Finite Group Databasebeta

← C2×#20287743 #28265057

Subgroups — C2×#20287743 #28265057

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811348C211yesmaximal, characteristic, complemented
2C2×#16811342C211yesmaximal, characteristic
3#20287743C2116yesmaximal, direct product factor
4C2×#16811014C211yesmaximal, characteristic
5C2×#16811001C211yesmaximal, characteristic, complemented
6C2×#16810843C211yesmaximal, characteristic
7C2×#16810842C211yesmaximal, characteristic
8C2×#16810831C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810830C211yesmaximal, characteristic, complemented
11C2×#16810826C211yesmaximal, characteristic
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810731C211yesmaximal, characteristic, complemented
14C2×#16810730C211yesmaximal, characteristic, complemented
15C2×SD16×Dic53C211yesmaximal, characteristic
16C2×C53×#497C211yesmaximal, characteristic
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22#16811348—24no—
23#16811348C2218yescomplemented
24#16811342—24no—
25#16811342C2218yes—
26C2×#13133215C2211yescharacteristic
27C2×#13133215C2211yescharacteristic
28C2×#13133215C2211yescharacteristic
29C2×#13133210—21no—
30C2×#13133210—21no—
31C2×#13133208—21no—
32C2×#13133207—21no—
33C2×#13133207—21no—
34C2×#13133204C2211yescharacteristic
35C2×#13133194—21no—
36C2×Q8×Dic53C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×Q8×Dic53C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×Dic106C2211yescharacteristic
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182—21no—
43C2×D4×Dic53C2211yescharacteristic
44C2×#13133173—21no—
45#16811014C2218yes—
46#16811001C2218yescomplemented
47#16810843C2218yes—
48#16810842C2218yes—
49#16810831C2218yescomplemented
50#16810831C2218yescomplemented
51#16810830C2218yescomplemented
52#16810826C2218yes—
53#16810751C2218yescomplemented
54#16810731C2218yescomplemented
55#16810730C2218yescomplemented
56SD16×Dic53C2218yes—
57C2×#13133149C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C22×SD16×C53C2211yescharacteristic
73C2×C4⋊Q8×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic
75C53×#497C2218yes—
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C23×Dic53—21no—
81C2×Dic212—24no—
82C2×Dic212C2314yes—
83C2×#11719925—42no—
84C2×#11719925—42no—
85C2×#11719925—42no—
86C2×#11719925C2314yes—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C2×#11719923—42no—
90C2×#11719923C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133215—22no—
94#13133215—22no—
95#13133215—22no—
96#13133215C2314yes—
97#13133215C2314yes—
98#13133215C2314yes—
99#13133210—28no—
100#13133210—28no—
101#13133208—28no—
102#13133207—28no—
103#13133207—28no—
104#13133204—22no—
105#13133204C2314yes—
106#13133194—28no—
107Q8×Dic53—22no—
108Q8×Dic53—22no—
109Q8×Dic53—22no—
110Q8×Dic53C2314yes—
111Q8×Dic53C2314yes—
112Q8×Dic53C2314yes—
113C4×Dic106—22no—
114C4×Dic106—22no—
115C4×Dic106D414yes—
116C4×Dic106C2314yes—
117C4×Dic106C2314yes—
118C4×Dic106C2314yes—
119#13133182—28no—
120D4×Dic53—22no—
121D4×Dic53C2314yes—
122#13133173—28no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919D411yescharacteristic
138C2×#11719919D411yescharacteristic
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133149C2314yes—
150C4⋊#88322C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133138C2314yes—
159#13133127C2314yes—
160C8×Dic53C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53C2311yescharacteristic
165C2×Q16×C53—24no—
166C2×Q16×C53—42no—
167C2×Q16×C53C2314yes—
168C2×Q16×C53C2314yes—
169C2×SD16×C53—24no—
170C2×SD16×C53—42no—
171C2×SD16×C53C2314yes—
172C2×SD16×C53C2314yes—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C4⋊Q8×C53—22no—
176C4⋊Q8×C53C2314yes—
177#124×C53—22no—
178#124×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53C2311yescharacteristic
184#97×C53C2314yes—
185C24×C53—21no—
186C2×Q8×C53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53C2412yes—
196C2×Q8×C53C2412yes—
197C2×Q8×C53C2412yes—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53C2412yes—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2411yescharacteristic
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C2×Dic106—24no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106C2×D414yes—
226C2×Dic106C2412yes—
227C2×Dic106C2412yes—
228Q16×C53—28no—
229Q16×C53—44no—
230SD16×C53—28no—
231SD16×C53—44no—
232C2×C8×C53—22no—
233C2×C8×C53#4114yes—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C42×C53C2×D412yes—
241C42×C53C2412yes—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245#11719925—44no—
246#11719925—44no—
247#11719925—44no—
248#11719923—44no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2×D414yes—
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—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280Dic212—28no—
281C23×C53—22no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53C22×D411yescharacteristic
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293Q8×C53—42no—
294Q8×C53—42no—
295D4×C53—22no—
296D4×C53—22no—
297D4×C53—42no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C53H(5,𝔽2)12yes—
311C2×C4×C53C2511yescharacteristic
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—48no—
324C2×Dic53#13714yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329Dic106—28no—
330Dic106—22no—
331Dic106—22no—
332Dic106—22no—
333Dic106—22no—
334Dic106—42no—
335Dic106—42no—
336C8×C53—22no—
337C8×C53C2×#4114yes—
338#88322—22no—
339#88322—22no—
340C2×#3398—531nomaximal, Sylow
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—84no—
345C22×C53#55012yes—
346C22×C53C2×#13712yes—
347C22×C53#57812yes—
348C22×C53C23×D411yescharacteristic
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53#55012yes—
355C4×C53C22×#4111yescharacteristic
356C4×C53C2×H(5,𝔽2)11yescharacteristic
357Dic53—22no—
358Dic53—22no—
359Dic53—22no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×#13714yes—
365C2×#557—531no—
366C2×#556—531no—
367#3398—5316no—
368C2×#497—531no—
369C2×#497D5311yescharacteristic
370C2×#494—531no—
371C2×#464—531no—
372C2×#464—531no—
373C2×#462—531no—
374C2×#462—531no—
375C2×#462—531no—
376C2×#461—531no—
377C2×#446—531no—
378C2×#441—531no—
379C2×#441—531no—
380C2×C4×SD16—531no—
381C2×C53—82no—
382C2×C53#339814yescomplemented
383C2×C53C2×#55011yescharacteristic
384C2×C53C22×#13711yescharacteristic
385C2×C53C2×#57811yescharacteristic
386C22×Q16—531no—
387C22×Q16—531no—
388C22×Q16—531no—
389C22×Q16—531no—
390C22×Q16C2×D5311yescharacteristic
391C22×Q16C2×D5311yescharacteristic
392C22×SD16—531no—
393C22×SD16C2×D5311yescharacteristic
394C22×SD16C2×D5311yescharacteristic
395#557—538no—
396#557—1064no—
397#556—538no—
398#556—1064no—
399C2×C4⋊Q8—531no—
400C2×C4⋊Q8—531no—
401C2×C4⋊Q8—531no—
402C2×C4⋊Q8C2×D5311yescharacteristic
403C2×#126—1061no—
404C2×#126—1061no—
405C2×#125—1061no—
406C2×#125—1061no—
407C2×#125—1061no—
408C2×#124—531no—
409C2×#124C2×D5311yescharacteristic
410C2×C22⋊Q8—1061no—
411C2×C4×Q8—531no—
412C2×C4×Q8—531no—
413C2×C4×Q8—531no—
414C2×C4×Q8—531no—
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8—1061no—
418C2×C4×D4—531no—
419C2×#117—1061no—
420#497—538no—
421#497C2×D5318yes—
422#494—538no—
423#464—538no—
424#464—538no—
425#462—538no—
426#462—538no—
427#462—538no—
428#461—538no—
429#446—538no—
430#441—538no—
431#441—538no—
432C4×SD16—538no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#97—531no—
444C2×#97C2×D5311yescharacteristic
445C2×C4×C8—531no—
446C53C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—531no—
448C22×Q8—531no—
449C22×Q8—531no—
450C22×Q8C22×D5311yescharacteristic
451C22×Q8C22×D5311yescharacteristic
452C22×Q8C22×D5311yescharacteristic
453C22×D4C22×D5311yescharacteristic
454C23×C4—1061no—
455C2×Q16—24no—
456C2×Q16—42no—
457C2×Q16—534no—
458C2×Q16—534no—
459C2×Q16—534no—
460C2×Q16—534no—
461C2×Q16—1064no—
462C2×Q16—2122no—
463C2×Q16—2122no—
464C2×Q16—2122no—
465C2×Q16C22×D5314yes—
466C2×Q16C22×D5314yes—
467C2×SD16—24no—
468C2×SD16—42no—
469C2×SD16—534no—
470C2×SD16—2122no—
471C2×SD16C22×D5314yes—
472C2×SD16C22×D5314yes—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5311yescharacteristic
477C4⋊Q8—22no—
478C4⋊Q8—534no—
479C4⋊Q8—534no—
480C4⋊Q8—534no—
481C4⋊Q8—1062no—
482C4⋊Q8—1062no—
483C4⋊Q8—1062no—
484C4⋊Q8C22×D5314yes—
485#126—1068no—
486#126—1068no—
487#125—1068no—
488#125—1068no—
489#125—1068no—
490#124—22no—
491#124—534no—
492#124—1062no—
493#124C22×D5314yes—
494C22⋊Q8—1068no—
495C4×Q8—534no—
496C4×Q8—534no—
497C4×Q8—534no—
498C4×Q8—534no—
499C4×Q8—534no—
500C4×Q8—534no—
501C4×Q8—534no—
502C4×Q8—1062no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8—1068no—
506C4×Q8—1062no—
507C4×Q8—1062no—
508C4×D4—534no—
509C4×D4—1062no—
510#117—1068no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C42—531no—
535C2×C42—531no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—1061no—
541C2×C42C22×D5311yescharacteristic
542#106—534no—
543C4⋊C8—534no—
544C4⋊C8—534no—
545C4⋊C8—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103—534no—
550#103—534no—
551#102—534no—
552#97—534no—
553#97C22×D5314yes—
554C4×C8—534no—
555C24—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—534no—
566C2×Q8—532no—
567C2×Q8—532no—
568C2×Q8—1064no—
569C2×Q8—1061no—
570C2×Q8—1061no—
571C2×Q8—1062no—
572C2×Q8—1062no—
573C2×Q8—1062no—
574C2×Q8—1062no—
575C2×Q8C23×D5312yes—
576C2×Q8C23×D5312yes—
577C2×Q8C23×D5312yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4C23×D5312yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—1064no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—2124no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598Q16—28no—
599Q16—44no—
600Q16—1068no—
601Q16—2124no—
602Q16—2124no—
603Q16—2124no—
604SD16—28no—
605SD16—44no—
606SD16—2124no—
607C2×C8—22no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8#1171994714yes—
613C2×C8C23×D5312yes—
614C2×C8C23×D5312yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—534no—
618C4⋊C4—534no—
619C4⋊C4—534no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1061no—
632C4⋊C4—1061no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C42—532no—
641C42—532no—
642C42—532no—
643C42—532no—
644C42—1064no—
645C42—1064no—
646C42—1064no—
647C42—1064no—
648C42—1064no—
649C42D4×D5312yes—
650C42C23×D5312yes—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—1068no—
666Q8—1062no—
667Q8—1062no—
668Q8—1062no—
669Q8—1062no—
670Q8—2122no—
671Q8—2122no—
672D4—22no—
673D4—22no—
674D4—42no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—534no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—2128no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994712yes—
704C2×C4#1313326212yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—1062no—
708C8—1062no—
709C8C2×#1171994714yes—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22#1681129312yes—
715C22#137×D5312yes—
716C22#1681143912yes—
717C22C22×D4×D5311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—534no—
724C4—1062no—
725C4—1062no—
726C4—1062no—
727C4—2122no—
728C4—2122no—
729C4—2122no—
730C4—2122no—
731C4#1681129312yes—
732C4C22×#1171994711yescharacteristic
733C4C2×#1313326211yescharacteristic
734C2—82no—
735C2#2028774314yesdirect product factor
736C2C2×#1681129311yescharacteristic
737C2C2×#137×D5311yescharacteristic
738C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#497C2
socleC23×C53C22×D4
prime radicalC22×D4×C53C23
hypercenterC2×#497D53
hypocenterC53C2×#3398
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#16811348C2semidirect
3. #20287743C2direct (N × H)
5. C2×#16811001C2semidirect
8. C2×#16810831C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810830C2semidirect
12. C2×#16810751C2semidirect
13. C2×#16810731C2semidirect
14. C2×#16810730C2semidirect
23. #16811348C22semidirect
46. #16811001C22semidirect
49. #16810831C22semidirect
50. #16810831C22semidirect
51. #16810830C22semidirect
53. #16810751C22semidirect
54. #16810731C22semidirect
55. #16810730C22semidirect
382. C2×C53#3398semidirect
446. C53C2×#3398semidirect
735. C2#20287743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113482
C2×#168113422
#202877432
C2×#168110142
C2×#168110012
C2×#168108432
C2×#168108422
C2×#168108312
C2×#168108302
C2×#168108262
C2×#168107512
C2×#168107312
C2×#168107302
C2×SD16×Dic532
C2×C53×#4972
C2×#339853