Finite Group Databasebeta

← #15883652

Subgroups — #15883652

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#13124054C211yesmaximal, characteristic
2C2×#11718806C211yesmaximal, characteristic, complemented
3#13123557C211yesmaximal, characteristic, complemented
4C22×#88077C211yesmaximal, characteristic, complemented
5#13115728C211yesmaximal, characteristic, complemented
6#13115550C211yesmaximal, characteristic, complemented
7#13115481C211yesmaximal, characteristic, complemented
8#13115277C211yesmaximal, characteristic, complemented
9#13115166C211yesmaximal, characteristic, complemented
10#13115163C211yesmaximal, characteristic, complemented
11#13115111C211yesmaximal, characteristic, complemented
12#13115040C211yesmaximal, characteristic, complemented
13#13114678C211yesmaximal, characteristic, complemented
14#13114600C211yesmaximal, characteristic, complemented
15C13×#2880C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C2×C13×#131C2211yescharacteristic
18C2×C13×#131C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20C2×#88204C2211yescharacteristic
21#11719496C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
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
37C2×#88077—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×#88055C2211yescharacteristic, 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
84C23×Dic13—21no—
85C2×#6127C2311yescharacteristic
86C13×#131—22no—
87C13×#131—22no—
88C13×#131—41no—
89C13×#131—41no—
90C2×C13×M16—21no—
91C2×C13×M16—21no—
92C2×C13×M16C2311yescharacteristic
93C2×C13×M16C2311yescharacteristic
94C22×C8×C13—21no—
95C22×C8×C13—21no—
96C22×C8×C13C2311yescharacteristic
97C22×C8×C13C2311yescharacteristic
98#88207—21no—
99#88204—22no—
100#88204—22no—
101#88204—41no—
102#88204—41no—
103C2×#6107C2×C411yescharacteristic, complemented
104C2×#6107C2×C411yescharacteristic, complemented
105C2×#6106C2×C411yescharacteristic, complemented
106C2×#6106C2×C411yescharacteristic, complemented
107C2×#6105C2×C411yescharacteristic, complemented
108C2×#6105C2×C411yescharacteristic, complemented
109C2×#6104C2×C411yescharacteristic, complemented
110C2×#6104C2×C411yescharacteristic, complemented
111#88184C2×C411yescharacteristic
112#88184C2×C411yescharacteristic
113#88183—21no—
114C4×C22⋊D13—21no—
115C4×C22⋊D13—21no—
116#88180C2311yescharacteristic
117#88178C2×C411yescharacteristic
118#88178C2×C411yescharacteristic
119C2×C4×Dic13—22no—
120C2×C4×Dic13—21no—
121C2×C4×Dic13—41no—
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, complemented
151#88075C2×C411yescharacteristic, complemented
152#88075C2×C411yescharacteristic, complemented
153#88075C2×C411yescharacteristic, complemented
154#88072C2×C411yescharacteristic, complemented
155#88072C2×C411yescharacteristic, complemented
156#88072C2×C411yescharacteristic, complemented
157#88072C2×C411yescharacteristic, complemented
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#88055—41no—
171#88054—21no—
172#88054—21no—
173C8×Dic13—21no—
174#22886—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—
231C22×Dic13—42no—
232C22×Dic13—42no—
233C22×Dic13—42no—
234#6127—21no—
235#6127—21no—
236#6127—21no—
237#6127—21no—
238C2×D52C22×C411yescharacteristic
239C2×C4×D13—21no—
240C2×Dic26C22×C411yescharacteristic
241C13×M16—21no—
242C13×M16—21no—
243C13×M16—21no—
244C13×M16—21no—
245C13×M16—42no—
246C13×M16—42no—
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
259C22⋊Dic13—21no—
260C22⋊Dic13—21no—
261C22⋊Dic13—21no—
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#6103—21no—
271#6103—21no—
272C4⋊Dic13C22×C411yescharacteristic
273C4⋊Dic13C22×C411yescharacteristic
274#6101—21no—
275#6101—21no—
276C4×Dic13—21no—
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—42no—
286#6099C2×D412yes—
287C2×#1055—21no—
288C2×#1055—21no—
289C2×#1055—21no—
290C2×#1055—21no—
291C2×#1055—21no—
292C2×#1055—21no—
293C2×#1055—42no—
294C2×#1055C22×C411yescharacteristic
295C2×#1055C22×C411yescharacteristic
296C2×#1055C22×C411yescharacteristic
297C2×#1055C22×C411yescharacteristic
298#6094—42no—
299C8×D13—42no—
300#3002—131no—
301C2×#444—131no—
302#2933—131no—
303C22×#104—131no—
304#2880D1311yescharacteristic, complemented
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—21no—
318C23×C13—22no—
319C23×C13—21no—
320C23×C13—41no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13—81no—
324C23×C13C4×D411yescharacteristic
325C23×C13C4×D411yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C22×D13—21no—
328Q8×C13—21no—
329Q8×C13—21no—
330Q8×C13—21no—
331Q8×C13—42no—
332Q8×C13C4×D412yes—
333D4×C13—22no—
334D4×C13—22no—
335D4×C13—21no—
336D4×C13—21no—
337D4×C13—21no—
338D4×C13—42no—
339D4×C13—42no—
340D4×C13—42no—
341D4×C13—41no—
342D4×C13—41no—
343D4×C13C4×D412yes—
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—21no—
352C2×C4×C13—21no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—21no—
356C2×C4×C13—21no—
357C2×C4×C13—21no—
358C2×C4×C13—42no—
359C2×C4×C13—42no—
360C2×C4×C13—42no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13C4×D411yescharacteristic
364C2×C4×C13C4×D411yescharacteristic
365C2×C4×C13C23×C411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C2×#4111yescharacteristic
369C2×C4×C13H(5,𝔽2)11yescharacteristic
370C2×C4×C13H(5,𝔽2)11yescharacteristic
371C22⋊D13—41no—
372C22⋊D13—41no—
373C22⋊D13—42no—
374C22⋊D13—81no—
375C2×Dic13—22no—
376C2×Dic13—21no—
377C2×Dic13—21no—
378C2×Dic13—21no—
379C2×Dic13—22no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—48no—
384C2×Dic13—41no—
385D52—21no—
386D52—21no—
387C4×D13—41no—
388C4×D13—41no—
389Dic26—21no—
390Dic26—21no—
391C8×C13—21no—
392C8×C13—21no—
393C8×C13—21no—
394C8×C13—21no—
395C8×C13—41no—
396C8×C13—41no—
397#1055—21no—
398#1055—21no—
399#1055—21no—
400#1055—21no—
401#1055—22no—
402#1055—41no—
403C22×#41C2×D1311yescharacteristic
404C2×#135—131no—
405C2×#135—131no—
406C2×#131—131no—
407C2×#131C2×D1311yescharacteristic
408C2×#131C2×D1311yescharacteristic
409C22×M16—131no—
410#525—131no—
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—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—131no—
433C2×#104—131no—
434C2×#104—264no—
435#416—131no—
436#416—131no—
437#408—21no—
438#408—21no—
439#408—131no—
440#408C2×D1311yescharacteristic
441#408C2×D1311yescharacteristic
442#407—21no—
443#407C2×D1311yescharacteristic
444C2×C22⋊C8—21no—
445C2×C22⋊C8—131no—
446C2×C22⋊C8C2×D1311yescharacteristic
447#405—131no—
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—22no—
462C22×C13—21no—
463C22×C13—21no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—41no—
467C22×C13—41no—
468C22×C13—41no—
469C22×C13—41no—
470C22×C13—41no—
471C22×C13—84no—
472C22×C13#44412yescomplemented
473C22×C13C2×C4×D411yescharacteristic
474C22×C13#54611yescharacteristic
475C22×C13#55111yescharacteristic
476C2×D13—41no—
477C2×D13—41no—
478C2×D13—41no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—22no—
482C4×C13—41no—
483C4×C13C2×C4×D411yescharacteristic
484C4×C13#51811yescharacteristic
485C4×C13D4211yescharacteristic
486C4×C13#54611yescharacteristic
487Dic13—42no—
488Dic13—42no—
489Dic13—41no—
490Dic13—41no—
491Dic13—41no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—131no—
499C2×#41C4×D1311yescharacteristic
500C2×#41C4×D1311yescharacteristic
501C2×#41C22×D1311yescharacteristic
502C2×#41C22×D1311yescharacteristic
503C22×Q8C4×D1311yescharacteristic
504C22×D4—21no—
505C22×D4C4×D1311yescharacteristic
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—22no—
522#131—22no—
523#131—41no—
524#131—41no—
525#131—262no—
526#131—521no—
527C2×M16—21no—
528C2×M16—21no—
529C2×M16—131no—
530C2×M16—131no—
531C2×M16—261no—
532C2×M16—261no—
533C2×M16—262no—
534C2×M16—521no—
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—261no—
546C22⋊Q8—131no—
547C22⋊Q8—131no—
548#121—131no—
549#121—131no—
550#120—261no—
551C4×D4—261no—
552C4×D4—261no—
553#117—131no—
554C2×C42—131no—
555C2×C42—131no—
556C2×C42—262no—
557C2×C42—261no—
558C2×C42—521no—
559#108—262no—
560#108—521no—
561C4⋊C8—261no—
562C4⋊C8—261no—
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—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8—131no—
584C22⋊C8—131no—
585C22⋊C8—131no—
586C22⋊C8—131no—
587C22⋊C8—261no—
588C22⋊C8—261no—
589C22⋊C8C22⋊D1311yescharacteristic
590C22⋊C8C22⋊D1311yescharacteristic
591C22⋊C8C22⋊D1311yescharacteristic
592C22⋊C8C22⋊D1311yescharacteristic
593#97—262no—
594#97—261no—
595#97—521no—
596C4×C8—261no—
597C2×C13—21no—
598C2×C13—22no—
599C2×C13—21no—
600C2×C13—41no—
601C2×C13—42no—
602C2×C13—81no—
603C2×C13#235811yescharacteristic
604C2×C13C2×#44411yescharacteristic
605C2×C13#295611yescharacteristic
606D13—81no—
607C24—21no—
608C24#612711yescharacteristic
609#41—21no—
610#41—21no—
611#41—22no—
612#41—22no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—42no—
618#41—42no—
619#41—41no—
620#41—41no—
621#41—42no—
622#41—42no—
623#41—261no—
624#41—261no—
625#41—261no—
626#41—261no—
627#41D4×D1312yes—
628#41#612912yes—
629C2×Q8—21no—
630C2×Q8—22no—
631C2×Q8—41no—
632C2×Q8—131no—
633C2×Q8C2×C4×D1311yescharacteristic
634C2×Q8C2×C4×D1311yescharacteristic
635C2×D4—21no—
636C2×D4—22no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—131no—
645C2×D4—261no—
646C2×D4—261no—
647C2×D4—261no—
648C2×D4C2×C4×D1311yescharacteristic
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—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
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—21no—
685M16—42no—
686M16—42no—
687M16—132no—
688M16—261no—
689M16—261no—
690M16—261no—
691M16—522no—
692M16—522no—
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—131no—
718C4⋊C4—131no—
719C4⋊C4—261no—
720C4⋊C4—261no—
721C22⋊C4—261no—
722C22⋊C4—261no—
723C22⋊C4—261no—
724C22⋊C4—261no—
725C22⋊C4—261no—
726C42—132no—
727C42—261no—
728C42—261no—
729C42—261no—
730C42—261no—
731C42—522no—
732C13#2288611yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—261no—
743C23C4×C22⋊D1311yescharacteristic
744C23C4×C22⋊D1311yescharacteristic
745C23C2×#612711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—261no—
751Q8—261no—
752Q8#8813512yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—261no—
764D4—261no—
765D4—521no—
766D4—521no—
767D4—522no—
768D4—1041no—
769D4#8813512yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—261no—
792C2×C4—261no—
793C2×C4—261no—
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×C4C2×#612911yescharacteristic
806C2×C4#8825111yescharacteristic
807C2×C4#8825111yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—261no—
816C8—261no—
817C8—261no—
818C8—261no—
819C8—262no—
820C8—521no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—521no—
838C22—521no—
839C22—521no—
840C22#1171880612yescomplemented
841C22#1171919511yescharacteristic
842C22#1171920011yescharacteristic
843C22C2×C4×C22⋊D1311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—522no—
849C4—522no—
850C4—521no—
851C4—521no—
852C4—521no—
853C4C2×#8813511yescharacteristic
854C4#1171919111yescharacteristic
855C4D4×C22⋊D1311yescharacteristic
856C4#1171951111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—1041no—
864C2#1311781511yescharacteristic
865C2C2×#1171880611yescharacteristic
866C2#1312374311yescharacteristic
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#22886
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. C22×#88077C2semidirect
5. #13115728C2semidirect
6. #13115550C2semidirect
7. #13115481C2semidirect
8. #13115277C2semidirect
9. #13115166C2semidirect
10. #13115163C2semidirect
11. #13115111C2semidirect
12. #13115040C2semidirect
13. #13114678C2semidirect
14. #13114600C2semidirect
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×#88055C22semidirect
63. #11718150C22semidirect
64. #11718150C22semidirect
65. #11718147C22semidirect
66. #11718147C22semidirect
67. #11718142C22semidirect
68. #11718142C22semidirect
103. C2×#6107C2×C4semidirect
104. C2×#6107C2×C4semidirect
105. C2×#6106C2×C4semidirect
106. C2×#6106C2×C4semidirect
107. C2×#6105C2×C4semidirect
108. C2×#6105C2×C4semidirect
109. C2×#6104C2×C4semidirect
110. C2×#6104C2×C4semidirect
149. #88077D4semidirect
150. #88075C2×C4semidirect
151. #88075C2×C4semidirect
152. #88075C2×C4semidirect
153. #88075C2×C4semidirect
154. #88072C2×C4semidirect
155. #88072C2×C4semidirect
156. #88072C2×C4semidirect
157. #88072C2×C4semidirect
304. #2880D13semidirect
472. 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
#131240542
C2×#117188062
#131235572
C22×#880772
#131157282
#131155502
#131154812
#131152772
#131151662
#131151632
#131151112
#131150402
#131146782
#131146002
C13×#28802
#2288613