Finite Group Databasebeta

← C2×#20287068 #28262511

Subgroups — C2×#20287068 #28262511

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic
3#20287068C2116yesmaximal, direct product factor
4C2×#16811020C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810941C211yesmaximal, characteristic, complemented
7C2×#16810955C211yesmaximal, characteristic, complemented
8C2×#16810953C211yesmaximal, characteristic, complemented
9C2×#16810907C211yesmaximal, characteristic, complemented
10C2×#16810912C211yesmaximal, characteristic, complemented
11C2×#16810853C211yesmaximal, characteristic, complemented
12C2×#16810852C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
15C2×#106×D53C211yesmaximal, characteristic, complemented
16C22×#106×C53C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719913C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811328—24no—
21#16811328C2218yescomplemented
22#16811274—24no—
23#16811274C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133202—21no—
28C2×#13133200—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133196—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×#13133192C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16811020C2218yescomplemented
43#16810955C2218yescomplemented
44#16810953C2218yescomplemented
45#16810943C2218yescomplemented
46#16810941C2218yescomplemented
47#16810912C2218yescomplemented
48#16810907C2218yescomplemented
49#16810853C2218yescomplemented
50#16810852C2218yescomplemented
51#16810710C2218yescomplemented
52C8×C22⋊D53C2218yescomplemented
53C2×#13133149C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58#106×D53C2218yescomplemented
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×C8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#106×C53C2218yescomplemented
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106C2311yescharacteristic
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53D411yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53C2311yescharacteristic
90C2×#11719913—24no—
91C2×#11719913C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C2×C8×D53—24no—
95C2×C8×D53C2314yes—
96#13133216—22no—
97#13133216—22no—
98#13133216C2314yes—
99#13133216C2314yes—
100#13133207—28no—
101#13133202—28no—
102#13133200—28no—
103#13133197—22no—
104#13133197C2314yes—
105#13133196—28no—
106#13133196—22no—
107#13133196C2314yes—
108#13133195—28no—
109#13133195—28no—
110#13133192—22no—
111#13133192C2314yes—
112#13133191—22no—
113#13133191C2314yes—
114#13133182—22no—
115#13133182C2314yes—
116#13133179—22no—
117#13133179C2314yes—
118C4×C22⋊D53—28no—
119C4×C22⋊D53D414yes—
120C4×C22⋊D53C2314yes—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53D411yescharacteristic
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144#13133149C2314yes—
145#13133148C2314yes—
146#13133148C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133142C2314yes—
151#13133140C2314yes—
152#13133140C2314yes—
153#13133139C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156C22⋊#88322C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C23×C4×C53—21no—
160C23×C4×C53—21no—
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53—24no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—22no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176#106×C53C2314yes—
177#106×C53C2314yes—
178#106×C53C2314yes—
179#106×C53C2314yes—
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C23×D53C2×D411yescharacteristic
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—24no—
190C22×C4×C53—24no—
191C22×C4×C53—44no—
192C22×C4×C53—82no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—44no—
199C2×C22⋊D53SD1618yescomplemented
200C2×C22⋊D53C2×D414yes—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207#11719945—432no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—24no—
211C2×D212—21no—
212C2×D212—44no—
213C2×D212C2412yes—
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53—24no—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—44no—
220C2×C4×D53—44no—
221C2×C4×D53—82no—
222C2×C4×D53C2×D412yes—
223C2×C4×D53C2412yes—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106—24no—
228C2×Dic106—24no—
229C2×Dic106—44no—
230C2×Dic106—82no—
231C2×Dic106C2412yes—
232C2×C8×C53—22no—
233C2×C8×C53—28no—
234C2×C8×C53#4114yescomplemented
235C2×C8×C53C2412yes—
236C2×C8×C53C2412yes—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C4⋊C4×C53C2412yes—
246C4⋊C4×C53C2412yes—
247C22⋊Dic53—24no—
248C22⋊Dic53C2×D414yes—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921C2×D414yes—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273#11719913—28no—
274C8×D53—28no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53C2×SD1614yes—
278C23×C53C22×D412yes—
279C23×C53C22×D411yescharacteristic
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53C2×SD1614yes—
287C22×D53C22×D412yes—
288C2×C4×C53—22no—
289C2×C4×C53—24no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—48no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—84no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4112yes—
305C2×C4×C532−1+412yes—
306C2×C4×C53C2511yescharacteristic
307C22⋊D53—48no—
308C22⋊D53C2×SD16116yescomplemented
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53C2×SD1614yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321D212—22no—
322D212—22no—
323D212—48no—
324D212—42no—
325C4×D53—24no—
326C4×D53—22no—
327C4×D53—22no—
328C4×D53—48no—
329C4×D53—48no—
330C4×D53—84no—
331Dic106—22no—
332Dic106—22no—
333Dic106—42no—
334Dic106—48no—
335Dic106—84no—
336C8×C53—22no—
337C8×C53C2×#4114yescomplemented
338#88322—22no—
339#88322—22no—
340C2×#3335—531nomaximal, Sylow
341C22×C53—28no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53#54712yes—
345C22×C53C22×SD1614yes—
346C22×C53C22×SD1612yes—
347C22×C53#57712yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—28no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—84no—
356C2×D53C22×SD1614yes—
357C4×C53—22no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#54712yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C2×2−1+411yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—42no—
368Dic53—42no—
369Dic53—42no—
370Dic53C22×SD1614yes—
371C2×#554—531no—
372C2×#547—531no—
373#3335—5316no—
374C2×#498—531no—
375C2×#481—531no—
376C2×#481—531no—
377C2×#483—531no—
378C2×#483—531no—
379C2×#475—531no—
380C2×#476—531no—
381C2×#465—531no—
382C2×#465—531no—
383C2×C4×SD16—531no—
384C2×C8×D4—531no—
385C22×#106—531no—
386C22×#106D5311yescharacteristic, complemented
387C2×C53—24no—
388C2×C53#333514yescomplemented
389C2×C53C2×#54711yescharacteristic
390C2×C53C23×SD1611yescharacteristic
391C2×C53C2×#57711yescharacteristic
392D53—24no—
393D53—82no—
394C22×#41—1061no—
395C22×SD16—531no—
396C23×C8—531no—
397C23×C8C2×D5311yescharacteristic
398#554—538no—
399#554—1064no—
400#547—538no—
401#547—1064no—
402C2×C4⋊Q8—531no—
403C2×C4⋊Q8—531no—
404C2×#125—1061no—
405C2×#123—1061no—
406C2×#123—1061no—
407C2×C22⋊Q8—531no—
408C2×C22⋊Q8—531no—
409C2×C22⋊Q8—1061no—
410C2×C22⋊Q8—1061no—
411C2×C22⋊Q8—1061no—
412C2×#121—531no—
413C2×#121—531no—
414C2×C4×Q8—531no—
415C2×C4×D4—531no—
416C2×C4×D4—531no—
417C2×C4×D4—1061no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4C2×D5311yescharacteristic
421C22×C4⋊C4C2×D5311yescharacteristic
422#498—538no—
423#483—538no—
424#483—538no—
425#481—538no—
426#481—538no—
427#476—538no—
428#475—538no—
429#465—538no—
430#465—538no—
431C4×SD16—538no—
432C8×D4—538no—
433C2×#106—531no—
434C2×#106—531no—
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×#106—538no—
439C2×#106C2×D5311yescharacteristic
440C2×#106C2×D5311yescharacteristic
441C2×#106C2×D5311yescharacteristic
442C2×#106C2×D5311yescharacteristic
443C2×#106C2×D5318yescomplemented
444C2×C4⋊C8—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#103—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×C22⋊C8—531no—
452C2×C22⋊C8—531no—
453C2×C4×C8—531no—
454C53C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—1068no—
456C2×#41—2128no—
457C22×Q8—531no—
458C22×Q8—1061no—
459C22×Q8—1061no—
460C22×D4—531no—
461C22×D4—531no—
462C22×D4—1061no—
463C22×D4—1061no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—531no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4—1061no—
470C23×C4C22×D5311yescharacteristic
471C2×SD16—534no—
472C2×SD16—1064no—
473C22×C8—24no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—534no—
477C22×C8—1064no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5314yes—
480C22×C8C22×D5311yescharacteristic
481C4⋊Q8—534no—
482C4⋊Q8—534no—
483C4⋊Q8—1062no—
484C4⋊Q8—1062no—
485#125—1068no—
486#123—1068no—
487#123—1068no—
488C22⋊Q8—534no—
489C22⋊Q8—534no—
490C22⋊Q8—1068no—
491C22⋊Q8—1068no—
492C22⋊Q8—1068no—
493C22⋊Q8—1062no—
494C22⋊Q8—1062no—
495#121—534no—
496#121—534no—
497#121—1062no—
498#121—1062no—
499C4×Q8—534no—
500C4×Q8—1062no—
501C4×D4—534no—
502C4×D4—534no—
503C4×D4—534no—
504C4×D4—1062no—
505C4×D4—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—1062no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1061no—
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⋊C4C22×D5311yescharacteristic
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5314yes—
529C2×C4⋊C4C22×D5314yes—
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×C42—531no—
538C2×C42—1061no—
539#106—534no—
540#106—534no—
541#106—534no—
542#106—534no—
543#106—534no—
544#106C22×D5314yes—
545#106C22×D5314yes—
546#106C22×D5314yes—
547#106C22×D5314yes—
548C4⋊C8—534no—
549#103—534no—
550#103—534no—
551#103—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555C22⋊C8—534no—
556C22⋊C8—534no—
557C4×C8—534no—
558C24—531no—
559C24—1061no—
560C24D4×D5311yescharacteristic
561#41—21232no—
562C2×Q8—532no—
563C2×Q8—1064no—
564C2×Q8—1064no—
565C2×Q8—1061no—
566C2×Q8—1062no—
567C2×Q8—1062no—
568C2×Q8—4242no—
569C2×Q8—2124no—
570C2×D4—538no—
571C2×D4—534no—
572C2×D4—532no—
573C2×D4—1064no—
574C2×D4—1064no—
575C2×D4—1061no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4—2124no—
579C2×D4—2124no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—531no—
591C22×C4—531no—
592C22×C4—531no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1064no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—4242no—
604C22×C4—2124no—
605C22×C4—2124no—
606C22×C4D4×D5312yes—
607C22×C4D4×D5311yescharacteristic
608C22×C4C23×D5312yes—
609C22×C4C23×D5311yescharacteristic
610SD16—1068no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—532no—
614C2×C8—532no—
615C2×C8—1062no—
616C2×C8—1062no—
617C2×C8—1068no—
618C2×C8#1171994514yescomplemented
619C2×C8C23×D5312yes—
620C2×C8C23×D5312yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—534no—
628C4⋊C4—532no—
629C4⋊C4—532no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1061no—
637C4⋊C4—1061no—
638C4⋊C4—1064no—
639C4⋊C4C23×D5312yes—
640C4⋊C4C23×D5312yes—
641C4⋊C4C23×D5312yes—
642C4⋊C4C23×D5312yes—
643C22⋊C4—534no—
644C22⋊C4—534no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—532no—
651C42—532no—
652C42—1064no—
653C23—22no—
654C23—22no—
655C23—534no—
656C23—532no—
657C23—1062no—
658C23—1062no—
659C23—1062no—
660C23—2122no—
661C23—2122no—
662C23—2122no—
663C23SD16×D5314yes—
664C23C2×D4×D5312yes—
665C23C2×D4×D5311yescharacteristic
666Q8—1062no—
667Q8—1062no—
668Q8—4244no—
669Q8—2128no—
670Q8—2122no—
671D4—5316no—
672D4—1062no—
673D4—1062no—
674D4—2128no—
675D4—2128no—
676D4—2122no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—534no—
692C2×C4—532no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1064no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—4244no—
704C2×C4—2128no—
705C2×C4—2128no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4C2×#1171994512yes—
712C2×C4#1313326512yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—1062no—
716C8—1062no—
717C8C2×#1171994514yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—534no—
722C22—1068no—
723C22—1062no—
724C22—1062no—
725C22—4244no—
726C22—2122no—
727C22—2122no—
728C22—2122no—
729C22#1681127412yes—
730C22C2×SD16×D5314yes—
731C22C2×SD16×D5312yes—
732C22#1681142912yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—534no—
740C4—1062no—
741C4—1062no—
742C4—2122no—
743C4—2122no—
744C4—2122no—
745C4#1681127412yes—
746C4C22×#1171994511yescharacteristic
747C4C2×#1313326511yescharacteristic
748C2—24no—
749C2—1064no—
750C2—4242no—
751C2#2028706814yesdirect product factor
752C2C2×#1681127411yescharacteristic
753C2C22×SD16×D5311yescharacteristic
754C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#106×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811274C2
hypercenterC22×#106D53
hypocenterC53C2×#3335
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#16811328C2semidirect
3. #20287068C2direct (N × H)
4. C2×#16811020C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810941C2semidirect
7. C2×#16810955C2semidirect
8. C2×#16810953C2semidirect
9. C2×#16810907C2semidirect
10. C2×#16810912C2semidirect
11. C2×#16810853C2semidirect
12. C2×#16810852C2semidirect
13. C2×#16810710C2semidirect
14. C2×C8×C22⋊D53C2semidirect
15. C2×#106×D53C2semidirect
16. C22×#106×C53C2semidirect
21. #16811328C22semidirect
42. #16811020C22semidirect
43. #16810955C22semidirect
44. #16810953C22semidirect
45. #16810943C22semidirect
46. #16810941C22semidirect
47. #16810912C22semidirect
48. #16810907C22semidirect
49. #16810853C22semidirect
50. #16810852C22semidirect
51. #16810710C22semidirect
52. C8×C22⋊D53C22semidirect
58. #106×D53C22semidirect
76. C2×#106×C53C22semidirect
199. C2×C22⋊D53SD16semidirect
234. C2×C8×C53#41semidirect
308. C22⋊D53C2×SD16semidirect
337. C8×C53C2×#41semidirect
386. C22×#106D53semidirect
388. C2×C53#3335semidirect
443. C2×#106C2×D53semidirect
454. C53C2×#3335semidirect
618. C2×C8#11719945semidirect
717. C8C2×#11719945semidirect
751. C2#20287068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112742
#202870682
C2×#168110202
C2×#168109432
C2×#168109412
C2×#168109552
C2×#168109532
C2×#168109072
C2×#168109122
C2×#168108532
C2×#168108522
C2×#168107102
C2×C8×C22⋊D532
C2×#106×D532
C22×#106×C532
C2×#333553