Finite Group Databasebeta

← C2×#13127457 #16741664

Subgroups — C2×#13127457 #16741664

Order 3328.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719321C211yesmaximal, characteristic
2C2×#11719340C211yesmaximal, characteristic, complemented
3#13127457C2116yesmaximal, direct product factor
4C2×#11718535C211yesmaximal, characteristic, complemented
5C2×#11718476C211yesmaximal, characteristic, complemented
6C2×#11718706C211yesmaximal, characteristic, complemented
7C2×#11718435C211yesmaximal, characteristic, complemented
8C2×#11718694C211yesmaximal, characteristic, complemented
9C2×#11718455C211yesmaximal, characteristic, complemented
10C2×#11718422C211yesmaximal, characteristic, complemented
11C2×#11718835C211yesmaximal, characteristic, complemented
12C2×SD16×Dic13C211yesmaximal, characteristic, complemented
13C2×#11718789C211yesmaximal, characteristic, complemented
14C2×#11718782C211yesmaximal, characteristic, complemented
15C2×#11718542C211yesmaximal, characteristic, complemented
16C2×C13×#468C211yesmaximal, characteristic, complemented
17C22×C13×SD16C2211yescharacteristic
18C22×C13×M16C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×#88200C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×#88193—21no—
24C2×#88192C2211yescharacteristic
25C2×#88190—21no—
26C2×D4×Dic13C2211yescharacteristic
27C2×C4×C22⋊D13C2211yescharacteristic
28C2×#88180C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6094C2211yescharacteristic
31#11719340—24no—
32#11719340C2218yescomplemented
33#11719321—24no—
34#11719321C2218yes—
35C2×#88151—21no—
36C2×#88146C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88143—21no—
39C2×#88142C2211yescharacteristic
40C2×#88142C2211yescharacteristic
41C2×#88139—21no—
42C2×#88135—21no—
43C2×#88132—21no—
44C2×#88131—21no—
45C13×#468C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718835C2218yescomplemented
55SD16×Dic13C2218yescomplemented
56#11718789C2218yescomplemented
57#11718782C2218yescomplemented
58C2×#88060C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88057C2211yescharacteristic
62C2×#88057C2211yescharacteristic
63C2×#88054C2211yescharacteristic
64C2×C8×Dic13C2211yescharacteristic
65#11718706C2218yescomplemented
66#11718694C2218yescomplemented
67C2×#88048C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718542C2218yescomplemented
72#11718535C2218yescomplemented
73#11718476C2218yescomplemented
74#11718455C2218yescomplemented
75#11718435C2218yescomplemented
76#11718422C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13D411yescharacteristic
83C23×Dic13—21no—
84C23×Dic13—21no—
85C22×C4×D13—21no—
86C22×C4×D13C2311yescharacteristic
87C22×Dic26—21no—
88C22×Dic26—21no—
89C2×C13×SD16—24no—
90C2×C13×SD16C2314yes—
91C2×C13×M16—24no—
92C2×C13×M16C2314yes—
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8C2314yes—
97C13×#121—22no—
98C13×#121C2314yes—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13D411yescharacteristic
108#88200—22no—
109#88200C2314yes—
110Q8×Dic13—22no—
111Q8×Dic13C2314yes—
112#88193—28no—
113#88192—22no—
114#88192C2314yes—
115#88190—28no—
116D4×Dic13—22no—
117D4×Dic13C2314yes—
118C4×C22⋊D13D414yes—
119C4×C22⋊D13C2314yes—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103D411yescharacteristic
123#88180—22no—
124#88180C2314yes—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—22no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×#6101D411yescharacteristic
138C2×C4×Dic13—21no—
139C2×C4×Dic13—21no—
140C2×C4×Dic13—21no—
141C2×C4×Dic13C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C2×#6094—24no—
145C2×#6094C2314yes—
146#88151—28no—
147#88146—22no—
148#88146C2314yes—
149C4⋊C4×D13—22no—
150C4⋊C4×D13C2314yes—
151#88143—28no—
152#88142—22no—
153#88142—22no—
154#88142C2314yes—
155#88142C2314yes—
156#88139—28no—
157#88135—28no—
158#88132—28no—
159#88131—28no—
160C13×#107C2314yes—
161C13×#103C2314yes—
162C13×#102C2314yes—
163#88075C2314yes—
164#88075C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167C22⋊#1055C2314yes—
168#88060C2314yes—
169#88058C2314yes—
170#88058C2314yes—
171#88057C2314yes—
172#88057C2314yes—
173#88054C2314yes—
174C8×Dic13C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179C2×#3357—131nomaximal, Sylow
180C24×C13—21no—
181C24×C13C2×D411yescharacteristic
182C23×D13C2×D411yescharacteristic
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13C2412yes—
187C2×D4×C13—24no—
188C2×D4×C13—21no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—82no—
192C2×D4×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—24no—
203C2×C22⋊D13—24no—
204C2×C22⋊D13—82no—
205C2×C22⋊D13C2×D414yes—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—24no—
211C22×Dic13—24no—
212C22×Dic13—44no—
213C22×Dic13—82no—
214C22×Dic13C2×D411yescharacteristic
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—24no—
220C2×C4×D13—82no—
221C2×C4×D13C2×D412yes—
222C2×C4×D13C2412yes—
223C2×Dic26—24no—
224C2×Dic26—24no—
225C2×Dic26—82no—
226C2×Dic26—82no—
227C13×SD16—28no—
228C13×M16—28no—
229C2×C8×C13—22no—
230C2×C8×C13#4114yes—
231C2×C8×C13C2412yes—
232C2×C8×C13C2412yes—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C22⋊Dic13—24no—
241C22⋊Dic13—24no—
242C22⋊Dic13—24no—
243C22⋊Dic13C2×D414yes—
244#6103—24no—
245#6103—24no—
246#6103C2×D414yes—
247C4⋊Dic13—21no—
248C4⋊Dic13—21no—
249C4⋊Dic13—24no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—24no—
253C4⋊Dic13C2412yes—
254C4⋊Dic13C2412yes—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101C2×D414yes—
262C4×Dic13—24no—
263C4×Dic13—24no—
264C4×Dic13—24no—
265C4×Dic13C2×D412yes—
266C4×Dic13C2412yes—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271#6094—28no—
272C2×#555—131no—
273C2×#554—131no—
274#3357—1316no—
275C2×#500—131no—
276C2×#485—131no—
277C2×#485—131no—
278C2×#480—131no—
279C2×#480—131no—
280C2×#477—131no—
281C2×#476—131no—
282C2×#468—131no—
283C2×#468D1311yescharacteristic, complemented
284C2×C4×SD16—131no—
285C2×#436—131no—
286C2×#428—131no—
287C2×#428—131no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—42no—
293C23×C13—42no—
294C23×C13—42no—
295C23×C13C22×D412yes—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13C22×D412yes—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—42no—
304D4×C13—22no—
305D4×C13—22no—
306D4×C13—42no—
307D4×C13—84no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13C22×D412yes—
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C13C2×#4112yes—
321C2×C4×C132−1+412yes—
322C2×C4×C13C2511yescharacteristic
323C22⋊D13—28no—
324C22⋊D13—84no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—48no—
336C2×Dic13—84no—
337C2×Dic13#13714yes—
338C2×Dic13C22×D412yes—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341C4×D13—24no—
342C4×D13—22no—
343C4×D13—22no—
344C4×D13—84no—
345Dic26—84no—
346Dic26—84no—
347C8×C13—22no—
348C8×C13C2×#4114yes—
349#1055—22no—
350#1055—22no—
351C22×SD16C2×D1311yescharacteristic
352C22×M16—131no—
353C22×M16C2×D1311yescharacteristic
354#555—138no—
355#555—264no—
356#554—138no—
357#554—264no—
358C2×C4⋊Q8—131no—
359C2×C4⋊Q8—131no—
360C2×#125—261no—
361C2×#124—261no—
362C2×#124—261no—
363C2×C22⋊Q8—131no—
364C2×C22⋊Q8—261no—
365C2×C22⋊Q8—261no—
366C2×C22⋊Q8C2×D1311yescharacteristic
367C2×#121—131no—
368C2×#121—261no—
369C2×#121C2×D1311yescharacteristic
370C2×C4×Q8—131no—
371C2×C4×D4—131no—
372C2×C4×D4—131no—
373C2×C4×D4—261no—
374C2×#117—131no—
375C2×#117—131no—
376C2×#117—261no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379#500—138no—
380#485—138no—
381#485—138no—
382#480—138no—
383#480—138no—
384#477—138no—
385#476—138no—
386#468—138no—
387#468C2×D1318yescomplemented
388C4×SD16—138no—
389#436—138no—
390#428—138no—
391#428—138no—
392C2×#107—131no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107C2×D1311yescharacteristic
398C2×#106—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103C2×D1311yescharacteristic
405C2×#102—131no—
406C2×#102—131no—
407C2×#102C2×D1311yescharacteristic
408C2×C22⋊C8—131no—
409C2×C22⋊C8—131no—
410C2×C4×C8—131no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13—44no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—84no—
419C22×C13#54712yes—
420C22×C13C2×#13712yes—
421C22×C13#57612yes—
422C22×C13C23×D411yescharacteristic
423C2×D13—22no—
424C2×D13—22no—
425C2×D13—22no—
426C2×D13—44no—
427C4×C13—22no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13#54712yes—
432C4×C13C22×#4111yescharacteristic
433C4×C13C2×2−1+411yescharacteristic
434Dic13—22no—
435Dic13—22no—
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13C2×#13714yes—
441C22×Q8—261no—
442C22×Q8—261no—
443C22×Q8C22×D1311yescharacteristic
444C22×D4—21no—
445C22×D4—131no—
446C22×D4—261no—
447C22×D4C22×D1311yescharacteristic
448C23×C4—131no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4—261no—
452C23×C4C22×D1311yescharacteristic
453C2×SD16—24no—
454C2×SD16C22×D1314yes—
455C2×M16—24no—
456C2×M16—134no—
457C2×M16—264no—
458C2×M16C22×D1314yes—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8C22×D1311yescharacteristic
462C22×C8C22×D1311yescharacteristic
463C4⋊Q8—134no—
464C4⋊Q8—134no—
465C4⋊Q8—262no—
466C4⋊Q8—262no—
467#125—268no—
468#124—268no—
469#124—268no—
470C22⋊Q8—22no—
471C22⋊Q8—134no—
472C22⋊Q8—268no—
473C22⋊Q8—268no—
474C22⋊Q8—262no—
475C22⋊Q8C22×D1314yes—
476#121—22no—
477#121—134no—
478#121—262no—
479#121—268no—
480#121C22×D1314yes—
481C4×Q8—134no—
482C4×Q8—262no—
483C4×D4—134no—
484C4×D4—134no—
485C4×D4—134no—
486C4×D4—262no—
487C4×D4—268no—
488#117—134no—
489#117—134no—
490#117—268no—
491#117—262no—
492#117—262no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—262no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—131no—
514C2×C22⋊C4—131no—
515C2×C22⋊C4—261no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C42—131no—
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524#107—134no—
525#107—134no—
526#107—134no—
527#107—134no—
528#107—134no—
529#107C22×D1314yes—
530#106—134no—
531#106—134no—
532#106—134no—
533C4⋊C8—134no—
534#103—134no—
535#103—134no—
536#103C22×D1314yes—
537#102—134no—
538#102—134no—
539#102C22×D1314yes—
540C22⋊C8—134no—
541C22⋊C8—134no—
542C4×C8—134no—
543C2×C13—42no—
544C2×C13—82no—
545C2×C13#335714yescomplemented
546C2×C13C2×#54711yescharacteristic
547C2×C13C22×#13711yescharacteristic
548C2×C13C2×#57611yescharacteristic
549D13—42no—
550C24—21no—
551C24—131no—
552C24D4×D1311yescharacteristic
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—264no—
557C2×Q8—264no—
558C2×Q8—1042no—
559C2×Q8—1042no—
560C2×Q8C23×D1312yes—
561C2×D4—24no—
562C2×D4—21no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—82no—
566C2×D4—134no—
567C2×D4—264no—
568C2×D4—264no—
569C2×D4—1042no—
570C2×D4C23×D1312yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—131no—
577C22×C4—131no—
578C22×C4—131no—
579C22×C4—132no—
580C22×C4—132no—
581C22×C4—264no—
582C22×C4—264no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—264no—
590C22×C4—524no—
591C22×C4—1042no—
592C22×C4—1042no—
593C22×C4D4×D1312yes—
594C22×C4D4×D1311yescharacteristic
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597SD16—28no—
598M16—28no—
599M16—268no—
600C2×C8—22no—
601C2×C8—132no—
602C2×C8—132no—
603C2×C8—262no—
604C2×C8—262no—
605C2×C8#612914yes—
606C2×C8C23×D1312yes—
607C2×C8C23×D1312yes—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—134no—
612C4⋊C4—132no—
613C4⋊C4—132no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—264no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—261no—
622C4⋊C4—264no—
623C4⋊C4—261no—
624C4⋊C4—261no—
625C4⋊C4—261no—
626C4⋊C4C23×D1312yes—
627C4⋊C4C23×D1312yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—134no—
631C22⋊C4—134no—
632C22⋊C4—264no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C42—132no—
638C42—132no—
639C42—264no—
640C42—264no—
641C42—264no—
642C13C2×#335711yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—132no—
651C23—262no—
652C23—262no—
653C23—262no—
654C23C2×D4×D1312yes—
655C23C2×D4×D1311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1044no—
660Q8—1044no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—268no—
666D4—1044no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—134no—
678C2×C4—132no—
679C2×C4—132no—
680C2×C4—132no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—264no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—528no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—1044no—
696C2×C4—1044no—
697C2×C4C2×D4×D1312yes—
698C2×C4C2×D4×D1311yescharacteristic
699C2×C4C2×#612912yes—
700C2×C4#8825712yes—
701C2×C4C24×D1311yescharacteristic
702C8—22no—
703C8—262no—
704C8—262no—
705C8C2×#612914yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—262no—
715C22—262no—
716C22—262no—
717C22—524no—
718C22#1171931612yes—
719C22#1171947912yes—
720C22D13×#13712yes—
721C22C22×D4×D1311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—134no—
727C4—262no—
728C4—262no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4#1171931612yes—
734C4C22×#612911yescharacteristic
735C4C2×#8825711yescharacteristic
736C2—42no—
737C2—82no—
738C2—522no—
739C2#1312745714yesdirect product factor
740C2C2×#1171931611yescharacteristic
741C2C2×D13×#13711yescharacteristic
742C2C2×#1171947911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#468C2
socleC23×C13C22×D4
prime radicalC2×#11719321C2
hypercenterC2×#468D13
hypocenterC13C2×#3357
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#11719340C2semidirect
3. #13127457C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718476C2semidirect
6. C2×#11718706C2semidirect
7. C2×#11718435C2semidirect
8. C2×#11718694C2semidirect
9. C2×#11718455C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718835C2semidirect
12. C2×SD16×Dic13C2semidirect
13. C2×#11718789C2semidirect
14. C2×#11718782C2semidirect
15. C2×#11718542C2semidirect
16. C2×C13×#468C2semidirect
32. #11719340C22semidirect
45. C13×#468C22semidirect
54. #11718835C22semidirect
55. SD16×Dic13C22semidirect
56. #11718789C22semidirect
57. #11718782C22semidirect
65. #11718706C22semidirect
66. #11718694C22semidirect
71. #11718542C22semidirect
72. #11718535C22semidirect
73. #11718476C22semidirect
74. #11718455C22semidirect
75. #11718435C22semidirect
76. #11718422C22semidirect
283. C2×#468D13semidirect
387. #468C2×D13semidirect
545. C2×C13#3357semidirect
642. C13C2×#3357semidirect
739. C2#13127457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193212
C2×#117193402
#131274572
C2×#117185352
C2×#117184762
C2×#117187062
C2×#117184352
C2×#117186942
C2×#117184552
C2×#117184222
C2×#117188352
C2×SD16×Dic132
C2×#117187892
C2×#117187822
C2×#117185422
C2×C13×#4682
C2×#335713