2×#13128659 #16771399

Order 3328.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128659C2132yesmaximal, direct product factor
2C2×#11719390C212yesmaximal, complemented
3C2×#11719426C212yesmaximal, complemented
4C2×#11719435C212yesmaximal, complemented
5C2×#11719340C214yesmaximal, complemented
6C2×#11719395C212yesmaximal, complemented
7C2×#11719341C214yesmaximal, complemented
8C2×#11719394C212yesmaximal, complemented
9C2×#11719224C211yesmaximal, characteristic, complemented
10C2×#11719434C212yesmaximal, complemented
11C2×#11719433C212yesmaximal, complemented
12C2×#11719222C211yesmaximal, characteristic, complemented
13C22×#88144C211yesmaximal, characteristic, complemented
14C2×D13×#125C212yesmaximal, complemented
15C2×#11719209C211yesmaximal, characteristic
16C2×#11719228C211yesmaximal, characteristic
17C2×#11719227C211yesmaximal, characteristic
18C2×C13×#544C211yesmaximal, characteristic, complemented
19C22×#6127C2211yescharacteristic
20C13×#544C22116yescomplemented
21C2×C13×C4⋊Q8C2212yes—
22C2×C13×C4⋊Q8C2212yes—
23C2×C13×#125C2212yes—
24C2×C13×#125C2212yes—
25C2×C13×C22⋊Q8C2214yes—
26C2×C13×#117C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×#88200C2214yes—
30C2×#88200C2214yes—
31C2×Q8×Dic13C2214yes—
32C2×#88198C2214yes—
33C2×C4×C22⋊D13C2214yes—
34C2×#88180C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2212yes—
37C22×#6101C2212yes—
38C22×C4×Dic13C2211yescharacteristic
39#11719435C22132yescomplemented
40#11719434C22132yescomplemented
41#11719433C22132yescomplemented
42#11719426C22132yescomplemented
43#11719395C22132yescomplemented
44#11719394C22132yescomplemented
45D13×#125C22132yescomplemented
46#11719390C22132yescomplemented
47#11719341C22164yescomplemented
48#11719340C22164yescomplemented
49#11719228C22116yes—
50#11719227C22116yes—
51#11719224C22116yescomplemented
52#11719222C22116yescomplemented
53C2×#88151C2214yes—
54C2×#88151C2214yes—
55C2×#88150C2214yes—
56C2×#88150C2214yes—
57#11719209C22116yes—
58C2×#88147C2211yescharacteristic
59C2×#88147C2211yescharacteristic
60C2×#88147C2212yes—
61C2×#88146C2212yes—
62C2×#88146C2212yes—
63C2×C4⋊C4×D13C2212yes—
64C2×C4⋊C4×D13C2212yes—
65C2×C4⋊C4×D13C2214yes—
66C2×C4⋊C4×D13C2214yes—
67C2×#88144C2212yes—
68C2×#88144C2212yes—
69C2×#88144C2211yescharacteristic
70C2×#88144C2212yes—
71C2×#88144C2212yes—
72C2×#88144C2212yes—
73C2×#88144C2211yescharacteristic
74C2×#88144C22116yescomplemented
75C2×#88143C2214yes—
76C2×#88143C2214yes—
77C2×#88143C2214yes—
78C2×#88143C2214yes—
79C2×#88142C2211yescharacteristic
80C2×#88142C2212yes—
81C2×#88142C2211yescharacteristic
82C2×#88142C2214yes—
83C2×#88141C2211yescharacteristic
84C2×#88141C2211yescharacteristic
85C2×#88141C2212yes—
86C2×#88141C2214yes—
87C2×#88135C2212yes—
88C2×#88135C2212yes—
89C2×#88135C2214yes—
90C2×#88132C2214yes—
91C2×#88132C2212yes—
92C2×#88132C2212yes—
93C2×C4×D52C2212yes—
94C2×#88126C2212yes—
95C2×C42×D13C2212yes—
96C2×#88124C2212yes—
97C2×#88123C2212yes—
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2314yes—
102C23×C4×C13C2312yes—
103C23×C4×C13C2311yescharacteristic
104C22×C22⋊D13C2312yes—
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2312yes—
108C2×#6127Q8116yescomplemented
109C2×#6127C2318yes—
110C22×D52C2311yescharacteristic
111C22×C4×D13C2312yes—
112C22×C4×D13C2312yes—
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C22×C4×D13C2312yes—
116C22×Dic26C2312yes—
117C22×Dic26C2312yes—
118C22×Dic26C2314yes—
119C22×Dic26C2311yescharacteristic
120C13×C4⋊Q8C23116yes—
121C13×C4⋊Q8C23116yes—
122C13×#125C23116yes—
123C13×#125C23116yes—
124C13×C22⋊Q8C23132yes—
125C13×#117C2318yes—
126C13×#117C2318yes—
127C2×C13×C4⋊C4C2311yescharacteristic
128C2×C13×C4⋊C4C2314yes—
129C2×C13×C4⋊C4C2312yes—
130C2×C13×C4⋊C4C2311yescharacteristic
131C2×C13×C4⋊C4C2314yes—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2311yescharacteristic
134C2×C13×C4⋊C4C2314yes—
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2318yes—
137C2×C13×C22⋊C4C2312yes—
138C2×C13×C22⋊C4C2312yes—
139C2×C42×C13C2312yes—
140C2×C42×C13C2312yes—
141C2×C22⋊Dic13C2312yes—
142#88200C23132yes—
143#88200C23132yes—
144Q8×Dic13C23132yes—
145#88198C23132yes—
146C4×C22⋊D13C23132yes—
147C2×#6103C2312yes—
148C2×#6103C2312yes—
149C2×#6103C2314yes—
150C2×#6103C2314yes—
151#88180C2318yes—
152C2×C4⋊Dic13C2312yes—
153C2×C4⋊Dic13C2312yes—
154C2×C4⋊Dic13C2312yes—
155C2×C4⋊Dic13C2311yescharacteristic
156C2×C4⋊Dic13C2312yes—
157C2×C4⋊Dic13C2314yes—
158C2×C4⋊Dic13C2311yescharacteristic
159C2×C4⋊Dic13C2314yes—
160C2×C4⋊Dic13C2314yes—
161C2×C4⋊Dic13C2318yes—
162C2×C4⋊Dic13C23116yes—
163C2×#6101C2312yes—
164C2×#6101C2312yes—
165C2×#6101C2312yes—
166C2×#6101C2312yes—
167C2×#6101C2314yes—
168C2×#6101C2314yes—
169C2×#6101C2314yes—
170C2×#6101C2312yes—
171C2×#6101C2312yes—
172C2×#6101C2314yes—
173C2×#6101C2314yes—
174C2×#6101C2314yes—
175C2×#6101C23116yes—
176C2×C4×Dic13C2312yes—
177C2×C4×Dic13C2311yescharacteristic
178C2×C4×Dic13C2311yescharacteristic
179C2×C4×Dic13C2314yes—
180C2×C4×Dic13C2311yescharacteristic
181C2×C4×Dic13C2312yes—
182C2×C4×Dic13C2312yes—
183C2×C4×Dic13C2311yescharacteristic
184C2×C4×Dic13C2314yes—
185C2×C4×Dic13C2318yes—
186#88151C23132yes—
187#88151C23132yes—
188#88150C23132yes—
189#88150C23132yes—
190#88147C2318yes—
191#88147C23116yes—
192#88147C2318yes—
193#88146C23116yes—
194#88146C23116yes—
195C4⋊C4×D13C23116yes—
196C4⋊C4×D13C23132yes—
197C4⋊C4×D13C23116yes—
198C4⋊C4×D13C23132yes—
199#88144C23116yes—
200#88144C23116yes—
201#88144C2318yes—
202#88144C23116yes—
203#88144C23116yes—
204#88144C23116yes—
205#88144C2318yes—
206#88143C23132yes—
207#88143C23132yes—
208#88143C23132yes—
209#88143C23132yes—
210#88142C2318yes—
211#88142C2318yes—
212#88142C23116yes—
213#88142C23132yes—
214#88141C2318yes—
215#88141C23116yes—
216#88141C23132yes—
217#88141C2318yes—
218#88135C23116yes—
219#88135C23116yes—
220#88135C23132yes—
221#88132C23116yes—
222#88132C23116yes—
223#88132C23132yes—
224C4×D52C23116yes—
225#88126C23116yes—
226C42×D13C23116yes—
227#88124C23116yes—
228#88123C23116yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C4×Dic26C23116yes—
232C2×#3504—131nomaximal, Sylow
233C24×C13C2411yescharacteristic
234C23×D13C2412yes—
235C2×Q8×C13—48no—
236C2×Q8×C13C24116yes—
237C22×C4×C13—44no—
238C22×C4×C13C2×Q818yes—
239C22×C4×C13C2412yes—
240C22×C4×C13C2412yes—
241C22×C4×C13C2414yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C2412yes—
244C22×C4×C13C2418yes—
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2411yescharacteristic
247C22×C4×C13C2414yes—
248C2×C22⋊D13C2×Q8116yes—
249C2×C22⋊D13C2418yes—
250C22×Dic13—42no—
251C22×Dic13—42no—
252C22×Dic13—44no—
253C22×Dic13C2411yescharacteristic
254C22×Dic13C2411yescharacteristic
255C22×Dic13C2412yes—
256C22×Dic13C2411yescharacteristic
257C22×Dic13C2411yescharacteristic
258C22×Dic13C2412yes—
259C22×Dic13C2414yes—
260C22×Dic13C2414yes—
261C22×Dic13C2414yes—
262C22×Dic13C2418yes—
263C22×Dic13C2412yes—
264#6127C2×Q8164yescomplemented
265C2×D52C2×Q818yes—
266C2×D52C2414yes—
267C2×C4×D13—48no—
268C2×C4×D13—48no—
269C2×C4×D13—44no—
270C2×C4×D13—44no—
271C2×C4×D13C2×Q8116yes—
272C2×C4×D13C2418yes—
273C2×C4×D13C2418yes—
274C2×C4×D13C24116yes—
275C2×C4×D13C24116yes—
276C2×C4×D13C2418yes—
277C2×Dic26—44no—
278C2×Dic26—48no—
279C2×Dic26—44no—
280C2×Dic26C2×Q818yes—
281C2×Dic26C2418yes—
282C2×Dic26C2418yes—
283C2×Dic26C24116yes—
284C2×Dic26C2414yes—
285C13×C4⋊C4C2414yes—
286C13×C4⋊C4C24116yes—
287C13×C4⋊C4C2418yes—
288C13×C4⋊C4C2414yes—
289C13×C4⋊C4C24116yes—
290C13×C4⋊C4C2414yes—
291C13×C4⋊C4C2414yes—
292C13×C4⋊C4C24116yes—
293C13×C4⋊C4C2418yes—
294C13×C22⋊C4C2418yes—
295C13×C22⋊C4C2418yes—
296C42×C13C2418yes—
297C42×C13C2418yes—
298C22⋊Dic13C2418yes—
299#6103C2418yes—
300#6103C2418yes—
301#6103C24116yes—
302#6103C24116yes—
303C4⋊Dic13C2418yes—
304C4⋊Dic13C2418yes—
305C4⋊Dic13C2418yes—
306C4⋊Dic13C2414yes—
307C4⋊Dic13C2418yes—
308C4⋊Dic13C24116yes—
309C4⋊Dic13C2414yes—
310C4⋊Dic13C24116yes—
311C4⋊Dic13C24116yes—
312#6101C2418yes—
313#6101C2418yes—
314#6101C2418yes—
315#6101C2418yes—
316#6101C24116yes—
317#6101C24116yes—
318#6101C24116yes—
319#6101C2418yes—
320#6101C2418yes—
321#6101C24116yes—
322#6101C24116yes—
323#6101C24116yes—
324C4×Dic13C2418yes—
325C4×Dic13C2414yes—
326C4×Dic13C2414yes—
327C4×Dic13C24116yes—
328C4×Dic13C2414yes—
329C4×Dic13C2418yes—
330C4×Dic13C2418yes—
331C4×Dic13C2414yes—
332C4×Dic13C24116yes—
333#3504—1332no—
334C2×#557—132no—
335C2×#557—132no—
336C2×#554—132no—
337C2×#554—132no—
338C2×#554—134no—
339C2×#554—134no—
340C2×#544—132no—
341C2×#544—132no—
342C2×#544—131no—
343C2×#544D1311yescharacteristic, complemented
344C2×#533—132no—
345C2×#533—131no—
346C22×#125—132no—
347C22×#125—131no—
348C2×#520—131no—
349C2×#520—131no—
350C2×C4×#41—131no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13C22×Q814yes—
354C23×C13C2512yes—
355C23×C13C2511yescharacteristic
356C22×D13—24no—
357C22×D13—24no—
358C22×D13C22×Q818yes—
359C22×D13C2514yes—
360Q8×C13—416no—
361C2×C4×C13—24no—
362C2×C4×C13—24no—
363C2×C4×C13—24no—
364C2×C4×C13—28no—
365C2×C4×C13—24no—
366C2×C4×C13—48no—
367C2×C4×C13C22×Q814yes—
368C2×C4×C13C22×Q814yes—
369C2×C4×C13C22×Q8116yes—
370C2×C4×C13C2514yes—
371C2×C4×C13C2514yes—
372C2×C4×C13C2518yes—
373C2×C4×C13C2514yes—
374C2×C4×C13C2514yes—
375C2×C4×C13C2512yes—
376C2×C4×C13C2512yes—
377C22⋊D13C22×Q8132yes—
378C2×Dic13—24no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—24no—
382C2×Dic13—28no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—48no—
388C2×Dic13C22×Q818yes—
389C2×Dic13C2512yes—
390C2×Dic13C2512yes—
391C2×Dic13C2514yes—
392C2×Dic13C2512yes—
393C2×Dic13C2512yes—
394C2×Dic13C2514yes—
395C2×Dic13C2518yes—
396C2×Dic13C2514yes—
397D52C22×Q8116yes—
398C4×D13—416no—
399C4×D13—416no—
400C4×D13—48no—
401C4×D13—48no—
402C4×D13C22×Q8132yes—
403Dic26—48no—
404Dic26—416no—
405Dic26—48no—
406Dic26C22×Q8116yes—
407C22×#41—131no—
408#557—1332no—
409#557—1332no—
410#554—1332no—
411#554—1332no—
412#554—1364no—
413#554—1364no—
414#544—1332no—
415#544—1332no—
416#544—1316no—
417#544C2×D13116yescomplemented
418#533—1332no—
419#533—1316no—
420C2×C4⋊Q8—134no—
421C2×C4⋊Q8—131no—
422C2×C4⋊Q8—131no—
423C2×C4⋊Q8—134no—
424C2×C4⋊Q8—132no—
425C2×C4⋊Q8—132no—
426C2×C4⋊Q8C2×D1312yes—
427C2×C4⋊Q8C2×D1312yes—
428C2×#125—1332no—
429C2×#125—134no—
430C2×#125—134no—
431C2×#125—134no—
432C2×#125—134no—
433C2×#125—131no—
434C2×#125—132no—
435C2×#125—132no—
436C2×#125—132no—
437C2×#125—132no—
438C2×#125—131no—
439C2×#125—132no—
440C2×#125—1316no—
441C2×#125—132no—
442C2×#125C2×D1312yes—
443C2×#125C2×D1312yes—
444C2×C22⋊Q8—134no—
445C2×C22⋊Q8—134no—
446C2×C22⋊Q8—134no—
447C2×C22⋊Q8—134no—
448C2×C22⋊Q8—134no—
449C2×C22⋊Q8—134no—
450C2×C22⋊Q8—132no—
451C2×C22⋊Q8—132no—
452C2×C22⋊Q8—134no—
453C2×C22⋊Q8C2×D1314yes—
454#520—1316no—
455#520—1316no—
456C4×#41—1316no—
457C2×C4×Q8—134no—
458C2×C4×Q8—131no—
459C2×C4×Q8—131no—
460C2×C4×Q8—132no—
461C2×C4×Q8—134no—
462C2×C4×Q8—132no—
463C2×C4×Q8—132no—
464C2×C4×Q8—132no—
465C2×C4×D4—134no—
466C2×C4×D4—131no—
467C2×C4×D4—131no—
468C2×C4×D4—132no—
469C2×C4×D4—132no—
470C2×C4×D4—132no—
471C2×C4×D4—134no—
472C2×C4×D4—132no—
473C2×#117—131no—
474C2×#117—132no—
475C2×#117—132no—
476C2×#117—132no—
477C2×#117C2×D1311yescharacteristic
478C2×#117C2×D1311yescharacteristic
479C22×C4⋊C4—132no—
480C22×C4⋊C4—131no—
481C22×C4⋊C4—132no—
482C22×C4⋊C4—132no—
483C22×C4⋊C4—132no—
484C22×C4⋊C4—134no—
485C22×C4⋊C4—134no—
486C22×C4⋊C4C2×D1311yescharacteristic
487C22×C42—131no—
488C22×C42—132no—
489C22×C13—22no—
490C22×C13—22no—
491C22×C13—28no—
492C22×C13C23×Q814yes—
493C22×C13C23×Q812yes—
494C22×C13#58512yes—
495C22×C13#58512yes—
496C22×C13C2611yescharacteristic
497C2×D13—24no—
498C2×D13—24no—
499C2×D13—216no—
500C2×D13C23×Q818yes—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—28no—
505C4×C13—24no—
506C4×C13C23×Q814yes—
507C4×C13C23×Q814yes—
508Dic13—24no—
509Dic13—22no—
510Dic13—22no—
511Dic13—24no—
512Dic13—28no—
513Dic13—22no—
514Dic13—22no—
515Dic13C23×Q818yes—
516C2×#41—1316no—
517C2×#41—138no—
518C22×Q8—131no—
519C22×Q8—132no—
520C22×Q8—134no—
521C22×Q8—132no—
522C22×Q8C22×D1314yes—
523C22×D4—132no—
524C22×D4—131no—
525C23×C4—132no—
526C23×C4—132no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—134no—
530C23×C4—134no—
531C23×C4—132no—
532C23×C4—132no—
533C23×C4C22×D1312yes—
534C23×C4C22×D1311yescharacteristic
535C4⋊Q8—1332no—
536C4⋊Q8—138no—
537C4⋊Q8—138no—
538C4⋊Q8—1332no—
539C4⋊Q8—1316no—
540C4⋊Q8—1316no—
541C4⋊Q8C22×D13116yes—
542C4⋊Q8C22×D13116yes—
543#125—138no—
544#125—1316no—
545#125—1316no—
546#125—1332no—
547#125—1332no—
548#125—1316no—
549#125—1316no—
550#125—138no—
551#125—1332no—
552#125—1332no—
553#125—1316no—
554#125—1316no—
555#125C22×D13116yes—
556#125C22×D13116yes—
557C22⋊Q8—1332no—
558C22⋊Q8—1332no—
559C22⋊Q8—1332no—
560C22⋊Q8—1332no—
561C22⋊Q8—1332no—
562C22⋊Q8—1332no—
563C22⋊Q8—1316no—
564C22⋊Q8—1316no—
565C22⋊Q8—1332no—
566C22⋊Q8C22×D13132yes—
567C4×Q8—1332no—
568C4×Q8—138no—
569C4×Q8—138no—
570C4×Q8—1316no—
571C4×Q8—1332no—
572C4×Q8—1316no—
573C4×Q8—1316no—
574C4×Q8—1316no—
575C4×D4—1332no—
576C4×D4—138no—
577C4×D4—138no—
578C4×D4—1316no—
579C4×D4—1316no—
580C4×D4—1316no—
581C4×D4—1332no—
582C4×D4—1316no—
583#117—138no—
584#117—1316no—
585#117—1316no—
586#117—1316no—
587#117C22×D1318yes—
588#117C22×D1318yes—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—131no—
591C2×C4⋊C4—134no—
592C2×C4⋊C4—132no—
593C2×C4⋊C4—134no—
594C2×C4⋊C4—132no—
595C2×C4⋊C4—134no—
596C2×C4⋊C4—134no—
597C2×C4⋊C4—132no—
598C2×C4⋊C4—138no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—134no—
601C2×C4⋊C4—134no—
602C2×C4⋊C4—134no—
603C2×C4⋊C4—1316no—
604C2×C4⋊C4—1316no—
605C2×C4⋊C4—131no—
606C2×C4⋊C4—132no—
607C2×C4⋊C4—132no—
608C2×C4⋊C4—132no—
609C2×C4⋊C4—132no—
610C2×C4⋊C4—132no—
611C2×C4⋊C4—132no—
612C2×C4⋊C4—134no—
613C2×C4⋊C4—1316no—
614C2×C4⋊C4—1316no—
615C2×C4⋊C4—1332no—
616C2×C4⋊C4—1332no—
617C2×C4⋊C4C22×D1311yescharacteristic
618C2×C4⋊C4C22×D1312yes—
619C2×C4⋊C4C22×D1314yes—
620C2×C4⋊C4C22×D1314yes—
621C2×C4⋊C4C22×D1312yes—
622C2×C4⋊C4C22×D1318yes—
623C2×C4⋊C4C22×D1311yescharacteristic
624C2×C4⋊C4C22×D1311yescharacteristic
625C2×C4⋊C4C22×D1311yescharacteristic
626C2×C4⋊C4C22×D1314yes—
627C2×C22⋊C4—132no—
628C2×C22⋊C4—134no—
629C2×C22⋊C4—132no—
630C2×C22⋊C4—132no—
631C2×C22⋊C4—134no—
632C2×C22⋊C4C22×D1312yes—
633C2×C22⋊C4C22×D1312yes—
634C2×C42—131no—
635C2×C42—134no—
636C2×C42—134no—
637C2×C42—132no—
638C2×C42—132no—
639C2×C42—132no—
640C2×C42—131no—
641C2×C42—131no—
642C2×C42—138no—
643C2×C42—131no—
644C2×C42—1316no—
645C2×C42C22×D1312yes—
646C2×C42C22×D1312yes—
647C2×C13—24no—
648C2×C13#350414yescomplemented
649C2×C13C24×Q811yescharacteristic
650C2×C13C2×#58511yescharacteristic
651C2×C13C2×#58511yescharacteristic
652D13—28no—
653C24—132no—
654C24C23×D1311yescharacteristic
655#41—1364no—
656C2×Q8—48no—
657C2×Q8—138no—
658C2×Q8—134no—
659C2×Q8—138no—
660C2×Q8—1316no—
661C2×Q8—138no—
662C2×Q8—524no—
663C2×Q8—524no—
664C2×Q8—528no—
665C2×Q8C23×D13116yes—
666C2×D4—1316no—
667C2×D4—138no—
668C2×D4—138no—
669C2×D4—134no—
670C22×C4—44no—
671C22×C4—132no—
672C22×C4—1316no—
673C22×C4—138no—
674C22×C4—131no—
675C22×C4—131no—
676C22×C4—132no—
677C22×C4—131no—
678C22×C4—131no—
679C22×C4—132no—
680C22×C4—134no—
681C22×C4—134no—
682C22×C4—134no—
683C22×C4—138no—
684C22×C4—138no—
685C22×C4—138no—
686C22×C4—1316no—
687C22×C4—1316no—
688C22×C4—528no—
689C22×C4—524no—
690C22×C4—528no—
691C22×C4—524no—
692C22×C4—522no—
693C22×C4—522no—
694C22×C4—524no—
695C22×C4Q8×D1318yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1314yes—
700C22×C4C23×D1312yes—
701C22×C4C23×D1318yes—
702C22×C4C23×D1314yes—
703C22×C4C23×D1311yescharacteristic
704C22×C4C23×D1311yescharacteristic
705C4⋊C4—138no—
706C4⋊C4—134no—
707C4⋊C4—1316no—
708C4⋊C4—138no—
709C4⋊C4—1316no—
710C4⋊C4—138no—
711C4⋊C4—1316no—
712C4⋊C4—1316no—
713C4⋊C4—138no—
714C4⋊C4—1316no—
715C4⋊C4—1316no—
716C4⋊C4—1316no—
717C4⋊C4—1316no—
718C4⋊C4—134no—
719C4⋊C4—138no—
720C4⋊C4—138no—
721C4⋊C4—138no—
722C4⋊C4—138no—
723C4⋊C4—138no—
724C4⋊C4—138no—
725C4⋊C4—1316no—
726C4⋊C4C23×D1314yes—
727C4⋊C4C23×D1318yes—
728C4⋊C4C23×D13116yes—
729C4⋊C4C23×D13116yes—
730C4⋊C4C23×D1318yes—
731C4⋊C4C23×D1314yes—
732C4⋊C4C23×D1314yes—
733C4⋊C4C23×D1314yes—
734C4⋊C4C23×D13116yes—
735C22⋊C4—138no—
736C22⋊C4—1316no—
737C22⋊C4—138no—
738C22⋊C4—138no—
739C22⋊C4—1316no—
740C22⋊C4C23×D1318yes—
741C22⋊C4C23×D1318yes—
742C42—134no—
743C42—134no—
744C42—138no—
745C42—138no—
746C42—134no—
747C42—134no—
748C42—1316no—
749C42—1316no—
750C42—138no—
751C42C23×D1318yes—
752C42C23×D1318yes—
753C13C2×#350411yescharacteristic, complemented, Sylow
754C23—22no—
755C23—22no—
756C23—138no—
757C23—134no—
758C23—264no—
759C23—264no—
760C23C2×Q8×D1314yes—
761C23C24×D1312yes—
762C23C24×D1311yescharacteristic
763Q8—416no—
764Q8—1316no—
765Q8—528no—
766Q8—528no—
767Q8—5216no—
768D4—1332no—
769D4—1316no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—138no—
777C2×C4—134no—
778C2×C4—1332no—
779C2×C4—132no—
780C2×C4—132no—
781C2×C4—134no—
782C2×C4—132no—
783C2×C4—132no—
784C2×C4—134no—
785C2×C4—138no—
786C2×C4—262no—
787C2×C4—264no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—268no—
791C2×C4—262no—
792C2×C4—264no—
793C2×C4—5216no—
794C2×C4—528no—
795C2×C4—5216no—
796C2×C4—528no—
797C2×C4—524no—
798C2×C4—524no—
799C2×C4—528no—
800C2×C4C2×Q8×D1314yes—
801C2×C4C2×Q8×D1314yes—
802C2×C4C2×Q8×D13116yes—
803C2×C4C24×D1314yes—
804C2×C4C24×D1314yes—
805C2×C4C24×D1314yes—
806C2×C4C24×D1318yes—
807C2×C4C24×D1314yes—
808C2×C4C24×D1312yes—
809C2×C4C24×D1312yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—138no—
814C22—264no—
815C22—264no—
816C22—2616no—
817C22C22×Q8×D1314yes—
818C22C22×Q8×D1312yes—
819C22#1171965012yes—
820C22#1171965212yes—
821C22C25×D1311yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—138no—
828C4—262no—
829C4—264no—
830C4—262no—
831C4—262no—
832C4—268no—
833C4—262no—
834C4—264no—
835C4C22×Q8×D1314yes—
836C4C22×Q8×D1314yes—
837C2—24no—
838C2—268no—
839C2#1312865914yesdirect product factor
840C2C23×Q8×D1311yescharacteristic
841C2C2×#1171965011yescharacteristic
842C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#544C2
socleC23×C13C25
prime radicalC22×#6127C22
hypercenterC2×#544D13
hypocenterC13C2×#3504
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13128659C2direct (N × H)
2. C2×#11719390C2semidirect
3. C2×#11719426C2semidirect
4. C2×#11719435C2semidirect
5. C2×#11719340C2semidirect
6. C2×#11719395C2semidirect
7. C2×#11719341C2semidirect
8. C2×#11719394C2semidirect
9. C2×#11719224C2semidirect
10. C2×#11719434C2semidirect
11. C2×#11719433C2semidirect
12. C2×#11719222C2semidirect
13. C22×#88144C2semidirect
14. C2×D13×#125C2semidirect
18. C2×C13×#544C2semidirect
20. C13×#544C22semidirect
39. #11719435C22semidirect
40. #11719434C22semidirect
41. #11719433C22semidirect
42. #11719426C22semidirect
43. #11719395C22semidirect
44. #11719394C22semidirect
45. D13×#125C22semidirect
46. #11719390C22semidirect
47. #11719341C22semidirect
48. #11719340C22semidirect
51. #11719224C22semidirect
52. #11719222C22semidirect
74. C2×#88144C22semidirect
108. C2×#6127Q8semidirect
264. #6127C2×Q8semidirect
343. C2×#544D13semidirect
417. #544C2×D13semidirect
648. C2×C13#3504semidirect
753. C13C2×#3504semidirect
839. C2#13128659direct (N × H)

Maximal subgroups

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

subgroupindex
#131286592
C2×#117193902
C2×#117194262
C2×#117194352
C2×#117193402
C2×#117193952
C2×#117193412
C2×#117193942
C2×#117192242
C2×#117194342
C2×#117194332
C2×#117192222
C22×#881442
C2×D13×#1252
C2×#117192092
C2×#117192282
C2×#117192272
C2×C13×#5442
C2×#350413