Finite Group Databasebeta

← C2×#20285419 #28254010

Subgroups — C2×#20285419 #28254010

Order 13568.

1998 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811175C211yesmaximal, characteristic, complemented
2C2×#16811159C211yesmaximal, characteristic
3#20285419C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811016C211yesmaximal, characteristic, complemented
6C2×#16810990C211yesmaximal, characteristic, complemented
7C2×#16810984C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810854C211yesmaximal, characteristic
10C2×#16810852C211yesmaximal, characteristic
11C2×#16810730C211yesmaximal, characteristic, complemented
12C2×#16810727C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C22×#13133127C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811175—24no—
22#16811175C2218yescomplemented
23C2×#13133216C2211yescharacteristic
24C2×#13133215C2211yescharacteristic
25#16811159—24no—
26#16811159C2218yes—
27C2×#13133212—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133201—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133191C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×#13133182—21no—
38C2×#13133182C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133177—21no—
41C2×#13133175—21no—
42C2×#13133173—21no—
43C22×C4×Dic53C2211yescharacteristic
44#16811031C2218yescomplemented
45#16811016C2218yescomplemented
46#16810990C2218yescomplemented
47#16810984C2218yescomplemented
48#16810862C2218yescomplemented
49#16810854C2218yes—
50#16810852C2218yes—
51#16810730C2218yescomplemented
52#16810727C2218yescomplemented
53#16810726C2218yescomplemented
54#16810722C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133127C2211yescharacteristic
65C2×#13133127C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2218yescomplemented
69C22×Q16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#467C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C23×Dic53D411yescharacteristic
82C23×Dic53D411yescharacteristic
83C22×C4×D53—21no—
84C2×#11719925—24no—
85C2×#11719925C2314yes—
86C2×#11719913—24no—
87C2×#11719913C2314yes—
88C2×#11719924—24no—
89C2×#11719924C2314yes—
90C22×#88322—24no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2314yes—
93C22×#88322C2311yescharacteristic
94#13133216—22no—
95#13133216C2314yes—
96#13133215—22no—
97#13133215C2314yes—
98#13133212—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133206—22no—
103#13133206C2314yes—
104#13133201—28no—
105#13133196—22no—
106#13133196C2314yes—
107#13133194—28no—
108#13133191—22no—
109#13133191C2314yes—
110Q8×Dic53—22no—
111Q8×Dic53—22no—
112Q8×Dic53C2314yes—
113Q8×Dic53C2314yes—
114#13133182—28no—
115#13133182—22no—
116#13133182C2314yes—
117#13133179—22no—
118#13133179C2314yes—
119#13133177—28no—
120#13133175—28no—
121#13133173—28no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D414yes—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2314yes—
147#13133150C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133142C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133140C2314yes—
154#13133139C2314yes—
155#13133137C2314yes—
156#13133127C2314yes—
157#13133127C2314yes—
158#13133127C2314yes—
159#13133127C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C23×C4×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53—24no—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22⋊Q8×C53—22no—
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172C22⋊Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179#107×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C22×Dic53—24no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—42no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D414yes—
214C22×Dic53C2×D414yes—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—21no—
218C2×D212C2412yes—
219C2×C4×D53—24no—
220C2×C4×D53—44no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—21no—
224C2×Dic106—24no—
225C2×Dic106—44no—
226C2×Dic106C2412yes—
227Q16×C53—28no—
228C2×C8×C53—22no—
229C2×C8×C53—28no—
230C2×C8×C53#4114yes—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊Dic53—24no—
242#11719925—28no—
243#11719924—28no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D414yes—
265C4×Dic53C2×D412yes—
266C4×Dic53C2×D414yes—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—28no—
272C2×#88322#4114yes—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275#11719913—28no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53#13714yes—
279C23×C53C22×D412yes—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—42no—
290Q8×C53—42no—
291C2×C4×C53—22no—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C53C2×#4112yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—48no—
309C2×Dic53—28no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—44no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—22no—
326D212—22no—
327D212—42no—
328C4×D53—48no—
329Dic106—22no—
330Dic106—22no—
331Dic106—48no—
332Dic106—42no—
333C8×C53—22no—
334C8×C53C2×#4114yes—
335#88322—22no—
336#88322C2×#4114yes—
337C2×#3181—531nomaximal, Sylow
338C22×C53—28no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53#53212yes—
342C22×C53C2×#13714yes—
343C22×C53C2×#13712yes—
344C22×C53#57512yes—
345C22×C53C23×D411yescharacteristic
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—84no—
350C4×C53—22no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#53212yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C22×#4111yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—22no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#533—531no—
366C2×#529—531no—
367#3181—5316no—
368C2×#501—531no—
369C2×#497—531no—
370C2×#491—531no—
371C2×#489—531no—
372C2×#467—531no—
373C2×#467D5311yescharacteristic, complemented
374C2×#465—531no—
375C2×#465—531no—
376C2×#441—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×#440—531no—
380C22×#97—531no—
381C2×C53—24no—
382C2×C53#318114yescomplemented
383C2×C53C2×#53211yescharacteristic
384C2×C53C22×#13711yescharacteristic
385C2×C53C2×#57511yescharacteristic
386D53—82no—
387C22×Q16—531no—
388C22×Q16C2×D5311yescharacteristic
389C22×SD16—531no—
390C22×SD16—531no—
391C23×C8—531no—
392C23×C8C2×D5311yescharacteristic
393#533—538no—
394#533—1064no—
395C2×C4⋊Q8—531no—
396C2×C4⋊Q8—531no—
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#125—1061no—
402C2×#124—531no—
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—1061no—
406C2×C22⋊Q8C2×D5311yescharacteristic
407C2×C22⋊Q8C2×D5311yescharacteristic
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—531no—
412C2×C4×Q8—1061no—
413C2×C4×D4—531no—
414C2×C4×D4—1061no—
415C2×#117—1061no—
416C2×#117—1061no—
417C22×C42—531no—
418#501—538no—
419#497—538no—
420#491—538no—
421#489—538no—
422#467—538no—
423#467C2×D5318yescomplemented
424#465—538no—
425#465—538no—
426#441—538no—
427#441—538no—
428#440—538no—
429#440—538no—
430C2×#107—531no—
431C2×#107C2×D5311yescharacteristic
432C2×#106—531no—
433C2×#106—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103C2×D5311yescharacteristic
439C2×#103C2×D5311yescharacteristic
440C2×#102—531no—
441C2×#102—531no—
442C2×#97—531no—
443C2×#97—531no—
444C2×#97—531no—
445C2×#97—531no—
446C2×#97—538no—
447C53C2×#318111yescharacteristic, complemented, Sylow
448C22×Q8—531no—
449C22×Q8—1061no—
450C22×Q8C22×D5311yescharacteristic
451C22×Q8C22×D5311yescharacteristic
452C22×D4—531no—
453C22×D4—1061no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—1061no—
457C23×C4C22×D5311yescharacteristic
458C2×Q16—24no—
459C2×Q16—534no—
460C2×Q16—1064no—
461C2×Q16C22×D5314yes—
462C2×SD16—534no—
463C2×SD16—534no—
464C2×SD16—1064no—
465C2×SD16—1064no—
466C22×C8—24no—
467C22×C8—531no—
468C22×C8—531no—
469C22×C8—534no—
470C22×C8—1064no—
471C22×C8C22×D5311yescharacteristic
472C22×C8C22×D5314yes—
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477C4⋊Q8—1062no—
478#126—1068no—
479#125—534no—
480#125—1062no—
481#125—1068no—
482#124—534no—
483#124—1062no—
484#123—1068no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—534no—
488C22⋊Q8—1068no—
489C22⋊Q8—1062no—
490C22⋊Q8C22×D5314yes—
491C22⋊Q8C22×D5314yes—
492#121—534no—
493#121—1062no—
494C4×Q8—534no—
495C4×Q8—534no—
496C4×Q8—534no—
497C4×Q8—1062no—
498C4×Q8—1068no—
499C4×Q8—1062no—
500C4×Q8—1062no—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1068no—
504#117—1068no—
505#117—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—534no—
531C2×C42—531no—
532C2×C42—531no—
533C2×C42—534no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42—1061no—
537#107—534no—
538#107C22×D5314yes—
539#106—534no—
540#106—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103C22×D5314yes—
546#103C22×D5314yes—
547#102—534no—
548#102—534no—
549#97—534no—
550#97—534no—
551#97—534no—
552#97—534no—
553C24—1061no—
554C24D4×D5311yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—532no—
562C2×Q8—1064no—
563C2×Q8—1061no—
564C2×Q8—1062no—
565C2×Q8—1062no—
566C2×Q8—2124no—
567C2×Q8C23×D5312yes—
568C2×Q8C23×D5312yes—
569C2×D4—532no—
570C2×D4—1064no—
571C2×D4—1061no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—2124no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—534no—
582C22×C4—531no—
583C22×C4—531no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—534no—
587C22×C4—1064no—
588C22×C4—1064no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—2124no—
593C22×C4—2122no—
594C22×C4D4×D5312yes—
595C22×C4D4×D5311yescharacteristic
596C22×C4C23×D5312yes—
597C22×C4C23×D5311yescharacteristic
598Q16—28no—
599Q16—1068no—
600SD16—1068no—
601SD16—1068no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8—534no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—1068no—
608C2×C8—1062no—
609C2×C8#1171994714yes—
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⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C42—534no—
639C42—532no—
640C42—534no—
641C42—532no—
642C42—532no—
643C42—532no—
644C42—1064no—
645C42—1064no—
646C42—1064no—
647C23—22no—
648C23—22no—
649C23—1062no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23#1313324914yes—
654C23C2×D4×D5312yes—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1062no—
663Q8—1062no—
664Q8—2128no—
665Q8—2122no—
666D4—1062no—
667D4—1062no—
668D4—2128no—
669D4—2122no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—532no—
683C2×C4—532no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—1068no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—2128no—
695C2×C4—2124no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4C2×D4×D5312yes—
700C2×C4C2×D4×D5311yescharacteristic
701C2×C4#41×D5312yes—
702C2×C4C2×#1171994712yes—
703C2×C4C24×D5311yescharacteristic
704C8—22no—
705C8—534no—
706C8—1062no—
707C8C2×#1171994714yes—
708C22—22no—
709C22—28no—
710C22—22no—
711C22—4244no—
712C22—2122no—
713C22—2122no—
714C22—2122no—
715C22#1681116812yes—
716C22C2×#1313324914yes—
717C22C2×#1313324912yes—
718C22#1681142012yes—
719C22C22×D4×D5311yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—1062no—
726C4—1062no—
727C4—1062no—
728C4—1062no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4#1681116812yes—
733C4C2×#41×D5311yescharacteristic
734C4C22×#1171994711yescharacteristic
735C2—24no—
736C2—4242no—
737C2#2028541914yesdirect product factor
738C2C2×#1681116811yescharacteristic
739C2C22×#1313324911yescharacteristic
740C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#467D53
hypocenterC53C2×#3181
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#16811175C2semidirect
3. #20285419C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811016C2semidirect
6. C2×#16810990C2semidirect
7. C2×#16810984C2semidirect
8. C2×#16810862C2semidirect
11. C2×#16810730C2semidirect
12. C2×#16810727C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810722C2semidirect
15. C22×#13133127C2semidirect
16. C2×C53×#467C2semidirect
22. #16811175C22semidirect
44. #16811031C22semidirect
45. #16811016C22semidirect
46. #16810990C22semidirect
47. #16810984C22semidirect
48. #16810862C22semidirect
51. #16810730C22semidirect
52. #16810727C22semidirect
53. #16810726C22semidirect
54. #16810722C22semidirect
68. C2×#13133127C22semidirect
73. C53×#467C22semidirect
373. C2×#467D53semidirect
382. C2×C53#3181semidirect
423. #467C2×D53semidirect
447. C53C2×#3181semidirect
737. C2#20285419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111752
C2×#168111592
#202854192
C2×#168110312
C2×#168110162
C2×#168109902
C2×#168109842
C2×#168108622
C2×#168108542
C2×#168108522
C2×#168107302
C2×#168107272
C2×#168107262
C2×#168107222
C22×#131331272
C2×C53×#4672
C2×#318153