Finite Group Databasebeta

← #27399574

Subgroups — #27399574

Order 13568.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811269C211yesmaximal, characteristic
2C2×#16810625C211yesmaximal, characteristic, complemented
3C22×#13133139C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic53C211yesmaximal, characteristic, complemented
5#20275645C211yesmaximal, characteristic, complemented
6#20275531C211yesmaximal, characteristic, complemented
7#20275153C211yesmaximal, characteristic, complemented
8#20275138C211yesmaximal, characteristic, complemented
9#20275030C211yesmaximal, characteristic, complemented
10#20275020C211yesmaximal, characteristic, complemented
11#20274716C211yesmaximal, characteristic, complemented
12#20274656C211yesmaximal, characteristic, complemented
13#20274647C211yesmaximal, characteristic, complemented
14#20274541C211yesmaximal, characteristic, complemented
15C2×C53×#435C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18#16811269—24no—
19#16811269C418yescomplemented
20C2×#13133205C2211yescharacteristic
21C2×#13133202—21no—
22C2×#13133196C2211yescharacteristic
23C2×#13133191C2211yescharacteristic
24C2×#13133190—21no—
25C2×#13133185—21no—
26C2×C4×D212C2211yescharacteristic
27C2×D4×Dic53—21no—
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic, complemented
30C2×C22⋊C4×D53—21no—
31#16810625—24no—
32C2×#13133142C2211yescharacteristic, complemented
33C2×#13133142C2211yescharacteristic, complemented
34C2×#13133142C2211yescharacteristic, complemented
35C2×#13133142C2211yescharacteristic, complemented
36C2×#13133139—24no—
37C2×#13133139C2211yescharacteristic
38C2×#13133139C2211yescharacteristic
39C2×#13133139C2211yescharacteristic
40C2×#13133139C2211yescharacteristic
41C2×#13133139C2211yescharacteristic
42C2×#13133139C2211yescharacteristic
43C2×#13133139C2211yescharacteristic
44C2×#13133139C2211yescharacteristic
45#16810522—21no—
46#16810498—21no—
47#16810498—21no—
48#16810493C2211yescharacteristic, complemented
49#16810483C2211yescharacteristic
50#16810483C2211yescharacteristic, complemented
51C4×C4⋊Dic53C2211yescharacteristic, complemented
52#16810386C2211yescharacteristic, complemented
53#16810386C2211yescharacteristic, complemented
54#16810386C2211yescharacteristic, complemented
55#16810386C2211yescharacteristic, complemented
56C22×M16×C53C2211yescharacteristic, complemented
57C23×C8×C53C2211yescharacteristic
58C2×C4×D4×C53C2211yescharacteristic
59C53×#435—24no—
60C2×C4⋊C8×C53C2211yescharacteristic, complemented
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×C22⋊C8×C53C2211yescharacteristic, complemented
63C2×#97×C53C2211yescharacteristic, complemented
64C24×D53—21no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—22no—
68C2×#11719945—41no—
69C2×#11719945—41no—
70C2×#11719945C2×C414yescomplemented
71C22×Dic106C2311yescharacteristic
72C22×D212—22no—
73C22×D212—22no—
74C22×D212—22no—
75C22×D212—21no—
76C22×D212—41no—
77C22×D212—41no—
78C22×D212C2×C414yescomplemented
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87#13133205—22no—
88#13133205C2×C414yescomplemented
89#13133202—28no—
90#13133196—22no—
91#13133196C2×C414yescomplemented
92#13133191—22no—
93#13133191C2×C414yescomplemented
94#13133190—28no—
95#13133185—28no—
96C4×D212—22no—
97C4×D212C2×C414yescomplemented
98D4×Dic53—44no—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—21no—
101C2×C4⋊Dic53—21no—
102C2×C4⋊Dic53—21no—
103C2×C4⋊Dic53—22no—
104C2×C4⋊Dic53—22no—
105C2×C4⋊Dic53—41no—
106C2×C4⋊Dic53—41no—
107C2×C4⋊Dic53C2311yescharacteristic
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×#11719919—21no—
113C2×C22⋊Dic53—21no—
114C2×C22⋊Dic53—21no—
115C2×C22⋊Dic53—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120C22⋊C4×D53—28no—
121C2×C4×Dic53—21no—
122#13133142—22no—
123#13133142—22no—
124#13133142—41no—
125#13133142—41no—
126#13133139—22no—
127#13133139—22no—
128#13133139—22no—
129#13133139—22no—
130#13133139—22no—
131#13133139—41no—
132#13133139—41no—
133#13133139D414yescomplemented
134#13133124—21no—
135#13133124—21no—
136#13133124—21no—
137C22×D4×C53D411yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C2×M16×C53—22no—
141C2×M16×C53—22no—
142C2×M16×C53—41no—
143C22×C8×C53—22no—
144C22×C8×C53—22no—
145C22×C8×C53—41no—
146C22×C8×C53C2311yescharacteristic
147C22×C8×C53C2311yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C22×C8×C53C2311yescharacteristic
150C4×D4×C53C2×C414yes—
151C4×D4×C53D414yes—
152C2×C4⋊C4×C53D411yescharacteristic
153C2×C22⋊C4×C53D411yescharacteristic
154C2×C22⋊C4×C53D411yescharacteristic
155C2×C42×C53C2311yescharacteristic
156C4⋊C8×C53—22no—
157C22⋊C8×C53—22no—
158C22⋊C8×C53—22no—
159#97×C53—22no—
160C24×C53C2×D411yescharacteristic
161C24×C53C2×D411yescharacteristic
162C23×D53—21no—
163C23×D53—21no—
164C23×D53—24no—
165C23×D53—42no—
166C23×D53—42no—
167C23×D53—42no—
168C23×D53—42no—
169C23×D53—81no—
170C23×D53—81no—
171C2×D4×C53—22no—
172C2×D4×C53—22no—
173C2×D4×C53C22⋊C414yes—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53C22×C412yes—
183C22×C4×C53C22×C412yes—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D412yes—
189C22×C4×C53C2×D412yes—
190C22×C4×C53C2411yescharacteristic
191C2×C22⋊D53—24no—
192C2×C22⋊D53—24no—
193C2×C22⋊D53—42no—
194C2×C22⋊D53—42no—
195C2×C22⋊D53—81no—
196C2×C22⋊D53—81no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—42no—
204C22×Dic53—42no—
205C22×Dic53—42no—
206C22×Dic53—42no—
207C22×Dic53—81no—
208C22×Dic53—81no—
209#11719945—28no—
210#11719945—44no—
211#11719945—44no—
212#11719945—44no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—28no—
221C2×D212—24no—
222C2×D212—21no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212—44no—
226C2×D212—42no—
227C2×D212—42no—
228C2×D212C22×C412yes—
229C2×D212C22×C412yes—
230C2×D212C2×D412yes—
231C2×D212#4112yes—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—42no—
235C2×C4×D53—42no—
236C2×C4×D53—81no—
237C2×C4×D53—81no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106C22×C412yes—
244M16×C53—44no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53—21no—
253C2×C8×C53—21no—
254C2×C8×C53—21no—
255C2×C8×C53—21no—
256C2×C8×C53—44no—
257C2×C8×C53C2×D412yes—
258C4⋊C4×C53C22⋊C414yes—
259C22⋊C4×C53C22⋊C414yes—
260C22⋊C4×C53C22⋊C414yes—
261C42×C53C22×C412yes—
262C42×C53C2×D412yes—
263C22⋊Dic53—24no—
264C22⋊Dic53—42no—
265C22⋊Dic53—42no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53—42no—
279C4⋊Dic53—42no—
280C4⋊Dic53—42no—
281C4⋊Dic53—81no—
282C4⋊Dic53C22×C412yes—
283C4⋊Dic53C2×D412yes—
284#11719919—24no—
285C4×Dic53—42no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—21no—
296C23×C53C2×C22⋊C412yes—
297C23×C53C2×C22⋊C412yes—
298C23×C53AGL(1,ℤ/8)12yes—
299C23×C53#13712yes—
300C23×C53C22×D411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—48no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—48no—
317C22×D53—84no—
318C22×D53—84no—
319C22×D53—84no—
320C22×D53—84no—
321C22×D53—84no—
322D4×C53—28no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53C2×C22⋊C412yes—
340C2×C4×C53C2×C22⋊C412yes—
341C2×C4×C53C2×C22⋊C412yes—
342C2×C4×C53C2×C22⋊C412yes—
343C2×C4×C53C23×C411yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C2×#4111yescharacteristic
347C2×C4×C53H(5,𝔽2)11yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C22⋊D53—48no—
350C22⋊D53—84no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—84no—
370C2×Dic53—84no—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—22no—
376D212—48no—
377D212—41no—
378D212—41no—
379D212C4×D414yescomplemented
380C4×D53—48no—
381C4×D53—84no—
382Dic106—22no—
383Dic106—22no—
384Dic106—41no—
385Dic106—41no—
386C8×C53—22no—
387C8×C53—41no—
388C8×C53—41no—
389C8×C53—41no—
390#22419—531nomaximal, Sylow
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—22no—
394C22×C53—22no—
395C22×C53—22no—
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—22no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—41no—
403C22×C53—41no—
404C22×C53#41714yescomplemented
405C22×C53C22×C22⋊C411yescharacteristic
406C22×C53D4211yescharacteristic
407C22×C53#54611yescharacteristic
408C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C53C2×#13711yescharacteristic
410C22×C53#57611yescharacteristic
411C22×C53#57711yescharacteristic
412C2×D53—24no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—816no—
423C2×D53—81no—
424C2×D53—81no—
425C2×D53—81no—
426C2×D53—81no—
427C4×C53—22no—
428C4×C53—22no—
429C4×C53—22no—
430C4×C53—22no—
431C4×C53C2×C4×D411yescharacteristic
432C4×C53#51811yescharacteristic
433C4×C53D4211yescharacteristic
434C4×C53#54611yescharacteristic
435Dic53—42no—
436Dic53—42no—
437Dic53—42no—
438Dic53—81no—
439Dic53—81no—
440Dic53—81no—
441C2×#546—531no—
442C2×#435D5311yescharacteristic, complemented
443C2×#417—531no—
444C22×#102—531no—
445D4×C4⋊C4—531no—
446#1983—531no—
447#1959—531no—
448#1895—531no—
449#1892—531no—
450#1874—531no—
451#1872—531no—
452#1802—531no—
453#1788—531no—
454#1786—531no—
455#1762—531no—
456C2×C53—24no—
457C2×C53—42no—
458C2×C53D4×C22⋊C411yescharacteristic
459C2×C53C2×#41711yescharacteristic
460C2×C53#289711yescharacteristic
461C2×C53#326411yescharacteristic
462C2×C53#326611yescharacteristic
463C2×C53#330611yescharacteristic
464C2×C53#331411yescharacteristic
465D53—44no—
466D53—82no—
467C22×#41—531no—
468C23×D4—531no—
469C22×M16C2×D5311yescharacteristic, complemented
470C23×C8C2×D5311yescharacteristic
471#546—538no—
472#546—1064no—
473C2×#124—531no—
474C2×#123—1061no—
475C2×C22⋊Q8—531no—
476C2×#121—531no—
477C2×#121—1061no—
478C2×#120—1061no—
479C2×C4×D4—531no—
480C2×C4×D4—1061no—
481C2×C4×D4C2×D5311yescharacteristic
482C22×C4⋊C4—531no—
483C22×C4⋊C4—531no—
484C22×C22⋊C4—1061no—
485#435—24no—
486C2×C4⋊C8C2×D5311yescharacteristic, complemented
487#417—1064no—
488C2×#103—531no—
489C2×#103—531no—
490C2×#103—531no—
491C2×#103—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×#102—531no—
495C2×#102—531no—
496C2×#102—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—1064no—
501C2×C22⋊C8C2×D5311yescharacteristic
502C2×C22⋊C8C2×D5311yescharacteristic, complemented
503C2×#97C2×D5311yescharacteristic, complemented
504#389—1061no—
505#385—1061no—
506#385—1061no—
507#384—531no—
508#380—531no—
509#380—531no—
510C4×C4⋊C4—531no—
511#340—531no—
512#340—531no—
513#340—531no—
514#340—531no—
515C53#2241911yescharacteristic, complemented, Sylow
516C25—1061no—
517C2×#41—534no—
518C2×#41—1062no—
519C2×#41—1062no—
520C2×#41—1062no—
521C2×#41—2121no—
522C2×#41—2121no—
523C22×Q8—531no—
524C22×D4—534no—
525C22×D4—531no—
526C22×D4—531no—
527C22×D4—1062no—
528C22×D4—1062no—
529C22×D4—1061no—
530C22×D4—1061no—
531C22×D4—1061no—
532C22×D4—1062no—
533C22×D4—2121no—
534C22×D4—2121no—
535C22×D4D21211yescharacteristic
536C23×C4—1061no—
537C23×C4—1061no—
538C23×C4—1061no—
539C23×C4—1061no—
540C23×C4C22×D5311yescharacteristic
541C23×C4C22×D5311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C22×D5311yescharacteristic
549C22×C8C22×D5311yescharacteristic
550C22×C8C22×D5311yescharacteristic
551C22×C8C22×D5311yescharacteristic
552#124—534no—
553#124—1062no—
554#123—1068no—
555C22⋊Q8—534no—
556C22⋊Q8—1062no—
557#121—534no—
558#121—1062no—
559#121—1068no—
560#120—1068no—
561C4×D4—534no—
562C4×D4—1062no—
563C4×D4—2124no—
564C4×D4C4×D5314yes—
565C4×D4C22⋊D5314yes—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—531no—
569C2×C4⋊C4—531no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—1062no—
572C2×C4⋊C4—1062no—
573C2×C4⋊C4—1061no—
574C2×C4⋊C4—1061no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1061no—
578C2×C4⋊C4—2121no—
579C2×C4⋊C4—2121no—
580C2×C4⋊C4D21211yescharacteristic
581C2×C22⋊C4—1061no—
582C2×C22⋊C4—1061no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C22⋊C4—1068no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4D21211yescharacteristic
590C2×C22⋊C4D21211yescharacteristic
591C2×C42—1061no—
592C2×C42C22×D5311yescharacteristic
593C4⋊C8—22no—
594#103—1062no—
595#103—1062no—
596#103—2121no—
597#103—2121no—
598#102—534no—
599#102—1062no—
600#102—1062no—
601#102—1062no—
602#102—1062no—
603#102—1062no—
604#102—2121no—
605#102—2121no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—1061no—
610#95—1061no—
611#95—1061no—
612C24—1061no—
613C24—1064no—
614C24—1061no—
615C24—4241no—
616C24—4241no—
617C24—2122no—
618C24—2122no—
619C24—2122no—
620C24—2122no—
621C24C2×D21211yescharacteristic
622C24C2×D21211yescharacteristic
623#41—1068no—
624#41—2124no—
625#41—2124no—
626#41—2124no—
627C2×Q8—532no—
628C2×Q8—1061no—
629C2×Q8—1061no—
630C2×Q8—1061no—
631C2×Q8—1061no—
632C2×Q8—1061no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—532no—
636C2×D4—532no—
637C2×D4—532no—
638C2×D4—532no—
639C2×D4—1068no—
640C2×D4—1064no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—1061no—
649C2×D4—1061no—
650C2×D4—1061no—
651C2×D4—4241no—
652C2×D4—4241no—
653C2×D4—2124no—
654C2×D4—2124no—
655C2×D4—2124no—
656C2×D4—2122no—
657C2×D4—2122no—
658C2×D4—2122no—
659C2×D4—2122no—
660C2×D4#1171992114yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—1061no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1064no—
673C22×C4—1064no—
674C22×C4—1061no—
675C22×C4—1061no—
676C22×C4—1061no—
677C22×C4—4241no—
678C22×C4—4241no—
679C22×C4—4241no—
680C22×C4—4241no—
681C22×C4—2122no—
682C22×C4—2122no—
683C22×C4—2122no—
684C22×C4—2122no—
685C22×C4—2122no—
686C22×C4—2122no—
687C22×C4C2×C4×D5312yes—
688C22×C4C2×C4×D5312yes—
689C22×C4C2×D21211yescharacteristic
690C22×C4C2×D21211yescharacteristic
691C22×C4C2×D21211yescharacteristic
692C22×C4C2×D21211yescharacteristic
693C22×C4C2×C22⋊D5312yes—
694C22×C4C2×C22⋊D5312yes—
695C22×C4C23×D5311yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8D4×D5312yes—
710C4⋊C4—532no—
711C4⋊C4—532no—
712C4⋊C4—1064no—
713C4⋊C4—1061no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—4241no—
722C4⋊C4—2122no—
723C4⋊C4—2122no—
724C4⋊C4—2122no—
725C4⋊C4#1171992114yes—
726C22⋊C4—1064no—
727C22⋊C4—1064no—
728C22⋊C4—1064no—
729C22⋊C4—1064no—
730C22⋊C4—1064no—
731C22⋊C4—2122no—
732C22⋊C4—2122no—
733C22⋊C4#1171992114yes—
734C22⋊C4#1171992114yes—
735C42—2122no—
736C42C2×C4×D5312yes—
737C42C2×C22⋊D5312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—1062no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—4244no—
753C23—4244no—
754C23—4244no—
755C23—4244no—
756C23—4244no—
757C23—2128no—
758C23—2121no—
759C23—2128no—
760C23—2121no—
761C23—2121no—
762C23—2121no—
763C23—2121no—
764C23—2121no—
765C23—2121no—
766C23—2121no—
767C23—2121no—
768C23—2121no—
769C23C2×#1171992112yes—
770C23C2×#1171992112yes—
771C23#1313324512yes—
772C23#1313325012yes—
773C23C22×D21211yescharacteristic
774Q8—1062no—
775Q8—1062no—
776Q8—2121no—
777Q8—2121no—
778D4—28no—
779D4—534no—
780D4—1062no—
781D4—1062no—
782D4—1062no—
783D4—1062no—
784D4—1062no—
785D4—4244no—
786D4—2128no—
787D4—2128no—
788D4—2121no—
789D4—2121no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—1062no—
807C2×C4—1062no—
808C2×C4—1062no—
809C2×C4—4244no—
810C2×C4—4244no—
811C2×C4—4244no—
812C2×C4—2128no—
813C2×C4—2121no—
814C2×C4—2121no—
815C2×C4—2121no—
816C2×C4—2121no—
817C2×C4—2121no—
818C2×C4—2121no—
819C2×C4—2121no—
820C2×C4—2121no—
821C2×C4—2121no—
822C2×C4—2121no—
823C2×C4—2121no—
824C2×C4—2121no—
825C2×C4—2121no—
826C2×C4—2121no—
827C2×C4—2121no—
828C2×C4C2×#1171992112yes—
829C2×C4C2×#1171992112yes—
830C2×C4C2×#1171992112yes—
831C2×C4C2×#1171992112yes—
832C2×C4C22×C4×D5311yescharacteristic
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4C22×C22⋊D5311yescharacteristic
835C2×C4#41×D5311yescharacteristic
836C2×C4#1313326211yescharacteristic
837C2×C4#1313326311yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—1064no—
856C22—42416no—
857C22—4241no—
858C22—4241no—
859C22—4241no—
860C22—4241no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2122no—
865C22—2122no—
866C22—2122no—
867C22—2122no—
868C22—2122no—
869C22—2122no—
870C22#1681062514yescomplemented
871C22C22×#1171992111yescharacteristic
872C22D4×D21211yescharacteristic
873C22#1681126811yescharacteristic
874C22C2×#1313324511yescharacteristic
875C22C2×#1313325011yescharacteristic
876C22#1681142811yescharacteristic
877C22#1681143511yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—4241no—
883C4—4241no—
884C4—4241no—
885C4—2122no—
886C4—2122no—
887C4—2122no—
888C4C4×D4×D5311yescharacteristic
889C4#1681109511yescharacteristic
890C4D4×C22⋊D5311yescharacteristic
891C4#1681126111yescharacteristic
892C2—24no—
893C2—42no—
894C2—4242no—
895C2—2124no—
896C2D4×#1171992111yescharacteristic
897C2C2×#1681062511yescharacteristic
898C2#2028324211yescharacteristic
899C2#2028620011yescharacteristic
900C2#2028623011yescharacteristic
901C2#2028667811yescharacteristic
902C2#2028679811yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenterC2×#435D53
hypocenterC53#22419
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16810625C2semidirect
3. C22×#13133139C2semidirect
4. D4×C4⋊Dic53C2semidirect
5. #20275645C2semidirect
6. #20275531C2semidirect
7. #20275153C2semidirect
8. #20275138C2semidirect
9. #20275030C2semidirect
10. #20275020C2semidirect
11. #20274716C2semidirect
12. #20274656C2semidirect
13. #20274647C2semidirect
14. #20274541C2semidirect
15. C2×C53×#435C2semidirect
19. #16811269C4semidirect
29. C22×C4⋊Dic53C22semidirect
32. C2×#13133142C22semidirect
33. C2×#13133142C22semidirect
34. C2×#13133142C22semidirect
35. C2×#13133142C22semidirect
48. #16810493C22semidirect
50. #16810483C22semidirect
51. C4×C4⋊Dic53C22semidirect
52. #16810386C22semidirect
53. #16810386C22semidirect
54. #16810386C22semidirect
55. #16810386C22semidirect
56. C22×M16×C53C22semidirect
60. C2×C4⋊C8×C53C22semidirect
62. C2×C22⋊C8×C53C22semidirect
63. C2×#97×C53C22semidirect
70. C2×#11719945C2×C4semidirect
78. C22×D212C2×C4semidirect
88. #13133205C2×C4semidirect
91. #13133196C2×C4semidirect
93. #13133191C2×C4semidirect
97. C4×D212C2×C4semidirect
133. #13133139D4semidirect
379. D212C4×D4semidirect
404. C22×C53#417semidirect
442. C2×#435D53semidirect
469. C22×M16C2×D53semidirect
486. C2×C4⋊C8C2×D53semidirect
502. C2×C22⋊C8C2×D53semidirect
503. C2×#97C2×D53semidirect
515. C53#22419semidirect
870. C22#16810625semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
C2×#168106252
C22×#131331392
D4×C4⋊Dic532
#202756452
#202755312
#202751532
#202751382
#202750302
#202750202
#202747162
#202746562
#202746472
#202745412
C2×C53×#4352
#2241953