Finite Group Databasebeta

← #16740778

Subgroups — #16740778

Order 3328.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128553C211yesmaximal, characteristic, complemented
2#13127104C212yesmaximal, complemented
3#13127078C212yesmaximal, complemented
4#13127022C212yesmaximal, complemented
5#13126872C212yesmaximal, complemented
6#13126857C212yesmaximal, complemented
7#13126842C212yesmaximal, complemented
8#13126775C212yesmaximal, complemented
9#13126686C212yesmaximal, complemented
10#13125190C211yesmaximal, characteristic, complemented
11#13124810C211yesmaximal, characteristic, complemented
12C2×#11718696C211yesmaximal, characteristic, complemented
13#13124698C211yesmaximal, characteristic, complemented
14#13124495C211yesmaximal, characteristic, complemented
15#13124451C211yesmaximal, characteristic, complemented
16#13124371C211yesmaximal, characteristic, complemented
17#13124140C211yesmaximal, characteristic, complemented
18#13124054C211yesmaximal, characteristic, complemented
19#13123709C211yesmaximal, characteristic, complemented
20#13123563C211yesmaximal, characteristic, complemented
21#13123362C211yesmaximal, characteristic, complemented
22#13123355C211yesmaximal, characteristic, complemented
23C13×#3488C211yesmaximal, characteristic, complemented
24C2×C13×H(5,𝔽2)C2211yescharacteristic
25C22×C13×#41C2211yescharacteristic
26C13×#550C2212yes—
27C13×#548C2212yes—
28C13×#546—22no—
29C13×#546C2212yes—
30D42×C13—22no—
31D42×C13C2212yes—
32C13×#537—21no—
33C13×#537C2211yescharacteristic
34C13×#535—21no—
35C13×#535C2211yescharacteristic
36C13×#525—21no—
37C13×#525C2211yescharacteristic
38C2×C13×#121—21no—
39C2×C13×#121C2211yescharacteristic
40C13×#520C2211yescharacteristic
41#11719538C2211yescharacteristic, complemented
42#11719532C2211yescharacteristic, complemented
43C2×#88204C2211yescharacteristic
44C2×#88204C2211yescharacteristic, complemented
45C2×#88202C2211yescharacteristic, complemented
46C2×#88186C2211yescharacteristic, complemented
47#11719496C2211yescharacteristic, complemented
48C2×#88180C2211yescharacteristic, complemented
49C22×#6099C2211yescharacteristic, complemented
50#11719354—22no—
51#11719346—21no—
52#11719344—21no—
53#11719321—21no—
54#11719319—21no—
55#11719298—22no—
56#11719270C2212yescomplemented
57#11719268C2212yescomplemented
58#11719247C2212yescomplemented
59#11719246C2212yescomplemented
60#11719228C2211yescharacteristic, complemented
61#11719224C2211yescharacteristic, complemented
62#11718900C2212yescomplemented
63#11718900C2211yescharacteristic, complemented
64#11718900C2211yescharacteristic, complemented
65#11718899C2211yescharacteristic, complemented
66#11718899C2212yescomplemented
67#11718899C2211yescharacteristic, complemented
68#11718895C2211yescharacteristic, complemented
69#11718894C2211yescharacteristic
70#11718894C2212yescomplemented
71#11718894C2212yescomplemented
72#11718894C2212yescomplemented
73#11718894C2211yescharacteristic, complemented
74#11718893C2211yescharacteristic
75#11718893C2211yescharacteristic
76#11718893C2211yescharacteristic, complemented
77#11718893C2211yescharacteristic, complemented
78#11718893C2212yescomplemented
79#11718889C2211yescharacteristic, complemented
80#11718888C2211yescharacteristic, complemented
81#11718886C2212yescomplemented
82#11718879C2212yescomplemented
83#11718879C2211yescharacteristic, complemented
84#11718878C2212yescomplemented
85#11718878C2211yescharacteristic, complemented
86#11718876C2212yescomplemented
87#11718876C2211yescharacteristic, complemented
88#11718876C2212yescomplemented
89C2×#88072C2211yescharacteristic, complemented
90C2×#88072C2212yescomplemented
91C2×#88072C2211yescharacteristic, complemented
92C2×C22⋊#1055C2211yescharacteristic, complemented
93#11718736C2212yescomplemented
94#11718733C2212yescomplemented
95#11718732C2212yescomplemented
96#11718731C2212yescomplemented
97#11718718C2212yescomplemented
98#11718717C2212yescomplemented
99#11718716C2212yescomplemented
100#11718715C2212yescomplemented
101#11718713C2212yescomplemented
102#11718709C2212yescomplemented
103#11718706C2212yescomplemented
104#11718705C2212yescomplemented
105#11718703C2212yescomplemented
106#11718702C2212yescomplemented
107#11718702C2212yescomplemented
108#11718700C2212yescomplemented
109#11718700C2212yescomplemented
110#11718699C2212yescomplemented
111#11718696C2212yescomplemented
112#11718696C2212yescomplemented
113#11718696C2212yescomplemented
114#11718696C2212yescomplemented
115#11718696C2212yescomplemented
116#11718694C2212yescomplemented
117C4×#6107C2212yescomplemented
118#11718687C2212yescomplemented
119#11718683C2212yescomplemented
120#11718681C2212yescomplemented
121#11718679C2212yescomplemented
122C4×#6104C2212yescomplemented
123#11718673C2212yescomplemented
124#11718672C2212yescomplemented
125#11718672C2212yescomplemented
126D4×#1055C2212yescomplemented
127#11718670C2212yescomplemented
128#11718669C2212yescomplemented
129#11718660C2211yescharacteristic, complemented
130#11718658C2211yescharacteristic, complemented
131#11718627C2211yescharacteristic, complemented
132#11718625C2211yescharacteristic, complemented
133C2×#88048C2211yescharacteristic, complemented
134C2×#88047C2211yescharacteristic, complemented
135C13×H(5,𝔽2)—24no—
136C13×H(5,𝔽2)—42no—
137C2×C13×#41—21no—
138C2×C13×#41—21no—
139C2×C13×#41—21no—
140C2×C13×#41—24no—
141C2×C13×#41—42no—
142C2×C13×#41C2311yescharacteristic
143C2×C13×#41C2311yescharacteristic
144C2×C13×#41C2312yes—
145C2×C13×#41C2311yescharacteristic
146C2×C13×#41C2311yescharacteristic
147C2×C13×#41C2311yescharacteristic
148C22×Q8×C13C2311yescharacteristic
149C22×D4×C13—21no—
150C22×D4×C13—21no—
151C22×D4×C13—21no—
152C22×D4×C13—22no—
153C22×D4×C13—22no—
154C22×D4×C13C2311yescharacteristic
155C22×D4×C13C2311yescharacteristic
156C22×D4×C13C2312yes—
157C23×C4×C13—21no—
158C23×C4×C13C2311yescharacteristic
159C2×#6127C2311yescharacteristic
160C13×#127—22no—
161C13×#127C2312yes—
162C13×#124—22no—
163C13×#124C2312yes—
164C13×#123—22no—
165C13×#123D412yes—
166C13×C22⋊Q8—21no—
167C13×C22⋊Q8—22no—
168C13×C22⋊Q8D411yescharacteristic
169C13×C22⋊Q8D411yescharacteristic
170C13×C22⋊Q8C2312yes—
171C13×#121—21no—
172C13×#121—22no—
173C13×#121—22no—
174C13×#121—21no—
175C13×#121—21no—
176C13×#121—21no—
177C13×#121—21no—
178C13×#121—22no—
179C13×#121—22no—
180C13×#121—22no—
181C13×#121—22no—
182C13×#121D411yescharacteristic
183C13×#121D411yescharacteristic
184C13×#121C2312yes—
185C13×#121C2312yes—
186C13×#121C2312yes—
187C13×#120—22no—
188C13×#120—22no—
189C13×#120—22no—
190C13×#120—22no—
191C13×#120D412yes—
192C4×Q8×C13C2312yes—
193C4×D4×C13—22no—
194C4×D4×C13—22no—
195C4×D4×C13—22no—
196C4×D4×C13C2312yes—
197C4×D4×C13C2312yes—
198C4×D4×C13C2312yes—
199C13×#117—21no—
200C13×#117C2311yescharacteristic
201C2×C13×C4⋊C4—21no—
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C13×C22⋊C4—21no—
204C2×C13×C22⋊C4—22no—
205#88207—21no—
206C2×C22⋊Dic13—21no—
207#88204—24no—
208#88204—42no—
209#88202—42no—
210#88200—21no—
211Q8×Dic13—21no—
212C2×#6107C2311yescharacteristic
213C2×#6107C2311yescharacteristic
214C2×#6106C2311yescharacteristic
215C2×#6106C2311yescharacteristic
216#88193—22no—
217#88193—22no—
218#88192—22no—
219#88192—21no—
220#88190—22no—
221#88189—22no—
222D4×Dic13—22no—
223D4×Dic13—21no—
224C2×#6105C2311yescharacteristic
225C2×#6105C2311yescharacteristic
226C2×#6105C2312yes—
227#88186—42no—
228C2×#6104C2311yescharacteristic
229C2×#6104C2312yes—
230C2×#6104C2311yescharacteristic
231#88184C2311yescharacteristic
232#88184C2311yescharacteristic
233#88184C2312yes—
234#88183—21no—
235C4×C22⋊D13—21no—
236C4×C22⋊D13—21no—
237#88180—21no—
238#88180—21no—
239#88180C2312yes—
240#88180C2312yes—
241#88180C2312yes—
242#88180C2311yescharacteristic
243C2×C4⋊Dic13C2312yes—
244C2×C4⋊Dic13C2311yescharacteristic
245C2×C4⋊Dic13C2311yescharacteristic
246#88178C2311yescharacteristic
247#88178C2312yes—
248#88178C2311yescharacteristic
249C2×C4×Dic13—21no—
250C2×#6099—42no—
251C2×#6099C2311yescharacteristic
252C2×#6099C2311yescharacteristic
253C2×#6099C2312yes—
254C2×#6099C2312yes—
255C22×#1055C2311yescharacteristic
256C22×#1055C2311yescharacteristic
257C22×#1055C2312yes—
258C22×#1055C2312yes—
259#88152—22no—
260#88146—21no—
261#88146—22no—
262C4⋊C4×D13—21no—
263#88144—21no—
264#88143—22no—
265#88142—21no—
266#88141—22no—
267#88139—22no—
268#88139—22no—
269#88137—22no—
270#88135—22no—
271#88135—22no—
272#88133—22no—
273#88133—22no—
274#88133—22no—
275#88132—22no—
276#88131—22no—
277C4×D52C2312yes—
278#88124C2312yes—
279#88123C2312yes—
280C4×Dic26C2312yes—
281#88075C2311yescharacteristic
282#88075C2312yes—
283#88075C2311yescharacteristic
284#88075C2312yes—
285#88075C2311yescharacteristic
286#88075C2312yes—
287#88075C2311yescharacteristic
288#88075C2312yes—
289#88072C2311yescharacteristic
290#88072C2312yes—
291#88072C2311yescharacteristic
292#88072C2312yes—
293#88072C2311yescharacteristic
294#88072C2312yes—
295#88072C2312yes—
296#88072C2312yes—
297#88072C2312yes—
298#88072C2312yes—
299#88072C2311yescharacteristic
300#88072C2312yes—
301#88072C2312yes—
302#88072C2312yes—
303C22⋊#1055C2311yescharacteristic
304C22⋊#1055C2312yes—
305C22⋊#1055C2312yes—
306C22⋊#1055C2311yescharacteristic
307C22⋊#1055C2311yescharacteristic
308C22⋊#1055C2311yescharacteristic
309#88050C2312yes—
310#88049C2312yes—
311#88048C2312yes—
312#88048C2312yes—
313#88048C2312yes—
314#88047C2312yes—
315#88047C2312yes—
316#88047C2312yes—
317C4⋊#1055C2312yes—
318C4⋊#1055C2312yes—
319#88043C2312yes—
320C4×#1055C2312yes—
321#61195—131nomaximal, Sylow
322C24×C13—21no—
323C24×C13—22no—
324C24×C13—21no—
325C24×C13C2×D411yescharacteristic
326C13×#41—22no—
327C13×#41—22no—
328C13×#41—22no—
329C13×#41—22no—
330C13×#41—24no—
331C13×#41—22no—
332C13×#41—22no—
333C13×#41—22no—
334C13×#41—44no—
335C13×#41—41no—
336C13×#41—41no—
337C13×#41—42no—
338C13×#41—44no—
339C13×#41—44no—
340C13×#41#4114yes—
341C2×Q8×C13—21no—
342C2×Q8×C13—22no—
343C2×Q8×C13—41no—
344C2×Q8×C13C2×D411yescharacteristic
345C2×Q8×C13C2411yescharacteristic
346C2×Q8×C13C2411yescharacteristic
347C2×D4×C13—21no—
348C2×D4×C13—22no—
349C2×D4×C13—24no—
350C2×D4×C13—22no—
351C2×D4×C13—21no—
352C2×D4×C13—21no—
353C2×D4×C13—22no—
354C2×D4×C13—21no—
355C2×D4×C13—22no—
356C2×D4×C13—22no—
357C2×D4×C13—21no—
358C2×D4×C13—22no—
359C2×D4×C13—21no—
360C2×D4×C13—22no—
361C2×D4×C13—22no—
362C2×D4×C13—22no—
363C2×D4×C13—22no—
364C2×D4×C13—41no—
365C2×D4×C13—42no—
366C2×D4×C13—44no—
367C2×D4×C13—48no—
368C2×D4×C13—44no—
369C2×D4×C13—84no—
370C2×D4×C13—82no—
371C2×D4×C13C2×D411yescharacteristic
372C2×D4×C13C2×D412yes—
373C2×D4×C13C2×D412yes—
374C2×D4×C13C2×D412yes—
375C2×D4×C13C2412yes—
376C2×D4×C13C2411yescharacteristic
377C2×D4×C13C2411yescharacteristic
378C22×C4×C13—21no—
379C22×C4×C13—22no—
380C22×C4×C13—22no—
381C22×C4×C13—21no—
382C22×C4×C13—21no—
383C22×C4×C13—21no—
384C22×C4×C13—21no—
385C22×C4×C13—22no—
386C22×C4×C13—21no—
387C22×C4×C13—22no—
388C22×C4×C13—44no—
389C22×C4×C13C2×D411yescharacteristic
390C22×C4×C13C2×D411yescharacteristic
391C22×C4×C13C2×D411yescharacteristic
392C22×C4×C13C2411yescharacteristic
393C22×C4×C13C2412yes—
394C22×C4×C13C2411yescharacteristic
395C22×C4×C13C2411yescharacteristic
396C2×C22⋊D13—21no—
397C2×C22⋊D13—22no—
398C2×C22⋊D13—21no—
399C2×C22⋊D13—21no—
400C22×Dic13—22no—
401C22×Dic13—21no—
402C22×Dic13—21no—
403#6127—22no—
404#6127—22no—
405C2×D52C2411yescharacteristic
406C2×C4×D13—21no—
407C2×C4×D13—22no—
408C2×Dic26—22no—
409C2×Dic26C2411yescharacteristic
410C13×C4⋊C4—21no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4—22no—
413C13×C4⋊C4C2×D412yes—
414C13×C4⋊C4C2×D411yescharacteristic
415C13×C4⋊C4C2×D412yes—
416C13×C4⋊C4C2×D411yescharacteristic
417C13×C4⋊C4C2412yes—
418C13×C22⋊C4—22no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4C2×D412yes—
426C13×C22⋊C4C2×D412yes—
427C13×C22⋊C4C2×D412yes—
428C13×C22⋊C4C2×D412yes—
429C13×C22⋊C4C2×D412yes—
430C42×C13—22no—
431C42×C13C2412yes—
432C22⋊Dic13—22no—
433C22⋊Dic13—21no—
434C22⋊Dic13—21no—
435C22⋊Dic13—21no—
436C22⋊Dic13—22no—
437C22⋊Dic13—22no—
438C22⋊Dic13—22no—
439#6107—22no—
440#6107—41no—
441#6106—22no—
442#6106—41no—
443#6105—22no—
444#6105—42no—
445#6105—41no—
446#6104—22no—
447#6104—42no—
448#6104—41no—
449#6103—22no—
450#6103—21no—
451#6103—22no—
452#6103—21no—
453C4⋊Dic13—22no—
454C4⋊Dic13—22no—
455C4⋊Dic13—21no—
456C4⋊Dic13—21no—
457C4⋊Dic13C2412yes—
458C4⋊Dic13C2411yescharacteristic
459C4⋊Dic13C2412yes—
460C4⋊Dic13C2411yescharacteristic
461#6101—22no—
462#6101—22no—
463#6101—22no—
464#6101—21no—
465#6101—21no—
466#6101—22no—
467C4×Dic13—22no—
468C4×Dic13—22no—
469C4×Dic13—22no—
470C4×Dic13—22no—
471C4×Dic13—21no—
472#6099—22no—
473#6099—22no—
474#6099—42no—
475#6099—42no—
476C2×#1055—22no—
477C2×#1055—22no—
478C2×#1055—42no—
479C2×#1055—42no—
480C2×#1055C2411yescharacteristic
481C2×#1055C2411yescharacteristic
482C2×#1055C2411yescharacteristic
483C2×#1055C2411yescharacteristic
484C2×#1055C2412yes—
485C2×#1055C2412yes—
486#3493—131no—
487#3488D1311yescharacteristic, complemented
488#3327—132no—
489#3325—132no—
490#3321—132no—
491#3311—132no—
492#3310—132no—
493#3309—132no—
494#3304—132no—
495#3297—132no—
496#3136—131no—
497#3098—131no—
498C2×#482—131no—
499#3084—131no—
500#3060—131no—
501#3055—131no—
502#3045—131no—
503#3012—131no—
504#3002—131no—
505#2951—131no—
506#2933—131no—
507#2897—131no—
508#2896—131no—
509C23×C13—21no—
510C23×C13—22no—
511C23×C13—22no—
512C23×C13—21no—
513C23×C13—41no—
514C23×C13—41no—
515C23×C13—42no—
516C23×C13—44no—
517C23×C13—42no—
518C23×C13—42no—
519C23×C13—81no—
520C23×C13—81no—
521C23×C13—82no—
522C23×C13—81no—
523C23×C13—82no—
524C23×C13C22×D411yescharacteristic
525C23×C13C22×D411yescharacteristic
526C23×C13C22×D412yes—
527C23×C13C22×D411yescharacteristic
528C22×D13—21no—
529Q8×C13—22no—
530Q8×C13—21no—
531Q8×C13—21no—
532Q8×C13—21no—
533Q8×C13—42no—
534Q8×C13C2×#4112yes—
535D4×C13—24no—
536D4×C13—24no—
537D4×C13—22no—
538D4×C13—22no—
539D4×C13—21no—
540D4×C13—21no—
541D4×C13—22no—
542D4×C13—21no—
543D4×C13—42no—
544D4×C13—42no—
545D4×C13—44no—
546D4×C13—42no—
547D4×C13—44no—
548D4×C13—42no—
549D4×C13—42no—
550D4×C13—44no—
551D4×C13—42no—
552D4×C13—42no—
553D4×C13—82no—
554D4×C13—82no—
555D4×C13—82no—
556D4×C13—82no—
557D4×C13C2×#4112yes—
558C2×C4×C13—22no—
559C2×C4×C13—21no—
560C2×C4×C13—22no—
561C2×C4×C13—22no—
562C2×C4×C13—24no—
563C2×C4×C13—21no—
564C2×C4×C13—21no—
565C2×C4×C13—22no—
566C2×C4×C13—21no—
567C2×C4×C13—22no—
568C2×C4×C13—21no—
569C2×C4×C13—22no—
570C2×C4×C13—21no—
571C2×C4×C13—42no—
572C2×C4×C13—44no—
573C2×C4×C13—42no—
574C2×C4×C13—42no—
575C2×C4×C13—42no—
576C2×C4×C13—82no—
577C2×C4×C13—81no—
578C2×C4×C13C22×D411yescharacteristic
579C2×C4×C13C22×D411yescharacteristic
580C2×C4×C13C22×D412yes—
581C2×C4×C13C22×D412yes—
582C2×C4×C13C22×D412yes—
583C2×C4×C13C22×D411yescharacteristic
584C2×C4×C13C2×#4112yes—
585C2×C4×C13H(5,𝔽2)12yes—
586C2×C4×C13C2511yescharacteristic
587C22⋊D13—42no—
588C22⋊D13—81no—
589C22⋊D13—82no—
590C22⋊D13—81no—
591C2×Dic13—22no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—22no—
595C2×Dic13—21no—
596C2×Dic13—81no—
597C2×Dic13—81no—
598C2×Dic13—82no—
599D52—21no—
600D52—21no—
601C4×D13—42no—
602C4×D13—82no—
603Dic26—21no—
604Dic26—21no—
605Dic26—82no—
606#1055—21no—
607#1055—21no—
608#1055—21no—
609#1055—21no—
610#1055—22no—
611#1055—22no—
612C2×H(5,𝔽2)C2×D1311yescharacteristic
613C22×#41C2×D1311yescharacteristic
614C2×AGL(1,ℤ/8)—131no—
615C2×#135—131no—
616C2×#135—131no—
617C2×#131—131no—
618C22×M16—131no—
619#556—132no—
620#556—261no—
621#555—132no—
622#555—261no—
623#553—132no—
624#553—261no—
625#552—132no—
626#552—261no—
627#550C2×D1312yes—
628#548C2×D1312yes—
629#546—22no—
630#546C2×D1312yes—
631D42—22no—
632D42C2×D1312yes—
633#544—131no—
634#538—262no—
635#537—21no—
636#537—131no—
637#537C2×D1311yescharacteristic
638#535—21no—
639#535C2×D1311yescharacteristic
640#529—262no—
641#525—21no—
642#525—131no—
643#525C2×D1311yescharacteristic
644C2×#121—21no—
645C2×#121C2×D1311yescharacteristic
646#520—131no—
647#520—131no—
648#520C2×D1311yescharacteristic
649C2×#117—131no—
650#490—132no—
651#489—132no—
652#488—132no—
653#486—132no—
654#485—132no—
655#484—132no—
656#482—132no—
657#482—132no—
658#482—132no—
659#482—132no—
660#482—132no—
661#480—132no—
662#479—132no—
663#478—132no—
664#476—132no—
665#475—132no—
666#470—132no—
667#469—132no—
668#469—132no—
669#468—132no—
670#466—132no—
671#465—132no—
672#465—132no—
673#465—132no—
674#464—132no—
675#463—132no—
676#460—132no—
677#459—132no—
678#452—131no—
679#452—131no—
680#452—132no—
681#451—131no—
682#450—131no—
683#450—132no—
684#449—131no—
685#449—131no—
686#449—132no—
687#448—131no—
688#447—131no—
689#447—132no—
690#440—132no—
691#440—132no—
692C4×Q16—132no—
693C4×D8—132no—
694#436—132no—
695#435—132no—
696#435—132no—
697C8×D4—132no—
698#428—131no—
699C2×#107—131no—
700C2×#106—131no—
701#424—131no—
702#419—132no—
703#418—131no—
704#418—132no—
705#418—132no—
706#417—131no—
707#417—131no—
708#417—131no—
709#417—131no—
710#417—132no—
711#417—131no—
712#416—131no—
713#416—131no—
714#416—132no—
715#416—132no—
716#416—132no—
717C2×#102—131no—
718C2×#102—131no—
719C2×#102—132no—
720#408—131no—
721C2×C22⋊C8—131no—
722#405—131no—
723C22×C13—21no—
724C22×C13—21no—
725C22×C13—22no—
726C22×C13—21no—
727C22×C13—21no—
728C22×C13—22no—
729C22×C13—21no—
730C22×C13—21no—
731C22×C13—21no—
732C22×C13—21no—
733C22×C13—22no—
734C22×C13—22no—
735C22×C13—41no—
736C22×C13—41no—
737C22×C13—41no—
738C22×C13—42no—
739C22×C13—42no—
740C22×C13—41no—
741C22×C13—41no—
742C22×C13—42no—
743C22×C13—82no—
744C22×C13—84no—
745C22×C13—162no—
746C22×C13—164no—
747C22×C13#54612yes—
748C22×C13C23×D411yescharacteristic
749C2×D13—41no—
750C2×D13—41no—
751C2×D13—41no—
752C4×C13—22no—
753C4×C13—22no—
754C4×C13—21no—
755C4×C13—21no—
756C4×C13—22no—
757C4×C13—22no—
758C4×C13—42no—
759C4×C13—41no—
760C4×C13#54612yes—
761C4×C13C22×#4111yescharacteristic
762C4×C13C2×H(5,𝔽2)11yescharacteristic
763Dic13—41no—
764Dic13—42no—
765Dic13—42no—
766Dic13—41no—
767Dic13—41no—
768H(5,𝔽2)—24no—
769H(5,𝔽2)—42no—
770C2×#41—21no—
771C2×#41—21no—
772C2×#41—21no—
773C2×#41—24no—
774C2×#41—42no—
775C2×#41—131no—
776C2×#41C22×D1311yescharacteristic
777C2×#41C22×D1311yescharacteristic
778C2×#41C22×D1312yes—
779C2×#41C22×D1311yescharacteristic
780C2×#41C22×D1311yescharacteristic
781C2×#41C22×D1311yescharacteristic
782C22×Q8C22×D1311yescharacteristic
783C22×D4—21no—
784C22×D4—21no—
785C22×D4—21no—
786C22×D4—22no—
787C22×D4—22no—
788C22×D4C22×D1311yescharacteristic
789C22×D4C22×D1311yescharacteristic
790C22×D4C22×D1312yes—
791C23×C4—21no—
792C23×C4C22×D1311yescharacteristic
793AGL(1,ℤ/8)—522no—
794#135—264no—
795#135—522no—
796C2×Q16—131no—
797C2×Q16—131no—
798C2×SD16—131no—
799C2×SD16—131no—
800C2×SD16—131no—
801C2×SD16—131no—
802C2×SD16—132no—
803C2×D8—131no—
804C2×D8—131no—
805C2×D8—132no—
806#131—522no—
807C2×M16—131no—
808C2×M16—131no—
809C2×M16—132no—
810C2×M16—132no—
811C2×M16—522no—
812C22×C8—131no—
813C22×C8—131no—
814C22×C8—132no—
815C22×C8—132no—
816C4⋊Q8—132no—
817C4⋊Q8—261no—
818#127—22no—
819#127C22×D1312yes—
820#126—262no—
821#126—262no—
822#126—262no—
823#126—262no—
824#125—132no—
825#125—262no—
826#125—261no—
827#124—22no—
828#124—262no—
829#124—262no—
830#124—262no—
831#124C22×D1312yes—
832#123—22no—
833#123—262no—
834#123—261no—
835#123—262no—
836#123C22⋊D1312yes—
837C22⋊Q8—21no—
838C22⋊Q8—22no—
839C22⋊Q8—131no—
840C22⋊Q8—131no—
841C22⋊Q8—132no—
842C22⋊Q8—261no—
843C22⋊Q8—262no—
844C22⋊Q8C22⋊D1311yescharacteristic
845C22⋊Q8C22⋊D1311yescharacteristic
846C22⋊Q8C22×D1312yes—
847#121—21no—
848#121—22no—
849#121—22no—
850#121—21no—
851#121—21no—
852#121—21no—
853#121—21no—
854#121—22no—
855#121—22no—
856#121—22no—
857#121—22no—
858#121—131no—
859#121—131no—
860#121—132no—
861#121—262no—
862#121—261no—
863#121—262no—
864#121—262no—
865#121C22⋊D1311yescharacteristic
866#121C22⋊D1311yescharacteristic
867#121C22×D1312yes—
868#121C22×D1312yes—
869#121C22×D1312yes—
870#120—22no—
871#120—22no—
872#120—22no—
873#120—22no—
874#120—261no—
875#120C22⋊D1312yes—
876C4×Q8—132no—
877C4×Q8—261no—
878C4×Q8—262no—
879C4×Q8C22×D1312yes—
880C4×D4—22no—
881C4×D4—22no—
882C4×D4—22no—
883C4×D4—132no—
884C4×D4—262no—
885C4×D4—261no—
886C4×D4—261no—
887C4×D4—261no—
888C4×D4—262no—
889C4×D4—262no—
890C4×D4C22×D1312yes—
891C4×D4C22×D1312yes—
892C4×D4C22×D1312yes—
893#117—21no—
894#117—132no—
895#117—132no—
896#117—131no—
897#117—132no—
898#117—261no—
899#117—261no—
900#117—261no—
901#117—262no—
902#117—262no—
903#117C22×D1311yescharacteristic
904C2×C4⋊C4—21no—
905C2×C4⋊C4—131no—
906C2×C4⋊C4—131no—
907C2×C4⋊C4—132no—
908C2×C4⋊C4—261no—
909C2×C4⋊C4C22×D1311yescharacteristic
910C2×C22⋊C4—21no—
911C2×C22⋊C4—22no—
912C2×C22⋊C4—261no—
913C2×C42—261no—
914#107—132no—
915#107—132no—
916#107—132no—
917#106—132no—
918#106—132no—
919#106—132no—
920C4⋊C8—132no—
921C4⋊C8—132no—
922#103—131no—
923#103—132no—
924#103—131no—
925#103—132no—
926#103—132no—
927#103—132no—
928#103—131no—
929#103—131no—
930#103—132no—
931#102—131no—
932#102—132no—
933#102—132no—
934#102—132no—
935#102—132no—
936#102—132no—
937#102—132no—
938#102—132no—
939#102—132no—
940#102—132no—
941#102—131no—
942#102—132no—
943#102—131no—
944#102—131no—
945#102—132no—
946C22⋊C8—131no—
947C22⋊C8—131no—
948C22⋊C8—131no—
949C22⋊C8—131no—
950C22⋊C8—132no—
951C22⋊C8—132no—
952#97—132no—
953C4×C8—132no—
954C2×C13—22no—
955C2×C13—41no—
956C2×C13—41no—
957C2×C13—42no—
958C2×C13—42no—
959C2×C13—81no—
960C2×C13—82no—
961C2×C13C2×#54611yescharacteristic
962C2×C13#358411yescharacteristic
963C2×C13#358511yescharacteristic
964D13—81no—
965C24—21no—
966C24—22no—
967C24—21no—
968C24C2×C22⋊D1311yescharacteristic
969#41—22no—
970#41—22no—
971#41—22no—
972#41—22no—
973#41—24no—
974#41—22no—
975#41—22no—
976#41—22no—
977#41—44no—
978#41—41no—
979#41—41no—
980#41—42no—
981#41—44no—
982#41—44no—
983#41—262no—
984#41—262no—
985#41#612914yes—
986C2×Q8—21no—
987C2×Q8—22no—
988C2×Q8—41no—
989C2×Q8—131no—
990C2×Q8—262no—
991C2×Q8C2×C22⋊D1311yescharacteristic
992C2×Q8C23×D1311yescharacteristic
993C2×Q8C23×D1311yescharacteristic
994C2×D4—21no—
995C2×D4—22no—
996C2×D4—24no—
997C2×D4—22no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—22no—
1001C2×D4—21no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—21no—
1007C2×D4—22no—
1008C2×D4—21no—
1009C2×D4—22no—
1010C2×D4—22no—
1011C2×D4—41no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—48no—
1015C2×D4—44no—
1016C2×D4—84no—
1017C2×D4—82no—
1018C2×D4—131no—
1019C2×D4—261no—
1020C2×D4—261no—
1021C2×D4—261no—
1022C2×D4—262no—
1023C2×D4C2×C22⋊D1312yes—
1024C2×D4C2×C22⋊D1311yescharacteristic
1025C2×D4C2×C22⋊D1312yes—
1026C2×D4C2×C22⋊D1312yes—
1027C2×D4C23×D1312yes—
1028C2×D4C23×D1311yescharacteristic
1029C2×D4C23×D1311yescharacteristic
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—21no—
1033C22×C4—21no—
1034C22×C4—21no—
1035C22×C4—21no—
1036C22×C4—21no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—22no—
1040C22×C4—44no—
1041C22×C4—261no—
1042C22×C4—261no—
1043C22×C4—262no—
1044C22×C4—261no—
1045C22×C4—262no—
1046C22×C4C2×C22⋊D1311yescharacteristic
1047C22×C4C2×C22⋊D1311yescharacteristic
1048C22×C4C2×C22⋊D1311yescharacteristic
1049C22×C4C23×D1312yes—
1050C22×C4C23×D1311yescharacteristic
1051C22×C4C23×D1311yescharacteristic
1052C22×C4C23×D1311yescharacteristic
1053Q16—262no—
1054Q16—521no—
1055SD16—262no—
1056SD16—262no—
1057SD16—521no—
1058SD16—522no—
1059SD16—521no—
1060D8—262no—
1061D8—521no—
1062D8—522no—
1063M16—262no—
1064M16—262no—
1065M16—522no—
1066M16—522no—
1067C2×C8—131no—
1068C2×C8—132no—
1069C2×C8—131no—
1070C2×C8—131no—
1071C2×C8—131no—
1072C2×C8—132no—
1073C2×C8—262no—
1074C2×C8—262no—
1075C2×C8—522no—
1076C2×C8—522no—
1077C4⋊C4—21no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—132no—
1081C4⋊C4—131no—
1082C4⋊C4—132no—
1083C4⋊C4—131no—
1084C4⋊C4—261no—
1085C4⋊C4—261no—
1086C4⋊C4—262no—
1087C4⋊C4—262no—
1088C4⋊C4—261no—
1089C4⋊C4—262no—
1090C4⋊C4—262no—
1091C4⋊C4—261no—
1092C4⋊C4—262no—
1093C4⋊C4—262no—
1094C4⋊C4C2×C22⋊D1311yescharacteristic
1095C4⋊C4C2×C22⋊D1311yescharacteristic
1096C4⋊C4C2×C22⋊D1312yes—
1097C4⋊C4C2×C22⋊D1312yes—
1098C4⋊C4C23×D1312yes—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—262no—
1107C22⋊C4—262no—
1108C22⋊C4—261no—
1109C22⋊C4—262no—
1110C22⋊C4—262no—
1111C22⋊C4—261no—
1112C22⋊C4—261no—
1113C22⋊C4—261no—
1114C22⋊C4—262no—
1115C22⋊C4—262no—
1116C22⋊C4—261no—
1117C22⋊C4C2×C22⋊D1312yes—
1118C22⋊C4C2×C22⋊D1312yes—
1119C22⋊C4C2×C22⋊D1312yes—
1120C22⋊C4C2×C22⋊D1312yes—
1121C22⋊C4C2×C22⋊D1312yes—
1122C42—22no—
1123C42—262no—
1124C42—262no—
1125C42—262no—
1126C42—261no—
1127C42—262no—
1128C42C23×D1312yes—
1129C13#6119511yescharacteristic, complemented, Sylow
1130C23—21no—
1131C23—22no—
1132C23—22no—
1133C23—21no—
1134C23—41no—
1135C23—41no—
1136C23—42no—
1137C23—44no—
1138C23—42no—
1139C23—42no—
1140C23—81no—
1141C23—81no—
1142C23—82no—
1143C23—81no—
1144C23—82no—
1145C23—261no—
1146C23C22×C22⋊D1312yes—
1147C23C22×C22⋊D1311yescharacteristic
1148C23C22×C22⋊D1311yescharacteristic
1149C23C22×C22⋊D1311yescharacteristic
1150Q8—22no—
1151Q8—21no—
1152Q8—21no—
1153Q8—21no—
1154Q8—42no—
1155Q8—261no—
1156Q8—261no—
1157Q8—1042no—
1158Q8C2×#612912yes—
1159D4—24no—
1160D4—24no—
1161D4—22no—
1162D4—22no—
1163D4—21no—
1164D4—21no—
1165D4—22no—
1166D4—21no—
1167D4—42no—
1168D4—42no—
1169D4—44no—
1170D4—42no—
1171D4—44no—
1172D4—42no—
1173D4—42no—
1174D4—44no—
1175D4—42no—
1176D4—42no—
1177D4—82no—
1178D4—82no—
1179D4—82no—
1180D4—82no—
1181D4—261no—
1182D4—261no—
1183D4—522no—
1184D4—1042no—
1185D4—1041no—
1186D4—1041no—
1187D4C2×#612912yes—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—42no—
1202C2×C4—44no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—82no—
1207C2×C4—81no—
1208C2×C4—262no—
1209C2×C4—261no—
1210C2×C4—262no—
1211C2×C4—261no—
1212C2×C4—261no—
1213C2×C4—522no—
1214C2×C4—1042no—
1215C2×C4—1041no—
1216C2×C4—1041no—
1217C2×C4—1042no—
1218C2×C4C2×#612912yes—
1219C2×C4#8825112yes—
1220C2×C4C22×C22⋊D1312yes—
1221C2×C4C22×C22⋊D1311yescharacteristic
1222C2×C4C22×C22⋊D1311yescharacteristic
1223C2×C4C22×C22⋊D1312yes—
1224C2×C4C22×C22⋊D1312yes—
1225C2×C4C22×C22⋊D1311yescharacteristic
1226C2×C4C24×D1311yescharacteristic
1227C8—261no—
1228C8—261no—
1229C8—261no—
1230C8—261no—
1231C8—262no—
1232C8—262no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—21no—
1237C22—22no—
1238C22—22no—
1239C22—21no—
1240C22—22no—
1241C22—21no—
1242C22—22no—
1243C22—21no—
1244C22—21no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—41no—
1250C22—42no—
1251C22—42no—
1252C22—41no—
1253C22—82no—
1254C22—84no—
1255C22—162no—
1256C22—164no—
1257C22—521no—
1258C22—521no—
1259C22—521no—
1260C22#1171951112yes—
1261C22C23×C22⋊D1311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—41no—
1269C4—42no—
1270C4—521no—
1271C4—522no—
1272C4—521no—
1273C4—522no—
1274C4—521no—
1275C4#1171951112yes—
1276C4C22×#612911yescharacteristic
1277C4C2×#8825111yescharacteristic
1278C2—22no—
1279C2—41no—
1280C2—41no—
1281C2—42no—
1282C2—42no—
1283C2—81no—
1284C2—82no—
1285C2—1041no—
1286C2C2×#1171951111yescharacteristic
1287C2#1312960711yescharacteristic
1288C2#1312961611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3488C2
socleC22×C13C23×D4
hypercenter#3488D13
hypocenterC13#61195
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #525 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13128553C2semidirect
2. #13127104C2semidirect
3. #13127078C2semidirect
4. #13127022C2semidirect
5. #13126872C2semidirect
6. #13126857C2semidirect
7. #13126842C2semidirect
8. #13126775C2semidirect
9. #13126686C2semidirect
10. #13125190C2semidirect
11. #13124810C2semidirect
12. C2×#11718696C2semidirect
13. #13124698C2semidirect
14. #13124495C2semidirect
15. #13124451C2semidirect
16. #13124371C2semidirect
17. #13124140C2semidirect
18. #13124054C2semidirect
19. #13123709C2semidirect
20. #13123563C2semidirect
21. #13123362C2semidirect
22. #13123355C2semidirect
23. C13×#3488C2semidirect
41. #11719538C22semidirect
42. #11719532C22semidirect
44. C2×#88204C22semidirect
45. C2×#88202C22semidirect
46. C2×#88186C22semidirect
47. #11719496C22semidirect
48. C2×#88180C22semidirect
49. C22×#6099C22semidirect
56. #11719270C22semidirect
57. #11719268C22semidirect
58. #11719247C22semidirect
59. #11719246C22semidirect
60. #11719228C22semidirect
61. #11719224C22semidirect
62. #11718900C22semidirect
63. #11718900C22semidirect
64. #11718900C22semidirect
65. #11718899C22semidirect
66. #11718899C22semidirect
67. #11718899C22semidirect
68. #11718895C22semidirect
70. #11718894C22semidirect
71. #11718894C22semidirect
72. #11718894C22semidirect
73. #11718894C22semidirect
76. #11718893C22semidirect
77. #11718893C22semidirect
78. #11718893C22semidirect
79. #11718889C22semidirect
80. #11718888C22semidirect
81. #11718886C22semidirect
82. #11718879C22semidirect
83. #11718879C22semidirect
84. #11718878C22semidirect
85. #11718878C22semidirect
86. #11718876C22semidirect
87. #11718876C22semidirect
88. #11718876C22semidirect
89. C2×#88072C22semidirect
90. C2×#88072C22semidirect
91. C2×#88072C22semidirect
92. C2×C22⋊#1055C22semidirect
93. #11718736C22semidirect
94. #11718733C22semidirect
95. #11718732C22semidirect
96. #11718731C22semidirect
97. #11718718C22semidirect
98. #11718717C22semidirect
99. #11718716C22semidirect
100. #11718715C22semidirect
101. #11718713C22semidirect
102. #11718709C22semidirect
103. #11718706C22semidirect
104. #11718705C22semidirect
105. #11718703C22semidirect
106. #11718702C22semidirect
107. #11718702C22semidirect
108. #11718700C22semidirect
109. #11718700C22semidirect
110. #11718699C22semidirect
111. #11718696C22semidirect
112. #11718696C22semidirect
113. #11718696C22semidirect
114. #11718696C22semidirect
115. #11718696C22semidirect
116. #11718694C22semidirect
117. C4×#6107C22semidirect
118. #11718687C22semidirect
119. #11718683C22semidirect
120. #11718681C22semidirect
121. #11718679C22semidirect
122. C4×#6104C22semidirect
123. #11718673C22semidirect
124. #11718672C22semidirect
125. #11718672C22semidirect
126. D4×#1055C22semidirect
127. #11718670C22semidirect
128. #11718669C22semidirect
129. #11718660C22semidirect
130. #11718658C22semidirect
131. #11718627C22semidirect
132. #11718625C22semidirect
133. C2×#88048C22semidirect
134. C2×#88047C22semidirect
487. #3488D13semidirect
1129. C13#61195semidirect

Maximal subgroups

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

subgroupindex
#131285532
#131271042
#131270782
#131270222
#131268722
#131268572
#131268422
#131267752
#131266862
#131251902
#131248102
C2×#117186962
#131246982
#131244952
#131244512
#131243712
#131241402
#131240542
#131237092
#131235632
#131233622
#131233552
C13×#34882
#6119513