Finite Group Databasebeta

← #15883653

Subgroups — #15883653

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124052C211yesmaximal, characteristic
2C2×#11718484C211yesmaximal, characteristic, complemented
3#13123563C211yesmaximal, characteristic, complemented
4C22×#88045C211yesmaximal, characteristic, complemented
5#13123286C211yesmaximal, characteristic, complemented
6#13115726C211yesmaximal, characteristic, complemented
7#13115548C211yesmaximal, characteristic, complemented
8#13115482C211yesmaximal, characteristic, complemented
9#13115161C211yesmaximal, characteristic, complemented
10#13115160C211yesmaximal, characteristic, complemented
11#13115112C211yesmaximal, characteristic, complemented
12#13115040C211yesmaximal, characteristic, complemented
13#13114677C211yesmaximal, characteristic, complemented
14#13114598C211yesmaximal, characteristic, complemented
15C13×#1896C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C13×#525C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21C2×#88202C2211yescharacteristic, complemented
22C22×#6099C2211yescharacteristic
23C2×#88161C2211yescharacteristic
24C2×#88161C2211yescharacteristic
25C2×C13×#104C2211yescharacteristic, complemented
26C2×C13×#104C2211yescharacteristic, complemented
27C13×#407C2211yescharacteristic
28#11718895C2211yescharacteristic, complemented
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718790C2211yescharacteristic
32#11718790C2211yescharacteristic
33C2×#88062C2211yescharacteristic, complemented
34C2×#88062C2211yescharacteristic, complemented
35#11718711C411yescharacteristic, complemented
36#11718708C411yescharacteristic, complemented
37#11718708C411yescharacteristic, complemented
38#11718707C411yescharacteristic, complemented
39#11718701C411yescharacteristic, complemented
40#11718698C411yescharacteristic, complemented
41#11718698C411yescharacteristic, complemented
42#11718697C411yescharacteristic, complemented
43#11718673—21no—
44#11718672—21no—
45#11718672—21no—
46D4×#1055—21no—
47#11718663C2211yescharacteristic
48#11718663C2211yescharacteristic
49#11718660C2211yescharacteristic, complemented
50#11718658C2211yescharacteristic, complemented
51C2×#88045—24no—
52C2×#88045C2211yescharacteristic
53C2×#88045C2211yescharacteristic
54C2×#88045C2211yescharacteristic
55C2×#88045C2211yescharacteristic
56C2×#88043C2211yescharacteristic, complemented
57C2×#88043C2211yescharacteristic, complemented
58#11718484—24no—
59#11718388—21no—
60#11718388—21no—
61#11718387—21no—
62D13×C22⋊C8—21no—
63C13×#339C2211yescharacteristic, complemented
64C13×#339C2211yescharacteristic, complemented
65#11718150C2211yescharacteristic, complemented
66#11718150C2211yescharacteristic, complemented
67#11718116C2211yescharacteristic, complemented
68#11718116C2211yescharacteristic, complemented
69C2×C13×#41C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13C2311yescharacteristic
72C22×C22⋊D13—21no—
73C2×#6127—21no—
74C2×#6127—21no—
75C2×#6127—22no—
76C2×#6127—22no—
77C2×#6127—41no—
78C2×#6127—41no—
79C2×#6127C2×C411yescharacteristic
80C2×#6127C2×C411yescharacteristic
81C2×#6127C2311yescharacteristic
82C2×#6127C2311yescharacteristic
83C22×D52C2×C411yescharacteristic
84C22×C4×D13—21no—
85C22×Dic26C2×C411yescharacteristic
86C2×C13×M16C2311yescharacteristic
87C2×C13×M16C2311yescharacteristic
88C13×#123—21no—
89C13×C22⋊Q8C2×C411yescharacteristic
90C13×C22⋊Q8C2×C411yescharacteristic
91C13×#121C2×C411yescharacteristic
92C13×#121C2×C411yescharacteristic
93C13×#120—21no—
94C4×D4×C13—21no—
95C4×D4×C13—21no—
96C13×#117C2311yescharacteristic
97C2×C42×C13—22no—
98C2×C42×C13—21no—
99C2×C42×C13—41no—
100C2×C42×C13C2311yescharacteristic
101C2×C42×C13C2311yescharacteristic
102#88204—22no—
103#88204—22no—
104#88204—41no—
105#88204—41no—
106#88202—22no—
107#88202—41no—
108C2×#6107C2×C411yescharacteristic, complemented
109C2×#6107C2×C411yescharacteristic, complemented
110C2×#6106C2×C411yescharacteristic, complemented
111C2×#6106C2×C411yescharacteristic, complemented
112C2×#6105C2×C411yescharacteristic, complemented
113C2×#6105C2×C411yescharacteristic, complemented
114C2×#6104C2×C411yescharacteristic, complemented
115C2×#6104C2×C411yescharacteristic, complemented
116C2×#6099—21no—
117C2×#6099—21no—
118C2×#6099—22no—
119C2×#6099—41no—
120C2×#6099C2311yescharacteristic
121C2×#6099C2311yescharacteristic
122C22×#1055—21no—
123C22×#1055—21no—
124C22×#1055C2311yescharacteristic
125C22×#1055C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128#88161—22no—
129#88161—22no—
130#88161—41no—
131#88161—41no—
132C2×#6094—21no—
133C2×#6094—21no—
134C2×C8×D13—21no—
135C2×C8×D13—21no—
136C13×#104—22no—
137C13×#104—41no—
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C22⋊#1055—21no—
141C22⋊#1055—21no—
142C22⋊#1055C2×C411yescharacteristic
143C22⋊#1055C2×C411yescharacteristic
144C22⋊#1055C2×C411yescharacteristic
145C22⋊#1055C2×C411yescharacteristic
146C22⋊#1055D411yescharacteristic
147C22⋊#1055D411yescharacteristic
148C22⋊#1055D411yescharacteristic
149C22⋊#1055D411yescharacteristic
150#88062—22no—
151#88062—41no—
152#88060—21no—
153#88060—21no—
154#88060—21no—
155#88060—21no—
156#88050C2×C411yescharacteristic, complemented
157#88050C2×C411yescharacteristic, complemented
158#88050C2×C411yescharacteristic, complemented
159#88050C2×C411yescharacteristic, complemented
160#88049C2×C411yescharacteristic, complemented
161#88049C2×C411yescharacteristic, complemented
162#88049C2×C411yescharacteristic, complemented
163#88049C2×C411yescharacteristic, complemented
164#88045—22no—
165#88045—22no—
166#88045—22no—
167#88045D414yescomplemented
168C4⋊#1055—21no—
169C4⋊#1055—21no—
170#88043—22no—
171#88043—21no—
172#88043—41no—
173C4×#1055—21no—
174#22886—131nomaximal, Sylow
175C24×C13#4111yescharacteristic
176C23×D13—21no—
177C13×#41—21no—
178C13×#41—21no—
179C13×#41—21no—
180C13×#41—21no—
181C2×Q8×C13C22×C411yescharacteristic
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—21no—
185C2×D4×C13C22×C411yescharacteristic
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—42no—
194C22×C4×C13—42no—
195C22×C4×C13—42no—
196C22×C4×C13C22×C411yescharacteristic
197C22×C4×C13C22×C411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13#4111yescharacteristic
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—21no—
203C2×C22⋊D13—21no—
204C2×C22⋊D13—21no—
205C2×C22⋊D13—21no—
206C2×C22⋊D13—42no—
207C2×C22⋊D13—42no—
208C22×Dic13—21no—
209#6127—21no—
210#6127—21no—
211#6127—21no—
212#6127—21no—
213#6127—21no—
214#6127—21no—
215#6127—22no—
216#6127—22no—
217#6127—41no—
218#6127—41no—
219#6127—42no—
220#6127—42no—
221#6127—42no—
222#6127—42no—
223#6127C2×D412yes—
224#6127#4112yes—
225C2×D52—22no—
226C2×D52—21no—
227C2×D52—41no—
228C2×D52C22×C411yescharacteristic
229C2×D52C22×C411yescharacteristic
230C2×C4×D13—21no—
231C2×C4×D13—21no—
232C2×C4×D13—21no—
233C2×C4×D13—21no—
234C2×C4×D13—42no—
235C2×C4×D13—42no—
236C2×Dic26—22no—
237C2×Dic26—21no—
238C2×Dic26—41no—
239C2×Dic26C22×C411yescharacteristic
240C2×Dic26C22×C411yescharacteristic
241C13×M16—21no—
242C13×M16—21no—
243C13×M16—21no—
244C13×M16—21no—
245C2×C8×C13—21no—
246C2×C8×C13—21no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4—21no—
249C13×C4⋊C4C22×C411yescharacteristic
250C13×C4⋊C4C22×C411yescharacteristic
251C13×C22⋊C4—21no—
252C13×C22⋊C4—21no—
253C13×C22⋊C4—21no—
254C13×C22⋊C4—21no—
255C13×C22⋊C4—21no—
256C42×C13—21no—
257C42×C13—21no—
258C42×C13—21no—
259C42×C13—21no—
260C42×C13—42no—
261C42×C13C2×D412yes—
262#6107—22no—
263#6107—41no—
264#6106—22no—
265#6106—41no—
266#6105—22no—
267#6105—41no—
268#6104—22no—
269#6104—41no—
270#6099—21no—
271#6099—21no—
272#6099—21no—
273#6099—42no—
274#6099—42no—
275#6099C2×D412yes—
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—
297#6094—42no—
298C8×D13—42no—
299C8×D13—42no—
300#3002—131no—
301C2×#444—131no—
302#2933—131no—
303C22×#104—131no—
304#2880—131no—
305#1975—131no—
306#1938—131no—
307#1929—131no—
308#1896D1311yescharacteristic, complemented
309#1876—131no—
310#1876—131no—
311#1866—131no—
312#1855—131no—
313#1765—131no—
314#1749—131no—
315C23×C13—21no—
316C23×C13—21no—
317C23×C13—22no—
318C23×C13—21no—
319C23×C13—41no—
320C23×C13C4×D411yescharacteristic
321C23×C13C4×D411yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C22×D13—21no—
324C22×D13—21no—
325C22×D13—42no—
326C22×D13—42no—
327C22×D13—81no—
328Q8×C13—21no—
329Q8×C13—21no—
330D4×C13—21no—
331D4×C13—21no—
332D4×C13—41no—
333D4×C13—41no—
334D4×C13—42no—
335D4×C13—81no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—21no—
339C2×C4×C13—21no—
340C2×C4×C13—21no—
341C2×C4×C13—21no—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—22no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—21no—
350C2×C4×C13—22no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—48no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13C4×D411yescharacteristic
359C2×C4×C13C4×D411yescharacteristic
360C2×C4×C13C23×C411yescharacteristic
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C2×#4111yescharacteristic
364C2×C4×C13H(5,𝔽2)11yescharacteristic
365C2×C4×C13H(5,𝔽2)11yescharacteristic
366C22⋊D13—22no—
367C22⋊D13—22no—
368C22⋊D13—42no—
369C22⋊D13—42no—
370C22⋊D13—41no—
371C22⋊D13—41no—
372C2×Dic13—21no—
373C2×Dic13—21no—
374C2×Dic13—42no—
375D52—21no—
376D52—21no—
377D52—21no—
378D52—42no—
379D52C4×D412yes—
380C4×D13—22no—
381C4×D13—22no—
382C4×D13—42no—
383C4×D13—42no—
384C4×D13—41no—
385C4×D13—41no—
386Dic26—21no—
387Dic26—21no—
388Dic26—21no—
389Dic26—42no—
390Dic26C4×D412yes—
391C8×C13—41no—
392C8×C13—41no—
393#1055—21no—
394#1055—21no—
395#1055—21no—
396#1055—21no—
397#1055—21no—
398#1055—21no—
399#1055—22no—
400#1055—21no—
401#1055—21no—
402#1055—41no—
403C22×#41—131no—
404C2×#135—131no—
405C2×#135—131no—
406C2×#131—131no—
407C2×#131—131no—
408C2×#131—131no—
409C22×M16—131no—
410#525C2×D1311yescharacteristic
411C22×C42C2×D1311yescharacteristic
412#452—131no—
413#452—131no—
414#451—131no—
415#450—131no—
416#449—131no—
417#449—131no—
418#448—131no—
419#447—131no—
420#444—264no—
421#436—261no—
422#435—261no—
423#435—261no—
424C8×D4—261no—
425C2×#108—131no—
426C2×#108—131no—
427#424—131no—
428C2×#104—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432C2×#104—264no—
433C2×#104C2×D1311yescharacteristic, complemented
434C2×#104C2×D1311yescharacteristic, complemented
435#416—131no—
436#416—131no—
437#408—131no—
438#408—131no—
439#408—131no—
440#408—261no—
441#408—261no—
442#407—261no—
443#407C2×D1311yescharacteristic
444C2×C22⋊C8—131no—
445C2×C22⋊C8—131no—
446C2×C22⋊C8—261no—
447#405—131no—
448C2×#97—131no—
449C2×#97—131no—
450#341—131no—
451#341—131no—
452#339C2×D1311yescharacteristic, complemented
453#339C2×D1311yescharacteristic, complemented
454#336—131no—
455#336—131no—
456C22×C13—21no—
457C22×C13—21no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—21no—
461C22×C13—21no—
462C22×C13—21no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13#44412yescomplemented
469C22×C13C2×C4×D411yescharacteristic
470C22×C13#54611yescharacteristic
471C22×C13#55111yescharacteristic
472C2×D13—22no—
473C2×D13—41no—
474C2×D13—41no—
475C2×D13—41no—
476C2×D13—41no—
477C2×D13—41no—
478C2×D13—84no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—42no—
482C4×C13—42no—
483C4×C13—41no—
484C4×C13—41no—
485C4×C13—41no—
486C4×C13C2×C4×D411yescharacteristic
487C4×C13#51811yescharacteristic
488C4×C13D4211yescharacteristic
489C4×C13#54611yescharacteristic
490Dic13—22no—
491Dic13—41no—
492C2×#41—131no—
493C2×#41—131no—
494C2×#41—131no—
495C2×#41—131no—
496C2×#41—262no—
497C2×#41—262no—
498C2×#41—261no—
499C2×#41—261no—
500C2×#41—521no—
501C2×#41—521no—
502C2×#41C22×D1311yescharacteristic
503C22×Q8—131no—
504C22×D4—131no—
505C22×D4—261no—
506C23×C4—21no—
507C23×C4—261no—
508C23×C4C22×D1311yescharacteristic
509#135—262no—
510#135—262no—
511#135—521no—
512#135—521no—
513C2×Q16—131no—
514C2×Q16—131no—
515C2×SD16—131no—
516C2×SD16—131no—
517C2×SD16—131no—
518C2×SD16—131no—
519C2×D8—131no—
520C2×D8—131no—
521#131—262no—
522#131—262no—
523#131—262no—
524#131—521no—
525#131—521no—
526#131—521no—
527C2×M16—131no—
528C2×M16—131no—
529C2×M16—261no—
530C2×M16—261no—
531C2×M16—261no—
532C2×M16—261no—
533C2×M16—262no—
534C2×M16—521no—
535C2×M16C22×D1311yescharacteristic
536C2×M16C22×D1311yescharacteristic
537C22×C8—131no—
538C22×C8—131no—
539C22×C8—131no—
540C22×C8—131no—
541C22×C8—261no—
542C22×C8—261no—
543C22×C8—261no—
544C22×C8—261no—
545#123—21no—
546C22⋊Q8C4×D1311yescharacteristic
547C22⋊Q8C4×D1311yescharacteristic
548#121C4×D1311yescharacteristic
549#121C4×D1311yescharacteristic
550#120—21no—
551C4×D4—21no—
552C4×D4—21no—
553#117C22×D1311yescharacteristic
554C2×C42—22no—
555C2×C42—21no—
556C2×C42—41no—
557C2×C42C22×D1311yescharacteristic
558C2×C42C22×D1311yescharacteristic
559#108—262no—
560#108—521no—
561C4⋊C8—261no—
562C4⋊C8—261no—
563#104—22no—
564#104—41no—
565#104—134no—
566#104—262no—
567#104—262no—
568#104—262no—
569#103—131no—
570#103—131no—
571#103—131no—
572#103—131no—
573#102—131no—
574#102—131no—
575#102—131no—
576#102—131no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—131no—
580C22⋊C8—131no—
581C22⋊C8—131no—
582C22⋊C8—131no—
583C22⋊C8—131no—
584C22⋊C8—131no—
585C22⋊C8—131no—
586C22⋊C8—131no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8—261no—
590C22⋊C8—261no—
591C22⋊C8—261no—
592C22⋊C8—261no—
593#97—261no—
594#97—262no—
595#97—521no—
596C4×C8—261no—
597C2×C13—21no—
598C2×C13—22no—
599C2×C13—21no—
600C2×C13—41no—
601C2×C13—81no—
602C2×C13#235811yescharacteristic
603C2×C13C2×#44411yescharacteristic
604C2×C13#295611yescharacteristic
605D13—42no—
606D13—81no—
607C24—261no—
608C24#612911yescharacteristic
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—132no—
614#41—132no—
615#41—262no—
616#41—262no—
617#41—261no—
618#41—261no—
619#41—261no—
620#41—261no—
621#41—261no—
622#41—261no—
623#41—522no—
624#41—522no—
625#41—521no—
626#41—521no—
627#41—522no—
628#41—522no—
629C2×Q8—131no—
630C2×Q8—131no—
631C2×Q8—262no—
632C2×Q8—261no—
633C2×Q8—521no—
634C2×Q8C2×C4×D1311yescharacteristic
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—131no—
639C2×D4—131no—
640C2×D4—262no—
641C2×D4—261no—
642C2×D4—261no—
643C2×D4—261no—
644C2×D4—261no—
645C2×D4—261no—
646C2×D4—521no—
647C2×D4—522no—
648C2×D4—522no—
649C2×D4C2×C4×D1311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—522no—
666C22×C4—522no—
667C22×C4C2×C4×D1311yescharacteristic
668C22×C4C2×C4×D1311yescharacteristic
669C22×C4D4×D1311yescharacteristic
670C22×C4D4×D1311yescharacteristic
671C22×C4#612911yescharacteristic
672C22×C4C23×D1311yescharacteristic
673Q16—262no—
674Q16—521no—
675SD16—262no—
676SD16—262no—
677SD16—521no—
678SD16—521no—
679D8—262no—
680D8—521no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—132no—
686M16—261no—
687M16—261no—
688M16—261no—
689M16—522no—
690M16—522no—
691M16—522no—
692M16—522no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—131no—
696C2×C8—131no—
697C2×C8—131no—
698C2×C8—131no—
699C2×C8—131no—
700C2×C8—131no—
701C2×C8—131no—
702C2×C8—131no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—261no—
710C2×C8—261no—
711C2×C8—261no—
712C2×C8—261no—
713C2×C8—522no—
714C2×C8—522no—
715C2×C8—522no—
716C2×C8—522no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4C2×C4×D1311yescharacteristic
720C4⋊C4C2×C4×D1311yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42D4×D1312yes—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—261no—
739C23—261no—
740C23—522no—
741C23—522no—
742C23—1041no—
743C23#8813511yescharacteristic
744C23#8813511yescharacteristic
745C23C2×#612911yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—132no—
749Q8—261no—
750Q8—261no—
751Q8—261no—
752Q8—522no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—132no—
760D4—262no—
761D4—262no—
762D4—261no—
763D4—261no—
764D4—261no—
765D4—522no—
766D4—522no—
767D4—522no—
768D4—521no—
769D4—521no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—261no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—261no—
796C2×C4—522no—
797C2×C4—522no—
798C2×C4—522no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4#8813511yescharacteristic
802C2×C4#8813511yescharacteristic
803C2×C4C22×C4×D1311yescharacteristic
804C2×C4C2×D4×D1311yescharacteristic
805C2×C4C2×D4×D1311yescharacteristic
806C2×C4#8825111yescharacteristic
807C2×C4#41×D1311yescharacteristic
808C2×C4#8825611yescharacteristic
809C8—41no—
810C8—41no—
811C8—261no—
812C8—261no—
813C8—261no—
814C8—261no—
815C8—261no—
816C8—261no—
817C8—262no—
818C8—261no—
819C8—261no—
820C8—521no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—262no—
834C22—521no—
835C22—521no—
836C22—521no—
837C22—521no—
838C22—521no—
839C22—1044no—
840C22#1171848412yescomplemented
841C22C2×#8813511yescharacteristic
842C22#1171929611yescharacteristic
843C22#1171936311yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—262no—
852C4—521no—
853C4C4×D4×D1311yescharacteristic
854C4#1171925011yescharacteristic
855C4#1171931411yescharacteristic
856C4#1171931511yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—522no—
863C2—1041no—
864C2#1311781611yescharacteristic
865C2C2×#1171848411yescharacteristic
866C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1896C2
socleC22×C13C2×C4×D4
prime radical#13124052C2
cosocleC22×C4×C13C24
hypercenter#1896D13
hypocenterC13#22886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#11718484C2semidirect
3. #13123563C2semidirect
4. C22×#88045C2semidirect
5. #13123286C2semidirect
6. #13115726C2semidirect
7. #13115548C2semidirect
8. #13115482C2semidirect
9. #13115161C2semidirect
10. #13115160C2semidirect
11. #13115112C2semidirect
12. #13115040C2semidirect
13. #13114677C2semidirect
14. #13114598C2semidirect
15. C13×#1896C2semidirect
21. C2×#88202C22semidirect
25. C2×C13×#104C22semidirect
26. C2×C13×#104C22semidirect
28. #11718895C22semidirect
33. C2×#88062C22semidirect
34. C2×#88062C22semidirect
35. #11718711C4semidirect
36. #11718708C4semidirect
37. #11718708C4semidirect
38. #11718707C4semidirect
39. #11718701C4semidirect
40. #11718698C4semidirect
41. #11718698C4semidirect
42. #11718697C4semidirect
49. #11718660C22semidirect
50. #11718658C22semidirect
56. C2×#88043C22semidirect
57. C2×#88043C22semidirect
63. C13×#339C22semidirect
64. C13×#339C22semidirect
65. #11718150C22semidirect
66. #11718150C22semidirect
67. #11718116C22semidirect
68. #11718116C22semidirect
108. C2×#6107C2×C4semidirect
109. C2×#6107C2×C4semidirect
110. C2×#6106C2×C4semidirect
111. C2×#6106C2×C4semidirect
112. C2×#6105C2×C4semidirect
113. C2×#6105C2×C4semidirect
114. C2×#6104C2×C4semidirect
115. C2×#6104C2×C4semidirect
156. #88050C2×C4semidirect
157. #88050C2×C4semidirect
158. #88050C2×C4semidirect
159. #88050C2×C4semidirect
160. #88049C2×C4semidirect
161. #88049C2×C4semidirect
162. #88049C2×C4semidirect
163. #88049C2×C4semidirect
167. #88045D4semidirect
308. #1896D13semidirect
433. C2×#104C2×D13semidirect
434. C2×#104C2×D13semidirect
452. #339C2×D13semidirect
453. #339C2×D13semidirect
468. C22×C13#444semidirect
732. C13#22886semidirect
840. C22#11718484semidirect

Maximal subgroups

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

subgroupindex
#131240522
C2×#117184842
#131235632
C22×#880452
#131232862
#131157262
#131155482
#131154822
#131151612
#131151602
#131151122
#131150402
#131146772
#131145982
C13×#18962
#2288613