Finite Group Databasebeta

← C2×#20285723 #28255383

Subgroups — C2×#20285723 #28255383

Order 13568.

2166 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811175C211yesmaximal, characteristic, complemented
2C2×#16811169C211yesmaximal, characteristic
3#20285723C2116yesmaximal, direct product factor
4C2×#16811016C211yesmaximal, characteristic, complemented
5C2×#16811014C211yesmaximal, characteristic, complemented
6C2×#16810984C211yesmaximal, characteristic, complemented
7C2×#16810981C211yesmaximal, characteristic, complemented
8C2×#16810832C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810822C211yesmaximal, characteristic, complemented
11C2×#16810821C211yesmaximal, characteristic, complemented
12C2×#16810787C211yesmaximal, characteristic, complemented
13C2×#16810785C211yesmaximal, characteristic, complemented
14C2×#16810783C211yesmaximal, characteristic, complemented
15C2×#16810677C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719923C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24#16811175—24no—
25#16811175C2218yescomplemented
26#16811169—24no—
27#16811169C2218yes—
28C2×#13133216C2211yescharacteristic
29C2×#13133215C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133213C2211yescharacteristic
32C2×#13133207—21no—
33C2×#13133206C2211yescharacteristic
34C2×#13133204C2211yescharacteristic
35C2×#13133196C2211yescharacteristic
36C2×#13133194—21no—
37C2×#13133189—21no—
38C2×#13133189—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×#13133182—21no—
41C2×#13133182C2211yescharacteristic
42C2×C4×C22⋊D53—21no—
43C2×C4×C22⋊D53—21no—
44C2×#13133173—21no—
45C22×C4×Dic53C2211yescharacteristic
46#16811016C2218yescomplemented
47#16811014C2218yescomplemented
48#16810984C2218yescomplemented
49#16810981C2218yescomplemented
50#16810832C2218yescomplemented
51#16810831C2218yescomplemented
52#16810822C2218yescomplemented
53#16810821C2218yescomplemented
54#16810787C2218yescomplemented
55#16810785C2218yescomplemented
56#16810783C2218yescomplemented
57#16810677C2218yescomplemented
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C23×Dic53D411yescharacteristic
89C23×Dic53D411yescharacteristic
90C22×C4×D53—21no—
91C2×Dic212—42no—
92C2×Dic212C2314yes—
93C2×#11719925—42no—
94C2×#11719925—42no—
95C2×#11719925C2314yes—
96C2×#11719925C2314yes—
97C2×#11719913—42no—
98C2×#11719913C2314yes—
99C2×#11719923—42no—
100C2×#11719923C2314yes—
101C2×#11719924—42no—
102C2×#11719924C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133215—22no—
108#13133215—22no—
109#13133215C2314yes—
110#13133215C2314yes—
111#13133213—22no—
112#13133213C2314yes—
113#13133207—28no—
114#13133206—22no—
115#13133206C2314yes—
116#13133204—22no—
117#13133204C2314yes—
118#13133196—22no—
119#13133196C2314yes—
120#13133194—28no—
121#13133189—28no—
122#13133189—28no—
123Q8×Dic53—22no—
124Q8×Dic53C2314yes—
125#13133182—28no—
126#13133182—22no—
127#13133182C2314yes—
128C4×C22⋊D53—28no—
129C4×C22⋊D53—28no—
130#13133173—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53D411yescharacteristic
148C2×C4×Dic53D411yescharacteristic
149C2×C4×Dic53D414yes—
150C2×C4×Dic53C2311yescharacteristic
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2314yes—
153#13133146C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133140C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160#13133137C2314yes—
161C22⋊#88322C2314yes—
162#13133127C2314yes—
163#13133127C2314yes—
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×Q8×C53C2311yescharacteristic
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C23×C4×C53—21no—
173C23×C4×C53C2311yescharacteristic
174C2×Q16×C53—42no—
175C2×Q16×C53C2314yes—
176C2×SD16×C53—42no—
177C2×SD16×C53C2314yes—
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yes—
186#102×C53C2314yes—
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191#41×C53—44no—
192#41×C53—44no—
193#41×C53—48no—
194C2×Q8×C53—21no—
195C2×Q8×C53—21no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×Q8×C53C2412yes—
202C2×D4×C53—24no—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—44no—
207C2×D4×C53C2412yes—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—44no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—44no—
224C2×C22⋊D53—44no—
225C22×Dic53—24no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—42no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D414yes—
234C22×Dic53C2×D414yes—
235C22×Dic53C2×D411yescharacteristic
236#11719945—44no—
237#11719945—44no—
238#11719945—48no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—21no—
242C2×D212C2412yes—
243C2×C4×D53—24no—
244C2×C4×D53—44no—
245C2×Dic106—22no—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—22no—
249C2×Dic106—21no—
250C2×Dic106—21no—
251C2×Dic106—24no—
252C2×Dic106—44no—
253C2×Dic106C2412yes—
254C2×Dic106C2412yes—
255Q16×C53—44no—
256SD16×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C22⋊C4×C53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268#11719925—44no—
269#11719925—44no—
270#11719924—44no—
271#11719923—44no—
272#11719921—24no—
273#11719921—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284C4×Dic53—24no—
285C4×Dic53—24no—
286C4×Dic53C2×D414yes—
287C4×Dic53C2×D414yes—
288C4×Dic53C2×D412yes—
289C4×Dic53C2×D412yes—
290C4×Dic53C2412yes—
291C4×Dic53C2412yes—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296Dic212—44no—
297#11719913—44no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53C22×D412yes—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—22no—
315Q8×C53—42no—
316Q8×C53—42no—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—48no—
320D4×C53—42no—
321C2×C4×C53—22no—
322C2×C4×C53—24no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—48no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53H(5,𝔽2)12yes—
335C2×C4×C53H(5,𝔽2)12yes—
336C2×C4×C53C2511yescharacteristic
337C22⋊D53—48no—
338C22⋊D53—48no—
339C22⋊D53—48no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—28no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—44no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53#13714yes—
352C2×Dic53C22×D412yes—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356D212—22no—
357D212—22no—
358D212—42no—
359C4×D53—48no—
360Dic106—22no—
361Dic106—22no—
362Dic106—22no—
363Dic106—22no—
364Dic106—48no—
365Dic106—42no—
366Dic106—42no—
367C8×C53—22no—
368C8×C53—22no—
369#88322—22no—
370#88322—22no—
371C2×#3216—531nomaximal, Sylow
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—44no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—84no—
380C22×C53#53512yes—
381C22×C53C2×#13712yes—
382C22×C53#57512yes—
383C22×C53C23×D411yescharacteristic
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—84no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#53512yes—
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—22no—
396Dic53—22no—
397Dic53—22no—
398Dic53—42no—
399Dic53—42no—
400Dic53—42no—
401Dic53C2×#13714yes—
402C2×#533—531no—
403C2×#532—531no—
404#3216—5316no—
405C2×#497—531no—
406C2×#497—531no—
407C2×#489—531no—
408C2×#489—531no—
409C2×#462—531no—
410C2×#462—531no—
411C2×#460—531no—
412C2×#460—531no—
413C2×#452—531no—
414C2×#452—531no—
415C2×#452—531no—
416C2×#452D5311yescharacteristic, complemented
417C2×#432—531no—
418C2×C53—42no—
419C2×C53—82no—
420C2×C53#321614yescomplemented
421C2×C53C2×#53511yescharacteristic
422C2×C53C22×#13711yescharacteristic
423C2×C53C2×#57511yescharacteristic
424D53—82no—
425C22×#41—531no—
426C22×#41C2×D5311yescharacteristic
427C22×Q16—531no—
428C22×Q16—531no—
429C22×Q16—531no—
430C22×Q16C2×D5311yescharacteristic
431C22×SD16—531no—
432C22×SD16—531no—
433C22×SD16—531no—
434C22×SD16C2×D5311yescharacteristic
435#533—538no—
436#533—1064no—
437#532—538no—
438#532—1064no—
439C2×C4⋊Q8—531no—
440C2×C4⋊Q8—531no—
441C2×C4⋊Q8—531no—
442C2×#127—531no—
443C2×#125—1061no—
444C2×#124—531no—
445C2×#124—531no—
446C2×C22⋊Q8—531no—
447C2×C22⋊Q8—1061no—
448C2×C22⋊Q8C2×D5311yescharacteristic
449C2×#121—1061no—
450C2×#121—1061no—
451C2×C4×Q8—531no—
452C2×C4×Q8—531no—
453C2×C4×Q8—1061no—
454C2×C4×D4—1061no—
455C2×C4×D4—1061no—
456C2×#117—1061no—
457C22×C42—531no—
458#497—538no—
459#497—538no—
460#489—538no—
461#489—538no—
462#462—538no—
463#462—538no—
464#460—538no—
465#460—538no—
466#452—538no—
467#452—538no—
468#452—538no—
469#452C2×D5318yescomplemented
470#432—538no—
471C2×C4⋊C8—531no—
472C2×C4⋊C8—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103C2×D5311yescharacteristic
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102C2×D5311yescharacteristic
481C2×C22⋊C8—531no—
482C2×C22⋊C8C2×D5311yescharacteristic
483C2×#97—531no—
484C2×#97—531no—
485C53C2×#321611yescharacteristic, complemented, Sylow
486C2×#41—22no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41—534no—
490C2×#41—1062no—
491C2×#41—2122no—
492C2×#41—2122no—
493C2×#41C22×D5314yes—
494C22×Q8—531no—
495C22×Q8—531no—
496C22×Q8—1061no—
497C22×Q8C22×D5311yescharacteristic
498C22×Q8C22×D5311yescharacteristic
499C22×D4—21no—
500C22×D4—531no—
501C22×D4—1061no—
502C22×D4—1061no—
503C22×D4—1061no—
504C22×D4C22×D5311yescharacteristic
505C23×C4—21no—
506C23×C4—531no—
507C23×C4—531no—
508C23×C4—1061no—
509C23×C4C22×D5311yescharacteristic
510C2×Q16—42no—
511C2×Q16—534no—
512C2×Q16—534no—
513C2×Q16—534no—
514C2×Q16—2122no—
515C2×Q16—2122no—
516C2×Q16—2122no—
517C2×Q16C22×D5314yes—
518C2×SD16—42no—
519C2×SD16—534no—
520C2×SD16—534no—
521C2×SD16—534no—
522C2×SD16—2122no—
523C2×SD16—2122no—
524C2×SD16—2122no—
525C2×SD16C22×D5314yes—
526C22×C8—531no—
527C22×C8—531no—
528C22×C8C22×D5311yescharacteristic
529C22×C8C22×D5311yescharacteristic
530C4⋊Q8—534no—
531C4⋊Q8—534no—
532C4⋊Q8—534no—
533C4⋊Q8—1062no—
534C4⋊Q8—1062no—
535C4⋊Q8—1062no—
536#127—534no—
537#127—1062no—
538#125—1068no—
539#124—534no—
540#124—534no—
541#124—1062no—
542#124—1062no—
543C22⋊Q8—22no—
544C22⋊Q8—534no—
545C22⋊Q8—1068no—
546C22⋊Q8—1062no—
547C22⋊Q8C22×D5314yes—
548#121—1068no—
549#121—1068no—
550C4×Q8—534no—
551C4×Q8—534no—
552C4×Q8—1062no—
553C4×Q8—1068no—
554C4×Q8—1062no—
555C4×D4—1068no—
556C4×D4—1068no—
557#117—1068no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C42—531no—
576C2×C42—531no—
577C2×C42—534no—
578C2×C42—531no—
579C2×C42—531no—
580C2×C42—534no—
581C2×C42—1061no—
582C2×C42—1061no—
583C4⋊C8—534no—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103C22×D5314yes—
589#102—534no—
590#102—534no—
591#102—534no—
592#102C22×D5314yes—
593C22⋊C8—534no—
594C22⋊C8C22×D5314yes—
595#97—534no—
596#97—534no—
597C24—21no—
598C24—1061no—
599C24D4×D5311yescharacteristic
600#41—44no—
601#41—44no—
602#41—48no—
603#41—2124no—
604#41—2124no—
605#41—2128no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—532no—
613C2×Q8—532no—
614C2×Q8—1064no—
615C2×Q8—1061no—
616C2×Q8—1061no—
617C2×Q8—1062no—
618C2×Q8—1062no—
619C2×Q8—1062no—
620C2×Q8—1062no—
621C2×Q8—2124no—
622C2×Q8C23×D5312yes—
623C2×Q8C23×D5312yes—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—532no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1064no—
633C2×D4—1061no—
634C2×D4—1062no—
635C2×D4—1062no—
636C2×D4—2124no—
637C2×D4—2124no—
638C2×D4—2124no—
639C2×D4C23×D5312yes—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—44no—
647C22×C4—531no—
648C22×C4—534no—
649C22×C4—531no—
650C22×C4—531no—
651C22×C4—531no—
652C22×C4—534no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1064no—
658C22×C4—2124no—
659C22×C4—2122no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—44no—
665Q16—2124no—
666Q16—2124no—
667Q16—2124no—
668SD16—44no—
669SD16—2124no—
670SD16—2124no—
671SD16—2124no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8C23×D5312yes—
679C2×C8C23×D5312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—532no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1061no—
691C4⋊C4—1064no—
692C4⋊C4C23×D5312yes—
693C22⋊C4—24no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C42—534no—
700C42—534no—
701C42—532no—
702C42—532no—
703C42—532no—
704C42—532no—
705C42—1064no—
706C42—1064no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—1062no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23C2×D4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—1062no—
727Q8—1062no—
728Q8—1062no—
729Q8—1062no—
730Q8—2128no—
731Q8—2122no—
732Q8—2122no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—42no—
737D4—1062no—
738D4—1062no—
739D4—2128no—
740D4—2128no—
741D4—2128no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—534no—
755C2×C4—532no—
756C2×C4—532no—
757C2×C4—532no—
758C2×C4—532no—
759C2×C4—1068no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—2128no—
767C2×C4—2124no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4—2122no—
771C2×C4C2×D4×D5312yes—
772C2×C4C2×D4×D5311yescharacteristic
773C2×C4#1313326212yes—
774C2×C4#1313326212yes—
775C2×C4C24×D5311yescharacteristic
776C8—22no—
777C8—22no—
778C8—1062no—
779C8—1062no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22—4244no—
789C22—2122no—
790C22—2122no—
791C22—2122no—
792C22#1681118812yes—
793C22#137×D5312yes—
794C22#1681142012yes—
795C22C22×D4×D5311yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—534no—
801C4—1062no—
802C4—1062no—
803C4—1062no—
804C4—2122no—
805C4—2122no—
806C4—2122no—
807C4#1681118812yes—
808C4C2×#1313326211yescharacteristic
809C4C2×#1313326211yescharacteristic
810C2—42no—
811C2—82no—
812C2—4242no—
813C2#2028572314yesdirect product factor
814C2C2×#1681118811yescharacteristic
815C2C2×#137×D5311yescharacteristic
816C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16811169C2
hypercenterC2×#452D53
hypocenterC53C2×#3216
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811175C2semidirect
3. #20285723C2direct (N × H)
4. C2×#16811016C2semidirect
5. C2×#16811014C2semidirect
6. C2×#16810984C2semidirect
7. C2×#16810981C2semidirect
8. C2×#16810832C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810822C2semidirect
11. C2×#16810821C2semidirect
12. C2×#16810787C2semidirect
13. C2×#16810785C2semidirect
14. C2×#16810783C2semidirect
15. C2×#16810677C2semidirect
16. C2×C53×#452C2semidirect
25. #16811175C22semidirect
46. #16811016C22semidirect
47. #16811014C22semidirect
48. #16810984C22semidirect
49. #16810981C22semidirect
50. #16810832C22semidirect
51. #16810831C22semidirect
52. #16810822C22semidirect
53. #16810821C22semidirect
54. #16810787C22semidirect
55. #16810785C22semidirect
56. #16810783C22semidirect
57. #16810677C22semidirect
73. C53×#452C22semidirect
416. C2×#452D53semidirect
420. C2×C53#3216semidirect
469. #452C2×D53semidirect
485. C53C2×#3216semidirect
813. C2#20285723direct (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×#168111692
#202857232
C2×#168110162
C2×#168110142
C2×#168109842
C2×#168109812
C2×#168108322
C2×#168108312
C2×#168108222
C2×#168108212
C2×#168107872
C2×#168107852
C2×#168107832
C2×#168106772
C2×C53×#4522
C2×#321653