Finite Group Databasebeta

← C2×#20287199 #28262670

Subgroups — C2×#20287199 #28262670

Order 13568.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811334C211yesmaximal, characteristic, complemented
2C2×#16811326C211yesmaximal, characteristic
3#20287199C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810967C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810927C211yesmaximal, characteristic, complemented
9C2×#16810900C211yesmaximal, characteristic, complemented
10C2×#16810870C211yesmaximal, characteristic, complemented
11C2×#16810853C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C2×#107×D53C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811334—24no—
21#16811334C2218yescomplemented
22#16811326—24no—
23#16811326C2218yes—
24C2×#13133212—21no—
25C2×#13133208—21no—
26C2×#13133202—21no—
27C2×#13133197C2211yescharacteristic
28C2×#13133197C2211yescharacteristic
29C2×#13133193—21no—
30C2×#13133193—21no—
31C2×#13133192—21no—
32C2×#13133192C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133179—21no—
38C2×#13133179—21no—
39C2×#13133175C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810967C2218yescomplemented
44#16810960C2218yescomplemented
45#16810943C2218yescomplemented
46#16810938C2218yescomplemented
47#16810927C2218yescomplemented
48#16810900C2218yescomplemented
49#16810870C2218yescomplemented
50#16810853C2218yescomplemented
51#16810725C2218yescomplemented
52#16810696C2218yescomplemented
53#16810662C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58#107×D53C2218yescomplemented
59C2×#13133148C2211yescharacteristic
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212D411yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C22×C4×D53C2311yescharacteristic
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90C2×#11719912—24no—
91C2×#11719912C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C2×C8×D53—24no—
95C2×C8×D53C2314yes—
96#13133212—28no—
97#13133208—28no—
98#13133202—28no—
99#13133197—22no—
100#13133197—22no—
101#13133197C2314yes—
102#13133197C2314yes—
103#13133193—28no—
104#13133193—28no—
105#13133192—28no—
106#13133192—22no—
107#13133192—22no—
108#13133192C2314yes—
109#13133192C2314yes—
110C4×Dic106—22no—
111C4×Dic106C2314yes—
112C4×D212—22no—
113C4×D212D414yes—
114C4×D212C2314yes—
115C4×D212C2314yes—
116#13133179—28no—
117#13133179—28no—
118#13133175—22no—
119#13133175C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145#13133151C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133148C2314yes—
150C4⋊#88322C2314yes—
151#13133142C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133139C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133129C2314yes—
158#13133129C2314yes—
159C22×Q8×C53—21no—
160C22×C8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C4⋊Q8×C53—22no—
163C4⋊Q8×C53C2314yes—
164#125×C53—22no—
165#125×C53C2314yes—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#107×C53C2314yes—
175#107×C53C2314yes—
176#106×C53C2314yes—
177#106×C53C2314yes—
178#97×C53C2314yes—
179C23×D53—21no—
180C23×D53C2×D411yescharacteristic
181C23×D53C2×D411yescharacteristic
182C2×Q8×C53—24no—
183C2×Q8×C53—82no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2411yescharacteristic
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53C2×D411yescharacteristic
195C22×Dic53C2×D411yescharacteristic
196C2×D212—24no—
197C2×D212—22no—
198C2×D212—22no—
199C2×D212—24no—
200C2×D212—21no—
201C2×D212—24no—
202C2×D212—44no—
203C2×D212—82no—
204C2×D212C2×D414yes—
205C2×D212C2412yes—
206C2×C4×D53—22no—
207C2×C4×D53—22no—
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—24no—
211C2×C4×D53—24no—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—82no—
215C2×C4×D53—82no—
216C2×C4×D53—82no—
217C2×C4×D53—82no—
218C2×C4×D53C2×D412yes—
219C2×C4×D53C2×D412yes—
220C2×C4×D53C2412yes—
221C2×C4×D53C2412yes—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—21no—
225C2×Dic106C2412yes—
226C2×C8×C53—22no—
227C2×C8×C53#4114yes—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243#11719921—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921C2×D414yes—
250#11719921C2×D414yes—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2×D414yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268#11719913—28no—
269#11719912—28no—
270C8×D53—28no—
271C23×C53C22×D411yescharacteristic
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53#13714yes—
282C22×D53C22×D412yes—
283C22×D53C22×D412yes—
284Q8×C53—84no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4112yes—
299C2×C4×C532−1+412yes—
300C2×C4×C53C2511yescharacteristic
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53C22×D412yes—
310C2×Dic53C22×D412yes—
311D212—28no—
312D212—22no—
313D212—22no—
314D212—48no—
315D212—42no—
316D212—84no—
317C4×D53—24no—
318C4×D53—24no—
319C4×D53—22no—
320C4×D53—22no—
321C4×D53—22no—
322C4×D53—22no—
323C4×D53—84no—
324C4×D53—84no—
325C4×D53—84no—
326C4×D53—84no—
327Dic106—22no—
328Dic106—22no—
329Dic106—42no—
330C8×C53—22no—
331C8×C53C2×#4114yes—
332#88322—22no—
333#88322—22no—
334C2×#3346—531nomaximal, Sylow
335C22×C53#54712yes—
336C22×C53C2×#13712yes—
337C22×C53#57612yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—28no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—44no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—84no—
350C2×D53C2×#13714yes—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#54712yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C2×2−1+411yescharacteristic
360Dic53—22no—
361Dic53—22no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#554—531no—
366C2×#553—531no—
367#3346—5316no—
368C2×#501D5311yescharacteristic, complemented
369C2×#484—531no—
370C2×#481—531no—
371C2×#485—531no—
372C2×#480—531no—
373C2×#479—531no—
374C2×#474—531no—
375C2×#468—531no—
376C2×#465—531no—
377C2×#440—531no—
378C2×#435—531no—
379C2×#428—531no—
380C22×#107—531no—
381C2×C53#334614yescomplemented
382C2×C53C2×#54711yescharacteristic
383C2×C53C22×#13711yescharacteristic
384C2×C53C2×#57611yescharacteristic
385D53—24no—
386D53—42no—
387D53—82no—
388C22×SD16—531no—
389C22×M16—531no—
390C23×C8—531no—
391#554—538no—
392#554—1064no—
393#553—538no—
394#553—1064no—
395C2×C4⋊Q8C2×D5311yescharacteristic
396C2×#126—1061no—
397C2×#125—1061no—
398C2×#125C2×D5311yescharacteristic
399C2×#123—1061no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8—1061no—
404C2×#121—531no—
405C2×#121—531no—
406C2×#121—1061no—
407C2×C4×Q8—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4—1061no—
411C2×C4×D4—1061no—
412C2×#117—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416#501C2×D5318yescomplemented
417#485—538no—
418#484—538no—
419#481—538no—
420#480—538no—
421#479—538no—
422#474—538no—
423#468—538no—
424#465—538no—
425#440—538no—
426#435—538no—
427#428—538no—
428C2×#107—531no—
429C2×#107—531no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—538no—
433C2×#107C2×D5311yescharacteristic
434C2×#107C2×D5311yescharacteristic
435C2×#106—531no—
436C2×#106C2×D5311yescharacteristic
437C2×#106C2×D5311yescharacteristic
438C2×C4⋊C8—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×#97C2×D5311yescharacteristic
448C53C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—531no—
451C22×D4—531no—
452C22×D4—531no—
453C22×D4—1061no—
454C22×D4—1061no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4—1061no—
461C2×SD16—534no—
462C2×SD16—1064no—
463C2×M16—534no—
464C2×M16—1064no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—534no—
468C22×C8—1064no—
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D5314yes—
473#126—1068no—
474#125—22no—
475#125—1068no—
476#125C22×D5314yes—
477#123—1068no—
478C22⋊Q8—534no—
479C22⋊Q8—534no—
480C22⋊Q8—1068no—
481C22⋊Q8—1068no—
482C22⋊Q8—1062no—
483C22⋊Q8—1062no—
484#121—534no—
485#121—534no—
486#121—1062no—
487#121—1062no—
488#121—1068no—
489C4×Q8—534no—
490C4×Q8—1062no—
491C4×D4—534no—
492C4×D4—534no—
493C4×D4—534no—
494C4×D4—1068no—
495C4×D4—1068no—
496C4×D4—1062no—
497#117—534no—
498#117—1062no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1062no—
510C2×C4⋊C4—1062no—
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⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532#107—534no—
533#107—534no—
534#107—534no—
535#107—534no—
536#107C22×D5314yes—
537#107C22×D5314yes—
538#106—534no—
539#106C22×D5314yes—
540#106C22×D5314yes—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548C22⋊C8—534no—
549C22⋊C8—534no—
550#97C22×D5314yes—
551C24—531no—
552C24—531no—
553C24—1061no—
554C2×Q8—24no—
555C2×Q8—82no—
556C2×Q8—532no—
557C2×Q8—1061no—
558C2×Q8—1062no—
559C2×Q8—1062no—
560C2×D4—534no—
561C2×D4—532no—
562C2×D4—1064no—
563C2×D4—1064no—
564C2×D4—1064no—
565C2×D4—1061no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—4242no—
569C2×D4—2124no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—532no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—1064no—
581C22×C4—1064no—
582C22×C4—1064no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1064no—
591C22×C4—4242no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4—4242no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598SD16—1068no—
599M16—1068no—
600C2×C8—22no—
601C2×C8—532no—
602C2×C8—532no—
603C2×C8—1062no—
604C2×C8—1062no—
605C2×C8—1068no—
606C2×C8#1171994914yes—
607C2×C8C23×D5312yes—
608C2×C8C23×D5312yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—534no—
617C4⋊C4—532no—
618C4⋊C4—532no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—1064no—
627C4⋊C4C23×D5312yes—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—534no—
632C22⋊C4—534no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—1064no—
640C42—1064no—
641C42D4×D5312yes—
642C42C23×D5312yes—
643C23—534no—
644C23—532no—
645C23—532no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—1062no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23C2×D4×D5311yescharacteristic
656Q8—84no—
657Q8—1062no—
658Q8—1062no—
659Q8—2122no—
660D4—1068no—
661D4—1062no—
662D4—1062no—
663D4—4244no—
664D4—2128no—
665D4—2122no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1064no—
681C2×C4—1064no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—4244no—
690C2×C4—4244no—
691C2×C4—4244no—
692C2×C4—4244no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4C2×D4×D5312yes—
697C2×C4C2×D4×D5312yes—
698C2×C4C2×D4×D5311yescharacteristic
699C2×C4C2×#1171994912yes—
700C2×C4#1313326512yes—
701C2×C4C24×D5311yescharacteristic
702C8—22no—
703C8—1062no—
704C8—1062no—
705C8C2×#1171994914yes—
706C22—534no—
707C22—1062no—
708C22—1062no—
709C22—1068no—
710C22—1062no—
711C22—1062no—
712C22—1062no—
713C22—4244no—
714C22—2122no—
715C22—2122no—
716C22—2122no—
717C22—2124no—
718C22#1681127612yes—
719C22#137×D5312yes—
720C22#1681142712yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—1062no—
729C4—1062no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681127612yes—
734C4C22×#1171994911yescharacteristic
735C4C2×#1313326511yescharacteristic
736C2—1064no—
737C2—4242no—
738C2—2122no—
739C2#2028719914yesdirect product factor
740C2C2×#1681127611yescharacteristic
741C2C2×#137×D5311yescharacteristic
742C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
prime radicalC2×#16811326C2
hypercenterC2×#501D53
hypocenterC53C2×#3346
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16811334C2semidirect
3. #20287199C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810967C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810927C2semidirect
9. C2×#16810900C2semidirect
10. C2×#16810870C2semidirect
11. C2×#16810853C2semidirect
12. C2×#16810725C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810662C2semidirect
15. C2×#107×D53C2semidirect
16. C2×C53×#501C2semidirect
21. #16811334C22semidirect
43. #16810967C22semidirect
44. #16810960C22semidirect
45. #16810943C22semidirect
46. #16810938C22semidirect
47. #16810927C22semidirect
48. #16810900C22semidirect
49. #16810870C22semidirect
50. #16810853C22semidirect
51. #16810725C22semidirect
52. #16810696C22semidirect
53. #16810662C22semidirect
58. #107×D53C22semidirect
71. C53×#501C22semidirect
368. C2×#501D53semidirect
381. C2×C53#3346semidirect
416. #501C2×D53semidirect
448. C53C2×#3346semidirect
739. C2#20287199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113342
C2×#168113262
#202871992
C2×#168109602
C2×#168109432
C2×#168109672
C2×#168109382
C2×#168109272
C2×#168109002
C2×#168108702
C2×#168108532
C2×#168107252
C2×#168106962
C2×#168106622
C2×#107×D532
C2×C53×#5012
C2×#334653