Finite Group Databasebeta

← C2×#13126806 #16739551

Subgroups — C2×#13126806 #16739551

Order 3328.

2190 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×#11719256C211yesmaximal, characteristic, complemented
2#13126806C2116yesmaximal, direct product factor
3C2×#11718730C211yesmaximal, characteristic, complemented
4C2×#11718657C211yesmaximal, characteristic, complemented
5C2×#11718632C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718703C211yesmaximal, characteristic, complemented
8C2×#11718702C211yesmaximal, characteristic, complemented
9C2×#11718680C211yesmaximal, characteristic, complemented
10C2×#11718698C211yesmaximal, characteristic, complemented
11C2×#11718698C211yesmaximal, characteristic, complemented
12C2×#11718675C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718627C211yesmaximal, characteristic, complemented
15C2×#11718663C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C22×#6127C2211yescharacteristic
19C13×#553—24no—
20C13×#553C2218yescomplemented
21C2×C13×#126—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×#121—21no—
25C2×C13×#121C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C2×#88192—21no—
33C22×#6105C2211yescharacteristic
34C22×#6105C2211yescharacteristic
35C22×#6104C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719256—24no—
41#11719256C2218yescomplemented
42C2×C4⋊C4×D13—21no—
43C2×#88137—21no—
44C2×#88137—21no—
45C2×C4×D52C2211yescharacteristic
46C2×#88123C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718730C2218yescomplemented
51#11718727C2218yescomplemented
52#11718703C2218yescomplemented
53#11718702C2218yescomplemented
54#11718698C2218yescomplemented
55#11718698C2218yescomplemented
56#11718680C2218yescomplemented
57#11718675C2218yescomplemented
58#11718672C2218yescomplemented
59#11718663C2218yescomplemented
60#11718657C2218yescomplemented
61#11718632C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68#11718627C2218yescomplemented
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×C22⋊D13—21no—
86C22×C22⋊D13—21no—
87C2×#6127—22no—
88C2×#6127—22no—
89C2×#6127—24no—
90C2×#6127—24no—
91C2×#6127—42no—
92C2×#6127—42no—
93C2×#6127C2314yes—
94C2×#6127C2314yes—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×C4×D13—21no—
98C22×C4×D13—21no—
99C22×Dic26C2311yescharacteristic
100C22×Dic26C2311yescharacteristic
101C13×#126—28no—
102C13×#125—22no—
103C13×#125C2314yes—
104C13×#123—28no—
105C13×#121—28no—
106C13×#121—22no—
107C13×#121—22no—
108C13×#121C2314yes—
109C13×#121C2314yes—
110C4×D4×C13—28no—
111C4×D4×C13—22no—
112C4×D4×C13D414yes—
113C4×D4×C13C2314yes—
114C4×D4×C13C2314yes—
115C13×#117—22no—
116C13×#117C2314yes—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C4⋊C4C2314yes—
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4D411yescharacteristic
131C2×C13×C22⋊C4D411yescharacteristic
132C2×C42×C13—21no—
133C2×C42×C13C2311yescharacteristic
134C2×C22⋊Dic13—21no—
135C2×C22⋊Dic13—21no—
136#88192—28no—
137C2×#6105—42no—
138C2×#6105—42no—
139C2×#6105C2314yes—
140C2×#6105C2314yes—
141C2×#6104—24no—
142C2×#6104C2314yes—
143C2×#6103—21no—
144C2×C4⋊Dic13—21no—
145C2×C4⋊Dic13—21no—
146C2×C4⋊Dic13C2311yescharacteristic
147#88178—22no—
148#88178—22no—
149#88178C2314yes—
150#88178C2314yes—
151C2×#6101—21no—
152C2×#6101—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161C4⋊C4×D13—28no—
162#88137—28no—
163#88137—28no—
164C4×D52—22no—
165C4×D52C2314yes—
166#88123—22no—
167#88123C2314yes—
168#88072C2314yes—
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88049C2314yes—
178#88049C2314yes—
179#88049C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3307—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13C2×D411yescharacteristic
188C24×C13C2×D411yescharacteristic
189C23×D13—21no—
190C2×D4×C13—24no—
191C2×D4×C13—24no—
192C2×D4×C13—21no—
193C2×D4×C13—22no—
194C2×D4×C13—22no—
195C2×D4×C13—42no—
196C2×D4×C13—44no—
197C2×D4×C13—82no—
198C2×D4×C13C2×D414yes—
199C2×D4×C13C2412yes—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—24no—
208C22×C4×C13—24no—
209C22×C4×C13—82no—
210C22×C4×C13—82no—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×D412yes—
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2411yescharacteristic
220C2×C22⋊D13—24no—
221C2×C22⋊D13—24no—
222C2×C22⋊D13—44no—
223C2×C22⋊D13—44no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227#6127—28no—
228#6127—28no—
229#6127—44no—
230#6127—44no—
231#6127—48no—
232#6127—48no—
233C2×D52—21no—
234C2×D52—22no—
235C2×D52#4114yes—
236C2×D52C2412yes—
237C2×C4×D13—24no—
238C2×C4×D13—24no—
239C2×C4×D13—24no—
240C2×C4×D13—44no—
241C2×C4×D13—44no—
242C2×C4×D13—44no—
243C2×Dic26—22no—
244C2×Dic26—22no—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—21no—
248C2×Dic26—21no—
249C2×Dic26C2412yes—
250C2×Dic26C2412yes—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—24no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4C2×D414yes—
258C13×C4⋊C4C2412yes—
259C13×C4⋊C4C2412yes—
260C13×C4⋊C4C2412yes—
261C13×C22⋊C4—24no—
262C13×C22⋊C4—24no—
263C13×C22⋊C4—24no—
264C13×C22⋊C4—24no—
265C13×C22⋊C4C2×D414yes—
266C13×C22⋊C4C2×D414yes—
267C42×C13—24no—
268C42×C13C2×D412yes—
269C42×C13C2412yes—
270C22⋊Dic13—24no—
271C22⋊Dic13—24no—
272#6105—44no—
273#6105—44no—
274#6104—28no—
275#6103—24no—
276C4⋊Dic13—24no—
277C4⋊Dic13—24no—
278C4⋊Dic13—21no—
279C4⋊Dic13C2412yes—
280#6101—24no—
281#6101—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×#553D1311yescharacteristic, complemented
293C2×#547—131no—
294#3307—1316no—
295C2×#491—131no—
296C2×#485—131no—
297C2×#483—131no—
298C2×#478—131no—
299C2×#468—131no—
300C2×#465—131no—
301C2×#461—131no—
302C2×#449—131no—
303C2×#449—131no—
304C2×#442—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—42no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13C22×D412yes—
319C23×C13C22×D412yes—
320C23×C13C22×D411yescharacteristic
321C22×D13—24no—
322C22×D13—22no—
323C22×D13—42no—
324C22×D13—42no—
325D4×C13—22no—
326D4×C13—22no—
327D4×C13—44no—
328D4×C13—48no—
329D4×C13—42no—
330D4×C13—84no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—24no—
336C2×C4×C13—24no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—84no—
348C2×C4×C13—84no—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D411yescharacteristic
354C2×C4×C13C2×#4112yes—
355C2×C4×C13H(5,𝔽2)12yes—
356C2×C4×C13C2511yescharacteristic
357C22⋊D13—48no—
358C22⋊D13—48no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365D52—24no—
366D52—22no—
367D52C2×#4114yes—
368C4×D13—48no—
369C4×D13—48no—
370C4×D13—48no—
371Dic26—22no—
372Dic26—22no—
373Dic26—22no—
374Dic26—22no—
375Dic26—42no—
376Dic26—42no—
377#1055—22no—
378#1055—22no—
379#1055—22no—
380#1055—22no—
381C22×#41—131no—
382C22×#41—131no—
383C22×SD16—131no—
384C22×SD16—131no—
385C22×D8—131no—
386C22×M16—131no—
387C23×C8—131no—
388#553—24no—
389#553C2×D1318yescomplemented
390#547—138no—
391#547—264no—
392C2×C4⋊Q8—131no—
393C2×#126—21no—
394C2×#125C2×D1311yescharacteristic
395C2×#123—21no—
396C2×#123—261no—
397C2×#123—261no—
398C2×C22⋊Q8—131no—
399C2×C22⋊Q8—131no—
400C2×#121—21no—
401C2×#121—261no—
402C2×#121C2×D1311yescharacteristic
403C2×#121C2×D1311yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4—131no—
406C2×C4×D4C2×D1311yescharacteristic
407C2×C4×D4C2×D1311yescharacteristic
408C2×#117C2×D1311yescharacteristic
409C22×C4⋊C4—261no—
410C22×C4⋊C4C2×D1311yescharacteristic
411#491—138no—
412#485—138no—
413#483—138no—
414#478—138no—
415#468—138no—
416#465—138no—
417#461—138no—
418#449—138no—
419#449—138no—
420#442—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×#103—131no—
433C2×#103—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—84no—
453C22×C13#54612yes—
454C22×C13#57512yes—
455C22×C13#57712yes—
456C22×C13C23×D411yescharacteristic
457C2×D13—24no—
458C2×D13—48no—
459C2×D13—42no—
460C2×D13—42no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#54612yes—
469C4×C13C22×#4111yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—134no—
475C2×#41—134no—
476C2×#41—264no—
477C2×#41—264no—
478C2×#41—262no—
479C2×#41—262no—
480C2×#41—522no—
481C2×#41—522no—
482C22×Q8—131no—
483C22×Q8—131no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—131no—
487C22×D4—261no—
488C22×D4—261no—
489C22×D4C22⋊D1311yescharacteristic
490C22×D4C22×D1311yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—261no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×SD16—134no—
499C2×SD16—134no—
500C2×SD16—522no—
501C2×SD16—522no—
502C2×D8—134no—
503C2×D8—264no—
504C2×M16—134no—
505C2×M16—522no—
506C22×C8—131no—
507C22×C8—131no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—134no—
511C22×C8—522no—
512C4⋊Q8—134no—
513C4⋊Q8—262no—
514#126—28no—
515#125—22no—
516#125C22×D1314yes—
517#123—28no—
518#123—268no—
519#123—268no—
520C22⋊Q8—134no—
521C22⋊Q8—134no—
522C22⋊Q8—262no—
523C22⋊Q8—262no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121—268no—
528#121C22×D1314yes—
529#121C22×D1314yes—
530C4×D4—28no—
531C4×D4—22no—
532C4×D4—134no—
533C4×D4—262no—
534C4×D4C22⋊D1314yes—
535C4×D4C22×D1314yes—
536C4×D4C22×D1314yes—
537#117—22no—
538#117C22×D1314yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—131no—
544C2×C4⋊C4—261no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4—261no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—268no—
549C2×C4⋊C4C22⋊D1311yescharacteristic
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1314yes—
553C2×C4⋊C4C22×D1311yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4C22⋊D1311yescharacteristic
562C2×C22⋊C4C22⋊D1311yescharacteristic
563C2×C42—21no—
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#103—134no—
574#103—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#330714yescomplemented
586C2×C13C2×#54611yescharacteristic
587C2×C13C2×#57511yescharacteristic
588C2×C13C2×#57711yescharacteristic
589D13—44no—
590C24—21no—
591C24—261no—
592C24C2×C22⋊D1311yescharacteristic
593C24C2×C22⋊D1311yescharacteristic
594#41—268no—
595#41—268no—
596#41—524no—
597#41—524no—
598#41—528no—
599#41—528no—
600C2×Q8—132no—
601C2×Q8—132no—
602C2×Q8—261no—
603C2×Q8—261no—
604C2×Q8—262no—
605C2×Q8—262no—
606C2×Q8—262no—
607C2×Q8—262no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—82no—
616C2×D4—134no—
617C2×D4—132no—
618C2×D4—264no—
619C2×D4—264no—
620C2×D4—262no—
621C2×D4—261no—
622C2×D4—524no—
623C2×D4—524no—
624C2×D4C2×C22⋊D1314yes—
625C2×D4C23×D1312yes—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—82no—
636C22×C4—82no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—264no—
641C22×C4—264no—
642C22×C4—264no—
643C22×C4—524no—
644C22×C4—524no—
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
655SD16—524no—
656SD16—524no—
657D8—268no—
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—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—132no—
675C4⋊C4—261no—
676C4⋊C4—264no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—264no—
680C4⋊C4C2×C22⋊D1314yes—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4C2×C22⋊D1314yes—
692C22⋊C4C2×C22⋊D1314yes—
693C42—24no—
694C42C2×C22⋊D1312yes—
695C42C23×D1312yes—
696C13C2×#330711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—264no—
708C23—262no—
709C23—522no—
710C23—522no—
711C23C22×C22⋊D1312yes—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—262no—
715Q8—262no—
716Q8—262no—
717Q8—262no—
718Q8—522no—
719Q8—522no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—42no—
725D4—84no—
726D4—134no—
727D4—264no—
728D4—262no—
729D4—528no—
730D4—528no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
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—84no—
748C2×C4—84no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—528no—
753C2×C4—528no—
754C2×C4—528no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4#41×D1312yes—
759C2×C4#8825612yes—
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—84no—
782C22—264no—
783C22—522no—
784C22—522no—
785C22—528no—
786C22#1171952712yes—
787C22#1171953412yes—
788C22#1171954112yes—
789C22C23×C22⋊D1311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4#1171953412yes—
801C4C2×#41×D1311yescharacteristic
802C4C2×#8825611yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—524no—
807C2#1312680614yesdirect product factor
808C2C2×#1171953411yescharacteristic
809C2C2×#1171952711yescharacteristic
810C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3307
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11719256C2semidirect
2. #13126806C2direct (N × H)
3. C2×#11718730C2semidirect
4. C2×#11718657C2semidirect
5. C2×#11718632C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718703C2semidirect
8. C2×#11718702C2semidirect
9. C2×#11718680C2semidirect
10. C2×#11718698C2semidirect
11. C2×#11718698C2semidirect
12. C2×#11718675C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718627C2semidirect
15. C2×#11718663C2semidirect
16. C2×C13×#553C2semidirect
20. C13×#553C22semidirect
41. #11719256C22semidirect
50. #11718730C22semidirect
51. #11718727C22semidirect
52. #11718703C22semidirect
53. #11718702C22semidirect
54. #11718698C22semidirect
55. #11718698C22semidirect
56. #11718680C22semidirect
57. #11718675C22semidirect
58. #11718672C22semidirect
59. #11718663C22semidirect
60. #11718657C22semidirect
61. #11718632C22semidirect
68. #11718627C22semidirect
292. C2×#553D13semidirect
389. #553C2×D13semidirect
585. C2×C13#3307semidirect
696. C13C2×#3307semidirect
807. C2#13126806direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192562
#131268062
C2×#117187302
C2×#117186572
C2×#117186322
C2×#117187272
C2×#117187032
C2×#117187022
C2×#117186802
C2×#117186982
C2×#117186752
C2×#117186722
C2×#117186272
C2×#117186632
C2×C13×#5532
C2×#330713