Finite Group Databasebeta

← C2×#20277743 #27543634

Subgroups — C2×#20277743 #27543634

Order 13568.

3310 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic
2C22×C4×Dic106C211yesmaximal, characteristic, complemented
3C22×#13133174C211yesmaximal, characteristic
4#20277743C2116yesmaximal, direct product factor
5C2×#16810527C211yesmaximal, characteristic, complemented
6C2×#16810518C211yesmaximal, characteristic, complemented
7C2×#16810515C211yesmaximal, characteristic
8C2×#16810514C211yesmaximal, characteristic
9C2×#16810514C211yesmaximal, characteristic
10C2×#16810513C211yesmaximal, characteristic
11C2×#16810509C211yesmaximal, characteristic, complemented
12C2×#16810507C211yesmaximal, characteristic, complemented
13C2×C4×#11719919C211yesmaximal, characteristic, complemented
14C2×#16810474C211yesmaximal, characteristic, complemented
15C2×#16810470C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C2×#13133195C4116yescomplemented
20C2×#13133195C2218yes—
21C2×C4×Dic106—28no—
22C2×C4×Dic106C2218yescomplemented
23C2×#13133174—28no—
24C2×#13133174C2218yes—
25C22×C4⋊Dic53C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42C22×C4×Dic53C2211yescharacteristic
43#16810527C2218yescomplemented
44#16810518C2218yescomplemented
45#16810515C2218yes—
46#16810514C2218yes—
47#16810514C2218yes—
48#16810513C2218yes—
49#16810509C2218yescomplemented
50#16810507C2218yescomplemented
51C4×#11719919C2218yescomplemented
52#16810474C2218yescomplemented
53#16810470C2218yes—
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C42×C53C2211yescharacteristic
65C22×C42×C53C2211yescharacteristic
66C22×C42×C53C2211yescharacteristic
67C4×C4⋊C4×C53C2218yescomplemented
68C2×#95×C53C2211yescharacteristic
69C2×#95×C53C2211yescharacteristic
70C24×D53C2311yescharacteristic
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106C2×C418yes—
74C22×Dic106C2314yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C22×C4×D53—24no—
83C22×C4×D53—24no—
84C22×C4×D53C2×C418yes—
85C22×C4×D53C2314yes—
86#13133195C2×C4164yescomplemented
87C4×Dic106—232no—
88#13133174—232no—
89C2×C4⋊Dic53—24no—
90C2×C4⋊Dic53C2314yes—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—24no—
94C2×#11719919C2×C418yes—
95C2×#11719919C2×C418yes—
96C2×#11719919D418yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719921—24no—
104C2×#11719921—24no—
105C2×#11719921—24no—
106C2×#11719921—24no—
107C2×#11719921C2×C418yes—
108C2×#11719921C2×C418yes—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113C2×#11719921C2314yes—
114C2×#11719921C2314yes—
115C2×C4×Dic53—24no—
116C2×C4×Dic53—24no—
117C2×C4×Dic53—24no—
118C2×C4×Dic53—24no—
119C2×C4×Dic53—24no—
120C2×C4×Dic53C2314yes—
121C2×C4×Dic53C2314yes—
122C2×C4×Dic53C2314yes—
123C2×C4×Dic53C2314yes—
124C2×C4×Dic53C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53—24no—
141C2×C4⋊C4×C53C2×C418yes—
142C2×C4⋊C4×C53C2314yes—
143C2×C4⋊C4×C53C2314yes—
144C2×C42×C53—24no—
145C2×C42×C53—24no—
146C2×C42×C53—24no—
147C2×C42×C53C2314yes—
148C2×C42×C53C2314yes—
149C2×C42×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×D53C22×C414yes—
160C23×D53C2412yes—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
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×C53C22×C414yes—
177C22×C4×C53C22×C414yes—
178C22×C4×C53C22×C414yes—
179C22×C4×C53C2×D414yes—
180C22×C4×C53#4114yes—
181C22×C4×C53#4114yes—
182C22×C4×C53C2412yes—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53C22×C414yes—
205C22×Dic53C22×C414yes—
206C22×Dic53C22×C414yes—
207C22×Dic53C2×D414yes—
208C22×Dic53C2×D414yes—
209C22×Dic53#4114yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C2×C4×D53—232no—
218C2×C4×D53—28no—
219C2×C4×D53—28no—
220C2×C4×D53C22×C4116yes—
221C2×Dic106—232no—
222C2×Dic106—28no—
223C2×Dic106—28no—
224C2×Dic106C22×C4116yes—
225C4⋊C4×C53—28no—
226C4⋊C4×C53C22×C4116yes—
227C42×C53—28no—
228C42×C53—28no—
229C42×C53—28no—
230#11719921—28no—
231#11719921—28no—
232#11719921—28no—
233#11719921—28no—
234#11719921C22×C4116yes—
235#11719921C22×C4116yes—
236C4⋊Dic53—28no—
237#11719919—28no—
238#11719919—28no—
239#11719919—28no—
240#11719919C22×C4116yes—
241#11719919C22×C4116yes—
242#11719919C2×D4116yes—
243C4×Dic53—28no—
244C4×Dic53—28no—
245C4×Dic53—28no—
246C4×Dic53—28no—
247C4×Dic53—28no—
248C23×C53C23×C412yes—
249C23×C53C22×D412yes—
250C23×C53C2×#4112yes—
251C23×C53C2×#4112yes—
252C23×C53C2×#4112yes—
253C23×C532−1+412yes—
254C23×C532−1+412yes—
255C23×C53C2511yescharacteristic
256C22×D53—28no—
257C22×D53—28no—
258C22×D53—28no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—44no—
266C22×D53—44no—
267C22×D53—44no—
268C22×D53—44no—
269C22×D53C23×C414yes—
270C2×C4×C53—28no—
271C2×C4×C53—28no—
272C2×C4×C53—28no—
273C2×C4×C53—28no—
274C2×C4×C53—28no—
275C2×C4×C53—28no—
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—44no—
292C2×C4×C53C23×C414yes—
293C2×C4×C53C23×C414yes—
294C2×C4×C53C23×C414yes—
295C2×C4×C53C22×D414yes—
296C2×C4×C53C2×#4114yes—
297C2×C4×C53C2×#4114yes—
298C2×Dic53—28no—
299C2×Dic53—28no—
300C2×Dic53—28no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—44no—
317C2×Dic53—44no—
318C2×Dic53—44no—
319C2×Dic53C4×D4116yes—
320C2×Dic53C23×C414yes—
321C2×Dic53C23×C414yes—
322C2×Dic53C23×C414yes—
323C2×Dic53C22×D414yes—
324C2×Dic53C22×D414yes—
325C2×Dic53C2×#4114yes—
326C4×D53—232no—
327Dic106—232no—
328C2×#2362—531nomaximal, Sylow
329C22×C53C2×C4×D414yes—
330C22×C53C4×#4114yes—
331C22×C53#51914yes—
332C22×C53#54714yes—
333C22×C53#54814yes—
334C22×C53#55214yes—
335C22×C53#55614yes—
336C22×C53C24×C411yescharacteristic
337C22×C53C23×D411yescharacteristic
338C22×C53C22×#4111yescharacteristic
339C22×C53C22×#4111yescharacteristic
340C22×C53C22×#4111yescharacteristic
341C22×C53C2×2−1+411yescharacteristic
342C22×C53C2×2−1+411yescharacteristic
343C2×D53—24no—
344C2×D53—24no—
345C2×D53—24no—
346C2×D53—416no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C4×C53—24no—
352C4×C53—24no—
353C4×C53—24no—
354C4×C53—24no—
355C4×C53—24no—
356C4×C53—24no—
357C4×C53—42no—
358Dic53—24no—
359Dic53—24no—
360Dic53—24no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×C4×D418yes—
365C22×C22⋊Q8—531no—
366C22×C4×Q8—531no—
367C22×#117—531no—
368#2362—5316no—
369C2×#391—531no—
370C2×#389—531no—
371C2×#388—531no—
372C2×#388—531no—
373C2×#388—531no—
374C2×#388—531no—
375C2×#387—531no—
376C2×#387—531no—
377C2×C4×C4⋊C4—531no—
378C2×C4×C4⋊C4—531no—
379C2×C4×C4⋊C4D5311yescharacteristic, complemented
380C2×C4×C22⋊C4—531no—
381C2×C53#236218yescomplemented
382C2×C53C22×C4×D411yescharacteristic
383C2×C53C2×C4×#4111yescharacteristic
384C2×C53C2×#51911yescharacteristic
385C2×C53C2×#54711yescharacteristic
386C2×C53C2×#54811yescharacteristic
387C2×C53C2×#55211yescharacteristic
388C2×C53C2×#55611yescharacteristic
389D53—44no—
390C23×Q8—531no—
391C24×C4—531no—
392C2×C22⋊Q8—5316no—
393C2×C22⋊Q8—538no—
394C2×C4×Q8—538no—
395C2×C4×Q8—1068no—
396C2×#117—538no—
397C2×#117—1068no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4C2×D5311yescharacteristic
406C22×C4⋊C4C2×D5311yescharacteristic
407C22×C22⋊C4—531no—
408C22×C22⋊C4—531no—
409C22×C22⋊C4—531no—
410C22×C22⋊C4—531no—
411C22×C22⋊C4—531no—
412C22×C22⋊C4—531no—
413C22×C42—531no—
414C22×C42—531no—
415C22×C42—531no—
416C22×C42—531no—
417C22×C42—531no—
418C22×C42C2×D5311yescharacteristic
419C22×C42C2×D5311yescharacteristic
420C22×C42C2×D5311yescharacteristic
421#391—538no—
422#389—538no—
423#388—538no—
424#388—538no—
425#388—538no—
426#388—538no—
427#387—538no—
428#387—538no—
429C4×C4⋊C4—538no—
430C4×C4⋊C4—538no—
431C4×C4⋊C4C2×D5318yescomplemented
432C4×C22⋊C4—538no—
433C2×#95—531no—
434C2×#95—531no—
435C2×#95—531no—
436C2×#95—531no—
437C2×#95—531no—
438C2×#95—531no—
439C2×#95—531no—
440C2×#95—531no—
441C2×#95C2×D5311yescharacteristic
442C2×#95C2×D5311yescharacteristic
443C53C2×#236211yescharacteristic, complemented, Sylow
444C25—531no—
445C22×Q8—538no—
446C22×Q8—534no—
447C22×Q8—1064no—
448C22×Q8—1064no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—538no—
454C23×C4—534no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—531no—
458C23×C4—1064no—
459C23×C4—1064no—
460C23×C4C22×D5311yescharacteristic
461C23×C4C22×D5311yescharacteristic
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C22⋊Q8—5364no—
468C4×Q8—10632no—
469#117—10632no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—538no—
472C2×C4⋊C4—538no—
473C2×C4⋊C4—538no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—1064no—
482C2×C4⋊C4—1064no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4C4×D5318yes—
486C2×C4⋊C4C22×D5314yes—
487C2×C4⋊C4C22×D5314yes—
488C2×C22⋊C4—538no—
489C2×C22⋊C4—538no—
490C2×C22⋊C4—534no—
491C2×C22⋊C4—534no—
492C2×C22⋊C4—534no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—1064no—
497C2×C22⋊C4—1064no—
498C2×C22⋊C4—1064no—
499C2×C22⋊C4—1064no—
500C2×C42—24no—
501C2×C42—24no—
502C2×C42—24no—
503C2×C42—534no—
504C2×C42—534no—
505C2×C42—534no—
506C2×C42—534no—
507C2×C42—534no—
508C2×C42—1064no—
509C2×C42—1064no—
510C2×C42—1064no—
511C2×C42—1064no—
512C2×C42—1064no—
513C2×C42C22×D5314yes—
514C2×C42C22×D5314yes—
515C2×C42C22×D5314yes—
516#95—534no—
517#95—534no—
518#95—534no—
519#95—534no—
520#95—534no—
521#95—534no—
522#95—534no—
523#95—534no—
524#95C22×D5314yes—
525#95C22×D5314yes—
526C24—534no—
527C24—532no—
528C24—1062no—
529C24—1062no—
530C24—1062no—
531C24—1062no—
532C24—1062no—
533C24—1062no—
534C24C23×D5311yescharacteristic
535C2×Q8—5316no—
536C2×Q8—1068no—
537C2×Q8—10632no—
538C2×Q8—1068no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—534no—
555C22×C4—534no—
556C22×C4—534no—
557C22×C4—532no—
558C22×C4—534no—
559C22×C4—534no—
560C22×C4—534no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—5316no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—1068no—
569C22×C4—10632no—
570C22×C4—1068no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4C2×C4×D5314yes—
587C22×C4C2×C4×D5314yes—
588C22×C4C2×C4×D5314yes—
589C22×C4#1171994514yes—
590C22×C4#1171994514yes—
591C22×C4D4×D5314yes—
592C22×C4C23×D5312yes—
593C22×C4C23×D5312yes—
594C22×C4C23×D5312yes—
595C22×C4C23×D5312yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5312yes—
598C22×C4C23×D5312yes—
599C4⋊C4—28no—
600C4⋊C4—5316no—
601C4⋊C4—5316no—
602C4⋊C4—5316no—
603C4⋊C4—1068no—
604C4⋊C4—1068no—
605C4⋊C4—1068no—
606C4⋊C4—1068no—
607C4⋊C4C2×C4×D53116yes—
608C22⋊C4—5316no—
609C22⋊C4—5316no—
610C22⋊C4—1068no—
611C22⋊C4—1068no—
612C22⋊C4—1068no—
613C22⋊C4—1068no—
614C42—28no—
615C42—28no—
616C42—28no—
617C42—1068no—
618C42—1068no—
619C42—1068no—
620C42—1068no—
621C42—1068no—
622C23—534no—
623C23—1068no—
624C23—1068no—
625C23—1068no—
626C23—1062no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23—1062no—
631C23—1062no—
632C23—2124no—
633C23—2124no—
634C23—2124no—
635C23—2124no—
636C23C22×C4×D5312yes—
637C23C2×D4×D5312yes—
638C23#41×D5312yes—
639C23C2×#1171994512yes—
640C23C2×#1171994512yes—
641C23#1313326412yes—
642C23#1313326512yes—
643C23C24×D5311yescharacteristic
644Q8—10632no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—5316no—
668C2×C4—534no—
669C2×C4—534no—
670C2×C4—534no—
671C2×C4—534no—
672C2×C4—534no—
673C2×C4—534no—
674C2×C4—10632no—
675C2×C4—1068no—
676C2×C4—1068no—
677C2×C4—1068no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2124no—
694C2×C4—2124no—
695C2×C4—2124no—
696C2×C4C22×C4×D5314yes—
697C2×C4C22×C4×D5314yes—
698C2×C4C22×C4×D5314yes—
699C2×C4C2×D4×D5314yes—
700C2×C4C2×#1171994514yes—
701C2×C4C2×#1171994514yes—
702C22—1064no—
703C22—1064no—
704C22—1064no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22—2122no—
709C22—21216no—
710C22C4×D4×D5314yes—
711C22C4×#1171994514yes—
712C22#1681109914yes—
713C22#1681127414yes—
714C22#1681128214yes—
715C22#1681130614yes—
716C22#1681134514yes—
717C22C23×C4×D5311yescharacteristic
718C22C22×D4×D5311yescharacteristic
719C22C2×#41×D5311yescharacteristic
720C22C22×#1171994511yescharacteristic
721C22C22×#1171994511yescharacteristic
722C22C2×#1313326411yescharacteristic
723C22C2×#1313326511yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—24no—
730C4—42no—
731C4—538no—
732C4—1064no—
733C4—1064no—
734C4—1064no—
735C4—2122no—
736C4—2122no—
737C4—2122no—
738C2—2124no—
739C2#2027774318yesdirect product factor
740C2C2×C4×D4×D5311yescharacteristic
741C2C2×C4×#1171994511yescharacteristic
742C2C2×#1681109911yescharacteristic
743C2C2×#1681127411yescharacteristic
744C2C2×#1681128211yescharacteristic
745C2C2×#1681130611yescharacteristic
746C2C2×#1681134511yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C4×C4⋊C4×C53C2
socleC24×C53C24
prime radicalC24×D53C23
cosocleC23×C53C25
hypercenterC2×C4×C4⋊C4D53
hypocenterC53C2×#2362
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic106C2semidirect
4. #20277743C2direct (N × H)
5. C2×#16810527C2semidirect
6. C2×#16810518C2semidirect
11. C2×#16810509C2semidirect
12. C2×#16810507C2semidirect
13. C2×C4×#11719919C2semidirect
14. C2×#16810474C2semidirect
16. C2×C4×C4⋊C4×C53C2semidirect
19. C2×#13133195C4semidirect
22. C2×C4×Dic106C22semidirect
43. #16810527C22semidirect
44. #16810518C22semidirect
49. #16810509C22semidirect
50. #16810507C22semidirect
51. C4×#11719919C22semidirect
52. #16810474C22semidirect
67. C4×C4⋊C4×C53C22semidirect
86. #13133195C2×C4semidirect
379. C2×C4×C4⋊C4D53semidirect
381. C2×C53#2362semidirect
431. C4×C4⋊C4C2×D53semidirect
443. C53C2×#2362semidirect
739. C2#20277743direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331952
C22×C4×Dic1062
C22×#131331742
#202777432
C2×#168105272
C2×#168105182
C2×#168105152
C2×#168105142
C2×#168105132
C2×#168105092
C2×#168105072
C2×C4×#117199192
C2×#168104742
C2×#168104702
C2×C4×C4⋊C4×C532
C2×#236253