Finite Group Databasebeta

← #27350159

Subgroups — #27350159

Order 13568.

1450 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133200C211yesmaximal, characteristic
2C2×#16810587C211yesmaximal, characteristic, complemented
3#20273064C214yesmaximal, complemented
4#20273061C214yesmaximal, complemented
5#20273044C212yesmaximal, complemented
6#20273041C212yesmaximal, complemented
7C2×C53×#407C211yesmaximal, characteristic, complemented
8C23×C22⋊D53C411yescharacteristic
9C22×#11719917—21no—
10C2×#13133200—21no—
11C2×#13133200—21no—
12C2×#13133200—21no—
13C2×#13133200—21no—
14C2×#13133200—21no—
15C2×#13133200—21no—
16C2×#13133200—21no—
17C2×#13133200—21no—
18C2×#13133200C412yes—
19C2×#13133200C412yes—
20C2×#13133200C2212yes—
21C2×#13133200C2212yes—
22C22×#11719919C411yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C411yescharacteristic
25C22×#11719921C411yescharacteristic
26C22×#11719921C2211yescharacteristic
27#16810587—21no—
28#16810587—21no—
29#16810587C2212yes—
30#16810587C2212yescomplemented
31C2×C22⋊#88322—21no—
32C2×C22⋊#88322C2212yescomplemented
33#16810348C2218yescomplemented
34#16810346C2218yescomplemented
35C24×C4×C53C2211yescharacteristic
36C22×M16×C53—21no—
37C53×#407—21no—
38C53×#407—21no—
39C53×#407C2212yes—
40C53×#407C2212yescomplemented
41C2×C22⋊C8×C53—21no—
42C2×C22⋊C8×C53C2212yescomplemented
43C24×D53C2×C411yescharacteristic
44C22×C22⋊D53—21no—
45C22×C22⋊D53—21no—
46C22×C22⋊D53—21no—
47C22×C22⋊D53—21no—
48C22×C22⋊D53—44no—
49C22×C22⋊D53C2×C412yes—
50C22×C22⋊D53C2×C412yes—
51C23×Dic53C2×C411yescharacteristic
52C23×Dic53C2×C411yescharacteristic
53C23×Dic53C2×C411yescharacteristic
54C2×#11719917—22no—
55C2×#11719917—22no—
56C2×#11719917—44no—
57C22×#88322—22no—
58#13133200—22no—
59#13133200—22no—
60#13133200—22no—
61#13133200—22no—
62#13133200—22no—
63#13133200—22no—
64#13133200—22no—
65#13133200—22no—
66#13133200—22no—
67#13133200—22no—
68#13133200—22no—
69#13133200—22no—
70#13133200—22no—
71#13133200—22no—
72#13133200—22no—
73#13133200—22no—
74C2×#11719919—21no—
75C2×#11719919—21no—
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×#11719919—21no—
79C2×#11719919—21no—
80C2×#11719919—21no—
81C2×#11719919—21no—
82C2×#11719919C2×C412yes—
83C2×#11719919C2×C412yes—
84C2×#11719919C2×C412yes—
85C2×#11719919C2312yes—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53C2×C412yes—
91C2×C22⋊Dic53C2×C412yes—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921C2×C412yes—
101C2×#11719921C2×C412yes—
102C2×#11719921C2×C412yes—
103C2×#11719921C2312yes—
104C22⋊#88322—22no—
105C22⋊#88322—22no—
106C22⋊#88322—22no—
107C22⋊#88322C2314yes—
108C25×C53C2×C411yescharacteristic
109C23×C4×C53—44no—
110C23×C4×C53C2×C411yescharacteristic
111C23×C4×C53C2×C411yescharacteristic
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53D411yescharacteristic
114C23×C4×C53D411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C2×M16×C53—22no—
125C2×M16×C53—22no—
126C2×M16×C53—44no—
127C22×C8×C53—22no—
128C22⋊C8×C53—22no—
129C22⋊C8×C53—22no—
130C22⋊C8×C53—22no—
131C22⋊C8×C53C2314yes—
132C24×C53—24no—
133C24×C53—42no—
134C24×C53—42no—
135C24×C53C22⋊C411yescharacteristic
136C24×C53C22⋊C411yescharacteristic
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C22×C411yescharacteristic
140C24×C53C22×C411yescharacteristic
141C24×C53C22×C411yescharacteristic
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—42no—
145C23×D53—42no—
146C23×D53—42no—
147C23×D53C22×C412yes—
148C22×C4×C53—24no—
149C22×C4×C53—24no—
150C22×C4×C53—42no—
151C22×C4×C53—42no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53—42no—
158C22×C4×C53—42no—
159C22×C4×C53—42no—
160C22×C4×C53—42no—
161C22×C4×C53—42no—
162C22×C4×C53C22⋊C411yescharacteristic
163C22×C4×C53C22⋊C411yescharacteristic
164C22×C4×C53C22⋊C411yescharacteristic
165C22×C4×C53C22⋊C411yescharacteristic
166C22×C4×C53C22⋊C411yescharacteristic
167C22×C4×C53C22⋊C411yescharacteristic
168C22×C4×C53C22⋊C411yescharacteristic
169C22×C4×C53C22⋊C411yescharacteristic
170C22×C4×C53C22⋊C411yescharacteristic
171C22×C4×C53C22⋊C411yescharacteristic
172C22×C4×C53C22⋊C411yescharacteristic
173C22×C4×C53C22⋊C411yescharacteristic
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C22×C411yescharacteristic
176C22×C4×C53C22×C411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2411yescharacteristic
190C2×C22⋊D53—22no—
191C2×C22⋊D53—22no—
192C2×C22⋊D53—22no—
193C2×C22⋊D53—22no—
194C2×C22⋊D53—44no—
195C2×C22⋊D53—44no—
196C2×C22⋊D53—44no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53—44no—
199C2×C22⋊D53—44no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—42no—
207C22×Dic53—42no—
208C22×Dic53—42no—
209C22×Dic53C22×C412yes—
210C22×Dic53C22×C412yes—
211C22×Dic53C22×C412yes—
212M16×C53—44no—
213M16×C53—44no—
214C2×C8×C53—24no—
215C2×C8×C53—44no—
216C22⋊Dic53—22no—
217C22⋊Dic53—22no—
218C22⋊Dic53—22no—
219C22⋊Dic53—22no—
220#11719921—22no—
221#11719921—22no—
222#11719921—22no—
223#11719921—22no—
224#11719921—22no—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228#11719919—22no—
229#11719919—22no—
230#11719919—22no—
231#11719919—22no—
232#11719919—22no—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719917—44no—
237#11719917—44no—
238C2×#88322—24no—
239C2×#88322—44no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—416no—
261C23×C53#9914yes—
262C23×C53C2×C22⋊C411yescharacteristic
263C23×C53C2×C22⋊C411yescharacteristic
264C23×C53C2×C22⋊C411yescharacteristic
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C23×C411yescharacteristic
269C22×D53—22no—
270C22×D53—24no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—88no—
280C2×C4×C53—22no—
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—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53C2×C22⋊C411yescharacteristic
309C2×C4×C53C2×C22⋊C411yescharacteristic
310C2×C4×C53C2×C22⋊C411yescharacteristic
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C2×C22⋊C411yescharacteristic
313C2×C4×C53C2×C22⋊C411yescharacteristic
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C22×D411yescharacteristic
316C22⋊D53—44no—
317C22⋊D53—44no—
318C22⋊D53—44no—
319C22⋊D53—44no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—24no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C8×C53—44no—
333#88322—44no—
334#17392—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—21no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—21no—
351C22×C53—21no—
352C22×C53—44no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53—44no—
356C22×C53—44no—
357C22×C53—44no—
358C22×C53C2×#9912yes—
359C22×C53C2×#9912yes—
360C22×C53C2×#9912yes—
361C22×C53#41312yes—
362C22×C53C22×C22⋊C411yescharacteristic
363C22×C53#56812yes—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—84no—
368C2×D53—84no—
369C2×D53—84no—
370C4×C53—21no—
371C4×C53—21no—
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—21no—
375C4×C53—21no—
376C4×C53—21no—
377C4×C53—21no—
378Dic53—42no—
379Dic53—42no—
380Dic53—42no—
381C22×#123—531no—
382C2×#407—531no—
383C2×#407D5311yescharacteristic, complemented
384#1468—534no—
385#1468—534no—
386#1463—532no—
387#1462—532no—
388C2×C53—22no—
389C2×C53—22no—
390C2×C53—22no—
391C2×C53—22no—
392C2×C53—22no—
393C2×C53—41no—
394C2×C53—41no—
395C2×C53#287911yescharacteristic
396C2×C53C22×#9911yescharacteristic
397C2×C53C2×#41311yescharacteristic
398D53—82no—
399C23×D4—531no—
400C24×C4C2×D5311yescharacteristic
401C22×M16—21no—
402C22×M16—1061no—
403C2×#123—532no—
404C2×#123—532no—
405C2×#123—532no—
406C2×#123—532no—
407C2×#123—1061no—
408C2×#123—1061no—
409C2×#123—1061no—
410C2×#123—1061no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×#123—1061no—
414C2×#123—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4—531no—
420#407—21no—
421#407—21no—
422#407—532no—
423#407—532no—
424#407—1061no—
425#407—1061no—
426#407C2×D5312yes—
427#407C2×D5312yescomplemented
428C2×C22⋊C8—21no—
429C2×C22⋊C8—532no—
430C2×C22⋊C8—1061no—
431C2×C22⋊C8C2×D5312yescomplemented
432#324—538no—
433#323—538no—
434C53#1739211yescharacteristic, complemented, Sylow
435C25—531no—
436C25C4×D5311yescharacteristic
437C22×D4—532no—
438C22×D4—532no—
439C22×D4—1061no—
440C22×D4—1061no—
441C22×D4—1061no—
442C22×D4—1061no—
443C22×D4—2124no—
444C23×C4—44no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4C4×D5311yescharacteristic
449C23×C4C4×D5311yescharacteristic
450C23×C4C4×D5311yescharacteristic
451C23×C4D21211yescharacteristic
452C23×C4D21211yescharacteristic
453C23×C4D21211yescharacteristic
454C23×C4D21211yescharacteristic
455C23×C4C22⋊D5311yescharacteristic
456C23×C4C22⋊D5311yescharacteristic
457C23×C4C22⋊D5311yescharacteristic
458C23×C4C22⋊D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C23×C4C22×D5311yescharacteristic
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—44no—
465C2×M16—1062no—
466C2×M16—1062no—
467C2×M16—2124no—
468C22×C8—22no—
469C22×C8—1062no—
470#123—1062no—
471#123—1062no—
472#123—1062no—
473#123—1062no—
474#123—1062no—
475#123—1062no—
476#123—1062no—
477#123—1062no—
478#123—1062no—
479#123—1062no—
480#123—1062no—
481#123—1062no—
482#123—1062no—
483#123—1062no—
484#123—1062no—
485#123—1062no—
486C2×C4⋊C4—532no—
487C2×C4⋊C4—532no—
488C2×C4⋊C4—532no—
489C2×C4⋊C4—532no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C22⋊C4—532no—
499C2×C22⋊C4—532no—
500C2×C22⋊C4—532no—
501C2×C22⋊C4—532no—
502C2×C22⋊C4—532no—
503C2×C22⋊C4—532no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—534no—
520C22⋊C8—1062no—
521C22⋊C8—1062no—
522C22⋊C8—1062no—
523C22⋊C8C22×D5314yes—
524C24—24no—
525C24—42no—
526C24—42no—
527C24—532no—
528C24—1061no—
529C24—1061no—
530C24—2122no—
531C24—2122no—
532C24—2122no—
533C24#1171992111yescharacteristic
534C24#1171992111yescharacteristic
535C24#1171992111yescharacteristic
536C24#1171992111yescharacteristic
537C24C2×C4×D5311yescharacteristic
538C24C2×C4×D5311yescharacteristic
539C24C2×C4×D5311yescharacteristic
540C2×D4—1062no—
541C2×D4—1062no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—2124no—
545C2×D4—2124no—
546C2×D4—2124no—
547C2×D4—2124no—
548C2×D4—2124no—
549C2×D4—2124no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4—2122no—
576C22×C4#1171992111yescharacteristic
577C22×C4#1171992111yescharacteristic
578C22×C4#1171992111yescharacteristic
579C22×C4#1171992111yescharacteristic
580C22×C4#1171992111yescharacteristic
581C22×C4#1171992111yescharacteristic
582C22×C4#1171992111yescharacteristic
583C22×C4#1171992111yescharacteristic
584C22×C4#1171992111yescharacteristic
585C22×C4#1171992111yescharacteristic
586C22×C4#1171992111yescharacteristic
587C22×C4#1171992111yescharacteristic
588C22×C4C2×C4×D5311yescharacteristic
589C22×C4C2×C4×D5311yescharacteristic
590C22×C4C2×C4×D5311yescharacteristic
591C22×C4C2×D21211yescharacteristic
592C22×C4C2×D21211yescharacteristic
593C22×C4C2×D21211yescharacteristic
594C22×C4C2×D21211yescharacteristic
595C22×C4C2×D21211yescharacteristic
596C22×C4C2×D21211yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C2×C22⋊D5311yescharacteristic
600C22×C4C2×C22⋊D5311yescharacteristic
601C22×C4C2×C22⋊D5311yescharacteristic
602C22×C4C2×C22⋊D5311yescharacteristic
603C22×C4C23×D5311yescharacteristic
604M16—44no—
605M16—44no—
606M16—2124no—
607M16—2124no—
608C2×C8—24no—
609C2×C8—44no—
610C2×C8—1064no—
611C2×C8—2124no—
612C4⋊C4—1062no—
613C4⋊C4—1062no—
614C4⋊C4—1062no—
615C4⋊C4—1062no—
616C4⋊C4—1062no—
617C4⋊C4—1062no—
618C4⋊C4—1062no—
619C4⋊C4—1062no—
620C22⋊C4—1062no—
621C22⋊C4—1062no—
622C22⋊C4—1062no—
623C22⋊C4—1062no—
624C22⋊C4—1062no—
625C22⋊C4—1062no—
626C22⋊C4—1062no—
627C22⋊C4—1062no—
628C22⋊C4—1062no—
629C22⋊C4—1062no—
630C22⋊C4—1062no—
631C22⋊C4—1062no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—416no—
653C23—1064no—
654C23—1062no—
655C23—4248no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23—2122no—
661C23—2122no—
662C23—2122no—
663C23—2122no—
664C23#1313313114yes—
665C23C2×#1171992111yescharacteristic
666C23C2×#1171992111yescharacteristic
667C23C2×#1171992111yescharacteristic
668C23C2×#1171992111yescharacteristic
669C23C2×#1171992111yescharacteristic
670C23C2×#1171992111yescharacteristic
671C23C22×C4×D5311yescharacteristic
672D4—2124no—
673D4—2124no—
674D4—2124no—
675D4—2124no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1064no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4C2×#1171992111yescharacteristic
717C2×C4C2×#1171992111yescharacteristic
718C2×C4C2×#1171992111yescharacteristic
719C2×C4C2×#1171992111yescharacteristic
720C2×C4C2×#1171992111yescharacteristic
721C2×C4C2×#1171992111yescharacteristic
722C2×C4C22×C22⋊D5311yescharacteristic
723C2×C4C22×D21211yescharacteristic
724C8—44no—
725C8—2124no—
726C22—28no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—4244no—
750C22—4244no—
751C22—4244no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22C2×#1313313112yes—
756C22C2×#1313313112yes—
757C22C2×#1313313112yes—
758C22#1681060512yes—
759C22C22×#1171992111yescharacteristic
760C22#1681138912yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—2122no—
770C4—2122no—
771C4—2122no—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—4242no—
780C2#2028315911yescharacteristic
781C2C22×#1313313111yescharacteristic
782C2C2×#1681060511yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#407C2
socleC22×C53C22×C22⋊C4
prime radicalC23×C22⋊D53C4
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53#17392
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16810587C2semidirect
3. #20273064C2semidirect
4. #20273061C2semidirect
5. #20273044C2semidirect
6. #20273041C2semidirect
7. C2×C53×#407C2semidirect
30. #16810587C22semidirect
32. C2×C22⋊#88322C22semidirect
33. #16810348C22semidirect
34. #16810346C22semidirect
40. C53×#407C22semidirect
42. C2×C22⋊C8×C53C22semidirect
383. C2×#407D53semidirect
427. #407C2×D53semidirect
431. C2×C22⋊C8C2×D53semidirect
434. C53#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#131332002
C2×#168105872
#202730642
#202730612
#202730442
#202730412
C2×C53×#4072
#1739253