Finite Group Databasebeta

← C2×#13126922 #16739450

Subgroups — C2×#13126922 #16739450

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719284C211yesmaximal, characteristic, complemented
2C2×#11719259C211yesmaximal, characteristic
3#13126922C2116yesmaximal, direct product factor
4C2×#11718375C211yesmaximal, characteristic, complemented
5C2×#11718545C211yesmaximal, characteristic, complemented
6C2×#11718543C211yesmaximal, characteristic, complemented
7C2×#11718668C211yesmaximal, characteristic, complemented
8C2×#11718473C211yesmaximal, characteristic, complemented
9C2×#11718474C211yesmaximal, characteristic, complemented
10C2×#11718689C211yesmaximal, characteristic, complemented
11C2×#11718834C211yesmaximal, characteristic, complemented
12C2×#11718830C211yesmaximal, characteristic, complemented
13C2×#11718367C211yesmaximal, characteristic, complemented
14C2×#11718432C211yesmaximal, characteristic, complemented
15C2×D13×#102C211yesmaximal, characteristic, complemented
16C2×C13×#440C211yesmaximal, characteristic, complemented
17C22×#6129C2211yescharacteristic
18C22×D4×D13C2211yescharacteristic
19C22×C13×SD16C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic, complemented
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88200C2211yescharacteristic
23C2×#88200C2211yescharacteristic, complemented
24C22×#6107C2211yescharacteristic, complemented
25C22×#6106C2211yescharacteristic
26C2×#88184—21no—
27C22×#6103—21no—
28C22×#6094C2211yescharacteristic, complemented
29C22×C8×D13C2211yescharacteristic
30#11719284—24no—
31#11719284C2218yescomplemented
32#11719259—24no—
33#11719259C2218yes—
34C2×#88151C2211yescharacteristic
35C2×#88150—21no—
36C2×#88150—21no—
37C2×#88149C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic, complemented
40C2×#88140—21no—
41C2×#88136—21no—
42C2×#88129C2211yescharacteristic
43C2×C4×D52—21no—
44C2×C4×D52C2211yescharacteristic
45C2×#88124—21no—
46C2×#88123C2211yescharacteristic, complemented
47C13×#440C2218yescomplemented
48C2×C13×#107C2211yescharacteristic, complemented
49C2×C13×#103C2211yescharacteristic, complemented
50C2×C13×#102C2211yescharacteristic
51C2×C13×#97C2211yescharacteristic, complemented
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718834C2218yescomplemented
55#11718830C2218yescomplemented
56C2×#88061C2211yescharacteristic
57C2×#88061C2211yescharacteristic
58C2×#88060C2211yescharacteristic
59C2×#88060C2211yescharacteristic, complemented
60C2×#88056C2211yescharacteristic, complemented
61C2×#88056C2211yescharacteristic, complemented
62#11718689C2218yescomplemented
63#11718668C2218yescomplemented
64C2×#88050C2211yescharacteristic, complemented
65C2×#88049C2211yescharacteristic
66C2×#88047C2211yescharacteristic, complemented
67C2×#88047C2211yescharacteristic, complemented
68C2×C4⋊#1055C2211yescharacteristic, complemented
69#11718545C2218yescomplemented
70#11718543C2218yescomplemented
71#11718474C2218yescomplemented
72#11718473C2218yescomplemented
73#11718432C2218yescomplemented
74D13×#102C2218yescomplemented
75#11718375C2218yescomplemented
76#11718367C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C22×C22⋊D13—21no—
82C22×C22⋊D13—21no—
83C23×Dic13—21no—
84C2×#6129—24no—
85C2×#6129—22no—
86C2×#6129—42no—
87C2×#6129C2314yes—
88C2×D4×D13—24no—
89C2×D4×D13—22no—
90C2×D4×D13—42no—
91C2×D4×D13C2314yes—
92C22×D52—21no—
93C22×D52D411yescharacteristic
94C22×D52C2311yescharacteristic
95C22×C4×D13—21no—
96C22×C4×D13—21no—
97C22×C4×D13C2311yescharacteristic
98C22×C4×D13C2311yescharacteristic
99C22×Dic26—21no—
100C22×Dic26C2311yescharacteristic
101C2×C13×SD16—24no—
102C2×C13×SD16C2314yes—
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2311yescharacteristic
105C4×Q8×C13—22no—
106C4×Q8×C13C2314yescomplemented
107C4×D4×C13—22no—
108C4×D4×C13C2314yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C42×C13—21no—
114C2×C42×C13C2311yescharacteristic
115#88200—22no—
116#88200—22no—
117#88200C2314yes—
118#88200C2314yescomplemented
119C2×#6107—42no—
120C2×#6107C2314yescomplemented
121C2×#6106—42no—
122C2×#6106C2314yes—
123#88184—28no—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103—21no—
129C2×#6103—21no—
130C2×#6103—28no—
131C2×#6103D411yescharacteristic
132C2×#6103D411yescharacteristic
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13—21no—
135C2×C4⋊Dic13D411yescharacteristic
136C2×C4⋊Dic13C2311yescharacteristic
137C2×C4⋊Dic13C2311yescharacteristic
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C2×#6094—42no—
145C2×#6094C2314yescomplemented
146C2×C8×D13—42no—
147C2×C8×D13C2314yes—
148#88151—22no—
149#88151C2314yes—
150#88150—28no—
151#88150—28no—
152#88149—22no—
153#88149C2314yes—
154C4⋊C4×D13—22no—
155C4⋊C4×D13—22no—
156C4⋊C4×D13C2314yes—
157C4⋊C4×D13C2314yescomplemented
158#88140—28no—
159#88136—28no—
160#88129—22no—
161#88129C2314yes—
162C4×D52—28no—
163C4×D52D414yes—
164C4×D52C2314yes—
165#88124—28no—
166#88123—22no—
167#88123C2314yescomplemented
168C13×#107C2314yescomplemented
169C13×#103C2314yescomplemented
170C13×#102C2314yes—
171C13×#97C2314yescomplemented
172#88072C2314yes—
173#88072C2314yes—
174#88061C2314yes—
175#88061C2314yes—
176#88060C2314yes—
177#88060C2314yescomplemented
178#88056C2314yescomplemented
179#88056C2314yescomplemented
180#88050C2314yescomplemented
181#88049C2314yes—
182#88047C2314yescomplemented
183#88047C2314yescomplemented
184C4⋊#1055C2314yescomplemented
185C2×#3314—131nomaximal, Sylow
186C24×C13—21no—
187C23×D13—21no—
188C23×D13—24no—
189C23×D13—44no—
190C23×D13—44no—
191C23×D13—82no—
192C23×D13C2×D411yescharacteristic
193C23×D13C2×D411yescharacteristic
194C2×Q8×C13—21no—
195C2×Q8×C13—22no—
196C2×Q8×C13—22no—
197C2×Q8×C13C2412yes—
198C2×D4×C13—21no—
199C2×D4×C13—22no—
200C2×D4×C13#4114yes—
201C2×D4×C13C2412yes—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—24no—
206C22×C4×C13—82no—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2411yescharacteristic
210C2×C22⋊D13—24no—
211C2×C22⋊D13—24no—
212C2×C22⋊D13—44no—
213C2×C22⋊D13—44no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—24no—
218C22×Dic13—44no—
219C22×Dic13C2×D411yescharacteristic
220C22×Dic13C2×D411yescharacteristic
221#6129—28no—
222#6129—44no—
223#6129—48no—
224D4×D13—28no—
225D4×D13—44no—
226D4×D13—48no—
227C2×D52—24no—
228C2×D52—22no—
229C2×D52—22no—
230C2×D52—21no—
231C2×D52—24no—
232C2×D52—82no—
233C2×D52C2×D414yes—
234C2×D52C2412yes—
235C2×C4×D13—22no—
236C2×C4×D13—22no—
237C2×C4×D13—22no—
238C2×C4×D13—22no—
239C2×C4×D13—24no—
240C2×C4×D13—24no—
241C2×C4×D13—82no—
242C2×C4×D13—82no—
243C2×C4×D13C2×D412yes—
244C2×C4×D13C2×D412yes—
245C2×C4×D13C2412yes—
246C2×C4×D13C2412yes—
247C2×Dic26—22no—
248C2×Dic26—22no—
249C2×Dic26—21no—
250C2×Dic26—24no—
251C2×Dic26—82no—
252C2×Dic26C2412yes—
253C13×SD16—28no—
254C2×C8×C13—22no—
255C2×C8×C13—22no—
256C2×C8×C13C2412yes—
257C2×C8×C13C2412yes—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—24no—
261C13×C4⋊C4C2412yes—
262C13×C4⋊C4C2412yes—
263C13×C22⋊C4—24no—
264C42×C13—24no—
265C42×C13C2×D412yes—
266C42×C13C2412yes—
267#6107—44no—
268#6106—44no—
269#6103—24no—
270#6103—24no—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274#6103—24no—
275#6103C2×D414yes—
276#6103C2×D414yes—
277C4⋊Dic13—21no—
278C4⋊Dic13—21no—
279C4⋊Dic13—24no—
280C4⋊Dic13—24no—
281C4⋊Dic13C2×D414yes—
282C4⋊Dic13C2412yes—
283C4⋊Dic13C2412yes—
284#6101—24no—
285#6101—24no—
286#6101—24no—
287#6101—24no—
288C2×#1055—22no—
289C2×#1055—22no—
290C2×#1055C2412yes—
291C2×#1055C2412yes—
292#6094—44no—
293C8×D13—44no—
294C2×#554—131no—
295C2×#546—131no—
296#3314—1316no—
297C2×#489—131no—
298C2×#484—131no—
299C2×#480—131no—
300C2×#474—131no—
301C2×#468—131no—
302C2×#467—131no—
303C2×#464—131no—
304C2×#452—131no—
305C2×#450—131no—
306C2×#440D1311yescharacteristic, complemented
307C2×#435—131no—
308C2×#417—131no—
309C22×#102—131no—
310C23×C13—24no—
311C23×C13—22no—
312C23×C13—42no—
313C23×C13—42no—
314C23×C13C22×D411yescharacteristic
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—48no—
322C22×D13—42no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—48no—
326C22×D13—84no—
327C22×D13—816no—
328C22×D13#13714yes—
329C22×D13C22×D412yes—
330C22×D13C22×D412yes—
331Q8×C13—22no—
332Q8×C13—22no—
333Q8×C13—42no—
334D4×C13—24no—
335D4×C13—22no—
336D4×C13C2×#4114yes—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—84no—
346C2×C4×C13C22×D412yes—
347C2×C4×C13C22×D412yes—
348C2×C4×C13C22×D411yescharacteristic
349C2×C4×C13C2×#4112yes—
350C2×C4×C13H(5,𝔽2)12yes—
351C2×C4×C13C2511yescharacteristic
352C22⋊D13—48no—
353C22⋊D13—48no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—48no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13C22×D412yes—
364C2×Dic13C22×D412yes—
365D52—28no—
366D52—22no—
367D52—22no—
368D52—42no—
369D52—84no—
370C4×D13—24no—
371C4×D13—24no—
372C4×D13—22no—
373C4×D13—22no—
374C4×D13—22no—
375C4×D13—22no—
376C4×D13—84no—
377C4×D13—84no—
378Dic26—22no—
379Dic26—22no—
380Dic26—42no—
381Dic26—84no—
382C8×C13—22no—
383C8×C13—22no—
384#1055—22no—
385#1055—22no—
386C22×#41—131no—
387C23×D4—131no—
388C22×Q16—131no—
389C22×SD16—131no—
390C22×SD16C2×D1311yescharacteristic
391C22×M16—131no—
392C23×C8—131no—
393#554—138no—
394#554—264no—
395#546—138no—
396#546—264no—
397C2×C4⋊Q8—131no—
398C2×#125—261no—
399C2×#124—131no—
400C2×#123—261no—
401C2×C22⋊Q8—131no—
402C2×C22⋊Q8—131no—
403C2×C22⋊Q8—131no—
404C2×C22⋊Q8—261no—
405C2×C22⋊Q8—261no—
406C2×#121—131no—
407C2×#121—261no—
408C2×#120—261no—
409C2×C4×Q8C2×D1311yescharacteristic, complemented
410C2×C4×D4—131no—
411C2×C4×D4—261no—
412C2×C4×D4C2×D1311yescharacteristic
413C22×C4⋊C4—131no—
414C22×C4⋊C4—131no—
415C22×C22⋊C4—261no—
416#489—138no—
417#484—138no—
418#480—138no—
419#474—138no—
420#468—138no—
421#467—138no—
422#464—138no—
423#452—138no—
424#450—138no—
425#440C2×D1318yescomplemented
426#435—138no—
427C2×#107—131no—
428C2×#107—131no—
429C2×#107C2×D1311yescharacteristic, complemented
430C2×C4⋊C8—131no—
431#417—138no—
432C2×#103—131no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103C2×D1311yescharacteristic, complemented
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×#102—131no—
440C2×#102—131no—
441C2×#102—138no—
442C2×#102C2×D1311yescharacteristic
443C2×C22⋊C8—131no—
444C2×C22⋊C8—131no—
445C2×#97C2×D1311yescharacteristic, complemented
446C22×C13—24no—
447C22×C13—48no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13#54612yes—
451C22×C13C2×#13712yes—
452C22×C13#57612yes—
453C22×C13C23×D411yescharacteristic
454C2×D13—22no—
455C2×D13—28no—
456C2×D13—22no—
457C2×D13—22no—
458C2×D13—22no—
459C2×D13—22no—
460C2×D13—44no—
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—816no—
465C2×D13—84no—
466C2×D13C2×#13714yes—
467C4×C13—22no—
468C4×C13—22no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13—42no—
472C4×C13#54612yes—
473C4×C13C22×#4111yescharacteristic
474C4×C13C2×H(5,𝔽2)11yescharacteristic
475Dic13—22no—
476Dic13—22no—
477Dic13—42no—
478Dic13—42no—
479Dic13—42no—
480C25—261no—
481C2×#41—134no—
482C2×#41—262no—
483C2×#41—264no—
484C2×#41—522no—
485C22×Q8—131no—
486C22×Q8—261no—
487C22×Q8C22×D1311yescharacteristic
488C22×D4—134no—
489C22×D4—131no—
490C22×D4—131no—
491C22×D4—261no—
492C22×D4—262no—
493C22×D4—261no—
494C22×D4—264no—
495C22×D4—261no—
496C22×D4—522no—
497C22×D4C22×D1311yescharacteristic
498C23×C4—21no—
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—261no—
502C23×C4—261no—
503C23×C4—261no—
504C2×Q16—134no—
505C2×Q16—522no—
506C2×SD16—24no—
507C2×SD16—134no—
508C2×SD16—522no—
509C2×SD16C22×D1314yes—
510C2×M16—134no—
511C2×M16—522no—
512C22×C8—131no—
513C22×C8—131no—
514C22×C8—134no—
515C22×C8—522no—
516C22×C8C22×D1311yescharacteristic
517C22×C8C22×D1311yescharacteristic
518C4⋊Q8—134no—
519C4⋊Q8—262no—
520#125—268no—
521#124—134no—
522#124—262no—
523#123—268no—
524C22⋊Q8—134no—
525C22⋊Q8—134no—
526C22⋊Q8—134no—
527C22⋊Q8—268no—
528C22⋊Q8—268no—
529C22⋊Q8—262no—
530C22⋊Q8—262no—
531C22⋊Q8—262no—
532#121—134no—
533#121—268no—
534#121—262no—
535#120—268no—
536C4×Q8—22no—
537C4×Q8C22×D1314yescomplemented
538C4×D4—22no—
539C4×D4—134no—
540C4×D4—134no—
541C4×D4—268no—
542C4×D4C22×D1314yes—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—131no—
545C2×C4⋊C4—131no—
546C2×C4⋊C4—131no—
547C2×C4⋊C4—134no—
548C2×C4⋊C4—134no—
549C2×C4⋊C4—262no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4—261no—
552C2×C4⋊C4—261no—
553C2×C4⋊C4—261no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4—261no—
556C2×C4⋊C4—261no—
557C2×C4⋊C4C22×D1311yescharacteristic
558C2×C4⋊C4C22×D1311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—131no—
561C2×C22⋊C4—131no—
562C2×C22⋊C4—268no—
563C2×C22⋊C4—261no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—261no—
567C2×C22⋊C4—261no—
568C2×C22⋊C4—261no—
569C2×C42—21no—
570C2×C42C22×D1311yescharacteristic
571#107—134no—
572#107—134no—
573#107C22×D1314yescomplemented
574C4⋊C8—134no—
575#103—134no—
576#103—134no—
577#103—134no—
578#103C22×D1314yescomplemented
579#102—134no—
580#102—134no—
581#102—134no—
582#102—134no—
583#102—134no—
584#102C22×D1314yes—
585C22⋊C8—134no—
586C22⋊C8—134no—
587#97C22×D1314yescomplemented
588C2×C13—44no—
589C2×C13#331414yescomplemented
590C2×C13C2×#54611yescharacteristic
591C2×C13C22×#13711yescharacteristic
592C2×C13C2×#57611yescharacteristic
593D13—24no—
594D13—42no—
595D13—82no—
596C24—21no—
597C24—131no—
598C24—131no—
599C24—264no—
600C24—261no—
601C24—524no—
602C24—524no—
603C24—1042no—
604#41—268no—
605#41—524no—
606#41—528no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—132no—
611C2×Q8—261no—
612C2×Q8—264no—
613C2×Q8—262no—
614C2×Q8—262no—
615C2×Q8—1042no—
616C2×Q8C23×D1312yes—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—134no—
620C2×D4—132no—
621C2×D4—264no—
622C2×D4—264no—
623C2×D4—264no—
624C2×D4—268no—
625C2×D4—264no—
626C2×D4—262no—
627C2×D4—261no—
628C2×D4—262no—
629C2×D4—524no—
630C2×D4—528no—
631C2×D4—524no—
632C2×D4—524no—
633C2×D4—1042no—
634C2×D4#612714yes—
635C2×D4C23×D1312yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—131no—
642C22×C4—131no—
643C22×C4—132no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—264no—
648C22×C4—264no—
649C22×C4—264no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4—262no—
653C22×C4—262no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—524no—
658C22×C4—1042no—
659C22×C4—1042no—
660C22×C4D4×D1311yescharacteristic
661C22×C4D4×D1311yescharacteristic
662C22×C4C23×D1311yescharacteristic
663Q16—524no—
664SD16—28no—
665SD16—524no—
666M16—524no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—132no—
670C2×C8—132no—
671C2×C8—262no—
672C2×C8—262no—
673C2×C8—524no—
674C2×C8C23×D1312yes—
675C2×C8C23×D1312yes—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—134no—
680C4⋊C4—132no—
681C4⋊C4—132no—
682C4⋊C4—264no—
683C4⋊C4—264no—
684C4⋊C4—264no—
685C4⋊C4—264no—
686C4⋊C4—264no—
687C4⋊C4—261no—
688C4⋊C4—261no—
689C4⋊C4—264no—
690C4⋊C4C23×D1312yes—
691C4⋊C4C23×D1312yes—
692C22⋊C4—24no—
693C22⋊C4—134no—
694C22⋊C4—134no—
695C22⋊C4—264no—
696C22⋊C4—264no—
697C22⋊C4—264no—
698C22⋊C4—264no—
699C22⋊C4—264no—
700C22⋊C4—264no—
701C42—24no—
702C42D4×D1312yes—
703C42C23×D1312yes—
704C13C2×#331411yescharacteristic, complemented, Sylow
705C23—24no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—134no—
710C23—132no—
711C23—132no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—262no—
716C23—262no—
717C23—262no—
718C23—528no—
719C23—528no—
720C23—522no—
721C23—522no—
722C23—522no—
723C23—1044no—
724C23—10416no—
725C23C2×D4×D1311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—262no—
730Q8—262no—
731Q8—522no—
732Q8—1044no—
733D4—24no—
734D4—22no—
735D4—268no—
736D4—262no—
737D4—262no—
738D4—528no—
739D4—528no—
740D4—522no—
741D4—1044no—
742D4C2×#612714yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—132no—
753C2×C4—132no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—264no—
757C2×C4—264no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—528no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—1044no—
770C2×C4—1044no—
771C2×C4C2×#612712yes—
772C2×C4C2×D4×D1312yes—
773C2×C4C2×D4×D1312yes—
774C2×C4C2×D4×D1311yescharacteristic
775C2×C4#8825612yes—
776C2×C4C24×D1311yescharacteristic
777C8—22no—
778C8—22no—
779C8—262no—
780C8—262no—
781C22—24no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—134no—
786C22—268no—
787C22—262no—
788C22—262no—
789C22—262no—
790C22—262no—
791C22—262no—
792C22—524no—
793C22—522no—
794C22—522no—
795C22—522no—
796C22—10416no—
797C22—1044no—
798C22#1171925512yes—
799C22#1171947912yes—
800C22D13×#13712yes—
801C22C22×D4×D1311yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—262no—
808C4—262no—
809C4—522no—
810C4—522no—
811C4—522no—
812C4#1171925512yes—
813C4C22×#612711yescharacteristic
814C4C2×#8825611yescharacteristic
815C2—44no—
816C2—264no—
817C2—522no—
818C2—1042no—
819C2#1312692214yesdirect product factor
820C2C2×#1171925511yescharacteristic
821C2C2×D13×#13711yescharacteristic
822C2C2×#1171947911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#440C2
socleC23×C13C22×D4
prime radicalC2×#11719259C2
hypercenterC2×#440D13
hypocenterC13C2×#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#11719284C2semidirect
3. #13126922C2direct (N × H)
4. C2×#11718375C2semidirect
5. C2×#11718545C2semidirect
6. C2×#11718543C2semidirect
7. C2×#11718668C2semidirect
8. C2×#11718473C2semidirect
9. C2×#11718474C2semidirect
10. C2×#11718689C2semidirect
11. C2×#11718834C2semidirect
12. C2×#11718830C2semidirect
13. C2×#11718367C2semidirect
14. C2×#11718432C2semidirect
15. C2×D13×#102C2semidirect
16. C2×C13×#440C2semidirect
20. C2×C4×Q8×C13C22semidirect
23. C2×#88200C22semidirect
24. C22×#6107C22semidirect
28. C22×#6094C22semidirect
31. #11719284C22semidirect
39. C2×C4⋊C4×D13C22semidirect
46. C2×#88123C22semidirect
47. C13×#440C22semidirect
48. C2×C13×#107C22semidirect
49. C2×C13×#103C22semidirect
51. C2×C13×#97C22semidirect
54. #11718834C22semidirect
55. #11718830C22semidirect
59. C2×#88060C22semidirect
60. C2×#88056C22semidirect
61. C2×#88056C22semidirect
62. #11718689C22semidirect
63. #11718668C22semidirect
64. C2×#88050C22semidirect
66. C2×#88047C22semidirect
67. C2×#88047C22semidirect
68. C2×C4⋊#1055C22semidirect
69. #11718545C22semidirect
70. #11718543C22semidirect
71. #11718474C22semidirect
72. #11718473C22semidirect
73. #11718432C22semidirect
74. D13×#102C22semidirect
75. #11718375C22semidirect
76. #11718367C22semidirect
106. C4×Q8×C13C23semidirect
118. #88200C23semidirect
120. C2×#6107C23semidirect
145. C2×#6094C23semidirect
157. C4⋊C4×D13C23semidirect
167. #88123C23semidirect
168. C13×#107C23semidirect
169. C13×#103C23semidirect
171. C13×#97C23semidirect
177. #88060C23semidirect
178. #88056C23semidirect
179. #88056C23semidirect
180. #88050C23semidirect
182. #88047C23semidirect
183. #88047C23semidirect
184. C4⋊#1055C23semidirect
306. C2×#440D13semidirect
409. C2×C4×Q8C2×D13semidirect
425. #440C2×D13semidirect
429. C2×#107C2×D13semidirect
435. C2×#103C2×D13semidirect
445. C2×#97C2×D13semidirect
537. C4×Q8C22×D13semidirect
573. #107C22×D13semidirect
578. #103C22×D13semidirect
587. #97C22×D13semidirect
589. C2×C13#3314semidirect
704. C13C2×#3314semidirect
819. C2#13126922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192842
C2×#117192592
#131269222
C2×#117183752
C2×#117185452
C2×#117185432
C2×#117186682
C2×#117184732
C2×#117184742
C2×#117186892
C2×#117188342
C2×#117188302
C2×#117183672
C2×#117184322
C2×D13×#1022
C2×C13×#4402
C2×#331413