Finite Group Databasebeta

← C2×#13127050 #16739730

Subgroups — C2×#13127050 #16739730

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719234C211yesmaximal, characteristic, complemented
2C2×#11719335C211yesmaximal, characteristic
3#13127050C2116yesmaximal, direct product factor
4C2×#11718461C211yesmaximal, characteristic, complemented
5C2×#11718524C211yesmaximal, characteristic, complemented
6C2×#11718552C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718547C211yesmaximal, characteristic, complemented
9C2×#11718459C211yesmaximal, characteristic, complemented
10C2×#11718471C211yesmaximal, characteristic, complemented
11C2×#11718392C211yesmaximal, characteristic, complemented
12C2×#11718513C211yesmaximal, characteristic, complemented
13C2×#11718390C211yesmaximal, characteristic, complemented
14C2×#11718464C211yesmaximal, characteristic, complemented
15C2×#11718662C211yesmaximal, characteristic, complemented
16C2×C13×#485C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#117C2211yescharacteristic
21C2×#88201C2211yescharacteristic
22C22×#6107C2211yescharacteristic, complemented
23C2×C4×C22⋊D13C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C22×#6095C2211yescharacteristic
27C22×#6095C2211yescharacteristic
28C22×#6094C2211yescharacteristic, complemented
29#11719335—24no—
30#11719335C2218yes—
31#11719234—24no—
32#11719234C2218yescomplemented
33C2×#88151C2211yescharacteristic, complemented
34C2×#88149—21no—
35C2×#88149C2211yescharacteristic
36C2×#88148—21no—
37C2×#88147C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic, complemented
39C2×#88144C2211yescharacteristic, complemented
40C2×#88141C2211yescharacteristic, complemented
41C2×#88137—21no—
42C2×#88136—21no—
43C2×C22⋊C4×D13—21no—
44C2×#88133—21no—
45C2×#88126—21no—
46C2×#88124—21no—
47C13×#485C2218yescomplemented
48C2×C13×#107C2211yescharacteristic, complemented
49C2×C13×#106C2211yescharacteristic, complemented
50C2×C13×#103C2211yescharacteristic, complemented
51C2×C13×#103C2211yescharacteristic, complemented
52C2×C13×C22⋊C8C2211yescharacteristic
53C2×#88075C2211yescharacteristic, complemented
54C2×#88061C2211yescharacteristic
55C2×#88061C2211yescharacteristic
56C2×#88060C2211yescharacteristic, complemented
57C2×#88054C2211yescharacteristic, complemented
58C2×C8×Dic13C2211yescharacteristic, complemented
59#11718713C2218yescomplemented
60#11718662C2218yescomplemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88049C2211yescharacteristic
66C2×#88048C2211yescharacteristic, complemented
67#11718552C2218yescomplemented
68#11718547C2218yescomplemented
69#11718524C2218yescomplemented
70#11718513C2218yescomplemented
71#11718471C2218yescomplemented
72#11718464C2218yescomplemented
73#11718461C2218yescomplemented
74#11718459C2218yescomplemented
75#11718392C2218yescomplemented
76#11718390C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13D411yescharacteristic
81C2×#6131—22no—
82C2×#6131—24no—
83C2×#6131—42no—
84C2×#6131C2314yes—
85C22×D52—24no—
86C22×D52—21no—
87C22×D52—21no—
88C22×D52—22no—
89C22×D52—21no—
90C22×D52—42no—
91C22×D52C2311yescharacteristic
92C22×D52C2314yes—
93C22×D52C2311yescharacteristic
94C22×C4×D13—21no—
95C22×C4×D13—21no—
96C22×C4×D13—21no—
97C22×C4×D13C2311yescharacteristic
98C22×Dic26C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2311yescharacteristic
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8C2314yes—
103C13×#117—22no—
104C13×#117C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C42×C13—21no—
112C2×C22⋊Dic13—21no—
113C2×C22⋊Dic13D411yescharacteristic
114#88201—22no—
115#88201C2314yes—
116C2×#6107—42no—
117C2×#6107C2314yescomplemented
118C4×C22⋊D13D414yes—
119C4×C22⋊D13C2314yes—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×#6103D411yescharacteristic
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13C2311yescharacteristic
129#88178—22no—
130#88178C2314yes—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101D411yescharacteristic
136C2×C4×Dic13—21no—
137C2×C4×Dic13C2311yescharacteristic
138C2×#6099—42no—
139C2×#6099C2314yes—
140C22×#1055C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142C2×#6095—24no—
143C2×#6095—42no—
144C2×#6095C2314yes—
145C2×#6095C2314yes—
146C2×#6094—42no—
147C2×#6094C2314yescomplemented
148#88151—22no—
149#88151C2314yescomplemented
150#88149—22no—
151#88149—28no—
152#88149C2314yes—
153#88148—28no—
154#88147—22no—
155#88147C2314yes—
156C4⋊C4×D13—22no—
157C4⋊C4×D13C2314yescomplemented
158#88144—22no—
159#88144C2314yescomplemented
160#88141—22no—
161#88141C2314yescomplemented
162#88137—28no—
163#88136—28no—
164C22⋊C4×D13—28no—
165#88133—28no—
166#88126—28no—
167#88124—28no—
168C13×#107C2314yescomplemented
169C13×#106C2314yescomplemented
170C13×#103C2314yescomplemented
171C13×#103C2314yescomplemented
172C13×C22⋊C8C2314yes—
173#88075C2314yescomplemented
174#88061C2314yes—
175#88061C2314yes—
176#88060C2314yescomplemented
177#88054C2314yescomplemented
178C8×Dic13C2314yescomplemented
179#88050C2314yescomplemented
180#88049C2314yes—
181#88049C2314yes—
182#88049C2314yes—
183#88049C2314yes—
184#88048C2314yescomplemented
185C2×#3323—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—22no—
196C2×Q8×C13—22no—
197C2×Q8×C13C2412yes—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2411yescharacteristic
208C2×C22⋊D13—42no—
209C2×C22⋊D13C2×D414yes—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13C2×D411yescharacteristic
213C22×Dic13C2×D411yescharacteristic
214C22×Dic13C2×D411yescharacteristic
215#6131—28no—
216#6131—44no—
217#6131—48no—
218C2×D52—21no—
219C2×D52—22no—
220C2×D52—22no—
221C2×D52—22no—
222C2×D52—28no—
223C2×D52—24no—
224C2×D52—24no—
225C2×D52—21no—
226C2×D52—24no—
227C2×D52—44no—
228C2×D52—48no—
229C2×D52—44no—
230C2×D52—44no—
231C2×D52—82no—
232C2×D52#4114yes—
233C2×D52C2412yes—
234C2×D52C2412yes—
235C2×C4×D13—22no—
236C2×C4×D13—22no—
237C2×C4×D13—24no—
238C2×C4×D13—24no—
239C2×C4×D13—24no—
240C2×C4×D13—44no—
241C2×C4×D13—44no—
242C2×C4×D13—82no—
243C2×C4×D13C2×D412yes—
244C2×C4×D13C2412yes—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—21no—
248C2×Dic26C2412yes—
249C2×C8×C13—22no—
250C2×C8×C13—22no—
251C2×C8×C13C2412yes—
252C2×C8×C13C2412yes—
253C13×C4⋊C4—21no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4C2412yes—
258C13×C4⋊C4C2412yes—
259C13×C4⋊C4C2412yes—
260C13×C22⋊C4—24no—
261C13×C22⋊C4—24no—
262C42×C13—24no—
263C22⋊Dic13—24no—
264C22⋊Dic13C2×D414yes—
265#6107—44no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271#6103C2×D414yes—
272C4⋊Dic13—21no—
273C4⋊Dic13—24no—
274C4⋊Dic13—24no—
275C4⋊Dic13C2412yes—
276#6101—24no—
277#6101—24no—
278#6101—24no—
279#6101—24no—
280#6101C2×D414yes—
281C4×Dic13—24no—
282C4×Dic13C2×D412yes—
283C4×Dic13C2412yes—
284#6099—44no—
285C2×#1055—22no—
286C2×#1055—22no—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289#6095—28no—
290#6095—44no—
291#6094—44no—
292C2×#552—131no—
293C2×#546—131no—
294#3323—1316no—
295C2×#488—131no—
296C2×#481—131no—
297C2×#485D1311yescharacteristic, complemented
298C2×#478—131no—
299C2×#470—131no—
300C2×#468—131no—
301C2×#464—131no—
302C2×#452—131no—
303C2×#450—131no—
304C2×C4×SD16—131no—
305C2×#436—131no—
306C2×#417—131no—
307C2×#418—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13C22×D412yes—
312C23×C13C22×D411yescharacteristic
313C22×D13—22no—
314C22×D13—24no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—48no—
320C22×D13—42no—
321C22×D13—42no—
322C22×D13—48no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—42no—
326C22×D13—84no—
327C22×D13—816no—
328C22×D13C22×D412yes—
329Q8×C13—22no—
330Q8×C13—22no—
331Q8×C13—42no—
332C2×C4×C13—22no—
333C2×C4×C13—24no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13C22×D412yes—
345C2×C4×C13C22×D411yescharacteristic
346C2×C4×C13C2×#4112yes—
347C2×C4×C13H(5,𝔽2)12yes—
348C2×C4×C13C2511yescharacteristic
349C22⋊D13—44no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13C22×D412yes—
358C2×Dic13C22×D412yes—
359C2×Dic13C22×D412yes—
360D52—24no—
361D52—22no—
362D52—22no—
363D52—22no—
364D52—48no—
365D52—48no—
366D52—42no—
367D52—84no—
368D52C2×#4114yes—
369C4×D13—24no—
370C4×D13—22no—
371C4×D13—22no—
372C4×D13—48no—
373C4×D13—48no—
374C4×D13—84no—
375Dic26—22no—
376Dic26—22no—
377Dic26—42no—
378C8×C13—22no—
379C8×C13—22no—
380#1055—22no—
381#1055—22no—
382C22×#41—131no—
383C23×D4—131no—
384C22×Q16—131no—
385C22×SD16—131no—
386C22×SD16—131no—
387C22×M16—131no—
388C22×M16—131no—
389#552—138no—
390#552—264no—
391#546—138no—
392#546—264no—
393C2×#126—261no—
394C2×#125—131no—
395C2×#125—261no—
396C2×#124—131no—
397C2×#123—261no—
398C2×#123—261no—
399C2×C22⋊Q8—131no—
400C2×C22⋊Q8—131no—
401C2×C22⋊Q8C2×D1311yescharacteristic
402C2×#121—131no—
403C2×#121—261no—
404C2×#120—261no—
405C2×C4×Q8—131no—
406C2×C4×D4—131no—
407C2×C4×D4—131no—
408C2×#117—261no—
409C2×#117C2×D1311yescharacteristic
410C22×C4⋊C4—131no—
411C22×C22⋊C4—261no—
412#488—138no—
413#485C2×D1318yescomplemented
414#481—138no—
415#478—138no—
416#470—138no—
417#468—138no—
418#464—138no—
419#452—138no—
420#450—138no—
421C4×SD16—138no—
422#436—138no—
423C2×#107C2×D1311yescharacteristic, complemented
424C2×#106—131no—
425C2×#106C2×D1311yescharacteristic, complemented
426C2×C4⋊C8—131no—
427#418—138no—
428#417—138no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103C2×D1311yescharacteristic, complemented
432C2×#103C2×D1311yescharacteristic, complemented
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×C22⋊C8—131no—
440C2×C22⋊C8C2×D1311yescharacteristic
441C2×C4×C8—131no—
442C22×C13—22no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—44no—
446C22×C13#54612yes—
447C22×C13#57512yes—
448C22×C13#57712yes—
449C22×C13C23×D411yescharacteristic
450C2×D13—22no—
451C2×D13—24no—
452C2×D13—22no—
453C2×D13—22no—
454C2×D13—44no—
455C2×D13—48no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—816no—
462C2×D13—84no—
463C4×C13—22no—
464C4×C13—42no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#54612yes—
469C4×C13C22×#4111yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—22no—
472Dic13—22no—
473Dic13—22no—
474Dic13—42no—
475Dic13—42no—
476C25—261no—
477C2×#41—134no—
478C2×#41—262no—
479C2×#41—264no—
480C2×#41—522no—
481C22×Q8—131no—
482C22×Q8C22×D1311yescharacteristic
483C22×D4—131no—
484C22×D4—131no—
485C22×D4—131no—
486C22×D4—134no—
487C22×D4—264no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4—261no—
491C22×D4—262no—
492C22×D4—522no—
493C23×C4—131no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4—261no—
497C23×C4C22×D1311yescharacteristic
498C2×Q16—134no—
499C2×Q16—522no—
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—264no—
503C2×SD16—522no—
504C2×M16—134no—
505C2×M16—134no—
506C2×M16—522no—
507C2×M16—522no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8C22×D1311yescharacteristic
511C22×C8C22×D1311yescharacteristic
512#126—268no—
513#125—134no—
514#125—268no—
515#125—262no—
516#124—134no—
517#124—262no—
518#123—268no—
519#123—268no—
520C22⋊Q8—22no—
521C22⋊Q8—134no—
522C22⋊Q8—134no—
523C22⋊Q8—262no—
524C22⋊Q8—262no—
525C22⋊Q8C22×D1314yes—
526#121—134no—
527#121—268no—
528#121—262no—
529#120—268no—
530C4×Q8—134no—
531C4×Q8—262no—
532C4×D4—134no—
533C4×D4—134no—
534C4×D4—134no—
535C4×D4—262no—
536#117—22no—
537#117—268no—
538#117C22×D1314yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—131no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—134no—
543C2×C4⋊C4—262no—
544C2×C4⋊C4—261no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4—261no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—131no—
556C2×C22⋊C4—131no—
557C2×C22⋊C4—268no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4—261no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C42—21no—
565C2×C42—131no—
566C2×C42—261no—
567#107C22×D1314yescomplemented
568#106—134no—
569#106C22×D1314yescomplemented
570C4⋊C8—134no—
571#103—134no—
572#103—134no—
573#103C22×D1314yescomplemented
574#103C22×D1314yescomplemented
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579#102—134no—
580#102—134no—
581C22⋊C8—134no—
582C22⋊C8C22×D1314yes—
583C4×C8—134no—
584C2×C13—42no—
585C2×C13#332314yescomplemented
586C2×C13C2×#54611yescharacteristic
587C2×C13C2×#57511yescharacteristic
588C2×C13C2×#57711yescharacteristic
589D13—42no—
590D13—44no—
591D13—82no—
592C24—131no—
593C24—261no—
594C24—261no—
595C24—264no—
596C24—524no—
597C24—524no—
598C24—1042no—
599C24D4×D1311yescharacteristic
600#41—268no—
601#41—524no—
602#41—528no—
603C2×Q8—21no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—132no—
607C2×Q8—261no—
608C2×Q8—262no—
609C2×Q8—262no—
610C2×Q8C23×D1312yes—
611C2×D4—134no—
612C2×D4—134no—
613C2×D4—132no—
614C2×D4—132no—
615C2×D4—268no—
616C2×D4—264no—
617C2×D4—264no—
618C2×D4—261no—
619C2×D4—264no—
620C2×D4—261no—
621C2×D4—262no—
622C2×D4—262no—
623C2×D4—262no—
624C2×D4—524no—
625C2×D4—528no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—522no—
629C2×D4—1042no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—131no—
637C22×C4—131no—
638C22×C4—131no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—264no—
642C22×C4—264no—
643C22×C4—264no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—524no—
649C22×C4—524no—
650C22×C4—1042no—
651C22×C4D4×D1312yes—
652C22×C4D4×D1311yescharacteristic
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—524no—
656SD16—268no—
657SD16—524no—
658M16—524no—
659M16—524no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—132no—
663C2×C8—132no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8C23×D1312yes—
667C2×C8C23×D1312yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—134no—
673C4⋊C4—132no—
674C4⋊C4—264no—
675C4⋊C4—264no—
676C4⋊C4—264no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—261no—
680C4⋊C4—264no—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—134no—
687C22⋊C4—134no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4—264no—
694C42—24no—
695C42—132no—
696C42—132no—
697C42—264no—
698C13C2×#332311yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—132no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—264no—
707C23—262no—
708C23—262no—
709C23—528no—
710C23—528no—
711C23—522no—
712C23—522no—
713C23—522no—
714C23—522no—
715C23—522no—
716C23—1044no—
717C23—10416no—
718C23C2×D4×D1312yes—
719C23C2×D4×D1311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—262no—
724Q8—262no—
725Q8—522no—
726D4—134no—
727D4—264no—
728D4—262no—
729D4—262no—
730D4—262no—
731D4—528no—
732D4—528no—
733D4—524no—
734D4—522no—
735D4—1044no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—132no—
749C2×C4—132no—
750C2×C4—132no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—264no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—528no—
760C2×C4—528no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—1044no—
764C2×C4C2×D4×D1312yes—
765C2×C4C2×D4×D1311yescharacteristic
766C2×C4#41×D1312yes—
767C2×C4#8825612yes—
768C2×C4C24×D1311yescharacteristic
769C8—22no—
770C8—22no—
771C8—262no—
772C8—262no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—262no—
778C22—264no—
779C22—262no—
780C22—262no—
781C22—522no—
782C22—522no—
783C22—524no—
784C22—528no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—10416no—
789C22—1044no—
790C22#1171935912yes—
791C22#1171947512yes—
792C22#1171948212yes—
793C22C22×D4×D1311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—262no—
800C4—262no—
801C4—262no—
802C4—522no—
803C4—522no—
804C4#1171935912yes—
805C4C2×#41×D1311yescharacteristic
806C4C2×#8825611yescharacteristic
807C2—42no—
808C2—522no—
809C2—524no—
810C2—1042no—
811C2#1312705014yesdirect product factor
812C2C2×#1171935911yescharacteristic
813C2C2×#1171948211yescharacteristic
814C2C2×#1171947511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#485C2
socleC23×C13C22×D4
prime radicalC2×#11719335C2
hypercenterC2×#485D13
hypocenterC13C2×#3323
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#11719234C2semidirect
3. #13127050C2direct (N × H)
4. C2×#11718461C2semidirect
5. C2×#11718524C2semidirect
6. C2×#11718552C2semidirect
7. C2×#11718713C2semidirect
8. C2×#11718547C2semidirect
9. C2×#11718459C2semidirect
10. C2×#11718471C2semidirect
11. C2×#11718392C2semidirect
12. C2×#11718513C2semidirect
13. C2×#11718390C2semidirect
14. C2×#11718464C2semidirect
15. C2×#11718662C2semidirect
16. C2×C13×#485C2semidirect
22. C22×#6107C22semidirect
28. C22×#6094C22semidirect
32. #11719234C22semidirect
33. C2×#88151C22semidirect
38. C2×C4⋊C4×D13C22semidirect
39. C2×#88144C22semidirect
40. C2×#88141C22semidirect
47. C13×#485C22semidirect
48. C2×C13×#107C22semidirect
49. C2×C13×#106C22semidirect
50. C2×C13×#103C22semidirect
51. C2×C13×#103C22semidirect
53. C2×#88075C22semidirect
56. C2×#88060C22semidirect
57. C2×#88054C22semidirect
58. C2×C8×Dic13C22semidirect
59. #11718713C22semidirect
60. #11718662C22semidirect
61. C2×#88050C22semidirect
66. C2×#88048C22semidirect
67. #11718552C22semidirect
68. #11718547C22semidirect
69. #11718524C22semidirect
70. #11718513C22semidirect
71. #11718471C22semidirect
72. #11718464C22semidirect
73. #11718461C22semidirect
74. #11718459C22semidirect
75. #11718392C22semidirect
76. #11718390C22semidirect
117. C2×#6107C23semidirect
147. C2×#6094C23semidirect
149. #88151C23semidirect
157. C4⋊C4×D13C23semidirect
159. #88144C23semidirect
161. #88141C23semidirect
168. C13×#107C23semidirect
169. C13×#106C23semidirect
170. C13×#103C23semidirect
171. C13×#103C23semidirect
173. #88075C23semidirect
176. #88060C23semidirect
177. #88054C23semidirect
178. C8×Dic13C23semidirect
179. #88050C23semidirect
184. #88048C23semidirect
297. C2×#485D13semidirect
413. #485C2×D13semidirect
423. C2×#107C2×D13semidirect
425. C2×#106C2×D13semidirect
431. C2×#103C2×D13semidirect
432. C2×#103C2×D13semidirect
567. #107C22×D13semidirect
569. #106C22×D13semidirect
573. #103C22×D13semidirect
574. #103C22×D13semidirect
585. C2×C13#3323semidirect
698. C13C2×#3323semidirect
811. C2#13127050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192342
C2×#117193352
#131270502
C2×#117184612
C2×#117185242
C2×#117185522
C2×#117187132
C2×#117185472
C2×#117184592
C2×#117184712
C2×#117183922
C2×#117185132
C2×#117183902
C2×#117184642
C2×#117186622
C2×C13×#4852
C2×#332313