Finite Group Databasebeta

← C2×#13127920 #16743945

Subgroups — C2×#13127920 #16743945

Order 3328.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719290C211yesmaximal, characteristic, complemented
2#13127920C2116yesmaximal, direct product factor
3C2×#11718719C211yesmaximal, characteristic, complemented
4C2×#11718735C211yesmaximal, characteristic, complemented
5C2×#11718720C211yesmaximal, characteristic, complemented
6C2×#11718689C211yesmaximal, characteristic, complemented
7C2×#11718715C211yesmaximal, characteristic, complemented
8C2×#11718677C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic, complemented
10C2×#11718676C211yesmaximal, characteristic, complemented
11C2×#11718733C211yesmaximal, characteristic, complemented
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718679C211yesmaximal, characteristic, complemented
14C2×#11718687C211yesmaximal, characteristic, complemented
15C2×C4×#6104C211yesmaximal, characteristic, complemented
16C2×C13×#559C211yesmaximal, characteristic, complemented
17C13×#559—24no—
18C13×#559C2218yescomplemented
19C2×C13×#127C2211yescharacteristic
20C2×C13×#124—21no—
21C2×C13×#124C2211yescharacteristic
22C2×C13×#124C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×#123—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×#88201—21no—
31C22×#6107C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C22×#6106C2211yescharacteristic
34C22×#6105C2211yescharacteristic
35C22×#6105C2211yescharacteristic
36C22×#6104C2211yescharacteristic
37C22×#6104C2211yescharacteristic
38C22×#6104C2211yescharacteristic
39C22×#6104C2211yescharacteristic
40#11719290—24no—
41#11719290C2218yescomplemented
42C2×#88148—21no—
43C2×#88148—21no—
44C2×#88147—21no—
45C2×#88129C2211yescharacteristic
46C2×#88129C2211yescharacteristic
47C2×#88128C2211yescharacteristic
48C2×C4×D52C2211yescharacteristic
49C2×C4×D52C2211yescharacteristic
50C2×C4×Dic26C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718735C2218yescomplemented
55#11718733C2218yescomplemented
56#11718720C2218yescomplemented
57#11718719C2218yescomplemented
58#11718718C2218yescomplemented
59#11718715C2218yescomplemented
60#11718689C2218yescomplemented
61#11718687C2218yescomplemented
62#11718685C2218yescomplemented
63#11718679C2218yescomplemented
64#11718677C2218yescomplemented
65#11718676C2218yescomplemented
66C4×#6104C2218yescomplemented
67C2×#88050C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88049C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×C4⋊#1055C2211yescharacteristic
72C2×C4⋊#1055C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13D411yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13C2311yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C23×C4×C13—21no—
84C23×C4×C13—21no—
85C22×D52—21no—
86C22×D52—21no—
87C22×D52C2311yescharacteristic
88C22×D52C2311yescharacteristic
89C22×C4×D13—21no—
90C22×C4×D13—21no—
91C22×Dic26C2311yescharacteristic
92C13×#127—22no—
93C13×#127C2314yes—
94C13×#124—28no—
95C13×#124—22no—
96C13×#124—22no—
97C13×#124C2314yes—
98C13×#124C2314yes—
99C13×#123—28no—
100C13×#123—28no—
101C4×Q8×C13—22no—
102C4×Q8×C13D414yes—
103C4×Q8×C13C2314yes—
104C4×Q8×C13C2314yes—
105C4×D4×C13—28no—
106C4×D4×C13—22no—
107C4×D4×C13—22no—
108C4×D4×C13C2314yes—
109C4×D4×C13C2314yes—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C42×C13—21no—
122C2×C42×C13C2311yescharacteristic
123C2×C42×C13C2311yescharacteristic
124C2×C42×C13C2311yescharacteristic
125#88201—28no—
126C2×#6107—42no—
127C2×#6107C2314yes—
128C2×#6106—24no—
129C2×#6106—42no—
130C2×#6106C2314yes—
131C2×#6106C2314yes—
132C2×#6105—24no—
133C2×#6105—42no—
134C2×#6105C2314yes—
135C2×#6105C2314yes—
136C2×#6104—24no—
137C2×#6104—42no—
138C2×#6104—42no—
139C2×#6104—42no—
140C2×#6104C2314yes—
141C2×#6104C2314yes—
142C2×#6104C2314yes—
143C2×#6104C2314yes—
144C2×#6103—21no—
145C2×#6103—21no—
146C2×#6103—21no—
147C2×#6103—21no—
148C2×#6103—21no—
149C2×#6103—21no—
150C2×C4⋊Dic13C2311yescharacteristic
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C22×#1055C2311yescharacteristic
154C22×#1055C2311yescharacteristic
155C22×#1055C2311yescharacteristic
156C22×#1055C2311yescharacteristic
157#88148—28no—
158#88148—28no—
159#88147—28no—
160#88129—22no—
161#88129—22no—
162#88129C2314yes—
163#88129C2314yes—
164#88128—22no—
165#88128C2314yes—
166C4×D52—22no—
167C4×D52—22no—
168C4×D52C2314yes—
169C4×D52C2314yes—
170C4×Dic26—22no—
171C4×Dic26C2314yes—
172#88075C2314yes—
173#88072C2314yes—
174#88072C2314yes—
175#88050C2314yes—
176#88049C2314yes—
177#88049C2314yes—
178#88047C2314yes—
179C4⋊#1055C2314yes—
180C4⋊#1055C2314yes—
181C4⋊#1055C2314yes—
182#88043C2314yes—
183#88043C2314yes—
184C4×#1055C2314yes—
185C2×#3403—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13—21no—
188C23×D13—21no—
189C23×D13—21no—
190C2×Q8×C13—21no—
191C2×Q8×C13—22no—
192C2×Q8×C13—22no—
193C2×Q8×C13—42no—
194C2×Q8×C13C2×D414yes—
195C2×Q8×C13C2412yes—
196C2×D4×C13—21no—
197C2×D4×C13—21no—
198C2×D4×C13—24no—
199C2×D4×C13—24no—
200C2×D4×C13—22no—
201C2×D4×C13—22no—
202C2×D4×C13—22no—
203C2×D4×C13—22no—
204C2×D4×C13—44no—
205C2×D4×C13—82no—
206C2×D4×C13C2412yes—
207C2×D4×C13C2412yes—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—24no—
211C22×C4×C13—24no—
212C22×C4×C13—82no—
213C22×C4×C13—82no—
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2411yescharacteristic
221C22×Dic13—21no—
222C22×Dic13—21no—
223C2×D52—22no—
224C2×D52—22no—
225C2×D52—22no—
226C2×D52—22no—
227C2×D52—21no—
228C2×D52—21no—
229C2×D52—24no—
230C2×D52—24no—
231C2×D52—44no—
232C2×D52—82no—
233C2×D52C2412yes—
234C2×D52C2412yes—
235C2×C4×D13—24no—
236C2×C4×D13—24no—
237C2×C4×D13—82no—
238C2×C4×D13—82no—
239C2×Dic26—22no—
240C2×Dic26—22no—
241C2×Dic26—21no—
242C2×Dic26C2412yes—
243C13×C4⋊C4—24no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4C2×D414yes—
246C13×C4⋊C4C2×D414yes—
247C13×C4⋊C4C2×D414yes—
248C13×C4⋊C4C2412yes—
249C13×C22⋊C4—24no—
250C13×C22⋊C4—24no—
251C13×C22⋊C4—24no—
252C13×C22⋊C4—24no—
253C13×C22⋊C4—24no—
254C13×C22⋊C4—24no—
255C42×C13—24no—
256C42×C13C2×D412yes—
257C42×C13C2×D412yes—
258C42×C13C2×D412yes—
259C42×C13C2412yes—
260C42×C13C2412yes—
261C42×C13C2412yes—
262#6107—44no—
263#6106—28no—
264#6106—44no—
265#6105—28no—
266#6105—44no—
267#6104—28no—
268#6104—44no—
269#6104—44no—
270#6104—44no—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274#6103—24no—
275#6103—24no—
276#6103—24no—
277C4⋊Dic13—21no—
278C4⋊Dic13C2412yes—
279#6101—24no—
280C4×Dic13—24no—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055#4114yes—
285C2×#1055C2412yes—
286C2×#1055C2412yes—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289C2×#559—131no—
290C2×#559D1311yescharacteristic, complemented
291#3403—1316no—
292C2×#496—131no—
293C2×#496—131no—
294C2×#495—131no—
295C2×#464—131no—
296C2×#464—131no—
297C2×#463—131no—
298C2×#463—131no—
299C2×#459—131no—
300C2×#459—131no—
301C2×#446—131no—
302C2×#440—131no—
303C2×#440—131no—
304C2×C4×D8—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—42no—
308C23×C13—42no—
309C23×C13—42no—
310C23×C13—42no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13C22×D411yescharacteristic
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—42no—
317C22×D13—42no—
318C22×D13—42no—
319C22×D13—42no—
320C22×D13—42no—
321C22×D13—42no—
322Q8×C13—22no—
323Q8×C13—22no—
324Q8×C13—44no—
325Q8×C13—42no—
326D4×C13—22no—
327D4×C13—22no—
328D4×C13—22no—
329D4×C13—22no—
330D4×C13—48no—
331D4×C13—42no—
332D4×C13—42no—
333D4×C13—84no—
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—22no—
341C2×C4×C13—22no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—84no—
345C2×C4×C13—84no—
346C2×C4×C13C22×D412yes—
347C2×C4×C13C22×D412yes—
348C2×C4×C13C22×D412yes—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D411yescharacteristic
353C2×C4×C13C2×#4112yes—
354C2×C4×C13H(5,𝔽2)12yes—
355C2×C4×C13C2511yescharacteristic
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360D52—22no—
361D52—22no—
362D52—22no—
363D52—22no—
364D52—48no—
365D52—42no—
366D52—42no—
367D52—84no—
368C4×D13—84no—
369C4×D13—84no—
370Dic26—22no—
371Dic26—22no—
372Dic26—42no—
373#1055—22no—
374#1055—22no—
375#1055—22no—
376#1055C2×#4114yes—
377C22×Q16—131no—
378C22×SD16—131no—
379C22×SD16—131no—
380C22×SD16—131no—
381C22×SD16—131no—
382C22×D8—131no—
383C22×D8—131no—
384C22×D8—131no—
385C22×D8—131no—
386#559—24no—
387#559—138no—
388#559—264no—
389#559C2×D1318yescomplemented
390C2×#127—131no—
391C2×#127C2×D1311yescharacteristic
392C2×#124—21no—
393C2×#124—131no—
394C2×#124—131no—
395C2×#124—261no—
396C2×#124C2×D1311yescharacteristic
397C2×#124C2×D1311yescharacteristic
398C2×#123—21no—
399C2×#123—21no—
400C2×#123—261no—
401C2×#123—261no—
402C2×C4×Q8—131no—
403C2×C4×Q8C2×D1311yescharacteristic
404C2×C4×Q8C2×D1311yescharacteristic
405C2×C4×D4—21no—
406C2×C4×D4—131no—
407C2×C4×D4—131no—
408C2×C4×D4—261no—
409C2×C4×D4C2×D1311yescharacteristic
410C2×C4×D4C2×D1311yescharacteristic
411#496—138no—
412#496—138no—
413#495—138no—
414#464—138no—
415#464—138no—
416#463—138no—
417#463—138no—
418#459—138no—
419#459—138no—
420#446—138no—
421#440—138no—
422#440—138no—
423C4×D8—138no—
424C2×#107—131no—
425C2×C4⋊C8—131no—
426C2×C4⋊C8—131no—
427C2×C4⋊C8—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#102—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#97—131no—
435C2×#97—131no—
436C2×C4×C8—131no—
437C22×C13—42no—
438C22×C13—42no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—84no—
444C22×C13—84no—
445C22×C13#55012yes—
446C22×C13#57512yes—
447C22×C13#57612yes—
448C22×C13C23×D411yescharacteristic
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—84no—
456C2×D13—84no—
457C4×C13—22no—
458C4×C13—22no—
459C4×C13—22no—
460C4×C13—22no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—42no—
464C4×C13—42no—
465C4×C13#55012yes—
466C4×C13C22×#4111yescharacteristic
467C4×C13C2×H(5,𝔽2)11yescharacteristic
468Dic13—42no—
469Dic13—42no—
470C22×Q8—131no—
471C22×Q8C22⋊D1311yescharacteristic
472C22×Q8C22×D1311yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—131no—
476C22×D4—131no—
477C22×D4—261no—
478C22×D4—261no—
479C22×D4C22×D1311yescharacteristic
480C22×D4C22×D1311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—261no—
484C23×C4—261no—
485C2×Q16—134no—
486C2×Q16—522no—
487C2×SD16—134no—
488C2×SD16—134no—
489C2×SD16—134no—
490C2×SD16—134no—
491C2×SD16—264no—
492C2×SD16—264no—
493C2×SD16—522no—
494C2×SD16—522no—
495C2×D8—134no—
496C2×D8—134no—
497C2×D8—134no—
498C2×D8—134no—
499C2×D8—264no—
500C2×D8—522no—
501C2×D8—522no—
502C2×D8—522no—
503C22×C8—131no—
504C22×C8—131no—
505C22×C8—131no—
506C22×C8—131no—
507#127—22no—
508#127—134no—
509#127—262no—
510#127C22×D1314yes—
511#124—28no—
512#124—22no—
513#124—22no—
514#124—134no—
515#124—134no—
516#124—268no—
517#124—262no—
518#124—262no—
519#124C22×D1314yes—
520#124C22×D1314yes—
521#123—28no—
522#123—28no—
523#123—268no—
524#123—268no—
525C4×Q8—22no—
526C4×Q8—134no—
527C4×Q8—262no—
528C4×Q8C22⋊D1314yes—
529C4×Q8C22×D1314yes—
530C4×Q8C22×D1314yes—
531C4×D4—28no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—134no—
535C4×D4—134no—
536C4×D4—268no—
537C4×D4—262no—
538C4×D4—262no—
539C4×D4C22×D1314yes—
540C4×D4C22×D1314yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—261no—
544C2×C4⋊C4C22⋊D1311yescharacteristic
545C2×C4⋊C4C22⋊D1311yescharacteristic
546C2×C4⋊C4C22⋊D1311yescharacteristic
547C2×C4⋊C4C22×D1311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—261no—
555C2×C22⋊C4—261no—
556C2×C22⋊C4—261no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C42—21no—
561C2×C42—261no—
562C2×C42C22×D1311yescharacteristic
563C2×C42C22×D1311yescharacteristic
564C2×C42C22×D1311yescharacteristic
565#107—134no—
566C4⋊C8—134no—
567C4⋊C8—134no—
568C4⋊C8—134no—
569#103—134no—
570#103—134no—
571#102—134no—
572#102—134no—
573#102—134no—
574#102—134no—
575#97—134no—
576#97—134no—
577C4×C8—134no—
578C2×C13—82no—
579C2×C13—82no—
580C2×C13#340314yescomplemented
581C2×C13C2×#55011yescharacteristic
582C2×C13C2×#57511yescharacteristic
583C2×C13C2×#57611yescharacteristic
584D13—82no—
585D13—82no—
586C24—21no—
587C24—21no—
588C24—261no—
589C24—261no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—42no—
594C2×Q8—132no—
595C2×Q8—261no—
596C2×Q8—262no—
597C2×Q8—262no—
598C2×Q8C2×C22⋊D1314yes—
599C2×Q8C23×D1312yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—44no—
609C2×D4—82no—
610C2×D4—132no—
611C2×D4—132no—
612C2×D4—262no—
613C2×D4—262no—
614C2×D4—262no—
615C2×D4—262no—
616C2×D4—264no—
617C2×D4—261no—
618C2×D4—261no—
619C2×D4—264no—
620C2×D4—524no—
621C2×D4—1042no—
622C2×D4C23×D1312yes—
623C2×D4C23×D1312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—264no—
633C22×C4—264no—
634C22×C4—1042no—
635C22×C4—1042no—
636C22×C4C2×C22⋊D1311yescharacteristic
637C22×C4C2×C22⋊D1311yescharacteristic
638C22×C4C2×C22⋊D1311yescharacteristic
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C2×C22⋊D1311yescharacteristic
641C22×C4C2×C22⋊D1311yescharacteristic
642C22×C4C23×D1311yescharacteristic
643Q16—524no—
644SD16—268no—
645SD16—268no—
646SD16—524no—
647SD16—524no—
648D8—268no—
649D8—524no—
650D8—524no—
651D8—524no—
652C2×C8—134no—
653C2×C8—132no—
654C2×C8—132no—
655C2×C8—132no—
656C2×C8—132no—
657C2×C8—262no—
658C2×C8—262no—
659C2×C8—262no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—132no—
663C4⋊C4—261no—
664C4⋊C4—264no—
665C4⋊C4C2×C22⋊D1314yes—
666C4⋊C4C2×C22⋊D1314yes—
667C4⋊C4C2×C22⋊D1314yes—
668C4⋊C4C23×D1312yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—264no—
676C22⋊C4—264no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C22⋊C4—264no—
680C22⋊C4—264no—
681C42—24no—
682C42—264no—
683C42C2×C22⋊D1312yes—
684C42C2×C22⋊D1312yes—
685C42C2×C22⋊D1312yes—
686C42C23×D1312yes—
687C42C23×D1312yes—
688C42C23×D1312yes—
689C13C2×#340311yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—262no—
699C23—262no—
700C23—522no—
701C23—522no—
702C23—522no—
703C23—522no—
704C23—522no—
705C23—522no—
706C23C22×C22⋊D1311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—262no—
712Q8—262no—
713Q8—522no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—262no—
723D4—262no—
724D4—262no—
725D4—262no—
726D4—528no—
727D4—522no—
728D4—522no—
729D4—1044no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—1044no—
747C2×C4—1044no—
748C2×C4#41×D1312yes—
749C2×C4#8825612yes—
750C2×C4C22×C22⋊D1312yes—
751C2×C4C22×C22⋊D1312yes—
752C2×C4C22×C22⋊D1312yes—
753C2×C4C22×C22⋊D1312yes—
754C2×C4C22×C22⋊D1312yes—
755C2×C4C22×C22⋊D1312yes—
756C2×C4C22×C22⋊D1311yescharacteristic
757C2×C4C24×D1311yescharacteristic
758C8—134no—
759C8—262no—
760C8—262no—
761C8—262no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—522no—
771C22—522no—
772C22—522no—
773C22—522no—
774C22—522no—
775C22—522no—
776C22—1044no—
777C22—1044no—
778C22#1171952712yes—
779C22#1171953912yes—
780C22#1171954012yes—
781C22C23×C22⋊D1311yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—522no—
791C4—522no—
792C4#1171953912yes—
793C4C2×#41×D1311yescharacteristic
794C4C2×#8825611yescharacteristic
795C2—82no—
796C2—82no—
797C2—1042no—
798C2—1042no—
799C2#1312792014yesdirect product factor
800C2C2×#1171953911yescharacteristic
801C2C2×#1171952711yescharacteristic
802C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#559C2
socleC23×C13C22×D4
hypercenterC2×#559D13
hypocenterC13C2×#3403
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#11719290C2semidirect
2. #13127920C2direct (N × H)
3. C2×#11718719C2semidirect
4. C2×#11718735C2semidirect
5. C2×#11718720C2semidirect
6. C2×#11718689C2semidirect
7. C2×#11718715C2semidirect
8. C2×#11718677C2semidirect
9. C2×#11718718C2semidirect
10. C2×#11718676C2semidirect
11. C2×#11718733C2semidirect
12. C2×#11718685C2semidirect
13. C2×#11718679C2semidirect
14. C2×#11718687C2semidirect
15. C2×C4×#6104C2semidirect
16. C2×C13×#559C2semidirect
18. C13×#559C22semidirect
41. #11719290C22semidirect
54. #11718735C22semidirect
55. #11718733C22semidirect
56. #11718720C22semidirect
57. #11718719C22semidirect
58. #11718718C22semidirect
59. #11718715C22semidirect
60. #11718689C22semidirect
61. #11718687C22semidirect
62. #11718685C22semidirect
63. #11718679C22semidirect
64. #11718677C22semidirect
65. #11718676C22semidirect
66. C4×#6104C22semidirect
290. C2×#559D13semidirect
389. #559C2×D13semidirect
580. C2×C13#3403semidirect
689. C13C2×#3403semidirect
799. C2#13127920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192902
#131279202
C2×#117187192
C2×#117187352
C2×#117187202
C2×#117186892
C2×#117187152
C2×#117186772
C2×#117187182
C2×#117186762
C2×#117187332
C2×#117186852
C2×#117186792
C2×#117186872
C2×C4×#61042
C2×C13×#5592
C2×#340313