Finite Group Databasebeta

← #27351254

Subgroups — #27351254

Order 13568.

1574 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
1C2×#16811134C211yesmaximal, characteristic
2C2×#16810587C211yesmaximal, characteristic, complemented
3#20273234C212yesmaximal, complemented
4#20273230C212yesmaximal, complemented
5#20273217C214yesmaximal, complemented
6#20273204C214yesmaximal, complemented
7C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9C22×#11719917—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134—21no—
14#16811134C412yescomplemented
15#16811134C412yescomplemented
16#16811134C2212yes—
17#16811134C2212yes—
18C2×#13133200—21no—
19C2×#13133196C411yescharacteristic, complemented
20C2×#13133196C2211yescharacteristic
21C2×#13133191C411yescharacteristic, complemented
22C2×#13133191C2211yescharacteristic
23C2×#13133186—21no—
24C2×C4×C22⋊D53—21no—
25C2×C4×C22⋊D53—21no—
26C2×#13133176C411yescharacteristic, complemented
27#16810587—21no—
28#16810587—21no—
29#16810587C2212yes—
30#16810587C2212yescomplemented
31C2×C22⋊#88322—21no—
32C2×C22⋊#88322C2212yescomplemented
33#16810359C2218yescomplemented
34#16810356C2218yescomplemented
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53—21no—
37C22×C42×C53—21no—
38C4×C22⋊C4×C53—21no—
39C4×C22⋊C4×C53—21no—
40C4×C22⋊C4×C53C2212yes—
41C4×C22⋊C4×C53C2212yescomplemented
42C2×#95×C53C2212yescomplemented
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—44no—
46C2×#11719945C2×C412yes—
47C2×#11719945C2×C412yescomplemented
48C22×Dic106C2×C411yescharacteristic, complemented
49C22×D212C2×C411yescharacteristic, complemented
50C22×C22⋊D53—21no—
51C22×C22⋊D53—21no—
52C22×C22⋊D53—21no—
53C22×C4×D53—21no—
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#13133196—21no—
63#13133196—21no—
64#13133196—21no—
65#13133196—21no—
66#13133196C2×C412yes—
67#13133196C2×C412yescomplemented
68#13133196C2×C412yescomplemented
69#13133196C2312yes—
70#13133191—21no—
71#13133191—21no—
72#13133191—21no—
73#13133191—21no—
74#13133191C2×C412yes—
75#13133191C2×C412yescomplemented
76#13133191C2×C412yescomplemented
77#13133191C2312yes—
78#13133186—22no—
79#13133186—22no—
80#13133186—22no—
81#13133186—22no—
82C4×C22⋊D53—22no—
83C4×C22⋊D53—22no—
84C4×C22⋊D53—22no—
85C4×C22⋊D53—22no—
86C4×C22⋊D53—22no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90#13133176—21no—
91#13133176—21no—
92#13133176C2×C412yes—
93#13133176C2×C412yescomplemented
94C2×C4⋊Dic53C2×C411yescharacteristic, complemented
95C2×C4⋊Dic53C2×C411yescharacteristic, complemented
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×C4×Dic53—21no—
104C22⋊#88322—22no—
105C22⋊#88322—22no—
106C22⋊#88322—22no—
107C22⋊#88322C2314yes—
108C25×C53D411yescharacteristic
109C23×C4×C53—22no—
110C23×C4×C53—44no—
111C23×C4×C53C2×C411yescharacteristic
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53C2×C411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53D411yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—28no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C42×C53—22no—
129C2×C42×C53—22no—
130C2×C42×C53—44no—
131#95×C53—22no—
132#95×C53C2314yes—
133C24×C53—24no—
134C24×C53—42no—
135C24×C53—42no—
136C24×C53C22⋊C411yescharacteristic
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C22⋊C411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C23×D53—21no—
144C22×C4×C53—24no—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—28no—
148C22×C4×C53—24no—
149C22×C4×C53—42no—
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—44no—
161C22×C4×C53—44no—
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×C53C22×C411yescharacteristic
178C22×C4×C53C22×C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
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—22no—
195C2×C22⋊D53—22no—
196C2×C22⋊D53—44no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53—44no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202#11719945—44no—
203#11719945—44no—
204#11719945—44no—
205#11719945—44no—
206C2×D212—21no—
207C2×D212—42no—
208C2×D212C22×C412yes—
209C2×C4×D53—22no—
210C2×C4×D53—22no—
211C2×C4×D53—44no—
212C2×Dic106—21no—
213C2×Dic106—42no—
214C2×Dic106C22×C412yes—
215C22⋊C4×C53—28no—
216C22⋊C4×C53—28no—
217C42×C53—44no—
218C42×C53—44no—
219C22⋊Dic53—22no—
220C22⋊Dic53—22no—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228#11719921—22no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53C22×C412yes—
232C4⋊Dic53C22×C412yes—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237C4×Dic53—22no—
238C4×Dic53—22no—
239#11719917—44no—
240#11719917—44no—
241C2×#88322—24no—
242C2×#88322—44no—
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—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—416no—
264C23×C53#10414yes—
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53C22×D411yescharacteristic
272C22×D53—22no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
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—28no—
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—416no—
305C2×C4×C53—44no—
306C2×C4×C53—44no—
307C2×C4×C53#9914yes—
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×C53C23×C411yescharacteristic
315C2×C4×C53C22×D411yescharacteristic
316C22⋊D53—44no—
317C22⋊D53—44no—
318C22⋊D53—44no—
319C22⋊D53—44no—
320C22⋊D53—44no—
321C22⋊D53—44no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328D212—42no—
329D212—42no—
330C4×D53—44no—
331C4×D53—44no—
332Dic106—42no—
333Dic106—42no—
334#88322—44no—
335#17542—531nomaximal, Sylow
336C22×C53—28no—
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—21no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53—44no—
356C22×C53—44no—
357C22×C53—44no—
358C22×C53—44no—
359C22×C53C2×#9912yes—
360C22×C53C2×#10412yes—
361C22×C53C2×#10412yes—
362C22×C53C2×#10412yes—
363C22×C53C22×C22⋊C411yescharacteristic
364C22×C53#57512yes—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—84no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53—21no—
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—21no—
375C4×C53—48no—
376C4×C53C2×#9912yes—
377C4×C53C2×#9912yes—
378Dic53—42no—
379Dic53—42no—
380Dic53—42no—
381C2×#525—531no—
382C2×#407—531no—
383C2×C4×C22⋊C4D5311yescharacteristic, complemented
384#1508—532no—
385#1507—532no—
386#1504—534no—
387#1501—534no—
388C2×C53—22no—
389C2×C53—22no—
390C2×C53—22no—
391C2×C53—22no—
392C2×C53—22no—
393C2×C53—41no—
394C2×C53—41no—
395C2×C53C22×#9911yescharacteristic
396C2×C53#289611yescharacteristic
397C2×C53C22×#10411yescharacteristic
398D53—82no—
399C22×#41—531no—
400C24×C4C2×D5311yescharacteristic
401C22×M16—1061no—
402#525—532no—
403#525—532no—
404#525—532no—
405#525—532no—
406#525—1061no—
407#525—1061no—
408#525—1061no—
409#525—1061no—
410C2×#123—1061no—
411C2×C22⋊Q8—531no—
412C2×C22⋊Q8—531no—
413C2×#121—531no—
414C2×#121—531no—
415C2×#120—1061no—
416C2×C4×D4—1061no—
417C2×C4×D4—1061no—
418C2×#117—531no—
419C22×C22⋊C4—21no—
420C22×C42—21no—
421#407—532no—
422#407—532no—
423#407—1061no—
424#407—1061no—
425C2×C22⋊C8—532no—
426C2×C22⋊C8—1061no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2×D5312yes—
430C4×C22⋊C4C2×D5312yescomplemented
431C2×#95C2×D5312yescomplemented
432#328—538no—
433#327—538no—
434C53#1754211yescharacteristic, complemented, Sylow
435C25C22⋊D5311yescharacteristic
436C2×#41—532no—
437C2×#41—532no—
438C2×#41—1061no—
439C2×#41—1061no—
440C2×#41—2124no—
441C22×Q8—531no—
442C22×D4—531no—
443C22×D4—1061no—
444C22×D4—1061no—
445C22×D4—1061no—
446C23×C4—22no—
447C23×C4—44no—
448C23×C4—1061no—
449C23×C4C4×D5311yescharacteristic
450C23×C4C4×D5311yescharacteristic
451C23×C4C4×D5311yescharacteristic
452C23×C4C4×D5311yescharacteristic
453C23×C4D21211yescharacteristic
454C23×C4D21211yescharacteristic
455C23×C4D21211yescharacteristic
456C23×C4D21211yescharacteristic
457C23×C4C22⋊D5311yescharacteristic
458C23×C4C22⋊D5311yescharacteristic
459C23×C4C22⋊D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C23×C4C22×D5311yescharacteristic
462C23×C4C22×D5311yescharacteristic
463C2×M16—1062no—
464C2×M16—1062no—
465C2×M16—2124no—
466C22×C8—1062no—
467#123—1062no—
468#123—1062no—
469#123—1062no—
470#123—1062no—
471C22⋊Q8—532no—
472C22⋊Q8—532no—
473C22⋊Q8—532no—
474C22⋊Q8—532no—
475C22⋊Q8—1061no—
476C22⋊Q8—1061no—
477C22⋊Q8—1061no—
478C22⋊Q8—1061no—
479#121—532no—
480#121—532no—
481#121—532no—
482#121—532no—
483#121—1061no—
484#121—1061no—
485#121—1061no—
486#121—1061no—
487#120—1062no—
488#120—1062no—
489#120—1062no—
490#120—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494C4×D4—1062no—
495C4×D4—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499#117—532no—
500#117—532no—
501#117—1061no—
502#117—1061no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C22⋊C4—28no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—44no—
518C2×C42—1061no—
519C22⋊C8—534no—
520C22⋊C8—1062no—
521C22⋊C8—1062no—
522C22⋊C8—1062no—
523#95—22no—
524#95C22×D5314yes—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—1061no—
529C24#1171992111yescharacteristic
530C24#1171992111yescharacteristic
531C24#1171992111yescharacteristic
532C24#1171992111yescharacteristic
533C24C2×C22⋊D5311yescharacteristic
534C24C2×C22⋊D5311yescharacteristic
535C24C2×C22⋊D5311yescharacteristic
536#41—2124no—
537#41—2124no—
538#41—2124no—
539#41—2124no—
540C2×Q8—532no—
541C2×Q8—1061no—
542C2×Q8—2122no—
543C2×D4—532no—
544C2×D4—1062no—
545C2×D4—1062no—
546C2×D4—1062no—
547C2×D4—1062no—
548C2×D4—1062no—
549C2×D4—1062no—
550C2×D4—1061no—
551C2×D4—2122no—
552C2×D4—2124no—
553C2×D4—2124no—
554C2×D4—2124no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—28no—
559C22×C4—24no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—2124no—
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×C4#1171992111yescharacteristic
589C22×C4#1171992111yescharacteristic
590C22×C4#1171992111yescharacteristic
591C22×C4C2×C4×D5311yescharacteristic
592C22×C4C2×C4×D5311yescharacteristic
593C22×C4C2×C4×D5311yescharacteristic
594C22×C4C2×C4×D5311yescharacteristic
595C22×C4C2×C4×D5311yescharacteristic
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4C2×D21211yescharacteristic
598C22×C4C2×D21211yescharacteristic
599C22×C4C2×D21211yescharacteristic
600C22×C4C2×D21211yescharacteristic
601C22×C4C2×D21211yescharacteristic
602C22×C4C2×D21211yescharacteristic
603C22×C4C2×C22⋊D5311yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C2×C22⋊D5311yescharacteristic
606C22×C4C23×D5311yescharacteristic
607M16—2124no—
608M16—2124no—
609C2×C8—1064no—
610C2×C8—2124no—
611C4⋊C4—532no—
612C4⋊C4—532no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1062no—
616C4⋊C4—1062no—
617C4⋊C4—1062no—
618C4⋊C4—1062no—
619C22⋊C4—28no—
620C22⋊C4—28no—
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—
631C42—44no—
632C42—44no—
633C42—1062no—
634C42—1062no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—1062no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23#1313314514yes—
661C23C2×#1171992111yescharacteristic
662C23C2×#1171992111yescharacteristic
663C23C2×#1171992111yescharacteristic
664C23C2×#1171992111yescharacteristic
665C23C2×#1171992111yescharacteristic
666C23C2×#1171992111yescharacteristic
667C23C22×C22⋊D5311yescharacteristic
668Q8—2122no—
669Q8—2122no—
670D4—2122no—
671D4—2124no—
672D4—2124no—
673D4—2124no—
674D4—2124no—
675D4—2124no—
676D4—2124no—
677D4—2122no—
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—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
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—41no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—2124no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2124no—
717C2×C4#1313313114yes—
718C2×C4C2×#1171992111yescharacteristic
719C2×C4C2×#1171992111yescharacteristic
720C2×C4C2×#1171992111yescharacteristic
721C2×C4C2×#1171992111yescharacteristic
722C2×C4C2×#1171992111yescharacteristic
723C2×C4C2×#1171992111yescharacteristic
724C2×C4C22×C4×D5311yescharacteristic
725C2×C4C22×D21211yescharacteristic
726C8—2124no—
727C22—28no—
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—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—4244no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22C2×#1313313112yes—
755C22C2×#1313314512yes—
756C22C2×#1313314512yes—
757C22C2×#1313314512yes—
758C22C22×#1171992111yescharacteristic
759C22#1681142112yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—48no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4C2×#1313313112yes—
771C4C2×#1313313112yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—4242no—
780C2C22×#1313313111yescharacteristic
781C2#2028323211yescharacteristic
782C2C22×#1313314511yescharacteristic
subgroupG/H
centerC2×C4C2×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C4×C22⋊C4×C53C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#17542
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810587C2semidirect
3. #20273234C2semidirect
4. #20273230C2semidirect
5. #20273217C2semidirect
6. #20273204C2semidirect
7. C2×C4×C22⋊C4×C53C2semidirect
8. C22×#11719945C4semidirect
14. #16811134C4semidirect
15. #16811134C4semidirect
19. C2×#13133196C4semidirect
21. C2×#13133191C4semidirect
26. C2×#13133176C4semidirect
30. #16810587C22semidirect
32. C2×C22⋊#88322C22semidirect
33. #16810359C22semidirect
34. #16810356C22semidirect
41. C4×C22⋊C4×C53C22semidirect
42. C2×#95×C53C22semidirect
47. C2×#11719945C2×C4semidirect
48. C22×Dic106C2×C4semidirect
49. C22×D212C2×C4semidirect
67. #13133196C2×C4semidirect
68. #13133196C2×C4semidirect
75. #13133191C2×C4semidirect
76. #13133191C2×C4semidirect
93. #13133176C2×C4semidirect
94. C2×C4⋊Dic53C2×C4semidirect
95. C2×C4⋊Dic53C2×C4semidirect
383. C2×C4×C22⋊C4D53semidirect
430. C4×C22⋊C4C2×D53semidirect
431. C2×#95C2×D53semidirect
434. C53#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C2×#168105872
#202732342
#202732302
#202732172
#202732042
C2×C4×C22⋊C4×C532
#1754253