Finite Group Databasebeta

← C2×#20277421 #27542874

Subgroups — C2×#20277421 #27542874

Order 13568.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133203C211yesmaximal, characteristic
2C22×#13133182C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D53C211yesmaximal, characteristic
4#20277421C2116yesmaximal, direct product factor
5C2×#16810527C211yesmaximal, characteristic, complemented
6C2×#16810523C211yesmaximal, characteristic
7C2×#16810517C211yesmaximal, characteristic, complemented
8C2×#16810516C211yesmaximal, characteristic, complemented
9C2×#16810513C211yesmaximal, characteristic, complemented
10C2×#16810512C211yesmaximal, characteristic, complemented
11C2×#16810497C211yesmaximal, characteristic, complemented
12C2×#16810496C211yesmaximal, characteristic, complemented
13C2×#16810494C211yesmaximal, characteristic, complemented
14C2×#16810492C211yesmaximal, characteristic, complemented
15C2×#16810468C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C22⋊D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133203C4116yescomplemented
21C2×#13133203C2218yes—
22C2×#13133182—28no—
23C2×#13133182C2218yescomplemented
24C2×C4×C22⋊D53—28no—
25C2×C4×C22⋊D53C2218yes—
26C22×C4⋊Dic53C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C22⋊Dic53C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42C22×C4×Dic53C2211yescharacteristic
43C22×C4×Dic53C2211yescharacteristic
44C22×C4×Dic53C2211yescharacteristic
45#16810527C2218yescomplemented
46#16810523C2218yes—
47#16810517C2218yescomplemented
48#16810516C2218yescomplemented
49#16810513C2218yescomplemented
50#16810512C2218yescomplemented
51#16810497C2218yescomplemented
52#16810496C2218yescomplemented
53#16810494C2218yescomplemented
54#16810492C2218yescomplemented
55#16810468C2218yescomplemented
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C24×C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C53×#385C2218yescomplemented
68C2×#95×C53C2211yescharacteristic
69C2×#95×C53C2211yescharacteristic
70C24×D53C2311yescharacteristic
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106C2×C418yescomplemented
74C22×Dic106C2314yes—
75C22×C22⋊D53—24no—
76C22×C22⋊D53—24no—
77C22×C22⋊D53C2×C418yes—
78C22×C22⋊D53C2314yes—
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C22×C4×D53—24no—
87C22×C4×D53—42no—
88C22×C4×D53—42no—
89C22×C4×D53C2314yes—
90#13133203C2×C4164yescomplemented
91#13133182—232no—
92C4×C22⋊D53—232no—
93C2×C4⋊Dic53—42no—
94C2×C4⋊Dic53C2314yes—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—24no—
98C2×#11719919—42no—
99C2×#11719919—42no—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×C22⋊Dic53—24no—
106C2×C22⋊Dic53—42no—
107C2×C22⋊Dic53C2×C418yescomplemented
108C2×C22⋊Dic53C2314yes—
109C2×C22⋊Dic53C2314yes—
110C2×C22⋊Dic53C2314yes—
111C2×#11719921—24no—
112C2×#11719921—42no—
113C2×#11719921—42no—
114C2×#11719921C2×C418yescomplemented
115C2×#11719921C2×C418yescomplemented
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×#11719921C2314yes—
120C2×#11719921C2314yes—
121C2×C4×Dic53—24no—
122C2×C4×Dic53—24no—
123C2×C4×Dic53—24no—
124C2×C4×Dic53C2×C418yescomplemented
125C2×C4×Dic53D418yes—
126C2×C4×Dic53C2314yes—
127C2×C4×Dic53C2314yes—
128C2×C4×Dic53C2314yes—
129C2×C4×Dic53C2314yes—
130C2×C4×Dic53C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135#13133124C2314yes—
136#13133124C2314yes—
137C25×C53C2311yescharacteristic
138C23×C4×C53—24no—
139C23×C4×C53—42no—
140C23×C4×C53—42no—
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2314yes—
148C2×C4⋊C4×C53—24no—
149C2×C4⋊C4×C53—42no—
150C2×C4⋊C4×C53C2314yes—
151C2×C4⋊C4×C53C2314yes—
152C2×C22⋊C4×C53—42no—
153C2×C22⋊C4×C53C2×C418yescomplemented
154C2×C22⋊C4×C53C2314yes—
155C2×C22⋊C4×C53C2314yes—
156#95×C53C2314yes—
157#95×C53C2314yes—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53C22×C414yes—
165C24×C53C2412yes—
166C24×C53C2411yescharacteristic
167C23×D53—22no—
168C23×D53—22no—
169C23×D53—22no—
170C23×D53—22no—
171C23×D53—22no—
172C23×D53—22no—
173C23×D53C22×C414yes—
174C23×D53C2412yes—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—28no—
191C22×C4×C53—44no—
192C22×C4×C53—44no—
193C22×C4×C53—416no—
194C22×C4×C53C22×C414yes—
195C22×C4×C53C22×C414yes—
196C22×C4×C53C2×D414yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2412yes—
203C2×C22⋊D53—232no—
204C2×C22⋊D53—28no—
205C2×C22⋊D53—28no—
206C2×C22⋊D53C22×C4116yes—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53—22no—
221C22×Dic53—22no—
222C22×Dic53C22×C414yes—
223C22×Dic53C22×C414yes—
224C22×Dic53C22×C414yes—
225C22×Dic53C2×D414yes—
226C22×Dic53C2×D414yes—
227C22×Dic53#4114yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C22×Dic53C2412yes—
234C22×Dic53C2412yes—
235C2×C4×D53—28no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53—416no—
239C2×Dic106—232no—
240C2×Dic106—28no—
241C2×Dic106—28no—
242C2×Dic106C22×C4116yescomplemented
243C4⋊C4×C53—28no—
244C4⋊C4×C53—44no—
245C22⋊C4×C53—44no—
246C22⋊C4×C53C22×C4116yescomplemented
247C22⋊Dic53—28no—
248C22⋊Dic53—44no—
249C22⋊Dic53C22×C4116yescomplemented
250#11719921—28no—
251#11719921—44no—
252#11719921—44no—
253#11719921C22×C4116yescomplemented
254#11719921C22×C4116yescomplemented
255C4⋊Dic53—44no—
256#11719919—28no—
257#11719919—28no—
258#11719919—28no—
259#11719919—44no—
260#11719919—44no—
261C4×Dic53—28no—
262C4×Dic53—28no—
263C4×Dic53—28no—
264C4×Dic53C22×C4116yescomplemented
265C4×Dic53C2×D4116yes—
266C23×C53—28no—
267C23×C53—28no—
268C23×C53—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—44no—
279C23×C53C23×C414yes—
280C23×C53C23×C412yes—
281C23×C53C22×D412yes—
282C23×C53C2×#4112yes—
283C23×C53H(5,𝔽2)12yes—
284C23×C53H(5,𝔽2)12yes—
285C23×C532−1+412yes—
286C23×C532−1+412yes—
287C23×C53C2511yescharacteristic
288C22×D53—28no—
289C22×D53—28no—
290C22×D53—28no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—44no—
298C22×D53—44no—
299C22×D53—44no—
300C22×D53—44no—
301C22×D53C23×C414yes—
302C2×C4×C53—28no—
303C2×C4×C53—28no—
304C2×C4×C53—28no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—416no—
321C2×C4×C53—44no—
322C2×C4×C53—44no—
323C2×C4×C53—44no—
324C2×C4×C53C23×C414yes—
325C2×C4×C53C23×C414yes—
326C2×C4×C53C22×D414yes—
327C22⋊D53—232no—
328C2×Dic53—28no—
329C2×Dic53—28no—
330C2×Dic53—28no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—44no—
347C2×Dic53—44no—
348C2×Dic53—44no—
349C2×Dic53C4×D4116yes—
350C2×Dic53C23×C414yes—
351C2×Dic53C23×C414yes—
352C2×Dic53C23×C414yes—
353C2×Dic53C22×D414yes—
354C2×Dic53C22×D414yes—
355C2×Dic53C2×#4114yes—
356C4×D53—416no—
357Dic106—232no—
358C2×#2326—531nomaximal, Sylow
359C22×C53—24no—
360C22×C53—24no—
361C22×C53—24no—
362C22×C53—416no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53C2×C4×D414yes—
368C22×C53#52014yes—
369C22×C53#52014yes—
370C22×C53#53514yes—
371C22×C53#53614yes—
372C22×C53#54214yes—
373C22×C53#54214yes—
374C22×C53C24×C411yescharacteristic
375C22×C53C23×D411yescharacteristic
376C22×C53C22×#4111yescharacteristic
377C22×C53C2×H(5,𝔽2)11yescharacteristic
378C22×C53C2×H(5,𝔽2)11yescharacteristic
379C22×C53C2×2−1+411yescharacteristic
380C22×C53C2×2−1+411yescharacteristic
381C2×D53—24no—
382C2×D53—24no—
383C2×D53—24no—
384C2×D53—416no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C4×C53—24no—
390C4×C53—24no—
391C4×C53—24no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395Dic53—24no—
396Dic53—24no—
397Dic53—24no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401Dic53C2×C4×D418yes—
402C22×#124—531no—
403C22×C4×Q8—531no—
404C22×C4×D4—531no—
405#2326—5316no—
406C2×#391—531no—
407C2×#390—531no—
408C2×#388—531no—
409C2×#388—531no—
410C2×#388—531no—
411C2×#388—531no—
412C2×#385—531no—
413C2×#385—531no—
414C2×#385—531no—
415C2×#385D5311yescharacteristic, complemented
416C2×#384—531no—
417C2×#376—531no—
418C2×C53—44no—
419C2×C53#232618yescomplemented
420C2×C53C22×C4×D411yescharacteristic
421C2×C53C2×#52011yescharacteristic
422C2×C53C2×#52011yescharacteristic
423C2×C53C2×#53511yescharacteristic
424C2×C53C2×#53611yescharacteristic
425C2×C53C2×#54211yescharacteristic
426C2×C53C2×#54211yescharacteristic
427D53—44no—
428C23×Q8—531no—
429C23×D4—531no—
430C24×C4—531no—
431C24×C4C2×D5311yescharacteristic
432C2×#124—5316no—
433C2×#124—538no—
434C2×C4×Q8—538no—
435C2×C4×Q8—1068no—
436C2×C4×D4—538no—
437C2×C4×D4—1068no—
438C22×C4⋊C4—531no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444C22×C4⋊C4C2×D5311yescharacteristic
445C22×C4⋊C4C2×D5311yescharacteristic
446C22×C22⋊C4—531no—
447C22×C22⋊C4—531no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—531no—
452C22×C22⋊C4—531no—
453C22×C22⋊C4—531no—
454C22×C22⋊C4C2×D5311yescharacteristic
455C22×C22⋊C4C2×D5311yescharacteristic
456C22×C42—531no—
457C22×C42—531no—
458C22×C42—531no—
459C22×C42—531no—
460C22×C42—531no—
461#391—538no—
462#390—538no—
463#388—538no—
464#388—538no—
465#388—538no—
466#388—538no—
467#385—538no—
468#385—538no—
469#385—538no—
470#385C2×D5318yescomplemented
471#384—538no—
472#376—538no—
473C2×#95—531no—
474C2×#95—531no—
475C2×#95—531no—
476C2×#95—531no—
477C2×#95—531no—
478C2×#95—531no—
479C2×#95C2×D5311yescharacteristic
480C2×#95C2×D5311yescharacteristic
481C53C2×#232611yescharacteristic, complemented, Sylow
482C25—531no—
483C25C22×D5311yescharacteristic
484C22×Q8—538no—
485C22×Q8—534no—
486C22×Q8—1064no—
487C22×Q8—1064no—
488C22×D4—538no—
489C22×D4—534no—
490C22×D4—1064no—
491C22×D4—1064no—
492C23×C4—24no—
493C23×C4—42no—
494C23×C4—42no—
495C23×C4—531no—
496C23×C4—531no—
497C23×C4—531no—
498C23×C4—531no—
499C23×C4—531no—
500C23×C4—531no—
501C23×C4—531no—
502C23×C4—534no—
503C23×C4—1064no—
504C23×C4—2122no—
505C23×C4—2122no—
506C23×C4C22×D5311yescharacteristic
507C23×C4C22×D5311yescharacteristic
508C23×C4C22×D5311yescharacteristic
509C23×C4C22×D5311yescharacteristic
510C23×C4C22×D5311yescharacteristic
511C23×C4C22×D5311yescharacteristic
512C23×C4C22×D5314yes—
513#124—5364no—
514C4×Q8—10632no—
515C4×D4—10632no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4—534no—
519C2×C4⋊C4—534no—
520C2×C4⋊C4—534no—
521C2×C4⋊C4—534no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—534no—
524C2×C4⋊C4—1064no—
525C2×C4⋊C4—1064no—
526C2×C4⋊C4—1064no—
527C2×C4⋊C4—2122no—
528C2×C4⋊C4—2122no—
529C2×C4⋊C4—2122no—
530C2×C4⋊C4C22×D5314yes—
531C2×C4⋊C4C22×D5314yes—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—538no—
534C2×C22⋊C4—534no—
535C2×C22⋊C4—538no—
536C2×C22⋊C4—538no—
537C2×C22⋊C4—534no—
538C2×C22⋊C4—534no—
539C2×C22⋊C4—534no—
540C2×C22⋊C4—534no—
541C2×C22⋊C4—534no—
542C2×C22⋊C4—534no—
543C2×C22⋊C4—534no—
544C2×C22⋊C4—1064no—
545C2×C22⋊C4—1064no—
546C2×C22⋊C4—2122no—
547C2×C22⋊C4—2122no—
548C2×C22⋊C4—2122no—
549C2×C22⋊C4C4×D5318yescomplemented
550C2×C22⋊C4C22×D5314yes—
551C2×C22⋊C4C22×D5314yes—
552C2×C42—538no—
553C2×C42—538no—
554C2×C42—534no—
555C2×C42—534no—
556C2×C42—534no—
557C2×C42—534no—
558C2×C42—534no—
559C2×C42—1064no—
560C2×C42—1064no—
561C2×C42—1064no—
562#95—534no—
563#95—534no—
564#95—534no—
565#95—534no—
566#95—534no—
567#95—534no—
568#95C22×D5314yes—
569#95C22×D5314yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—534no—
577C24—532no—
578C24—1062no—
579C24—1062no—
580C24—1062no—
581C24—1062no—
582C24—1062no—
583C24—1062no—
584C24C2×C4×D5314yes—
585C24C23×D5312yes—
586C24C23×D5311yescharacteristic
587C2×Q8—5316no—
588C2×Q8—1068no—
589C2×Q8—10632no—
590C2×Q8—1068no—
591C2×D4—5316no—
592C2×D4—1068no—
593C2×D4—10632no—
594C2×D4—1068no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—28no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—416no—
614C22×C4—534no—
615C22×C4—534no—
616C22×C4—534no—
617C22×C4—532no—
618C22×C4—534no—
619C22×C4—534no—
620C22×C4—534no—
621C22×C4—532no—
622C22×C4—532no—
623C22×C4—532no—
624C22×C4—532no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1062no—
637C22×C4—1062no—
638C22×C4—1062no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1062no—
642C22×C4—1068no—
643C22×C4—2124no—
644C22×C4—2124no—
645C22×C4—21216no—
646C22×C4C2×C4×D5314yes—
647C22×C4C2×C4×D5314yes—
648C22×C4D4×D5314yes—
649C22×C4C23×D5312yes—
650C22×C4C23×D5312yes—
651C22×C4C23×D5312yes—
652C22×C4C23×D5312yes—
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C4⋊C4—28no—
656C4⋊C4—44no—
657C4⋊C4—1068no—
658C4⋊C4—1068no—
659C4⋊C4—1068no—
660C4⋊C4—2124no—
661C4⋊C4—2124no—
662C4⋊C4—2124no—
663C22⋊C4—44no—
664C22⋊C4—5316no—
665C22⋊C4—5316no—
666C22⋊C4—5316no—
667C22⋊C4—1068no—
668C22⋊C4—1068no—
669C22⋊C4—2124no—
670C22⋊C4—2124no—
671C22⋊C4—2124no—
672C22⋊C4C2×C4×D53116yescomplemented
673C42—5316no—
674C42—5316no—
675C42—1068no—
676C42—1068no—
677C42—1068no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—534no—
692C23—1068no—
693C23—1068no—
694C23—1068no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23—1062no—
701C23—2124no—
702C23—2124no—
703C23—2124no—
704C23—2124no—
705C23C22×C4×D5314yes—
706C23C22×C4×D5312yes—
707C23C2×D4×D5312yes—
708C23#41×D5312yes—
709C23#1313326212yes—
710C23#1313326212yes—
711C23#1313326412yes—
712C23#1313326512yes—
713C23C24×D5311yescharacteristic
714Q8—10632no—
715D4—10632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—5316no—
739C2×C4—534no—
740C2×C4—534no—
741C2×C4—534no—
742C2×C4—534no—
743C2×C4—534no—
744C2×C4—534no—
745C2×C4—1068no—
746C2×C4—1068no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1068no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—21216no—
764C2×C4—2124no—
765C2×C4—2124no—
766C2×C4—2124no—
767C2×C4C22×C4×D5314yes—
768C2×C4C22×C4×D5314yes—
769C2×C4C2×D4×D5314yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—1064no—
779C22—1064no—
780C22—1064no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—21216no—
786C22C4×D4×D5314yes—
787C22#1681110214yes—
788C22#1681110414yes—
789C22#1681118814yes—
790C22#1681119614yes—
791C22#1681124114yes—
792C22#1681124314yes—
793C22C23×C4×D5311yescharacteristic
794C22C22×D4×D5311yescharacteristic
795C22C2×#41×D5311yescharacteristic
796C22C2×#1313326211yescharacteristic
797C22C2×#1313326211yescharacteristic
798C22C2×#1313326411yescharacteristic
799C22C2×#1313326511yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—538no—
807C4—1064no—
808C4—1064no—
809C4—1064no—
810C4—2122no—
811C4—2122no—
812C4—2122no—
813C2—44no—
814C2—2124no—
815C2#2027742118yesdirect product factor
816C2C2×C4×D4×D5311yescharacteristic
817C2C2×#1681110211yescharacteristic
818C2C2×#1681110411yescharacteristic
819C2C2×#1681118811yescharacteristic
820C2C2×#1681119611yescharacteristic
821C2C2×#1681124111yescharacteristic
822C2C2×#1681124311yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
cosocleC23×C53C25
hypercenterC2×#385D53
hypocenterC53C2×#2326
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13133182C2semidirect
4. #20277421C2direct (N × H)
5. C2×#16810527C2semidirect
7. C2×#16810517C2semidirect
8. C2×#16810516C2semidirect
9. C2×#16810513C2semidirect
10. C2×#16810512C2semidirect
11. C2×#16810497C2semidirect
12. C2×#16810496C2semidirect
13. C2×#16810494C2semidirect
14. C2×#16810492C2semidirect
15. C2×#16810468C2semidirect
16. C2×C53×#385C2semidirect
20. C2×#13133203C4semidirect
23. C2×#13133182C22semidirect
45. #16810527C22semidirect
47. #16810517C22semidirect
48. #16810516C22semidirect
49. #16810513C22semidirect
50. #16810512C22semidirect
51. #16810497C22semidirect
52. #16810496C22semidirect
53. #16810494C22semidirect
54. #16810492C22semidirect
55. #16810468C22semidirect
67. C53×#385C22semidirect
73. C22×Dic106C2×C4semidirect
90. #13133203C2×C4semidirect
107. C2×C22⋊Dic53C2×C4semidirect
114. C2×#11719921C2×C4semidirect
115. C2×#11719921C2×C4semidirect
124. C2×C4×Dic53C2×C4semidirect
153. C2×C22⋊C4×C53C2×C4semidirect
242. C2×Dic106C22×C4semidirect
246. C22⋊C4×C53C22×C4semidirect
249. C22⋊Dic53C22×C4semidirect
253. #11719921C22×C4semidirect
254. #11719921C22×C4semidirect
264. C4×Dic53C22×C4semidirect
415. C2×#385D53semidirect
419. C2×C53#2326semidirect
470. #385C2×D53semidirect
481. C53C2×#2326semidirect
549. C2×C22⋊C4C4×D53semidirect
672. C22⋊C4C2×C4×D53semidirect
815. C2#20277421direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332032
C22×#131331822
C22×C4×C22⋊D532
#202774212
C2×#168105272
C2×#168105232
C2×#168105172
C2×#168105162
C2×#168105132
C2×#168105122
C2×#168104972
C2×#168104962
C2×#168104942
C2×#168104922
C2×#168104682
C2×C53×#3852
C2×#232653