Finite Group Databasebeta

← C2×#13125035 #16731166

Subgroups — C2×#13125035 #16731166

Order 3328.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719240C211yesmaximal, characteristic, complemented
2#13125035C2116yesmaximal, direct product factor
3C2×#11718629C211yesmaximal, characteristic, complemented
4C2×#11718628C211yesmaximal, characteristic, complemented
5C2×#11718683C211yesmaximal, characteristic, complemented
6C2×#11718670C211yesmaximal, characteristic, complemented
7C2×#11718688C211yesmaximal, characteristic, complemented
8C2×#11718676C211yesmaximal, characteristic, complemented
9C2×#11718899C211yesmaximal, characteristic, complemented
10C2×#11718899C211yesmaximal, characteristic, complemented
11C2×#11718675C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×C4×#6106C211yesmaximal, characteristic, complemented
14C2×C4×#6104C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#520C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C13×#520—24no—
19C13×#520C2218yescomplemented
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4—21no—
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6104C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88184C2211yescharacteristic
36#11719240—24no—
37#11719240C2218yescomplemented
38C2×#88148—21no—
39C2×#88148—21no—
40C2×#88138—21no—
41C2×#88138—21no—
42C2×#88128C2211yescharacteristic
43C2×C4×D52C2211yescharacteristic
44C2×C4×D52C2211yescharacteristic
45C2×#88124C2211yescharacteristic
46#11718899C2218yescomplemented
47#11718899C2218yescomplemented
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718688C2218yescomplemented
55#11718687C2218yescomplemented
56C4×#6106C2218yescomplemented
57#11718683C2218yescomplemented
58#11718676C2218yescomplemented
59#11718675C2218yescomplemented
60C4×#6104C2218yescomplemented
61#11718670C2218yescomplemented
62#11718661C2218yescomplemented
63#11718629C2218yescomplemented
64#11718628C2218yescomplemented
65C2×#88049C2211yescharacteristic
66C2×#88049C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C2×C13×#41—24no—
78C2×C13×#41—24no—
79C2×C13×#41—22no—
80C2×C13×#41C2314yes—
81C22×Q8×C13C2311yescharacteristic
82C22×D4×C13—21no—
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13—21no—
87C23×C4×C13—21no—
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—21no—
90C22×C22⋊D13—21no—
91C22×D52—21no—
92C22×D52—21no—
93C22×D52C2311yescharacteristic
94C22×D52C2311yescharacteristic
95C22×C4×D13—21no—
96C22×C4×D13—21no—
97C4×Q8×C13—22no—
98C4×Q8×C13—22no—
99C4×Q8×C13C2314yes—
100C4×Q8×C13C2314yes—
101C4×D4×C13—28no—
102C4×D4×C13—28no—
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13C2314yes—
106C4×D4×C13C2314yes—
107C13×#117—28no—
108C13×#117D414yes—
109C13×#117C2314yes—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—28no—
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4D411yescharacteristic
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C42×C13—21no—
125C2×C42×C13—21no—
126C2×C42×C13C2311yescharacteristic
127C2×C42×C13C2311yescharacteristic
128C2×#6106—24no—
129C2×#6106—24no—
130C2×#6106C2314yes—
131C2×#6106C2314yes—
132C2×#6104—24no—
133C2×#6104—24no—
134C2×#6104C2314yes—
135C2×#6104C2314yes—
136#88184—22no—
137#88184—22no—
138#88184C2314yes—
139#88184C2314yes—
140C2×#6103—21no—
141C2×#6103—21no—
142C2×#6103—21no—
143C2×#6103—21no—
144C2×C4⋊Dic13C2311yescharacteristic
145C2×C4⋊Dic13C2311yescharacteristic
146C2×#6101—21no—
147C2×#6101—21no—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152#88148—28no—
153#88148—28no—
154#88138—28no—
155#88138—28no—
156#88128—22no—
157#88128C2314yes—
158C4×D52—22no—
159C4×D52—22no—
160C4×D52C2314yes—
161C4×D52C2314yes—
162#88124—22no—
163#88124C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168C22⋊#1055C2314yes—
169C22⋊#1055C2314yes—
170#88049C2314yes—
171#88049C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180#88043C2314yes—
181C4×#1055C2314yes—
182C2×#3119—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C23×D13—21no—
187C13×#41—216no—
188C13×#41—28no—
189C13×#41—28no—
190C2×Q8×C13—21no—
191C2×Q8×C13—22no—
192C2×Q8×C13#4114yes—
193C2×Q8×C13C2412yes—
194C2×D4×C13—28no—
195C2×D4×C13—24no—
196C2×D4×C13—21no—
197C2×D4×C13—22no—
198C2×D4×C13#4114yes—
199C2×D4×C13C2412yes—
200C22×C4×C13—28no—
201C22×C4×C13—21no—
202C22×C4×C13—24no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—24no—
208C22×C4×C13—24no—
209C22×C4×C13—24no—
210C22×C4×C13—82no—
211C22×C4×C13—82no—
212C22×C4×C13—82no—
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2411yescharacteristic
221C2×C22⋊D13—24no—
222C2×C22⋊D13—24no—
223C2×C22⋊D13—82no—
224C2×C22⋊D13—82no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C2×D52—22no—
228C2×D52—22no—
229C2×D52—22no—
230C2×D52—22no—
231C2×D52—21no—
232C2×D52—21no—
233C2×D52—24no—
234C2×D52—24no—
235C2×D52—82no—
236C2×D52—82no—
237C2×D52C2412yes—
238C2×D52C2412yes—
239C2×C4×D13—24no—
240C2×C4×D13—24no—
241C2×C4×D13—82no—
242C2×C4×D13—82no—
243C13×C4⋊C4—24no—
244C13×C4⋊C4—24no—
245C13×C4⋊C4—24no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4C2×D414yes—
249C13×C4⋊C4C2×D414yes—
250C13×C4⋊C4C2412yes—
251C13×C4⋊C4C2412yes—
252C13×C22⋊C4—24no—
253C13×C22⋊C4—24no—
254C13×C22⋊C4C2×D414yes—
255C13×C22⋊C4C2×D414yes—
256C42×C13—24no—
257C42×C13—24no—
258C42×C13C2×D412yes—
259C42×C13C2×D412yes—
260C42×C13C2412yes—
261C42×C13C2412yes—
262#6106—28no—
263#6106—28no—
264#6104—28no—
265#6104—28no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270C4⋊Dic13—21no—
271C4⋊Dic13—21no—
272C4⋊Dic13C2412yes—
273C4⋊Dic13C2412yes—
274#6101—24no—
275#6101—24no—
276C2×#1055—22no—
277C2×#1055—22no—
278C2×#1055—22no—
279C2×#1055—22no—
280C2×#1055C2412yes—
281C2×#1055C2412yes—
282C2×#1055C2412yes—
283C2×#1055C2412yes—
284C2×#540—131no—
285C2×#520D1311yescharacteristic, complemented
286#3119—1316no—
287C2×#481—131no—
288C2×#480—131no—
289C2×#479—131no—
290C2×#478—131no—
291C2×#460—131no—
292C2×#459—131no—
293C2×#449—131no—
294C2×#449—131no—
295C2×#442—131no—
296C2×#440—131no—
297C2×C4×SD16—131no—
298C2×C4×D8—131no—
299C2×#433—131no—
300C23×C13—22no—
301C23×C13—24no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—42no—
306C23×C13—42no—
307C23×C13C22×D412yes—
308C23×C13C22×D411yescharacteristic
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—42no—
312C22×D13—42no—
313C22×D13—42no—
314C22×D13—42no—
315C22×D13—42no—
316C22×D13—42no—
317Q8×C13—24no—
318Q8×C13—22no—
319Q8×C13C2×#4114yes—
320D4×C13—216no—
321D4×C13—24no—
322D4×C13—22no—
323D4×C13C2×#4114yes—
324C2×C4×C13—216no—
325C2×C4×C13—22no—
326C2×C4×C13—24no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—24no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—84no—
340C2×C4×C13—84no—
341C2×C4×C13—84no—
342C2×C4×C13C22×D412yes—
343C2×C4×C13C22×D412yes—
344C2×C4×C13C22×D412yes—
345C2×C4×C13C22×D412yes—
346C2×C4×C13C22×D412yes—
347C2×C4×C13C22×D411yescharacteristic
348C2×C4×C13C2×#4112yes—
349C2×C4×C13C2×#4112yes—
350C2×C4×C13C2511yescharacteristic
351C22⋊D13—84no—
352C22⋊D13—84no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357D52—22no—
358D52—22no—
359D52—22no—
360D52—22no—
361D52—42no—
362D52—42no—
363D52—84no—
364D52—84no—
365C4×D13—84no—
366C4×D13—84no—
367#1055—22no—
368#1055—22no—
369#1055—22no—
370#1055—22no—
371C22×#41C2×D1311yescharacteristic
372C22×SD16—131no—
373C22×SD16—131no—
374C22×D8—131no—
375C22×D8—131no—
376#540—138no—
377#540—264no—
378C2×#127—131no—
379C2×#125—131no—
380C2×#123—261no—
381C2×#123—261no—
382C2×#121—131no—
383C2×#121—131no—
384C2×#121—261no—
385C2×#121—261no—
386#520—24no—
387#520C2×D1318yescomplemented
388C2×C4×Q8C2×D1311yescharacteristic
389C2×C4×Q8C2×D1311yescharacteristic
390C2×C4×D4—21no—
391C2×C4×D4—21no—
392C2×C4×D4—131no—
393C2×C4×D4—131no—
394C2×C4×D4C2×D1311yescharacteristic
395C2×C4×D4C2×D1311yescharacteristic
396C2×#117—21no—
397C2×#117C2×D1311yescharacteristic
398C22×C4⋊C4—21no—
399C22×C4⋊C4C2×D1311yescharacteristic
400#481—138no—
401#480—138no—
402#479—138no—
403#478—138no—
404#460—138no—
405#459—138no—
406#449—138no—
407#449—138no—
408#442—138no—
409#440—138no—
410C4×SD16—138no—
411C4×D8—138no—
412#433—138no—
413C2×#107—131no—
414C2×#107—131no—
415C2×#106—131no—
416C2×#106—131no—
417C2×C4⋊C8—131no—
418C2×C4⋊C8—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#102—131no—
422C2×#102—131no—
423C2×#102—131no—
424C2×#102—131no—
425C2×#102—131no—
426C2×#102—131no—
427C2×C22⋊C8—131no—
428C2×C22⋊C8—131no—
429C2×#97—131no—
430C2×C4×C8—131no—
431C22×C13—22no—
432C22×C13—24no—
433C22×C13—22no—
434C22×C13—22no—
435C22×C13—44no—
436C22×C13—48no—
437C22×C13—42no—
438C22×C13—42no—
439C22×C13#52512yes—
440C22×C13#57612yes—
441C22×C13#57712yes—
442C22×C13C23×D411yescharacteristic
443C2×D13—42no—
444C2×D13—42no—
445C2×D13—42no—
446C2×D13—42no—
447C2×D13—42no—
448C2×D13—42no—
449C2×D13—84no—
450C2×D13—84no—
451C4×C13—22no—
452C4×C13—24no—
453C4×C13—22no—
454C4×C13—22no—
455C4×C13—22no—
456C4×C13—22no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13#52512yes—
460C4×C13C22×#4111yescharacteristic
461C4×C13C22×#4111yescharacteristic
462Dic13—42no—
463Dic13—42no—
464C2×#41—24no—
465C2×#41—24no—
466C2×#41—22no—
467C2×#41C22×D1314yes—
468C22×Q8C22×D1311yescharacteristic
469C22×D4—21no—
470C22×D4—131no—
471C22×D4—131no—
472C22×D4—261no—
473C22×D4—261no—
474C22×D4—261no—
475C22×D4—261no—
476C22×D4C22×D1311yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—261no—
482C23×C4—261no—
483C23×C4C22×D1311yescharacteristic
484C2×SD16—134no—
485C2×SD16—134no—
486C2×SD16—264no—
487C2×SD16—264no—
488C2×D8—134no—
489C2×D8—134no—
490C2×D8—264no—
491C2×D8—264no—
492C22×C8—131no—
493C22×C8—131no—
494C22×C8—131no—
495C22×C8—131no—
496#127—134no—
497#127—262no—
498#125—134no—
499#125—262no—
500#123—268no—
501#123—268no—
502#121—134no—
503#121—134no—
504#121—262no—
505#121—262no—
506#121—268no—
507#121—268no—
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8C22×D1314yes—
511C4×Q8C22×D1314yes—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—134no—
517C4×D4—134no—
518C4×D4—262no—
519C4×D4—262no—
520C4×D4C22×D1314yes—
521C4×D4C22×D1314yes—
522#117—28no—
523#117C22⋊D1314yes—
524#117C22×D1314yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—131no—
531C2×C4⋊C4—131no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4C22⋊D1311yescharacteristic
535C2×C4⋊C4C22⋊D1311yescharacteristic
536C2×C4⋊C4C22×D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C4⋊C4C22×D1314yes—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C22⋊C4—261no—
544C2×C22⋊C4—261no—
545C2×C22⋊C4C22⋊D1311yescharacteristic
546C2×C22⋊C4C22⋊D1311yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C22×D1311yescharacteristic
550C2×C42C22×D1311yescharacteristic
551#107—134no—
552#107—134no—
553#106—134no—
554#106—134no—
555C4⋊C8—134no—
556C4⋊C8—134no—
557#103—134no—
558#103—134no—
559#102—134no—
560#102—134no—
561#102—134no—
562#102—134no—
563#102—134no—
564#102—134no—
565C22⋊C8—134no—
566C22⋊C8—134no—
567#97—134no—
568C4×C8—134no—
569C2×C13—42no—
570C2×C13—44no—
571C2×C13#311914yescomplemented
572C2×C13C2×#52511yescharacteristic
573C2×C13C2×#57611yescharacteristic
574C2×C13C2×#57711yescharacteristic
575D13—82no—
576D13—82no—
577C24—21no—
578C24—261no—
579C24—261no—
580C24C2×C22⋊D1311yescharacteristic
581#41—216no—
582#41—28no—
583#41—28no—
584C2×Q8—22no—
585C2×Q8—21no—
586C2×Q8#612714yes—
587C2×Q8C23×D1312yes—
588C2×D4—28no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—132no—
593C2×D4—132no—
594C2×D4—264no—
595C2×D4—264no—
596C2×D4—262no—
597C2×D4—262no—
598C2×D4—262no—
599C2×D4—262no—
600C2×D4—261no—
601C2×D4—261no—
602C2×D4—264no—
603C2×D4—264no—
604C2×D4—1042no—
605C2×D4—1042no—
606C2×D4—1042no—
607C2×D4—1042no—
608C2×D4#612714yes—
609C2×D4C23×D1312yes—
610C22×C4—28no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—264no—
626C22×C4—264no—
627C22×C4—1042no—
628C22×C4—1042no—
629C22×C4C2×C22⋊D1312yes—
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C2×C22⋊D1311yescharacteristic
635C22×C4C23×D1312yes—
636C22×C4C23×D1311yescharacteristic
637SD16—268no—
638SD16—268no—
639D8—268no—
640D8—268no—
641C2×C8—132no—
642C2×C8—132no—
643C2×C8—132no—
644C2×C8—132no—
645C2×C8—262no—
646C2×C8—262no—
647C2×C8—262no—
648C2×C8—262no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—132no—
655C4⋊C4—132no—
656C4⋊C4—261no—
657C4⋊C4—261no—
658C4⋊C4—264no—
659C4⋊C4—264no—
660C4⋊C4C2×C22⋊D1314yes—
661C4⋊C4C2×C22⋊D1314yes—
662C4⋊C4C23×D1312yes—
663C4⋊C4C23×D1312yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—264no—
667C22⋊C4—264no—
668C22⋊C4—264no—
669C22⋊C4—264no—
670C22⋊C4C2×C22⋊D1314yes—
671C22⋊C4C2×C22⋊D1314yes—
672C42—24no—
673C42—24no—
674C42C2×C22⋊D1312yes—
675C42C2×C22⋊D1312yes—
676C42C23×D1312yes—
677C42C23×D1312yes—
678C13C2×#311911yescharacteristic, complemented, Sylow
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—262no—
687C23—262no—
688C23—522no—
689C23—522no—
690C23—522no—
691C23—522no—
692C23—522no—
693C23—522no—
694C23C22×C22⋊D1312yes—
695C23C22×C22⋊D1311yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#612714yes—
699D4—216no—
700D4—24no—
701D4—22no—
702D4—262no—
703D4—262no—
704D4—262no—
705D4—262no—
706D4—522no—
707D4—522no—
708D4—1044no—
709D4—1044no—
710D4—1044no—
711D4—1044no—
712D4C2×#612714yes—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—1044no—
736C2×C4—1044no—
737C2×C4C2×#612712yes—
738C2×C4C2×#612712yes—
739C2×C4C22×C22⋊D1312yes—
740C2×C4C22×C22⋊D1312yes—
741C2×C4C22×C22⋊D1312yes—
742C2×C4C22×C22⋊D1312yes—
743C2×C4C22×C22⋊D1312yes—
744C2×C4C22×C22⋊D1311yescharacteristic
745C2×C4C24×D1311yescharacteristic
746C8—262no—
747C8—262no—
748C8—262no—
749C8—262no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22—1044no—
765C22—1044no—
766C22#1171949612yes—
767C22#1171954012yes—
768C22#1171954212yes—
769C22C23×C22⋊D1311yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—522no—
779C4—522no—
780C4#1171949612yes—
781C4C22×#612711yescharacteristic
782C4C22×#612711yescharacteristic
783C2—42no—
784C2—44no—
785C2—1042no—
786C2—1042no—
787C2#1312503514yesdirect product factor
788C2C2×#1171949611yescharacteristic
789C2C2×#1171954011yescharacteristic
790C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
hypercenterC2×#520D13
hypocenterC13C2×#3119
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11719240C2semidirect
2. #13125035C2direct (N × H)
3. C2×#11718629C2semidirect
4. C2×#11718628C2semidirect
5. C2×#11718683C2semidirect
6. C2×#11718670C2semidirect
7. C2×#11718688C2semidirect
8. C2×#11718676C2semidirect
9. C2×#11718899C2semidirect
10. C2×#11718899C2semidirect
11. C2×#11718675C2semidirect
12. C2×#11718687C2semidirect
13. C2×C4×#6106C2semidirect
14. C2×C4×#6104C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#520C2semidirect
19. C13×#520C22semidirect
37. #11719240C22semidirect
46. #11718899C22semidirect
47. #11718899C22semidirect
54. #11718688C22semidirect
55. #11718687C22semidirect
56. C4×#6106C22semidirect
57. #11718683C22semidirect
58. #11718676C22semidirect
59. #11718675C22semidirect
60. C4×#6104C22semidirect
61. #11718670C22semidirect
62. #11718661C22semidirect
63. #11718629C22semidirect
64. #11718628C22semidirect
285. C2×#520D13semidirect
387. #520C2×D13semidirect
571. C2×C13#3119semidirect
678. C13C2×#3119semidirect
787. C2#13125035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192402
#131250352
C2×#117186292
C2×#117186282
C2×#117186832
C2×#117186702
C2×#117186882
C2×#117186762
C2×#117188992
C2×#117186752
C2×#117186872
C2×C4×#61062
C2×C4×#61042
C2×#117186612
C2×C13×#5202
C2×#311913