Finite Group Databasebeta

← C2×#20287615 #28264570

Subgroups — C2×#20287615 #28264570

Order 13568.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811332C211yesmaximal, characteristic, complemented
2C2×D4×Dic106C211yesmaximal, characteristic, complemented
3#20287615C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16811030C211yesmaximal, characteristic, complemented
6C2×#16811020C211yesmaximal, characteristic, complemented
7C2×#16810923C211yesmaximal, characteristic, complemented
8C2×#16810921C211yesmaximal, characteristic, complemented
9C2×#16810913C211yesmaximal, characteristic, complemented
10C2×#16810911C211yesmaximal, characteristic, complemented
11C2×#16810911C211yesmaximal, characteristic, complemented
12C2×#16810901C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810735C211yesmaximal, characteristic
15C2×D8×Dic53C211yesmaximal, characteristic
16C2×C53×#442C211yesmaximal, characteristic
17C23×Dic106—21no—
18#16811332—24no—
19#16811332C2218yescomplemented
20D4×Dic106—24no—
21D4×Dic106C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133216C2211yescharacteristic
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133209C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133196—21no—
29C2×#13133196—21no—
30C2×#13133194—21no—
31C2×#13133194—21no—
32C2×#13133194—21no—
33C2×#13133194—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C22×#11719919—21no—
40#16811032C2218yescomplemented
41#16811030C2218yescomplemented
42#16811020C2218yescomplemented
43#16810923C2218yescomplemented
44#16810921C2218yescomplemented
45#16810913C2218yescomplemented
46#16810911C2218yescomplemented
47#16810911C2218yescomplemented
48#16810901C2218yescomplemented
49#16810751C2218yescomplemented
50#16810735C2218yes—
51D8×Dic53C2218yes—
52C2×#13133151C2211yescharacteristic
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yes—
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—28no—
82C22×Dic106—48no—
83C22×Dic106D411yescharacteristic
84C23×Dic53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C23×Dic53—21no—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90#13133217—22no—
91#13133217C2314yes—
92#13133216—22no—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133216C2314yes—
98#13133209—22no—
99#13133209C2314yes—
100#13133208—22no—
101#13133208C2314yes—
102#13133196—28no—
103#13133196—28no—
104#13133194—28no—
105#13133194—28no—
106#13133194—28no—
107#13133194—28no—
108C4×Dic106D414yes—
109C4×Dic106C2314yes—
110D4×Dic53—22no—
111D4×Dic53—22no—
112D4×Dic53—22no—
113D4×Dic53—22no—
114D4×Dic53C2314yes—
115D4×Dic53C2314yes—
116D4×Dic53C2314yes—
117D4×Dic53C2314yes—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53D411yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—28no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C4×Dic53C2311yescharacteristic
139C2×C4×Dic53C2311yescharacteristic
140#13133151C2314yes—
141#13133151C2314yes—
142#13133150C2314yes—
143#13133149C2314yes—
144#13133149C2314yes—
145#13133148C2314yes—
146#13133148C2314yes—
147#13133148C2314yes—
148C4⋊#88322C2314yes—
149#13133146C2314yes—
150#13133146C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133127C2314yes—
156C8×Dic53C2314yes—
157C22×D4×C53C2311yescharacteristic
158C22×D4×C53C2311yescharacteristic
159C23×C4×C53—21no—
160C23×C4×C53—21no—
161C2×D8×C53Q818yescomplemented
162C2×D8×C53C2314yes—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4×D4×C53—22no—
166C4×D4×C53—22no—
167C4×D4×C53C2314yes—
168C4×D4×C53C2314yes—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#106×C53C2314yes—
175#102×C53C2314yes—
176#102×C53C2314yes—
177#97×C53C2314yes—
178C24×C53—21no—
179C24×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—22no—
183C2×D4×C53—22no—
184C2×D4×C53C2×Q814yes—
185C2×D4×C53C2×Q814yescomplemented
186C2×D4×C53C2412yes—
187C2×D4×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—24no—
191C22×C4×C53—24no—
192C22×C4×C53—44no—
193C22×C4×C53—82no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—24no—
202C22×Dic53—24no—
203C22×Dic53—24no—
204C22×Dic53—24no—
205C22×Dic53—44no—
206C22×Dic53—44no—
207C22×Dic53—44no—
208C22×Dic53—82no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C2×Dic106—24no—
214C2×Dic106—24no—
215C2×Dic106—24no—
216C2×Dic106—24no—
217C2×Dic106—24no—
218C2×Dic106—432no—
219C2×Dic106—44no—
220C2×Dic106—44no—
221C2×Dic106—44no—
222C2×Dic106—82no—
223C2×Dic106C2×D414yes—
224D8×C53C2×Q8116yescomplemented
225C2×C8×C53—22no—
226C2×C8×C53C2×Q814yescomplemented
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—24no—
235C42×C53C2×D412yes—
236C42×C53C2412yes—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240C22⋊Dic53—24no—
241C4⋊Dic53—24no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—24no—
247C4⋊Dic53C2×D414yes—
248C4⋊Dic53C2412yes—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919C2×D414yes—
259#11719919C2×D414yes—
260C4×Dic53C2×D412yes—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C23×C53—24no—
269C23×C53—24no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D411yescharacteristic
277D4×C53—24no—
278D4×C53—24no—
279D4×C53—22no—
280D4×C53—22no—
281D4×C53C22×Q814yes—
282D4×C53C22×Q814yescomplemented
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—48no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—84no—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D412yes—
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C22×Q812yes—
295C2×C4×C532−1+412yes—
296C2×C4×C53C2511yescharacteristic
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—48no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—48no—
310C2×Dic53—48no—
311C2×Dic53—84no—
312C2×Dic53AGL(1,ℤ/8)14yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317Dic106—28no—
318Dic106—48no—
319Dic106—48no—
320Dic106—48no—
321Dic106—84no—
322C8×C53—22no—
323C8×C53C22×Q814yescomplemented
324#88322—22no—
325#88322—22no—
326C2×#3384—531nomaximal, Sylow
327C22×C53—24no—
328C22×C53—24no—
329C22×C53—48no—
330C22×C53—48no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53D4×Q812yes—
336C22×C53C2×AGL(1,ℤ/8)12yes—
337C22×C53#57712yes—
338C22×C53C23×D411yescharacteristic
339C4×C53—22no—
340C4×C53—22no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53D4×Q812yes—
344C4×C53C23×Q811yescharacteristic
345C4×C53C2×2−1+411yescharacteristic
346Dic53—22no—
347Dic53—22no—
348Dic53—22no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53C2×AGL(1,ℤ/8)14yes—
354C2×#554—531no—
355C2×D4×Q8—531no—
356#3384—5316no—
357C2×#501—531no—
358C2×#501—531no—
359C2×#498—531no—
360C2×#478—531no—
361C2×#478—531no—
362C2×#476—531no—
363C2×#476—531no—
364C2×#476—531no—
365C2×#474—531no—
366C2×#446—531no—
367C2×#442—531no—
368C2×#442D5311yescharacteristic
369C2×C4×D8—531no—
370C2×C53—44no—
371C2×C53—44no—
372C2×C53#338414yescomplemented
373C2×C53C2×D4×Q811yescharacteristic
374C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
375C2×C53C2×#57711yescharacteristic
376C23×Q8—1061no—
377C22×D8C2×D5311yescharacteristic
378#554—538no—
379#554—1064no—
380D4×Q8—538no—
381D4×Q8—1064no—
382C2×C4⋊Q8—531no—
383C2×C4⋊Q8—531no—
384C2×C4⋊Q8—531no—
385C2×C4⋊Q8—531no—
386C2×#125—531no—
387C2×#125—531no—
388C2×C22⋊Q8—1061no—
389C2×C22⋊Q8—1061no—
390C2×C22⋊Q8—1061no—
391C2×C22⋊Q8—1061no—
392C2×C22⋊Q8—1061no—
393C2×C22⋊Q8—1061no—
394C2×C4×Q8—531no—
395C2×C4×D4—531no—
396C2×C4×D4—531no—
397C2×C4×D4—531no—
398C2×C4×D4—531no—
399C2×C4×D4C2×D5311yescharacteristic
400C2×C4×D4C2×D5311yescharacteristic
401C22×C4⋊C4—1061no—
402#501—538no—
403#501—538no—
404#498—538no—
405#478—538no—
406#478—538no—
407#476—538no—
408#476—538no—
409#476—538no—
410#474—538no—
411#446—538no—
412#442—538no—
413#442C2×D5318yes—
414C4×D8—538no—
415C2×#107—531no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#106—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106C2×D5311yescharacteristic
424C2×C4⋊C8—531no—
425C2×C4⋊C8—531no—
426C2×C4⋊C8—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102C2×D5311yescharacteristic
432C2×#102C2×D5311yescharacteristic
433C2×#97—531no—
434C2×#97C2×D5311yescharacteristic
435C2×C4×C8—531no—
436C53C2×#338411yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8—1061no—
439C22×Q8—1061no—
440C22×Q8—1061no—
441C22×Q8—1068no—
442C22×Q8—1061no—
443C22×Q8—2128no—
444C22×D4C22×D5311yescharacteristic
445C22×D4C22×D5311yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—1061no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4—1061no—
452C2×D8Dic10618yescomplemented
453C2×D8C22×D5314yes—
454C22×C8—531no—
455C22×C8—531no—
456C22×C8C22×D5311yescharacteristic
457C22×C8C22×D5311yescharacteristic
458C4⋊Q8—534no—
459C4⋊Q8—534no—
460C4⋊Q8—534no—
461C4⋊Q8—534no—
462C4⋊Q8—1062no—
463C4⋊Q8—1062no—
464C4⋊Q8—1062no—
465C4⋊Q8—1062no—
466#125—534no—
467#125—534no—
468#125—1062no—
469#125—1062no—
470C22⋊Q8—1068no—
471C22⋊Q8—1068no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—534no—
481C4×D4—534no—
482C4×D4—534no—
483C4×D4—534no—
484C4×D4—1062no—
485C4×D4—1062no—
486C4×D4—1062no—
487C4×D4—1062no—
488C4×D4C22×D5314yes—
489C4×D4C22×D5314yes—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—1068no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C42—531no—
515C2×C42—531no—
516C2×C42C22×D5311yescharacteristic
517#107—534no—
518#107—534no—
519#107—534no—
520#106—534no—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525#106C22×D5314yes—
526C4⋊C8—534no—
527C4⋊C8—534no—
528C4⋊C8—534no—
529#102—534no—
530#102—534no—
531#102—534no—
532#102—534no—
533#102C22×D5314yes—
534#102C22×D5314yes—
535#97—534no—
536#97C22×D5314yes—
537C4×C8—534no—
538C24—21no—
539C24—21no—
540C2×Q8—534no—
541C2×Q8—1064no—
542C2×Q8—1064no—
543C2×Q8—1064no—
544C2×Q8—1064no—
545C2×Q8—1064no—
546C2×Q8—4242no—
547C2×Q8—2124no—
548C2×Q8—2124no—
549C2×Q8—2124no—
550C2×Q8—21232no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4C2×Dic10614yes—
556C2×D4C2×Dic10614yescomplemented
557C2×D4C23×D5312yes—
558C2×D4C23×D5312yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—44no—
564C22×C4—82no—
565C22×C4—531no—
566C22×C4—531no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—1064no—
570C22×C4—1064no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—4242no—
578C22×C4—2124no—
579C22×C4—2124no—
580C22×C4—2124no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584D8C2×Dic106116yescomplemented
585C2×C8—22no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1062no—
589C2×C8—1062no—
590C2×C8C2×Dic10614yescomplemented
591C2×C8C23×D5312yes—
592C2×C8C23×D5312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—534no—
596C4⋊C4—534no—
597C4⋊C4—534no—
598C4⋊C4—532no—
599C4⋊C4—532no—
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4C23×D5312yes—
615C4⋊C4C23×D5312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C42—532no—
623C42—532no—
624C42—532no—
625C42—532no—
626C42D4×D5312yes—
627C42C23×D5312yes—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23C2×D4×D5311yescharacteristic
637Q8—1068no—
638Q8—4244no—
639Q8—2128no—
640Q8—2128no—
641Q8—2128no—
642D4—24no—
643D4—24no—
644D4—22no—
645D4—22no—
646D4C22×Dic10614yes—
647D4C22×Dic10614yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—84no—
656C2×C4—534no—
657C2×C4—532no—
658C2×C4—532no—
659C2×C4—532no—
660C2×C4—532no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—4244no—
669C2×C4—2128no—
670C2×C4—2128no—
671C2×C4—2128no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4C2×D4×D5312yes—
677C2×C4C2×D4×D5312yes—
678C2×C4C2×D4×D5311yescharacteristic
679C2×C4C22×Dic10612yes—
680C2×C4#1313326412yes—
681C2×C4C24×D5311yescharacteristic
682C8—22no—
683C8—1062no—
684C8—1062no—
685C8C22×Dic10614yescomplemented
686C22—24no—
687C22—24no—
688C22—48no—
689C22—48no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22D4×Dic10612yes—
695C22AGL(1,ℤ/8)×D5312yes—
696C22#1681143312yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—534no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4D4×Dic10612yes—
711C4C23×Dic10611yescharacteristic
712C4C2×#1313326411yescharacteristic
713C2—44no—
714C2—44no—
715C2#2028761514yesdirect product factor
716C2C2×D4×Dic10611yescharacteristic
717C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
718C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
prime radicalC22×D8×C53C22
hypercenterC2×#442D53
hypocenterC53C2×#3384
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811332C2semidirect
2. C2×D4×Dic106C2semidirect
3. #20287615C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16811030C2semidirect
6. C2×#16811020C2semidirect
7. C2×#16810923C2semidirect
8. C2×#16810921C2semidirect
9. C2×#16810913C2semidirect
10. C2×#16810911C2semidirect
11. C2×#16810911C2semidirect
12. C2×#16810901C2semidirect
13. C2×#16810751C2semidirect
19. #16811332C22semidirect
21. D4×Dic106C22semidirect
40. #16811032C22semidirect
41. #16811030C22semidirect
42. #16811020C22semidirect
43. #16810923C22semidirect
44. #16810921C22semidirect
45. #16810913C22semidirect
46. #16810911C22semidirect
47. #16810911C22semidirect
48. #16810901C22semidirect
49. #16810751C22semidirect
161. C2×D8×C53Q8semidirect
185. C2×D4×C53C2×Q8semidirect
224. D8×C53C2×Q8semidirect
226. C2×C8×C53C2×Q8semidirect
282. D4×C53C22×Q8semidirect
323. C8×C53C22×Q8semidirect
372. C2×C53#3384semidirect
436. C53C2×#3384semidirect
452. C2×D8Dic106semidirect
556. C2×D4C2×Dic106semidirect
584. D8C2×Dic106semidirect
590. C2×C8C2×Dic106semidirect
647. D4C22×Dic106semidirect
685. C8C22×Dic106semidirect
715. C2#20287615direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113322
C2×D4×Dic1062
#202876152
C2×#168110322
C2×#168110302
C2×#168110202
C2×#168109232
C2×#168109212
C2×#168109132
C2×#168109112
C2×#168109012
C2×#168107512
C2×#168107352
C2×D8×Dic532
C2×C53×#4422
C2×#338453