Finite Group Databasebeta

← #28254829

Subgroups — #28254829

Order 13568.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133191C211yesmaximal, characteristic, complemented
2#20285525C214yesmaximal, complemented
3#20285517C212yesmaximal, complemented
4#20285512C212yesmaximal, complemented
5#20285476C214yesmaximal, complemented
6#20285468C212yesmaximal, complemented
7#20285463C212yesmaximal, complemented
8#20284655C212yesmaximal, complemented
9#20284635C212yesmaximal, complemented
10#20284336C214yesmaximal, complemented
11#20283967C212yesmaximal, complemented
12#20283941C212yesmaximal, complemented
13C2×#16810587C211yesmaximal, characteristic, complemented
14C2×C53×#525C211yesmaximal, characteristic, complemented
15C23×D212C2211yescharacteristic, complemented
16C23×C22⋊D53—21no—
17C2×#13133242C2214yescomplemented
18C22×#11719917C2212yescomplemented
19C2×#13133191—21no—
20C2×#13133191—21no—
21C2×#13133191—21no—
22C2×#13133191—21no—
23C2×#13133191—21no—
24C2×#13133191—21no—
25C2×#13133191C2212yes—
26C2×#13133191C2212yes—
27C2×#13133191C2212yes—
28C2×#13133191C2212yescomplemented
29C2×#13133191C2212yescomplemented
30C2×#13133191C2212yescomplemented
31C22×C4⋊Dic53C2211yescharacteristic, complemented
32C22×#11719921—21no—
33#16810956C2214yescomplemented
34#16810951C2214yescomplemented
35#16810947C2218yescomplemented
36#16810941C2214yescomplemented
37#16810939C2214yescomplemented
38#16810936C2214yescomplemented
39#16810934C2214yescomplemented
40#16810874C2218yescomplemented
41#16810871C2218yescomplemented
42#16810857C2218yescomplemented
43#16810854C2218yescomplemented
44#16810773C2214yescomplemented
45#16810773C2214yescomplemented
46#16810768C2218yescomplemented
47#16810762C2214yescomplemented
48#16810757C2214yescomplemented
49#16810756C2214yescomplemented
50#16810756C2214yescomplemented
51#16810666C2214yescomplemented
52#16810627C2214yescomplemented
53#16810624C2214yescomplemented
54#16810587C2212yescomplemented
55#16810587C2212yescomplemented
56#16810587C2212yescomplemented
57#16810587C2212yescomplemented
58C2×C22⋊#88322C2212yescomplemented
59C2×C22⋊#88322C2212yescomplemented
60C22×#41×C53C2211yescharacteristic, complemented
61C24×C4×C53C2211yescharacteristic
62C53×#525—21no—
63C53×#525—21no—
64C53×#525—21no—
65C53×#525—21no—
66C53×#525C2212yes—
67C53×#525C2212yescomplemented
68C53×#525C2212yescomplemented
69C53×#525C2212yescomplemented
70C2×#123×C53—21no—
71C2×C22⋊Q8×C53C2211yescharacteristic, complemented
72C2×C22⋊Q8×C53C2211yescharacteristic, complemented
73C2×#121×C53C2211yescharacteristic, complemented
74C2×#121×C53C2211yescharacteristic, complemented
75C2×#120×C53—21no—
76C2×C4×D4×C53—21no—
77C2×C4×D4×C53—21no—
78C2×#117×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212—44no—
84C22×D212C2312yes—
85C22×D212C2312yes—
86C22×D212C2312yes—
87C22×C22⋊D53—22no—
88C22×C22⋊D53—22no—
89C22×C22⋊D53—22no—
90C22×C22⋊D53—22no—
91C22×C22⋊D53—22no—
92C22×C22⋊D53—22no—
93C22×C22⋊D53—48no—
94C23×Dic53—21no—
95#13133242—48no—
96C2×#11719924C2318yescomplemented
97C2×#11719922C2318yescomplemented
98C2×#11719917—44no—
99C2×#11719917C2314yes—
100C2×#11719917C2314yescomplemented
101C22×#88322C2314yescomplemented
102#13133191—22no—
103#13133191—22no—
104#13133191—22no—
105#13133191—22no—
106#13133191—22no—
107#13133191—22no—
108#13133191—22no—
109#13133191—22no—
110#13133191—22no—
111#13133191—22no—
112#13133191—22no—
113#13133191—22no—
114#13133191C2314yes—
115#13133191C2314yes—
116#13133191C2314yes—
117#13133191C2314yes—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2312yes—
122C2×C4⋊Dic53C2312yes—
123C2×C4⋊Dic53C2312yes—
124C2×#11719921—22no—
125C2×#11719921—22no—
126C2×#11719921—22no—
127C2×#11719921—22no—
128C2×#11719921—22no—
129C2×#11719921—22no—
130#13133150C2318yescomplemented
131#13133148C2318yescomplemented
132#13133141C2318yescomplemented
133#13133138C2318yescomplemented
134#13133137C2318yescomplemented
135#13133137C2318yescomplemented
136C22⋊#88322C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yescomplemented
139C22⋊#88322C2314yescomplemented
140C25×C53D411yescharacteristic
141C2×#41×C53—21no—
142C2×#41×C53—21no—
143C2×#41×C53—44no—
144C2×#41×C53C2312yes—
145C2×#41×C53C2312yescomplemented
146C22×Q8×C53C2311yescharacteristic, complemented
147C22×D4×C53—21no—
148C22×D4×C53—21no—
149C22×D4×C53—21no—
150C22×D4×C53C2311yescharacteristic, complemented
151C23×C4×C53—21no—
152C23×C4×C53—44no—
153C23×C4×C53D411yescharacteristic
154C23×C4×C53D411yescharacteristic
155C23×C4×C53D411yescharacteristic
156C23×C4×C53D411yescharacteristic
157C23×C4×C53D411yescharacteristic
158C23×C4×C53D411yescharacteristic
159C23×C4×C53D411yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C23×C4×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167#123×C53—22no—
168#123×C53—22no—
169#123×C53—22no—
170#123×C53—22no—
171C22⋊Q8×C53—21no—
172C22⋊Q8×C53—21no—
173C22⋊Q8×C53—21no—
174C22⋊Q8×C53—21no—
175C22⋊Q8×C53C2312yes—
176C22⋊Q8×C53C2312yes—
177C22⋊Q8×C53C2312yescomplemented
178C22⋊Q8×C53C2312yescomplemented
179#121×C53—21no—
180#121×C53—21no—
181#121×C53—21no—
182#121×C53—21no—
183#121×C53C2312yes—
184#121×C53C2312yes—
185#121×C53C2312yescomplemented
186#121×C53C2312yescomplemented
187#120×C53—22no—
188#120×C53—22no—
189#120×C53—22no—
190#120×C53—22no—
191C4×D4×C53—22no—
192C4×D4×C53—22no—
193C4×D4×C53—22no—
194C4×D4×C53—22no—
195C4×D4×C53—22no—
196C4×D4×C53—22no—
197C4×D4×C53—22no—
198C4×D4×C53—22no—
199#117×C53—21no—
200#117×C53—21no—
201#117×C53C2312yes—
202#117×C53C2312yescomplemented
203C2×C4⋊C4×C53—21no—
204C2×C4⋊C4×C53—21no—
205C2×C4⋊C4×C53C2311yescharacteristic, complemented
206C2×C4⋊C4×C53C2311yescharacteristic, complemented
207C2×C22⋊C4×C53—21no—
208C2×C22⋊C4×C53—21no—
209C2×C22⋊C4×C53—21no—
210C2×C22⋊C4×C53—21no—
211C2×C22⋊C4×C53—21no—
212C2×C42×C53—21no—
213C24×C53—24no—
214C24×C53—21no—
215C24×C53—42no—
216C24×C53—42no—
217C24×C53C2×D411yescharacteristic
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220C24×C53C2×D411yescharacteristic
221C24×C53C2×D411yescharacteristic
222C24×C53C2×D411yescharacteristic
223C24×C53C2×D411yescharacteristic
224C23×D53—22no—
225C23×D53—22no—
226C23×D53—22no—
227C23×D53—44no—
228C23×D53—44no—
229C23×D53—44no—
230#41×C53—28no—
231#41×C53—44no—
232#41×C53—44no—
233#41×C53—44no—
234C2×Q8×C53—21no—
235C2×Q8×C53—42no—
236C2×Q8×C53C2412yes—
237C2×D4×C53—22no—
238C2×D4×C53—22no—
239C2×D4×C53—22no—
240C2×D4×C53—22no—
241C2×D4×C53—22no—
242C2×D4×C53—22no—
243C2×D4×C53—21no—
244C2×D4×C53—42no—
245C2×D4×C53—44no—
246C2×D4×C53—44no—
247C2×D4×C53—44no—
248C2×D4×C53C2412yes—
249C22×C4×C53—24no—
250C22×C4×C53—24no—
251C22×C4×C53—24no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—22no—
256C22×C4×C53—22no—
257C22×C4×C53—42no—
258C22×C4×C53—42no—
259C22×C4×C53—42no—
260C22×C4×C53—42no—
261C22×C4×C53—42no—
262C22×C4×C53—42no—
263C22×C4×C53—42no—
264C22×C4×C53—42no—
265C22×C4×C53—42no—
266C22×C4×C53—42no—
267C22×C4×C53—42no—
268C22×C4×C53—44no—
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2×D411yescharacteristic
275C22×C4×C53C2×D411yescharacteristic
276C22×C4×C53C2×D411yescharacteristic
277C22×C4×C53C2×D411yescharacteristic
278C22×C4×C53C2×D411yescharacteristic
279C22×C4×C53C2×D411yescharacteristic
280C22×C4×C53C2×D411yescharacteristic
281C22×C4×C53C2×D411yescharacteristic
282C22×C4×C53C2×D411yescharacteristic
283C22×C4×C53C2×D411yescharacteristic
284C22×C4×C53C2×D411yescharacteristic
285C22×C4×C53C2×D411yescharacteristic
286C22×C4×C53C2×D411yescharacteristic
287C22×C4×C53C2×D411yescharacteristic
288C22×C4×C53C2×D411yescharacteristic
289C22×C4×C53C2×D411yescharacteristic
290C22×C4×C53C2411yescharacteristic
291C22×C4×C53C2411yescharacteristic
292C22×C4×C53C2411yescharacteristic
293C22×C4×C53C2411yescharacteristic
294C22×C4×C53C2411yescharacteristic
295C22×C4×C53C2411yescharacteristic
296C22×C4×C53C2411yescharacteristic
297C2×C22⋊D53—24no—
298C2×C22⋊D53—24no—
299C2×C22⋊D53—24no—
300C2×C22⋊D53—24no—
301C2×C22⋊D53—48no—
302C2×C22⋊D53—48no—
303C2×C22⋊D53—48no—
304C2×C22⋊D53—48no—
305C2×C22⋊D53—48no—
306C2×C22⋊D53—48no—
307C22×Dic53—22no—
308C22×Dic53—22no—
309C22×Dic53—22no—
310C22×Dic53—44no—
311C2×D212—28no—
312C2×D212—22no—
313C2×D212—22no—
314C2×D212—22no—
315C2×D212—44no—
316C2×D212—44no—
317C2×D212—44no—
318C2×D212—44no—
319C2×D212—44no—
320C2×D212C2414yes—
321C4⋊C4×C53—22no—
322C4⋊C4×C53—22no—
323C4⋊C4×C53—22no—
324C4⋊C4×C53—22no—
325C4⋊C4×C53—21no—
326C4⋊C4×C53—21no—
327C4⋊C4×C53C2412yes—
328C4⋊C4×C53C2412yes—
329C22⋊C4×C53—22no—
330C22⋊C4×C53—22no—
331C22⋊C4×C53—22no—
332C22⋊C4×C53—22no—
333C22⋊C4×C53—22no—
334C22⋊C4×C53—22no—
335C22⋊C4×C53—22no—
336C22⋊C4×C53—22no—
337C22⋊C4×C53—22no—
338C22⋊C4×C53—22no—
339C42×C53—22no—
340C42×C53—22no—
341#11719924—48no—
342#11719922—48no—
343#11719921—24no—
344#11719921—24no—
345#11719921—24no—
346#11719921—24no—
347C4⋊Dic53—22no—
348C4⋊Dic53—22no—
349C4⋊Dic53—22no—
350C4⋊Dic53C2414yes—
351#11719917—28no—
352#11719917—44no—
353C2×#88322—44no—
354C2×#88322C2418yes—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—416no—
377C23×C53—42no—
378C23×C53—42no—
379C23×C53—42no—
380C23×C53AGL(1,ℤ/8)14yescomplemented
381C23×C53C22×D411yescharacteristic
382C23×C53C22×D411yescharacteristic
383C23×C53C22×D411yescharacteristic
384C23×C53C22×D411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C22×D53—24no—
389C22×D53—44no—
390C22×D53—44no—
391C22×D53—44no—
392C22×D53—44no—
393C22×D53—44no—
394C22×D53—44no—
395C22×D53—44no—
396C22×D53—44no—
397C22×D53—44no—
398C22×D53—816no—
399Q8×C53—24no—
400Q8×C53—42no—
401D4×C53—24no—
402D4×C53—42no—
403D4×C53—44no—
404D4×C53—44no—
405D4×C53—44no—
406D4×C53—44no—
407D4×C53—44no—
408D4×C53—44no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—44no—
440C2×C4×C53—42no—
441C2×C4×C53—42no—
442C2×C4×C53—42no—
443C2×C4×C53—44no—
444C2×C4×C53C22×D411yescharacteristic
445C2×C4×C53C22×D411yescharacteristic
446C2×C4×C53C22×D411yescharacteristic
447C2×C4×C53C22×D411yescharacteristic
448C2×C4×C53C22×D411yescharacteristic
449C2×C4×C53C22×D411yescharacteristic
450C2×C4×C53C22×D411yescharacteristic
451C2×C4×C53H(5,𝔽2)14yes—
452C2×C4×C53C2511yescharacteristic
453C22⋊D53—48no—
454C22⋊D53—48no—
455C22⋊D53—48no—
456C22⋊D53—48no—
457C2×Dic53—24no—
458C2×Dic53—44no—
459C2×Dic53—44no—
460C2×Dic53—44no—
461D212—28no—
462D212—44no—
463D212—44no—
464D212—44no—
465#88322—28no—
466#60750—531nomaximal, Sylow
467C22×C53—28no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—21no—
477C22×C53—21no—
478C22×C53—21no—
479C22×C53—21no—
480C22×C53—21no—
481C22×C53—21no—
482C22×C53—21no—
483C22×C53—21no—
484C22×C53—44no—
485C22×C53—44no—
486C22×C53—44no—
487C22×C53—44no—
488C22×C53—44no—
489C22×C53—44no—
490C22×C53—42no—
491C22×C53—42no—
492C22×C53—42no—
493C22×C53—84no—
494C22×C53#53412yes—
495C22×C53C2×AGL(1,ℤ/8)12yes—
496C22×C53C2×AGL(1,ℤ/8)12yes—
497C22×C53C2×AGL(1,ℤ/8)12yes—
498C22×C53#57512yes—
499C22×C53C23×D411yescharacteristic
500C2×D53—44no—
501C2×D53—44no—
502C2×D53—44no—
503C2×D53—88no—
504C2×D53—88no—
505C2×D53—88no—
506C4×C53—21no—
507C4×C53—21no—
508C4×C53—21no—
509C4×C53—21no—
510C4×C53—21no—
511C4×C53—21no—
512C4×C53—42no—
513C4×C53—42no—
514C4×C53—42no—
515C4×C53#53412yes—
516C4×C53C2×H(5,𝔽2)12yes—
517Dic53—44no—
518C2×#525D5311yescharacteristic, complemented
519C22×#121—531no—
520#3194—534no—
521#3193—532no—
522#3192—532no—
523#3188—534no—
524#3187—532no—
525#3186—532no—
526#3094—532no—
527#3092—532no—
528#3055—534no—
529#3006—532no—
530#3003—532no—
531C2×#407—531no—
532C2×C53—22no—
533C2×C53—22no—
534C2×C53—22no—
535C2×C53—22no—
536C2×C53—22no—
537C2×C53—41no—
538C2×C53—41no—
539C2×C53—82no—
540C2×C53C2×#53411yescharacteristic
541C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C53C2×#57511yescharacteristic
543D53—84no—
544C22×#41C2×D5311yescharacteristic, complemented
545C23×D4—531no—
546C23×D4—1061no—
547C24×C4C2×D5311yescharacteristic
548C2×AGL(1,ℤ/8)—534no—
549C22×M16—532no—
550#525—21no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525C2×D5312yes—
555#525C2×D5312yescomplemented
556#525C2×D5312yescomplemented
557#525C2×D5312yescomplemented
558C2×#123—21no—
559C2×C22⋊Q8C2×D5311yescharacteristic, complemented
560C2×C22⋊Q8C2×D5311yescharacteristic, complemented
561C2×#121—532no—
562C2×#121—532no—
563C2×#121—532no—
564C2×#121—532no—
565C2×#121—532no—
566C2×#121—532no—
567C2×#121—1061no—
568C2×#121—1061no—
569C2×#121—1061no—
570C2×#121—1061no—
571C2×#121—1061no—
572C2×#121—1061no—
573C2×#121C2×D5311yescharacteristic, complemented
574C2×#121C2×D5311yescharacteristic, complemented
575C2×#120—21no—
576C2×C4×D4—21no—
577C2×C4×D4—21no—
578C2×#117C2×D5311yescharacteristic, complemented
579C22×C4⋊C4—531no—
580C22×C22⋊C4—1061no—
581#484—534no—
582#483—534no—
583#482—538no—
584#481—534no—
585#481—534no—
586#480—534no—
587#480—534no—
588#469—538no—
589#468—538no—
590#466—538no—
591#465—538no—
592#450—534no—
593#450—534no—
594#449—538no—
595#448—534no—
596#447—534no—
597#447—534no—
598#447—534no—
599#428—534no—
600#418—534no—
601#417—534no—
602#407—532no—
603#407—532no—
604#407—532no—
605#407—532no—
606C2×C22⋊C8—532no—
607C2×C22⋊C8—532no—
608C53#6075011yescharacteristic, complemented, Sylow
609C25—1061no—
610C25C22⋊D5311yescharacteristic
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—44no—
614C2×#41C22×D5312yes—
615C2×#41C22×D5312yescomplemented
616C22×Q8C22×D5311yescharacteristic, complemented
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4—532no—
621C22×D4—532no—
622C22×D4—532no—
623C22×D4—1062no—
624C22×D4—1062no—
625C22×D4—1062no—
626C22×D4—1062no—
627C22×D4—1062no—
628C22×D4—1062no—
629C22×D4—1061no—
630C22×D4—1061no—
631C22×D4—1061no—
632C22×D4—2124no—
633C22×D4—2128no—
634C22×D4C22×D5311yescharacteristic, complemented
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1061no—
638C23×C4C22⋊D5311yescharacteristic
639C23×C4C22⋊D5311yescharacteristic
640C23×C4C22⋊D5311yescharacteristic
641C23×C4C22⋊D5311yescharacteristic
642C23×C4C22⋊D5311yescharacteristic
643C23×C4C22⋊D5311yescharacteristic
644C23×C4C22⋊D5311yescharacteristic
645C23×C4C22×D5311yescharacteristic
646C23×C4C22×D5311yescharacteristic
647C23×C4C22×D5311yescharacteristic
648C23×C4C22×D5311yescharacteristic
649C23×C4C22×D5311yescharacteristic
650C23×C4C22×D5311yescharacteristic
651C23×C4C22×D5311yescharacteristic
652AGL(1,ℤ/8)—2128no—
653C2×SD16—538no—
654C2×D8—538no—
655C2×M16—534no—
656C2×M16—534no—
657C2×M16—2124no—
658C22×C8—534no—
659#123—22no—
660#123—22no—
661#123—22no—
662#123—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8C22×D5312yes—
668C22⋊Q8C22×D5312yes—
669C22⋊Q8C22×D5312yescomplemented
670C22⋊Q8C22×D5312yescomplemented
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—534no—
676#121—534no—
677#121—534no—
678#121—534no—
679#121—1062no—
680#121—1062no—
681#121—1062no—
682#121—1062no—
683#121—1062no—
684#121—1062no—
685#121—1062no—
686#121—1062no—
687#121—1062no—
688#121—1062no—
689#121—1062no—
690#121—1062no—
691#121C22×D5312yes—
692#121C22×D5312yes—
693#121C22×D5312yescomplemented
694#121C22×D5312yescomplemented
695#120—22no—
696#120—22no—
697#120—22no—
698#120—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—22no—
707#117—21no—
708#117—21no—
709#117C22×D5312yes—
710#117C22×D5312yescomplemented
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—532no—
714C2×C4⋊C4—532no—
715C2×C4⋊C4—532no—
716C2×C4⋊C4—1061no—
717C2×C4⋊C4—1061no—
718C2×C4⋊C4—1061no—
719C2×C4⋊C4C22×D5311yescharacteristic, complemented
720C2×C4⋊C4C22×D5311yescharacteristic, complemented
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—1062no—
727C2×C22⋊C4—1062no—
728C2×C22⋊C4—1062no—
729C2×C22⋊C4—1062no—
730C2×C22⋊C4—1062no—
731C2×C22⋊C4—1062no—
732C2×C42—21no—
733#107—538no—
734#106—538no—
735#103—538no—
736#102—538no—
737#102—538no—
738#102—538no—
739C22⋊C8—534no—
740C22⋊C8—534no—
741C22⋊C8—534no—
742C22⋊C8—534no—
743C24—24no—
744C24—21no—
745C24—42no—
746C24—42no—
747C24—1062no—
748C24—1062no—
749C24—1062no—
750C24—2124no—
751C24—2124no—
752C24—2124no—
753C24C2×C22⋊D5311yescharacteristic
754C24C2×C22⋊D5311yescharacteristic
755C24C2×C22⋊D5311yescharacteristic
756C24C2×C22⋊D5311yescharacteristic
757C24C2×C22⋊D5311yescharacteristic
758C24C2×C22⋊D5311yescharacteristic
759C24C2×C22⋊D5311yescharacteristic
760#41—28no—
761#41—44no—
762#41—44no—
763#41—44no—
764C2×Q8—21no—
765C2×Q8—42no—
766C2×Q8C23×D5312yes—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—534no—
779C2×D4—1064no—
780C2×D4—1064no—
781C2×D4—1064no—
782C2×D4—1064no—
783C2×D4—1062no—
784C2×D4—1062no—
785C2×D4—1062no—
786C2×D4—1068no—
787C2×D4—2124no—
788C2×D4—2124no—
789C2×D4—2124no—
790C2×D4—2124no—
791C2×D4—2124no—
792C2×D4—2128no—
793C2×D4—2128no—
794C2×D4—2128no—
795C2×D4—2128no—
796C2×D4—2128no—
797C2×D4—2128no—
798C2×D4C23×D5312yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—44no—
819C22×C4—1062no—
820C22×C4—1062no—
821C22×C4—1062no—
822C22×C4—2124no—
823C22×C4C2×C22⋊D5311yescharacteristic
824C22×C4C2×C22⋊D5311yescharacteristic
825C22×C4C2×C22⋊D5311yescharacteristic
826C22×C4C2×C22⋊D5311yescharacteristic
827C22×C4C2×C22⋊D5311yescharacteristic
828C22×C4C2×C22⋊D5311yescharacteristic
829C22×C4C2×C22⋊D5311yescharacteristic
830C22×C4C2×C22⋊D5311yescharacteristic
831C22×C4C2×C22⋊D5311yescharacteristic
832C22×C4C2×C22⋊D5311yescharacteristic
833C22×C4C2×C22⋊D5311yescharacteristic
834C22×C4C2×C22⋊D5311yescharacteristic
835C22×C4C2×C22⋊D5311yescharacteristic
836C22×C4C2×C22⋊D5311yescharacteristic
837C22×C4C2×C22⋊D5311yescharacteristic
838C22×C4C2×C22⋊D5311yescharacteristic
839C22×C4C2×C22⋊D5311yescharacteristic
840C22×C4C2×C22⋊D5311yescharacteristic
841C22×C4C2×C22⋊D5311yescharacteristic
842C22×C4C2×C22⋊D5311yescharacteristic
843C22×C4C2×C22⋊D5311yescharacteristic
844C22×C4C23×D5311yescharacteristic
845C22×C4C23×D5311yescharacteristic
846C22×C4C23×D5311yescharacteristic
847C22×C4C23×D5311yescharacteristic
848C22×C4C23×D5311yescharacteristic
849C22×C4C23×D5311yescharacteristic
850C22×C4C23×D5311yescharacteristic
851SD16—2128no—
852D8—2128no—
853M16—1068no—
854M16—2124no—
855C2×C8—538no—
856C2×C8—2124no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—534no—
864C4⋊C4—1062no—
865C4⋊C4—1062no—
866C4⋊C4—1062no—
867C4⋊C4C23×D5312yes—
868C4⋊C4C23×D5312yes—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—1064no—
880C22⋊C4—1064no—
881C22⋊C4—1064no—
882C22⋊C4—1064no—
883C42—22no—
884C42—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—1064no—
911C23—42416no—
912C23—2124no—
913C23—2124no—
914C23—2124no—
915C23—2124no—
916C23—2124no—
917C23—2124no—
918C23—2124no—
919C23—2124no—
920C23—2124no—
921C23#1313324214yescomplemented
922C23C22×C22⋊D5311yescharacteristic
923C23C22×C22⋊D5311yescharacteristic
924C23C22×C22⋊D5311yescharacteristic
925C23C22×C22⋊D5311yescharacteristic
926C23C22×C22⋊D5311yescharacteristic
927C23C22×C22⋊D5311yescharacteristic
928C23C22×C22⋊D5311yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—1068no—
940D4—2124no—
941D4—2124no—
942D4—2128no—
943D4—2128no—
944D4—2128no—
945D4—2128no—
946D4—2124no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—1064no—
983C2×C4—2124no—
984C2×C4—2124no—
985C2×C4—2124no—
986C2×C4C22×C22⋊D5311yescharacteristic
987C2×C4C22×C22⋊D5311yescharacteristic
988C2×C4C22×C22⋊D5311yescharacteristic
989C2×C4C22×C22⋊D5311yescharacteristic
990C2×C4C22×C22⋊D5311yescharacteristic
991C2×C4C22×C22⋊D5311yescharacteristic
992C2×C4C22×C22⋊D5311yescharacteristic
993C2×C4#1313326214yes—
994C2×C4C24×D5311yescharacteristic
995C8—1068no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—4248no—
1024C22—4248no—
1025C22—4248no—
1026C22—2124no—
1027C22—2124no—
1028C22—2124no—
1029C22#1681118212yes—
1030C22C2×#1313324212yes—
1031C22C2×#1313324212yes—
1032C22C2×#1313324212yes—
1033C22#1681142112yes—
1034C22C23×C22⋊D5311yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—2124no—
1045C4#1681118212yes—
1046C4C2×#1313326212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—4244no—
1056C2C2×#1681118211yescharacteristic
1057C2C22×#1313324211yescharacteristic
1058C2C2×#1681142111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#525C2
socleC22×C53C23×D4
hypercenterC2×#525D53
hypocenterC53#60750
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#13133191C2semidirect
2. #20285525C2semidirect
3. #20285517C2semidirect
4. #20285512C2semidirect
5. #20285476C2semidirect
6. #20285468C2semidirect
7. #20285463C2semidirect
8. #20284655C2semidirect
9. #20284635C2semidirect
10. #20284336C2semidirect
11. #20283967C2semidirect
12. #20283941C2semidirect
13. C2×#16810587C2semidirect
14. C2×C53×#525C2semidirect
15. C23×D212C22semidirect
17. C2×#13133242C22semidirect
18. C22×#11719917C22semidirect
28. C2×#13133191C22semidirect
29. C2×#13133191C22semidirect
30. C2×#13133191C22semidirect
31. C22×C4⋊Dic53C22semidirect
33. #16810956C22semidirect
34. #16810951C22semidirect
35. #16810947C22semidirect
36. #16810941C22semidirect
37. #16810939C22semidirect
38. #16810936C22semidirect
39. #16810934C22semidirect
40. #16810874C22semidirect
41. #16810871C22semidirect
42. #16810857C22semidirect
43. #16810854C22semidirect
44. #16810773C22semidirect
45. #16810773C22semidirect
46. #16810768C22semidirect
47. #16810762C22semidirect
48. #16810757C22semidirect
49. #16810756C22semidirect
50. #16810756C22semidirect
51. #16810666C22semidirect
52. #16810627C22semidirect
53. #16810624C22semidirect
54. #16810587C22semidirect
55. #16810587C22semidirect
56. #16810587C22semidirect
57. #16810587C22semidirect
58. C2×C22⋊#88322C22semidirect
59. C2×C22⋊#88322C22semidirect
60. C22×#41×C53C22semidirect
67. C53×#525C22semidirect
68. C53×#525C22semidirect
69. C53×#525C22semidirect
71. C2×C22⋊Q8×C53C22semidirect
72. C2×C22⋊Q8×C53C22semidirect
73. C2×#121×C53C22semidirect
74. C2×#121×C53C22semidirect
78. C2×#117×C53C22semidirect
96. C2×#11719924C23semidirect
97. C2×#11719922C23semidirect
100. C2×#11719917C23semidirect
101. C22×#88322C23semidirect
130. #13133150C23semidirect
131. #13133148C23semidirect
132. #13133141C23semidirect
133. #13133138C23semidirect
134. #13133137C23semidirect
135. #13133137C23semidirect
138. C22⋊#88322C23semidirect
139. C22⋊#88322C23semidirect
145. C2×#41×C53C23semidirect
146. C22×Q8×C53C23semidirect
150. C22×D4×C53C23semidirect
177. C22⋊Q8×C53C23semidirect
178. C22⋊Q8×C53C23semidirect
185. #121×C53C23semidirect
186. #121×C53C23semidirect
202. #117×C53C23semidirect
205. C2×C4⋊C4×C53C23semidirect
206. C2×C4⋊C4×C53C23semidirect
380. C23×C53AGL(1,ℤ/8)semidirect
518. C2×#525D53semidirect
544. C22×#41C2×D53semidirect
555. #525C2×D53semidirect
556. #525C2×D53semidirect
557. #525C2×D53semidirect
559. C2×C22⋊Q8C2×D53semidirect
560. C2×C22⋊Q8C2×D53semidirect
573. C2×#121C2×D53semidirect
574. C2×#121C2×D53semidirect
578. C2×#117C2×D53semidirect
608. C53#60750semidirect
615. C2×#41C22×D53semidirect
616. C22×Q8C22×D53semidirect
634. C22×D4C22×D53semidirect
669. C22⋊Q8C22×D53semidirect
670. C22⋊Q8C22×D53semidirect
693. #121C22×D53semidirect
694. #121C22×D53semidirect
710. #117C22×D53semidirect
719. C2×C4⋊C4C22×D53semidirect
720. C2×C4⋊C4C22×D53semidirect
921. C23#13133242semidirect

Maximal subgroups

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

subgroupindex
C22×#131331912
#202855252
#202855172
#202855122
#202854762
#202854682
#202854632
#202846552
#202846352
#202843362
#202839672
#202839412
C2×#168105872
C2×C53×#5252
#6075053