Finite Group Databasebeta

← C2×#20285009 #28252442

Subgroups — C2×#20285009 #28252442

Order 13568.

1994 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×#16811233C211yesmaximal, characteristic
2C2×#16811101C211yesmaximal, characteristic
3#20285009C2116yesmaximal, direct product factor
4C2×#16810965C211yesmaximal, characteristic
5C2×#16810961C211yesmaximal, characteristic
6C2×#16810932C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810831C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810779C211yesmaximal, characteristic
11C2×#16810730C211yesmaximal, characteristic, complemented
12C2×#16810727C211yesmaximal, characteristic, complemented
13C2×Q16×Dic53C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic
16C2×C53×#451C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19#16811233—24no—
20#16811233C2218yes—
21C2×#13133215C2211yescharacteristic
22C2×#13133210—21no—
23C2×#13133210—21no—
24C2×#13133208—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133196C2211yescharacteristic
28#16811101—24no—
29#16811101C2218yes—
30C2×Q8×Dic53—21no—
31C2×Q8×Dic53—21no—
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×#13133182C2211yescharacteristic
38C2×#13133176—21no—
39C2×#13133176—21no—
40C2×#13133176C2211yescharacteristic
41C2×#13133176C2211yescharacteristic
42#16810965C2218yes—
43#16810961C2218yes—
44#16810932C2218yescomplemented
45#16810928C2218yescomplemented
46#16810831C2218yescomplemented
47#16810831C2218yescomplemented
48#16810779C2218yes—
49#16810730C2218yescomplemented
50#16810727C2218yescomplemented
51Q16×Dic53C2218yescomplemented
52#16810715C2218yescomplemented
53#16810681C2218yes—
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#451C2218yes—
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C2×#11719925—24no—
79C2×#11719925—24no—
80C2×#11719925C2314yes—
81C2×#11719925C2314yes—
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84#13133215—22no—
85#13133215C2314yes—
86#13133210—28no—
87#13133210—28no—
88#13133208—28no—
89#13133208—22no—
90#13133208C2314yes—
91#13133207—28no—
92#13133196—22no—
93#13133196C2314yes—
94Q8×Dic53—28no—
95Q8×Dic53—28no—
96Q8×Dic53—22no—
97Q8×Dic53—22no—
98Q8×Dic53—22no—
99Q8×Dic53—22no—
100Q8×Dic53—22no—
101Q8×Dic53C2314yes—
102Q8×Dic53C2314yes—
103Q8×Dic53C2314yes—
104Q8×Dic53C2314yes—
105Q8×Dic53C2314yes—
106#13133182—22no—
107#13133182C2314yes—
108#13133176—28no—
109#13133176—28no—
110#13133176—22no—
111#13133176D414yes—
112#13133176C2314yes—
113#13133176C2314yes—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53D411yescharacteristic
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53D411yescharacteristic
133C2×C22⋊Dic53D411yescharacteristic
134C2×C4×Dic53—21no—
135C2×C4×Dic53—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133142C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155C22⋊#88322C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53—24no—
159C22×Q8×C53—24no—
160C22×Q8×C53—21no—
161C22×Q8×C53—22no—
162C22×Q8×C53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C2×Q16×C53—24no—
169C2×Q16×C53—24no—
170C2×Q16×C53C2314yes—
171C2×Q16×C53C2314yes—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22⋊Q8×C53—22no—
175C22⋊Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C2×Q8×C53—216no—
184C2×Q8×C53—28no—
185C2×Q8×C53—28no—
186C2×Q8×C53—28no—
187C2×Q8×C53—24no—
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53#4114yes—
196C2×Q8×C53#4114yes—
197C2×Q8×C53C2412yes—
198C2×Q8×C53C2412yes—
199C2×Q8×C53C2412yes—
200C22×C4×C53—28no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2411yescharacteristic
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—21no—
223C2×Dic106C2412yes—
224Q16×C53—28no—
225Q16×C53—28no—
226C2×C8×C53—22no—
227C2×C8×C53—22no—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2412yes—
233C22⋊C4×C53—24no—
234C22⋊Dic53—24no—
235C22⋊Dic53—24no—
236C22⋊Dic53C2×D414yes—
237C22⋊Dic53C2×D414yes—
238#11719925—28no—
239#11719925—28no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—24no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53C2×D414yes—
250C4⋊Dic53C2×D414yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53C2×D412yes—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53C22×D412yes—
278C23×C53C22×D411yescharacteristic
279Q8×C53—216no—
280Q8×C53—24no—
281Q8×C53—24no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—42no—
287Q8×C53C2×#4114yes—
288Q8×C53C2×#4114yes—
289C2×C4×C53—216no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—24no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4112yes—
305C2×C4×C53C2×#4112yes—
306C2×C4×C53C2511yescharacteristic
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—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323Dic106—22no—
324Dic106—22no—
325Dic106—42no—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322—22no—
330C2×#3127—531nomaximal, Sylow
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—44no—
335C22×C53#52512yes—
336C22×C53#57812yes—
337C22×C53#57812yes—
338C22×C53C23×D411yescharacteristic
339C4×C53—24no—
340C4×C53—24no—
341C4×C53—22no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53#52512yes—
345C4×C53C22×#4111yescharacteristic
346C4×C53C22×#4111yescharacteristic
347Dic53—22no—
348Dic53—22no—
349Dic53—22no—
350Dic53—22no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355C2×#541—531no—
356C2×#519—531no—
357#3127—5316no—
358C2×#485—531no—
359C2×#485—531no—
360C2×#479—531no—
361C2×#479—531no—
362C2×#462—531no—
363C2×#462—531no—
364C2×#451—531no—
365C2×#451D5311yescharacteristic
366C2×#441—531no—
367C2×#441—531no—
368C2×C4×Q16—531no—
369C2×C4×Q16—531no—
370C2×#433—531no—
371C2×C53—42no—
372C2×C53#312714yescomplemented
373C2×C53C2×#52511yescharacteristic
374C2×C53C2×#57811yescharacteristic
375C2×C53C2×#57811yescharacteristic
376C23×Q8C2×D5311yescharacteristic
377C22×Q16—531no—
378C22×Q16—531no—
379C22×Q16C2×D5311yescharacteristic
380C22×Q16C2×D5311yescharacteristic
381#541—538no—
382#541—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#125—531no—
387C2×#125—1061no—
388C2×#125—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8C2×D5311yescharacteristic
391#519—538no—
392#519—1064no—
393C2×C4×Q8—531no—
394C2×C4×Q8—531no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8—1061no—
400C2×C4×Q8—1061no—
401C2×#117—531no—
402C2×#117—531no—
403C2×#117—1061no—
404C2×#117—1061no—
405#485—538no—
406#485—538no—
407#479—538no—
408#479—538no—
409#462—538no—
410#462—538no—
411#451—538no—
412#451C2×D5318yes—
413#441—538no—
414#441—538no—
415C4×Q16—538no—
416C4×Q16—538no—
417#433—538no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103C2×D5311yescharacteristic
431C2×#103C2×D5311yescharacteristic
432C2×C22⋊C8—531no—
433C2×C22⋊C8C2×D5311yescharacteristic
434C2×#97—531no—
435C2×C4×C8—531no—
436C53C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—24no—
438C22×Q8—24no—
439C22×Q8—21no—
440C22×Q8—22no—
441C22×Q8—531no—
442C22×Q8C22×D5311yescharacteristic
443C22×Q8C22×D5314yes—
444C22×Q8C22×D5311yescharacteristic
445C22×Q8C22×D5311yescharacteristic
446C23×C4—21no—
447C23×C4C22×D5311yescharacteristic
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16—534no—
451C2×Q16—534no—
452C2×Q16—1064no—
453C2×Q16—1064no—
454C2×Q16C22×D5314yes—
455C2×Q16C22×D5314yes—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8C22×D5311yescharacteristic
459C22×C8C22×D5311yescharacteristic
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462#126—1068no—
463#126—1068no—
464#125—534no—
465#125—1062no—
466#125—1068no—
467#125—1068no—
468C22⋊Q8—22no—
469C22⋊Q8—534no—
470C22⋊Q8—1062no—
471C22⋊Q8C22×D5314yes—
472C4×Q8—534no—
473C4×Q8—534no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×Q8—1062no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×Q8—1062no—
484C4×Q8—1068no—
485C4×Q8—1068no—
486#117—534no—
487#117—534no—
488#117—534no—
489#117—1068no—
490#117—1068no—
491#117—1062no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
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⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4C22×D5311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—531no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—531no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42—1061no—
524#107—534no—
525#107—534no—
526#106—534no—
527#106—534no—
528C4⋊C8—534no—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536#103C22×D5314yes—
537#103C22×D5314yes—
538C22⋊C8—534no—
539C22⋊C8C22×D5314yes—
540#97—534no—
541C4×C8—534no—
542C24D4×D5311yescharacteristic
543C2×Q8—216no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—24no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—532no—
556C2×Q8—1061no—
557C2×Q8—1062no—
558C2×Q8—1062no—
559C2×Q8#1171994714yes—
560C2×Q8#1171994714yes—
561C2×Q8C23×D5312yes—
562C2×Q8C23×D5312yes—
563C2×Q8C23×D5312yes—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4D4×D5312yes—
581C22×C4D4×D5311yescharacteristic
582C22×C4C23×D5312yes—
583C22×C4C23×D5311yescharacteristic
584Q16—28no—
585Q16—28no—
586Q16—1068no—
587Q16—1068no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—532no—
591C2×C8—532no—
592C2×C8—1062no—
593C2×C8—1062no—
594C2×C8C23×D5312yes—
595C2×C8C23×D5312yes—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—534no—
599C4⋊C4—534no—
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1064no—
617C4⋊C4C23×D5312yes—
618C22⋊C4—24no—
619C22⋊C4—534no—
620C22⋊C4—534no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—532no—
624C42—532no—
625C42—532no—
626C42—532no—
627C42—1064no—
628C42—1064no—
629C42—1064no—
630C42—1064no—
631C42—1064no—
632C42—1064no—
633C42—1064no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23C2×D4×D5312yes—
638C23C2×D4×D5311yescharacteristic
639Q8—216no—
640Q8—24no—
641Q8—24no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—42no—
647Q8—1062no—
648Q8—1062no—
649Q8—2122no—
650Q8C2×#1171994714yes—
651Q8C2×#1171994714yes—
652C2×C4—216no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—532no—
666C2×C4—532no—
667C2×C4—532no—
668C2×C4—532no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4—2122no—
681C2×C4C2×D4×D5312yes—
682C2×C4C2×D4×D5311yescharacteristic
683C2×C4C2×#1171994712yes—
684C2×C4C2×#1171994712yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—44no—
694C22#1681112912yes—
695C22#1681143612yes—
696C22#1681143912yes—
697C22C22×D4×D5311yescharacteristic
698C4—24no—
699C4—24no—
700C4—22no—
701C4—42no—
702C4—42no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—1062no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4#1681112912yes—
712C4C22×#1171994711yescharacteristic
713C4C22×#1171994711yescharacteristic
714C2—42no—
715C2#2028500914yesdirect product factor
716C2C2×#1681112911yescharacteristic
717C2C2×#1681143611yescharacteristic
718C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC24×C53C2×D4
hypercenterC2×#451D53
hypocenterC53C2×#3127
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #20285009C2direct (N × H)
6. C2×#16810932C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810831C2semidirect
9. C2×#16810831C2semidirect
11. C2×#16810730C2semidirect
12. C2×#16810727C2semidirect
13. C2×Q16×Dic53C2semidirect
14. C2×#16810715C2semidirect
44. #16810932C22semidirect
45. #16810928C22semidirect
46. #16810831C22semidirect
47. #16810831C22semidirect
49. #16810730C22semidirect
50. #16810727C22semidirect
51. Q16×Dic53C22semidirect
52. #16810715C22semidirect
372. C2×C53#3127semidirect
436. C53C2×#3127semidirect
715. C2#20285009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168111012
#202850092
C2×#168109652
C2×#168109612
C2×#168109322
C2×#168109282
C2×#168108312
C2×#168107792
C2×#168107302
C2×#168107272
C2×Q16×Dic532
C2×#168107152
C2×#168106812
C2×C53×#4512
C2×#312753