Finite Group Databasebeta

← #27393898

Subgroups — #27393898

Order 13568.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277098C211yesmaximal, characteristic, complemented
2C2×#16810483C211yesmaximal, characteristic, complemented
3#20275701C212yesmaximal, complemented
4#20275552C212yesmaximal, complemented
5#20275169C214yesmaximal, complemented
6#20274703C214yesmaximal, complemented
7C2×C53×#525C211yesmaximal, characteristic
8C2×#13133176—21no—
9C22×C4⋊Dic53—21no—
10C22×C22⋊Dic53C2212yes—
11C2×#13133132C2218yes—
12#16810486—21no—
13#16810483—21no—
14#16810483—21no—
15#16810483—21no—
16#16810483C2212yes—
17#16810483C2212yes—
18#16810483C2212yes—
19#16810479C2212yes—
20C4×C22⋊Dic53—21no—
21C4×C22⋊Dic53C2212yes—
22C2×#13133124—21no—
23#16810390C2218yes—
24C22×#41×C53C411yescharacteristic, complemented
25C24×C4×C53C2211yescharacteristic
26C53×#525—21no—
27C53×#525—21no—
28C53×#525—21no—
29C53×#525—21no—
30C53×#525—21no—
31C53×#525—21no—
32C53×#525—21no—
33C53×#525—21no—
34C2×#123×C53C412yescomplemented
35C2×C22⋊Q8×C53C411yescharacteristic, complemented
36C2×C22⋊Q8×C53C2211yescharacteristic
37C2×#121×C53C411yescharacteristic, complemented
38C2×#121×C53C2211yescharacteristic
39C2×#120×C53C2212yes—
40C2×C4×D4×C53C412yescomplemented
41C2×C4×D4×C53C2212yes—
42C2×#117×C53C411yescharacteristic, complemented
43C23×Dic53—22no—
44#13133176—44no—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—44no—
49C2×C22⋊Dic53—22no—
50C2×C22⋊Dic53—22no—
51C2×C22⋊Dic53—22no—
52C2×C22⋊Dic53—44no—
53C2×C22⋊Dic53C2314yes—
54C2×C22⋊Dic53C2314yes—
55C2×C4×Dic53—22no—
56#13133132—48no—
57#13133124—22no—
58#13133124—22no—
59#13133124—22no—
60#13133124—22no—
61C25×C53C2311yescharacteristic
62C2×#41×C53—21no—
63C2×#41×C53—21no—
64C2×#41×C53—21no—
65C2×#41×C53—21no—
66C2×#41×C53—44no—
67C22×Q8×C53C2×C411yescharacteristic, complemented
68C22×D4×C53C2×C412yes—
69C22×D4×C53C2×C412yes—
70C22×D4×C53C2×C411yescharacteristic, complemented
71C22×D4×C53C2312yes—
72C23×C4×C53—44no—
73C23×C4×C53C2×C411yescharacteristic
74C23×C4×C53C2×C411yescharacteristic
75C23×C4×C53C2×C411yescharacteristic
76C23×C4×C53C2×C411yescharacteristic
77C23×C4×C53C2×C412yescomplemented
78C23×C4×C53D411yescharacteristic
79C23×C4×C53D411yescharacteristic
80C23×C4×C53D411yescharacteristic
81C23×C4×C53D411yescharacteristic
82C23×C4×C53D411yescharacteristic
83C23×C4×C53D411yescharacteristic
84C23×C4×C53D411yescharacteristic
85C23×C4×C53D411yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88#123×C53—22no—
89#123×C53—22no—
90#123×C53—22no—
91#123×C53—22no—
92C22⋊Q8×C53—21no—
93C22⋊Q8×C53—21no—
94C22⋊Q8×C53—21no—
95C22⋊Q8×C53—21no—
96C22⋊Q8×C53—21no—
97C22⋊Q8×C53—21no—
98C22⋊Q8×C53—21no—
99C22⋊Q8×C53—21no—
100#121×C53—21no—
101#121×C53—21no—
102#121×C53—21no—
103#121×C53—21no—
104#121×C53—21no—
105#121×C53—21no—
106#121×C53—21no—
107#121×C53—21no—
108#120×C53—22no—
109#120×C53—22no—
110#120×C53—22no—
111#120×C53—22no—
112C4×D4×C53—22no—
113C4×D4×C53—22no—
114C4×D4×C53—22no—
115C4×D4×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—22no—
119C4×D4×C53—22no—
120#117×C53—21no—
121#117×C53—21no—
122#117×C53—21no—
123#117×C53—21no—
124C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
125C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
126C2×C4⋊C4×C53C2×C412yescomplemented
127C2×C4⋊C4×C53C2×C412yescomplemented
128C2×C22⋊C4×C53C2×C412yes—
129C2×C22⋊C4×C53C2×C412yes—
130C2×C22⋊C4×C53C2×C412yescomplemented
131C2×C22⋊C4×C53C2×C412yescomplemented
132C2×C22⋊C4×C53C2312yes—
133C2×C42×C53C2×C412yescomplemented
134C24×C53—22no—
135C24×C53—22no—
136C24×C53—42no—
137C24×C53—42no—
138C24×C53C22×C411yescharacteristic
139C24×C53C22×C411yescharacteristic
140C24×C53C22×C412yes—
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C24×C53C2×D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C24×C53C2411yescharacteristic
146#41×C53—44no—
147#41×C53—44no—
148#41×C53—44no—
149#41×C53—44no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—42no—
153C2×D4×C53—22no—
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—22no—
159C2×D4×C53—24no—
160C2×D4×C53—24no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—42no—
164C2×D4×C53—44no—
165C2×D4×C53—44no—
166C22×C4×C53—24no—
167C22×C4×C53—24no—
168C22×C4×C53—24no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—42no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53—42no—
181C22×C4×C53—42no—
182C22×C4×C53—44no—
183C22×C4×C53C22⋊C411yescharacteristic
184C22×C4×C53C22⋊C411yescharacteristic
185C22×C4×C53C22⋊C411yescharacteristic
186C22×C4×C53C22⋊C411yescharacteristic
187C22×C4×C53C22⋊C411yescharacteristic
188C22×C4×C53C22⋊C411yescharacteristic
189C22×C4×C53C22⋊C411yescharacteristic
190C22×C4×C53C22⋊C411yescharacteristic
191C22×C4×C53C22⋊C411yescharacteristic
192C22×C4×C53C22⋊C411yescharacteristic
193C22×C4×C53C22⋊C411yescharacteristic
194C22×C4×C53C22⋊C411yescharacteristic
195C22×C4×C53C22⋊C411yescharacteristic
196C22×C4×C53C22⋊C411yescharacteristic
197C22×C4×C53C22⋊C411yescharacteristic
198C22×C4×C53C22⋊C411yescharacteristic
199C22×C4×C53C22×C412yes—
200C22×C4×C53C22×C411yescharacteristic
201C22×C4×C53C22×C411yescharacteristic
202C22×C4×C53C22×C412yes—
203C22×C4×C53C22×C412yes—
204C22×C4×C53C22×C411yescharacteristic
205C22×C4×C53C22×C411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×Dic53—24no—
215C22×Dic53—24no—
216C22×Dic53—44no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—22no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—22no—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53—22no—
232C22⋊C4×C53—22no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—22no—
237C42×C53—22no—
238C42×C53—22no—
239C22⋊Dic53—24no—
240C22⋊Dic53—28no—
241C22⋊Dic53—24no—
242C22⋊Dic53—44no—
243C22⋊Dic53—44no—
244C22⋊Dic53—44no—
245C4⋊Dic53—44no—
246C4⋊Dic53—44no—
247C4⋊Dic53—44no—
248C4×Dic53—44no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—24no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—48no—
274C23×C53—48no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53C2×C22⋊C411yescharacteristic
278C23×C53C2×C22⋊C411yescharacteristic
279C23×C53C2×C22⋊C411yescharacteristic
280C23×C53C2×C22⋊C411yescharacteristic
281C23×C53C23×C411yescharacteristic
282C23×C53C22×D411yescharacteristic
283C23×C53C22×D411yescharacteristic
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286Q8×C53—42no—
287Q8×C53—42no—
288D4×C53—42no—
289D4×C53—44no—
290D4×C53—44no—
291D4×C53—42no—
292D4×C53—42no—
293D4×C53—44no—
294D4×C53—44no—
295D4×C53—44no—
296D4×C53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—24no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—41no—
328C2×C4×C53—44no—
329C2×C4×C53—44no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53#9914yescomplemented
333C2×C4×C53C2×C22⋊C411yescharacteristic
334C2×C4×C53C2×C22⋊C411yescharacteristic
335C2×C4×C53C2×C22⋊C411yescharacteristic
336C2×C4×C53C2×C22⋊C411yescharacteristic
337C2×C4×C53C2×C22⋊C411yescharacteristic
338C2×C4×C53C2×C22⋊C411yescharacteristic
339C2×C4×C53C2×C22⋊C411yescharacteristic
340C2×C4×C53C2×C22⋊C411yescharacteristic
341C2×Dic53—44no—
342C2×Dic53—44no—
343C2×Dic53—44no—
344C2×Dic53—44no—
345C2×Dic53—44no—
346C2×Dic53—44no—
347C2×Dic53—88no—
348#21874—531nomaximal, Sylow
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—21no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—21no—
361C22×C53—21no—
362C22×C53—21no—
363C22×C53—21no—
364C22×C53—21no—
365C22×C53—21no—
366C22×C53—21no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—44no—
370C22×C53—44no—
371C22×C53—44no—
372C22×C53—44no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—84no—
379C22×C53C2×#9912yes—
380C22×C53#41012yes—
381C22×C53C22×C22⋊C411yescharacteristic
382C22×C53#52012yes—
383C22×C53#53511yescharacteristic
384C22×C53#53611yescharacteristic
385C22×C53#53712yes—
386C4×C53—21no—
387C4×C53—21no—
388C4×C53—21no—
389C4×C53—21no—
390C4×C53—21no—
391C4×C53—21no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53C2×#9912yes—
396C4×C53C2×#9912yes—
397Dic53—84no—
398Dic53—84no—
399C2×#525D5311yescharacteristic
400#2280—531no—
401C2×#380—531no—
402#1996—532no—
403#1964—532no—
404#1898—534no—
405#1799—534no—
406C2×C53—21no—
407C2×C53—22no—
408C2×C53—21no—
409C2×C53—22no—
410C2×C53—22no—
411C2×C53—22no—
412C2×C53—41no—
413C2×C53—41no—
414C2×C53—82no—
415C2×C53#231111yescharacteristic
416C2×C53C22×#9911yescharacteristic
417C2×C53C2×#41011yescharacteristic
418C22×#41Dic5311yescharacteristic, complemented
419C24×C4C2×D5311yescharacteristic
420#525—21no—
421#525—21no—
422#525—21no—
423#525—21no—
424#525—21no—
425#525—21no—
426#525—21no—
427#525—21no—
428C2×#123Dic5312yescomplemented
429C2×C22⋊Q8Dic5311yescharacteristic, complemented
430C2×C22⋊Q8C2×D5311yescharacteristic
431C2×#121Dic5311yescharacteristic, complemented
432C2×#121C2×D5311yescharacteristic
433C2×#120C2×D5312yes—
434C2×C4×D4Dic5312yescomplemented
435C2×C4×D4C2×D5312yes—
436C2×#117—1061no—
437C2×#117Dic5311yescharacteristic, complemented
438C22×C4⋊C4—1061no—
439C22×C22⋊C4—532no—
440C2×#99—538no—
441#381—1061no—
442#380—532no—
443#380—532no—
444#380—532no—
445#380—1061no—
446#380—1061no—
447#380—1061no—
448#379—532no—
449C4×C22⋊C4—532no—
450C4×C22⋊C4—1061no—
451C2×#95—1061no—
452#342—538no—
453C53#2187411yescharacteristic, complemented, Sylow
454C25C22×D5311yescharacteristic
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—44no—
460C22×Q8C2×Dic5311yescharacteristic, complemented
461C22×D4C2×Dic5312yes—
462C22×D4C2×Dic5312yes—
463C22×D4C2×Dic5311yescharacteristic, complemented
464C22×D4C22×D5312yes—
465C23×C4—44no—
466C23×C4—1062no—
467C23×C4C2×Dic5311yescharacteristic
468C23×C4C2×Dic5311yescharacteristic
469C23×C4C2×Dic5311yescharacteristic
470C23×C4C2×Dic5311yescharacteristic
471C23×C4C2×Dic5312yescomplemented
472C23×C4C22⋊D5311yescharacteristic
473C23×C4C22⋊D5311yescharacteristic
474C23×C4C22⋊D5311yescharacteristic
475C23×C4C22⋊D5311yescharacteristic
476C23×C4C22⋊D5311yescharacteristic
477C23×C4C22⋊D5311yescharacteristic
478C23×C4C22⋊D5311yescharacteristic
479C23×C4C22⋊D5311yescharacteristic
480C23×C4C22×D5311yescharacteristic
481C23×C4C22×D5311yescharacteristic
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—2124no—
519C2×C4⋊C4—1062no—
520C2×C4⋊C4—1062no—
521C2×C4⋊C4—1062no—
522C2×C4⋊C4—2124no—
523C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
524C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
525C2×C4⋊C4C2×Dic5312yescomplemented
526C2×C4⋊C4C2×Dic5312yescomplemented
527C2×C22⋊C4—534no—
528C2×C22⋊C4—534no—
529C2×C22⋊C4—1062no—
530C2×C22⋊C4—1062no—
531C2×C22⋊C4—1062no—
532C2×C22⋊C4—2124no—
533C2×C22⋊C4C2×Dic5312yes—
534C2×C22⋊C4C2×Dic5312yes—
535C2×C22⋊C4C2×Dic5312yescomplemented
536C2×C22⋊C4C2×Dic5312yescomplemented
537C2×C22⋊C4C22×D5312yes—
538C2×C42—1062no—
539C2×C42C2×Dic5312yescomplemented
540#99—2128no—
541#95—1062no—
542#95—1062no—
543#95—1062no—
544#95—1062no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×Dic5311yescharacteristic
550C24C22×Dic5311yescharacteristic
551C24C22×Dic5312yes—
552C24C2×C22⋊D5311yescharacteristic
553C24C2×C22⋊D5311yescharacteristic
554C24C2×C22⋊D5311yescharacteristic
555C24C2×C22⋊D5311yescharacteristic
556C24C23×D5311yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—1064no—
595C22×C4—1064no—
596C22×C4—2124no—
597C22×C4—2124no—
598C22×C4—2124no—
599C22×C4C22⋊Dic5311yescharacteristic
600C22×C4C22⋊Dic5311yescharacteristic
601C22×C4C22⋊Dic5311yescharacteristic
602C22×C4C22⋊Dic5311yescharacteristic
603C22×C4C22⋊Dic5311yescharacteristic
604C22×C4C22⋊Dic5311yescharacteristic
605C22×C4C22⋊Dic5311yescharacteristic
606C22×C4C22⋊Dic5311yescharacteristic
607C22×C4C22⋊Dic5311yescharacteristic
608C22×C4C22⋊Dic5311yescharacteristic
609C22×C4C22⋊Dic5311yescharacteristic
610C22×C4C22⋊Dic5311yescharacteristic
611C22×C4C22⋊Dic5311yescharacteristic
612C22×C4C22⋊Dic5311yescharacteristic
613C22×C4C22⋊Dic5311yescharacteristic
614C22×C4C22⋊Dic5311yescharacteristic
615C22×C4C22×Dic5312yes—
616C22×C4C22×Dic5311yescharacteristic
617C22×C4C22×Dic5311yescharacteristic
618C22×C4C22×Dic5312yes—
619C22×C4C22×Dic5312yes—
620C22×C4C22×Dic5311yescharacteristic
621C22×C4C22×Dic5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C2×C22⋊D5311yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—2124no—
639C4⋊C4—2124no—
640C4⋊C4—2124no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—1064no—
652C22⋊C4—1068no—
653C22⋊C4—1064no—
654C22⋊C4—2124no—
655C22⋊C4—2124no—
656C22⋊C4—2124no—
657C42—22no—
658C42—22no—
659C42—2124no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊Dic5311yescharacteristic
689C23C2×C22⋊Dic5311yescharacteristic
690C23C2×C22⋊Dic5311yescharacteristic
691C23C2×C22⋊Dic5311yescharacteristic
692C23C23×Dic5311yescharacteristic
693C23C22×C22⋊D5311yescharacteristic
694C23C22×C22⋊D5311yescharacteristic
695C23#1313326312yes—
696C23#1313326412yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—42no—
705D4—42no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—4248no—
744C2×C4—2124no—
745C2×C4—2124no—
746C2×C4—2124no—
747C2×C4—2124no—
748C2×C4—2124no—
749C2×C4—2124no—
750C2×C4#1313313214yescomplemented
751C2×C4C2×C22⋊Dic5311yescharacteristic
752C2×C4C2×C22⋊Dic5311yescharacteristic
753C2×C4C2×C22⋊Dic5311yescharacteristic
754C2×C4C2×C22⋊Dic5311yescharacteristic
755C2×C4C2×C22⋊Dic5311yescharacteristic
756C2×C4C2×C22⋊Dic5311yescharacteristic
757C2×C4C2×C22⋊Dic5311yescharacteristic
758C2×C4C2×C22⋊Dic5311yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#1313313212yes—
790C22#1681059712yes—
791C22C22×C22⋊Dic5311yescharacteristic
792C22#1681110612yes—
793C22#1681118711yescharacteristic
794C22#1681119411yescharacteristic
795C22#1681120112yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—4244no—
806C4—4244no—
807C4C2×#1313313212yes—
808C4C2×#1313313212yes—
809C2—21no—
810C2—22no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2#2027730711yescharacteristic
819C2C22×#1313313211yescharacteristic
820C2C2×#1681059711yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC23×C53C23×C4
FrattiniC24C23×D53
Fitting, prime radicalC2×C53×#525C2
socleC22×C53C22×C22⋊C4
cosocleC24×C53C24
hypercenterC2×#525D53
hypocenterC53#21874
LCSG ▷ C23×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. #20277098C2semidirect
2. C2×#16810483C2semidirect
3. #20275701C2semidirect
4. #20275552C2semidirect
5. #20275169C2semidirect
6. #20274703C2semidirect
24. C22×#41×C53C4semidirect
34. C2×#123×C53C4semidirect
35. C2×C22⋊Q8×C53C4semidirect
37. C2×#121×C53C4semidirect
40. C2×C4×D4×C53C4semidirect
42. C2×#117×C53C4semidirect
67. C22×Q8×C53C2×C4semidirect
70. C22×D4×C53C2×C4semidirect
77. C23×C4×C53C2×C4semidirect
124. C2×C4⋊C4×C53C2×C4semidirect
125. C2×C4⋊C4×C53C2×C4semidirect
126. C2×C4⋊C4×C53C2×C4semidirect
127. C2×C4⋊C4×C53C2×C4semidirect
130. C2×C22⋊C4×C53C2×C4semidirect
131. C2×C22⋊C4×C53C2×C4semidirect
133. C2×C42×C53C2×C4semidirect
332. C2×C4×C53#99semidirect
418. C22×#41Dic53semidirect
428. C2×#123Dic53semidirect
429. C2×C22⋊Q8Dic53semidirect
431. C2×#121Dic53semidirect
434. C2×C4×D4Dic53semidirect
437. C2×#117Dic53semidirect
453. C53#21874semidirect
460. C22×Q8C2×Dic53semidirect
463. C22×D4C2×Dic53semidirect
471. C23×C4C2×Dic53semidirect
523. C2×C4⋊C4C2×Dic53semidirect
524. C2×C4⋊C4C2×Dic53semidirect
525. C2×C4⋊C4C2×Dic53semidirect
526. C2×C4⋊C4C2×Dic53semidirect
535. C2×C22⋊C4C2×Dic53semidirect
536. C2×C22⋊C4C2×Dic53semidirect
539. C2×C42C2×Dic53semidirect
750. C2×C4#13133132semidirect

Maximal subgroups

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

subgroupindex
#202770982
C2×#168104832
#202757012
#202755522
#202751692
#202747032
C2×C53×#5252
#2187453