Finite Group Databasebeta

← C2×#20284752 #28252128

Subgroups — C2×#20284752 #28252128

Order 13568.

2138 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic
2C2×C4×Q8×D53C211yesmaximal, characteristic
3#20284752C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic
5C2×#16810957C211yesmaximal, characteristic
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810832C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810780C211yesmaximal, characteristic
11C2×#16810777C211yesmaximal, characteristic
12C2×C4×Dic212C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×C4×#11719925C211yesmaximal, characteristic, complemented
15C2×#16810674C211yesmaximal, characteristic
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21#16811177—24no—
22#16811177C2218yes—
23C2×#13133216C2211yescharacteristic
24C2×#13133215C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133197C2211yescharacteristic
27C2×#13133195—21no—
28C2×#13133193C2211yescharacteristic
29C2×Q8×Dic53C2211yescharacteristic
30C2×C4×Dic106—21no—
31C2×C4×Dic106—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×C4×Dic106C2211yescharacteristic
34C2×#13133182—21no—
35C2×#13133182C2211yescharacteristic
36C4×Q8×D53—24no—
37C4×Q8×D53C2218yes—
38C2×#13133174—21no—
39C2×C4⋊C4×D53—21no—
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C42×D53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810960C2218yes—
44#16810957C2218yes—
45#16810917C2218yescomplemented
46#16810916C2218yescomplemented
47#16810832C2218yescomplemented
48#16810831C2218yescomplemented
49#16810780C2218yes—
50#16810777C2218yes—
51C4×Dic212C2218yescomplemented
52C4×#11719925C2218yescomplemented
53C4×#11719925C2218yescomplemented
54#16810674C2218yes—
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C4×Q16×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—24no—
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53C2314yes—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53D411yescharacteristic
88C22×C4×D53D411yescharacteristic
89C22×C4×D53C2311yescharacteristic
90C2×Dic212—24no—
91C2×Dic212C2314yes—
92C2×#11719925—24no—
93C2×#11719925—24no—
94C2×#11719925C2314yes—
95C2×#11719925C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98#13133216—22no—
99#13133216C2314yes—
100#13133215—22no—
101#13133215C2314yes—
102#13133207—28no—
103#13133197—22no—
104#13133197C2314yes—
105#13133195—28no—
106#13133193—22no—
107#13133193C2314yes—
108Q8×Dic53—22no—
109Q8×Dic53C2314yes—
110C4×Dic106—22no—
111C4×Dic106—22no—
112C4×Dic106—28no—
113C4×Dic106—28no—
114C4×Dic106C2314yes—
115C4×Dic106C2314yes—
116#13133182—22no—
117#13133182—28no—
118#13133182C2314yes—
119#13133174—28no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C4⋊C4×D53—28no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144C42×D53—28no—
145C42×D53D414yes—
146C42×D53C2314yes—
147#13133151C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160C4×#88322C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×Q8×C53—22no—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×Q8×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C4×C8×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53#4114yes—
189C2×Q8×C53C2412yes—
190C2×Q8×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205Q8×D53—216no—
206Q8×D53—28no—
207Q8×D53—28no—
208C2×C4×D53—28no—
209C2×C4×D53—24no—
210C2×C4×D53—22no—
211C2×C4×D53—22no—
212C2×C4×D53—24no—
213C2×C4×D53—42no—
214C2×C4×D53—44no—
215C2×C4×D53Q1618yescomplemented
216C2×C4×D53C2×D412yes—
217C2×C4×D53C2×D414yes—
218C2×C4×D53C2×D414yes—
219C2×C4×D53C2412yes—
220C2×Dic106—28no—
221C2×Dic106—21no—
222C2×Dic106—22no—
223C2×Dic106—24no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106—24no—
228C2×Dic106—44no—
229C2×Dic106#4114yes—
230C2×Dic106C2412yes—
231C2×Dic106C2412yes—
232Q16×C53—28no—
233C2×C8×C53—22no—
234C2×C8×C53—22no—
235C2×C8×C53C2412yes—
236C2×C8×C53C2412yes—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C2412yes—
242C4⋊C4×C53C2412yes—
243C42×C53—24no—
244C42×C53—24no—
245C42×C53C2×D412yes—
246C42×C53C2412yes—
247#11719925—28no—
248#11719925—28no—
249#11719921—24no—
250#11719921—24no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D414yes—
271C4×Dic53C2×D414yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277Dic212—28no—
278C23×C53C22×D411yescharacteristic
279C22×D53—22no—
280C22×D53—22no—
281C22×D53C2×Q1614yes—
282C22×D53C22×D412yes—
283Q8×C53—24no—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—42no—
288Q8×C53C2×#4114yes—
289C2×C4×C53—24no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C2×Q1614yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C22×D412yes—
302C2×C4×C53C2×#4112yes—
303C2×C4×C53C2×#4112yes—
304C2×C4×C53C2511yescharacteristic
305C2×Dic53—22no—
306C2×Dic53—24no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53C2×Q1614yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C4×D53—216no—
320C4×D53—24no—
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—44no—
324C4×D53—48no—
325C4×D53C2×Q16116yescomplemented
326Dic106—216no—
327Dic106—24no—
328Dic106—22no—
329Dic106—22no—
330Dic106—22no—
331Dic106—48no—
332Dic106—42no—
333Dic106C2×#4114yes—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3104—531nomaximal, Sylow
339C22×C53#52512yes—
340C22×C53C22×Q1612yes—
341C22×C53#57512yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—28no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53C22×Q1614yes—
347C4×C53—24no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#52512yes—
353C4×C53C22×Q1614yes—
354C4×C53C22×#4111yescharacteristic
355C4×C53C22×#4111yescharacteristic
356Dic53—22no—
357Dic53—24no—
358Dic53—22no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53C22×Q1614yes—
363C2×#533—531no—
364C22×C4×Q8—531no—
365#3104—5316no—
366C2×#484—531no—
367C2×#484—531no—
368C2×#477—531no—
369C2×#477—531no—
370C2×#462—531no—
371C2×#462—531no—
372C2×#451—531no—
373C2×#451—531no—
374C2×C4×Q16—531no—
375C2×C4×Q16—531no—
376C2×C4×Q16—531no—
377C2×C4×Q16D5311yescharacteristic, complemented
378C2×#431—531no—
379C2×C53#310414yescomplemented
380C2×C53C2×#52511yescharacteristic
381C2×C53C23×Q1611yescharacteristic
382C2×C53C2×#57511yescharacteristic
383D53—24no—
384C23×Q8—531no—
385C22×Q16—531no—
386C22×Q16—531no—
387C22×Q16—531no—
388C22×Q16C2×D5311yescharacteristic
389#533—538no—
390#533—1064no—
391C2×C4⋊Q8—531no—
392C2×C4⋊Q8—531no—
393C2×#125—1061no—
394C2×C22⋊Q8—531no—
395C2×C22⋊Q8—531no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—538no—
399C2×C4×Q8—531no—
400C2×C4×Q8—531no—
401C2×C4×Q8—531no—
402C2×C4×Q8—1061no—
403C2×C4×Q8—1061no—
404C2×C4×Q8—1061no—
405C2×C4×Q8—1064no—
406C2×C4×Q8C2×D5311yescharacteristic
407C2×C4×Q8C2×D5311yescharacteristic
408C2×#117—1061no—
409C22×C4⋊C4—531no—
410C22×C4⋊C4—1061no—
411C22×C42—531no—
412C22×C42—1061no—
413#484—538no—
414#484—538no—
415#477—538no—
416#477—538no—
417#462—538no—
418#462—538no—
419#451—538no—
420#451—538no—
421C4×Q16—538no—
422C4×Q16—538no—
423C4×Q16—538no—
424C4×Q16C2×D5318yescomplemented
425#431—538no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#107—531no—
429C2×#107C2×D5311yescharacteristic
430C2×C4⋊C8—531no—
431C2×C4⋊C8—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103C2×D5311yescharacteristic
439C2×#103C2×D5311yescharacteristic
440C2×C22⋊C8—531no—
441C2×C22⋊C8—531no—
442C2×C4×C8—531no—
443C2×C4×C8C2×D5311yescharacteristic
444C53C2×#310411yescharacteristic, complemented, Sylow
445C22×Q8—534no—
446C22×Q8—531no—
447C22×Q8—531no—
448C22×Q8—1061no—
449C22×Q8—1061no—
450C22×Q8—1062no—
451C22×Q8—1064no—
452C22×Q8—1064no—
453C22×Q8C22×D5311yescharacteristic
454C22×Q8C22×D5311yescharacteristic
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—531no—
458C23×C4—1061no—
459C23×C4—1061no—
460C2×Q16—24no—
461C2×Q16—534no—
462C2×Q16—534no—
463C2×Q16—534no—
464C2×Q16—1064no—
465C2×Q16—1064no—
466C2×Q16—1064no—
467C2×Q16C22×D5314yes—
468C22×C8—531no—
469C22×C8—531no—
470C22×C8C22×D5311yescharacteristic
471C22×C8C22×D5311yescharacteristic
472C4⋊Q8—534no—
473C4⋊Q8—534no—
474C4⋊Q8—1062no—
475C4⋊Q8—1062no—
476#125—1068no—
477C22⋊Q8—534no—
478C22⋊Q8—534no—
479C22⋊Q8—1062no—
480C22⋊Q8—1068no—
481C22⋊Q8—1062no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—534no—
485C4×Q8—534no—
486C4×Q8—534no—
487C4×Q8—534no—
488C4×Q8—1068no—
489C4×Q8—1068no—
490C4×Q8—1068no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×Q8—1062no—
494C4×Q8—1062no—
495C4×Q8C22×D5314yes—
496C4×Q8C22×D5314yes—
497#117—1068no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1068no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4C22×D5311yescharacteristic
516C2×C4⋊C4C22×D5311yescharacteristic
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—531no—
522C2×C42—531no—
523C2×C42—531no—
524C2×C42—534no—
525C2×C42—534no—
526C2×C42—1068no—
527C2×C42—1061no—
528C2×C42—1061no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532#107—534no—
533#107—534no—
534#107—534no—
535#107C22×D5314yes—
536C4⋊C8—534no—
537C4⋊C8—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103C22×D5314yes—
545#103C22×D5314yes—
546C22⋊C8—534no—
547C22⋊C8—534no—
548C4×C8—534no—
549C4×C8C22×D5314yes—
550C24—531no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—534no—
557C2×Q8—532no—
558C2×Q8—532no—
559C2×Q8—1064no—
560C2×Q8—1064no—
561C2×Q8—1068no—
562C2×Q8—1068no—
563C2×Q8—10616no—
564C2×Q8—1068no—
565C2×Q8—1061no—
566C2×Q8—1061no—
567C2×Q8—1062no—
568C2×Q8—1062no—
569C2×Q8—1062no—
570C2×Q8—2124no—
571C2×Q8#1171994514yes—
572C2×Q8C23×D5312yes—
573C2×Q8C23×D5312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—531no—
579C22×C4—538no—
580C22×C4—534no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—534no—
586C22×C4—1064no—
587C22×C4—1068no—
588C22×C4—1064no—
589C22×C4—1061no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—2122no—
596C22×C4—2124no—
597C22×C4D4×D5311yescharacteristic
598C22×C4D4×D5311yescharacteristic
599C22×C4C23×D5311yescharacteristic
600Q16—28no—
601Q16—1068no—
602Q16—1068no—
603Q16—1068no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1062no—
609C2×C8—1062no—
610C2×C8C23×D5312yes—
611C2×C8C23×D5312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—532no—
617C4⋊C4—532no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4C23×D5312yes—
631C4⋊C4C23×D5312yes—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C42—24no—
635C42—24no—
636C42—534no—
637C42—534no—
638C42—532no—
639C42—532no—
640C42—1064no—
641C42—1064no—
642C42—1064no—
643C42—1064no—
644C42D4×D5312yes—
645C42C23×D5312yes—
646C23—534no—
647C23—532no—
648C23—1062no—
649C23—1062no—
650C23C2×D4×D5311yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—534no—
657Q8—10616no—
658Q8—1064no—
659Q8—1062no—
660Q8—1062no—
661Q8—1062no—
662Q8—2128no—
663Q8—2122no—
664Q8C2×#1171994514yes—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—534no—
675C2×C4—532no—
676C2×C4—5316no—
677C2×C4—532no—
678C2×C4—532no—
679C2×C4—10616no—
680C2×C4—1062no—
681C2×C4—1064no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1064no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—2124no—
691C2×C4—2128no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4Q16×D5314yes—
696C2×C4C2×D4×D5312yes—
697C2×C4C2×D4×D5311yescharacteristic
698C2×C4C2×D4×D5312yes—
699C2×C4#41×D5312yes—
700C2×C4C2×#1171994512yes—
701C2×C4C24×D5311yescharacteristic
702C8—22no—
703C8—22no—
704C8—1062no—
705C8—1062no—
706C22—534no—
707C22—1068no—
708C22—1062no—
709C22—1062no—
710C22#1681113212yes—
711C22C2×Q16×D5312yes—
712C22#1681142012yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—534no—
720C4—1062no—
721C4—1062no—
722C4—1064no—
723C4—2122no—
724C4—2122no—
725C4—2122no—
726C4#1681113212yes—
727C4C2×Q16×D5314yes—
728C4C2×#41×D5311yescharacteristic
729C4C22×#1171994511yescharacteristic
730C2—1064no—
731C2#2028475214yesdirect product factor
732C2C2×#1681113211yescharacteristic
733C2C22×Q16×D5311yescharacteristic
734C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3104
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #20284752C2direct (N × H)
6. C2×#16810917C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810832C2semidirect
9. C2×#16810831C2semidirect
12. C2×C4×Dic212C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×C4×#11719925C2semidirect
16. C2×C4×Q16×C53C2semidirect
45. #16810917C22semidirect
46. #16810916C22semidirect
47. #16810832C22semidirect
48. #16810831C22semidirect
51. C4×Dic212C22semidirect
52. C4×#11719925C22semidirect
53. C4×#11719925C22semidirect
72. C4×Q16×C53C22semidirect
215. C2×C4×D53Q16semidirect
325. C4×D53C2×Q16semidirect
377. C2×C4×Q16D53semidirect
379. C2×C53#3104semidirect
424. C4×Q16C2×D53semidirect
444. C53C2×#3104semidirect
731. C2#20284752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×C4×Q8×D532
#202847522
C2×#168109602
C2×#168109572
C2×#168109172
C2×#168109162
C2×#168108322
C2×#168108312
C2×#168107802
C2×#168107772
C2×C4×Dic2122
C2×C4×#117199252
C2×#168106742
C2×C4×Q16×C532
C2×#310453