Finite Group Databasebeta

← #27394346

Subgroups — #27394346

Order 13568.

1030 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810589C211yesmaximal, characteristic
2C2×#16810588C211yesmaximal, characteristic
3#20277201C211yesmaximal, characteristic
4#20274900C211yesmaximal, characteristic, complemented
5#20274897C211yesmaximal, characteristic, complemented
6#20274896C211yesmaximal, characteristic, complemented
7#20274896C211yesmaximal, characteristic, complemented
8#20274894C211yesmaximal, characteristic, complemented
9#20274894C211yesmaximal, characteristic, complemented
10#20274893C211yesmaximal, characteristic, complemented
11#20274698C211yesmaximal, characteristic, complemented
12#20274696C211yesmaximal, characteristic, complemented
13#20274694C211yesmaximal, characteristic, complemented
14#20274692C211yesmaximal, characteristic, complemented
15C53×#1850C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C2×#13133174C2211yescharacteristic
21C2×C42×D53C2211yescharacteristic
22C2×C4⋊#88322C2211yescharacteristic
23C2×C4⋊#88322C2211yescharacteristic
24C2×#13133146C2211yescharacteristic
25C2×#13133146C2211yescharacteristic
26C2×#13133146C2211yescharacteristic
27C2×#13133146C2211yescharacteristic
28#16810589—24no—
29#16810588—24no—
30C2×C22⋊#88322C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37#16810527C411yescharacteristic
38#16810527C411yescharacteristic
39#16810523C411yescharacteristic
40#16810523C411yescharacteristic
41#16810501C411yescharacteristic
42#16810501C411yescharacteristic
43#16810499C411yescharacteristic
44#16810499C411yescharacteristic
45C4×#11719921C2211yescharacteristic
46C4×#11719921C2211yescharacteristic
47C4×C22⋊Dic53C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C23×C8×C53C2211yescharacteristic
55C2×C4⋊C8×C53C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C22⋊C8×C53C2211yescharacteristic
58C4×C22⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C53×#336C2211yescharacteristic
61C2×#11719945—41no—
62C2×#11719945—41no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C2×#11719945D414yes—
66C2×#11719945Q814yes—
67C22×Dic106C2×C411yescharacteristic
68C22×D212C2×C411yescharacteristic
69C22×C22⋊D53C2×C411yescharacteristic
70C22×C22⋊D53C2×C411yescharacteristic
71C22×C4×D53C2×C411yescharacteristic
72C22×C4×D53C2×C411yescharacteristic
73C22×C4×D53C2311yescharacteristic
74C22×C4×D53C2311yescharacteristic
75C2×#11719917—22no—
76C2×#11719917—41no—
77C2×#11719917—41no—
78C2×#11719912—22no—
79C2×#11719912—41no—
80C2×#11719912—41no—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C2×C8×D53—22no—
86C2×C8×D53—41no—
87C2×C8×D53—41no—
88#13133174—41no—
89#13133174—41no—
90C2×#11719919C2×C411yescharacteristic
91C2×#11719919C2×C411yescharacteristic
92C2×C22⋊Dic53C2×C411yescharacteristic
93C2×C22⋊Dic53C2×C411yescharacteristic
94C2×#11719921C2×C411yescharacteristic
95C2×#11719921C2×C411yescharacteristic
96C2×#11719921C2×C411yescharacteristic
97C2×#11719921C2×C411yescharacteristic
98C2×#11719921C2×C411yescharacteristic
99C2×#11719921C2×C411yescharacteristic
100C2×C4×Dic53C2×C411yescharacteristic
101C2×C4×Dic53C2×C411yescharacteristic
102C2×C4×Dic53C2311yescharacteristic
103C2×C4×Dic53C2311yescharacteristic
104C42×D53—41no—
105C42×D53—41no—
106C4⋊#88322—41no—
107C4⋊#88322—41no—
108#13133146—41no—
109#13133146—41no—
110#13133146—41no—
111#13133146—41no—
112C22⋊#88322—22no—
113#13133129—22no—
114#13133129—22no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133124C2×C411yescharacteristic
120#13133124C2×C411yescharacteristic
121#13133124C2×C411yescharacteristic
122#13133124C2×C411yescharacteristic
123#13133124C2×C411yescharacteristic
124#13133124C2×C411yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53—22no—
127C22×C8×C53—41no—
128C22×C8×C53—41no—
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C2×C22⋊C4×C53C2×C411yescharacteristic
134C2×C22⋊C4×C53C2×C411yescharacteristic
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C4⋊C8×C53—41no—
138C4⋊C8×C53—41no—
139C22⋊C8×C53—22no—
140#95×C53C2×C411yescharacteristic
141#95×C53C2×C411yescharacteristic
142C24×C53C22×C411yescharacteristic
143C23×D53C22×C411yescharacteristic
144C23×D53C22×C411yescharacteristic
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53C22×C411yescharacteristic
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×Q812yes—
156C22×C4×C53C2411yescharacteristic
157C2×C22⋊D53—41no—
158C2×C22⋊D53—41no—
159C2×C22⋊D53—41no—
160C2×C22⋊D53—41no—
161C2×C22⋊D53C4⋊C414yes—
162C2×C22⋊D53C4⋊C414yes—
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169#11719945—44no—
170#11719945—44no—
171#11719945—44no—
172#11719945—44no—
173C2×D212—41no—
174C2×D212—41no—
175C2×D212C4⋊C414yes—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—22no—
185C2×C4×D53—22no—
186C2×C4×D53—41no—
187C2×C4×D53—41no—
188C2×C4×D53—41no—
189C2×C4×D53—41no—
190C2×C4×D53C2×D412yes—
191C2×C4×D53C2×D412yes—
192C2×C4×D53C2×Q812yes—
193C2×C4×D53C2×Q812yes—
194C2×Dic106—41no—
195C2×Dic106—41no—
196C2×Dic106C4⋊C414yes—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—44no—
210C22⋊C4×C53—22no—
211C22⋊C4×C53—41no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C22⋊Dic53—22no—
217C22⋊Dic53—41no—
218#11719921—22no—
219#11719921—22no—
220#11719921—41no—
221#11719921—41no—
222#11719921—41no—
223#11719921—41no—
224#11719919—41no—
225#11719919—41no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—41no—
231C4×Dic53—41no—
232#11719917—44no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245#11719912—44no—
246C8×D53—44no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53C2×C4⋊C412yes—
254C23×C53C23×C411yescharacteristic
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53—21no—
266C22×D53—21no—
267C22×D53C2×C4⋊C412yes—
268C22×D53C2×C4⋊C412yes—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53C2×C4⋊C412yes—
287C2×C4×C53#13112yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C22×Q811yescharacteristic
290C2×C4×C53H(5,𝔽2)11yescharacteristic
291C2×C4×C53H(5,𝔽2)11yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C22⋊D53—44no—
295C22⋊D53—44no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53C2×C4⋊C412yes—
312C2×Dic53C2×C4⋊C412yes—
313C2×Dic53#13112yes—
314D212—44no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—22no—
318C4×D53—22no—
319C4×D53—22no—
320C4×D53—22no—
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—44no—
324C4×D53—44no—
325Dic106—44no—
326C8×C53—41no—
327C8×C53—41no—
328C8×C53—41no—
329C8×C53—41no—
330#88322—41no—
331#88322—41no—
332#88322—41no—
333#88322—41no—
334#21937—531nomaximal, Sylow
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—41no—
342C22×C53C22×C4⋊C411yescharacteristic
343C22×C53#51811yescharacteristic
344C22×C53#51811yescharacteristic
345C22×C53C2×#13111yescharacteristic
346C22×C53C2×#13111yescharacteristic
347C22×C53#56811yescharacteristic
348C22×C53#56811yescharacteristic
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—41no—
356C2×D53—41no—
357C2×D53—41no—
358C2×D53—41no—
359C2×D53—41no—
360C2×D53—41no—
361C2×D53—41no—
362C2×D53—41no—
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—41no—
368C4×C53#53411yescharacteristic
369C4×C53#53411yescharacteristic
370C4×C53#54311yescharacteristic
371C4×C53#54311yescharacteristic
372Dic53—22no—
373Dic53—22no—
374Dic53—22no—
375Dic53—41no—
376Dic53—41no—
377Dic53—41no—
378C2×#408—531no—
379C2×#408—531no—
380#2297—531no—
381#1851—531no—
382#1851—531no—
383#1851—531no—
384#1851—531no—
385#1850—531no—
386#1850—531no—
387#1850—531no—
388#1850D5311yescharacteristic, complemented
389#1798—531no—
390#1798—531no—
391#1797—531no—
392#1797—531no—
393C2×C53—42no—
394C2×C53#231511yescharacteristic
395C2×C53#290611yescharacteristic
396C2×C53#290611yescharacteristic
397C2×C53#297711yescharacteristic
398C2×C53#297811yescharacteristic
399C2×C53#298111yescharacteristic
400C2×C53#298111yescharacteristic
401D53—42no—
402D53—42no—
403C22×#41—531no—
404C22×M16—531no—
405C22×M16—531no—
406C23×C8—531no—
407C23×C8C2×D5311yescharacteristic
408C2×#117—531no—
409C22×C42—531no—
410C2×C4⋊C8—531no—
411C2×C4⋊C8—531no—
412C2×C4⋊C8—531no—
413C2×C4⋊C8—531no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×C4⋊C8C2×D5311yescharacteristic
417C2×C4⋊C8C2×D5311yescharacteristic
418#408—1064no—
419#408—1064no—
420C2×C22⋊C8—531no—
421C2×C22⋊C8—531no—
422C2×C22⋊C8—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C2×C22⋊C8—531no—
426C2×C22⋊C8—531no—
427C2×C22⋊C8C2×D5311yescharacteristic
428#391—531no—
429#391—531no—
430#390—531no—
431#390—531no—
432#386—531no—
433#386—531no—
434#386—531no—
435#386—531no—
436C4×C22⋊C4—531no—
437C4×C22⋊C4—531no—
438C4×C22⋊C4—531no—
439C4×C22⋊C4C2×D5311yescharacteristic
440#336—531no—
441#336—531no—
442#336—531no—
443#336—531no—
444#336—531no—
445#336—531no—
446#336C2×D5311yescharacteristic
447#336C2×D5311yescharacteristic
448C53#2193711yescharacteristic, complemented, Sylow
449C2×#41—534no—
450C2×#41—534no—
451C2×#41—2121no—
452C2×#41—2121no—
453C2×#41—2121no—
454C2×#41—2121no—
455C22×Q8—531no—
456C22×D4—531no—
457C22×D4—531no—
458C22×D4—531no—
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—531no—
462C23×C4—531no—
463C23×C4C22×D5311yescharacteristic
464C2×M16—1062no—
465C2×M16—1062no—
466C2×M16—2121no—
467C2×M16—2121no—
468C2×M16—2121no—
469C2×M16—2121no—
470C22×C8—22no—
471C22×C8—41no—
472C22×C8—41no—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—1062no—
478C22×C8—2121no—
479C22×C8—2121no—
480C22×C8C22×D5311yescharacteristic
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483C22×C8C22×D5311yescharacteristic
484#117—2121no—
485#117—2121no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C22⋊C4—531no—
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—531no—
495C2×C22⋊C4—531no—
496C2×C22⋊C4C4×D5311yescharacteristic
497C2×C22⋊C4C4×D5311yescharacteristic
498C2×C42—531no—
499C2×C42—531no—
500C2×C42—531no—
501C2×C42—531no—
502C2×C42—2121no—
503C2×C42—2121no—
504C2×C42C22×D5311yescharacteristic
505C2×C42C22×D5311yescharacteristic
506C4⋊C8—41no—
507C4⋊C8—41no—
508C4⋊C8—2121no—
509C4⋊C8—2121no—
510C4⋊C8—2121no—
511C4⋊C8—2121no—
512C4⋊C8—2121no—
513C4⋊C8—2121no—
514C22⋊C8—22no—
515C22⋊C8—1062no—
516C22⋊C8—1062no—
517C22⋊C8—1062no—
518C22⋊C8—1062no—
519C22⋊C8—1062no—
520C22⋊C8—1062no—
521C22⋊C8—1062no—
522#95—531no—
523#95—531no—
524#95—531no—
525#95—531no—
526#95—531no—
527#95—531no—
528#95C4×D5311yescharacteristic
529#95C4×D5311yescharacteristic
530C24—531no—
531C24—531no—
532C24C2×C4×D5311yescharacteristic
533#41—2124no—
534#41—2124no—
535#41—2124no—
536#41—2124no—
537C2×Q8—534no—
538C2×Q8—2121no—
539C2×Q8—2121no—
540C2×D4—534no—
541C2×D4—534no—
542C2×D4—534no—
543C2×D4—2121no—
544C2×D4—2121no—
545C2×D4—2121no—
546C2×D4—2121no—
547C2×D4—2121no—
548C2×D4—2121no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—531no—
561C22×C4—531no—
562C22×C4—531no—
563C22×C4—1062no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1062no—
573C22×C4—2121no—
574C22×C4—2121no—
575C22×C4—2121no—
576C22×C4—2121no—
577C22×C4C2×C4×D5311yescharacteristic
578C22×C4C2×C4×D5311yescharacteristic
579C22×C4C2×C4×D5311yescharacteristic
580C22×C4C2×C4×D5311yescharacteristic
581C22×C4C2×C4×D5311yescharacteristic
582C22×C4D4×D5312yes—
583C22×C4Q8×D5312yes—
584C22×C4C23×D5311yescharacteristic
585M16—2124no—
586M16—2124no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—44no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C2×C8—1061no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—2124no—
613C4⋊C4—2121no—
614C4⋊C4—2121no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—1062no—
618C22⋊C4—1062no—
619C22⋊C4—1062no—
620C22⋊C4—2121no—
621C22⋊C4—2121no—
622C22⋊C4—2121no—
623C22⋊C4—2121no—
624C22⋊C4—2121no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—1061no—
630C42—1061no—
631C42—1061no—
632C42—1061no—
633C42—2121no—
634C42—2121no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—532no—
642C23—532no—
643C23—1061no—
644C23—1061no—
645C23—1061no—
646C23—1061no—
647C23—1061no—
648C23—1061no—
649C23—1061no—
650C23—1061no—
651C23—1061no—
652C23—1061no—
653C23—1061no—
654C23—1061no—
655C23C4⋊C4×D5312yes—
656C23C22×C4×D5311yescharacteristic
657Q8—2124no—
658D4—2124no—
659D4—2124no—
660D4—2124no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—532no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1061no—
696C2×C4—1061no—
697C2×C4—1061no—
698C2×C4—1061no—
699C2×C4—1061no—
700C2×C4—1061no—
701C2×C4—1061no—
702C2×C4—1061no—
703C2×C4—1061no—
704C2×C4—2124no—
705C2×C4—2124no—
706C2×C4C4⋊C4×D5312yes—
707C2×C4#1313322312yes—
708C2×C4C2×D4×D5311yescharacteristic
709C2×C4C2×Q8×D5311yescharacteristic
710C2×C4#1313326211yescharacteristic
711C2×C4#1313326211yescharacteristic
712C2×C4#1313326311yescharacteristic
713C2×C4#1313326311yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—2121no—
719C8—2121no—
720C8—2121no—
721C8—2121no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—1062no—
730C22—1062no—
731C22—1062no—
732C22—1062no—
733C22—1062no—
734C22—1062no—
735C22—2121no—
736C22—2121no—
737C22—2121no—
738C22—2121no—
739C22—2121no—
740C22—2121no—
741C22—2121no—
742C22—2121no—
743C22C2×C4⋊C4×D5311yescharacteristic
744C22#1681109511yescharacteristic
745C22#1681109511yescharacteristic
746C22#131×D5311yescharacteristic
747C22C2×#1313322311yescharacteristic
748C22#1681138811yescharacteristic
749C22#1681138911yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—1062no—
756C4—1062no—
757C4—1062no—
758C4—2121no—
759C4—2121no—
760C4—2121no—
761C4#1681118311yescharacteristic
762C4#1681118411yescharacteristic
763C4#1681124811yescharacteristic
764C4#1681124811yescharacteristic
765C2—42no—
766C2—2122no—
767C2—2122no—
768C2#2027732611yescharacteristic
769C2#2028328011yescharacteristic
770C2#2028328211yescharacteristic
771C2#2028376811yescharacteristic
772C2#2028377411yescharacteristic
773C2#2028378711yescharacteristic
774C2#2028378911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1850C2
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1850D53
hypocenterC53#21937
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
4. #20274900C2semidirect
5. #20274897C2semidirect
6. #20274896C2semidirect
7. #20274896C2semidirect
8. #20274894C2semidirect
9. #20274894C2semidirect
10. #20274893C2semidirect
11. #20274698C2semidirect
12. #20274696C2semidirect
13. #20274694C2semidirect
14. #20274692C2semidirect
15. C53×#1850C2semidirect
388. #1850D53semidirect
448. C53#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#168105892
C2×#168105882
#202772012
#202749002
#202748972
#202748962
#202748942
#202748932
#202746982
#202746962
#202746942
#202746922
C53×#18502
#2193753