Finite Group Databasebeta

← C2×#13128813 #16771036

Subgroups — C2×#13128813 #16771036

Order 3328.

7142 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#13128813C2132yesmaximal, direct product factor
2C2×#11719284C211yesmaximal, characteristic, complemented
3C2×#11719284C211yesmaximal, characteristic, complemented
4C2×#11719400C212yesmaximal, complemented
5C2×#11719286C212yesmaximal, complemented
6C2×#11719286C212yesmaximal, complemented
7C2×#11719398C214yesmaximal, complemented
8C2×#11719431C211yesmaximal, characteristic, complemented
9C2×#11719431C212yesmaximal, complemented
10C2×#11719436C212yesmaximal, complemented
11C2×#11719397C214yesmaximal, complemented
12C2×#11719433C211yesmaximal, characteristic, complemented
13C2×#11719285C212yesmaximal, complemented
14C2×#11719285C211yesmaximal, characteristic, complemented
15C2×D13×#125C212yesmaximal, complemented
16C2×#11719279C212yesmaximal, complemented
17C2×C4×#6131C211yesmaximal, characteristic, complemented
18C2×C13×#557C211yesmaximal, characteristic, complemented
19C22×#6131C2211yescharacteristic
20C22×#6131C2212yes—
21C13×#557C22116yescomplemented
22C2×C13×C4⋊Q8C2212yes—
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×#125C2214yes—
25C2×C13×#125C2212yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2212yes—
28C2×C4×Q8×C13C2212yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×#88201C2211yescharacteristic
31C2×#88200C2212yes—
32C2×#88200C2212yes—
33C2×#88200C2212yes—
34C2×#88200C2211yescharacteristic
35C2×#88200C2212yes—
36C2×Q8×Dic13C2211yescharacteristic
37C2×Q8×Dic13C2212yes—
38#11719436C22132yescomplemented
39#11719433C22116yescomplemented
40#11719431C22116yescomplemented
41#11719431C22132yescomplemented
42#11719400C22132yescomplemented
43#11719398C22164yescomplemented
44#11719397C22164yescomplemented
45D13×#125C22132yescomplemented
46#11719286C22132yescomplemented
47#11719286C22132yescomplemented
48#11719285C22116yescomplemented
49#11719285C22132yescomplemented
50#11719284C22116yescomplemented
51#11719284C22116yescomplemented
52#11719279C22132yescomplemented
53C4×#6131C22116yescomplemented
54C2×#88152C2214yes—
55C2×#88152C2214yes—
56C2×#88152C2212yes—
57C2×#88151C2212yes—
58C2×#88150C2214yes—
59C2×#88150C2214yes—
60C2×#88149C2212yes—
61C2×#88149C2214yes—
62C2×#88149C2211yescharacteristic
63C2×#88148C2214yes—
64C2×#88148C2214yes—
65C2×#88148C2214yes—
66C2×#88148C2214yes—
67C2×#88148C2212yes—
68C2×#88147C2211yescharacteristic
69C2×#88147C2212yes—
70C2×#88147C2214yes—
71C2×#88146C2212yes—
72C2×#88146C2211yescharacteristic
73C2×#88146C2212yes—
74C2×C4⋊C4×D13C2214yes—
75C2×C4⋊C4×D13C2212yes—
76C2×C4⋊C4×D13C2214yes—
77C2×C4⋊C4×D13C2212yes—
78C2×C4⋊C4×D13C2212yes—
79C2×#88144C2211yescharacteristic
80C2×#88144C2212yes—
81C2×#88143C2214yes—
82C2×#88143C2214yes—
83C2×#88143C2214yes—
84C2×#88141C2212yes—
85C2×#88130C2214yes—
86C2×C4×D52C2211yescharacteristic
87C2×C4×D52C2212yes—
88C2×C4×D52C2212yes—
89C2×C4×D52C2214yes—
90C2×C4×D52C2212yes—
91C2×C4×D52C2211yescharacteristic
92C2×C4×D52C2212yes—
93C2×#88126C2212yes—
94C2×#88126C2214yes—
95C2×#88126C2214yes—
96C2×C42×D13C2212yes—
97C2×C42×D13C2211yescharacteristic
98C2×#88124C2212yes—
99C2×#88124C2212yes—
100C2×#88123C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2312yes—
103C22×Q8×C13C2311yescharacteristic
104C2×#6131—28no—
105C2×#6131—216no—
106C2×#6131C2318yes—
107C2×#6131C23116yes—
108C22×D52C2311yescharacteristic
109C22×D52C2312yes—
110C22×D52C2314yes—
111C22×D52C2312yes—
112C22×D52C2311yescharacteristic
113C22×C4×D13C2312yes—
114C22×C4×D13C2311yescharacteristic
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2312yes—
117C22×C4×D13C2312yes—
118C22×C4×D13C2314yes—
119C22×C4×D13C2312yes—
120C22×C4×D13C2311yescharacteristic
121C22×C4×D13C2314yes—
122C22×C4×D13C2314yes—
123C22×Dic26C2312yes—
124C13×C4⋊Q8C2318yes—
125C13×C4⋊Q8C23116yes—
126C13×#125C23116yes—
127C13×#125C23132yes—
128C4×Q8×C13C2318yes—
129C4×Q8×C13C23116yes—
130C4×Q8×C13C2318yes—
131C4×Q8×C13C23116yes—
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2314yes—
134C2×C13×C4⋊C4C2314yes—
135C2×C13×C4⋊C4C2314yes—
136C2×C13×C4⋊C4C2311yescharacteristic
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2312yes—
140C2×C13×C4⋊C4C2312yes—
141C2×C42×C13C2311yescharacteristic
142C2×C42×C13C2312yes—
143C2×C42×C13C2312yes—
144C2×C42×C13C2314yes—
145#88201C2318yes—
146#88200C23116yes—
147#88200C23116yes—
148#88200C23116yes—
149#88200C23116yes—
150#88200C2318yes—
151Q8×Dic13C23116yes—
152Q8×Dic13C2318yes—
153C2×#6103C2312yes—
154C2×#6103C2312yes—
155C2×#6103C2314yes—
156C2×#6103C2312yes—
157C2×#6103C2312yes—
158C2×#6103C2314yes—
159C2×#6103C2312yes—
160C2×#6103C2312yes—
161C2×#6103C2312yes—
162C2×#6103C2312yes—
163C2×#6103C2314yes—
164C2×#6103C2314yes—
165C2×C4⋊Dic13C2312yes—
166C2×C4⋊Dic13C2312yes—
167C2×C4⋊Dic13C2311yescharacteristic
168C2×C4⋊Dic13C2311yescharacteristic
169C2×C4⋊Dic13C2312yes—
170C2×C4⋊Dic13C2312yes—
171C2×C4⋊Dic13C2314yes—
172C2×#6101C2314yes—
173C2×#6101C2314yes—
174C2×#6101C2314yes—
175C2×#6101C2314yes—
176C2×#6101C2312yes—
177C2×#6101C2314yes—
178C2×#6101C2312yes—
179C2×#6101C2314yes—
180C2×C4×Dic13C2311yescharacteristic
181C2×C4×Dic13C2312yes—
182C2×C4×Dic13C2311yescharacteristic
183C2×C4×Dic13C2311yescharacteristic
184C2×C4×Dic13C2312yes—
185C2×C4×Dic13C2314yes—
186#88152C23132yes—
187#88152C23132yes—
188#88152C23116yes—
189#88151C23116yes—
190#88150C23132yes—
191#88150C23132yes—
192#88149C23116yes—
193#88149C23132yes—
194#88149C2318yes—
195#88148C23132yes—
196#88148C23132yes—
197#88148C23132yes—
198#88148C23116yes—
199#88148C23132yes—
200#88147C2318yes—
201#88147C23116yes—
202#88147C23132yes—
203#88146C23116yes—
204#88146C2318yes—
205#88146C23116yes—
206C4⋊C4×D13C23116yes—
207C4⋊C4×D13C23132yes—
208C4⋊C4×D13C23116yes—
209C4⋊C4×D13C23132yes—
210C4⋊C4×D13C23116yes—
211#88144C23116yes—
212#88144C2318yes—
213#88143C23132yes—
214#88143C23132yes—
215#88143C23132yes—
216#88141C23116yes—
217#88130C23132yes—
218C4×D52C2318yes—
219C4×D52C23116yes—
220C4×D52C2318yes—
221C4×D52C23116yes—
222C4×D52C23116yes—
223C4×D52C23132yes—
224C4×D52C23116yes—
225#88126C23116yes—
226#88126C23132yes—
227#88126C23132yes—
228C42×D13C2318yes—
229C42×D13C23116yes—
230#88124C23116yes—
231#88124C23116yes—
232#88123C2318yes—
233C2×#3515—131nomaximal, Sylow
234C23×D13C2411yescharacteristic
235C23×D13C2412yes—
236C23×D13C2412yes—
237C2×Q8×C13—24no—
238C2×Q8×C13—28no—
239C2×Q8×C13—24no—
240C2×Q8×C13C2418yes—
241C2×Q8×C13C2414yes—
242C2×Q8×C13C2414yes—
243C22×C4×C13C2412yes—
244C22×C4×C13C2414yes—
245C22×C4×C13C2412yes—
246C22×C4×C13C2411yescharacteristic
247C22×C4×C13C2412yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2411yescharacteristic
250C22×C4×C13C2411yescharacteristic
251C22×Dic13C2411yescharacteristic
252C22×Dic13C2411yescharacteristic
253C22×Dic13C2411yescharacteristic
254C22×Dic13C2412yes—
255C22×Dic13C2414yes—
256C22×Dic13C2412yes—
257#6131—232no—
258#6131—264no—
259C2×D52—28no—
260C2×D52—216no—
261C2×D52—24no—
262C2×D52—44no—
263C2×D52#4118yes—
264C2×D52C2414yes—
265C2×D52C2418yes—
266C2×D52C24116yes—
267C2×D52C2418yes—
268C2×D52C2414yes—
269C2×C4×D13—28no—
270C2×C4×D13—216no—
271C2×C4×D13—24no—
272C2×C4×D13—28no—
273C2×C4×D13—28no—
274C2×C4×D13—24no—
275C2×C4×D13—48no—
276C2×C4×D13—48no—
277C2×C4×D13—42no—
278C2×C4×D13—44no—
279C2×C4×D13C2418yes—
280C2×C4×D13C2414yes—
281C2×C4×D13C2414yes—
282C2×C4×D13C2418yes—
283C2×C4×D13C2418yes—
284C2×C4×D13C24116yes—
285C2×C4×D13C2418yes—
286C2×C4×D13C2414yes—
287C2×C4×D13C24116yes—
288C2×C4×D13C24116yes—
289C2×Dic26—44no—
290C2×Dic26C2418yes—
291C13×C4⋊C4C2418yes—
292C13×C4⋊C4C24116yes—
293C13×C4⋊C4C24116yes—
294C13×C4⋊C4C24116yes—
295C13×C4⋊C4C2414yes—
296C13×C4⋊C4C2418yes—
297C13×C4⋊C4C2414yes—
298C13×C4⋊C4C2418yes—
299C13×C4⋊C4C2418yes—
300C42×C13C2414yes—
301C42×C13C2418yes—
302C42×C13C2418yes—
303C42×C13C24116yes—
304#6103C2418yes—
305#6103C2418yes—
306#6103C24116yes—
307#6103C2418yes—
308#6103C2418yes—
309#6103C24116yes—
310#6103C2418yes—
311#6103C2418yes—
312#6103C2418yes—
313#6103C2418yes—
314#6103C24116yes—
315#6103C24116yes—
316C4⋊Dic13C2418yes—
317C4⋊Dic13C2418yes—
318C4⋊Dic13C2414yes—
319C4⋊Dic13C2414yes—
320C4⋊Dic13C2418yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C24116yes—
323#6101C24116yes—
324#6101C24116yes—
325#6101C24116yes—
326#6101C24116yes—
327#6101C2418yes—
328#6101C24116yes—
329#6101C2418yes—
330#6101C24116yes—
331C4×Dic13C2414yes—
332C4×Dic13C2418yes—
333C4×Dic13C2414yes—
334C4×Dic13C2414yes—
335C4×Dic13C2418yes—
336C4×Dic13C24116yes—
337#3515—1332no—
338C2×#557D1311yescharacteristic, complemented
339C2×#554—131no—
340C2×#554—131no—
341C2×#553—132no—
342C2×#552—134no—
343C2×#552—132no—
344C2×#552—132no—
345C2×#547—131no—
346C2×#547—132no—
347C2×#541—132no—
348C2×#539—134no—
349C2×#533—131no—
350C2×#529—131no—
351C2×#529—132no—
352C22×#125—132no—
353C2×#520—132no—
354C2×C4×#41—131no—
355C23×C13C2511yescharacteristic
356C22×D13—24no—
357C22×D13—24no—
358C22×D13—22no—
359C22×D13—24no—
360C22×D13—22no—
361C22×D13—24no—
362C22×D13—24no—
363C22×D13—22no—
364C22×D13C2×#4118yes—
365C22×D13C2512yes—
366C22×D13C2514yes—
367C22×D13C2514yes—
368Q8×C13—28no—
369Q8×C13—216no—
370Q8×C13—28no—
371C2×C4×C13—24no—
372C2×C4×C13—28no—
373C2×C4×C13—24no—
374C2×C4×C13—22no—
375C2×C4×C13—24no—
376C2×C4×C13—24no—
377C2×C4×C13C2×#4114yes—
378C2×C4×C132−1+414yes—
379C2×C4×C13C2514yes—
380C2×C4×C13C2518yes—
381C2×C4×C13C2514yes—
382C2×C4×C13C2512yes—
383C2×C4×C13C2514yes—
384C2×C4×C13C2514yes—
385C2×C4×C13C2512yes—
386C2×C4×C13C2512yes—
387C2×Dic13—22no—
388C2×Dic13—24no—
389C2×Dic13—22no—
390C2×Dic13—24no—
391C2×Dic13—28no—
392C2×Dic13—22no—
393C2×Dic13C2512yes—
394C2×Dic13C2512yes—
395C2×Dic13C2512yes—
396C2×Dic13C2514yes—
397C2×Dic13C2518yes—
398C2×Dic13C2514yes—
399D52—216no—
400D52—232no—
401D52—28no—
402D52—48no—
403D52C2×#41116yes—
404C4×D13—216no—
405C4×D13—232no—
406C4×D13—28no—
407C4×D13—216no—
408C4×D13—216no—
409C4×D13—28no—
410C4×D13—416no—
411C4×D13—416no—
412C4×D13—44no—
413C4×D13—48no—
414Dic26—48no—
415C22×#41—131no—
416C22×#41—132no—
417#557C2×D13116yescomplemented
418#554—1316no—
419#554—1316no—
420#553—1332no—
421#552—1364no—
422#552—1332no—
423#552—1332no—
424#547—1316no—
425#547—1332no—
426#541—1332no—
427#539—1364no—
428#533—1316no—
429C2×C4⋊Q8—131no—
430C2×C4⋊Q8C2×D1311yescharacteristic
431C2×C4⋊Q8C2×D1312yes—
432#529—1332no—
433#529—1316no—
434C2×#126—134no—
435C2×#126—132no—
436C2×#126—134no—
437C2×#126—134no—
438C2×#125—1332no—
439C2×#125—134no—
440C2×#125—134no—
441C2×#125—134no—
442C2×#125—131no—
443C2×#125—132no—
444C2×#125—132no—
445C2×#125—132no—
446C2×#125C2×D1312yes—
447C2×#125C2×D1314yes—
448C2×#124—131no—
449C2×#123—132no—
450C2×#123—134no—
451C2×#123—134no—
452C2×#123—134no—
453C2×#123—134no—
454C2×C22⋊Q8—131no—
455C2×C22⋊Q8—132no—
456C2×C22⋊Q8—132no—
457C2×C22⋊Q8—132no—
458C2×C22⋊Q8—132no—
459C2×C22⋊Q8—134no—
460C2×C22⋊Q8—134no—
461C2×C22⋊Q8—132no—
462C2×#121—132no—
463C2×#121—131no—
464C2×#121—134no—
465#520—1332no—
466C4×#41—1316no—
467C2×C4×Q8—131no—
468C2×C4×Q8—132no—
469C2×C4×Q8—132no—
470C2×C4×Q8C2×D1311yescharacteristic
471C2×C4×Q8C2×D1312yes—
472C2×C4×Q8C2×D1312yes—
473C2×C4×Q8C2×D1311yescharacteristic
474C2×C4×D4—131no—
475C2×C4×D4—132no—
476C2×C4×D4—134no—
477C2×C4×D4—131no—
478C2×C4×D4—132no—
479C2×C4×D4—134no—
480C2×C4×D4—132no—
481C2×C4×D4—132no—
482C2×C4×D4—131no—
483C2×C4×D4—132no—
484C2×#117—131no—
485C2×#117—132no—
486C2×#117—132no—
487C2×#117—132no—
488C2×#117—134no—
489C2×#117—134no—
490C22×C4⋊C4—134no—
491C22×C4⋊C4—132no—
492C22×C4⋊C4—132no—
493C22×C4⋊C4—134no—
494C22×C4⋊C4—132no—
495C22×C42—132no—
496C22×C42—131no—
497C22×C13C22×#4112yes—
498C22×C13C2×2−1+412yes—
499C22×C13#58512yes—
500C22×C13C2611yescharacteristic
501C2×D13—24no—
502C2×D13—24no—
503C2×D13—216no—
504C2×D13—22no—
505C2×D13—24no—
506C2×D13—22no—
507C2×D13—24no—
508C2×D13—24no—
509C2×D13—22no—
510C2×D13—44no—
511C2×D13—48no—
512C2×D13C22×#4118yes—
513C4×C13—24no—
514C4×C13—28no—
515C4×C13—24no—
516C4×C13—22no—
517C4×C13—24no—
518C4×C13—24no—
519C4×C13C22×#4114yes—
520C4×C13C2×2−1+414yes—
521Dic13—22no—
522Dic13—24no—
523Dic13—22no—
524Dic13—24no—
525Dic13—28no—
526Dic13—22no—
527C2×#41—138no—
528C2×#41—1316no—
529C2×#41—268no—
530C2×#41—2616no—
531C22×Q8—132no—
532C22×Q8C22×D1311yescharacteristic
533C22×Q8C22×D1312yes—
534C22×Q8C22×D1311yescharacteristic
535C22×D4—131no—
536C22×D4—131no—
537C22×D4—132no—
538C22×D4—134no—
539C22×D4—132no—
540C23×C4—134no—
541C23×C4—132no—
542C23×C4—132no—
543C23×C4—132no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—134no—
547C23×C4—132no—
548C23×C4—134no—
549C23×C4—131no—
550C4⋊Q8—138no—
551C4⋊Q8C22×D1318yes—
552C4⋊Q8C22×D13116yes—
553#126—1332no—
554#126—1316no—
555#126—1332no—
556#126—1332no—
557#125—138no—
558#125—1316no—
559#125—1332no—
560#125—1332no—
561#125—1332no—
562#125—1316no—
563#125—1316no—
564#125C22×D13116yes—
565#125C22×D13132yes—
566#124—138no—
567#123—1316no—
568#123—1332no—
569#123—1332no—
570#123—1332no—
571#123—1332no—
572C22⋊Q8—138no—
573C22⋊Q8—1316no—
574C22⋊Q8—1316no—
575C22⋊Q8—1316no—
576C22⋊Q8—1316no—
577C22⋊Q8—1316no—
578C22⋊Q8—1332no—
579C22⋊Q8—1332no—
580#121—1316no—
581#121—138no—
582#121—1332no—
583C4×Q8—138no—
584C4×Q8—1316no—
585C4×Q8—1316no—
586C4×Q8C22×D1318yes—
587C4×Q8C22×D13116yes—
588C4×Q8C22×D13116yes—
589C4×Q8C22×D1318yes—
590C4×D4—138no—
591C4×D4—1316no—
592C4×D4—1332no—
593C4×D4—138no—
594C4×D4—1316no—
595C4×D4—1332no—
596C4×D4—1316no—
597C4×D4—1316no—
598C4×D4—138no—
599C4×D4—1316no—
600#117—138no—
601#117—1316no—
602#117—1316no—
603#117—1316no—
604#117—1332no—
605#117—1332no—
606C2×C4⋊C4—134no—
607C2×C4⋊C4—132no—
608C2×C4⋊C4—131no—
609C2×C4⋊C4—132no—
610C2×C4⋊C4—132no—
611C2×C4⋊C4—134no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—134no—
617C2×C4⋊C4—132no—
618C2×C4⋊C4—131no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4—134no—
621C2×C4⋊C4—1332no—
622C2×C4⋊C4—1316no—
623C2×C4⋊C4—1316no—
624C2×C4⋊C4—1332no—
625C2×C4⋊C4—1316no—
626C2×C4⋊C4C22×D1311yescharacteristic
627C2×C4⋊C4C22×D1311yescharacteristic
628C2×C4⋊C4C22×D1312yes—
629C2×C4⋊C4C22×D1314yes—
630C2×C4⋊C4C22×D1314yes—
631C2×C4⋊C4C22×D1312yes—
632C2×C4⋊C4C22×D1312yes—
633C2×C4⋊C4C22×D1312yes—
634C2×C4⋊C4C22×D1314yes—
635C2×C22⋊C4—132no—
636C2×C22⋊C4—132no—
637C2×C22⋊C4—132no—
638C2×C22⋊C4—132no—
639C2×C22⋊C4—134no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—132no—
642C2×C22⋊C4—134no—
643C2×C22⋊C4—134no—
644C2×C22⋊C4—134no—
645C2×C22⋊C4—132no—
646C2×C22⋊C4—132no—
647C2×C42—132no—
648C2×C42—131no—
649C2×C42—134no—
650C2×C42—131no—
651C2×C42—132no—
652C2×C42—131no—
653C2×C42—1316no—
654C2×C42—138no—
655C2×C42C22×D1314yes—
656C2×C42C22×D1312yes—
657C2×C42C22×D1312yes—
658C2×C42C22×D1311yescharacteristic
659C2×C13#351514yescomplemented
660C2×C13C23×#4111yescharacteristic
661C2×C13C22×2−1+411yescharacteristic
662C2×C13C2×#58511yescharacteristic
663D13—28no—
664D13—42no—
665D13—44no—
666C24—132no—
667C24—131no—
668C24—132no—
669#41—2632no—
670#41—2664no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—138no—
675C2×Q8—524no—
676C2×Q8C23×D1314yes—
677C2×Q8C23×D1318yes—
678C2×Q8C23×D1314yes—
679C2×D4—138no—
680C2×D4—134no—
681C2×D4—134no—
682C2×D4—138no—
683C2×D4—1316no—
684C2×D4—138no—
685C2×D4—268no—
686C2×D4—2616no—
687C2×D4—264no—
688C2×D4—524no—
689C22×C4—131no—
690C22×C4—131no—
691C22×C4—131no—
692C22×C4—132no—
693C22×C4—134no—
694C22×C4—132no—
695C22×C4—138no—
696C22×C4—138no—
697C22×C4—134no—
698C22×C4—134no—
699C22×C4—1316no—
700C22×C4—138no—
701C22×C4—138no—
702C22×C4—134no—
703C22×C4—1316no—
704C22×C4—1316no—
705C22×C4—2616no—
706C22×C4—268no—
707C22×C4—268no—
708C22×C4—264no—
709C22×C4—268no—
710C22×C4—264no—
711C22×C4—524no—
712C22×C4—528no—
713C22×C4—528no—
714C22×C4—522no—
715C22×C4C23×D1312yes—
716C22×C4C23×D1311yescharacteristic
717C22×C4C23×D1314yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1311yescharacteristic
723C4⋊C4—1316no—
724C4⋊C4—138no—
725C4⋊C4—134no—
726C4⋊C4—138no—
727C4⋊C4—138no—
728C4⋊C4—1316no—
729C4⋊C4—138no—
730C4⋊C4—1316no—
731C4⋊C4—1316no—
732C4⋊C4—1316no—
733C4⋊C4—1316no—
734C4⋊C4—138no—
735C4⋊C4—134no—
736C4⋊C4—138no—
737C4⋊C4—1316no—
738C4⋊C4C23×D1314yes—
739C4⋊C4C23×D1314yes—
740C4⋊C4C23×D1318yes—
741C4⋊C4C23×D13116yes—
742C4⋊C4C23×D13116yes—
743C4⋊C4C23×D1318yes—
744C4⋊C4C23×D1318yes—
745C4⋊C4C23×D1318yes—
746C4⋊C4C23×D13116yes—
747C22⋊C4—138no—
748C22⋊C4—138no—
749C22⋊C4—138no—
750C22⋊C4—138no—
751C22⋊C4—1316no—
752C22⋊C4—138no—
753C22⋊C4—138no—
754C22⋊C4—1316no—
755C22⋊C4—1316no—
756C22⋊C4—1316no—
757C22⋊C4—138no—
758C22⋊C4—138no—
759C42—134no—
760C42—138no—
761C42—134no—
762C42—134no—
763C42—138no—
764C42—1316no—
765C42C23×D1318yes—
766C42C23×D1314yes—
767C42C23×D13116yes—
768C42C23×D1318yes—
769C13C2×#351511yescharacteristic, complemented, Sylow
770C23—138no—
771C23—134no—
772C23—132no—
773C23—134no—
774C23—264no—
775C23—264no—
776C23—262no—
777C23—264no—
778C23—262no—
779C23—264no—
780C23—264no—
781C23—262no—
782C23C24×D1311yescharacteristic
783Q8—28no—
784Q8—28no—
785Q8—216no—
786Q8—528no—
787D4—1316no—
788D4—2616no—
789D4—2632no—
790D4—268no—
791D4—528no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—132no—
799C2×C4—132no—
800C2×C4—132no—
801C2×C4—134no—
802C2×C4—138no—
803C2×C4—134no—
804C2×C4—2616no—
805C2×C4—2632no—
806C2×C4—262no—
807C2×C4—264no—
808C2×C4—262no—
809C2×C4—264no—
810C2×C4—262no—
811C2×C4—268no—
812C2×C4—2616no—
813C2×C4—268no—
814C2×C4—268no—
815C2×C4—2616no—
816C2×C4—528no—
817C2×C4—5216no—
818C2×C4—5216no—
819C2×C4—524no—
820C2×C4#8825414yes—
821C2×C4#41×D1314yes—
822C2×C4C24×D1314yes—
823C2×C4C24×D1312yes—
824C2×C4C24×D1314yes—
825C2×C4C24×D1318yes—
826C2×C4C24×D1314yes—
827C2×C4C24×D1314yes—
828C2×C4C24×D1312yes—
829C2×C4C24×D1312yes—
830C22—138no—
831C22—2616no—
832C22—264no—
833C22—264no—
834C22—262no—
835C22—264no—
836C22—262no—
837C22—264no—
838C22—264no—
839C22—262no—
840C22—524no—
841C22—528no—
842C22C2×#8825412yes—
843C22C2×#41×D1312yes—
844C22#1171965212yes—
845C22C25×D1311yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—262no—
853C4—264no—
854C4—262no—
855C4—264no—
856C4—262no—
857C4—268no—
858C4C2×#8825414yes—
859C4C2×#41×D1314yes—
860C2—268no—
861C2—522no—
862C2—524no—
863C2#1312881314yesdirect product factor
864C2C22×#41×D1311yescharacteristic
865C2C22×#8825411yescharacteristic
866C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#557C2
socleC23×C13C25
hypercenterC2×#557D13
hypocenterC13C2×#3515
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13128813C2direct (N × H)
2. C2×#11719284C2semidirect
3. C2×#11719284C2semidirect
4. C2×#11719400C2semidirect
5. C2×#11719286C2semidirect
6. C2×#11719286C2semidirect
7. C2×#11719398C2semidirect
8. C2×#11719431C2semidirect
9. C2×#11719431C2semidirect
10. C2×#11719436C2semidirect
11. C2×#11719397C2semidirect
12. C2×#11719433C2semidirect
13. C2×#11719285C2semidirect
14. C2×#11719285C2semidirect
15. C2×D13×#125C2semidirect
16. C2×#11719279C2semidirect
17. C2×C4×#6131C2semidirect
18. C2×C13×#557C2semidirect
21. C13×#557C22semidirect
38. #11719436C22semidirect
39. #11719433C22semidirect
40. #11719431C22semidirect
41. #11719431C22semidirect
42. #11719400C22semidirect
43. #11719398C22semidirect
44. #11719397C22semidirect
45. D13×#125C22semidirect
46. #11719286C22semidirect
47. #11719286C22semidirect
48. #11719285C22semidirect
49. #11719285C22semidirect
50. #11719284C22semidirect
51. #11719284C22semidirect
52. #11719279C22semidirect
53. C4×#6131C22semidirect
338. C2×#557D13semidirect
417. #557C2×D13semidirect
659. C2×C13#3515semidirect
769. C13C2×#3515semidirect
863. C2#13128813direct (N × H)

Maximal subgroups

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

subgroupindex
#131288132
C2×#117192842
C2×#117194002
C2×#117192862
C2×#117193982
C2×#117194312
C2×#117194362
C2×#117193972
C2×#117194332
C2×#117192852
C2×D13×#1252
C2×#117192792
C2×C4×#61312
C2×C13×#5572
C2×#351513