Finite Group Databasebeta

← #15883657

Subgroups — #15883657

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×#11718806C211yesmaximal, characteristic, complemented
3C22×#88065C211yesmaximal, characteristic, complemented
4#13123282C211yesmaximal, characteristic, complemented
5#13115728C211yesmaximal, characteristic, complemented
6#13115546C211yesmaximal, characteristic, complemented
7#13115484C211yesmaximal, characteristic, complemented
8#13115280C211yesmaximal, characteristic, complemented
9#13115166C211yesmaximal, characteristic, complemented
10#13115163C211yesmaximal, characteristic, complemented
11#13115110C211yesmaximal, characteristic, complemented
12#13115041C211yesmaximal, characteristic, complemented
13#13114682C211yesmaximal, characteristic, complemented
14#13114600C211yesmaximal, characteristic, complemented
15C13×#2933C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#131C2211yescharacteristic, complemented
18C22×C13×M16C2211yescharacteristic
19C13×#525C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21C2×#88204C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×#88155C2211yescharacteristic
24C2×#88155C2211yescharacteristic
25C13×#436—21no—
26C13×#435—21no—
27C13×#435—21no—
28C8×D4×C13—21no—
29C13×#424C2211yescharacteristic, complemented
30C13×#408C2211yescharacteristic, complemented
31C2×C13×C22⋊C8C2211yescharacteristic
32C13×#405C2211yescharacteristic, complemented
33C2×#88077C2211yescharacteristic, complemented
34C2×#88077C2211yescharacteristic, complemented
35#11718868C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718806—24no—
38C2×#88065—24no—
39C2×#88065C2211yescharacteristic
40C2×#88065C2211yescharacteristic
41C2×#88065C2211yescharacteristic
42C2×#88065C2211yescharacteristic
43C2×#88062C2211yescharacteristic, complemented
44C2×#88062C2211yescharacteristic, complemented
45#11718771C2211yescharacteristic
46#11718771C2211yescharacteristic
47C2×#88055C2211yescharacteristic, complemented
48C2×#88055C2211yescharacteristic, complemented
49#11718711C411yescharacteristic, complemented
50#11718708C411yescharacteristic, complemented
51#11718708C411yescharacteristic, complemented
52#11718707C411yescharacteristic, complemented
53#11718701C411yescharacteristic, complemented
54#11718698C411yescharacteristic, complemented
55#11718698C411yescharacteristic, complemented
56#11718697C411yescharacteristic, complemented
57#11718663C2211yescharacteristic
58#11718663C2211yescharacteristic
59#11718388—21no—
60#11718388—21no—
61#11718387—21no—
62D13×C22⋊C8—21no—
63#11718150C2211yescharacteristic, complemented
64#11718150C2211yescharacteristic, complemented
65#11718142C2211yescharacteristic, complemented
66#11718142C2211yescharacteristic, complemented
67#11718124C2211yescharacteristic, complemented
68#11718124C2211yescharacteristic, complemented
69C2×C13×#41C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C22×C22⋊D13—21no—
72C23×Dic13—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
86C13×#131—22no—
87C13×#131—41no—
88C2×C13×M16—21no—
89C2×C13×M16—21no—
90C2×C13×M16—22no—
91C2×C13×M16—41no—
92C2×C13×M16C2311yescharacteristic
93C2×C13×M16C2311yescharacteristic
94C22×C8×C13—21no—
95C22×C8×C13—21no—
96C22×C8×C13C2311yescharacteristic
97C22×C8×C13C2311yescharacteristic
98C13×#123—21no—
99C13×C22⋊Q8C2×C411yescharacteristic
100C13×C22⋊Q8C2×C411yescharacteristic
101C13×#121C2×C411yescharacteristic
102C13×#121C2×C411yescharacteristic
103C13×#120—21no—
104C4×D4×C13—21no—
105C4×D4×C13—21no—
106C13×#117C2311yescharacteristic
107#88204—22no—
108#88204—22no—
109#88204—41no—
110#88204—41no—
111C2×#6107C2×C411yescharacteristic, complemented
112C2×#6107C2×C411yescharacteristic, complemented
113C2×#6106C2×C411yescharacteristic, complemented
114C2×#6106C2×C411yescharacteristic, complemented
115C2×#6105C2×C411yescharacteristic, complemented
116C2×#6105C2×C411yescharacteristic, complemented
117C2×#6104C2×C411yescharacteristic, complemented
118C2×#6104C2×C411yescharacteristic, complemented
119C2×C4×Dic13—22no—
120C2×C4×Dic13—21no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13C2311yescharacteristic
123C2×C4×Dic13C2311yescharacteristic
124C2×#6099C2311yescharacteristic
125C2×#6099C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128#88155—22no—
129#88155—22no—
130#88155—41no—
131#88155—41no—
132C2×#6094—21no—
133C2×#6094—21no—
134C2×C8×D13—21no—
135C2×C8×D13—21no—
136C13×C4⋊C8—21no—
137C13×C4⋊C8—21no—
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8D411yescharacteristic
141C13×C22⋊C8D411yescharacteristic
142C13×C22⋊C8D411yescharacteristic
143C13×C22⋊C8D411yescharacteristic
144C13×#97—21no—
145C4×C8×C13—21no—
146#88077—22no—
147#88077—41no—
148C22⋊#1055—21no—
149C22⋊#1055—21no—
150C22⋊#1055C2×C411yescharacteristic
151C22⋊#1055C2×C411yescharacteristic
152C22⋊#1055C2×C411yescharacteristic
153C22⋊#1055C2×C411yescharacteristic
154#88065—22no—
155#88065—22no—
156#88065—22no—
157#88065D414yescomplemented
158#88062—22no—
159#88062—41no—
160#88060—21no—
161#88060—21no—
162#88060—21no—
163#88060—21no—
164#88055—22no—
165#88055—41no—
166#88050C2×C411yescharacteristic, complemented
167#88050C2×C411yescharacteristic, complemented
168#88050C2×C411yescharacteristic, complemented
169#88050C2×C411yescharacteristic, complemented
170#88049C2×C411yescharacteristic, complemented
171#88049C2×C411yescharacteristic, complemented
172#88049C2×C411yescharacteristic, complemented
173#88049C2×C411yescharacteristic, complemented
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×C13C22×C411yescharacteristic
192C22×C4×C13C22×C411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13#4111yescharacteristic
196C22×C4×C13C2411yescharacteristic
197C2×C22⋊D13—21no—
198C2×C22⋊D13—21no—
199C2×C22⋊D13—21no—
200C2×C22⋊D13—21no—
201C2×C22⋊D13—42no—
202C2×C22⋊D13—42no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—42no—
207C22×Dic13—42no—
208C22×Dic13—42no—
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—42no—
245C13×M16—42no—
246C13×M16C2×D412yes—
247C2×C8×C13—21no—
248C2×C8×C13—21no—
249C2×C8×C13—21no—
250C2×C8×C13—21no—
251C2×C8×C13—21no—
252C2×C8×C13—21no—
253C2×C8×C13—42no—
254C2×C8×C13—42no—
255C2×C8×C13C2×D411yescharacteristic
256C2×C8×C13C2×D411yescharacteristic
257C2×C8×C13C2×D411yescharacteristic
258C2×C8×C13C2×D411yescharacteristic
259C13×C4⋊C4—21no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4C22×C411yescharacteristic
262C13×C4⋊C4C22×C411yescharacteristic
263C13×C22⋊C4—21no—
264C13×C22⋊C4—21no—
265C13×C22⋊C4—21no—
266C13×C22⋊C4—21no—
267C13×C22⋊C4—21no—
268C42×C13—21no—
269#6107—22no—
270#6107—41no—
271#6106—22no—
272#6106—41no—
273#6105—22no—
274#6105—41no—
275#6104—22no—
276#6104—41no—
277C4×Dic13—21no—
278C4×Dic13—21no—
279C4×Dic13—21no—
280C4×Dic13—42no—
281C4×Dic13C2×D412yes—
282#6099—21no—
283#6099—21no—
284#6099—21no—
285#6099—21no—
286C2×#1055—21no—
287C2×#1055—21no—
288C2×#1055—21no—
289C2×#1055—21no—
290C2×#1055—21no—
291C2×#1055—21no—
292C2×#1055C22×C411yescharacteristic
293C2×#1055C22×C411yescharacteristic
294C2×#1055C22×C411yescharacteristic
295C2×#1055C22×C411yescharacteristic
296#6094—42no—
297#6094—42no—
298C8×D13—42no—
299C8×D13—42no—
300#3002—131no—
301C2×#444—131no—
302#2933D1311yescharacteristic, complemented
303C22×#104—131no—
304#2880—131no—
305#1975—131no—
306#1938—131no—
307#1929—131no—
308#1896—131no—
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—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13C4×D411yescharacteristic
352C2×C4×C13C4×D411yescharacteristic
353C2×C4×C13C23×C411yescharacteristic
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13C22×D411yescharacteristic
356C2×C4×C13C2×#4111yescharacteristic
357C2×C4×C13H(5,𝔽2)11yescharacteristic
358C2×C4×C13H(5,𝔽2)11yescharacteristic
359C22⋊D13—22no—
360C22⋊D13—22no—
361C22⋊D13—42no—
362C22⋊D13—42no—
363C22⋊D13—41no—
364C22⋊D13—41no—
365C2×Dic13—21no—
366C2×Dic13—22no—
367C2×Dic13—21no—
368C2×Dic13—22no—
369C2×Dic13—42no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—48no—
374C2×Dic13—41no—
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—21no—
392C8×C13—21no—
393C8×C13—22no—
394C8×C13—21no—
395C8×C13—21no—
396C8×C13—41no—
397#1055—21no—
398#1055—21no—
399#1055—21no—
400#1055—21no—
401#1055—41no—
402#1055—41no—
403C22×#41—131no—
404C2×#135—131no—
405C2×#135—131no—
406C2×#131—131no—
407C2×#131—131no—
408C2×#131C2×D1311yescharacteristic, complemented
409C22×M16C2×D1311yescharacteristic
410#525C2×D1311yescharacteristic
411C22×C42—131no—
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—21no—
422#435—21no—
423#435—21no—
424C8×D4—21no—
425C2×#108—131no—
426C2×#108—131no—
427#424C2×D1311yescharacteristic, complemented
428C2×#104—131no—
429C2×#104—131no—
430C2×#104—131no—
431C2×#104—131no—
432C2×#104—131no—
433C2×#104—131no—
434C2×#104—264no—
435#416—131no—
436#416—131no—
437#408—131no—
438#408—131no—
439#408—261no—
440#408—261no—
441#408C2×D1311yescharacteristic, complemented
442#407—131no—
443#407—261no—
444C2×C22⋊C8—131no—
445C2×C22⋊C8—261no—
446C2×C22⋊C8C2×D1311yescharacteristic
447#405C2×D1311yescharacteristic, complemented
448C2×#97—131no—
449C2×#97—131no—
450#341—131no—
451#341—131no—
452#339—131no—
453#339—131no—
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—41no—
482C4×C13—41no—
483C4×C13—41no—
484C4×C13C2×C4×D411yescharacteristic
485C4×C13#51811yescharacteristic
486C4×C13D4211yescharacteristic
487C4×C13#54611yescharacteristic
488Dic13—22no—
489Dic13—42no—
490Dic13—42no—
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—261no—
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—22no—
522#131—41no—
523#131—262no—
524#131—262no—
525#131—521no—
526#131—521no—
527C2×M16—21no—
528C2×M16—21no—
529C2×M16—22no—
530C2×M16—41no—
531C2×M16—131no—
532C2×M16—131no—
533C2×M16—261no—
534C2×M16—261no—
535C2×M16C22×D1311yescharacteristic
536C2×M16C22×D1311yescharacteristic
537C22×C8—21no—
538C22×C8—21no—
539C22×C8—131no—
540C22×C8—131no—
541C22×C8—261no—
542C22×C8—261no—
543C22×C8C22×D1311yescharacteristic
544C22×C8C22×D1311yescharacteristic
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—131no—
555C2×C42—131no—
556C2×C42—262no—
557C2×C42—261no—
558C2×C42—521no—
559#108—262no—
560#108—521no—
561C4⋊C8—21no—
562C4⋊C8—21no—
563#104—134no—
564#104—262no—
565#104—262no—
566#104—262no—
567#104—262no—
568#104—521no—
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—261no—
584C22⋊C8—261no—
585C22⋊C8—261no—
586C22⋊C8—261no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8C22⋊D1311yescharacteristic
590C22⋊C8C22⋊D1311yescharacteristic
591C22⋊C8C22⋊D1311yescharacteristic
592C22⋊C8C22⋊D1311yescharacteristic
593#97—21no—
594#97—262no—
595#97—521no—
596C4×C8—21no—
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#612711yescharacteristic
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—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—522no—
663C22×C4—522no—
664C22×C4—522no—
665C22×C4—522no—
666C22×C4—522no—
667C22×C4C2×C4×D1311yescharacteristic
668C22×C4C2×C4×D1311yescharacteristic
669C22×C4#612711yescharacteristic
670C22×C4C2×C22⋊D1311yescharacteristic
671C22×C4C2×C22⋊D1311yescharacteristic
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—42no—
685M16—42no—
686M16—261no—
687M16—261no—
688M16—261no—
689M16—261no—
690M16—522no—
691M16—522no—
692M16D4×D1312yes—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—131no—
702C2×C8—131no—
703C2×C8—131no—
704C2×C8—131no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—261no—
709C2×C8—261no—
710C2×C8—261no—
711C2×C8—522no—
712C2×C8—522no—
713C2×C8C2×C22⋊D1311yescharacteristic
714C2×C8C2×C22⋊D1311yescharacteristic
715C2×C8C2×C22⋊D1311yescharacteristic
716C2×C8C2×C22⋊D1311yescharacteristic
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—132no—
728C42—261no—
729C42—261no—
730C42—261no—
731C42—522no—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—41no—
738C23—261no—
739C23—261no—
740C23—522no—
741C23—522no—
742C23—1041no—
743C23C4×C22⋊D1311yescharacteristic
744C23C4×C22⋊D1311yescharacteristic
745C23C2×#612711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—132no—
749Q8—261no—
750Q8—261no—
751Q8—261no—
752Q8—522no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—41no—
757D4—42no—
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—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—261no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—261no—
790C2×C4—262no—
791C2×C4—522no—
792C2×C4—522no—
793C2×C4—522no—
794C2×C4—521no—
795C2×C4—521no—
796C2×C4—521no—
797C2×C4—528no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4C4×C22⋊D1311yescharacteristic
802C2×C4C4×C22⋊D1311yescharacteristic
803C2×C4C22×C4×D1311yescharacteristic
804C2×C4C2×D4×D1311yescharacteristic
805C2×C4#8825111yescharacteristic
806C2×C4#41×D1311yescharacteristic
807C2×C4#8825611yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—261no—
816C8—261no—
817C8—261no—
818C8—261no—
819C8—521no—
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#1171880612yescomplemented
841C22#1171925511yescharacteristic
842C22#1171926111yescharacteristic
843C22C2×C4×C22⋊D1311yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—262no—
850C4—522no—
851C4—522no—
852C4—521no—
853C4C4×D4×D1311yescharacteristic
854C4#1171925011yescharacteristic
855C4D4×C22⋊D1311yescharacteristic
856C4#1171953411yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—522no—
863C2—1041no—
864C2#1311781311yescharacteristic
865C2C2×#1171880611yescharacteristic
866C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2933C2
socleC22×C13C2×C4×D4
prime radical#13124052C2
cosocleC22×C4×C13C24
hypercenter#2933D13
hypocenterC13#22886
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#11718806C2semidirect
3. C22×#88065C2semidirect
4. #13123282C2semidirect
5. #13115728C2semidirect
6. #13115546C2semidirect
7. #13115484C2semidirect
8. #13115280C2semidirect
9. #13115166C2semidirect
10. #13115163C2semidirect
11. #13115110C2semidirect
12. #13115041C2semidirect
13. #13114682C2semidirect
14. #13114600C2semidirect
15. C13×#2933C2semidirect
17. C2×C13×#131C22semidirect
29. C13×#424C22semidirect
30. C13×#408C22semidirect
32. C13×#405C22semidirect
33. C2×#88077C22semidirect
34. C2×#88077C22semidirect
43. C2×#88062C22semidirect
44. C2×#88062C22semidirect
47. C2×#88055C22semidirect
48. C2×#88055C22semidirect
49. #11718711C4semidirect
50. #11718708C4semidirect
51. #11718708C4semidirect
52. #11718707C4semidirect
53. #11718701C4semidirect
54. #11718698C4semidirect
55. #11718698C4semidirect
56. #11718697C4semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718142C22semidirect
66. #11718142C22semidirect
67. #11718124C22semidirect
68. #11718124C22semidirect
111. C2×#6107C2×C4semidirect
112. C2×#6107C2×C4semidirect
113. C2×#6106C2×C4semidirect
114. C2×#6106C2×C4semidirect
115. C2×#6105C2×C4semidirect
116. C2×#6105C2×C4semidirect
117. C2×#6104C2×C4semidirect
118. C2×#6104C2×C4semidirect
157. #88065D4semidirect
166. #88050C2×C4semidirect
167. #88050C2×C4semidirect
168. #88050C2×C4semidirect
169. #88050C2×C4semidirect
170. #88049C2×C4semidirect
171. #88049C2×C4semidirect
172. #88049C2×C4semidirect
173. #88049C2×C4semidirect
302. #2933D13semidirect
408. C2×#131C2×D13semidirect
427. #424C2×D13semidirect
441. #408C2×D13semidirect
447. #405C2×D13semidirect
468. C22×C13#444semidirect
732. C13#22886semidirect
840. C22#11718806semidirect

Maximal subgroups

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

subgroupindex
#131240522
C2×#117188062
C22×#880652
#131232822
#131157282
#131155462
#131154842
#131152802
#131151662
#131151632
#131151102
#131150412
#131146822
#131146002
C13×#29332
#2288613