Finite Group Databasebeta

← C2×#20279156 #27553864

Subgroups — C2×#20279156 #27553864

Order 13568.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133202C211yesmaximal, characteristic
2C22×#13133174C211yesmaximal, characteristic, complemented
3#20279156C2116yesmaximal, direct product factor
4C2×#16810564C211yesmaximal, characteristic, complemented
5C2×#16810558C211yesmaximal, characteristic, complemented
6C2×#16810557C211yesmaximal, characteristic, complemented
7C2×#16810552C211yesmaximal, characteristic, complemented
8C2×#16810515C211yesmaximal, characteristic, complemented
9C2×#16810514C211yesmaximal, characteristic, complemented
10C2×#16810504C211yesmaximal, characteristic, complemented
11C2×#16810501C211yesmaximal, characteristic
12C2×#16810501C211yesmaximal, characteristic
13C2×#16810482C211yesmaximal, characteristic, complemented
14C2×#16810480C211yesmaximal, characteristic, complemented
15C2×#95×D53C211yesmaximal, characteristic, complemented
16C2×C53×#387C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C2×#13133202—28no—
22C2×#13133202C2218yes—
23C2×#13133174—28no—
24C2×#13133174C2218yescomplemented
25C22×C4⋊Dic53C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41#16810564C2218yescomplemented
42#16810558C2218yescomplemented
43#16810557C2218yescomplemented
44#16810552C2218yescomplemented
45#16810515C2218yescomplemented
46#16810514C2218yescomplemented
47#16810504C2218yescomplemented
48#16810501C2218yes—
49#16810501C2218yes—
50#16810482C2218yescomplemented
51#16810480C2218yescomplemented
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60#95×D53C2218yescomplemented
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C53×#387C2218yescomplemented
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C24×D53C2311yescharacteristic
71C22×D212—24no—
72C22×D212—24no—
73C22×D212—24no—
74C22×D212C2314yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C22×C4×D53—24no—
82C22×C4×D53—24no—
83C22×C4×D53—24no—
84C22×C4×D53—24no—
85C22×C4×D53—24no—
86C22×C4×D53—24no—
87C22×C4×D53—42no—
88C22×C4×D53—42no—
89C22×C4×D53D418yes—
90C22×C4×D53C2314yes—
91C22×C4×D53C2314yes—
92C22×C4×D53C2314yes—
93#13133202—232no—
94#13133174—232no—
95C2×C4⋊Dic53—42no—
96C2×C4⋊Dic53C2314yes—
97C2×#11719919—24no—
98C2×#11719919—24no—
99C2×#11719919—24no—
100C2×#11719919—24no—
101C2×#11719919—42no—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719921—24no—
108C2×#11719921—24no—
109C2×#11719921—24no—
110C2×#11719921—24no—
111C2×#11719921—24no—
112C2×#11719921—24no—
113C2×#11719921—24no—
114C2×#11719921—42no—
115C2×#11719921—42no—
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×#11719921C2314yes—
120C2×#11719921C2314yes—
121C2×#11719921C2314yes—
122C2×#11719921C2314yes—
123C2×#11719921C2314yes—
124C2×#11719921C2314yes—
125C2×C4×Dic53—24no—
126C2×C4×Dic53C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53—24no—
143C2×C4⋊C4×C53—24no—
144C2×C4⋊C4×C53C2314yes—
145C2×C4⋊C4×C53C2314yes—
146C2×C42×C53—24no—
147C2×C42×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150#95×C53C2314yes—
151#95×C53C2314yes—
152C24×C53C2411yescharacteristic
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53—22no—
158C23×D53—22no—
159C23×D53—22no—
160C23×D53—22no—
161C23×D53—22no—
162C23×D53—22no—
163C23×D53—22no—
164C23×D53C2×D414yes—
165C23×D53#4114yes—
166C23×D53#4114yes—
167C23×D53C2412yes—
168C23×D53C2412yes—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
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×C53C2×D414yes—
189C22×C4×C53#4114yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53C2×D414yes—
214C22×Dic53#4114yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C2×D212—28no—
222C2×D212—28no—
223C2×D212—28no—
224C2×D212—416no—
225C2×C4×D53—232no—
226C2×C4×D53—28no—
227C2×C4×D53—28no—
228C2×C4×D53—28no—
229C2×C4×D53—28no—
230C2×C4×D53—28no—
231C2×C4×D53—28no—
232C2×C4×D53—44no—
233C2×C4×D53—44no—
234C2×C4×D53—416no—
235C2×C4×D53—416no—
236C2×C4×D53C2×D4116yes—
237C4⋊C4×C53—28no—
238C4⋊C4×C53—28no—
239C42×C53—28no—
240#11719921—28no—
241#11719921—28no—
242#11719921—28no—
243#11719921—28no—
244#11719921—28no—
245#11719921—28no—
246#11719921—28no—
247#11719921—44no—
248#11719921—44no—
249C4⋊Dic53—44no—
250#11719919—28no—
251#11719919—28no—
252#11719919—28no—
253#11719919—28no—
254#11719919—44no—
255C4×Dic53—28no—
256C23×C53C22×D412yes—
257C23×C53C2×#4112yes—
258C23×C53C2×#4112yes—
259C23×C53C2×#4112yes—
260C23×C53C2×#4112yes—
261C23×C53H(5,𝔽2)12yes—
262C23×C532−1+412yes—
263C23×C53C2511yescharacteristic
264C22×D53—28no—
265C22×D53—28no—
266C22×D53—28no—
267C22×D53—28no—
268C22×D53—28no—
269C22×D53—28no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—44no—
282C22×D53—44no—
283C22×D53—44no—
284C22×D53—44no—
285C22×D53—44no—
286C22×D53—44no—
287C22×D53—44no—
288C22×D53#123116yes—
289C22×D53C22×D414yes—
290C22×D53C2×#4114yes—
291C22×D53C2×#4114yes—
292C2×C4×C53—28no—
293C2×C4×C53—28no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
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—44no—
314C2×C4×C53—44no—
315C2×C4×C53—44no—
316C2×C4×C53—44no—
317C2×C4×C53—44no—
318C2×C4×C53C22×D414yes—
319C2×C4×C53C2×#4114yes—
320C2×Dic53—28no—
321C2×Dic53—28no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—44no—
339C2×Dic53—44no—
340C2×Dic53—44no—
341C2×Dic53—44no—
342C2×Dic53C22×D414yes—
343C2×Dic53C2×#4114yes—
344D212—416no—
345C4×D53—232no—
346C4×D53—416no—
347C4×D53—416no—
348C2×#2498—531nomaximal, Sylow
349C22×C53C2×#12314yes—
350C22×C53#53214yes—
351C22×C53#53714yes—
352C22×C53#55114yes—
353C22×C53#55114yes—
354C22×C53#55214yes—
355C22×C53#55214yes—
356C22×C53C23×D411yescharacteristic
357C22×C53C22×#4111yescharacteristic
358C22×C53C22×#4111yescharacteristic
359C22×C53C22×#4111yescharacteristic
360C22×C53C22×#4111yescharacteristic
361C22×C53C2×H(5,𝔽2)11yescharacteristic
362C22×C53C2×2−1+411yescharacteristic
363C2×D53—24no—
364C2×D53—24no—
365C2×D53—24no—
366C2×D53—24no—
367C2×D53—24no—
368C2×D53—24no—
369C2×D53—232no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—88no—
378C2×D53C2×#12318yes—
379C4×C53—24no—
380C4×C53—24no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53—42no—
386Dic53—24no—
387Dic53—24no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391Dic53—42no—
392C22×#123—531no—
393C22×#117—531no—
394#2498—5316no—
395C2×#400—531no—
396C2×#399—531no—
397C2×#398—531no—
398C2×#397—531no—
399C2×#388—531no—
400C2×#388—531no—
401C2×#387—531no—
402C2×#387D5311yescharacteristic, complemented
403C2×#386—531no—
404C2×#386—531no—
405C2×#380—531no—
406C2×#380—531no—
407C22×#95—531no—
408C2×C53#249818yescomplemented
409C2×C53C22×#12311yescharacteristic
410C2×C53C2×#53211yescharacteristic
411C2×C53C2×#53711yescharacteristic
412C2×C53C2×#55111yescharacteristic
413C2×C53C2×#55111yescharacteristic
414C2×C53C2×#55211yescharacteristic
415C2×C53C2×#55211yescharacteristic
416D53—28no—
417D53—82no—
418C23×D4—531no—
419C24×C4—531no—
420C24×C4—531no—
421C24×C4—531no—
422C2×#123—538no—
423C2×#123—1068no—
424C2×#117—538no—
425C2×#117—1068no—
426C22×C4⋊C4—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4C2×D5311yescharacteristic
433C22×C4⋊C4C2×D5311yescharacteristic
434C22×C22⋊C4—531no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4—531no—
439C22×C22⋊C4—531no—
440C22×C22⋊C4—531no—
441C22×C22⋊C4—531no—
442C22×C22⋊C4—531no—
443C22×C42—531no—
444C22×C42C2×D5311yescharacteristic
445#400—538no—
446#399—538no—
447#398—538no—
448#397—538no—
449#388—538no—
450#388—538no—
451#387—538no—
452#387C2×D5318yescomplemented
453#386—538no—
454#386—538no—
455#380—538no—
456#380—538no—
457C2×#95—531no—
458C2×#95—531no—
459C2×#95—531no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95—538no—
466C2×#95C2×D5311yescharacteristic
467C2×#95C2×D5311yescharacteristic
468C2×#95C2×D5311yescharacteristic
469C2×#95C2×D5311yescharacteristic
470C53C2×#249811yescharacteristic, complemented, Sylow
471C25—531no—
472C25—531no—
473C22×D4—534no—
474C22×D4—1064no—
475C22×D4—1064no—
476C22×D4—1064no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—538no—
480C23×C4—534no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—534no—
486C23×C4—534no—
487C23×C4—1064no—
488C23×C4—1064no—
489C23×C4—1064no—
490C23×C4—1064no—
491C23×C4—1064no—
492C23×C4—1064no—
493C23×C4—2122no—
494C23×C4—2122no—
495C23×C4C22×D5311yescharacteristic
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5311yescharacteristic
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5311yescharacteristic
501C23×C4C22×D5311yescharacteristic
502#123—10632no—
503#117—10632no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—534no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—1064no—
514C2×C4⋊C4—1064no—
515C2×C4⋊C4—1064no—
516C2×C4⋊C4—2122no—
517C2×C4⋊C4—2122no—
518C2×C4⋊C4C22×D5314yes—
519C2×C4⋊C4C22×D5314yes—
520C2×C22⋊C4—534no—
521C2×C22⋊C4—534no—
522C2×C22⋊C4—534no—
523C2×C22⋊C4—534no—
524C2×C22⋊C4—534no—
525C2×C22⋊C4—534no—
526C2×C22⋊C4—534no—
527C2×C22⋊C4—534no—
528C2×C22⋊C4—534no—
529C2×C22⋊C4—1064no—
530C2×C22⋊C4—1064no—
531C2×C22⋊C4—1064no—
532C2×C22⋊C4—1064no—
533C2×C22⋊C4—1064no—
534C2×C22⋊C4—1064no—
535C2×C22⋊C4—1064no—
536C2×C22⋊C4—2122no—
537C2×C22⋊C4—2122no—
538C2×C42—24no—
539C2×C42—534no—
540C2×C42—1064no—
541C2×C42C22×D5314yes—
542#95—534no—
543#95—534no—
544#95—534no—
545#95—534no—
546#95—534no—
547#95—534no—
548#95—534no—
549#95—534no—
550#95C22×D5314yes—
551#95C22×D5314yes—
552#95C22×D5314yes—
553#95C22×D5314yes—
554C24—534no—
555C24—534no—
556C24—534no—
557C24—532no—
558C24—532no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24—1062no—
563C24—1062no—
564C24—1062no—
565C24—1062no—
566C24—1062no—
567C24—1062no—
568C24—1062no—
569C24—1062no—
570C24C23×D5311yescharacteristic
571C2×D4—1068no—
572C2×D4—1068no—
573C2×D4—1068no—
574C2×D4—21216no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—534no—
595C22×C4—534no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—5316no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—1068no—
604C22×C4—10632no—
605C22×C4—1068no—
606C22×C4—1068no—
607C22×C4—1068no—
608C22×C4—1068no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1068no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—21216no—
629C22×C4—21216no—
630C22×C4#1171994514yes—
631C22×C4D4×D5314yes—
632C22×C4C23×D5312yes—
633C22×C4C23×D5312yes—
634C22×C4C23×D5312yes—
635C22×C4C23×D5312yes—
636C22×C4C23×D5312yes—
637C22×C4C23×D5312yes—
638C22×C4C23×D5312yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—1068no—
642C4⋊C4—1068no—
643C4⋊C4—1068no—
644C4⋊C4—1068no—
645C4⋊C4—2124no—
646C4⋊C4—2124no—
647C22⋊C4—1068no—
648C22⋊C4—1068no—
649C22⋊C4—1068no—
650C22⋊C4—1068no—
651C22⋊C4—1068no—
652C22⋊C4—1068no—
653C22⋊C4—1068no—
654C22⋊C4—2124no—
655C22⋊C4—2124no—
656C42—28no—
657C42—1068no—
658C23—5316no—
659C23—534no—
660C23—534no—
661C23—534no—
662C23—1068no—
663C23—1068no—
664C23—1068no—
665C23—1068no—
666C23—1068no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1068no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23—2124no—
680C23—2124no—
681C23—2124no—
682C23—2124no—
683C23—2124no—
684C23—2124no—
685C23—2124no—
686C23C2×D4×D5312yes—
687C23#41×D5312yes—
688C23#41×D5312yes—
689C23#41×D5312yes—
690C23C2×#1171994512yes—
691C23#1313326312yes—
692C23#1313326512yes—
693C23C24×D5311yescharacteristic
694D4—21216no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—534no—
722C2×C4—534no—
723C2×C4—10632no—
724C2×C4—1068no—
725C2×C4—1068no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—21216no—
743C2×C4—21216no—
744C2×C4—2124no—
745C2×C4—2124no—
746C2×C4—2124no—
747C2×C4—2124no—
748C2×C4C2×D4×D5314yes—
749C2×C4C2×#1171994514yes—
750C22—538no—
751C22—1064no—
752C22—10632no—
753C22—1064no—
754C22—1064no—
755C22—1064no—
756C22—1064no—
757C22—1064no—
758C22—4248no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22#123×D5314yes—
767C22#1681117014yes—
768C22#1681120314yes—
769C22#1681129714yes—
770C22#1681129814yes—
771C22#1681130514yes—
772C22#1681131414yes—
773C22C22×D4×D5311yescharacteristic
774C22C2×#41×D5311yescharacteristic
775C22C2×#41×D5311yescharacteristic
776C22C2×#41×D5311yescharacteristic
777C22C22×#1171994511yescharacteristic
778C22C2×#1313326311yescharacteristic
779C22C2×#1313326511yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—1064no—
788C4—1064no—
789C4—2122no—
790C4—2122no—
791C4—2122no—
792C4—2122no—
793C2—1068no—
794C2—4242no—
795C2#2027915618yesdirect product factor
796C2C2×#123×D5311yescharacteristic
797C2C2×#1681117011yescharacteristic
798C2C2×#1681120311yescharacteristic
799C2C2×#1681129711yescharacteristic
800C2C2×#1681129811yescharacteristic
801C2C2×#1681130511yescharacteristic
802C2C2×#1681131411yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#387C2
socleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×#387D53
hypocenterC53C2×#2498
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#13133174C2semidirect
3. #20279156C2direct (N × H)
4. C2×#16810564C2semidirect
5. C2×#16810558C2semidirect
6. C2×#16810557C2semidirect
7. C2×#16810552C2semidirect
8. C2×#16810515C2semidirect
9. C2×#16810514C2semidirect
10. C2×#16810504C2semidirect
13. C2×#16810482C2semidirect
14. C2×#16810480C2semidirect
15. C2×#95×D53C2semidirect
16. C2×C53×#387C2semidirect
24. C2×#13133174C22semidirect
41. #16810564C22semidirect
42. #16810558C22semidirect
43. #16810557C22semidirect
44. #16810552C22semidirect
45. #16810515C22semidirect
46. #16810514C22semidirect
47. #16810504C22semidirect
50. #16810482C22semidirect
51. #16810480C22semidirect
60. #95×D53C22semidirect
64. C53×#387C22semidirect
402. C2×#387D53semidirect
408. C2×C53#2498semidirect
452. #387C2×D53semidirect
470. C53C2×#2498semidirect
795. C2#20279156direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332022
C22×#131331742
#202791562
C2×#168105642
C2×#168105582
C2×#168105572
C2×#168105522
C2×#168105152
C2×#168105142
C2×#168105042
C2×#168105012
C2×#168104822
C2×#168104802
C2×#95×D532
C2×C53×#3872
C2×#249853