Finite Group Databasebeta

← C2×#13126962 #16739637

Subgroups — C2×#13126962 #16739637

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic, complemented
2#13126962C2116yesmaximal, direct product factor
3C2×#11718732C211yesmaximal, characteristic, complemented
4C2×#11718695C211yesmaximal, characteristic, complemented
5C2×#11718696C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718703C211yesmaximal, characteristic, complemented
8C2×#11718702C211yesmaximal, characteristic, complemented
9C2×#11718736C211yesmaximal, characteristic, complemented
10C2×#11718900C211yesmaximal, characteristic, complemented
11C2×#11718900C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718893C211yesmaximal, characteristic, complemented
15C2×#11718894C211yesmaximal, characteristic, complemented
16C2×C13×#550C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C22×C13×#41C2211yescharacteristic
19C13×#550—24no—
20C13×#550C2218yes—
21C2×C13×#127—21no—
22C2×C13×#127C2211yescharacteristic
23C2×C13×#121—21no—
24C2×C13×#121—21no—
25C2×C13×#121C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13—21no—
29C2×C4×D4×C13C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C2×#88189—21no—
32C22×#6105C2211yescharacteristic
33C22×#6105C2211yescharacteristic
34C2×#88180C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719246—24no—
41#11719246C2218yescomplemented
42C2×#88143—21no—
43C2×#88133—21no—
44C2×#88131—21no—
45C2×#88124C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47#11718900C2218yescomplemented
48#11718900C2218yescomplemented
49#11718894C2218yescomplemented
50#11718893C2218yescomplemented
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88072C2211yescharacteristic
55C2×#88072C2211yescharacteristic
56C2×#88072C2211yescharacteristic
57C2×#88072C2211yescharacteristic
58C2×#88072C2211yescharacteristic
59C2×#88072C2211yescharacteristic
60C2×C22⋊#1055C2211yescharacteristic
61C2×C22⋊#1055C2211yescharacteristic
62#11718736C2218yescomplemented
63#11718732C2218yescomplemented
64#11718703C2218yescomplemented
65#11718702C2218yescomplemented
66#11718696C2218yescomplemented
67#11718695C2218yescomplemented
68#11718691C2218yescomplemented
69#11718683C2218yescomplemented
70#11718672C2218yescomplemented
71C2×#88050C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C2×C13×#41—22no—
78C2×C13×#41—22no—
79C2×C13×#41—24no—
80C2×C13×#41—24no—
81C2×C13×#41—42no—
82C2×C13×#41—42no—
83C2×C13×#41C2314yes—
84C2×C13×#41C2314yes—
85C22×Q8×C13C2311yescharacteristic
86C22×D4×C13—21no—
87C22×D4×C13—21no—
88C22×D4×C13—21no—
89C22×D4×C13—21no—
90C22×D4×C13—21no—
91C22×D4×C13—21no—
92C22×D4×C13D411yescharacteristic
93C22×D4×C13C2311yescharacteristic
94C22×D4×C13C2311yescharacteristic
95C23×C4×C13—21no—
96C23×C4×C13—21no—
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×Dic13—21no—
100C22×Dic26C2311yescharacteristic
101C13×#127—28no—
102C13×#127—22no—
103C13×#127C2314yes—
104C13×#121—22no—
105C13×#121—22no—
106C13×#121—28no—
107C13×#121—28no—
108C13×#121C2314yes—
109C13×#121C2314yes—
110C4×Q8×C13—22no—
111C4×Q8×C13C2314yes—
112C4×D4×C13—28no—
113C4×D4×C13D414yes—
114C4×D4×C13C2314yes—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4D411yescharacteristic
121C2×C13×C22⋊C4D411yescharacteristic
122C2×C42×C13—21no—
123C2×C42×C13C2311yescharacteristic
124C2×C22⋊Dic13—21no—
125C2×C22⋊Dic13—21no—
126C2×C22⋊Dic13—21no—
127C2×#6107—24no—
128C2×#6107C2314yes—
129#88189—28no—
130C2×#6105—42no—
131C2×#6105—42no—
132C2×#6105C2314yes—
133C2×#6105C2314yes—
134#88180—22no—
135#88180C2314yes—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—22no—
138C2×C4⋊Dic13C2311yescharacteristic
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2314yes—
142#88178—22no—
143#88178—22no—
144#88178C2314yes—
145#88178C2314yes—
146C2×#6101—21no—
147C2×#6101—21no—
148C2×#6101—21no—
149C2×#6101—21no—
150C2×#6101—21no—
151C2×C4×Dic13—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88143—28no—
162#88133—28no—
163#88131—28no—
164#88124—22no—
165#88124C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88072C2314yes—
172#88072C2314yes—
173#88072C2314yes—
174#88072C2314yes—
175#88072C2314yes—
176#88072C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3317—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13—21no—
188C24×C13C2×D411yescharacteristic
189C24×C13C2×D411yescharacteristic
190C13×#41—28no—
191C13×#41—28no—
192C13×#41—44no—
193C13×#41—44no—
194C13×#41—48no—
195C13×#41—48no—
196C2×Q8×C13—21no—
197C2×Q8×C13—22no—
198C2×Q8×C13#4114yes—
199C2×Q8×C13C2412yes—
200C2×D4×C13—24no—
201C2×D4×C13—24no—
202C2×D4×C13—24no—
203C2×D4×C13—24no—
204C2×D4×C13—24no—
205C2×D4×C13—21no—
206C2×D4×C13—21no—
207C2×D4×C13—24no—
208C2×D4×C13—22no—
209C2×D4×C13—22no—
210C2×D4×C13—22no—
211C2×D4×C13—22no—
212C2×D4×C13—42no—
213C2×D4×C13—44no—
214C2×D4×C13—44no—
215C2×D4×C13—44no—
216C2×D4×C13—82no—
217C2×D4×C13—82no—
218C2×D4×C13—82no—
219C2×D4×C13C2×D414yes—
220C2×D4×C13C2412yes—
221C2×D4×C13C2412yes—
222C22×C4×C13—21no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—22no—
227C22×C4×C13—21no—
228C22×C4×C13—24no—
229C22×C4×C13—24no—
230C22×C4×C13—44no—
231C22×C4×C13—44no—
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D412yes—
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2412yes—
239C22×C4×C13C2412yes—
240C22×C4×C13C2411yescharacteristic
241C22×Dic13—24no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—44no—
247C2×Dic26—22no—
248C2×Dic26—22no—
249C2×Dic26—21no—
250C2×Dic26C2412yes—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4C2×D414yes—
254C13×C4⋊C4C2412yes—
255C13×C22⋊C4—24no—
256C13×C22⋊C4—24no—
257C13×C22⋊C4C2×D414yes—
258C13×C22⋊C4C2×D414yes—
259C42×C13—24no—
260C42×C13C2×D412yes—
261C42×C13C2412yes—
262C22⋊Dic13—24no—
263C22⋊Dic13—24no—
264C22⋊Dic13—24no—
265#6107—28no—
266#6105—44no—
267#6105—44no—
268C4⋊Dic13—21no—
269C4⋊Dic13—21no—
270C4⋊Dic13—21no—
271C4⋊Dic13—24no—
272C4⋊Dic13C2412yes—
273C4⋊Dic13C2412yes—
274C4⋊Dic13C2412yes—
275#6101—24no—
276#6101—24no—
277#6101—24no—
278#6101—24no—
279#6101—24no—
280C4×Dic13—24no—
281C4×Dic13—24no—
282#6099—44no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—22no—
287C2×#1055—44no—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#1055C2412yes—
292C2×#552—131no—
293C2×#550D1311yescharacteristic
294#3317—1316no—
295C2×#490—131no—
296C2×#481—131no—
297C2×#482—131no—
298C2×#479—131no—
299C2×#468—131no—
300C2×#465—131no—
301C2×#460—131no—
302C2×#452—131no—
303C2×#452—131no—
304C2×#441—131no—
305C2×#435—131no—
306C2×#417—131no—
307C2×#416—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13C22×D412yes—
323C23×C13C22×D412yes—
324C23×C13C22×D411yescharacteristic
325Q8×C13—24no—
326Q8×C13—22no—
327Q8×C13C2×#4114yes—
328D4×C13—22no—
329D4×C13—22no—
330D4×C13—22no—
331D4×C13—22no—
332D4×C13—44no—
333D4×C13—48no—
334D4×C13—48no—
335D4×C13—48no—
336D4×C13—42no—
337D4×C13—42no—
338D4×C13—84no—
339D4×C13—84no—
340D4×C13—84no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—24no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—24no—
348C2×C4×C13—24no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—48no—
355C2×C4×C13—48no—
356C2×C4×C13—42no—
357C2×C4×C13C22×D412yes—
358C2×C4×C13C22×D412yes—
359C2×C4×C13C22×D412yes—
360C2×C4×C13C22×D412yes—
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C2×#4112yes—
363C2×C4×C13H(5,𝔽2)12yes—
364C2×C4×C13C2511yescharacteristic
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—48no—
370C2×Dic13—42no—
371C2×Dic13—42no—
372C2×Dic13—42no—
373C2×Dic13—42no—
374Dic26—22no—
375Dic26—22no—
376Dic26—42no—
377#1055—22no—
378#1055—22no—
379#1055—22no—
380#1055—22no—
381C22×#41C2×D1311yescharacteristic
382C22×#41C2×D1311yescharacteristic
383C22×Q16—131no—
384C22×SD16—131no—
385C22×SD16—131no—
386C22×M16—131no—
387C23×C8—131no—
388#552—138no—
389#552—264no—
390#550—24no—
391#550C2×D1318yes—
392C2×#127—21no—
393C2×#127C2×D1311yescharacteristic
394C2×#126—261no—
395C2×#125—131no—
396C2×#125—261no—
397C2×#123—261no—
398C2×C22⋊Q8—131no—
399C2×C22⋊Q8—131no—
400C2×#121—21no—
401C2×#121—21no—
402C2×#121C2×D1311yescharacteristic
403C2×#121C2×D1311yescharacteristic
404C2×C4×Q8—131no—
405C2×C4×Q8C2×D1311yescharacteristic
406C2×C4×D4—21no—
407C2×C4×D4C2×D1311yescharacteristic
408C2×#117—131no—
409C2×#117—261no—
410C22×C4⋊C4—131no—
411#490—138no—
412#482—138no—
413#481—138no—
414#479—138no—
415#468—138no—
416#465—138no—
417#460—138no—
418#452—138no—
419#452—138no—
420#441—138no—
421#435—138no—
422C2×#107—131no—
423C2×#106—131no—
424C2×#106—131no—
425C2×C4⋊C8—131no—
426#417—138no—
427#416—138no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×C22⋊C8—131no—
439C2×C22⋊C8—131no—
440C2×#97—131no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—44no—
448C22×C13—44no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—84no—
456C22×C13—84no—
457C22×C13#54612yes—
458C22×C13#57512yes—
459C22×C13#57712yes—
460C22×C13C23×D411yescharacteristic
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—24no—
464C4×C13—22no—
465C4×C13—22no—
466C4×C13—42no—
467C4×C13#54612yes—
468C4×C13C22×#4111yescharacteristic
469C4×C13C2×H(5,𝔽2)11yescharacteristic
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—24no—
478C2×#41—42no—
479C2×#41—42no—
480C2×#41C22×D1314yes—
481C2×#41C22×D1314yes—
482C22×Q8—131no—
483C22×Q8C22×D1311yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D1311yescharacteristic
491C22×D4C22×D1311yescharacteristic
492C22×D4C22×D1311yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×Q16—134no—
499C2×Q16—264no—
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—522no—
503C2×SD16—522no—
504C2×M16—134no—
505C2×M16—522no—
506C22×C8—131no—
507C22×C8—131no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—134no—
511C22×C8—522no—
512#127—28no—
513#127—22no—
514#127C22×D1314yes—
515#126—268no—
516#125—134no—
517#125—268no—
518#125—262no—
519#123—268no—
520C22⋊Q8—134no—
521C22⋊Q8—134no—
522C22⋊Q8—262no—
523C22⋊Q8—262no—
524#121—22no—
525#121—22no—
526#121—28no—
527#121—28no—
528#121C22×D1314yes—
529#121C22×D1314yes—
530C4×Q8—22no—
531C4×Q8—134no—
532C4×Q8—262no—
533C4×Q8C22×D1314yes—
534C4×D4—28no—
535C4×D4C22⋊D1314yes—
536C4×D4C22×D1314yes—
537#117—134no—
538#117—262no—
539#117—268no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—131no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4—262no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4—261no—
551C2×C4⋊C4—261no—
552C2×C4⋊C4C22⋊D1311yescharacteristic
553C2×C4⋊C4C22×D1311yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—261no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4C22⋊D1311yescharacteristic
560C2×C22⋊C4C22⋊D1311yescharacteristic
561C2×C42—21no—
562C2×C42—261no—
563C2×C42—261no—
564C2×C42C22×D1311yescharacteristic
565#107—134no—
566#106—134no—
567#106—134no—
568C4⋊C8—134no—
569#103—134no—
570#103—134no—
571#103—134no—
572#103—134no—
573#102—134no—
574#102—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579C22⋊C8—134no—
580C22⋊C8—134no—
581#97—134no—
582C2×C13—42no—
583C2×C13—42no—
584C2×C13—82no—
585C2×C13—82no—
586C2×C13#331714yescomplemented
587C2×C13C2×#54611yescharacteristic
588C2×C13C2×#57511yescharacteristic
589C2×C13C2×#57711yescharacteristic
590C24—21no—
591C24—21no—
592C24C2×C22⋊D1311yescharacteristic
593C24C2×C22⋊D1311yescharacteristic
594#41—28no—
595#41—28no—
596#41—44no—
597#41—44no—
598#41—48no—
599#41—48no—
600C2×Q8—22no—
601C2×Q8—21no—
602C2×Q8—132no—
603C2×Q8—261no—
604C2×Q8—262no—
605C2×Q8—262no—
606C2×Q8#612914yes—
607C2×Q8C23×D1312yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—24no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—82no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4C2×C22⋊D1314yes—
628C2×D4C23×D1312yes—
629C2×D4C23×D1312yes—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—264no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—524no—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—268no—
656SD16—524no—
657SD16—524no—
658M16—524no—
659C2×C8—132no—
660C2×C8—132no—
661C2×C8—132no—
662C2×C8—132no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—262no—
667C2×C8—524no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—132no—
671C4⋊C4—132no—
672C4⋊C4—132no—
673C4⋊C4—261no—
674C4⋊C4—261no—
675C4⋊C4—264no—
676C4⋊C4—261no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—264no—
680C4⋊C4—264no—
681C4⋊C4—264no—
682C4⋊C4C2×C22⋊D1314yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—264no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4C2×C22⋊D1314yes—
690C22⋊C4C2×C22⋊D1314yes—
691C42—24no—
692C42—264no—
693C42—264no—
694C42C2×C22⋊D1312yes—
695C42C23×D1312yes—
696C13C2×#331711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×C22⋊D1312yes—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—262no—
717Q8—262no—
718Q8—522no—
719Q8C2×#612914yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—528no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4C2×#612912yes—
759C2×C4#8825112yes—
760C2×C4C22×C22⋊D1312yes—
761C2×C4C22×C22⋊D1312yes—
762C2×C4C22×C22⋊D1312yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1311yescharacteristic
765C2×C4C24×D1311yescharacteristic
766C8—262no—
767C8—262no—
768C8—262no—
769C8—262no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#1171951112yes—
787C22#1171952712yes—
788C22#1171954112yes—
789C22C23×C22⋊D1311yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—522no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4#1171951112yes—
801C4C22×#612911yescharacteristic
802C4C2×#8825111yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#1312696214yesdirect product factor
808C2C2×#1171951111yescharacteristic
809C2C2×#1171952711yescharacteristic
810C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#550C2
socleC23×C13C22×D4
hypercenterC2×#550D13
hypocenterC13C2×#3317
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#11719246C2semidirect
2. #13126962C2direct (N × H)
3. C2×#11718732C2semidirect
4. C2×#11718695C2semidirect
5. C2×#11718696C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718703C2semidirect
8. C2×#11718702C2semidirect
9. C2×#11718736C2semidirect
10. C2×#11718900C2semidirect
11. C2×#11718900C2semidirect
12. C2×#11718691C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718893C2semidirect
15. C2×#11718894C2semidirect
41. #11719246C22semidirect
47. #11718900C22semidirect
48. #11718900C22semidirect
49. #11718894C22semidirect
50. #11718893C22semidirect
62. #11718736C22semidirect
63. #11718732C22semidirect
64. #11718703C22semidirect
65. #11718702C22semidirect
66. #11718696C22semidirect
67. #11718695C22semidirect
68. #11718691C22semidirect
69. #11718683C22semidirect
70. #11718672C22semidirect
586. C2×C13#3317semidirect
696. C13C2×#3317semidirect
807. C2#13126962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
#131269622
C2×#117187322
C2×#117186952
C2×#117186962
C2×#117186832
C2×#117187032
C2×#117187022
C2×#117187362
C2×#117189002
C2×#117186912
C2×#117186722
C2×#117188932
C2×#117188942
C2×C13×#5502
C2×#331713