Finite Group Databasebeta

← #16740590

Subgroups — #16740590

Order 3328.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128573C211yesmaximal, characteristic, complemented
2#13127141C212yesmaximal, complemented
3#13127037C212yesmaximal, complemented
4#13126992C212yesmaximal, complemented
5#13126812C212yesmaximal, complemented
6#13126812C212yesmaximal, complemented
7#13126797C212yesmaximal, complemented
8#13126764C212yesmaximal, complemented
9#13126686C212yesmaximal, complemented
10#13125201C211yesmaximal, characteristic, complemented
11#13124799C211yesmaximal, characteristic, complemented
12#13124745C211yesmaximal, characteristic, complemented
13#13124667C211yesmaximal, characteristic, complemented
14#13124477C211yesmaximal, characteristic, complemented
15#13124457C211yesmaximal, characteristic, complemented
16#13124344C211yesmaximal, characteristic, complemented
17#13124104C211yesmaximal, characteristic, complemented
18C2×#11718899C211yesmaximal, characteristic, complemented
19#13123686C211yesmaximal, characteristic, complemented
20#13123563C211yesmaximal, characteristic, complemented
21#13123362C211yesmaximal, characteristic, complemented
22#13123355C211yesmaximal, characteristic, complemented
23C13×#3485C211yesmaximal, characteristic, complemented
24C2×C13×H(5,𝔽2)C2211yescharacteristic
25C22×C13×#41C2211yescharacteristic
26C13×#547—21no—
27C13×#547—21no—
28C13×#547C2212yescomplemented
29C13×#547C2212yescomplemented
30C13×#546—21no—
31C13×#546—21no—
32C13×#546C2212yescomplemented
33C13×#546C2212yescomplemented
34C13×#536C2211yescharacteristic
35C13×#536C2211yescharacteristic
36C13×#534—22no—
37C13×#525C2211yescharacteristic
38C13×#525C2211yescharacteristic
39C2×C13×#123—22no—
40C13×#518C2211yescharacteristic
41#11719535C2211yescharacteristic
42#11719532C2211yescharacteristic
43C2×#88203C2211yescharacteristic
44C2×#88202C2211yescharacteristic
45C22×#6106C2211yescharacteristic, complemented
46C22×#6104C2211yescharacteristic
47C2×#88184C2211yescharacteristic, complemented
48C2×#88180C2211yescharacteristic, complemented
49C22×#6099C2211yescharacteristic, complemented
50#11719363—22no—
51#11719348—21no—
52#11719329—21no—
53#11719324—21no—
54#11719301—21no—
55#11719296—22no—
56#11719270C2212yescomplemented
57#11719270C2212yescomplemented
58#11719268C2212yescomplemented
59#11719260C2212yescomplemented
60#11719226C2211yescharacteristic, complemented
61#11719224C2211yescharacteristic, complemented
62#11718899C2212yescomplemented
63#11718899C2212yescomplemented
64#11718899C2212yescomplemented
65#11718899C2212yescomplemented
66#11718899C2212yescomplemented
67#11718899C2212yescomplemented
68#11718895C2211yescharacteristic
69#11718894C2211yescharacteristic
70#11718894C2211yescharacteristic
71#11718894C2212yescomplemented
72#11718894C2212yescomplemented
73#11718894C2212yescomplemented
74#11718893C2211yescharacteristic
75#11718893C2212yescomplemented
76#11718893C2212yescomplemented
77#11718893C2212yescomplemented
78#11718886C2211yescharacteristic, complemented
79#11718886C2211yescharacteristic, complemented
80C2×#88075C2211yescharacteristic, complemented
81#11718878C2212yescomplemented
82#11718878C2212yescomplemented
83#11718876C2211yescharacteristic
84#11718876C2211yescharacteristic
85#11718876C2212yescomplemented
86C2×#88072C2211yescharacteristic
87C2×#88072C2212yescomplemented
88C2×C22⋊#1055C2211yescharacteristic, complemented
89#11718744C2212yescomplemented
90#11718744C2212yescomplemented
91#11718743C2212yescomplemented
92#11718742C2212yescomplemented
93#11718718C2212yescomplemented
94#11718718C2212yescomplemented
95#11718717C2212yescomplemented
96#11718716C2212yescomplemented
97#11718710C2212yescomplemented
98#11718710C2212yescomplemented
99#11718710C2212yescomplemented
100#11718709C2212yescomplemented
101#11718709C2212yescomplemented
102#11718709C2212yescomplemented
103#11718706C2212yescomplemented
104#11718706C2211yescharacteristic, complemented
105#11718706C2212yescomplemented
106#11718706C2211yescharacteristic, complemented
107#11718705C2212yescomplemented
108#11718705C2211yescharacteristic, complemented
109#11718704C2211yescharacteristic, complemented
110#11718704C2212yescomplemented
111#11718700C2212yescomplemented
112#11718699C2212yescomplemented
113#11718696C2211yescharacteristic, complemented
114#11718696C2211yescharacteristic, complemented
115#11718695C2211yescharacteristic, complemented
116#11718694C2211yescharacteristic, complemented
117#11718675C2212yescomplemented
118#11718675C2212yescomplemented
119C4×#6104C2212yescomplemented
120C4×#6104C2212yescomplemented
121#11718673C2212yescomplemented
122#11718672C2212yescomplemented
123#11718672C2212yescomplemented
124D4×#1055C2212yescomplemented
125#11718670C2212yescomplemented
126#11718670C2212yescomplemented
127#11718669C2212yescomplemented
128#11718668C2212yescomplemented
129#11718662C2211yescharacteristic, complemented
130#11718660C2211yescharacteristic, complemented
131#11718659C2211yescharacteristic, complemented
132#11718659C2211yescharacteristic, complemented
133#11718658C2211yescharacteristic, complemented
134#11718656C2211yescharacteristic, 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×#41C2312yes—
144C2×C13×#41C2312yes—
145C2×C13×#41C2312yes—
146C2×C13×#41C2311yescharacteristic
147C22×Q8×C13C2311yescharacteristic
148C22×D4×C13—21no—
149C22×D4×C13—22no—
150C22×D4×C13—21no—
151C22×D4×C13C2312yes—
152C22×D4×C13C2311yescharacteristic
153C23×C4×C13—21no—
154C23×C4×C13C2311yescharacteristic
155C22×C22⋊D13—21no—
156C2×#6129—22no—
157C22×D52C2311yescharacteristic
158C13×C4⋊Q8—21no—
159C13×C4⋊Q8C2312yes—
160C13×#124—21no—
161C13×#124C2312yes—
162C13×#123—22no—
163C13×#123—21no—
164C13×#123—22no—
165C13×#123—22no—
166C13×#123—22no—
167C13×#123—22no—
168C13×#123—22no—
169C13×#123—22no—
170C13×#123—22no—
171C13×#123D412yes—
172C13×C22⋊Q8—21no—
173C13×C22⋊Q8—21no—
174C13×C22⋊Q8D411yescharacteristic
175C13×C22⋊Q8D411yescharacteristic
176C13×C22⋊Q8C2311yescharacteristic
177C13×C22⋊Q8C2312yes—
178C13×C22⋊Q8C2312yes—
179C13×C22⋊Q8C2311yescharacteristic
180C13×#121—22no—
181C13×#121—22no—
182C13×#121—22no—
183C13×#121—22no—
184C13×#121D411yescharacteristic
185C13×#121D411yescharacteristic
186C13×#121C2311yescharacteristic
187C13×#121C2311yescharacteristic
188C13×#120—21no—
189C13×#120—22no—
190C13×#120—22no—
191C13×#120D412yes—
192C4×D4×C13—21no—
193C4×D4×C13—21no—
194C4×D4×C13—21no—
195C4×D4×C13—21no—
196C4×D4×C13C2312yes—
197C4×D4×C13C2312yes—
198C4×D4×C13C2312yes—
199C4×D4×C13C2312yes—
200C13×#117C2311yescharacteristic
201C13×#117C2311yescharacteristic
202C2×C13×C4⋊C4—22no—
203C2×C13×C4⋊C4—22no—
204C2×C13×C22⋊C4—22no—
205C2×C13×C22⋊C4—22no—
206C2×C13×C22⋊C4—22no—
207C2×C22⋊Dic13—21no—
208#88203—42no—
209#88202—42no—
210#88201—21no—
211Q8×Dic13—21no—
212C2×#6106—42no—
213C2×#6106C2312yes—
214C2×#6106C2312yes—
215C2×#6106C2312yes—
216#88194—21no—
217#88193—22no—
218#88193—22no—
219#88192—22no—
220#88191—22no—
221D4×Dic13—22no—
222D4×Dic13—21no—
223C2×#6104—24no—
224C2×#6104C2312yes—
225C2×#6104C2312yes—
226C2×#6104C2312yes—
227#88184—21no—
228#88184—21no—
229#88184C2312yes—
230#88184C2312yes—
231#88184C2312yes—
232#88184C2312yes—
233C2×#6103—21no—
234#88180—21no—
235#88180—21no—
236#88180C2311yescharacteristic
237#88180C2311yescharacteristic
238#88180C2311yescharacteristic
239#88180C2311yescharacteristic
240#88180C2312yes—
241C2×C4⋊Dic13C2311yescharacteristic
242C2×C4⋊Dic13C2311yescharacteristic
243C2×C4⋊Dic13C2311yescharacteristic
244C2×C4⋊Dic13C2312yes—
245C2×C4×Dic13—21no—
246C2×#6099—42no—
247C2×#6099C2311yescharacteristic
248C2×#6099C2311yescharacteristic
249C2×#6099C2312yes—
250C2×#6099C2312yes—
251C22×#1055C2311yescharacteristic
252C22×#1055C2311yescharacteristic
253C22×#1055C2312yes—
254C22×#1055C2312yes—
255#88152—22no—
256#88152—22no—
257#88151—22no—
258#88147—21no—
259#88147—21no—
260#88146—22no—
261#88144—21no—
262#88142—21no—
263#88140—22no—
264#88140—22no—
265#88139—22no—
266#88139—22no—
267#88137—22no—
268#88137—22no—
269#88135—22no—
270#88135—22no—
271C22⋊C4×D13—22no—
272#88132—22no—
273C4×D52C2312yes—
274C4×D52C2312yes—
275#88124C2312yes—
276#88123C2312yes—
277#88075C2312yes—
278#88075C2312yes—
279#88075C2311yescharacteristic
280#88075C2311yescharacteristic
281#88075C2312yes—
282#88075C2311yescharacteristic
283#88075C2311yescharacteristic
284#88075C2312yes—
285#88075C2312yes—
286#88075C2312yes—
287#88075C2312yes—
288#88072C2312yes—
289#88072C2312yes—
290#88072C2312yes—
291#88072C2312yes—
292#88072C2312yes—
293#88072C2312yes—
294#88072C2311yescharacteristic
295#88072C2311yescharacteristic
296#88072C2311yescharacteristic
297#88072C2311yescharacteristic
298#88072C2312yes—
299C22⋊#1055C2311yescharacteristic
300C22⋊#1055C2312yes—
301C22⋊#1055C2311yescharacteristic
302C22⋊#1055C2311yescharacteristic
303C22⋊#1055C2312yes—
304C22⋊#1055C2311yescharacteristic
305#88049C2312yes—
306#88049C2312yes—
307#88048C2312yes—
308#88048C2311yescharacteristic
309#88048C2311yescharacteristic
310#88048C2311yescharacteristic
311#88048C2311yescharacteristic
312#88047C2312yes—
313#88047C2311yescharacteristic
314#88047C2311yescharacteristic
315#88047C2311yescharacteristic
316#88047C2311yescharacteristic
317C4⋊#1055C2312yes—
318C4⋊#1055C2312yes—
319#88043C2312yes—
320C4×#1055C2312yes—
321#61187—131nomaximal, Sylow
322C24×C13—21no—
323C24×C13—22no—
324C24×C13C2×D411yescharacteristic
325C23×D13—21no—
326C13×#41—22no—
327C13×#41—22no—
328C13×#41—24no—
329C13×#41—24no—
330C13×#41—24no—
331C13×#41—22no—
332C13×#41—22no—
333C13×#41—42no—
334C13×#41—42no—
335C13×#41—42no—
336C13×#41—44no—
337C13×#41—44no—
338C13×#41—44no—
339C2×Q8×C13—21no—
340C2×Q8×C13—22no—
341C2×Q8×C13—22no—
342C2×Q8×C13C2×D411yescharacteristic
343C2×Q8×C13C2412yes—
344C2×Q8×C13C2411yescharacteristic
345C2×D4×C13—24no—
346C2×D4×C13—22no—
347C2×D4×C13—22no—
348C2×D4×C13—21no—
349C2×D4×C13—22no—
350C2×D4×C13—21no—
351C2×D4×C13—21no—
352C2×D4×C13—21no—
353C2×D4×C13—22no—
354C2×D4×C13—22no—
355C2×D4×C13—42no—
356C2×D4×C13—44no—
357C2×D4×C13—48no—
358C2×D4×C13—44no—
359C2×D4×C13C2×D412yes—
360C2×D4×C13C2×D411yescharacteristic
361C2×D4×C13C2×D412yes—
362C2×D4×C13C2×D412yes—
363C2×D4×C13#4114yescomplemented
364C2×D4×C13C2411yescharacteristic
365C2×D4×C13C2412yes—
366C22×C4×C13—22no—
367C22×C4×C13—22no—
368C22×C4×C13—21no—
369C22×C4×C13—22no—
370C22×C4×C13—22no—
371C22×C4×C13—22no—
372C22×C4×C13—21no—
373C22×C4×C13—22no—
374C22×C4×C13—22no—
375C22×C4×C13—44no—
376C22×C4×C13C2×D411yescharacteristic
377C22×C4×C13C2×D411yescharacteristic
378C22×C4×C13C2×D411yescharacteristic
379C22×C4×C13C2411yescharacteristic
380C22×C4×C13C2412yes—
381C22×C4×C13C2411yescharacteristic
382C22×C4×C13C2411yescharacteristic
383C2×C22⋊D13—22no—
384C2×C22⋊D13—22no—
385C2×C22⋊D13—22no—
386C2×C22⋊D13—22no—
387C2×C22⋊D13—82no—
388C22×Dic13—21no—
389C22×Dic13—21no—
390C22×Dic13—21no—
391C22×Dic13—22no—
392#6129—84no—
393C2×D52—22no—
394C2×D52—22no—
395C2×D52—21no—
396C2×D52C2412yes—
397C2×C4×D13—22no—
398C2×C4×D13—22no—
399C2×Dic26—22no—
400C13×C4⋊C4—21no—
401C13×C4⋊C4—21no—
402C13×C4⋊C4—22no—
403C13×C4⋊C4—22no—
404C13×C4⋊C4—22no—
405C13×C4⋊C4—22no—
406C13×C4⋊C4C2×D411yescharacteristic
407C13×C4⋊C4C2×D411yescharacteristic
408C13×C4⋊C4C2×D412yes—
409C13×C4⋊C4C2×D412yes—
410C13×C4⋊C4C2411yescharacteristic
411C13×C4⋊C4C2411yescharacteristic
412C13×C22⋊C4—21no—
413C13×C22⋊C4—22no—
414C13×C22⋊C4—22no—
415C13×C22⋊C4—21no—
416C13×C22⋊C4—21no—
417C13×C22⋊C4—21no—
418C13×C22⋊C4—21no—
419C13×C22⋊C4—22no—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4C2×D412yes—
424C13×C22⋊C4C2×D412yes—
425C13×C22⋊C4C2×D412yes—
426C13×C22⋊C4C2×D412yes—
427C13×C22⋊C4C2×D412yes—
428C42×C13—21no—
429C42×C13C2412yes—
430C22⋊Dic13—21no—
431C22⋊Dic13—21no—
432C22⋊Dic13—21no—
433C22⋊Dic13—22no—
434C22⋊Dic13—21no—
435#6106—42no—
436#6106—42no—
437#6106—42no—
438#6104—24no—
439#6104—24no—
440#6104—42no—
441#6103—22no—
442#6103—22no—
443#6103—22no—
444#6103—22no—
445#6103—22no—
446#6103—22no—
447C4⋊Dic13—22no—
448C4⋊Dic13—21no—
449C4⋊Dic13—22no—
450C4⋊Dic13—21no—
451C4⋊Dic13—21no—
452C4⋊Dic13C2411yescharacteristic
453C4⋊Dic13C2412yes—
454C4⋊Dic13C2411yescharacteristic
455C4⋊Dic13C2411yescharacteristic
456C4⋊Dic13C2411yescharacteristic
457#6101—22no—
458#6101—22no—
459C4×Dic13—21no—
460C4×Dic13—22no—
461C4×Dic13—21no—
462C4×Dic13—21no—
463C4×Dic13—21no—
464#6099—22no—
465#6099—22no—
466#6099—42no—
467#6099—42no—
468C2×#1055—22no—
469C2×#1055—22no—
470C2×#1055—42no—
471C2×#1055—42no—
472C2×#1055C2411yescharacteristic
473C2×#1055C2411yescharacteristic
474C2×#1055C2411yescharacteristic
475C2×#1055C2411yescharacteristic
476C2×#1055C2412yes—
477C2×#1055C2412yes—
478#3494—131no—
479#3485D1311yescharacteristic, complemented
480#3330—132no—
481#3322—132no—
482#3319—132no—
483#3307—132no—
484#3307—132no—
485#3306—132no—
486#3303—132no—
487#3297—132no—
488#3137—131no—
489#3097—131no—
490#3091—131no—
491#3081—131no—
492#3057—131no—
493#3055—131no—
494#3042—131no—
495#3008—131no—
496C2×#449—131no—
497#2948—131no—
498#2933—131no—
499#2897—131no—
500#2896—131no—
501C23×C13—22no—
502C23×C13—22no—
503C23×C13—24no—
504C23×C13—21no—
505C23×C13—41no—
506C23×C13—41no—
507C23×C13—44no—
508C23×C13—81no—
509C23×C13—81no—
510C23×C13—82no—
511C23×C13—82no—
512C23×C13C22×D411yescharacteristic
513C23×C13C22×D412yes—
514C23×C13C22×D411yescharacteristic
515C23×C13C22×D411yescharacteristic
516C22×D13—22no—
517C22×D13—42no—
518C22×D13—81no—
519C22×D13—81no—
520Q8×C13—22no—
521Q8×C13—22no—
522Q8×C13—21no—
523Q8×C13—22no—
524Q8×C13—21no—
525Q8×C13—42no—
526D4×C13—24no—
527D4×C13—24no—
528D4×C13—22no—
529D4×C13—21no—
530D4×C13—22no—
531D4×C13—21no—
532D4×C13—42no—
533D4×C13—42no—
534D4×C13—44no—
535D4×C13—44no—
536D4×C13—44no—
537D4×C13—44no—
538D4×C13—42no—
539D4×C13—81no—
540D4×C13—81no—
541D4×C13C2×#4114yes—
542C2×C4×C13—22no—
543C2×C4×C13—22no—
544C2×C4×C13—22no—
545C2×C4×C13—21no—
546C2×C4×C13—21no—
547C2×C4×C13—22no—
548C2×C4×C13—21no—
549C2×C4×C13—22no—
550C2×C4×C13—21no—
551C2×C4×C13—21no—
552C2×C4×C13—21no—
553C2×C4×C13—22no—
554C2×C4×C13—21no—
555C2×C4×C13—44no—
556C2×C4×C13—44no—
557C2×C4×C13—44no—
558C2×C4×C13—42no—
559C2×C4×C13—42no—
560C2×C4×C13—82no—
561C2×C4×C13—82no—
562C2×C4×C13C22×D411yescharacteristic
563C2×C4×C13C22×D412yes—
564C2×C4×C13C22×D412yes—
565C2×C4×C13C22×D412yes—
566C2×C4×C13C22×D411yescharacteristic
567C2×C4×C13C22×D411yescharacteristic
568C2×C4×C13C2×#4112yes—
569C2×C4×C13H(5,𝔽2)12yes—
570C2×C4×C13C2511yescharacteristic
571C22⋊D13—44no—
572C22⋊D13—82no—
573C22⋊D13—82no—
574C22⋊D13—82no—
575C2×Dic13—21no—
576C2×Dic13—21no—
577C2×Dic13—21no—
578C2×Dic13—21no—
579C2×Dic13—22no—
580C2×Dic13—42no—
581C2×Dic13—82no—
582C2×Dic13—81no—
583C2×Dic13—81no—
584D52—22no—
585D52—22no—
586D52—42no—
587C4×D13—82no—
588C4×D13—82no—
589Dic26—82no—
590#1055—21no—
591#1055—21no—
592#1055—21no—
593#1055—21no—
594#1055—22no—
595#1055—22no—
596C2×H(5,𝔽2)C2×D1311yescharacteristic
597C22×#41C2×D1311yescharacteristic
598C2×AGL(1,ℤ/8)—131no—
599C22×SD16—131no—
600C22×D8—131no—
601C2×#131—131no—
602C22×M16—131no—
603#555—132no—
604#553—132no—
605#553—132no—
606#551—262no—
607#547—21no—
608#547—21no—
609#547—132no—
610#547C2×D1312yescomplemented
611#547C2×D1312yescomplemented
612#546—21no—
613#546—21no—
614#546—262no—
615#546C2×D1312yescomplemented
616#546C2×D1312yescomplemented
617#544—131no—
618#542—261no—
619#540—261no—
620#536C2×D1311yescharacteristic
621#536C2×D1311yescharacteristic
622#535—131no—
623#534—22no—
624#532—261no—
625#529—261no—
626#525C2×D1311yescharacteristic
627#525C2×D1311yescharacteristic
628C2×#123—22no—
629C2×#121—131no—
630#520—131no—
631#518—131no—
632#518C2×D1311yescharacteristic
633C2×#117—131no—
634#491—132no—
635#489—132no—
636#488—132no—
637#487—132no—
638#485—131no—
639#485—131no—
640#485—132no—
641#485—132no—
642#484—131no—
643#484—132no—
644#483—131no—
645#483—132no—
646#482—131no—
647#482—131no—
648#481—131no—
649#480—131no—
650#478—132no—
651#478—132no—
652#476—132no—
653#474—132no—
654#469—132no—
655#468—132no—
656#468—132no—
657#468—132no—
658#466—132no—
659#465—132no—
660#465—132no—
661#465—132no—
662#463—132no—
663#463—132no—
664#461—132no—
665#461—132no—
666#449—132no—
667#449—132no—
668#449—132no—
669#449—132no—
670#449—132no—
671#449—132no—
672#447—132no—
673#447—132no—
674#442—132no—
675#442—132no—
676C4×D8—132no—
677C4×D8—132no—
678#436—132no—
679#435—132no—
680#435—132no—
681C8×D4—132no—
682#428—131no—
683#427—131no—
684#427—131no—
685#424—131no—
686#419—131no—
687#419—131no—
688#418—131no—
689#418—131no—
690#418—132no—
691#418—131no—
692#417—132no—
693#417—132no—
694#417—131no—
695#417—132no—
696#416—131no—
697#416—131no—
698#416—132no—
699#416—132no—
700#416—132no—
701C2×#103—131no—
702C2×#102—131no—
703C2×#102—132no—
704#408—131no—
705C2×C22⋊C8—131no—
706#405—131no—
707C22×C13—21no—
708C22×C13—21no—
709C22×C13—21no—
710C22×C13—22no—
711C22×C13—21no—
712C22×C13—21no—
713C22×C13—22no—
714C22×C13—21no—
715C22×C13—21no—
716C22×C13—21no—
717C22×C13—22no—
718C22×C13—24no—
719C22×C13—42no—
720C22×C13—42no—
721C22×C13—41no—
722C22×C13—41no—
723C22×C13—41no—
724C22×C13—82no—
725C22×C13—84no—
726C22×C13—164no—
727C22×C13#54612yes—
728C22×C13C23×D411yescharacteristic
729C2×D13—42no—
730C2×D13—42no—
731C2×D13—42no—
732C2×D13—162no—
733C4×C13—22no—
734C4×C13—22no—
735C4×C13—21no—
736C4×C13—21no—
737C4×C13—22no—
738C4×C13—41no—
739C4×C13—41no—
740C4×C13—41no—
741C4×C13—42no—
742C4×C13#54612yes—
743C4×C13C22×#4111yescharacteristic
744C4×C13C2×H(5,𝔽2)11yescharacteristic
745Dic13—41no—
746Dic13—41no—
747Dic13—41no—
748Dic13—42no—
749Dic13—41no—
750H(5,𝔽2)—24no—
751H(5,𝔽2)—42no—
752C2×#41—21no—
753C2×#41—21no—
754C2×#41—21no—
755C2×#41—24no—
756C2×#41—42no—
757C2×#41—262no—
758C2×#41C22×D1311yescharacteristic
759C2×#41C22×D1312yes—
760C2×#41C22×D1312yes—
761C2×#41C22×D1312yes—
762C2×#41C22×D1311yescharacteristic
763C22×Q8C22×D1311yescharacteristic
764C22×D4—21no—
765C22×D4—22no—
766C22×D4—21no—
767C22×D4—131no—
768C22×D4—261no—
769C22×D4C22×D1312yes—
770C22×D4C22×D1311yescharacteristic
771C23×C4—21no—
772C23×C4C22×D1311yescharacteristic
773AGL(1,ℤ/8)—522no—
774C2×SD16—132no—
775C2×SD16—132no—
776C2×SD16—132no—
777C2×SD16—522no—
778C2×D8—132no—
779C2×D8—132no—
780C2×D8—132no—
781C2×D8—264no—
782#131—522no—
783C2×M16—131no—
784C2×M16—131no—
785C2×M16—132no—
786C2×M16—132no—
787C2×M16—522no—
788C22×C8—131no—
789C22×C8—131no—
790C22×C8—132no—
791C22×C8—132no—
792C4⋊Q8—21no—
793C4⋊Q8—132no—
794C4⋊Q8—261no—
795C4⋊Q8C22×D1312yes—
796#127—261no—
797#126—262no—
798#126—262no—
799#125—132no—
800#125—261no—
801#124—21no—
802#124—261no—
803#124—262no—
804#124—262no—
805#124C22×D1312yes—
806#123—22no—
807#123—21no—
808#123—22no—
809#123—22no—
810#123—22no—
811#123—22no—
812#123—22no—
813#123—22no—
814#123—22no—
815#123—262no—
816#123—262no—
817#123—262no—
818#123—262no—
819#123C22⋊D1312yes—
820C22⋊Q8—21no—
821C22⋊Q8—21no—
822C22⋊Q8—262no—
823C22⋊Q8—262no—
824C22⋊Q8C22⋊D1311yescharacteristic
825C22⋊Q8C22⋊D1311yescharacteristic
826C22⋊Q8C22×D1311yescharacteristic
827C22⋊Q8C22×D1311yescharacteristic
828C22⋊Q8C22×D1312yes—
829C22⋊Q8C22×D1312yes—
830#121—22no—
831#121—22no—
832#121—22no—
833#121—22no—
834#121—132no—
835#121—132no—
836#121—132no—
837#121—132no—
838#121—262no—
839#121—262no—
840#121—262no—
841#121—261no—
842#121—261no—
843#121C22⋊D1311yescharacteristic
844#121C22⋊D1311yescharacteristic
845#121C22×D1311yescharacteristic
846#121C22×D1311yescharacteristic
847#120—21no—
848#120—22no—
849#120—22no—
850#120—262no—
851#120C22⋊D1312yes—
852C4×Q8—261no—
853C4×D4—21no—
854C4×D4—21no—
855C4×D4—21no—
856C4×D4—21no—
857C4×D4—132no—
858C4×D4—132no—
859C4×D4—261no—
860C4×D4—262no—
861C4×D4—261no—
862C4×D4—261no—
863C4×D4—262no—
864C4×D4—262no—
865C4×D4C22×D1312yes—
866C4×D4C22×D1312yes—
867C4×D4C22×D1312yes—
868C4×D4C22×D1312yes—
869#117—131no—
870#117—131no—
871#117—131no—
872#117—131no—
873#117—132no—
874#117—261no—
875#117—261no—
876#117—262no—
877#117C22×D1311yescharacteristic
878#117C22×D1311yescharacteristic
879C2×C4⋊C4—22no—
880C2×C4⋊C4—22no—
881C2×C4⋊C4—131no—
882C2×C4⋊C4—131no—
883C2×C4⋊C4—131no—
884C2×C4⋊C4—132no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—261no—
889C2×C22⋊C4—261no—
890C2×C22⋊C4—262no—
891C2×C42—261no—
892#107—131no—
893#107—131no—
894#107—131no—
895#107—131no—
896#107—132no—
897#106—131no—
898#106—131no—
899#106—131no—
900#106—131no—
901#106—132no—
902C4⋊C8—132no—
903C4⋊C8—132no—
904#103—132no—
905#103—132no—
906#103—131no—
907#103—131no—
908#103—132no—
909#103—132no—
910#103—132no—
911#103—132no—
912#103—132no—
913#103—131no—
914#103—131no—
915#102—132no—
916#102—131no—
917#102—132no—
918#102—132no—
919#102—132no—
920#102—132no—
921#102—132no—
922#102—132no—
923#102—131no—
924#102—131no—
925#102—131no—
926#102—132no—
927#102—132no—
928C22⋊C8—131no—
929C22⋊C8—131no—
930C22⋊C8—131no—
931C22⋊C8—131no—
932C22⋊C8—132no—
933C22⋊C8—132no—
934#97—132no—
935C4×C8—132no—
936C2×C13—22no—
937C2×C13—41no—
938C2×C13—41no—
939C2×C13—42no—
940C2×C13—44no—
941C2×C13—81no—
942C2×C13C2×#54611yescharacteristic
943C2×C13#358411yescharacteristic
944C2×C13#358511yescharacteristic
945D13—82no—
946C24—21no—
947C24—22no—
948C24—261no—
949C24C2×C22⋊D1311yescharacteristic
950#41—22no—
951#41—22no—
952#41—24no—
953#41—24no—
954#41—24no—
955#41—22no—
956#41—22no—
957#41—42no—
958#41—42no—
959#41—42no—
960#41—44no—
961#41—44no—
962#41—44no—
963#41—1044no—
964C2×Q8—21no—
965C2×Q8—22no—
966C2×Q8—22no—
967C2×Q8—262no—
968C2×Q8C2×C22⋊D1311yescharacteristic
969C2×Q8C23×D1312yes—
970C2×Q8C23×D1311yescharacteristic
971C2×D4—24no—
972C2×D4—22no—
973C2×D4—22no—
974C2×D4—21no—
975C2×D4—22no—
976C2×D4—21no—
977C2×D4—21no—
978C2×D4—22no—
979C2×D4—21no—
980C2×D4—22no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—48no—
984C2×D4—44no—
985C2×D4—132no—
986C2×D4—262no—
987C2×D4—262no—
988C2×D4—262no—
989C2×D4—262no—
990C2×D4—262no—
991C2×D4—262no—
992C2×D4—261no—
993C2×D4—1042no—
994C2×D4#612914yescomplemented
995C2×D4C2×C22⋊D1312yes—
996C2×D4C2×C22⋊D1311yescharacteristic
997C2×D4C2×C22⋊D1312yes—
998C2×D4C2×C22⋊D1312yes—
999C2×D4C23×D1311yescharacteristic
1000C2×D4C23×D1312yes—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—21no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—21no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—44no—
1011C22×C4—261no—
1012C22×C4—261no—
1013C22×C4—261no—
1014C22×C4—262no—
1015C22×C4—262no—
1016C22×C4—262no—
1017C22×C4C2×C22⋊D1311yescharacteristic
1018C22×C4C2×C22⋊D1311yescharacteristic
1019C22×C4C2×C22⋊D1311yescharacteristic
1020C22×C4C23×D1311yescharacteristic
1021C22×C4C23×D1312yes—
1022C22×C4C23×D1311yescharacteristic
1023C22×C4C23×D1311yescharacteristic
1024SD16—522no—
1025SD16—522no—
1026SD16—522no—
1027D8—264no—
1028D8—264no—
1029D8—522no—
1030M16—262no—
1031M16—262no—
1032M16—522no—
1033M16—522no—
1034C2×C8—131no—
1035C2×C8—132no—
1036C2×C8—131no—
1037C2×C8—131no—
1038C2×C8—131no—
1039C2×C8—132no—
1040C2×C8—262no—
1041C2×C8—262no—
1042C2×C8—522no—
1043C2×C8—522no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—131no—
1051C4⋊C4—132no—
1052C4⋊C4—131no—
1053C4⋊C4—131no—
1054C4⋊C4—131no—
1055C4⋊C4—261no—
1056C4⋊C4—261no—
1057C4⋊C4—261no—
1058C4⋊C4—262no—
1059C4⋊C4—262no—
1060C4⋊C4—262no—
1061C4⋊C4—262no—
1062C4⋊C4C2×C22⋊D1312yes—
1063C4⋊C4C2×C22⋊D1312yes—
1064C4⋊C4C2×C22⋊D1311yescharacteristic
1065C4⋊C4C2×C22⋊D1311yescharacteristic
1066C4⋊C4C23×D1311yescharacteristic
1067C4⋊C4C23×D1311yescharacteristic
1068C22⋊C4—21no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—21no—
1072C22⋊C4—21no—
1073C22⋊C4—21no—
1074C22⋊C4—21no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—261no—
1080C22⋊C4—261no—
1081C22⋊C4—261no—
1082C22⋊C4—261no—
1083C22⋊C4—262no—
1084C22⋊C4—262no—
1085C22⋊C4—262no—
1086C22⋊C4—262no—
1087C22⋊C4—262no—
1088C22⋊C4—262no—
1089C22⋊C4—262no—
1090C22⋊C4C2×C22⋊D1312yes—
1091C22⋊C4C2×C22⋊D1312yes—
1092C22⋊C4C2×C22⋊D1312yes—
1093C22⋊C4C2×C22⋊D1312yes—
1094C22⋊C4C2×C22⋊D1312yes—
1095C42—21no—
1096C42—261no—
1097C42—261no—
1098C42—261no—
1099C42—261no—
1100C42—262no—
1101C42C23×D1312yes—
1102C13#6118711yescharacteristic, complemented, Sylow
1103C23—22no—
1104C23—22no—
1105C23—24no—
1106C23—21no—
1107C23—41no—
1108C23—41no—
1109C23—44no—
1110C23—81no—
1111C23—81no—
1112C23—82no—
1113C23—82no—
1114C23—262no—
1115C23—522no—
1116C23—1041no—
1117C23—1041no—
1118C23C22×C22⋊D1312yes—
1119C23C22×C22⋊D1311yescharacteristic
1120C23C22×C22⋊D1311yescharacteristic
1121C23C22×C22⋊D1311yescharacteristic
1122Q8—22no—
1123Q8—22no—
1124Q8—21no—
1125Q8—22no—
1126Q8—21no—
1127Q8—42no—
1128Q8—1042no—
1129D4—24no—
1130D4—24no—
1131D4—22no—
1132D4—21no—
1133D4—22no—
1134D4—21no—
1135D4—42no—
1136D4—42no—
1137D4—44no—
1138D4—44no—
1139D4—44no—
1140D4—44no—
1141D4—42no—
1142D4—81no—
1143D4—81no—
1144D4—262no—
1145D4—262no—
1146D4—524no—
1147D4—522no—
1148D4—1042no—
1149D4—1042no—
1150D4—1042no—
1151D4C2×#612914yes—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—82no—
1171C2×C4—82no—
1172C2×C4—261no—
1173C2×C4—261no—
1174C2×C4—261no—
1175C2×C4—261no—
1176C2×C4—262no—
1177C2×C4—522no—
1178C2×C4—1042no—
1179C2×C4—1042no—
1180C2×C4—1041no—
1181C2×C4—1041no—
1182C2×C4—1042no—
1183C2×C4C2×#612912yes—
1184C2×C4#8825112yes—
1185C2×C4C22×C22⋊D1311yescharacteristic
1186C2×C4C22×C22⋊D1312yes—
1187C2×C4C22×C22⋊D1312yes—
1188C2×C4C22×C22⋊D1312yes—
1189C2×C4C22×C22⋊D1311yescharacteristic
1190C2×C4C22×C22⋊D1311yescharacteristic
1191C2×C4C24×D1311yescharacteristic
1192C8—261no—
1193C8—261no—
1194C8—261no—
1195C8—261no—
1196C8—262no—
1197C8—262no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—22no—
1203C22—24no—
1204C22—21no—
1205C22—21no—
1206C22—22no—
1207C22—21no—
1208C22—22no—
1209C22—21no—
1210C22—42no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—82no—
1216C22—84no—
1217C22—164no—
1218C22—522no—
1219C22—522no—
1220C22—522no—
1221C22—2082no—
1222C22#1171951112yes—
1223C22C23×C22⋊D1311yescharacteristic
1224C4—21no—
1225C4—21no—
1226C4—22no—
1227C4—22no—
1228C4—22no—
1229C4—41no—
1230C4—42no—
1231C4—41no—
1232C4—41no—
1233C4—521no—
1234C4—521no—
1235C4—521no—
1236C4—521no—
1237C4—522no—
1238C4#1171951112yes—
1239C4C22×#612911yescharacteristic
1240C4C2×#8825111yescharacteristic
1241C2—22no—
1242C2—41no—
1243C2—41no—
1244C2—42no—
1245C2—44no—
1246C2—81no—
1247C2—1042no—
1248C2C2×#1171951111yescharacteristic
1249C2#1312960711yescharacteristic
1250C2#1312961511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3485C2
socleC22×C13C23×D4
hypercenter#3485D13
hypocenterC13#61187
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #525 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #13128573C2semidirect
2. #13127141C2semidirect
3. #13127037C2semidirect
4. #13126992C2semidirect
5. #13126812C2semidirect
6. #13126812C2semidirect
7. #13126797C2semidirect
8. #13126764C2semidirect
9. #13126686C2semidirect
10. #13125201C2semidirect
11. #13124799C2semidirect
12. #13124745C2semidirect
13. #13124667C2semidirect
14. #13124477C2semidirect
15. #13124457C2semidirect
16. #13124344C2semidirect
17. #13124104C2semidirect
18. C2×#11718899C2semidirect
19. #13123686C2semidirect
20. #13123563C2semidirect
21. #13123362C2semidirect
22. #13123355C2semidirect
23. C13×#3485C2semidirect
28. C13×#547C22semidirect
29. C13×#547C22semidirect
32. C13×#546C22semidirect
33. C13×#546C22semidirect
45. C22×#6106C22semidirect
47. C2×#88184C22semidirect
48. C2×#88180C22semidirect
49. C22×#6099C22semidirect
56. #11719270C22semidirect
57. #11719270C22semidirect
58. #11719268C22semidirect
59. #11719260C22semidirect
60. #11719226C22semidirect
61. #11719224C22semidirect
62. #11718899C22semidirect
63. #11718899C22semidirect
64. #11718899C22semidirect
65. #11718899C22semidirect
66. #11718899C22semidirect
67. #11718899C22semidirect
71. #11718894C22semidirect
72. #11718894C22semidirect
73. #11718894C22semidirect
75. #11718893C22semidirect
76. #11718893C22semidirect
77. #11718893C22semidirect
78. #11718886C22semidirect
79. #11718886C22semidirect
80. C2×#88075C22semidirect
81. #11718878C22semidirect
82. #11718878C22semidirect
85. #11718876C22semidirect
87. C2×#88072C22semidirect
88. C2×C22⋊#1055C22semidirect
89. #11718744C22semidirect
90. #11718744C22semidirect
91. #11718743C22semidirect
92. #11718742C22semidirect
93. #11718718C22semidirect
94. #11718718C22semidirect
95. #11718717C22semidirect
96. #11718716C22semidirect
97. #11718710C22semidirect
98. #11718710C22semidirect
99. #11718710C22semidirect
100. #11718709C22semidirect
101. #11718709C22semidirect
102. #11718709C22semidirect
103. #11718706C22semidirect
104. #11718706C22semidirect
105. #11718706C22semidirect
106. #11718706C22semidirect
107. #11718705C22semidirect
108. #11718705C22semidirect
109. #11718704C22semidirect
110. #11718704C22semidirect
111. #11718700C22semidirect
112. #11718699C22semidirect
113. #11718696C22semidirect
114. #11718696C22semidirect
115. #11718695C22semidirect
116. #11718694C22semidirect
117. #11718675C22semidirect
118. #11718675C22semidirect
119. C4×#6104C22semidirect
120. C4×#6104C22semidirect
121. #11718673C22semidirect
122. #11718672C22semidirect
123. #11718672C22semidirect
124. D4×#1055C22semidirect
125. #11718670C22semidirect
126. #11718670C22semidirect
127. #11718669C22semidirect
128. #11718668C22semidirect
129. #11718662C22semidirect
130. #11718660C22semidirect
131. #11718659C22semidirect
132. #11718659C22semidirect
133. #11718658C22semidirect
134. #11718656C22semidirect
363. C2×D4×C13#41semidirect
479. #3485D13semidirect
610. #547C2×D13semidirect
611. #547C2×D13semidirect
615. #546C2×D13semidirect
616. #546C2×D13semidirect
994. C2×D4#6129semidirect
1102. C13#61187semidirect

Maximal subgroups

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

subgroupindex
#131285732
#131271412
#131270372
#131269922
#131268122
#131267972
#131267642
#131266862
#131252012
#131247992
#131247452
#131246672
#131244772
#131244572
#131243442
#131241042
C2×#117188992
#131236862
#131235632
#131233622
#131233552
C13×#34852
#6118713