Finite Group Databasebeta

← #27389887

Subgroups — #27389887

Order 13568.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811101C211yesmaximal, characteristic
2C2×#16810730C211yesmaximal, characteristic, complemented
3C2×Q16×Dic53C211yesmaximal, characteristic, complemented
4#20277399C211yesmaximal, characteristic
5#20275058C211yesmaximal, characteristic, complemented
6#20275058C211yesmaximal, characteristic, complemented
7#20275028C211yesmaximal, characteristic
8#20274985C211yesmaximal, characteristic, complemented
9#20274971C211yesmaximal, characteristic, complemented
10#20274916C211yesmaximal, characteristic
11#20274650C211yesmaximal, characteristic
12#20274547C211yesmaximal, characteristic, complemented
13#103×Dic53C211yesmaximal, characteristic, complemented
14#20274483C211yesmaximal, characteristic
15C2×C53×#451C211yesmaximal, characteristic
16#16811101—24no—
17#16811101—24no—
18C2×Q8×Dic53—21no—
19C2×Q8×Dic53—21no—
20C2×Q8×Dic53C2211yescharacteristic
21C2×Q8×Dic53C2211yescharacteristic
22C2×Q8×Dic53C2211yescharacteristic
23C2×Q8×Dic53C2211yescharacteristic
24C2×Q8×Dic53C2211yescharacteristic
25C2×#13133176—21no—
26C2×#13133176—21no—
27C2×#13133176C2211yescharacteristic
28C2×#13133176C2211yescharacteristic
29#16810730—24no—
30Q16×Dic53—24no—
31C2×#13133151C2211yescharacteristic
32C2×#13133149C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133141C2211yescharacteristic
37C2×#13133141C2211yescharacteristic
38C2×#13133141C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×#13133127C2211yescharacteristic
41C2×C8×Dic53C2211yescharacteristic
42#16810530C2211yescharacteristic
43#16810522—21no—
44#16810522C2211yescharacteristic
45#16810516—21no—
46#16810516—21no—
47#16810509—21no—
48#16810483C2211yescharacteristic
49C4⋊C4×Dic53C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C23×Q8×C53C2211yescharacteristic
57C22×Q16×C53C2211yescharacteristic
58C22×Q16×C53C2211yescharacteristic
59C2×C22⋊Q8×C53C2211yescharacteristic
60C53×#451C418yescomplemented
61C2×#103×C53C2211yescharacteristic
62C2×#103×C53C2211yescharacteristic
63C2×C22⋊C8×C53C2211yescharacteristic
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66Q8×Dic53—28no—
67Q8×Dic53—28no—
68Q8×Dic53—22no—
69Q8×Dic53—22no—
70Q8×Dic53—22no—
71Q8×Dic53—22no—
72Q8×Dic53—22no—
73Q8×Dic53—22no—
74Q8×Dic53—22no—
75Q8×Dic53—22no—
76Q8×Dic53D414yes—
77Q8×Dic53D414yes—
78#13133176—28no—
79#13133176—28no—
80#13133176—22no—
81#13133176—22no—
82#13133176—22no—
83#13133176—22no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53D411yescharacteristic
91C2×C4⋊Dic53D411yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C22⋊Dic53—21no—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53D411yescharacteristic
99C2×C22⋊Dic53D411yescharacteristic
100C2×C4×Dic53—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53—21no—
104C2×C4×Dic53—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53C2311yescharacteristic
108C2×C4×Dic53C2311yescharacteristic
109#13133151—22no—
110#13133149—22no—
111#13133141—22no—
112#13133141—22no—
113#13133141—22no—
114#13133141—22no—
115#13133141—22no—
116#13133141—22no—
117C22⋊#88322—22no—
118#13133127—22no—
119C8×Dic53—22no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123#13133124—21no—
124#13133124—21no—
125C22×Q8×C53—22no—
126C22×Q8×C53—22no—
127C22×Q8×C53—22no—
128C22×Q8×C53—22no—
129C22×Q8×C53—21no—
130C22×Q8×C53—22no—
131C22×Q8×C53C2×C414yes—
132C22×Q8×C53C2311yescharacteristic
133C22×Q8×C53C2311yescharacteristic
134C22×Q8×C53C2311yescharacteristic
135C23×C4×C53—21no—
136C23×C4×C53C2311yescharacteristic
137C2×Q16×C53—22no—
138C2×Q16×C53—22no—
139C2×Q16×C53—22no—
140C2×Q16×C53—22no—
141C2×Q16×C53C2×C414yes—
142C2×Q16×C53C2×C414yes—
143C22×C8×C53C2311yescharacteristic
144C22×C8×C53C2311yescharacteristic
145C22⋊Q8×C53—22no—
146C22⋊Q8×C53C2×C414yes—
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C22⋊C4×C53—21no—
150#103×C53C2×C414yes—
151#103×C53C2×C414yes—
152C22⋊C8×C53C2×C414yes—
153C24×C53C2×D411yescharacteristic
154C2×Q8×C53—28no—
155C2×Q8×C53—28no—
156C2×Q8×C53—24no—
157C2×Q8×C53—24no—
158C2×Q8×C53—28no—
159C2×Q8×C53—28no—
160C2×Q8×C53—24no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53C22×C412yes—
173C2×Q8×C53C22×C412yes—
174C2×Q8×C53C22×C412yes—
175C2×Q8×C53C2×D412yes—
176C2×Q8×C53C2×D412yes—
177C2×Q8×C53#4112yes—
178C2×Q8×C53#4112yes—
179C22×C4×C53—24no—
180C22×C4×C53—24no—
181C22×C4×C53—24no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C22×C412yes—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53#4112yes—
193C22×C4×C53C2411yescharacteristic
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202Q16×C53—28no—
203Q16×C53—28no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53C22×C412yes—
209C2×C8×C53C22×C412yes—
210C4⋊C4×C53—24no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53C22×C412yes—
213C22⋊C4×C53—24no—
214C22⋊Dic53—24no—
215C22⋊Dic53—22no—
216C22⋊Dic53—22no—
217C22⋊Dic53—81no—
218C4⋊Dic53—24no—
219C4⋊Dic53—24no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—24no—
223C4⋊Dic53—24no—
224C4⋊Dic53—22no—
225C4⋊Dic53—22no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—42no—
231C4⋊Dic53—81no—
232C4⋊Dic53C2×D412yes—
233C4⋊Dic53C2×D412yes—
234C4×Dic53—24no—
235C4×Dic53—24no—
236C4×Dic53—24no—
237C4×Dic53—21no—
238C4×Dic53—21no—
239C4×Dic53—24no—
240C4×Dic53—24no—
241C4×Dic53—42no—
242C4×Dic53—81no—
243C4×Dic53C2×D412yes—
244C4×Dic53C2×D412yes—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53C4×D412yes—
258C23×C53C22×D411yescharacteristic
259Q8×C53—216no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—22no—
264Q8×C53—22no—
265Q8×C53—22no—
266Q8×C53—22no—
267Q8×C53—22no—
268Q8×C53—41no—
269Q8×C53—41no—
270Q8×C53C4×D414yes—
271Q8×C53C4×D414yes—
272C2×C4×C53—216no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—21no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—21no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53C4×D412yes—
292C2×C4×C53C23×C411yescharacteristic
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53#12012yes—
321C2×Dic53#12012yes—
322C8×C53—22no—
323C8×C53—22no—
324#88322—41no—
325#88322—41no—
326#21463—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53C2×C4×D411yescharacteristic
335C22×C53C2×#12011yescharacteristic
336C22×C53#52511yescharacteristic
337C22×C53#57711yescharacteristic
338C22×C53#57811yescharacteristic
339C22×C53#57811yescharacteristic
340C22×C53#57811yescharacteristic
341C4×C53—24no—
342C4×C53—24no—
343C4×C53—22no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53C2×C4×D411yescharacteristic
347C4×C53C2×C4×D411yescharacteristic
348C4×C53#52511yescharacteristic
349C4×C53#52511yescharacteristic
350Dic53—22no—
351Dic53—22no—
352Dic53—41no—
353Dic53—42no—
354Dic53—41no—
355Dic53—42no—
356Dic53—81no—
357Dic53—81no—
358C2×#519—531no—
359C2×#451D5311yescharacteristic
360C2×#441—531no—
361C2×C4×Q16—531no—
362#2323—531no—
363#1878—531no—
364#1878—531no—
365#1873—531no—
366#1865—531no—
367#1863—531no—
368#1854—531no—
369#1787—531no—
370#1763—531no—
371C4×#103—531no—
372#1750—531no—
373C2×C53—42no—
374C2×C53C4×#12011yescharacteristic
375C2×C53#294711yescharacteristic
376C2×C53#295011yescharacteristic
377C2×C53#301111yescharacteristic
378C2×C53#301311yescharacteristic
379C2×C53#312111yescharacteristic
380C2×C53#312711yescharacteristic
381C23×Q8C2×D5311yescharacteristic
382C22×Q16C2×D5311yescharacteristic
383C22×Q16C2×D5311yescharacteristic
384C2×C22⋊Q8C2×D5311yescharacteristic
385#519—1064no—
386#519—1064no—
387C2×C4×Q8—531no—
388C2×C4×Q8—531no—
389C2×C4×Q8—531no—
390C2×C4×Q8—531no—
391C2×C4×Q8—531no—
392C2×C4×Q8—1061no—
393C2×C4×Q8—1061no—
394C2×#117—531no—
395C2×#117—531no—
396C2×#117—1061no—
397C2×#117—1061no—
398#451Dic5318yescomplemented
399#441—1064no—
400C4×Q16—1064no—
401C2×#107—531no—
402C2×#106—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103C2×D5311yescharacteristic
410C2×#103C2×D5311yescharacteristic
411C2×C22⋊C8—531no—
412C2×C22⋊C8C2×D5311yescharacteristic
413C2×#97—531no—
414C2×C4×C8—531no—
415#391—531no—
416#389—531no—
417#389—1061no—
418#388—1061no—
419#388—1061no—
420#387—1061no—
421#380—531no—
422C4×C4⋊C4—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#336—531no—
428#336—531no—
429C53#2146311yescharacteristic, complemented, Sylow
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—21no—
435C22×Q8—22no—
436C22×Q8C2×Dic5314yes—
437C22×Q8C22×D5311yescharacteristic
438C22×Q8C22×D5311yescharacteristic
439C22×Q8C22×D5311yescharacteristic
440C23×C4—21no—
441C23×C4C22×D5311yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16C2×Dic5314yes—
447C2×Q16C2×Dic5314yes—
448C22×C8—531no—
449C22×C8—531no—
450C22×C8C22×D5311yescharacteristic
451C22×C8C22×D5311yescharacteristic
452C22⋊Q8—22no—
453C22⋊Q8C2×Dic5314yes—
454C4×Q8—534no—
455C4×Q8—534no—
456C4×Q8—1062no—
457C4×Q8—1062no—
458C4×Q8—1062no—
459C4×Q8—1062no—
460C4×Q8—1062no—
461C4×Q8—1062no—
462C4×Q8—1068no—
463C4×Q8—1068no—
464C4×Q8—1062no—
465C4×Q8—1062no—
466#117—1062no—
467#117—1062no—
468#117—1062no—
469#117—1062no—
470#117—1068no—
471#117—1068no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—531no—
488C2×C22⋊C4—531no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C42—531no—
492C2×C42—531no—
493C2×C42—1061no—
494C2×C42—1061no—
495C2×C42—1061no—
496C2×C42—1061no—
497C2×C42—1061no—
498C2×C42—1061no—
499C2×C42—1061no—
500#107—1062no—
501#106—1062no—
502#103—1062no—
503#103—1062no—
504#103—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103C2×Dic5314yes—
509#103C2×Dic5314yes—
510C22⋊C8—1062no—
511C22⋊C8C2×Dic5314yes—
512#97—1062no—
513C4×C8—1062no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519C24D4×D5311yescharacteristic
520C2×Q8—24no—
521C2×Q8—28no—
522C2×Q8—28no—
523C2×Q8—24no—
524C2×Q8—28no—
525C2×Q8—28no—
526C2×Q8—24no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8D4×D5312yes—
539C2×Q8D4×D5312yes—
540C2×Q8#1171994712yes—
541C2×Q8#1171994712yes—
542C2×Q8C22×Dic5312yes—
543C2×Q8C22×Dic5312yes—
544C2×Q8C22×Dic5312yes—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4D4×D5311yescharacteristic
565C22×C4#1171994712yes—
566C22×C4C22×Dic5312yes—
567C22×C4C23×D5311yescharacteristic
568Q16—28no—
569Q16—28no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8C22×Dic5312yes—
581C2×C8C22×Dic5312yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—532no—
585C4⋊C4—532no—
586C4⋊C4—1062no—
587C4⋊C4—1062no—
588C4⋊C4—1064no—
589C4⋊C4—1064no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—4241no—
599C4⋊C4—2122no—
600C4⋊C4C22×Dic5312yes—
601C22⋊C4—24no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1064no—
605C22⋊C4—4241no—
606C42—532no—
607C42—532no—
608C42—1064no—
609C42—1064no—
610C42—1064no—
611C42—1064no—
612C42—1064no—
613C42—1061no—
614C42—1061no—
615C42—4241no—
616C42—2122no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23D4×Dic5312yes—
624C23C2×D4×D5311yescharacteristic
625Q8—216no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8D4×Dic5314yes—
637Q8D4×Dic5314yes—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—532no—
658C2×C4—532no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4D4×Dic5312yes—
682C2×C4C23×Dic5311yescharacteristic
683C2×C4C2×D4×D5311yescharacteristic
684C2×C4C2×D4×D5311yescharacteristic
685C2×C4C2×#1171994711yescharacteristic
686C2×C4C2×#1171994711yescharacteristic
687C2×C4C2×#1171994711yescharacteristic
688C8—22no—
689C8—22no—
690C8—2121no—
691C8—2121no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22C2×D4×Dic5311yescharacteristic
700C22#120×D5311yescharacteristic
701C22#1681112911yescharacteristic
702C22#1681143211yescharacteristic
703C22#1681143611yescharacteristic
704C22#1681143611yescharacteristic
705C22#1681143911yescharacteristic
706C4—24no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—1062no—
712C4—1062no—
713C4—4241no—
714C4—4241no—
715C4—2121no—
716C4—2122no—
717C4—2121no—
718C4—2122no—
719C4C2×D4×Dic5311yescharacteristic
720C4C2×D4×Dic5311yescharacteristic
721C4#1681112911yescharacteristic
722C4#1681112911yescharacteristic
723C2—42no—
724C2#120×Dic5311yescharacteristic
725C2#2028355911yescharacteristic
726C2#2028358311yescharacteristic
727C2#2028400511yescharacteristic
728C2#2028403111yescharacteristic
729C2#2028494511yescharacteristic
730C2#2028500911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC24×C53C2×D4
cosocleC22×C4×C53C24
hypercenterC2×#451D53
hypocenterC53#21463
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#16810730C2semidirect
3. C2×Q16×Dic53C2semidirect
5. #20275058C2semidirect
6. #20275058C2semidirect
8. #20274985C2semidirect
9. #20274971C2semidirect
12. #20274547C2semidirect
13. #103×Dic53C2semidirect
60. C53×#451C4semidirect
398. #451Dic53semidirect
429. C53#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#168111012
C2×#168107302
C2×Q16×Dic532
#202773992
#202750582
#202750282
#202749852
#202749712
#202749162
#202746502
#202745472
#103×Dic532
#202744832
C2×C53×#4512
#2146353