Finite Group Databasebeta

← C2×#20286175 #28257056

Subgroups — C2×#20286175 #28257056

Order 13568.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811247C211yesmaximal, characteristic, complemented
2C2×#16811238C211yesmaximal, characteristic, complemented
3#20286175C2116yesmaximal, direct product factor
4C2×#16810917C211yesmaximal, characteristic, complemented
5C2×#16810915C211yesmaximal, characteristic, complemented
6C2×#16810902C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810868C211yesmaximal, characteristic, complemented
9C2×#16810865C211yesmaximal, characteristic, complemented
10C2×#16810858C211yesmaximal, characteristic
11C2×#16810846C211yesmaximal, characteristic, complemented
12C2×#16810844C211yesmaximal, characteristic, complemented
13C2×#16810838C211yesmaximal, characteristic, complemented
14C2×#16810837C211yesmaximal, characteristic, complemented
15C2×#16810648C211yesmaximal, characteristic, complemented
16C2×C53×#474C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811247—24no—
24#16811247C2218yescomplemented
25#16811238—24no—
26#16811238C2218yescomplemented
27C2×#13133216C2211yescharacteristic
28C2×#13133212—21no—
29C2×#13133210—21no—
30C2×#13133206—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133204C2211yescharacteristic
33C2×#13133203—21no—
34C2×#13133202—21no—
35C2×#13133200—21no—
36C2×#13133197C2211yescharacteristic
37C2×#13133197C2211yescharacteristic
38C2×#13133196—21no—
39C2×#13133193—21no—
40C2×#13133192C2211yescharacteristic
41C2×#13133188C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133174C2211yescharacteristic
46#16810917C2218yescomplemented
47#16810915C2218yescomplemented
48#16810902C2218yescomplemented
49#16810870C2218yescomplemented
50#16810868C2218yescomplemented
51#16810865C2218yescomplemented
52#16810858C2218yes—
53#16810846C2218yescomplemented
54#16810844C2218yescomplemented
55#16810838C2218yescomplemented
56#16810837C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#474C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×Dic212—42no—
86C2×Dic212C2314yes—
87C2×#11719913—42no—
88C2×#11719913C2314yes—
89C2×#11719923—42no—
90C2×#11719923C2314yes—
91C2×#11719922—42no—
92C2×#11719922C2314yes—
93C2×#11719912—42no—
94C2×#11719912C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C2×C8×D53—42no—
98C2×C8×D53C2314yes—
99#13133216—22no—
100#13133216C2314yes—
101#13133212—28no—
102#13133210—28no—
103#13133206—28no—
104#13133205—22no—
105#13133205C2314yes—
106#13133204—22no—
107#13133204C2314yes—
108#13133203—28no—
109#13133202—28no—
110#13133200—28no—
111#13133197—22no—
112#13133197—22no—
113#13133197C2314yes—
114#13133197C2314yes—
115#13133196—28no—
116#13133193—28no—
117#13133192—22no—
118#13133192C2314yes—
119#13133188—22no—
120#13133188C2314yes—
121C4×Dic106—22no—
122C4×Dic106C2314yes—
123#13133182—22no—
124#13133182C2314yes—
125#13133179—22no—
126#13133179C2314yes—
127#13133174D414yes—
128#13133174C2314yes—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×#11719919D411yescharacteristic
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×#11719921D411yescharacteristic
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133150C2314yes—
152#13133150C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133139C2314yes—
161#13133137C2314yes—
162C22×Q8×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4⋊Q8×C53—22no—
168C4⋊Q8×C53C2314yes—
169C4×D4×C53—22no—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#107×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—24no—
186C2×Q8×C53—82no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—24no—
195C22×C4×C53—82no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—24no—
200C2×C22⋊D53—82no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C2×D212—22no—
208C2×D212—22no—
209C2×D212—21no—
210C2×D212—24no—
211C2×D212—82no—
212C2×D212C2412yes—
213C2×C4×D53—22no—
214C2×C4×D53—22no—
215C2×C4×D53—24no—
216C2×C4×D53—82no—
217C2×C4×D53C2×D412yes—
218C2×C4×D53C2412yes—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—24no—
226C2×Dic106—82no—
227C2×Dic106C2412yes—
228C2×Dic106C2412yes—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719923—44no—
247#11719922—44no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921C2×D414yes—
255#11719921C2×D414yes—
256C4⋊Dic53—21no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919C2×D414yes—
264#11719919C2×D414yes—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273Dic212—44no—
274#11719913—44no—
275#11719912—44no—
276C8×D53—44no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53C22×D412yes—
290Q8×C53—84no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
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—84no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53H(5,𝔽2)12yes—
307C2×C4×C532−1+412yes—
308C2×C4×C53C2511yescharacteristic
309C22⋊D53—84no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322D212—22no—
323D212—22no—
324D212—42no—
325D212—84no—
326C4×D53—24no—
327C4×D53—22no—
328C4×D53—22no—
329C4×D53—84no—
330Dic106—22no—
331Dic106—22no—
332Dic106—22no—
333Dic106—22no—
334Dic106—42no—
335Dic106—42no—
336Dic106—84no—
337C8×C53—22no—
338C8×C53—22no—
339#88322—22no—
340#88322—22no—
341C2×#3262—531nomaximal, Sylow
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—84no—
346C22×C53#53712yes—
347C22×C53#57612yes—
348C22×C53#57812yes—
349C22×C53C23×D411yescharacteristic
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—44no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—84no—
358C4×C53—22no—
359C4×C53—22no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#53712yes—
364C4×C53C2×H(5,𝔽2)11yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#542—531no—
373C2×#542—531no—
374#3262—5316no—
375C2×#477—531no—
376C2×#477—531no—
377C2×#474—531no—
378C2×#474D5311yescharacteristic, complemented
379C2×#468—531no—
380C2×#468—531no—
381C2×#467—531no—
382C2×#466—531no—
383C2×#464—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#463—531no—
387C2×#424—531no—
388C2×C53—82no—
389C2×C53#326214yescomplemented
390C2×C53C2×#53711yescharacteristic
391C2×C53C2×#57611yescharacteristic
392C2×C53C2×#57811yescharacteristic
393D53—42no—
394D53—82no—
395C22×Q16—531no—
396C22×SD16—531no—
397C22×SD16—531no—
398C22×D8—531no—
399C22×M16—531no—
400C23×C8—531no—
401#542—538no—
402#542—538no—
403#542—1064no—
404#542—1064no—
405C2×C4⋊Q8—531no—
406C2×C4⋊Q8C2×D5311yescharacteristic
407C2×#126—1061no—
408C2×#126—1061no—
409C2×#124—531no—
410C2×#124—531no—
411C2×#124—1061no—
412C2×#124—1061no—
413C2×#123—1061no—
414C2×#123—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8—531no—
417C2×C22⋊Q8—1061no—
418C2×C22⋊Q8—1061no—
419C2×#121—531no—
420C2×#121—531no—
421C2×C4×Q8—531no—
422C2×C4×Q8—531no—
423C2×C4×D4—531no—
424C2×C4×D4C2×D5311yescharacteristic
425C2×#117—531no—
426#477—538no—
427#477—538no—
428#474—538no—
429#474C2×D5318yescomplemented
430#468—538no—
431#468—538no—
432#467—538no—
433#466—538no—
434#464—538no—
435#464—538no—
436#463—538no—
437#463—538no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107C2×D5311yescharacteristic
441C2×#107C2×D5311yescharacteristic
442#424—538no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×C4⋊C8—531no—
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×#103—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102C2×D5311yescharacteristic
454C2×#102C2×D5311yescharacteristic
455C53C2×#326211yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—531no—
458C22×Q8—531no—
459C22×Q8—1061no—
460C22×D4—531no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—21no—
465C23×C4—531no—
466C23×C4—1061no—
467C2×Q16—534no—
468C2×Q16—2122no—
469C2×SD16—534no—
470C2×SD16—534no—
471C2×SD16—2122no—
472C2×SD16—2122no—
473C2×D8—534no—
474C2×D8—2122no—
475C2×M16—534no—
476C2×M16—2122no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—534no—
480C22×C8—2122no—
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483C4⋊Q8—22no—
484C4⋊Q8—534no—
485C4⋊Q8—1062no—
486C4⋊Q8C22×D5314yes—
487#126—1068no—
488#126—1068no—
489#124—534no—
490#124—534no—
491#124—1062no—
492#124—1068no—
493#124—1068no—
494#124—1062no—
495#123—1068no—
496#123—1068no—
497C22⋊Q8—534no—
498C22⋊Q8—534no—
499C22⋊Q8—1062no—
500C22⋊Q8—1062no—
501C22⋊Q8—1068no—
502C22⋊Q8—1068no—
503#121—534no—
504#121—534no—
505#121—1062no—
506#121—1062no—
507C4×Q8—534no—
508C4×Q8—534no—
509C4×Q8—1062no—
510C4×Q8—1062no—
511C4×D4—22no—
512C4×D4—534no—
513C4×D4—1062no—
514C4×D4C22×D5314yes—
515#117—534no—
516#117—534no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C42—531no—
542C2×C42—1061no—
543C2×C42—1061no—
544C2×C42C22×D5311yescharacteristic
545#107—534no—
546#107—534no—
547#107C22×D5314yes—
548#107C22×D5314yes—
549C4⋊C8—534no—
550C4⋊C8—534no—
551C4⋊C8—534no—
552C4⋊C8C22×D5314yes—
553#103—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#102—534no—
558#102—534no—
559#102C22×D5314yes—
560#102C22×D5314yes—
561C24—21no—
562C24—531no—
563C24—1061no—
564C2×Q8—24no—
565C2×Q8—82no—
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×Q8—4242no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—532no—
580C2×D4—1064no—
581C2×D4—1064no—
582C2×D4—1061no—
583C2×D4—1062no—
584C2×D4—1062no—
585C2×D4—4242no—
586C2×D4—4242no—
587C2×D4C23×D5312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—1064no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—4242no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—2124no—
609SD16—2124no—
610SD16—2124no—
611D8—2124no—
612M16—2124no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—532no—
616C2×C8—532no—
617C2×C8—1062no—
618C2×C8—1062no—
619C2×C8—2124no—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—534no—
627C4⋊C4—534no—
628C4⋊C4—532no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1061no—
634C4⋊C4—1064no—
635C4⋊C4C23×D5312yes—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—24no—
639C22⋊C4—534no—
640C22⋊C4—534no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—532no—
651C42—532no—
652C42—1064no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—532no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—84no—
670Q8—1062no—
671Q8—1062no—
672Q8—1062no—
673Q8—1062no—
674Q8—4244no—
675Q8—2122no—
676Q8—2122no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—1062no—
681D4—1062no—
682D4—4244no—
683D4—4244no—
684D4—2122no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—532no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—4244no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4C2×D4×D5312yes—
711C2×C4C2×D4×D5312yes—
712C2×C4C2×D4×D5311yescharacteristic
713C2×C4#1313326312yes—
714C2×C4#1313326512yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1062no—
719C8—1062no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—1062no—
725C22—1062no—
726C22—1062no—
727C22—4244no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2124no—
732C22#1681120312yes—
733C22#1681142412yes—
734C22#1681143912yes—
735C22C22×D4×D5311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—1062no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4#1681120312yes—
748C4C2×#1313326311yescharacteristic
749C4C2×#1313326511yescharacteristic
750C2—82no—
751C2—4242no—
752C2—2122no—
753C2#2028617514yesdirect product factor
754C2C2×#1681120311yescharacteristic
755C2C2×#1681142411yescharacteristic
756C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#474C2
socleC23×C53C22×D4
prime radicalC2×#16810858C2
hypercenterC2×#474D53
hypocenterC53C2×#3262
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16811247C2semidirect
2. C2×#16811238C2semidirect
3. #20286175C2direct (N × H)
4. C2×#16810917C2semidirect
5. C2×#16810915C2semidirect
6. C2×#16810902C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810868C2semidirect
9. C2×#16810865C2semidirect
11. C2×#16810846C2semidirect
12. C2×#16810844C2semidirect
13. C2×#16810838C2semidirect
14. C2×#16810837C2semidirect
15. C2×#16810648C2semidirect
16. C2×C53×#474C2semidirect
24. #16811247C22semidirect
26. #16811238C22semidirect
46. #16810917C22semidirect
47. #16810915C22semidirect
48. #16810902C22semidirect
49. #16810870C22semidirect
50. #16810868C22semidirect
51. #16810865C22semidirect
53. #16810846C22semidirect
54. #16810844C22semidirect
55. #16810838C22semidirect
56. #16810837C22semidirect
59. #16810648C22semidirect
71. C53×#474C22semidirect
378. C2×#474D53semidirect
389. C2×C53#3262semidirect
429. #474C2×D53semidirect
455. C53C2×#3262semidirect
753. C2#20286175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112472
C2×#168112382
#202861752
C2×#168109172
C2×#168109152
C2×#168109022
C2×#168108702
C2×#168108682
C2×#168108652
C2×#168108582
C2×#168108462
C2×#168108442
C2×#168108382
C2×#168108372
C2×#168106482
C2×C53×#4742
C2×#326253