Finite Group Databasebeta

← #15883667

Subgroups — #15883667

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×#11718806C211yesmaximal, characteristic, complemented
3#13123557C211yesmaximal, characteristic, complemented
4C2×#11718897C211yesmaximal, characteristic, complemented
5#13115723C211yesmaximal, characteristic, complemented
6#13115550C211yesmaximal, characteristic, complemented
7#13115481C211yesmaximal, characteristic, complemented
8#13115282C211yesmaximal, characteristic, complemented
9#13115166C211yesmaximal, characteristic, complemented
10#13115163C211yesmaximal, characteristic, complemented
11#13115111C211yesmaximal, characteristic, complemented
12#13115040C211yesmaximal, characteristic, complemented
13#13114671C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic, complemented
15C13×#2880C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C2×C13×#131C2211yescharacteristic
18C2×C13×#131C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21#11719496C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C2×#88155C2211yescharacteristic, complemented
25C13×#408—21no—
26C13×#408—21no—
27C13×#408C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#407—21no—
30C13×#407C2211yescharacteristic
31C2×C13×C22⋊C8—21no—
32C2×C13×C22⋊C8C2211yescharacteristic
33#11718900C411yescharacteristic, complemented
34#11718900C411yescharacteristic, complemented
35#11718899C411yescharacteristic, complemented
36#11718899C411yescharacteristic, complemented
37#11718897—24no—
38C2×#88077C2211yescharacteristic
39C2×#88077C2211yescharacteristic
40C2×#88077C2211yescharacteristic
41C2×#88077C2211yescharacteristic
42#11718894C2211yescharacteristic
43#11718894C2211yescharacteristic
44#11718889C411yescharacteristic, complemented
45#11718888C411yescharacteristic, complemented
46#11718879C411yescharacteristic, complemented
47#11718878C411yescharacteristic, complemented
48C2×C22⋊#1055C2211yescharacteristic
49#11718806—24no—
50C2×#88065C2211yescharacteristic, complemented
51C2×#88065C2211yescharacteristic, complemented
52C2×#88062C2211yescharacteristic, complemented
53C2×#88062C2211yescharacteristic, complemented
54#11718771C2211yescharacteristic, complemented
55#11718763C2211yescharacteristic, complemented
56#11718762C2211yescharacteristic, complemented
57C2×#88055C2211yescharacteristic, complemented
58C2×C8×Dic13C2211yescharacteristic, complemented
59#11718391—21no—
60#11718390—21no—
61#11718389—21no—
62#11718386—21no—
63#11718150C2211yescharacteristic, complemented
64#11718150C2211yescharacteristic, complemented
65#11718147C2211yescharacteristic, complemented
66#11718147C2211yescharacteristic, complemented
67#11718142C2211yescharacteristic, complemented
68#11718142C2211yescharacteristic, 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
85C13×#131—22no—
86C13×#131—22no—
87C13×#131—41no—
88C13×#131—41no—
89C2×C13×M16—21no—
90C2×C13×M16—21no—
91C2×C13×M16C2311yescharacteristic
92C2×C13×M16C2311yescharacteristic
93C22×C8×C13—21no—
94C22×C8×C13—21no—
95C22×C8×C13C2311yescharacteristic
96C22×C8×C13C2311yescharacteristic
97#88207—21no—
98C2×C22⋊Dic13—21no—
99#88204—22no—
100#88204—22no—
101#88204—41no—
102#88204—41no—
103C2×#6107C2×C411yescharacteristic
104C2×#6107C2×C411yescharacteristic
105C2×#6106C2×C411yescharacteristic
106C2×#6106C2×C411yescharacteristic
107C2×#6105C2×C411yescharacteristic
108C2×#6105C2×C411yescharacteristic
109C2×#6104C2×C411yescharacteristic
110C2×#6104C2×C411yescharacteristic
111#88184C2×C411yescharacteristic
112#88184C2×C411yescharacteristic
113#88183—21no—
114C4×C22⋊D13—21no—
115C4×C22⋊D13—21no—
116#88180—22no—
117#88180—41no—
118#88180C2311yescharacteristic
119C2×C4⋊Dic13—21no—
120#88178C2×C411yescharacteristic
121#88178C2×C411yescharacteristic
122C2×C4×Dic13C2311yescharacteristic
123C2×C4×Dic13C2311yescharacteristic
124C2×#6099—21no—
125C2×#6099—22no—
126C2×#6099—41no—
127C2×#6099C2311yescharacteristic
128C2×#6099C2311yescharacteristic
129C22×#1055—21no—
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132#88155—22no—
133#88155—41no—
134C2×#6094—21no—
135C2×C8×D13—21no—
136C13×C22⋊C8—21no—
137C13×C22⋊C8—21no—
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8—21no—
142C13×C22⋊C8D411yescharacteristic
143C13×C22⋊C8D411yescharacteristic
144C13×C22⋊C8D411yescharacteristic
145C13×C22⋊C8D411yescharacteristic
146#88077—22no—
147#88077—22no—
148#88077—22no—
149#88077D414yescomplemented
150#88075C2×C411yescharacteristic
151#88075C2×C411yescharacteristic
152#88075C2×C411yescharacteristic
153#88075C2×C411yescharacteristic
154#88072C2×C411yescharacteristic
155#88072C2×C411yescharacteristic
156#88072C2×C411yescharacteristic
157#88072C2×C411yescharacteristic
158C22⋊#1055C2×C411yescharacteristic
159C22⋊#1055C2×C411yescharacteristic
160C22⋊#1055C2×C411yescharacteristic
161C22⋊#1055C2×C411yescharacteristic
162#88065—22no—
163#88065—41no—
164#88062—22no—
165#88062—41no—
166#88060—21no—
167#88060—21no—
168#88055—21no—
169#88055—22no—
170#88054—21no—
171#88054—21no—
172C8×Dic13—21no—
173C8×Dic13—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—42no—
219C22×C4×C13—42no—
220C22×C4×C13C22×C411yescharacteristic
221C22×C4×C13C22×C411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13#4111yescharacteristic
225C22×C4×C13C2411yescharacteristic
226C2×C22⋊D13—21no—
227C2×C22⋊D13—21no—
228C2×C22⋊D13—21no—
229C22×Dic13—21no—
230C22×Dic13—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—21no—
242C13×M16—42no—
243C13×M16—42no—
244C2×C8×C13—21no—
245C2×C8×C13—21no—
246C2×C8×C13—21no—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13—21no—
250C2×C8×C13—42no—
251C2×C8×C13—42no—
252C2×C8×C13C2×D411yescharacteristic
253C2×C8×C13C2×D411yescharacteristic
254C2×C8×C13C2×D411yescharacteristic
255C2×C8×C13C2×D411yescharacteristic
256C22⋊Dic13—21no—
257C22⋊Dic13—21no—
258C22⋊Dic13—21no—
259C22⋊Dic13—42no—
260#6107—22no—
261#6107—41no—
262#6106—22no—
263#6106—41no—
264#6105—22no—
265#6105—41no—
266#6104—22no—
267#6104—41no—
268#6103—21no—
269#6103—21no—
270C4⋊Dic13—42no—
271C4⋊Dic13C22×C411yescharacteristic
272C4⋊Dic13C22×C411yescharacteristic
273#6101—21no—
274#6101—21no—
275C4×Dic13—21no—
276C4×Dic13—21no—
277C4×Dic13—21no—
278C4×Dic13—21no—
279C4×Dic13C2×D412yes—
280#6099—21no—
281#6099—21no—
282#6099—21no—
283#6099—42no—
284#6099C2×D412yes—
285C2×#1055—21no—
286C2×#1055—21no—
287C2×#1055—21no—
288C2×#1055—21no—
289C2×#1055—21no—
290C2×#1055—21no—
291C2×#1055—42no—
292C2×#1055C22×C411yescharacteristic
293C2×#1055C22×C411yescharacteristic
294C2×#1055C22×C411yescharacteristic
295C2×#1055C22×C411yescharacteristic
296#6094—42no—
297C8×D13—42no—
298#3002—131no—
299C2×#444—131no—
300#2933—131no—
301C2×#421—131no—
302#2880D1311yescharacteristic, complemented
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—21no—
350C2×C4×C13—21no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—42no—
357C2×C4×C13—42no—
358C2×C4×C13—42no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13C4×D411yescharacteristic
362C2×C4×C13C4×D411yescharacteristic
363C2×C4×C13C23×C411yescharacteristic
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C22×D411yescharacteristic
366C2×C4×C13C2×#4111yescharacteristic
367C2×C4×C13H(5,𝔽2)11yescharacteristic
368C2×C4×C13H(5,𝔽2)11yescharacteristic
369C22⋊D13—42no—
370C22⋊D13—41no—
371C22⋊D13—41no—
372C22⋊D13—81no—
373C2×Dic13—21no—
374C2×Dic13—21no—
375C2×Dic13—21no—
376C2×Dic13—22no—
377C2×Dic13—41no—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382D52—21no—
383D52—21no—
384C4×D13—41no—
385C4×D13—41no—
386Dic26—21no—
387Dic26—21no—
388C8×C13—21no—
389C8×C13—21no—
390C8×C13—21no—
391C8×C13—21no—
392C8×C13—41no—
393C8×C13—41no—
394#1055—21no—
395#1055—21no—
396#1055—21no—
397#1055—21no—
398#1055—22no—
399#1055—41no—
400C22×#41C2×D1311yescharacteristic
401C2×#135—131no—
402C2×#135—131no—
403C2×#131—131no—
404C2×#131C2×D1311yescharacteristic
405C2×#131C2×D1311yescharacteristic
406C22×M16—131no—
407#525—131no—
408C2×#117—131no—
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—264no—
426C2×#104—131no—
427C2×#104—131no—
428C2×#104—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432#416—131no—
433#416—131no—
434#408—21no—
435#408—21no—
436#408—131no—
437#408C2×D1311yescharacteristic
438#408C2×D1311yescharacteristic
439#407—21no—
440#407C2×D1311yescharacteristic
441C2×C22⋊C8—21no—
442C2×C22⋊C8—131no—
443C2×C22⋊C8C2×D1311yescharacteristic
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—41no—
480C4×C13C2×C4×D411yescharacteristic
481C4×C13#51811yescharacteristic
482C4×C13D4211yescharacteristic
483C4×C13#54611yescharacteristic
484Dic13—42no—
485Dic13—41no—
486Dic13—41no—
487Dic13—41no—
488Dic13—81no—
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—22no—
518#131—22no—
519#131—41no—
520#131—41no—
521#131—262no—
522#131—521no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16—131no—
526C2×M16—131no—
527C2×M16—261no—
528C2×M16—261no—
529C2×M16—262no—
530C2×M16—521no—
531C2×M16C22×D1311yescharacteristic
532C2×M16C22×D1311yescharacteristic
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—131no—
536C22×C8—131no—
537C22×C8—261no—
538C22×C8—261no—
539C22×C8C22×D1311yescharacteristic
540C22×C8C22×D1311yescharacteristic
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—131no—
550#117—262no—
551#117—521no—
552C2×C4⋊C4—261no—
553C2×C22⋊C4—261no—
554C2×C42—131no—
555C2×C42—131no—
556#108—262no—
557#108—521no—
558C4⋊C8—261no—
559C4⋊C8—261no—
560#104—134no—
561#104—262no—
562#104—262no—
563#104—262no—
564#104—262no—
565#104—521no—
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—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—131no—
581C22⋊C8—131no—
582C22⋊C8—131no—
583C22⋊C8—131no—
584C22⋊C8—261no—
585C22⋊C8—261no—
586C22⋊C8C22⋊D1311yescharacteristic
587C22⋊C8C22⋊D1311yescharacteristic
588C22⋊C8C22⋊D1311yescharacteristic
589C22⋊C8C22⋊D1311yescharacteristic
590#97—262no—
591#97—261no—
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#612711yescharacteristic
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#41D4×D1312yes—
625#41#612912yes—
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—42no—
657C22×C4—42no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4C2×C4×D1311yescharacteristic
662C22×C4C2×C4×D1311yescharacteristic
663C22×C4#612711yescharacteristic
664C22×C4C2×C22⋊D1311yescharacteristic
665C22×C4C2×C22⋊D1311yescharacteristic
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—21no—
679M16—42no—
680M16—42no—
681M16—132no—
682M16—261no—
683M16—261no—
684M16—261no—
685M16—522no—
686M16—522no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—131no—
696C2×C8—131no—
697C2×C8—131no—
698C2×C8—131no—
699C2×C8—261no—
700C2×C8—261no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—522no—
706C2×C8—522no—
707C2×C8C2×C22⋊D1311yescharacteristic
708C2×C8C2×C22⋊D1311yescharacteristic
709C2×C8C2×C22⋊D1311yescharacteristic
710C2×C8C2×C22⋊D1311yescharacteristic
711C4⋊C4—131no—
712C4⋊C4—131no—
713C4⋊C4—261no—
714C4⋊C4—261no—
715C4⋊C4—522no—
716C22⋊C4—261no—
717C22⋊C4—261no—
718C22⋊C4—261no—
719C22⋊C4—261no—
720C22⋊C4—261no—
721C22⋊C4—522no—
722C42—132no—
723C42—261no—
724C42—261no—
725C42—261no—
726C42—261no—
727C13#2288711yescharacteristic, complemented, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—261no—
738C23C4×C22⋊D1311yescharacteristic
739C23C4×C22⋊D1311yescharacteristic
740C23C2×#612711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—261no—
746Q8—261no—
747Q8#8813512yes—
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—
764D4#8813512yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—262no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—521no—
789C2×C4—521no—
790C2×C4—521no—
791C2×C4—521no—
792C2×C4—521no—
793C2×C4—521no—
794C2×C4—521no—
795C2×C4C4×C22⋊D1311yescharacteristic
796C2×C4C4×C22⋊D1311yescharacteristic
797C2×C4C22×C4×D1311yescharacteristic
798C2×C4C2×D4×D1311yescharacteristic
799C2×C4C2×#612911yescharacteristic
800C2×C4#8825111yescharacteristic
801C2×C4#8825111yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—261no—
810C8—261no—
811C8—261no—
812C8—261no—
813C8—262no—
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—
835C22#1171919511yescharacteristic
836C22#1171920011yescharacteristic
837C22C2×C4×C22⋊D1311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—522no—
843C4—521no—
844C4—521no—
845C4—521no—
846C4—1041no—
847C4C2×#8813511yescharacteristic
848C4#1171919111yescharacteristic
849C4D4×C22⋊D1311yescharacteristic
850C4#1171951111yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—1041no—
858C2#1311781511yescharacteristic
859C2#1312373711yescharacteristic
860C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2880C2
socleC22×C13C2×C4×D4
prime radical#13124054C2
cosocleC22×C4×C13C24
hypercenter#2880D13
hypocenterC13#22887
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#11718806C2semidirect
3. #13123557C2semidirect
4. C2×#11718897C2semidirect
5. #13115723C2semidirect
6. #13115550C2semidirect
7. #13115481C2semidirect
8. #13115282C2semidirect
9. #13115166C2semidirect
10. #13115163C2semidirect
11. #13115111C2semidirect
12. #13115040C2semidirect
13. #13114671C2semidirect
14. #13114604C2semidirect
15. C13×#2880C2semidirect
24. C2×#88155C22semidirect
33. #11718900C4semidirect
34. #11718900C4semidirect
35. #11718899C4semidirect
36. #11718899C4semidirect
44. #11718889C4semidirect
45. #11718888C4semidirect
46. #11718879C4semidirect
47. #11718878C4semidirect
50. C2×#88065C22semidirect
51. C2×#88065C22semidirect
52. C2×#88062C22semidirect
53. C2×#88062C22semidirect
54. #11718771C22semidirect
55. #11718763C22semidirect
56. #11718762C22semidirect
57. C2×#88055C22semidirect
58. C2×C8×Dic13C22semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718147C22semidirect
66. #11718147C22semidirect
67. #11718142C22semidirect
68. #11718142C22semidirect
149. #88077D4semidirect
302. #2880D13semidirect
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×#117188062
#131235572
C2×#117188972
#131157232
#131155502
#131154812
#131152822
#131151662
#131151632
#131151112
#131150402
#131146712
#131146042
C13×#28802
#2288713