Finite Group Databasebeta

← #15880283

Subgroups — #15880283

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123494C211yesmaximal, characteristic, complemented
2#13123353C211yesmaximal, characteristic
3#13123286C211yesmaximal, characteristic
4#13115548C211yesmaximal, characteristic, complemented
5#13115541C211yesmaximal, characteristic, complemented
6#13115482C211yesmaximal, characteristic, complemented
7#13115482C211yesmaximal, characteristic, complemented
8#13115112C211yesmaximal, characteristic, complemented
9#13115112C211yesmaximal, characteristic, complemented
10#13114876C211yesmaximal, characteristic, complemented
11#13114781C211yesmaximal, characteristic
12#13114677C211yesmaximal, characteristic, complemented
13#13114670C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#1826C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×#88161C2211yescharacteristic
20C2×#88161C2211yescharacteristic
21C13×#407C2211yescharacteristic
22C4×C13×C22⋊C4C2211yescharacteristic
23#11718868C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25#11718790C2211yescharacteristic
26#11718790C2211yescharacteristic
27C2×#88062C2211yescharacteristic, complemented
28C2×#88062C2211yescharacteristic, complemented
29#11718665C411yescharacteristic, complemented
30#11718665C411yescharacteristic, complemented
31#11718663C2211yescharacteristic
32#11718663C2211yescharacteristic
33#11718663C2211yescharacteristic
34#11718663C2211yescharacteristic
35#11718662C411yescharacteristic, complemented
36#11718662C411yescharacteristic, complemented
37#11718661—21no—
38#11718661—21no—
39#11718660C2211yescharacteristic, complemented
40#11718660C2211yescharacteristic, complemented
41#11718658C2211yescharacteristic, complemented
42#11718658C2211yescharacteristic, complemented
43#11718627C411yescharacteristic, complemented
44#11718627C411yescharacteristic, complemented
45#11718627C411yescharacteristic, complemented
46#11718627C411yescharacteristic, complemented
47C2×#88045C2211yescharacteristic
48C2×#88045C2211yescharacteristic
49C2×#88045C2211yescharacteristic
50C2×#88045C2211yescharacteristic
51#11718587—21no—
52#11718586—21no—
53C2×#88043C2211yescharacteristic, complemented
54C2×C4×#1055C2211yescharacteristic, complemented
55#11718388—21no—
56#11718388—21no—
57#11718387—21no—
58D13×C22⋊C8—21no—
59C13×#339C2211yescharacteristic, complemented
60C13×#339C2211yescharacteristic, complemented
61C13×#339C2211yescharacteristic, complemented
62C13×#339C2211yescharacteristic, complemented
63#11718150C2211yescharacteristic, complemented
64#11718150C2211yescharacteristic, complemented
65#11718116C2211yescharacteristic, complemented
66#11718116C2211yescharacteristic, complemented
67C23×C4×C13C2311yescharacteristic
68C22×C22⋊D13—21no—
69C2×#6127—21no—
70C2×#6127—21no—
71C2×#6127—22no—
72C2×#6127—22no—
73C2×#6127—41no—
74C2×#6127—41no—
75C2×#6127C2×C411yescharacteristic
76C2×#6127C2×C411yescharacteristic
77C2×#6127C2311yescharacteristic
78C2×#6127C2311yescharacteristic
79C22×D52C2×C411yescharacteristic
80C22×C4×D13—21no—
81C22×Dic26C2×C411yescharacteristic
82C2×C13×M16C2311yescharacteristic
83C2×C13×M16C2311yescharacteristic
84C13×#117—21no—
85C13×#117—21no—
86C13×#117C2×C411yescharacteristic
87C13×#117C2×C411yescharacteristic
88C13×#117C2311yescharacteristic
89C13×#117C2311yescharacteristic
90C2×C13×C4⋊C4C2×C411yescharacteristic
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C42×C13—21no—
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×#6099—41no—
98C2×#6099—41no—
99C2×#6099C2×C411yescharacteristic
100C2×#6099C2×C411yescharacteristic
101C2×#6099C2×C411yescharacteristic
102C2×#6099C2×C411yescharacteristic
103C2×#6099C2311yescharacteristic
104C2×#6099C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88161—22no—
110#88161—22no—
111#88161—41no—
112#88161—41no—
113C2×#6094—21no—
114C2×#6094—21no—
115C2×C8×D13—21no—
116C2×C8×D13—21no—
117C13×C22⋊C8—21no—
118C13×C22⋊C8—21no—
119C13×#95—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122C22⋊#1055D411yescharacteristic
123C22⋊#1055D411yescharacteristic
124C22⋊#1055D411yescharacteristic
125C22⋊#1055D411yescharacteristic
126#88062—41no—
127#88062—41no—
128#88060—21no—
129#88060—21no—
130#88060—21no—
131#88060—21no—
132#88050C2×C411yescharacteristic
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88050C2×C411yescharacteristic
136#88050C2×C411yescharacteristic
137#88050C2×C411yescharacteristic
138#88050C2×C411yescharacteristic
139#88050C2×C411yescharacteristic
140#88049C2×C411yescharacteristic
141#88049C2×C411yescharacteristic
142#88049C2×C411yescharacteristic
143#88049C2×C411yescharacteristic
144#88049C2×C411yescharacteristic
145#88049C2×C411yescharacteristic
146#88049C2×C411yescharacteristic
147#88049C2×C411yescharacteristic
148#88045—22no—
149#88045—22no—
150#88045—41no—
151#88045—41no—
152C4⋊#1055—21no—
153C4⋊#1055—21no—
154C4⋊#1055—21no—
155C4⋊#1055—21no—
156#88043—21no—
157#88043—21no—
158#88043—41no—
159C4×#1055—21no—
160C4×#1055—21no—
161C4×#1055—41no—
162#22588—131nomaximal, Sylow
163C24×C13#4111yescharacteristic
164C23×D13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13C22×C411yescharacteristic
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13#4111yescharacteristic
178C22×C4×C13C2411yescharacteristic
179C2×C22⋊D13—21no—
180C2×C22⋊D13—21no—
181C2×C22⋊D13—21no—
182C2×C22⋊D13—21no—
183C2×C22⋊D13—42no—
184C2×C22⋊D13—42no—
185C22×Dic13—21no—
186#6127—21no—
187#6127—21no—
188#6127—21no—
189#6127—21no—
190#6127—21no—
191#6127—21no—
192#6127—22no—
193#6127—22no—
194#6127—41no—
195#6127—41no—
196#6127—42no—
197#6127—42no—
198#6127—42no—
199#6127—42no—
200#6127#4112yes—
201#6127#4112yes—
202C2×D52—22no—
203C2×D52—21no—
204C2×D52—41no—
205C2×D52C22×C411yescharacteristic
206C2×D52C22×C411yescharacteristic
207C2×C4×D13—21no—
208C2×C4×D13—21no—
209C2×C4×D13—21no—
210C2×C4×D13—21no—
211C2×C4×D13—42no—
212C2×C4×D13—42no—
213C2×Dic26—22no—
214C2×Dic26—21no—
215C2×Dic26—41no—
216C2×Dic26C22×C411yescharacteristic
217C2×Dic26C22×C411yescharacteristic
218C13×M16—21no—
219C13×M16—21no—
220C13×M16—21no—
221C13×M16—21no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4C22×C411yescharacteristic
227C13×C4⋊C4C22×C411yescharacteristic
228C13×C4⋊C4C22×C411yescharacteristic
229C13×C4⋊C4C22×C411yescharacteristic
230C13×C22⋊C4—21no—
231C13×C22⋊C4—21no—
232C13×C22⋊C4—21no—
233C13×C22⋊C4—21no—
234C13×C22⋊C4—42no—
235C42×C13—21no—
236C42×C13—21no—
237C42×C13—21no—
238C42×C13—21no—
239C42×C13—21no—
240C42×C13—21no—
241C42×C13—21no—
242C42×C13—21no—
243#6099—21no—
244#6099—21no—
245#6099—21no—
246#6099—21no—
247#6099—41no—
248#6099—41no—
249#6099—41no—
250#6099—41no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055C22×C411yescharacteristic
262C2×#1055C22×C411yescharacteristic
263C2×#1055C22×C411yescharacteristic
264C2×#1055C22×C411yescharacteristic
265C2×#1055C2×D411yescharacteristic
266C2×#1055C2×D411yescharacteristic
267C2×#1055C2×D411yescharacteristic
268C2×#1055C2×D411yescharacteristic
269#6094—42no—
270#6094—42no—
271C8×D13—42no—
272C8×D13—42no—
273#2924—131no—
274#2896—131no—
275#2880—131no—
276#1938—131no—
277#1937—131no—
278#1929—131no—
279#1929—131no—
280#1866—131no—
281#1866—131no—
282#1826D1311yescharacteristic, complemented
283#1811—131no—
284#1789—131no—
285#1765—131no—
286#1764—131no—
287#1753—131no—
288C23×C13—21no—
289C23×C13—21no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13C4×D411yescharacteristic
293C23×C13C4×D411yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C22×D13—21no—
296C22×D13—21no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—81no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—22no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—41no—
316C2×C4×C13—42no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—81no—
322C2×C4×C13C4×D411yescharacteristic
323C2×C4×C13C4×D411yescharacteristic
324C2×C4×C13C23×C411yescharacteristic
325C2×C4×C13C22×D411yescharacteristic
326C2×C4×C13C2×#4111yescharacteristic
327C2×C4×C13C2×#4111yescharacteristic
328C2×C4×C13H(5,𝔽2)11yescharacteristic
329C2×C4×C13H(5,𝔽2)11yescharacteristic
330C22⋊D13—22no—
331C22⋊D13—22no—
332C22⋊D13—42no—
333C22⋊D13—42no—
334C22⋊D13—41no—
335C22⋊D13—41no—
336C2×Dic13—21no—
337C2×Dic13—21no—
338C2×Dic13—42no—
339D52—21no—
340D52—21no—
341D52—21no—
342D52—42no—
343D52#11712yes—
344C4×D13—22no—
345C4×D13—22no—
346C4×D13—42no—
347C4×D13—42no—
348C4×D13—41no—
349C4×D13—41no—
350Dic26—21no—
351Dic26—21no—
352Dic26—21no—
353Dic26—42no—
354Dic26#11712yes—
355C8×C13—41no—
356C8×C13—41no—
357#1055—21no—
358#1055—21no—
359#1055—21no—
360#1055—21no—
361#1055—21no—
362#1055—21no—
363#1055—21no—
364#1055—21no—
365#1055—41no—
366#1055—41no—
367C22×#41—131no—
368C2×#131—131no—
369C2×#131—131no—
370C22×M16—131no—
371C2×#117C2×D1311yescharacteristic
372#433—261no—
373#433—261no—
374#432—261no—
375#431—261no—
376C2×#108—131no—
377C2×#108—131no—
378#424—131no—
379#424—131no—
380C2×#104—131no—
381C2×#104—131no—
382C2×#104—131no—
383C2×#104—131no—
384#419—131no—
385#419—131no—
386#418—131no—
387#418—131no—
388#417—131no—
389#417—131no—
390#417—131no—
391#417—131no—
392#416—131no—
393#416—131no—
394#416—131no—
395#416—131no—
396#408—131no—
397#408—131no—
398#408—261no—
399#408—261no—
400#407—131no—
401#407—261no—
402#407C2×D1311yescharacteristic
403C2×C22⋊C8—131no—
404C2×C22⋊C8—261no—
405#405—131no—
406#405—131no—
407C2×#97—131no—
408C2×C4×C8—131no—
409C4×C22⋊C4C2×D1311yescharacteristic
410#341—131no—
411#341—131no—
412#339C2×D1311yescharacteristic, complemented
413#339C2×D1311yescharacteristic, complemented
414#339C2×D1311yescharacteristic, complemented
415#339C2×D1311yescharacteristic, complemented
416#336—131no—
417#336—131no—
418C22×C13—21no—
419C22×C13—21no—
420C22×C13—21no—
421C22×C13—21no—
422C22×C13—21no—
423C22×C13—21no—
424C22×C13—21no—
425C22×C13—21no—
426C22×C13—81no—
427C22×C13—81no—
428C22×C13C2×C4×D411yescharacteristic
429C22×C13#55111yescharacteristic
430C22×C13#55111yescharacteristic
431C2×D13—22no—
432C2×D13—41no—
433C2×D13—41no—
434C2×D13—41no—
435C2×D13—41no—
436C2×D13—41no—
437C2×D13—84no—
438C4×C13—21no—
439C4×C13—21no—
440C4×C13—42no—
441C4×C13—41no—
442C4×C13—41no—
443C4×C13—41no—
444C4×C13—41no—
445C4×C13—81no—
446C4×C13C2×#11711yescharacteristic
447C4×C13#51811yescharacteristic
448C4×C13#54611yescharacteristic
449C4×C13#54611yescharacteristic
450Dic13—22no—
451Dic13—41no—
452C2×#41—131no—
453C2×#41—131no—
454C2×#41—131no—
455C2×#41—131no—
456C2×#41—262no—
457C2×#41—262no—
458C2×#41—261no—
459C2×#41—261no—
460C2×#41—521no—
461C2×#41—521no—
462C22×Q8—131no—
463C22×D4—131no—
464C22×D4—261no—
465C23×C4—261no—
466C23×C4C22×D1311yescharacteristic
467#131—262no—
468#131—262no—
469#131—521no—
470#131—521no—
471C2×M16—131no—
472C2×M16—131no—
473C2×M16—131no—
474C2×M16—131no—
475C2×M16—131no—
476C2×M16—131no—
477C2×M16—261no—
478C2×M16—261no—
479C2×M16—521no—
480C2×M16—521no—
481C2×M16C22×D1311yescharacteristic
482C2×M16C22×D1311yescharacteristic
483C22×C8—131no—
484C22×C8—131no—
485C22×C8—131no—
486C22×C8—131no—
487C22×C8—261no—
488C22×C8—261no—
489#117—21no—
490#117—21no—
491#117C4×D1311yescharacteristic
492#117C4×D1311yescharacteristic
493#117C22×D1311yescharacteristic
494#117C22×D1311yescharacteristic
495C2×C4⋊C4C4×D1311yescharacteristic
496C2×C4⋊C4C4×D1311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C42—21no—
500C2×C42C22×D1311yescharacteristic
501C2×C42C22×D1311yescharacteristic
502#108—521no—
503#108—521no—
504C4⋊C8—261no—
505C4⋊C8—261no—
506C4⋊C8—261no—
507C4⋊C8—261no—
508#104—262no—
509#104—262no—
510#104—521no—
511#104—521no—
512#103—131no—
513#103—131no—
514#103—131no—
515#103—131no—
516#103—131no—
517#103—131no—
518#103—131no—
519#103—131no—
520#102—131no—
521#102—131no—
522#102—131no—
523#102—131no—
524#102—131no—
525#102—131no—
526#102—131no—
527#102—131no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—131no—
531C22⋊C8—131no—
532C22⋊C8—131no—
533C22⋊C8—131no—
534C22⋊C8—261no—
535C22⋊C8—261no—
536C22⋊C8—261no—
537C22⋊C8—261no—
538C22⋊C8—261no—
539C22⋊C8—261no—
540#97—261no—
541#97—261no—
542#97—521no—
543C4×C8—261no—
544C4×C8—261no—
545C4×C8—521no—
546#95—21no—
547C2×C13—21no—
548C2×C13—21no—
549C2×C13—41no—
550C2×C13—41no—
551C2×C13#234211yescharacteristic
552C2×C13#295511yescharacteristic
553C2×C13#295611yescharacteristic
554D13—42no—
555D13—81no—
556C24—261no—
557C24#612911yescharacteristic
558#41—132no—
559#41—132no—
560#41—262no—
561#41—262no—
562#41—261no—
563#41—261no—
564#41—261no—
565#41—261no—
566#41—261no—
567#41—261no—
568#41—522no—
569#41—522no—
570#41—521no—
571#41—521no—
572#41—522no—
573#41—522no—
574C2×Q8—131no—
575C2×Q8—131no—
576C2×Q8—262no—
577C2×Q8—261no—
578C2×Q8—521no—
579C2×D4—131no—
580C2×D4—131no—
581C2×D4—262no—
582C2×D4—261no—
583C2×D4—261no—
584C2×D4—261no—
585C2×D4—261no—
586C2×D4—261no—
587C2×D4—521no—
588C2×D4—522no—
589C2×D4—522no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—522no—
604C22×C4—522no—
605C22×C4C2×C4×D1311yescharacteristic
606C22×C4C2×C4×D1311yescharacteristic
607C22×C4D4×D1311yescharacteristic
608C22×C4D4×D1311yescharacteristic
609C22×C4#612911yescharacteristic
610C22×C4C23×D1311yescharacteristic
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—261no—
616M16—261no—
617M16—261no—
618M16—261no—
619M16—522no—
620M16—522no—
621M16—521no—
622M16—521no—
623M16—521no—
624M16—521no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—131no—
628C2×C8—131no—
629C2×C8—131no—
630C2×C8—131no—
631C2×C8—131no—
632C2×C8—131no—
633C2×C8—131no—
634C2×C8—131no—
635C2×C8—261no—
636C2×C8—261no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8—261no—
644C2×C8—261no—
645C2×C8—522no—
646C2×C8—522no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×C4×D1311yescharacteristic
650C4⋊C4C2×C4×D1311yescharacteristic
651C4⋊C4C2×C4×D1311yescharacteristic
652C4⋊C4C2×C4×D1311yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—42no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C13#2258811yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—261no—
672C23—261no—
673C23—522no—
674C23—522no—
675C23—1041no—
676C23#8813511yescharacteristic
677C23#8813511yescharacteristic
678C23C2×#612911yescharacteristic
679Q8—132no—
680Q8—261no—
681Q8—261no—
682Q8—261no—
683Q8—522no—
684D4—132no—
685D4—262no—
686D4—262no—
687D4—261no—
688D4—261no—
689D4—261no—
690D4—522no—
691D4—522no—
692D4—522no—
693D4—521no—
694D4—521no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—81no—
717C2×C4—261no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—261no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4#8813511yescharacteristic
727C2×C4#8813511yescharacteristic
728C2×C4C22×C4×D1311yescharacteristic
729C2×C4C2×D4×D1311yescharacteristic
730C2×C4#41×D1311yescharacteristic
731C2×C4#41×D1311yescharacteristic
732C2×C4#8825611yescharacteristic
733C2×C4#8825611yescharacteristic
734C8—41no—
735C8—41no—
736C8—261no—
737C8—261no—
738C8—261no—
739C8—261no—
740C8—261no—
741C8—261no—
742C8—261no—
743C8—261no—
744C8—521no—
745C8—521no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—262no—
757C22—521no—
758C22—521no—
759C22—521no—
760C22—521no—
761C22—521no—
762C22—1044no—
763C22C2×#8813511yescharacteristic
764C22#1171936311yescharacteristic
765C22#1171936311yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—262no—
775C4—521no—
776C4D13×#11711yescharacteristic
777C4#1171922611yescharacteristic
778C4#1171935911yescharacteristic
779C4#1171935911yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—522no—
785C2—1041no—
786C2#1311767811yescharacteristic
787C2#1312373511yescharacteristic
788C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1826C2
socleC22×C13C2×C4×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#1826D13
hypocenterC13#22588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
1. #13123494C2semidirect
4. #13115548C2semidirect
5. #13115541C2semidirect
6. #13115482C2semidirect
7. #13115482C2semidirect
8. #13115112C2semidirect
9. #13115112C2semidirect
10. #13114876C2semidirect
12. #13114677C2semidirect
13. #13114670C2semidirect
14. #13114620C2semidirect
15. C13×#1826C2semidirect
27. C2×#88062C22semidirect
28. C2×#88062C22semidirect
29. #11718665C4semidirect
30. #11718665C4semidirect
35. #11718662C4semidirect
36. #11718662C4semidirect
39. #11718660C22semidirect
40. #11718660C22semidirect
41. #11718658C22semidirect
42. #11718658C22semidirect
43. #11718627C4semidirect
44. #11718627C4semidirect
45. #11718627C4semidirect
46. #11718627C4semidirect
53. C2×#88043C22semidirect
54. C2×C4×#1055C22semidirect
59. C13×#339C22semidirect
60. C13×#339C22semidirect
61. C13×#339C22semidirect
62. C13×#339C22semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718116C22semidirect
66. #11718116C22semidirect
282. #1826D13semidirect
412. #339C2×D13semidirect
413. #339C2×D13semidirect
414. #339C2×D13semidirect
415. #339C2×D13semidirect
666. C13#22588semidirect

Maximal subgroups

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

subgroupindex
#131234942
#131233532
#131232862
#131155482
#131155412
#131154822
#131151122
#131148762
#131147812
#131146772
#131146702
#131146202
C13×#18262
#2258813