Finite Group Databasebeta

← C2×#13126919 #16739447

Subgroups — C2×#13126919 #16739447

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×#11719248C211yesmaximal, characteristic, complemented
2C2×#11719255C211yesmaximal, characteristic
3#13126919C2116yesmaximal, direct product factor
4C2×#11718375C211yesmaximal, characteristic, complemented
5C2×#11718383C211yesmaximal, characteristic, complemented
6C2×#11718397C211yesmaximal, characteristic, complemented
7C2×#11718507C211yesmaximal, characteristic, complemented
8C2×#11718795C211yesmaximal, characteristic, complemented
9C2×#11718777C211yesmaximal, characteristic, complemented
10C2×#11718506C211yesmaximal, characteristic, complemented
11C2×#11718394C211yesmaximal, characteristic, complemented
12C2×#11718392C211yesmaximal, characteristic, complemented
13C2×#11718371C211yesmaximal, characteristic, complemented
14C2×#11718794C211yesmaximal, characteristic, complemented
15C22×#88061C211yesmaximal, characteristic, complemented
16C2×C13×#435C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C22×C13×M16C2211yescharacteristic, complemented
20C23×C8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88191—21no—
23C2×D4×Dic13—21no—
24C2×#88184C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic, complemented
27C2×#88178C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C2×#88178C2211yescharacteristic, complemented
30C22×Dic52C2211yescharacteristic, complemented
31C22×#6095C2211yescharacteristic
32C22×#6095C2211yescharacteristic
33#11719255—24no—
34#11719255C2218yes—
35#11719248—24no—
36#11719248C2218yescomplemented
37C2×#88148—21no—
38C2×#88144—21no—
39C2×#88138—21no—
40C2×C22⋊C4×D13—21no—
41C2×#88132—21no—
42C2×#88132—21no—
43C2×#88129C2211yescharacteristic
44C2×C4×D52C2211yescharacteristic
45C2×#88123C2211yescharacteristic, complemented
46C2×C4×Dic26C2211yescharacteristic, complemented
47C13×#435C2218yescomplemented
48C2×C13×C4⋊C8C2211yescharacteristic, complemented
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic, complemented
51C2×C13×#97C2211yescharacteristic, complemented
52#11718795C2218yescomplemented
53#11718794C2218yescomplemented
54#11718777C2218yescomplemented
55C2×#88061C2211yescharacteristic
56C2×#88061C2211yescharacteristic
57C2×#88061C2211yescharacteristic
58C2×#88061C2211yescharacteristic
59C2×#88061C2211yescharacteristic
60C2×#88061C2211yescharacteristic
61C2×#88061C2218yescomplemented
62C2×#88058C2211yescharacteristic, complemented
63C2×#88058C2211yescharacteristic, complemented
64C2×#88058C2211yescharacteristic, complemented
65C2×#88056C2211yescharacteristic, complemented
66C2×#88056C2211yescharacteristic, complemented
67C2×#88056C2211yescharacteristic, complemented
68C2×#88056C2211yescharacteristic, complemented
69#11718507C2218yescomplemented
70#11718506C2218yescomplemented
71#11718397C2218yescomplemented
72#11718394C2218yescomplemented
73#11718392C2218yescomplemented
74#11718383C2218yescomplemented
75#11718375C2218yescomplemented
76#11718371C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13D411yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13—21no—
83C23×Dic13—21no—
84C23×Dic13—21no—
85C2×#6127—22no—
86C2×#6127—24no—
87C2×#6127—42no—
88C2×#6127C2314yes—
89C22×D52—24no—
90C22×D52—21no—
91C22×D52—22no—
92C22×D52—42no—
93C22×D52C2311yescharacteristic
94C22×D52C2314yes—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×C4×D13—21no—
98C22×Dic26—21no—
99C22×Dic26C2311yescharacteristic
100C22×Dic26C2311yescharacteristic
101C2×C13×M16—42no—
102C2×C13×M16C2314yescomplemented
103C22×C8×C13—42no—
104C22×C8×C13C2311yescharacteristic
105C22×C8×C13C2311yescharacteristic
106C22×C8×C13C2311yescharacteristic
107C22×C8×C13C2311yescharacteristic
108C22×C8×C13C2314yes—
109C4×D4×C13D414yes—
110C4×D4×C13C2314yes—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C22⋊C4D411yescharacteristic
113C2×C13×C22⋊C4D411yescharacteristic
114C2×C42×C13C2311yescharacteristic
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117C2×C22⋊Dic13—21no—
118#88191—28no—
119D4×Dic13—28no—
120#88184—22no—
121#88184C2314yes—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13—22no—
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2314yes—
136C2×C4⋊Dic13C2314yescomplemented
137#88178—22no—
138#88178—22no—
139#88178—22no—
140#88178C2314yes—
141#88178C2314yes—
142#88178C2314yescomplemented
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×#6101—21no—
147C2×C4×Dic13—21no—
148C2×Dic52—42no—
149C2×Dic52C2314yescomplemented
150C2×#6095—24no—
151C2×#6095—42no—
152C2×#6095C2314yes—
153C2×#6095C2314yes—
154#88148—28no—
155#88144—28no—
156#88138—28no—
157C22⋊C4×D13—28no—
158#88132—28no—
159#88132—28no—
160#88129—22no—
161#88129C2314yes—
162C4×D52—22no—
163C4×D52C2314yes—
164#88123—22no—
165#88123C2314yescomplemented
166C4×Dic26—22no—
167C4×Dic26C2314yescomplemented
168C13×C4⋊C8C2314yescomplemented
169C13×C22⋊C8C2314yes—
170C13×C22⋊C8C2314yescomplemented
171C13×#97C2314yescomplemented
172#88061C2314yes—
173#88061C2314yes—
174#88061C2314yes—
175#88061C2314yes—
176#88061C2314yes—
177#88061C2314yes—
178#88058C2314yescomplemented
179#88058C2314yescomplemented
180#88058C2314yescomplemented
181#88056C2314yescomplemented
182#88056C2314yescomplemented
183#88056C2314yescomplemented
184#88056C2314yescomplemented
185C2×#3314—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C23×D13—21no—
190C23×D13—24no—
191C23×D13—44no—
192C23×D13—44no—
193C23×D13—82no—
194C2×D4×C13—24no—
195C2×D4×C13C2×D414yes—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2411yescharacteristic
209C2×C22⋊D13—24no—
210C2×C22⋊D13—24no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13—82no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—24no—
220C22×Dic13—24no—
221C22×Dic13—82no—
222C22×Dic13—82no—
223#6127—28no—
224#6127—44no—
225#6127—48no—
226C2×D52—21no—
227C2×D52—22no—
228C2×D52—22no—
229C2×D52—22no—
230C2×D52—28no—
231C2×D52—21no—
232C2×D52—24no—
233C2×D52—44no—
234C2×D52—48no—
235C2×D52—44no—
236C2×D52#4114yes—
237C2×D52C2412yes—
238C2×D52C2412yes—
239C2×C4×D13—24no—
240C2×C4×D13—24no—
241C2×C4×D13—44no—
242C2×C4×D13—82no—
243C2×Dic26—22no—
244C2×Dic26—22no—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—21no—
248C2×Dic26—21no—
249C2×Dic26—24no—
250C2×Dic26—82no—
251C2×Dic26C2412yes—
252C2×Dic26C2412yes—
253C13×M16—44no—
254C2×C8×C13—22no—
255C2×C8×C13—22no—
256C2×C8×C13—22no—
257C2×C8×C13—22no—
258C2×C8×C13—44no—
259C2×C8×C13C2412yes—
260C2×C8×C13C2412yes—
261C2×C8×C13C2412yes—
262C2×C8×C13C2412yes—
263C13×C4⋊C4C2×D414yes—
264C13×C22⋊C4C2×D414yes—
265C13×C22⋊C4C2×D414yes—
266C42×C13C2×D412yes—
267C42×C13C2412yes—
268C22⋊Dic13—24no—
269C22⋊Dic13—24no—
270C22⋊Dic13—24no—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274#6103—24no—
275C4⋊Dic13—21no—
276C4⋊Dic13—21no—
277C4⋊Dic13—21no—
278C4⋊Dic13—24no—
279C4⋊Dic13—21no—
280C4⋊Dic13—24no—
281C4⋊Dic13—24no—
282C4⋊Dic13C2412yes—
283C4⋊Dic13C2412yes—
284C4⋊Dic13C2412yes—
285C4⋊Dic13C2412yes—
286#6101—24no—
287#6101—24no—
288#6101—24no—
289#6101—24no—
290C4×Dic13—24no—
291Dic52—44no—
292#6095—28no—
293#6095—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×#440—131no—
307C2×#435D1311yescharacteristic, complemented
308C2×#417—131no—
309C22×#102—131no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13#13714yes—
316C23×C13C22×D412yes—
317C23×C13C22×D412yes—
318C23×C13C22×D411yescharacteristic
319C22×D13—24no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—48no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—42no—
326C22×D13—48no—
327C22×D13—42no—
328C22×D13—42no—
329C22×D13—84no—
330C22×D13—816no—
331D4×C13—28no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—24no—
337C2×C4×C13—24no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13C22×D412yes—
343C2×C4×C13C22×D412yes—
344C2×C4×C13C22×D412yes—
345C2×C4×C13C22×D412yes—
346C2×C4×C13C22×D411yescharacteristic
347C2×C4×C13C2×#4112yes—
348C2×C4×C13H(5,𝔽2)12yes—
349C2×C4×C13C2511yescharacteristic
350C22⋊D13—48no—
351C22⋊D13—84no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—84no—
365C2×Dic13—84no—
366D52—24no—
367D52—22no—
368D52—22no—
369D52—22no—
370D52—48no—
371D52—42no—
372D52C2×#4114yes—
373C4×D13—48no—
374C4×D13—84no—
375Dic26—22no—
376Dic26—22no—
377Dic26—22no—
378Dic26—22no—
379Dic26—42no—
380Dic26—42no—
381Dic26—84no—
382C8×C13—22no—
383C8×C13—22no—
384C8×C13—22no—
385C8×C13—22no—
386C22×#41—131no—
387C23×D4—131no—
388C22×Q16—131no—
389C22×SD16—131no—
390C22×SD16—131no—
391C22×M16C2×D1311yescharacteristic, complemented
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—131no—
403C2×C22⋊Q8—131no—
404C2×C22⋊Q8—261no—
405C2×C22⋊Q8—261no—
406C2×#121—131no—
407C2×#121—261no—
408C2×#120—261no—
409C2×C4×Q8—131no—
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#440—138no—
426#435C2×D1318yescomplemented
427C2×#107—131no—
428C2×#107—131no—
429C2×#107—131no—
430C2×C4⋊C8C2×D1311yescharacteristic, complemented
431#417—138no—
432C2×#103—131no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×#102—131no—
440C2×#102—131no—
441C2×#102—138no—
442C2×#102—131no—
443C2×C22⋊C8C2×D1311yescharacteristic
444C2×C22⋊C8C2×D1311yescharacteristic, complemented
445C2×#97C2×D1311yescharacteristic, complemented
446C22×C13—22no—
447C22×C13—28no—
448C22×C13—22no—
449C22×C13—22no—
450C22×C13—22no—
451C22×C13—22no—
452C22×C13—44no—
453C22×C13#54612yes—
454C22×C13C2×#13714yes—
455C22×C13C2×#13712yes—
456C22×C13#57612yes—
457C22×C13C23×D411yescharacteristic
458C2×D13—24no—
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—22no—
469C4×C13—22no—
470C4×C13—22no—
471C4×C13#54612yes—
472C4×C13C22×#4111yescharacteristic
473C4×C13C2×H(5,𝔽2)11yescharacteristic
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479Dic13—42no—
480C25—261no—
481C2×#41—134no—
482C2×#41—264no—
483C2×#41—262no—
484C2×#41—522no—
485C22×Q8—131no—
486C22×Q8—131no—
487C22×Q8—261no—
488C22×D4—131no—
489C22×D4—131no—
490C22×D4—134no—
491C22×D4—264no—
492C22×D4—261no—
493C22×D4—261no—
494C22×D4—261no—
495C22×D4—262no—
496C22×D4—522no—
497C22×D4D5211yescharacteristic
498C23×C4—261no—
499C23×C4—261no—
500C23×C4—261no—
501C23×C4—261no—
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C2×Q16—134no—
505C2×Q16—522no—
506C2×SD16—134no—
507C2×SD16—134no—
508C2×SD16—264no—
509C2×SD16—522no—
510C2×M16—42no—
511C2×M16C22×D1314yescomplemented
512C22×C8—42no—
513C22×C8C22×D1311yescharacteristic
514C22×C8C22×D1311yescharacteristic
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—134no—
525C22⋊Q8—134no—
526C22⋊Q8—134no—
527C22⋊Q8—262no—
528C22⋊Q8—262no—
529C22⋊Q8—262no—
530C22⋊Q8—268no—
531C22⋊Q8—268no—
532#121—134no—
533#121—262no—
534#121—268no—
535#120—268no—
536C4×Q8—134no—
537C4×Q8—262no—
538C4×D4—134no—
539C4×D4—268no—
540C4×D4—262no—
541C4×D4D5214yes—
542C4×D4C22×D1314yes—
543C2×C4⋊C4—131no—
544C2×C4⋊C4—131no—
545C2×C4⋊C4—131no—
546C2×C4⋊C4—134no—
547C2×C4⋊C4—134no—
548C2×C4⋊C4—131no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4—261no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4—262no—
553C2×C4⋊C4—261no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4—261no—
556C2×C4⋊C4—261no—
557C2×C4⋊C4—261no—
558C2×C4⋊C4D5211yescharacteristic
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4—261no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—268no—
567C2×C22⋊C4D5211yescharacteristic
568C2×C22⋊C4D5211yescharacteristic
569C2×C42—261no—
570C2×C42C22×D1311yescharacteristic
571#107—134no—
572#107—134no—
573#107—134no—
574C4⋊C8C22×D1314yescomplemented
575#103—134no—
576#103—134no—
577#103—134no—
578#103—134no—
579#102—134no—
580#102—134no—
581#102—134no—
582#102—134no—
583#102—134no—
584#102—134no—
585C22⋊C8C22×D1314yes—
586C22⋊C8C22×D1314yescomplemented
587#97C22×D1314yescomplemented
588C2×C13—24no—
589C2×C13—42no—
590C2×C13#331414yescomplemented
591C2×C13C2×#54611yescharacteristic
592C2×C13C22×#13711yescharacteristic
593C2×C13C2×#57611yescharacteristic
594D13—44no—
595D13—82no—
596C24—261no—
597C24—261no—
598C24—264no—
599C24—524no—
600C24—524no—
601C24—1042no—
602C24C2×D5211yescharacteristic
603C24C2×D5211yescharacteristic
604#41—268no—
605#41—524no—
606#41—528no—
607C2×Q8—132no—
608C2×Q8—132no—
609C2×Q8—261no—
610C2×Q8—261no—
611C2×Q8—264no—
612C2×Q8—262no—
613C2×Q8—262no—
614C2×Q8—262no—
615C2×Q8—262no—
616C2×Q8—1042no—
617C2×D4—24no—
618C2×D4—134no—
619C2×D4—132no—
620C2×D4—132no—
621C2×D4—268no—
622C2×D4—264no—
623C2×D4—264no—
624C2×D4—261no—
625C2×D4—264no—
626C2×D4—261no—
627C2×D4—262no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—524no—
631C2×D4—528no—
632C2×D4—524no—
633C2×D4—524no—
634C2×D4—1042no—
635C2×D4C2×D5214yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—264no—
647C22×C4—264no—
648C22×C4—264no—
649C22×C4—264no—
650C22×C4—524no—
651C22×C4—1042no—
652C22×C4—1042no—
653C22×C4—1042no—
654C22×C4C2×D5212yes—
655C22×C4C2×D5212yes—
656C22×C4C2×D5211yescharacteristic
657C22×C4C2×D5211yescharacteristic
658C22×C4C2×D5211yescharacteristic
659C22×C4C2×D5211yescharacteristic
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C22×C4C23×D1311yescharacteristic
663Q16—524no—
664SD16—268no—
665SD16—524no—
666M16—44no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—44no—
672C2×C8C23×D1312yes—
673C2×C8C23×D1312yes—
674C2×C8C23×D1312yes—
675C2×C8C23×D1312yes—
676C4⋊C4—132no—
677C4⋊C4—132no—
678C4⋊C4—132no—
679C4⋊C4—132no—
680C4⋊C4—261no—
681C4⋊C4—264no—
682C4⋊C4—264no—
683C4⋊C4—261no—
684C4⋊C4—261no—
685C4⋊C4—261no—
686C4⋊C4—264no—
687C4⋊C4—264no—
688C4⋊C4—264no—
689C4⋊C4—264no—
690C4⋊C4—264no—
691C4⋊C4C2×D5214yes—
692C22⋊C4—264no—
693C22⋊C4—264no—
694C22⋊C4—264no—
695C22⋊C4—264no—
696C22⋊C4—264no—
697C22⋊C4—264no—
698C22⋊C4—264no—
699C22⋊C4C2×D5214yes—
700C22⋊C4C2×D5214yes—
701C42—264no—
702C42C2×D5212yes—
703C42C23×D1312yes—
704C13C2×#331411yescharacteristic, complemented, Sylow
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—264no—
711C23—262no—
712C23—262no—
713C23—528no—
714C23—522no—
715C23—522no—
716C23—528no—
717C23—522no—
718C23—522no—
719C23—522no—
720C23—1044no—
721C23—10416no—
722C23#8816314yes—
723C23C22×D5212yes—
724C23C22×D5212yes—
725C23C22×D5211yescharacteristic
726Q8—262no—
727Q8—262no—
728Q8—262no—
729Q8—262no—
730Q8—522no—
731Q8—522no—
732Q8—1044no—
733D4—28no—
734D4—134no—
735D4—264no—
736D4—262no—
737D4—262no—
738D4—262no—
739D4—528no—
740D4—528no—
741D4—522no—
742D4—1044no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—528no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—1044no—
767C2×C4—1044no—
768C2×C4—1044no—
769C2×C4C22×D5212yes—
770C2×C4C22×D5212yes—
771C2×C4C22×D5212yes—
772C2×C4C22×D5212yes—
773C2×C4C22×D5211yescharacteristic
774C2×C4#8825112yes—
775C2×C4#41×D1312yes—
776C2×C4C24×D1311yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—264no—
789C22—528no—
790C22—522no—
791C22—522no—
792C22—522no—
793C22—522no—
794C22—522no—
795C22—10416no—
796C22—1044no—
797C22#1171925912yes—
798C22C2×#8816314yes—
799C22C2×#8816312yes—
800C22#1171945712yes—
801C22C23×D5211yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—522no—
807C4—522no—
808C4—522no—
809C4—522no—
810C4—522no—
811C4—522no—
812C4#1171925912yes—
813C4C2×#8825111yescharacteristic
814C4C2×#41×D1311yescharacteristic
815C2—24no—
816C2—42no—
817C2—524no—
818C2—1042no—
819C2#1312691914yesdirect product factor
820C2C2×#1171925911yescharacteristic
821C2C22×#8816311yescharacteristic
822C2C2×#1171945711yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#435C2
socleC23×C13C22×D4
prime radicalC2×#11719255C2
hypercenterC2×#435D13
hypocenterC13C2×#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11719248C2semidirect
3. #13126919C2direct (N × H)
4. C2×#11718375C2semidirect
5. C2×#11718383C2semidirect
6. C2×#11718397C2semidirect
7. C2×#11718507C2semidirect
8. C2×#11718795C2semidirect
9. C2×#11718777C2semidirect
10. C2×#11718506C2semidirect
11. C2×#11718394C2semidirect
12. C2×#11718392C2semidirect
13. C2×#11718371C2semidirect
14. C2×#11718794C2semidirect
15. C22×#88061C2semidirect
16. C2×C13×#435C2semidirect
19. C22×C13×M16C22semidirect
26. C22×C4⋊Dic13C22semidirect
29. C2×#88178C22semidirect
30. C22×Dic52C22semidirect
36. #11719248C22semidirect
45. C2×#88123C22semidirect
46. C2×C4×Dic26C22semidirect
47. C13×#435C22semidirect
48. C2×C13×C4⋊C8C22semidirect
50. C2×C13×C22⋊C8C22semidirect
51. C2×C13×#97C22semidirect
52. #11718795C22semidirect
53. #11718794C22semidirect
54. #11718777C22semidirect
61. C2×#88061C22semidirect
62. C2×#88058C22semidirect
63. C2×#88058C22semidirect
64. C2×#88058C22semidirect
65. C2×#88056C22semidirect
66. C2×#88056C22semidirect
67. C2×#88056C22semidirect
68. C2×#88056C22semidirect
69. #11718507C22semidirect
70. #11718506C22semidirect
71. #11718397C22semidirect
72. #11718394C22semidirect
73. #11718392C22semidirect
74. #11718383C22semidirect
75. #11718375C22semidirect
76. #11718371C22semidirect
102. C2×C13×M16C23semidirect
136. C2×C4⋊Dic13C23semidirect
142. #88178C23semidirect
149. C2×Dic52C23semidirect
165. #88123C23semidirect
167. C4×Dic26C23semidirect
168. C13×C4⋊C8C23semidirect
170. C13×C22⋊C8C23semidirect
171. C13×#97C23semidirect
178. #88058C23semidirect
179. #88058C23semidirect
180. #88058C23semidirect
181. #88056C23semidirect
182. #88056C23semidirect
183. #88056C23semidirect
184. #88056C23semidirect
307. C2×#435D13semidirect
391. C22×M16C2×D13semidirect
426. #435C2×D13semidirect
430. C2×C4⋊C8C2×D13semidirect
444. C2×C22⋊C8C2×D13semidirect
445. C2×#97C2×D13semidirect
511. C2×M16C22×D13semidirect
574. C4⋊C8C22×D13semidirect
586. C22⋊C8C22×D13semidirect
587. #97C22×D13semidirect
590. C2×C13#3314semidirect
704. C13C2×#3314semidirect
819. C2#13126919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192482
C2×#117192552
#131269192
C2×#117183752
C2×#117183832
C2×#117183972
C2×#117185072
C2×#117187952
C2×#117187772
C2×#117185062
C2×#117183942
C2×#117183922
C2×#117183712
C2×#117187942
C22×#880612
C2×C13×#4352
C2×#331413