Finite Group Databasebeta

← #15883671

Subgroups — #15883671

Order 3328.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124054C211yesmaximal, characteristic
2C2×#11718484C211yesmaximal, characteristic, complemented
3#13123561C211yesmaximal, characteristic, complemented
4#13123285C211yesmaximal, characteristic, complemented
5#13115721C211yesmaximal, characteristic, complemented
6#13115544C211yesmaximal, characteristic, complemented
7#13115487C211yesmaximal, characteristic, complemented
8#13115284C211yesmaximal, characteristic, complemented
9#13115161C211yesmaximal, characteristic, complemented
10#13115160C211yesmaximal, characteristic, complemented
11#13115109C211yesmaximal, characteristic, complemented
12#13115041C211yesmaximal, characteristic, complemented
13#13114674C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C2×C13×#421C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic
23#11719496C2211yescharacteristic
24C2×#88161C2211yescharacteristic, complemented
25C13×#421—24no—
26C2×C13×#104C2211yescharacteristic
27C2×C13×#104C2211yescharacteristic
28C2×C13×#104C2211yescharacteristic
29C2×C13×#104C2211yescharacteristic
30#11718900C411yescharacteristic, complemented
31#11718900C411yescharacteristic, complemented
32#11718899C411yescharacteristic, complemented
33#11718899C411yescharacteristic, complemented
34#11718895—21no—
35#11718895—21no—
36#11718895C2211yescharacteristic
37#11718895C2211yescharacteristic
38#11718894C2211yescharacteristic
39#11718894C2211yescharacteristic
40#11718889C411yescharacteristic, complemented
41#11718888C411yescharacteristic, complemented
42#11718879C411yescharacteristic, complemented
43#11718878C411yescharacteristic, complemented
44#11718868—21no—
45#11718868C2211yescharacteristic
46C2×C22⋊#1055—21no—
47C2×C22⋊#1055C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49#11718790C2211yescharacteristic, complemented
50#11718789—21no—
51#11718788—21no—
52C2×#88062C2211yescharacteristic, complemented
53C2×#88062C2211yescharacteristic, complemented
54#11718783C2211yescharacteristic, complemented
55#11718780C2211yescharacteristic, complemented
56#11718772—21no—
57C8×C22⋊D13—21no—
58C2×#88045C2211yescharacteristic, complemented
59C2×#88045C2211yescharacteristic, complemented
60C2×#88043C2211yescharacteristic, complemented
61C2×C4×#1055C2211yescharacteristic, complemented
62#11718484—24no—
63#11718150C2211yescharacteristic, complemented
64#11718150C2211yescharacteristic, complemented
65#11718116C2211yescharacteristic, complemented
66#11718116C2211yescharacteristic, complemented
67#11718115C2211yescharacteristic, complemented
68#11718115C2211yescharacteristic, complemented
69C2×C13×#41—21no—
70C2×C13×#41—21no—
71C2×C13×#41—22no—
72C2×C13×#41—22no—
73C2×C13×#41—41no—
74C2×C13×#41—41no—
75C2×C13×#41C2×C411yescharacteristic
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41C2311yescharacteristic
78C2×C13×#41C2311yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic
80C22×D4×C13—21no—
81C22×D4×C13C2×C411yescharacteristic
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C2×#6127C2311yescharacteristic
85C2×C13×M16—21no—
86C2×C13×M16—22no—
87C2×C13×M16—41no—
88C2×C13×M16C2311yescharacteristic
89C2×C13×M16C2311yescharacteristic
90C22×C8×C13—21no—
91C13×#117—22no—
92C13×#117—41no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97#88207—21no—
98#88204—22no—
99#88204—22no—
100#88204—41no—
101#88204—41no—
102#88202—22no—
103#88202—22no—
104#88202—41no—
105#88202—41no—
106C2×#6107C2×C411yescharacteristic
107C2×#6107C2×C411yescharacteristic
108C2×#6106C2×C411yescharacteristic
109C2×#6106C2×C411yescharacteristic
110C2×#6105C2×C411yescharacteristic
111C2×#6105C2×C411yescharacteristic
112C2×#6104C2×C411yescharacteristic
113C2×#6104C2×C411yescharacteristic
114#88184C2×C411yescharacteristic
115#88184C2×C411yescharacteristic
116#88183—21no—
117C4×C22⋊D13—21no—
118C4×C22⋊D13—21no—
119#88180C2311yescharacteristic
120#88178C2×C411yescharacteristic
121#88178C2×C411yescharacteristic
122C2×#6099—21no—
123C2×#6099—21no—
124C2×#6099C2311yescharacteristic
125C2×#6099C2311yescharacteristic
126C22×#1055—21no—
127C22×#1055—21no—
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132#88161—22no—
133#88161—41no—
134C2×#6094—21no—
135C2×C8×D13—21no—
136C13×#104—22no—
137C13×#104—22no—
138C13×#104—22no—
139C13×#104D414yescomplemented
140#88075C2×C411yescharacteristic
141#88075C2×C411yescharacteristic
142#88075C2×C411yescharacteristic
143#88075C2×C411yescharacteristic
144#88072C2×C411yescharacteristic
145#88072C2×C411yescharacteristic
146#88072C2×C411yescharacteristic
147#88072C2×C411yescharacteristic
148C22⋊#1055—21no—
149C22⋊#1055—21no—
150C22⋊#1055—21no—
151C22⋊#1055—21no—
152C22⋊#1055—21no—
153C22⋊#1055—21no—
154C22⋊#1055C2×C411yescharacteristic
155C22⋊#1055C2×C411yescharacteristic
156C22⋊#1055C2×C411yescharacteristic
157C22⋊#1055C2×C411yescharacteristic
158C22⋊#1055D411yescharacteristic
159C22⋊#1055D411yescharacteristic
160C22⋊#1055D411yescharacteristic
161C22⋊#1055D411yescharacteristic
162#88062—22no—
163#88062—41no—
164#88060—21no—
165#88060—21no—
166#88055—21no—
167#88054—21no—
168#88054—21no—
169C8×Dic13—21no—
170#88045—22no—
171#88045—41no—
172#88043—22no—
173C4×#1055—41no—
174#22887—131nomaximal, Sylow
175C24×C13—21no—
176C24×C13#4111yescharacteristic
177C13×#41—21no—
178C13×#41—21no—
179C13×#41—22no—
180C13×#41—22no—
181C13×#41—21no—
182C13×#41—21no—
183C13×#41—21no—
184C13×#41—21no—
185C13×#41—42no—
186C13×#41—42no—
187C13×#41—41no—
188C13×#41—41no—
189C13×#41—42no—
190C13×#41—42no—
191C13×#41C2×D412yes—
192C13×#41#4112yes—
193C2×Q8×C13—21no—
194C2×Q8×C13—22no—
195C2×Q8×C13—41no—
196C2×Q8×C13C22×C411yescharacteristic
197C2×Q8×C13C22×C411yescharacteristic
198C2×D4×C13—21no—
199C2×D4×C13—22no—
200C2×D4×C13—21no—
201C2×D4×C13—21no—
202C2×D4×C13—21no—
203C2×D4×C13—21no—
204C2×D4×C13—41no—
205C2×D4×C13—42no—
206C2×D4×C13—42no—
207C2×D4×C13C22×C411yescharacteristic
208C2×D4×C13C22×C411yescharacteristic
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—42no—
221C22×C4×C13—42no—
222C22×C4×C13C22×C411yescharacteristic
223C22×C4×C13C22×C411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13#4111yescharacteristic
227C22×C4×C13C2411yescharacteristic
228C2×C22⋊D13—21no—
229C2×C22⋊D13—21no—
230C2×C22⋊D13—21no—
231#6127—21no—
232#6127—21no—
233#6127—21no—
234#6127—21no—
235C2×D52C22×C411yescharacteristic
236C2×C4×D13—21no—
237C2×Dic26C22×C411yescharacteristic
238C13×M16—21no—
239C13×M16—21no—
240C13×M16—21no—
241C13×M16—42no—
242C13×M16C2×D412yes—
243C2×C8×C13—21no—
244C2×C8×C13—21no—
245C2×C8×C13—42no—
246C13×C4⋊C4—42no—
247C13×C22⋊C4—42no—
248C42×C13—21no—
249C42×C13—21no—
250C42×C13—21no—
251C42×C13C2×D412yes—
252C22⋊Dic13—21no—
253C22⋊Dic13—21no—
254C22⋊Dic13—21no—
255#6107—22no—
256#6107—41no—
257#6106—22no—
258#6106—41no—
259#6105—22no—
260#6105—41no—
261#6104—22no—
262#6104—41no—
263#6103—21no—
264#6103—21no—
265C4⋊Dic13C22×C411yescharacteristic
266C4⋊Dic13C22×C411yescharacteristic
267#6101—21no—
268#6101—21no—
269C4×Dic13—21no—
270#6099—21no—
271#6099—21no—
272#6099—21no—
273#6099—21no—
274#6099—42no—
275#6099—42no—
276C2×#1055—21no—
277C2×#1055—21no—
278C2×#1055—21no—
279C2×#1055—21no—
280C2×#1055—21no—
281C2×#1055—21no—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—21no—
286C2×#1055—42no—
287C2×#1055—42no—
288C2×#1055C22×C411yescharacteristic
289C2×#1055C22×C411yescharacteristic
290C2×#1055C22×C411yescharacteristic
291C2×#1055C22×C411yescharacteristic
292C2×#1055C2×D411yescharacteristic
293C2×#1055C2×D411yescharacteristic
294C2×#1055C2×D411yescharacteristic
295C2×#1055C2×D411yescharacteristic
296#6094—42no—
297C8×D13—42no—
298#3002—131no—
299C2×#444—131no—
300#2933—131no—
301C2×#421D1311yescharacteristic, complemented
302#2880—131no—
303#1974—131no—
304#1938—131no—
305#1929—131no—
306#1897—131no—
307#1876—131no—
308#1876—131no—
309#1866—131no—
310#1855—131no—
311#1764—131no—
312#1750—131no—
313C23×C13—21no—
314C23×C13—21no—
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13—81no—
322C23×C13C4×D411yescharacteristic
323C23×C13C4×D411yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C22×D13—21no—
326Q8×C13—21no—
327Q8×C13—21no—
328Q8×C13—21no—
329Q8×C13—42no—
330Q8×C13C4×D412yes—
331D4×C13—22no—
332D4×C13—22no—
333D4×C13—21no—
334D4×C13—21no—
335D4×C13—21no—
336D4×C13—42no—
337D4×C13—42no—
338D4×C13—42no—
339D4×C13—41no—
340D4×C13—41no—
341D4×C13C4×D412yes—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—22no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—22no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—22no—
357C2×C4×C13—42no—
358C2×C4×C13—42no—
359C2×C4×C13—42no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13C4×D411yescharacteristic
368C2×C4×C13C4×D411yescharacteristic
369C2×C4×C13C23×C411yescharacteristic
370C2×C4×C13C22×D411yescharacteristic
371C2×C4×C13C22×D411yescharacteristic
372C2×C4×C13C2×#4111yescharacteristic
373C2×C4×C13H(5,𝔽2)11yescharacteristic
374C2×C4×C13H(5,𝔽2)11yescharacteristic
375C22⋊D13—42no—
376C22⋊D13—41no—
377C22⋊D13—41no—
378C22⋊D13—81no—
379C2×Dic13—21no—
380C2×Dic13—21no—
381C2×Dic13—21no—
382D52—21no—
383D52—21no—
384C4×D13—41no—
385C4×D13—41no—
386Dic26—21no—
387Dic26—21no—
388C8×C13—22no—
389C8×C13—41no—
390#1055—21no—
391#1055—21no—
392#1055—21no—
393#1055—21no—
394#1055—21no—
395#1055—21no—
396#1055—21no—
397#1055—21no—
398#1055—41no—
399#1055—41no—
400C22×#41C2×D1311yescharacteristic
401C2×#135—131no—
402C2×#135—131no—
403C2×#131—131no—
404C2×#131—131no—
405C2×#131—131no—
406C22×M16C2×D1311yescharacteristic
407#525—131no—
408C2×#117C2×D1311yescharacteristic
409#452—131no—
410#452—131no—
411#451—131no—
412#450—131no—
413#449—131no—
414#449—131no—
415#448—131no—
416#447—131no—
417#444—264no—
418#436—261no—
419#435—261no—
420#435—261no—
421C8×D4—261no—
422C2×#108—131no—
423C2×#108—131no—
424#424—131no—
425#421—24no—
426C2×#104—131no—
427C2×#104—131no—
428C2×#104C2×D1311yescharacteristic
429C2×#104C2×D1311yescharacteristic
430C2×#104C2×D1311yescharacteristic
431C2×#104C2×D1311yescharacteristic
432#416—131no—
433#416—131no—
434#408—131no—
435#408—131no—
436#408—131no—
437#408—261no—
438#408—261no—
439#407—131no—
440#407—261no—
441C2×C22⋊C8—131no—
442C2×C22⋊C8—131no—
443C2×C22⋊C8—261no—
444#405—131no—
445C2×#97—131no—
446C2×C4×C8—131no—
447#341—131no—
448#341—131no—
449#339—131no—
450#339—131no—
451#336—131no—
452#336—131no—
453C22×C13—21no—
454C22×C13—21no—
455C22×C13—21no—
456C22×C13—21no—
457C22×C13—22no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—21no—
462C22×C13—41no—
463C22×C13—41no—
464C22×C13—41no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13—81no—
468C22×C13—81no—
469C22×C13—84no—
470C22×C13C2×C4×D411yescharacteristic
471C22×C13#54611yescharacteristic
472C22×C13#55111yescharacteristic
473C2×D13—41no—
474C2×D13—41no—
475C2×D13—41no—
476C4×C13—21no—
477C4×C13—21no—
478C4×C13—22no—
479C4×C13—42no—
480C4×C13—41no—
481C4×C13—81no—
482C4×C13C2×C4×D411yescharacteristic
483C4×C13#51811yescharacteristic
484C4×C13D4211yescharacteristic
485C4×C13#54611yescharacteristic
486Dic13—41no—
487Dic13—41no—
488Dic13—41no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—131no—
496C2×#41C4×D1311yescharacteristic
497C2×#41C4×D1311yescharacteristic
498C2×#41C22×D1311yescharacteristic
499C2×#41C22×D1311yescharacteristic
500C22×Q8C4×D1311yescharacteristic
501C22×D4—21no—
502C22×D4C4×D1311yescharacteristic
503C23×C4—21no—
504C23×C4C22×D1311yescharacteristic
505#135—262no—
506#135—262no—
507#135—521no—
508#135—521no—
509C2×Q16—131no—
510C2×Q16—131no—
511C2×SD16—131no—
512C2×SD16—131no—
513C2×SD16—131no—
514C2×SD16—131no—
515C2×D8—131no—
516C2×D8—131no—
517#131—262no—
518#131—262no—
519#131—262no—
520#131—521no—
521#131—521no—
522#131—521no—
523C2×M16—21no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—131no—
527C2×M16—131no—
528C2×M16—261no—
529C2×M16—261no—
530C2×M16—261no—
531C2×M16C22×D1311yescharacteristic
532C2×M16C22×D1311yescharacteristic
533C22×C8—21no—
534C22×C8—131no—
535C22×C8—131no—
536C22×C8—131no—
537C22×C8—131no—
538C22×C8—261no—
539C22×C8—261no—
540C22×C8—261no—
541#123—261no—
542C22⋊Q8—131no—
543C22⋊Q8—131no—
544#121—131no—
545#121—131no—
546#120—261no—
547C4×D4—261no—
548C4×D4—261no—
549#117—22no—
550#117—41no—
551#117—131no—
552C2×C4⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42C22×D1311yescharacteristic
555C2×C42C22×D1311yescharacteristic
556#108—262no—
557#108—521no—
558C4⋊C8—261no—
559C4⋊C8—261no—
560#104—22no—
561#104—22no—
562#104—22no—
563#104—262no—
564#104—521no—
565#104C22⋊D1314yescomplemented
566#103—131no—
567#103—131no—
568#103—131no—
569#103—131no—
570#102—131no—
571#102—131no—
572#102—131no—
573#102—131no—
574C22⋊C8—131no—
575C22⋊C8—131no—
576C22⋊C8—131no—
577C22⋊C8—131no—
578C22⋊C8—131no—
579C22⋊C8—131no—
580C22⋊C8—131no—
581C22⋊C8—131no—
582C22⋊C8—261no—
583C22⋊C8—261no—
584C22⋊C8—261no—
585C22⋊C8—261no—
586C22⋊C8—261no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8—261no—
590#97—261no—
591#97—262no—
592C4×C8—261no—
593C4×C8—521no—
594C2×C13—21no—
595C2×C13—21no—
596C2×C13—41no—
597C2×C13—41no—
598C2×C13—42no—
599C2×C13—81no—
600C2×C13#235811yescharacteristic
601C2×C13#295511yescharacteristic
602C2×C13#295711yescharacteristic
603D13—81no—
604C24—21no—
605C24#612911yescharacteristic
606#41—21no—
607#41—21no—
608#41—22no—
609#41—22no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—42no—
615#41—42no—
616#41—41no—
617#41—41no—
618#41—42no—
619#41—42no—
620#41—261no—
621#41—261no—
622#41—261no—
623#41—261no—
624#41#612712yes—
625#41C2×C22⋊D1312yes—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—41no—
629C2×Q8—131no—
630C2×Q8C2×C4×D1311yescharacteristic
631C2×Q8C2×C4×D1311yescharacteristic
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—41no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—131no—
642C2×D4—261no—
643C2×D4—261no—
644C2×D4—261no—
645C2×D4C2×C4×D1311yescharacteristic
646C2×D4C2×C4×D1311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—261no—
661C22×C4C2×C4×D1311yescharacteristic
662C22×C4C2×C4×D1311yescharacteristic
663C22×C4D4×D1311yescharacteristic
664C22×C4D4×D1311yescharacteristic
665C22×C4#612911yescharacteristic
666C22×C4C23×D1311yescharacteristic
667Q16—262no—
668Q16—521no—
669SD16—262no—
670SD16—262no—
671SD16—521no—
672SD16—521no—
673D8—262no—
674D8—521no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—261no—
680M16—261no—
681M16—261no—
682M16—261no—
683M16—522no—
684M16—522no—
685M16—522no—
686M16C2×C22⋊D1312yes—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—131no—
691C2×C8—131no—
692C2×C8—131no—
693C2×C8—131no—
694C2×C8—131no—
695C2×C8—131no—
696C2×C8—131no—
697C2×C8—131no—
698C2×C8—261no—
699C2×C8—261no—
700C2×C8—261no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—522no—
709C2×C8—522no—
710C2×C8—522no—
711C4⋊C4—42no—
712C4⋊C4—131no—
713C4⋊C4—131no—
714C4⋊C4—261no—
715C4⋊C4—261no—
716C22⋊C4—42no—
717C22⋊C4—261no—
718C22⋊C4—261no—
719C22⋊C4—261no—
720C22⋊C4—261no—
721C22⋊C4—261no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—261no—
726C42C2×C22⋊D1312yes—
727C13#2288711yescharacteristic, complemented, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—261no—
738C23#8813511yescharacteristic
739C23#8813511yescharacteristic
740C23C2×#612911yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—261no—
746Q8—261no—
747Q8C4×C22⋊D1312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—261no—
759D4—261no—
760D4—522no—
761D4—521no—
762D4—521no—
763D4—1041no—
764D4C4×C22⋊D1312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—261no—
791C2×C4—261no—
792C2×C4—261no—
793C2×C4—521no—
794C2×C4—521no—
795C2×C4#8813511yescharacteristic
796C2×C4#8813511yescharacteristic
797C2×C4C22×C4×D1311yescharacteristic
798C2×C4C2×#612711yescharacteristic
799C2×C4C2×D4×D1311yescharacteristic
800C2×C4#8825111yescharacteristic
801C2×C4#8825111yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C8—22no—
804C8—41no—
805C8—261no—
806C8—261no—
807C8—261no—
808C8—261no—
809C8—261no—
810C8—261no—
811C8—261no—
812C8—261no—
813C8—521no—
814C8—521no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—521no—
833C22—521no—
834C22—521no—
835C22C2×#8813511yescharacteristic
836C22#1171920011yescharacteristic
837C22#1171951111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—81no—
844C4—521no—
845C4—521no—
846C4—521no—
847C4#1171919111yescharacteristic
848C4#1171919511yescharacteristic
849C4C2×C4×C22⋊D1311yescharacteristic
850C4D4×C22⋊D1311yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—1041no—
858C2#1311781511yescharacteristic
859C2#1312373511yescharacteristic
860C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#421C2
socleC22×C13C2×C4×D4
prime radical#13124054C2
cosocleC22×C4×C13C24
hypercenterC2×#421D13
hypocenterC13#22887
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#11718484C2semidirect
3. #13123561C2semidirect
4. #13123285C2semidirect
5. #13115721C2semidirect
6. #13115544C2semidirect
7. #13115487C2semidirect
8. #13115284C2semidirect
9. #13115161C2semidirect
10. #13115160C2semidirect
11. #13115109C2semidirect
12. #13115041C2semidirect
13. #13114674C2semidirect
14. #13114602C2semidirect
15. C2×C13×#421C2semidirect
24. C2×#88161C22semidirect
30. #11718900C4semidirect
31. #11718900C4semidirect
32. #11718899C4semidirect
33. #11718899C4semidirect
40. #11718889C4semidirect
41. #11718888C4semidirect
42. #11718879C4semidirect
43. #11718878C4semidirect
49. #11718790C22semidirect
52. C2×#88062C22semidirect
53. C2×#88062C22semidirect
54. #11718783C22semidirect
55. #11718780C22semidirect
58. C2×#88045C22semidirect
59. C2×#88045C22semidirect
60. C2×#88043C22semidirect
61. C2×C4×#1055C22semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718116C22semidirect
66. #11718116C22semidirect
67. #11718115C22semidirect
68. #11718115C22semidirect
139. C13×#104D4semidirect
301. C2×#421D13semidirect
565. #104C22⋊D13semidirect
727. C13#22887semidirect

Maximal subgroups

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

subgroupindex
#131240542
C2×#117184842
#131235612
#131232852
#131157212
#131155442
#131154872
#131152842
#131151612
#131151602
#131151092
#131150412
#131146742
#131146022
C2×C13×#4212
#2288713