Finite Group Databasebeta

← C2×#13126923 #16739451

Subgroups — C2×#13126923 #16739451

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×#11719340C211yesmaximal, characteristic, complemented
2C2×#11719335C211yesmaximal, characteristic
3#13126923C2116yesmaximal, direct product factor
4C2×#11718456C211yesmaximal, characteristic, complemented
5C2×#11718705C211yesmaximal, characteristic, complemented
6C2×#11718543C211yesmaximal, characteristic, complemented
7C2×#11718551C211yesmaximal, characteristic, complemented
8C2×#11718473C211yesmaximal, characteristic, complemented
9C2×#11718846C211yesmaximal, characteristic, complemented
10C2×#11718848C211yesmaximal, characteristic, complemented
11C2×#11718707C211yesmaximal, characteristic, complemented
12C2×#11718478C211yesmaximal, characteristic, complemented
13C2×#11718772C211yesmaximal, characteristic, complemented
14C2×#11718464C211yesmaximal, characteristic, complemented
15C22×#88061C211yesmaximal, characteristic, complemented
16C2×C13×#467C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C22×C13×Q16C2211yescharacteristic, complemented
20C23×C8×C13C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×#88201C2211yescharacteristic
24C2×#88200C2211yescharacteristic, complemented
25C2×Q8×Dic13C2211yescharacteristic, complemented
26C22×#6106C2211yescharacteristic
27C22×#6106C2211yescharacteristic
28C2×C4×C22⋊D13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6094C2211yescharacteristic, complemented
31#11719340—24no—
32#11719340C2218yescomplemented
33#11719335—24no—
34#11719335C2218yes—
35C2×#88151—21no—
36C2×#88149—21no—
37C2×#88149C2211yescharacteristic
38C2×#88148—21no—
39C2×#88147C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic, complemented
41C2×#88143—21no—
42C2×#88142C2211yescharacteristic, complemented
43C2×#88136—21no—
44C2×#88135—21no—
45C2×C22⋊C4×D13—21no—
46C2×#88132—21no—
47C13×#467C2218yescomplemented
48C2×C13×#107C2211yescharacteristic, complemented
49C2×C13×#103C2211yescharacteristic, complemented
50C2×C13×#103C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×#88075C2211yescharacteristic, complemented
53C2×C22⋊#1055C2211yescharacteristic
54#11718848C2218yescomplemented
55#11718846C2218yescomplemented
56C2×#88061C2211yescharacteristic
57C2×#88061C2211yescharacteristic
58C2×#88061C2211yescharacteristic
59C2×#88061C2211yescharacteristic
60C2×#88061C2218yescomplemented
61#11718772C2218yescomplemented
62C2×#88060C2211yescharacteristic, complemented
63C2×#88055C2211yescharacteristic, complemented
64C2×#88054C2211yescharacteristic, complemented
65#11718707C2218yescomplemented
66#11718705C2218yescomplemented
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88047C2211yescharacteristic, complemented
70C2×#88047C2211yescharacteristic, complemented
71#11718551C2218yescomplemented
72#11718543C2218yescomplemented
73#11718478C2218yescomplemented
74#11718473C2218yescomplemented
75#11718464C2218yescomplemented
76#11718456C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13D411yescharacteristic
82C23×Dic13—21no—
83C2×#6131—22no—
84C2×#6131—24no—
85C2×#6131—42no—
86C2×#6131C2314yes—
87C22×D52—24no—
88C22×D52—21no—
89C22×D52—21no—
90C22×D52—22no—
91C22×D52—21no—
92C22×D52—42no—
93C22×D52C2311yescharacteristic
94C22×D52C2314yes—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×C4×D13—21no—
98C22×C4×D13—21no—
99C22×C4×D13C2311yescharacteristic
100C22×Dic26—21no—
101C2×C13×Q16—42no—
102C2×C13×Q16C2314yescomplemented
103C22×C8×C13—42no—
104C22×C8×C13C2311yescharacteristic
105C22×C8×C13C2311yescharacteristic
106C22×C8×C13C2314yes—
107C13×C22⋊Q8—22no—
108C13×C22⋊Q8—22no—
109C13×C22⋊Q8C2314yes—
110C13×C22⋊Q8C2314yes—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C22⋊Dic13D411yescharacteristic
118#88201—22no—
119#88201C2314yes—
120#88200—22no—
121#88200C2314yescomplemented
122Q8×Dic13—22no—
123Q8×Dic13C2314yescomplemented
124C2×#6106—24no—
125C2×#6106—42no—
126C2×#6106C2314yes—
127C2×#6106C2314yes—
128C4×C22⋊D13D414yes—
129C4×C22⋊D13C2314yes—
130C2×#6103—21no—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×#6103—21no—
134C2×#6103—21no—
135C2×#6103D411yescharacteristic
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—22no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2314yes—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101D411yescharacteristic
146C2×C4×Dic13—21no—
147C2×C4×Dic13C2311yescharacteristic
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C2×#6094—42no—
151C2×#6094C2314yescomplemented
152#88151—28no—
153#88149—22no—
154#88149—28no—
155#88149C2314yes—
156#88148—28no—
157#88147—22no—
158#88147C2314yes—
159C4⋊C4×D13—22no—
160C4⋊C4×D13C2314yescomplemented
161#88143—28no—
162#88142—22no—
163#88142C2314yescomplemented
164#88136—28no—
165#88135—28no—
166C22⋊C4×D13—28no—
167#88132—28no—
168C13×#107C2314yescomplemented
169C13×#103C2314yescomplemented
170C13×#103C2314yescomplemented
171#88075C2314yescomplemented
172#88075C2314yescomplemented
173C22⋊#1055C2314yes—
174#88061C2314yes—
175#88061C2314yes—
176#88061C2314yes—
177#88061C2314yes—
178#88060C2314yescomplemented
179#88055C2314yescomplemented
180#88054C2314yescomplemented
181#88049C2314yes—
182#88049C2314yes—
183#88047C2314yescomplemented
184#88047C2314yescomplemented
185C2×#3314—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C23×D13—21no—
188C23×D13—21no—
189C23×D13—24no—
190C23×D13—44no—
191C23×D13—44no—
192C23×D13—82no—
193C23×D13C2×D411yescharacteristic
194C2×Q8×C13—21no—
195C2×Q8×C13—21no—
196C2×Q8×C13—22no—
197C2×Q8×C13—22no—
198C2×Q8×C13—22no—
199C2×Q8×C13—22no—
200C2×Q8×C13C2412yes—
201C2×Q8×C13C2412yes—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2411yescharacteristic
212C2×C22⋊D13—24no—
213C2×C22⋊D13C2×D414yes—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—24no—
217C22×Dic13—82no—
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220C22×Dic13C2×D411yescharacteristic
221#6131—28no—
222#6131—44no—
223#6131—48no—
224C2×D52—21no—
225C2×D52—22no—
226C2×D52—22no—
227C2×D52—22no—
228C2×D52—28no—
229C2×D52—24no—
230C2×D52—24no—
231C2×D52—21no—
232C2×D52—24no—
233C2×D52—44no—
234C2×D52—48no—
235C2×D52—44no—
236C2×D52—44no—
237C2×D52—82no—
238C2×D52#4114yes—
239C2×D52C2412yes—
240C2×D52C2412yes—
241C2×C4×D13—22no—
242C2×C4×D13—22no—
243C2×C4×D13—24no—
244C2×C4×D13—24no—
245C2×C4×D13—24no—
246C2×C4×D13—44no—
247C2×C4×D13—82no—
248C2×C4×D13—82no—
249C2×C4×D13C2×D412yes—
250C2×C4×D13C2412yes—
251C2×Dic26—24no—
252C2×Dic26—82no—
253C13×Q16—44no—
254C2×C8×C13—22no—
255C2×C8×C13—22no—
256C2×C8×C13—44no—
257C2×C8×C13C2412yes—
258C2×C8×C13C2412yes—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—24no—
261C13×C4⋊C4—21no—
262C13×C4⋊C4—24no—
263C13×C4⋊C4C2412yes—
264C13×C4⋊C4C2412yes—
265C13×C22⋊C4—24no—
266C13×C22⋊C4—24no—
267C22⋊Dic13C2×D414yes—
268#6106—28no—
269#6106—44no—
270#6103—24no—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274#6103—24no—
275#6103C2×D414yes—
276C4⋊Dic13—21no—
277C4⋊Dic13—24no—
278C4⋊Dic13—21no—
279C4⋊Dic13—24no—
280C4⋊Dic13C2412yes—
281C4⋊Dic13C2412yes—
282#6101—24no—
283#6101—24no—
284#6101—24no—
285#6101C2×D414yes—
286C4×Dic13—24no—
287C4×Dic13C2×D412yes—
288C4×Dic13C2412yes—
289C2×#1055—22no—
290C2×#1055—22no—
291C2×#1055C2412yes—
292C2×#1055C2412yes—
293#6094—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×#467D1311yescharacteristic, complemented
303C2×#464—131no—
304C2×#452—131no—
305C2×#450—131no—
306C2×#440—131no—
307C2×#435—131no—
308C2×#417—131no—
309C22×#102—131no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13#13714yes—
313C23×C13C22×D412yes—
314C23×C13C22×D411yescharacteristic
315C22×D13—22no—
316C22×D13—24no—
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—42no—
327C22×D13—42no—
328C22×D13—84no—
329C22×D13—816no—
330C22×D13C22×D412yes—
331Q8×C13—22no—
332Q8×C13—22no—
333Q8×C13—22no—
334Q8×C13—22no—
335Q8×C13—42no—
336Q8×C13—42no—
337C2×C4×C13—22no—
338C2×C4×C13—24no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—42no—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D411yescharacteristic
351C2×C4×C13C2×#4112yes—
352C2×C4×C13H(5,𝔽2)12yes—
353C2×C4×C13C2511yescharacteristic
354C22⋊D13—28no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—84no—
363C2×Dic13C22×D412yes—
364C2×Dic13C22×D412yes—
365C2×Dic13C22×D412yes—
366D52—24no—
367D52—22no—
368D52—22no—
369D52—22no—
370D52—48no—
371D52—48no—
372D52—42no—
373D52—84no—
374D52C2×#4114yes—
375C4×D13—24no—
376C4×D13—22no—
377C4×D13—22no—
378C4×D13—48no—
379C4×D13—84no—
380C4×D13—84no—
381Dic26—84no—
382C8×C13—22no—
383C8×C13—22no—
384#1055—22no—
385#1055—22no—
386C22×#41—131no—
387C23×D4—131no—
388C22×Q16C2×D1311yescharacteristic, complemented
389C22×SD16—131no—
390C22×SD16—131no—
391C22×M16—131no—
392C23×C8C2×D1311yescharacteristic
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—261no—
403C2×C22⋊Q8—261no—
404C2×C22⋊Q8C2×D1311yescharacteristic
405C2×C22⋊Q8C2×D1311yescharacteristic
406C2×#121—131no—
407C2×#121—261no—
408C2×#120—261no—
409C2×C4×Q8—131no—
410C2×C4×D4—131no—
411C2×C4×D4—131no—
412C2×C4×D4—261no—
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#467C2×D1318yescomplemented
422#464—138no—
423#452—138no—
424#450—138no—
425#440—138no—
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×#103C2×D1311yescharacteristic, complemented
435C2×#103C2×D1311yescharacteristic, complemented
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×#102—131no—
440C2×#102—138no—
441C2×#102—131no—
442C2×#102—131no—
443C2×C22⋊C8—131no—
444C2×C22⋊C8—131no—
445C2×#97—131no—
446C22×C13—22no—
447C22×C13—28no—
448C22×C13—22no—
449C22×C13#54612yes—
450C22×C13C2×#13714yes—
451C22×C13C2×#13712yes—
452C22×C13#57612yes—
453C22×C13C23×D411yescharacteristic
454C2×D13—22no—
455C2×D13—24no—
456C2×D13—22no—
457C2×D13—22no—
458C2×D13—44no—
459C2×D13—48no—
460C2×D13—42no—
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—816no—
466C2×D13—84no—
467C4×C13—22no—
468C4×C13—42no—
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—22no—
478Dic13—42no—
479Dic13—42no—
480C25—261no—
481C2×#41—134no—
482C2×#41—262no—
483C2×#41—264no—
484C2×#41—522no—
485C22×Q8—261no—
486C22×Q8C22×D1311yescharacteristic
487C22×Q8C22×D1311yescharacteristic
488C22×D4—131no—
489C22×D4—131no—
490C22×D4—131no—
491C22×D4—134no—
492C22×D4—264no—
493C22×D4—261no—
494C22×D4—261no—
495C22×D4—261no—
496C22×D4—262no—
497C22×D4—522no—
498C23×C4—131no—
499C23×C4—261no—
500C23×C4—261no—
501C23×C4—261no—
502C23×C4—261no—
503C23×C4C22×D1311yescharacteristic
504C2×Q16—42no—
505C2×Q16C22×D1314yescomplemented
506C2×SD16—134no—
507C2×SD16—134no—
508C2×SD16—264no—
509C2×SD16—522no—
510C2×M16—134no—
511C2×M16—522no—
512C22×C8—42no—
513C22×C8—131no—
514C22×C8—131no—
515C22×C8C22×D1311yescharacteristic
516C22×C8C22×D1311yescharacteristic
517C22×C8C22×D1314yes—
518C4⋊Q8—134no—
519C4⋊Q8—262no—
520#125—268no—
521#124—134no—
522#124—262no—
523#123—268no—
524C22⋊Q8—22no—
525C22⋊Q8—22no—
526C22⋊Q8—134no—
527C22⋊Q8—268no—
528C22⋊Q8—268no—
529C22⋊Q8—262no—
530C22⋊Q8C22×D1314yes—
531C22⋊Q8C22×D1314yes—
532#121—134no—
533#121—268no—
534#121—262no—
535#120—268no—
536C4×Q8—134no—
537C4×Q8—262no—
538C4×D4—134no—
539C4×D4—134no—
540C4×D4—134no—
541C4×D4—262no—
542C4×D4—268no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—131no—
546C2×C4⋊C4—131no—
547C2×C4⋊C4—131no—
548C2×C4⋊C4—134no—
549C2×C4⋊C4—134no—
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—262no—
557C2×C4⋊C4C22×D1311yescharacteristic
558C2×C4⋊C4C22×D1311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—131no—
562C2×C22⋊C4—131no—
563C2×C22⋊C4—268no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—261no—
567C2×C22⋊C4—261no—
568C2×C22⋊C4—261no—
569C2×C42—131no—
570C2×C42—261no—
571#107—134no—
572#107—134no—
573#107C22×D1314yescomplemented
574C4⋊C8—134no—
575#103—134no—
576#103—134no—
577#103C22×D1314yescomplemented
578#103C22×D1314yescomplemented
579#102—134no—
580#102—134no—
581#102—134no—
582#102—134no—
583#102—134no—
584#102—134no—
585C22⋊C8—134no—
586C22⋊C8—134no—
587#97—134no—
588C2×C13—24no—
589C2×C13#331414yescomplemented
590C2×C13C2×#54611yescharacteristic
591C2×C13C22×#13711yescharacteristic
592C2×C13C2×#57611yescharacteristic
593D13—42no—
594D13—44no—
595D13—82no—
596C24—131no—
597C24—261no—
598C24—261no—
599C24—264no—
600C24—524no—
601C24—524no—
602C24—1042no—
603C24D4×D1311yescharacteristic
604#41—268no—
605#41—524no—
606#41—528no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—264no—
614C2×Q8—1042no—
615C2×Q8C23×D1312yes—
616C2×Q8C23×D1312yes—
617C2×D4—134no—
618C2×D4—134no—
619C2×D4—132no—
620C2×D4—132no—
621C2×D4—268no—
622C2×D4—264no—
623C2×D4—264no—
624C2×D4—264no—
625C2×D4—261no—
626C2×D4—264no—
627C2×D4—261no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—262no—
631C2×D4—524no—
632C2×D4—528no—
633C2×D4—524no—
634C2×D4—524no—
635C2×D4—1042no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—131no—
643C22×C4—131no—
644C22×C4—131no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—264no—
648C22×C4—264no—
649C22×C4—264no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—264no—
655C22×C4—524no—
656C22×C4—1042no—
657C22×C4—1042no—
658C22×C4—1042no—
659C22×C4D4×D1312yes—
660C22×C4D4×D1311yescharacteristic
661C22×C4C23×D1312yes—
662C22×C4C23×D1311yescharacteristic
663Q16—44no—
664SD16—268no—
665SD16—524no—
666M16—524no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—44no—
670C2×C8—132no—
671C2×C8—132no—
672C2×C8—262no—
673C2×C8—262no—
674C2×C8C23×D1312yes—
675C2×C8C23×D1312yes—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—134no—
681C4⋊C4—132no—
682C4⋊C4—132no—
683C4⋊C4—264no—
684C4⋊C4—264no—
685C4⋊C4—264no—
686C4⋊C4—264no—
687C4⋊C4—261no—
688C4⋊C4—264no—
689C4⋊C4—261no—
690C4⋊C4C23×D1312yes—
691C4⋊C4C23×D1312yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—134no—
695C22⋊C4—134no—
696C22⋊C4—264no—
697C22⋊C4—264no—
698C22⋊C4—264no—
699C22⋊C4—264no—
700C22⋊C4—264no—
701C42—132no—
702C42—132no—
703C42—264no—
704C13C2×#331411yescharacteristic, complemented, Sylow
705C23—22no—
706C23—22no—
707C23—132no—
708C23—262no—
709C23—262no—
710C23—262no—
711C23—264no—
712C23—262no—
713C23—262no—
714C23—528no—
715C23—522no—
716C23—522no—
717C23—528no—
718C23—522no—
719C23—522no—
720C23—522no—
721C23—1044no—
722C23—10416no—
723C23#8817214yes—
724C23C2×D4×D1312yes—
725C23C2×D4×D1311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—1044no—
733D4—134no—
734D4—268no—
735D4—264no—
736D4—262no—
737D4—262no—
738D4—262no—
739D4—528no—
740D4—528no—
741D4—522no—
742D4—1044no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—132no—
756C2×C4—132no—
757C2×C4—132no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—264no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—528no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—1044no—
770C2×C4—1044no—
771C2×C4—1044no—
772C2×C4C2×D4×D1312yes—
773C2×C4C2×D4×D1311yescharacteristic
774C2×C4#8825112yes—
775C2×C4#41×D1312yes—
776C2×C4C24×D1311yescharacteristic
777C8—22no—
778C8—22no—
779C8—262no—
780C8—262no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—262no—
785C22—264no—
786C22—262no—
787C22—262no—
788C22—524no—
789C22—528no—
790C22—522no—
791C22—522no—
792C22—522no—
793C22—522no—
794C22—522no—
795C22—10416no—
796C22—1044no—
797C22#1171931512yes—
798C22C2×#8817214yes—
799C22C2×#8817212yes—
800C22#1171947412yes—
801C22C22×D4×D1311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—262no—
808C4—262no—
809C4—262no—
810C4—522no—
811C4—522no—
812C4#1171931512yes—
813C4C2×#8825111yescharacteristic
814C4C2×#41×D1311yescharacteristic
815C2—24no—
816C2—522no—
817C2—524no—
818C2—1042no—
819C2#1312692314yesdirect product factor
820C2C2×#1171931511yescharacteristic
821C2C22×#8817211yescharacteristic
822C2C2×#1171947411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#467C2
socleC23×C13C22×D4
prime radicalC2×#11719335C2
hypercenterC2×#467D13
hypocenterC13C2×#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#11719340C2semidirect
3. #13126923C2direct (N × H)
4. C2×#11718456C2semidirect
5. C2×#11718705C2semidirect
6. C2×#11718543C2semidirect
7. C2×#11718551C2semidirect
8. C2×#11718473C2semidirect
9. C2×#11718846C2semidirect
10. C2×#11718848C2semidirect
11. C2×#11718707C2semidirect
12. C2×#11718478C2semidirect
13. C2×#11718772C2semidirect
14. C2×#11718464C2semidirect
15. C22×#88061C2semidirect
16. C2×C13×#467C2semidirect
19. C22×C13×Q16C22semidirect
24. C2×#88200C22semidirect
25. C2×Q8×Dic13C22semidirect
30. C22×#6094C22semidirect
32. #11719340C22semidirect
40. C2×C4⋊C4×D13C22semidirect
42. C2×#88142C22semidirect
47. C13×#467C22semidirect
48. C2×C13×#107C22semidirect
49. C2×C13×#103C22semidirect
50. C2×C13×#103C22semidirect
51. C2×#88075C22semidirect
52. C2×#88075C22semidirect
54. #11718848C22semidirect
55. #11718846C22semidirect
60. C2×#88061C22semidirect
61. #11718772C22semidirect
62. C2×#88060C22semidirect
63. C2×#88055C22semidirect
64. C2×#88054C22semidirect
65. #11718707C22semidirect
66. #11718705C22semidirect
69. C2×#88047C22semidirect
70. C2×#88047C22semidirect
71. #11718551C22semidirect
72. #11718543C22semidirect
73. #11718478C22semidirect
74. #11718473C22semidirect
75. #11718464C22semidirect
76. #11718456C22semidirect
102. C2×C13×Q16C23semidirect
121. #88200C23semidirect
123. Q8×Dic13C23semidirect
151. C2×#6094C23semidirect
160. C4⋊C4×D13C23semidirect
163. #88142C23semidirect
168. C13×#107C23semidirect
169. C13×#103C23semidirect
170. C13×#103C23semidirect
171. #88075C23semidirect
172. #88075C23semidirect
178. #88060C23semidirect
179. #88055C23semidirect
180. #88054C23semidirect
183. #88047C23semidirect
184. #88047C23semidirect
302. C2×#467D13semidirect
388. C22×Q16C2×D13semidirect
421. #467C2×D13semidirect
429. C2×#107C2×D13semidirect
434. C2×#103C2×D13semidirect
435. C2×#103C2×D13semidirect
505. C2×Q16C22×D13semidirect
573. #107C22×D13semidirect
577. #103C22×D13semidirect
578. #103C22×D13semidirect
589. C2×C13#3314semidirect
704. C13C2×#3314semidirect
819. C2#13126923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193402
C2×#117193352
#131269232
C2×#117184562
C2×#117187052
C2×#117185432
C2×#117185512
C2×#117184732
C2×#117188462
C2×#117188482
C2×#117187072
C2×#117184782
C2×#117187722
C2×#117184642
C22×#880612
C2×C13×#4672
C2×#331413