Finite Group Databasebeta

← #16740475

Subgroups — #16740475

Order 3328.

2092 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128573C211yesmaximal, characteristic, complemented
2#13127141C212yesmaximal, complemented
3#13127130C212yesmaximal, complemented
4#13127089C212yesmaximal, complemented
5#13127037C212yesmaximal, complemented
6#13127007C212yesmaximal, complemented
7#13126992C212yesmaximal, complemented
8#13126827C212yesmaximal, complemented
9#13126812C212yesmaximal, complemented
10#13125201C211yesmaximal, characteristic, complemented
11#13124810C211yesmaximal, characteristic, complemented
12#13124780C211yesmaximal, characteristic, complemented
13#13124687C211yesmaximal, characteristic, complemented
14#13124518C211yesmaximal, characteristic, complemented
15C2×#11718710C211yesmaximal, characteristic, complemented
16#13124344C211yesmaximal, characteristic, complemented
17#13124122C211yesmaximal, characteristic, complemented
18#13124088C211yesmaximal, characteristic, complemented
19#13123664C211yesmaximal, characteristic, complemented
20#13123540C211yesmaximal, characteristic, complemented
21#13123369C211yesmaximal, characteristic, complemented
22#13123355C211yesmaximal, characteristic, complemented
23C13×#3489C211yesmaximal, characteristic, complemented
24C2×C13×2−1+4C2211yescharacteristic
25C22×C13×#41C2211yescharacteristic
26D4×Q8×C13C2212yescomplemented
27C13×#548C2212yescomplemented
28C13×#547—22no—
29C13×#547C2212yescomplemented
30C13×#546—22no—
31C13×#546C2212yescomplemented
32C13×#537—21no—
33C13×#537C2211yescharacteristic
34C13×#536—21no—
35C13×#536C2211yescharacteristic
36C13×#525—21no—
37C13×#525C2211yescharacteristic
38C2×C13×C22⋊Q8—21no—
39C2×C13×C22⋊Q8C2211yescharacteristic
40C13×#520C2211yescharacteristic
41#11719535C2211yescharacteristic, complemented
42#11719532C2211yescharacteristic, complemented
43C2×#88203C2211yescharacteristic
44C2×#88203C2211yescharacteristic
45C2×#88202C2211yescharacteristic, complemented
46C22×#6106C2211yescharacteristic, complemented
47C2×#88184C2211yescharacteristic
48C2×#88180C2211yescharacteristic
49C22×#6099C2211yescharacteristic
50#11719363—22no—
51#11719348—21no—
52#11719329—21no—
53#11719324—21no—
54#11719301—21no—
55#11719296—22no—
56#11719270C2212yes—
57#11719270C2212yescomplemented
58#11719268C2212yes—
59#11719260C2212yescomplemented
60#11719226C2211yescharacteristic, complemented
61#11719224C2211yescharacteristic, complemented
62#11718899C2212yes—
63#11718899C2212yes—
64#11718899C2212yescomplemented
65#11718899C2212yescomplemented
66#11718895C2211yescharacteristic, complemented
67#11718894C2211yescharacteristic
68#11718894C2211yescharacteristic
69#11718894C2211yescharacteristic
70#11718894C2211yescharacteristic
71#11718894C2212yescomplemented
72#11718893C2211yescharacteristic
73#11718893C2211yescharacteristic
74#11718893C2211yescharacteristic, complemented
75#11718893C2211yescharacteristic, complemented
76#11718893C2211yescharacteristic, complemented
77#11718893C2211yescharacteristic, complemented
78#11718893C2212yescomplemented
79#11718888C2212yes—
80#11718888C2212yescomplemented
81#11718888C2212yescomplemented
82#11718886C2211yescharacteristic, complemented
83#11718886C2211yescharacteristic, complemented
84#11718886C2211yescharacteristic, complemented
85#11718886C2211yescharacteristic, complemented
86#11718886C2212yescomplemented
87C2×#88075C2211yescharacteristic, complemented
88C2×#88075C2212yescomplemented
89#11718878C2212yes—
90#11718876C2211yescharacteristic, complemented
91#11718876C2211yescharacteristic, complemented
92#11718868C2211yescharacteristic
93#11718744C2212yescomplemented
94#11718744C2212yescomplemented
95#11718743C2212yescomplemented
96#11718742C2212yescomplemented
97#11718718C2212yescomplemented
98#11718718C2212yescomplemented
99#11718717C2212yescomplemented
100#11718716C2212yescomplemented
101#11718710C2212yes—
102#11718710C2212yes—
103#11718710C2212yescomplemented
104#11718710C2212yescomplemented
105#11718710C2212yescomplemented
106#11718709C2212yescomplemented
107#11718706C2212yescomplemented
108#11718706C2212yescomplemented
109#11718706C2212yescomplemented
110#11718705C2212yescomplemented
111#11718705C2212yescomplemented
112#11718704C2212yescomplemented
113#11718700C2212yescomplemented
114#11718699C2212yescomplemented
115#11718696C2212yescomplemented
116#11718694C2212yescomplemented
117#11718687C2212yescomplemented
118C4×#6106C2212yescomplemented
119#11718683C2212yescomplemented
120#11718682C2212yescomplemented
121#11718675C2212yescomplemented
122C4×#6104C2212yescomplemented
123#11718673C2212yescomplemented
124#11718673C2212yescomplemented
125#11718672C2212yescomplemented
126#11718672C2212yescomplemented
127#11718670C2212yescomplemented
128#11718668C2212yescomplemented
129#11718660C2211yescharacteristic, complemented
130#11718658C2211yescharacteristic, complemented
131C2×#88049C2211yescharacteristic, complemented
132#11718625C2211yescharacteristic, complemented
133#11718625C2211yescharacteristic, complemented
134C2×#88047C2211yescharacteristic, complemented
135C13×2−1+4—24no—
136C13×2−1+4—42no—
137C2×C13×#41—21no—
138C2×C13×#41—22no—
139C2×C13×#41—21no—
140C2×C13×#41—21no—
141C2×C13×#41—24no—
142C2×C13×#41—42no—
143C2×C13×#41C2311yescharacteristic
144C2×C13×#41C2312yes—
145C2×C13×#41C2311yescharacteristic
146C2×C13×#41C2311yescharacteristic
147C2×C13×#41C2311yescharacteristic
148C2×C13×#41C2311yescharacteristic
149C22×Q8×C13—21no—
150C22×Q8×C13C2311yescharacteristic
151C22×Q8×C13C2312yes—
152C22×Q8×C13C2311yescharacteristic
153C22×D4×C13—21no—
154C22×D4×C13C2311yescharacteristic
155C23×C4×C13—21no—
156C23×C4×C13C2311yescharacteristic
157C22×C22⋊D13—21no—
158C2×#6129—22no—
159C22×D52C2311yescharacteristic
160C13×C4⋊Q8—22no—
161C13×C4⋊Q8C2312yes—
162C13×#124—22no—
163C13×#124C2312yes—
164C13×#123—22no—
165C13×#123—22no—
166C13×#123—22no—
167C13×#123—22no—
168C13×#123D412yes—
169C13×C22⋊Q8—21no—
170C13×C22⋊Q8—21no—
171C13×C22⋊Q8—21no—
172C13×C22⋊Q8—21no—
173C13×C22⋊Q8—22no—
174C13×C22⋊Q8—21no—
175C13×C22⋊Q8—22no—
176C13×C22⋊Q8—22no—
177C13×C22⋊Q8D411yescharacteristic
178C13×C22⋊Q8D411yescharacteristic
179C13×C22⋊Q8C2312yes—
180C13×C22⋊Q8C2312yes—
181C13×C22⋊Q8C2312yes—
182C13×#121—21no—
183C13×#121—22no—
184C13×#121—22no—
185C13×#121—22no—
186C13×#121—22no—
187C13×#121D411yescharacteristic
188C13×#121D411yescharacteristic
189C13×#121C2312yes—
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⋊C4—21no—
203C2×C13×C4⋊C4—22no—
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C22⋊C4—21no—
206C2×C13×C22⋊C4—22no—
207C2×C22⋊Dic13—21no—
208#88203—24no—
209#88203—42no—
210#88202—42no—
211#88201—21no—
212Q8×Dic13—21no—
213C2×#6106—42no—
214C2×#6106C2312yes—
215C2×#6106C2312yes—
216C2×#6106C2312yes—
217C2×#6106C2312yes—
218#88194—21no—
219#88193—22no—
220#88193—22no—
221#88192—22no—
222#88191—22no—
223D4×Dic13—22no—
224D4×Dic13—21no—
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#88180C2312yes—
237#88180C2311yescharacteristic
238#88180C2311yescharacteristic
239#88180C2311yescharacteristic
240#88180C2311yescharacteristic
241C2×C4⋊Dic13C2312yes—
242C2×C4⋊Dic13C2311yescharacteristic
243C2×C4⋊Dic13C2311yescharacteristic
244C2×C4⋊Dic13C2311yescharacteristic
245C2×C4×Dic13—21no—
246C2×#6099—42no—
247C2×#6099C2311yescharacteristic
248C2×#6099C2311yescharacteristic
249C2×#6099C2311yescharacteristic
250C2×#6099C2311yescharacteristic
251C2×#6099C2312yes—
252C2×#6099C2311yescharacteristic
253C2×#6099C2311yescharacteristic
254C22×#1055C2311yescharacteristic
255C22×#1055C2311yescharacteristic
256C22×#1055C2312yes—
257#88152—22no—
258#88152—22no—
259#88151—22no—
260#88147—21no—
261#88147—21no—
262#88146—22no—
263#88144—21no—
264#88142—21no—
265#88140—22no—
266#88140—22no—
267#88139—22no—
268#88139—22no—
269#88137—22no—
270#88137—22no—
271#88135—22no—
272#88135—22no—
273C22⋊C4×D13—22no—
274#88132—22no—
275C4×D52C2312yes—
276C4×D52C2312yes—
277#88124C2312yes—
278#88123C2312yes—
279#88075C2311yescharacteristic
280#88075C2312yes—
281#88075C2311yescharacteristic
282#88075C2311yescharacteristic
283#88075C2311yescharacteristic
284#88075C2312yes—
285#88075C2312yes—
286#88075C2311yescharacteristic
287#88075C2312yes—
288#88075C2312yes—
289#88075C2312yes—
290#88075C2311yescharacteristic
291#88075C2311yescharacteristic
292#88075C2312yes—
293#88075C2312yes—
294#88075C2311yescharacteristic
295#88072C2311yescharacteristic
296#88072C2312yes—
297#88072C2311yescharacteristic
298#88072C2311yescharacteristic
299#88072C2311yescharacteristic
300#88072C2311yescharacteristic
301#88072C2312yes—
302#88072C2311yescharacteristic
303#88072C2311yescharacteristic
304#88072C2311yescharacteristic
305C22⋊#1055C2312yes—
306C22⋊#1055C2312yes—
307C22⋊#1055C2312yes—
308C22⋊#1055C2312yes—
309#88049C2312yes—
310#88049C2312yes—
311#88048C2312yes—
312#88048C2312yes—
313#88047C2312yes—
314#88047C2312yes—
315#88047C2312yes—
316#88047C2312yes—
317C4⋊#1055C2312yes—
318C4⋊#1055C2312yes—
319#88043C2312yes—
320C4×#1055C2312yes—
321#61182—131nomaximal, Sylow
322C24×C13—21no—
323C24×C13C2×D411yescharacteristic
324C23×D13—21no—
325C13×#41—22no—
326C13×#41—22no—
327C13×#41—22no—
328C13×#41—22no—
329C13×#41—22no—
330C13×#41—24no—
331C13×#41—22no—
332C13×#41—22no—
333C13×#41—44no—
334C13×#41—41no—
335C13×#41—41no—
336C13×#41—42no—
337C13×#41—44no—
338C13×#41—44no—
339C13×#41—48no—
340C13×#41#4114yescomplemented
341C2×Q8×C13—21no—
342C2×Q8×C13—22no—
343C2×Q8×C13—21no—
344C2×Q8×C13—22no—
345C2×Q8×C13—24no—
346C2×Q8×C13—22no—
347C2×Q8×C13—22no—
348C2×Q8×C13—41no—
349C2×Q8×C13—42no—
350C2×Q8×C13—44no—
351C2×Q8×C13C2×D411yescharacteristic
352C2×Q8×C13C2412yes—
353C2×Q8×C13C2411yescharacteristic
354C2×Q8×C13C2411yescharacteristic
355C2×D4×C13—21no—
356C2×D4×C13—22no—
357C2×D4×C13—22no—
358C2×D4×C13—21no—
359C2×D4×C13—21no—
360C2×D4×C13—21no—
361C2×D4×C13—22no—
362C2×D4×C13—21no—
363C2×D4×C13—41no—
364C2×D4×C13—44no—
365C2×D4×C13C2×D412yes—
366C2×D4×C13C2×D411yescharacteristic
367C2×D4×C13C2×D412yes—
368C2×D4×C13C2×D412yes—
369C2×D4×C13C2411yescharacteristic
370C2×D4×C13C2411yescharacteristic
371C22×C4×C13—21no—
372C22×C4×C13—22no—
373C22×C4×C13—22no—
374C22×C4×C13—21no—
375C22×C4×C13—22no—
376C22×C4×C13—21no—
377C22×C4×C13—21no—
378C22×C4×C13—22no—
379C22×C4×C13—21no—
380C22×C4×C13—21no—
381C22×C4×C13—21no—
382C22×C4×C13—22no—
383C22×C4×C13—44no—
384C22×C4×C13C2×D411yescharacteristic
385C22×C4×C13C2×D411yescharacteristic
386C22×C4×C13C2×D411yescharacteristic
387C22×C4×C13C2412yes—
388C22×C4×C13C2411yescharacteristic
389C22×C4×C13C2411yescharacteristic
390C22×C4×C13C2411yescharacteristic
391C2×C22⋊D13—22no—
392C2×C22⋊D13—22no—
393C2×C22⋊D13—22no—
394C2×C22⋊D13—22no—
395C2×C22⋊D13—82no—
396C22×Dic13—21no—
397C22×Dic13—21no—
398C22×Dic13—21no—
399C22×Dic13—22no—
400#6129—84no—
401C2×D52—22no—
402C2×D52—22no—
403C2×D52—21no—
404C2×D52C2412yes—
405C2×C4×D13—22no—
406C2×C4×D13—22no—
407C2×Dic26—22no—
408C13×C4⋊C4—22no—
409C13×C4⋊C4—21no—
410C13×C4⋊C4—22no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4—22no—
413C13×C4⋊C4—22no—
414C13×C4⋊C4—22no—
415C13×C4⋊C4C2×D411yescharacteristic
416C13×C4⋊C4C2×D411yescharacteristic
417C13×C4⋊C4C2×D412yes—
418C13×C4⋊C4C2×D412yes—
419C13×C4⋊C4C2412yes—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4—22no—
426C13×C22⋊C4—22no—
427C13×C22⋊C4C2×D412yes—
428C13×C22⋊C4C2×D412yes—
429C13×C22⋊C4C2×D412yes—
430C13×C22⋊C4C2×D412yes—
431C13×C22⋊C4C2×D412yes—
432C42×C13—22no—
433C42×C13C2412yes—
434C22⋊Dic13—21no—
435C22⋊Dic13—21no—
436C22⋊Dic13—21no—
437C22⋊Dic13—22no—
438C22⋊Dic13—21no—
439#6106—24no—
440#6106—42no—
441#6106—42no—
442#6106—42no—
443#6104—24no—
444#6104—42no—
445#6103—22no—
446#6103—22no—
447#6103—22no—
448#6103—22no—
449#6103—22no—
450#6103—22no—
451C4⋊Dic13—22no—
452C4⋊Dic13—21no—
453C4⋊Dic13—22no—
454C4⋊Dic13—21no—
455C4⋊Dic13—21no—
456C4⋊Dic13C2411yescharacteristic
457C4⋊Dic13C2412yes—
458C4⋊Dic13C2411yescharacteristic
459C4⋊Dic13C2411yescharacteristic
460C4⋊Dic13C2411yescharacteristic
461#6101—22no—
462#6101—22no—
463C4×Dic13—21no—
464C4×Dic13—22no—
465C4×Dic13—21no—
466C4×Dic13—21no—
467C4×Dic13—21no—
468#6099—22no—
469#6099—22no—
470#6099—41no—
471#6099—41no—
472#6099—41no—
473#6099—41no—
474#6099—42no—
475C2×#1055—22no—
476C2×#1055—22no—
477C2×#1055—42no—
478C2×#1055C2412yes—
479C2×#1055C2411yescharacteristic
480C2×#1055C2411yescharacteristic
481C2×#1055C2412yes—
482C2×#1055C2411yescharacteristic
483C2×#1055C2411yescharacteristic
484#3494—131no—
485#3489D1311yescharacteristic, complemented
486#3330—132no—
487#3329—132no—
488#3326—132no—
489#3322—132no—
490#3320—132no—
491#3319—132no—
492#3308—132no—
493#3307—132no—
494#3137—131no—
495#3098—131no—
496#3095—131no—
497#3083—131no—
498#3062—131no—
499C2×#468—131no—
500#3042—131no—
501#3010—131no—
502#3006—131no—
503#2946—131no—
504#2930—131no—
505#2898—131no—
506#2896—131no—
507C23×C13—21no—
508C23×C13—22no—
509C23×C13—21no—
510C23×C13—41no—
511C23×C13—41no—
512C23×C13—42no—
513C23×C13—42no—
514C23×C13—81no—
515C23×C13C22×D411yescharacteristic
516C23×C13C22×D412yes—
517C23×C13C22×D411yescharacteristic
518C23×C13C22×D411yescharacteristic
519C22×D13—22no—
520C22×D13—42no—
521C22×D13—81no—
522C22×D13—81no—
523Q8×C13—22no—
524Q8×C13—21no—
525Q8×C13—22no—
526Q8×C13—21no—
527Q8×C13—22no—
528Q8×C13—21no—
529Q8×C13—44no—
530Q8×C13—42no—
531Q8×C13—42no—
532Q8×C13C2×#4112yes—
533D4×C13—24no—
534D4×C13—24no—
535D4×C13—22no—
536D4×C13—21no—
537D4×C13—21no—
538D4×C13—21no—
539D4×C13—42no—
540D4×C13—42no—
541D4×C13—42no—
542D4×C13—42no—
543D4×C13—42no—
544D4×C13—44no—
545D4×C13—42no—
546D4×C13—82no—
547D4×C13C2×#4112yes—
548C2×C4×C13—22no—
549C2×C4×C13—21no—
550C2×C4×C13—22no—
551C2×C4×C13—22no—
552C2×C4×C13—24no—
553C2×C4×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—22no—
556C2×C4×C13—22no—
557C2×C4×C13—21no—
558C2×C4×C13—21no—
559C2×C4×C13—22no—
560C2×C4×C13—22no—
561C2×C4×C13—21no—
562C2×C4×C13—42no—
563C2×C4×C13—42no—
564C2×C4×C13—42no—
565C2×C4×C13—44no—
566C2×C4×C13—44no—
567C2×C4×C13—42no—
568C2×C4×C13—42no—
569C2×C4×C13—82no—
570C2×C4×C13—81no—
571C2×C4×C13C22×D411yescharacteristic
572C2×C4×C13C22×D412yes—
573C2×C4×C13C22×D412yes—
574C2×C4×C13C22×D412yes—
575C2×C4×C13C22×D411yescharacteristic
576C2×C4×C13C22×D411yescharacteristic
577C2×C4×C13C2×#4112yes—
578C2×C4×C13H(5,𝔽2)12yes—
579C2×C4×C13C2511yescharacteristic
580C22⋊D13—44no—
581C22⋊D13—82no—
582C22⋊D13—82no—
583C22⋊D13—82no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—22no—
589C2×Dic13—42no—
590C2×Dic13—82no—
591C2×Dic13—81no—
592C2×Dic13—81no—
593D52—22no—
594D52—22no—
595D52—42no—
596C4×D13—82no—
597C4×D13—82no—
598Dic26—82no—
599#1055—22no—
600#1055—21no—
601#1055—21no—
602#1055—21no—
603#1055—21no—
604#1055—22no—
605C2×2−1+4C2×D1311yescharacteristic
606C22×#41C2×D1311yescharacteristic
607C2×AGL(1,ℤ/8)—131no—
608C2×AGL(1,ℤ/8)—131no—
609C22×SD16—131no—
610C2×#131—131no—
611C22×M16—131no—
612#555—132no—
613#553—132no—
614#553—132no—
615#551—262no—
616D4×Q8C2×D1312yescomplemented
617#548C2×D1312yescomplemented
618#547—22no—
619#547—132no—
620#547C2×D1312yescomplemented
621#546—22no—
622#546—262no—
623#546C2×D1312yescomplemented
624#544—131no—
625#542—261no—
626#540—261no—
627#537—21no—
628#537C2×D1311yescharacteristic
629#536—21no—
630#536C2×D1311yescharacteristic
631#535—131no—
632#532—261no—
633#529—261no—
634#525—21no—
635#525C2×D1311yescharacteristic
636C2×C22⋊Q8—21no—
637C2×C22⋊Q8C2×D1311yescharacteristic
638C2×#121—131no—
639#520—131no—
640#520C2×D1311yescharacteristic
641#518—131no—
642C2×#117—131no—
643#491—132no—
644#489—132no—
645#488—132no—
646#487—132no—
647#485—132no—
648#485—132no—
649#485—132no—
650#484—132no—
651#484—132no—
652#483—132no—
653#482—132no—
654#480—132no—
655#479—132no—
656#478—132no—
657#477—132no—
658#474—132no—
659#469—132no—
660#468—132no—
661#468—132no—
662#468—132no—
663#468—132no—
664#468—132no—
665#466—132no—
666#465—132no—
667#463—132no—
668#463—132no—
669#461—132no—
670#461—132no—
671#449—132no—
672#449—132no—
673#449—132no—
674#449—132no—
675#448—132no—
676#448—132no—
677#448—132no—
678#447—132no—
679#442—132no—
680#440—132no—
681C4×SD16—132no—
682C4×D8—132no—
683#436—132no—
684#436—132no—
685#435—132no—
686#435—132no—
687#428—131no—
688#428—131no—
689C2×#107—131no—
690#424—131no—
691#419—131no—
692#419—132no—
693#419—131no—
694#419—131no—
695#419—131no—
696#418—131no—
697#418—131no—
698#417—131no—
699#417—132no—
700#417—131no—
701#417—131no—
702#417—131no—
703#417—131no—
704#417—131no—
705#416—131no—
706#416—131no—
707#416—131no—
708#416—131no—
709#416—132no—
710C2×#103—131no—
711C2×#103—132no—
712C2×#102—131no—
713#408—131no—
714#407—131no—
715#405—131no—
716C22×C13—21no—
717C22×C13—21no—
718C22×C13—21no—
719C22×C13—22no—
720C22×C13—21no—
721C22×C13—21no—
722C22×C13—22no—
723C22×C13—21no—
724C22×C13—21no—
725C22×C13—21no—
726C22×C13—22no—
727C22×C13—22no—
728C22×C13—41no—
729C22×C13—41no—
730C22×C13—41no—
731C22×C13—41no—
732C22×C13—41no—
733C22×C13—82no—
734C22×C13—84no—
735C22×C13#54612yes—
736C22×C13C23×D411yescharacteristic
737C2×D13—42no—
738C2×D13—42no—
739C2×D13—42no—
740C2×D13—162no—
741C4×C13—22no—
742C4×C13—22no—
743C4×C13—21no—
744C4×C13—21no—
745C4×C13—22no—
746C4×C13—22no—
747C4×C13—42no—
748C4×C13—41no—
749C4×C13—42no—
750C4×C13#54612yes—
751C4×C13C22×#4111yescharacteristic
752C4×C13C2×H(5,𝔽2)11yescharacteristic
753Dic13—41no—
754Dic13—42no—
755Dic13—41no—
756Dic13—41no—
757Dic13—41no—
7582−1+4—24no—
7592−1+4—42no—
760C2×#41—21no—
761C2×#41—22no—
762C2×#41—21no—
763C2×#41—21no—
764C2×#41—24no—
765C2×#41—42no—
766C2×#41—262no—
767C2×#41C22×D1311yescharacteristic
768C2×#41C22×D1312yes—
769C2×#41C22×D1311yescharacteristic
770C2×#41C22×D1311yescharacteristic
771C2×#41C22×D1311yescharacteristic
772C2×#41C22×D1311yescharacteristic
773C22×Q8—21no—
774C22×Q8C22×D1311yescharacteristic
775C22×Q8C22×D1312yes—
776C22×Q8C22×D1311yescharacteristic
777C22×D4—21no—
778C22×D4—131no—
779C22×D4—261no—
780C22×D4C22×D1311yescharacteristic
781C23×C4—21no—
782C23×C4C22×D1311yescharacteristic
783AGL(1,ℤ/8)—264no—
784AGL(1,ℤ/8)—522no—
785C2×SD16—132no—
786C2×SD16—132no—
787C2×SD16—132no—
788C2×SD16—132no—
789C2×SD16—522no—
790C2×D8—132no—
791C2×D8—132no—
792#131—522no—
793C2×M16—131no—
794C2×M16—131no—
795C2×M16—131no—
796C2×M16—131no—
797C2×M16—131no—
798C2×M16—131no—
799C2×M16—132no—
800C2×M16—522no—
801C22×C8—131no—
802C22×C8—131no—
803C22×C8—132no—
804C4⋊Q8—22no—
805C4⋊Q8—132no—
806C4⋊Q8—261no—
807C4⋊Q8C22×D1312yes—
808#127—261no—
809#126—262no—
810#126—262no—
811#125—132no—
812#125—261no—
813#124—22no—
814#124—261no—
815#124—262no—
816#124—262no—
817#124C22×D1312yes—
818#123—22no—
819#123—22no—
820#123—22no—
821#123—22no—
822#123—262no—
823#123—262no—
824#123—262no—
825#123—262no—
826#123C22⋊D1312yes—
827C22⋊Q8—21no—
828C22⋊Q8—21no—
829C22⋊Q8—21no—
830C22⋊Q8—21no—
831C22⋊Q8—22no—
832C22⋊Q8—21no—
833C22⋊Q8—22no—
834C22⋊Q8—22no—
835C22⋊Q8—262no—
836C22⋊Q8—262no—
837C22⋊Q8C22⋊D1311yescharacteristic
838C22⋊Q8C22⋊D1311yescharacteristic
839C22⋊Q8C22×D1312yes—
840C22⋊Q8C22×D1312yes—
841C22⋊Q8C22×D1312yes—
842#121—21no—
843#121—22no—
844#121—22no—
845#121—22no—
846#121—22no—
847#121—132no—
848#121—132no—
849#121—132no—
850#121—132no—
851#121—262no—
852#121—262no—
853#121—262no—
854#121—261no—
855#121—261no—
856#121C22⋊D1311yescharacteristic
857#121C22⋊D1311yescharacteristic
858#121C22×D1312yes—
859#120—22no—
860#120—262no—
861#120C22⋊D1312yes—
862C4×Q8—261no—
863C4×Q8C22×D1312yes—
864C4×D4—22no—
865C4×D4—22no—
866C4×D4—22no—
867C4×D4—132no—
868C4×D4—132no—
869C4×D4—261no—
870C4×D4—262no—
871C4×D4—261no—
872C4×D4—261no—
873C4×D4—262no—
874C4×D4—262no—
875C4×D4C22×D1312yes—
876C4×D4C22×D1312yes—
877C4×D4C22×D1312yes—
878#117—21no—
879#117—131no—
880#117—131no—
881#117—131no—
882#117—131no—
883#117—132no—
884#117—261no—
885#117—261no—
886#117—262no—
887#117C22×D1311yescharacteristic
888C2×C4⋊C4—21no—
889C2×C4⋊C4—21no—
890C2×C4⋊C4—22no—
891C2×C4⋊C4—131no—
892C2×C4⋊C4—131no—
893C2×C4⋊C4—131no—
894C2×C4⋊C4—132no—
895C2×C4⋊C4C22×D1311yescharacteristic
896C2×C22⋊C4—21no—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—261no—
899C2×C22⋊C4—261no—
900C2×C22⋊C4—262no—
901C2×C42—261no—
902#107—132no—
903#107—132no—
904#107—132no—
905#107—132no—
906#106—132no—
907#106—132no—
908C4⋊C8—132no—
909C4⋊C8—132no—
910#103—131no—
911#103—132no—
912#103—132no—
913#103—132no—
914#103—132no—
915#103—131no—
916#103—131no—
917#103—131no—
918#103—131no—
919#103—131no—
920#103—131no—
921#103—131no—
922#103—132no—
923#103—132no—
924#103—132no—
925#103—132no—
926#102—131no—
927#102—131no—
928#102—132no—
929#102—131no—
930#102—131no—
931#102—131no—
932#102—131no—
933#102—131no—
934#102—131no—
935#102—132no—
936#102—132no—
937#102—132no—
938C22⋊C8—132no—
939C22⋊C8—132no—
940C22⋊C8—132no—
941C22⋊C8—132no—
942#97—132no—
943C4×C8—132no—
944C2×C13—22no—
945C2×C13—42no—
946C2×C13—41no—
947C2×C13—41no—
948C2×C13—42no—
949C2×C13—81no—
950C2×C13C2×#54611yescharacteristic
951C2×C13#358511yescharacteristic
952C2×C13#358611yescharacteristic
953D13—82no—
954C24—21no—
955C24—261no—
956C24C2×C22⋊D1311yescharacteristic
957#41—22no—
958#41—22no—
959#41—22no—
960#41—22no—
961#41—22no—
962#41—24no—
963#41—22no—
964#41—22no—
965#41—44no—
966#41—41no—
967#41—41no—
968#41—42no—
969#41—44no—
970#41—44no—
971#41—48no—
972#41—1044no—
973#41#612914yescomplemented
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—21no—
977C2×Q8—22no—
978C2×Q8—24no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—41no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—262no—
985C2×Q8C2×C22⋊D1311yescharacteristic
986C2×Q8C23×D1312yes—
987C2×Q8C23×D1311yescharacteristic
988C2×Q8C23×D1311yescharacteristic
989C2×D4—21no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—21no—
993C2×D4—21no—
994C2×D4—21no—
995C2×D4—22no—
996C2×D4—21no—
997C2×D4—41no—
998C2×D4—44no—
999C2×D4—132no—
1000C2×D4—262no—
1001C2×D4—262no—
1002C2×D4—262no—
1003C2×D4—262no—
1004C2×D4—262no—
1005C2×D4—262no—
1006C2×D4—261no—
1007C2×D4—1042no—
1008C2×D4C2×C22⋊D1312yes—
1009C2×D4C2×C22⋊D1311yescharacteristic
1010C2×D4C2×C22⋊D1312yes—
1011C2×D4C2×C22⋊D1312yes—
1012C2×D4C23×D1311yescharacteristic
1013C2×D4C23×D1311yescharacteristic
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—22no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—22no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—21no—
1025C22×C4—22no—
1026C22×C4—44no—
1027C22×C4—261no—
1028C22×C4—261no—
1029C22×C4—261no—
1030C22×C4—262no—
1031C22×C4—262no—
1032C22×C4—262no—
1033C22×C4C2×C22⋊D1311yescharacteristic
1034C22×C4C2×C22⋊D1311yescharacteristic
1035C22×C4C2×C22⋊D1311yescharacteristic
1036C22×C4C23×D1311yescharacteristic
1037C22×C4C23×D1312yes—
1038C22×C4C23×D1311yescharacteristic
1039C22×C4C23×D1311yescharacteristic
1040SD16—264no—
1041SD16—522no—
1042SD16—522no—
1043SD16—522no—
1044D8—264no—
1045D8—522no—
1046M16—262no—
1047M16—262no—
1048M16—521no—
1049M16—521no—
1050M16—521no—
1051M16—521no—
1052M16—522no—
1053C2×C8—131no—
1054C2×C8—132no—
1055C2×C8—131no—
1056C2×C8—131no—
1057C2×C8—131no—
1058C2×C8—132no—
1059C2×C8—262no—
1060C2×C8—262no—
1061C2×C8—522no—
1062C4⋊C4—22no—
1063C4⋊C4—21no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—131no—
1070C4⋊C4—131no—
1071C4⋊C4—131no—
1072C4⋊C4—132no—
1073C4⋊C4—131no—
1074C4⋊C4—261no—
1075C4⋊C4—261no—
1076C4⋊C4—261no—
1077C4⋊C4—262no—
1078C4⋊C4—262no—
1079C4⋊C4—262no—
1080C4⋊C4—262no—
1081C4⋊C4C2×C22⋊D1311yescharacteristic
1082C4⋊C4C2×C22⋊D1312yes—
1083C4⋊C4C2×C22⋊D1311yescharacteristic
1084C4⋊C4C2×C22⋊D1312yes—
1085C4⋊C4C23×D1312yes—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—261no—
1094C22⋊C4—261no—
1095C22⋊C4—261no—
1096C22⋊C4—261no—
1097C22⋊C4—262no—
1098C22⋊C4—262no—
1099C22⋊C4—262no—
1100C22⋊C4—262no—
1101C22⋊C4—262no—
1102C22⋊C4—262no—
1103C22⋊C4—262no—
1104C22⋊C4C2×C22⋊D1312yes—
1105C22⋊C4C2×C22⋊D1312yes—
1106C22⋊C4C2×C22⋊D1312yes—
1107C22⋊C4C2×C22⋊D1312yes—
1108C22⋊C4C2×C22⋊D1312yes—
1109C42—22no—
1110C42—261no—
1111C42—261no—
1112C42—261no—
1113C42—261no—
1114C42—262no—
1115C42C23×D1312yes—
1116C13#6118211yescharacteristic, complemented, Sylow
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—41no—
1121C23—41no—
1122C23—42no—
1123C23—42no—
1124C23—81no—
1125C23—262no—
1126C23—522no—
1127C23—1041no—
1128C23—1041no—
1129C23C22×C22⋊D1311yescharacteristic
1130C23C22×C22⋊D1311yescharacteristic
1131C23C22×C22⋊D1312yes—
1132C23C22×C22⋊D1311yescharacteristic
1133Q8—22no—
1134Q8—21no—
1135Q8—22no—
1136Q8—21no—
1137Q8—22no—
1138Q8—21no—
1139Q8—44no—
1140Q8—42no—
1141Q8—42no—
1142Q8—1042no—
1143Q8C2×#612912yes—
1144D4—24no—
1145D4—24no—
1146D4—22no—
1147D4—21no—
1148D4—21no—
1149D4—21no—
1150D4—42no—
1151D4—42no—
1152D4—42no—
1153D4—42no—
1154D4—42no—
1155D4—44no—
1156D4—42no—
1157D4—82no—
1158D4—262no—
1159D4—262no—
1160D4—524no—
1161D4—522no—
1162D4—1042no—
1163D4—1042no—
1164D4—1042no—
1165D4C2×#612912yes—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—82no—
1188C2×C4—81no—
1189C2×C4—261no—
1190C2×C4—261no—
1191C2×C4—261no—
1192C2×C4—261no—
1193C2×C4—262no—
1194C2×C4—522no—
1195C2×C4—1042no—
1196C2×C4—1042no—
1197C2×C4—1041no—
1198C2×C4—1041no—
1199C2×C4—1042no—
1200C2×C4C2×#612912yes—
1201C2×C4#8825112yes—
1202C2×C4C22×C22⋊D1312yes—
1203C2×C4C22×C22⋊D1311yescharacteristic
1204C2×C4C22×C22⋊D1312yes—
1205C2×C4C22×C22⋊D1312yes—
1206C2×C4C22×C22⋊D1311yescharacteristic
1207C2×C4C22×C22⋊D1311yescharacteristic
1208C2×C4C24×D1311yescharacteristic
1209C8—262no—
1210C8—261no—
1211C8—261no—
1212C8—261no—
1213C8—261no—
1214C8—262no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—22no—
1220C22—22no—
1221C22—21no—
1222C22—22no—
1223C22—21no—
1224C22—21no—
1225C22—21no—
1226C22—22no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—82no—
1233C22—84no—
1234C22—522no—
1235C22—522no—
1236C22—522no—
1237C22—2082no—
1238C22#1171951112yes—
1239C22C23×C22⋊D1311yescharacteristic
1240C4—21no—
1241C4—21no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—521no—
1250C4—521no—
1251C4—522no—
1252C4—521no—
1253C4—521no—
1254C4#1171951112yes—
1255C4C22×#612911yescharacteristic
1256C4C2×#8825111yescharacteristic
1257C2—22no—
1258C2—41no—
1259C2—41no—
1260C2—42no—
1261C2—42no—
1262C2—81no—
1263C2—1042no—
1264C2C2×#1171951111yescharacteristic
1265C2#1312961511yescharacteristic
1266C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3489C2
socleC22×C13C23×D4
hypercenter#3489D13
hypocenterC13#61182
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13128573C2semidirect
2. #13127141C2semidirect
3. #13127130C2semidirect
4. #13127089C2semidirect
5. #13127037C2semidirect
6. #13127007C2semidirect
7. #13126992C2semidirect
8. #13126827C2semidirect
9. #13126812C2semidirect
10. #13125201C2semidirect
11. #13124810C2semidirect
12. #13124780C2semidirect
13. #13124687C2semidirect
14. #13124518C2semidirect
15. C2×#11718710C2semidirect
16. #13124344C2semidirect
17. #13124122C2semidirect
18. #13124088C2semidirect
19. #13123664C2semidirect
20. #13123540C2semidirect
21. #13123369C2semidirect
22. #13123355C2semidirect
23. C13×#3489C2semidirect
26. D4×Q8×C13C22semidirect
27. C13×#548C22semidirect
29. C13×#547C22semidirect
31. C13×#546C22semidirect
41. #11719535C22semidirect
42. #11719532C22semidirect
45. C2×#88202C22semidirect
46. C22×#6106C22semidirect
57. #11719270C22semidirect
59. #11719260C22semidirect
60. #11719226C22semidirect
61. #11719224C22semidirect
64. #11718899C22semidirect
65. #11718899C22semidirect
66. #11718895C22semidirect
71. #11718894C22semidirect
74. #11718893C22semidirect
75. #11718893C22semidirect
76. #11718893C22semidirect
77. #11718893C22semidirect
78. #11718893C22semidirect
80. #11718888C22semidirect
81. #11718888C22semidirect
82. #11718886C22semidirect
83. #11718886C22semidirect
84. #11718886C22semidirect
85. #11718886C22semidirect
86. #11718886C22semidirect
87. C2×#88075C22semidirect
88. C2×#88075C22semidirect
90. #11718876C22semidirect
91. #11718876C22semidirect
93. #11718744C22semidirect
94. #11718744C22semidirect
95. #11718743C22semidirect
96. #11718742C22semidirect
97. #11718718C22semidirect
98. #11718718C22semidirect
99. #11718717C22semidirect
100. #11718716C22semidirect
103. #11718710C22semidirect
104. #11718710C22semidirect
105. #11718710C22semidirect
106. #11718709C22semidirect
107. #11718706C22semidirect
108. #11718706C22semidirect
109. #11718706C22semidirect
110. #11718705C22semidirect
111. #11718705C22semidirect
112. #11718704C22semidirect
113. #11718700C22semidirect
114. #11718699C22semidirect
115. #11718696C22semidirect
116. #11718694C22semidirect
117. #11718687C22semidirect
118. C4×#6106C22semidirect
119. #11718683C22semidirect
120. #11718682C22semidirect
121. #11718675C22semidirect
122. C4×#6104C22semidirect
123. #11718673C22semidirect
124. #11718673C22semidirect
125. #11718672C22semidirect
126. #11718672C22semidirect
127. #11718670C22semidirect
128. #11718668C22semidirect
129. #11718660C22semidirect
130. #11718658C22semidirect
131. C2×#88049C22semidirect
132. #11718625C22semidirect
133. #11718625C22semidirect
134. C2×#88047C22semidirect
340. C13×#41#41semidirect
485. #3489D13semidirect
616. D4×Q8C2×D13semidirect
617. #548C2×D13semidirect
620. #547C2×D13semidirect
623. #546C2×D13semidirect
973. #41#6129semidirect
1116. C13#61182semidirect

Maximal subgroups

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

subgroupindex
#131285732
#131271412
#131271302
#131270892
#131270372
#131270072
#131269922
#131268272
#131268122
#131252012
#131248102
#131247802
#131246872
#131245182
C2×#117187102
#131243442
#131241222
#131240882
#131236642
#131235402
#131233692
#131233552
C13×#34892
#6118213