Finite Group Databasebeta

← #15768439

Subgroups — #15768439

Order 3328.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719209C211yesmaximal, characteristic
2C22×#88045C211yesmaximal, characteristic
3C2×#11718627C211yesmaximal, characteristic
4C2×#11718122C211yesmaximal, characteristic, complemented
5#13114555C211yesmaximal, characteristic, complemented
6C2×#11718115C211yesmaximal, characteristic, complemented
7C13×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C2×C4×C22⋊D13—22no—
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16#11719209—22no—
17#11719209—22no—
18#11719209—22no—
19#11719209C414yescomplemented
20C2×#88147—21no—
21C2×#88146—21no—
22C2×C4⋊C4×D13—21no—
23C2×#88141—21no—
24C2×C13×#95—22no—
25C2×#88050—21no—
26#11718627—22no—
27#11718627C414yescomplemented
28C2×#88049—21no—
29C2×#88045—22no—
30C2×#88045—22no—
31C2×#88045C414yescomplemented
32#11718122—22no—
33#11718121—21no—
34#11718121—21no—
35#11718115—22no—
36C23×C4×C13—21no—
37C23×C4×C13—21no—
38C23×C4×C13D412yes—
39C23×C4×C13C2311yescharacteristic
40C22×C22⋊D13—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127C2×C412yes—
48C2×#6127C2×C412yes—
49C2×#6127C2×C412yes—
50C2×#6127D412yes—
51C2×#6127D412yes—
52C2×#6127Q812yes—
53C22×D52D411yescharacteristic
54C22×C4×D13—21no—
55C22×C4×D13—22no—
56C22×Dic26D411yescharacteristic
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2×C412yes—
67C2×C13×C4⋊C4C2×C412yescomplemented
68C2×C13×C4⋊C4D412yes—
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13C2×C412yescomplemented
75C2×C22⋊Dic13—21no—
76C4×C22⋊D13—28no—
77C4×C22⋊D13—28no—
78C2×#6103—22no—
79#88180—21no—
80#88180—21no—
81#88180C2×C412yes—
82#88180D412yes—
83C2×C4⋊Dic13D411yescharacteristic
84C2×C4⋊Dic13D411yescharacteristic
85C2×#6101—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099—21no—
91C2×#6099—21no—
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099—21no—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099C2×C412yescomplemented
99C2×#6099C2×C412yescomplemented
100C22×#1055—21no—
101C22×#1055—21no—
102#88147—24no—
103#88147—24no—
104#88146—24no—
105#88146—24no—
106C4⋊C4×D13—24no—
107C4⋊C4×D13—24no—
108#88141—24no—
109#88141—24no—
110C13×#95—44no—
111#88050—24no—
112#88049—24no—
113#88045—28no—
114#10781—131nomaximal, Sylow
115C24×C13C2×D411yescharacteristic
116C23×D13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13C22⋊C414yes—
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×Q811yescharacteristic
144C22×C4×C13#4111yescharacteristic
145C22×C4×C13#4111yescharacteristic
146C22×C4×C13#4111yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—22no—
149C2×C22⋊D13—22no—
150C2×C22⋊D13—22no—
151C2×C22⋊D13—22no—
152C2×C22⋊D13—22no—
153C2×C22⋊D13—22no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157#6127—22no—
158#6127—22no—
159#6127—22no—
160#6127—22no—
161#6127—22no—
162#6127—22no—
163#6127—22no—
164#6127—22no—
165#6127—22no—
166#6127—22no—
167#6127—22no—
168#6127—22no—
169#6127C4214yes—
170#6127C22⋊C414yes—
171#6127C4⋊C414yes—
172#6127C4⋊C414yes—
173C2×D52—21no—
174C2×D52—21no—
175C2×D52—21no—
176C2×D52C22⋊C412yes—
177C2×D52C22⋊C412yes—
178C2×D52C4⋊C412yes—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
183C2×C4×D13—22no—
184C2×C4×D13—22no—
185C2×C4×D13—28no—
186C2×C4×D13—82no—
187C2×C4×D13—82no—
188C2×Dic26—21no—
189C2×Dic26—21no—
190C2×Dic26—21no—
191C2×Dic26C22⋊C412yes—
192C2×Dic26C22⋊C412yes—
193C2×Dic26C4⋊C412yes—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—41no—
202C42×C13—22no—
203C42×C13—22no—
204C42×C13—41no—
205C42×C13—41no—
206C22⋊Dic13—22no—
207C22⋊Dic13—22no—
208#6103—28no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13C22⋊C412yes—
212C4⋊Dic13C22⋊C412yes—
213#6101—28no—
214C4×Dic13—28no—
215C4×Dic13—22no—
216C4×Dic13—22no—
217#6099—22no—
218#6099—22no—
219#6099—22no—
220#6099—22no—
221#6099—41no—
222#6099—41no—
223#6099—41no—
224#6099—41no—
225C2×#1055—22no—
226C2×#1055—22no—
227C2×#1055—41no—
228C2×#1055—41no—
229C2×#1055—41no—
230C2×#1055—41no—
231C2×#520—131no—
232C22×#104—131no—
233C2×#417—131no—
234C2×#343—131no—
235#1736—131no—
236C2×#339—131no—
237C4⋊#95D1311yescharacteristic, complemented
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13C2×C22⋊C411yescharacteristic
243C23×C13C4×D411yescharacteristic
244C23×C13C4×D411yescharacteristic
245C23×C13#12011yescharacteristic
246C23×C13#12011yescharacteristic
247C23×C13#12111yescharacteristic
248C23×C13C22⋊Q811yescharacteristic
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C22×D13—41no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—44no—
267C2×C4×C13—44no—
268C2×C4×C13—42no—
269C2×C4×C13—82no—
270C2×C4×C13—82no—
271C2×C4×C13—81no—
272C2×C4×C13—81no—
273C2×C4×C13C2×C4211yescharacteristic
274C2×C4×C13C2×C22⋊C411yescharacteristic
275C2×C4×C13C2×C22⋊C411yescharacteristic
276C2×C4×C13C2×C22⋊C411yescharacteristic
277C2×C4×C13C2×C22⋊C411yescharacteristic
278C2×C4×C13C2×C4⋊C411yescharacteristic
279C2×C4×C13C2×C4⋊C411yescharacteristic
280C2×C4×C13C2×C4⋊C411yescharacteristic
281C2×C4×C13#11711yescharacteristic
282C2×C4×C13#11711yescharacteristic
283C2×C4×C13C4×D411yescharacteristic
284C2×C4×C13C4×D411yescharacteristic
285C2×C4×C13C4×D411yescharacteristic
286C2×C4×C13C4×D411yescharacteristic
287C2×C4×C13C4×D411yescharacteristic
288C2×C4×C13C4×D411yescharacteristic
289C2×C4×C13#12011yescharacteristic
290C2×C4×C13#12011yescharacteristic
291C2×C4×C13#12111yescharacteristic
292C2×C4×C13#12111yescharacteristic
293C2×C4×C13#12111yescharacteristic
294C2×C4×C13C22⋊Q811yescharacteristic
295C2×C4×C13C22⋊Q811yescharacteristic
296C2×C4×C13C22⋊Q811yescharacteristic
297C2×C4×C13#12311yescharacteristic
298C2×C4×C13#12311yescharacteristic
299C2×C4×C13#12311yescharacteristic
300C2×C4×C13#12311yescharacteristic
301C22⋊D13—24no—
302C22⋊D13—24no—
303C22⋊D13—24no—
304C22⋊D13—24no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314D52—22no—
315D52—22no—
316D52—22no—
317D52#9514yescomplemented
318C4×D13—24no—
319C4×D13—24no—
320C4×D13—24no—
321C4×D13—24no—
322C4×D13—88no—
323Dic26—22no—
324Dic26—22no—
325Dic26—22no—
326Dic26#9514yescomplemented
327#1055—42no—
328#1055—42no—
329C22×#41—131no—
330C22×M16—131no—
331C22×M16—131no—
332#520—134no—
333#520—262no—
334#520—262no—
335#520—262no—
336C2×C4×Q8—261no—
337C2×C4×D4—261no—
338C2×C4×D4—262no—
339C2×#117—131no—
340C2×#117—261no—
341C22×C4⋊C4—261no—
342C22×C4⋊C4C2×D1311yescharacteristic
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C42C2×D1311yescharacteristic
345C2×#104—134no—
346C2×#104—262no—
347C2×#104—262no—
348#417—134no—
349#417—262no—
350C2×#103—261no—
351C2×#102—261no—
352C2×#95—22no—
353#343—262no—
354#340—261no—
355#340—261no—
356#339—262no—
357C22×C13—21no—
358C22×C13—21no—
359C22×C13—21no—
360C22×C13—21no—
361C22×C13—21no—
362C22×C13—21no—
363C22×C13—21no—
364C22×C13—21no—
365C22×C13—21no—
366C22×C13—21no—
367C22×C13—21no—
368C22×C13—21no—
369C22×C13C4×C22⋊C411yescharacteristic
370C22×C13#37911yescharacteristic
371C22×C13#38011yescharacteristic
372C22×C13#38511yescharacteristic
373C22×C13#38511yescharacteristic
374C22×C13#38611yescharacteristic
375C22×C13#38611yescharacteristic
376C22×C13#45311yescharacteristic
377C22×C13#45411yescharacteristic
378C22×C13#45511yescharacteristic
379C22×C13#45611yescharacteristic
380C2×D13—24no—
381C2×D13—42no—
382C2×D13—42no—
383C2×D13—42no—
384C2×D13—42no—
385C2×D13—42no—
386C2×D13—42no—
387C4×C13—44no—
388C4×C13—44no—
389C4×C13—82no—
390C4×C13C2×#9511yescharacteristic
391C4×C13C4×C22⋊C411yescharacteristic
392C4×C13#38011yescharacteristic
393C4×C13#38111yescharacteristic
394C4×C13#38511yescharacteristic
395C4×C13#38511yescharacteristic
396C4×C13#38611yescharacteristic
397C4×C13#38611yescharacteristic
398Dic13—24no—
399Dic13—42no—
400Dic13—42no—
401C2×#41—132no—
402C2×#41—132no—
403C2×#41—132no—
404C2×#41—132no—
405C2×#41—132no—
406C2×#41—132no—
407C2×#41—261no—
408C2×#41—261no—
409C2×#41—261no—
410C2×#41—261no—
411C2×#41—261no—
412C2×#41—261no—
413C22×Q8—131no—
414C22×D4—131no—
415C22×D4—261no—
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—262no—
419C23×C4—261no—
420C23×C4C22⋊D1312yes—
421C23×C4C22×D1311yescharacteristic
422C2×M16—132no—
423C2×M16—132no—
424C2×M16—261no—
425C2×M16—261no—
426C2×M16—261no—
427C2×M16—261no—
428C2×M16—261no—
429C2×M16—261no—
430C2×M16—261no—
431C2×M16—261no—
432C2×M16—261no—
433C2×M16—261no—
434C22×C8—261no—
435C22×C8—261no—
436C4×Q8—264no—
437C4×Q8—264no—
438C4×D4—264no—
439C4×D4—264no—
440C4×D4—268no—
441C4×D4—268no—
442#117—132no—
443#117—132no—
444#117—264no—
445#117—264no—
446#117—261no—
447#117—261no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—264no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4C4×D1312yes—
463C2×C4⋊C4C4×D1312yescomplemented
464C2×C4⋊C4D5212yes—
465C2×C22⋊C4—262no—
466C2×C22⋊C4—261no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—262no—
473C2×C42—261no—
474C2×C42C4×D1312yescomplemented
475#104—268no—
476#103—264no—
477#102—264no—
478#95—44no—
479C2×C13—21no—
480C2×C13—21no—
481C2×C13—21no—
482C2×C13—21no—
483C2×C13C22⋊#9511yescharacteristic
484C2×C13#179211yescharacteristic
485C2×C13#179311yescharacteristic
486C2×C13#185911yescharacteristic
487C2×C13#186011yescharacteristic
488C2×C13#188211yescharacteristic
489C2×C13#188311yescharacteristic
490D13—44no—
491C24—261no—
492C24C2×C22⋊D1311yescharacteristic
493#41—134no—
494#41—134no—
495#41—134no—
496#41—134no—
497#41—262no—
498#41—262no—
499#41—262no—
500#41—262no—
501#41—262no—
502#41—262no—
503#41—262no—
504#41—262no—
505#41—262no—
506#41—262no—
507#41—262no—
508#41—262no—
509C2×Q8—132no—
510C2×Q8—132no—
511C2×Q8—132no—
512C2×Q8—261no—
513C2×Q8—261no—
514C2×Q8—261no—
515C2×D4—132no—
516C2×D4—132no—
517C2×D4—132no—
518C2×D4—262no—
519C2×D4—262no—
520C2×D4—262no—
521C2×D4—262no—
522C2×D4—262no—
523C2×D4—262no—
524C2×D4—261no—
525C2×D4—261no—
526C2×D4—261no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—268no—
544C22×C4—261no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—1042no—
554C22×C4—1042no—
555C22×C4#610314yes—
556C22×C4C2×C4×D1311yescharacteristic
557C22×C4C2×C4×D1311yescharacteristic
558C22×C4C2×C4×D1311yescharacteristic
559C22×C4C2×D5211yescharacteristic
560C22×C4#612711yescharacteristic
561C22×C4#612711yescharacteristic
562C22×C4D4×D1311yescharacteristic
563C22×C4D4×D1311yescharacteristic
564C22×C4D4×D1311yescharacteristic
565C22×C4D4×D1311yescharacteristic
566C22×C4D4×D1311yescharacteristic
567C22×C4#612911yescharacteristic
568C22×C4Q8×D1311yescharacteristic
569C22×C4#613111yescharacteristic
570M16—262no—
571M16—262no—
572M16—262no—
573M16—262no—
574M16—521no—
575M16—521no—
576M16—521no—
577M16—521no—
578C2×C8—262no—
579C2×C8—262no—
580C2×C8—521no—
581C2×C8—521no—
582C2×C8—521no—
583C2×C8—521no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—132no—
593C4⋊C4—132no—
594C4⋊C4—268no—
595C4⋊C4—261no—
596C4⋊C4—261no—
597C22⋊C4—268no—
598C22⋊C4—262no—
599C22⋊C4—262no—
600C42—22no—
601C42—22no—
602C42—41no—
603C42—41no—
604C42—268no—
605C42—262no—
606C42—262no—
607C13#1078111yescharacteristic, complemented, Sylow
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—262no—
613C23—262no—
614C23—262no—
615C23—521no—
616C23—521no—
617C23—521no—
618C23—521no—
619C23C2×#610311yescharacteristic
620C23C4×C22⋊D1311yescharacteristic
621C23C4×C22⋊D1311yescharacteristic
622C23#8819111yescharacteristic
623C23#8819111yescharacteristic
624C23#8819211yescharacteristic
625C23#8820011yescharacteristic
626Q8—134no—
627Q8—262no—
628Q8—262no—
629Q8—262no—
630D4—134no—
631D4—264no—
632D4—264no—
633D4—264no—
634D4—264no—
635D4—262no—
636D4—262no—
637D4—262no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—42no—
651C2×C4—82no—
652C2×C4—82no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—262no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—264no—
659C2×C4—264no—
660C2×C4—264no—
661C2×C4—264no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—521no—
665C2×C4—521no—
666C2×C4—521no—
667C2×C4—521no—
668C2×C4—1048no—
669C2×C4C42×D1311yescharacteristic
670C2×C4#8812611yescharacteristic
671C2×C4C4×D5211yescharacteristic
672C2×C4C4×D5211yescharacteristic
673C2×C4C22⋊C4×D1311yescharacteristic
674C2×C4C22⋊C4×D1311yescharacteristic
675C2×C4C22⋊C4×D1311yescharacteristic
676C2×C4C22⋊C4×D1311yescharacteristic
677C2×C4#8813511yescharacteristic
678C2×C4#8813511yescharacteristic
679C2×C4#8813611yescharacteristic
680C2×C4#8813611yescharacteristic
681C2×C4#8813711yescharacteristic
682C2×C4#8813711yescharacteristic
683C2×C4#8813811yescharacteristic
684C2×C4#8813811yescharacteristic
685C2×C4C4⋊C4×D1311yescharacteristic
686C2×C4C4⋊C4×D1311yescharacteristic
687C2×C4C4⋊C4×D1311yescharacteristic
688C2×C4#8814611yescharacteristic
689C2×C4#8814711yescharacteristic
690C2×C4#8814711yescharacteristic
691C2×C4#8814811yescharacteristic
692C2×C4#8814811yescharacteristic
693C2×C4#8814911yescharacteristic
694C2×C4#8815011yescharacteristic
695C2×C4#8815011yescharacteristic
696C2×C4#8815111yescharacteristic
697C8—522no—
698C8—522no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—264no—
712C22—522no—
713C22—522no—
714C22—522no—
715C22—522no—
716C22—522no—
717C22—522no—
718C22C4×#610311yescharacteristic
719C22#1171861611yescharacteristic
720C22#1171861711yescharacteristic
721C22#1171861711yescharacteristic
722C22#1171864811yescharacteristic
723C22#1171865011yescharacteristic
724C22#1171865011yescharacteristic
725C22#1171872211yescharacteristic
726C22#1171872311yescharacteristic
727C22#1171873811yescharacteristic
728C22#1171875611yescharacteristic
729C4—44no—
730C4—44no—
731C4—82no—
732C4—264no—
733C4—522no—
734C4—522no—
735C4D13×#9511yescharacteristic
736C4#1171832511yescharacteristic
737C4#1171832611yescharacteristic
738C4#1171832611yescharacteristic
739C4#1171832711yescharacteristic
740C4#1171832811yescharacteristic
741C4#1171832911yescharacteristic
742C4#1171832911yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—524no—
748C2#1311305711yescharacteristic
749C2#1311478911yescharacteristic
750C2#1311479411yescharacteristic
751C2#1311506111yescharacteristic
752C2#1311506811yescharacteristic
753C2#1311520811yescharacteristic
754C2#1311521511yescharacteristic
subgroupG/H
centerC23#88191
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×C4⋊#95C2
socleC23×C13#120
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC4⋊#95D13
hypocenterC13#10781
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718122C2semidirect
5. #13114555C2semidirect
6. C2×#11718115C2semidirect
7. C13×C4⋊#95C2semidirect
19. #11719209C4semidirect
27. #11718627C4semidirect
31. C2×#88045C4semidirect
67. C2×C13×C4⋊C4C2×C4semidirect
74. C2×C42×C13C2×C4semidirect
98. C2×#6099C2×C4semidirect
99. C2×#6099C2×C4semidirect
237. C4⋊#95D13semidirect
317. D52#95semidirect
326. Dic26#95semidirect
463. C2×C4⋊C4C4×D13semidirect
474. C2×C42C4×D13semidirect
607. C13#10781semidirect

Maximal subgroups

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

subgroupindex
C2×#117192092
C22×#880452
C2×#117186272
C2×#117181222
#131145552
C2×#117181152
C13×C4⋊#952
#1078113