Finite Group Databasebeta

← C2×#20287016 #28260997

Subgroups — C2×#20287016 #28260997

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811274C211yesmaximal, characteristic, complemented
2C2×#16811272C211yesmaximal, characteristic, complemented
3#20287016C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810958C211yesmaximal, characteristic, complemented
6C2×#16810957C211yesmaximal, characteristic, complemented
7C2×#16810901C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810869C211yesmaximal, characteristic, complemented
10C2×#16810827C211yesmaximal, characteristic, complemented
11C2×#16810769C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810703C211yesmaximal, characteristic, complemented
14C2×#16810699C211yesmaximal, characteristic, complemented
15C2×#16810621C211yesmaximal, characteristic, complemented
16C2×C53×#417C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719947C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23#16811274—24no—
24#16811274C2218yescomplemented
25#16811272—24no—
26#16811272C2218yescomplemented
27C2×#13133216C2211yescharacteristic
28C2×#13133215C2211yescharacteristic
29C2×#13133202—21no—
30C2×#13133200—21no—
31C2×#13133200—21no—
32C2×#13133198—21no—
33C2×#13133196C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133191C2211yescharacteristic
38C2×#13133189—21no—
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53C2211yescharacteristic
42C22×#11719919—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810972C2218yescomplemented
45#16810958C2218yescomplemented
46#16810957C2218yescomplemented
47#16810901C2218yescomplemented
48#16810872C2218yescomplemented
49#16810869C2218yescomplemented
50#16810827C2218yescomplemented
51#16810769C2218yescomplemented
52#16810768C2218yescomplemented
53#16810703C2218yescomplemented
54#16810699C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59#16810621C2218yescomplemented
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C53×#417C2218yescomplemented
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C2×#11719947—24no—
80C2×#11719947—22no—
81C2×#11719947—42no—
82C2×#11719947C2314yes—
83C22×Dic106—21no—
84C22×Dic106C2311yescharacteristic
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53D411yescharacteristic
90C23×Dic53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×#11719913—42no—
96C2×#11719913C2314yes—
97C2×#11719924—42no—
98C2×#11719924C2314yes—
99C2×#11719922—24no—
100C2×#11719922C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133215—22no—
108#13133215C2314yes—
109#13133202—28no—
110#13133200—28no—
111#13133200—28no—
112#13133198—28no—
113#13133196—22no—
114#13133196C2314yes—
115#13133195—28no—
116#13133193—22no—
117#13133193C2314yes—
118#13133192—22no—
119#13133192C2314yes—
120#13133191—22no—
121#13133191C2314yes—
122#13133189—28no—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125#13133179—22no—
126#13133179C2314yes—
127C4×C22⋊D53D414yes—
128C4×C22⋊D53C2314yes—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—28no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C4⋊C4×D53—22no—
140C4⋊C4×D53C2314yes—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×C4×Dic53C2311yescharacteristic
150#13133151C2314yes—
151#13133150C2314yes—
152#13133150C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C2×#41×C53—22no—
164C2×#41×C53—24no—
165C2×#41×C53—42no—
166C2×#41×C53C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C2×M16×C53—42no—
174C2×M16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C2×C4⋊C4×C53—22no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2311yescharacteristic
182#103×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185#102×C53C2314yes—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190#41×C53—28no—
191#41×C53—44no—
192#41×C53—48no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C2×D4×C53—24no—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—44no—
201C2×D4×C53#4114yescomplemented
202C2×D4×C53C2412yes—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—24no—
208C22×C4×C53—21no—
209C22×C4×C53—24no—
210C22×C4×C53—44no—
211C22×C4×C53—44no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53C2×D414yes—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—24no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228C22×Dic53—44no—
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232#11719947—28no—
233#11719947—44no—
234#11719947—48no—
235#11719945—432no—
236C2×D212—22no—
237C2×D212—22no—
238C2×D212—24no—
239C2×D212—21no—
240C2×D212—44no—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—24no—
245C2×C4×D53—24no—
246C2×C4×D53—44no—
247C2×C4×D53—44no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2412yes—
250C2×Dic106—22no—
251C2×Dic106—22no—
252C2×Dic106—21no—
253C2×Dic106—24no—
254C2×Dic106—44no—
255C2×Dic106C2412yes—
256M16×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—24no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268C22⋊Dic53C2×D414yes—
269#11719924—44no—
270#11719922—28no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921C2×D414yes—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286#11719919C2×D414yes—
287C4×Dic53C2×D412yes—
288C4×Dic53C2412yes—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293#11719913—44no—
294#11719912—44no—
295C23×C53—24no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53C22×D412yes—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53C22×D412yes—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—42no—
315D4×C53—24no—
316D4×C53—22no—
317D4×C53—48no—
318D4×C53C2×#4114yescomplemented
319C2×C4×C53—22no—
320C2×C4×C53—24no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—48no—
327C2×C4×C53—48no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C2×#4112yes—
334C2×C4×C53H(5,𝔽2)12yes—
335C2×C4×C53C2511yescharacteristic
336C22⋊D53—28no—
337C22⋊D53—48no—
338C22⋊D53—48no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—48no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—48no—
349C2×Dic53AGL(1,ℤ/8)14yes—
350C2×Dic53C22×D412yes—
351C2×Dic53C22×D412yes—
352C2×Dic53C22×D412yes—
353D212—22no—
354D212—22no—
355D212—48no—
356D212—42no—
357C4×D53—24no—
358C4×D53—22no—
359C4×D53—22no—
360C4×D53—48no—
361C4×D53—48no—
362Dic106—22no—
363Dic106—22no—
364Dic106—42no—
365Dic106—48no—
366C8×C53—22no—
367C8×C53—22no—
368#88322—22no—
369#88322—22no—
370C2×#3330—531nomaximal, Sylow
371C22×C53—24no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—44no—
376C22×C53—48no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53#54612yes—
380C22×C53C2×AGL(1,ℤ/8)12yes—
381C22×C53#57812yes—
382C22×C53C23×D411yescharacteristic
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—22no—
386C2×D53—44no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—84no—
391C4×C53—22no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53#54612yes—
396C4×C53C22×#4111yescharacteristic
397C4×C53C2×H(5,𝔽2)11yescharacteristic
398Dic53—22no—
399Dic53—22no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53C2×AGL(1,ℤ/8)14yes—
404C2×#547—531no—
405C2×#547—531no—
406#3330—5316no—
407C2×#487—531no—
408C2×#484—531no—
409C2×#484—531no—
410C2×#474—531no—
411C2×#468—531no—
412C2×#468—531no—
413C2×#461—531no—
414C2×#449—531no—
415C2×#449—531no—
416C2×C4×D8—531no—
417C2×#436—531no—
418C2×#417—531no—
419C2×#417D5311yescharacteristic, complemented
420C2×C53—42no—
421C2×C53—44no—
422C2×C53#333014yescomplemented
423C2×C53C2×#54611yescharacteristic
424C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C53C2×#57811yescharacteristic
426D53—42no—
427D53—82no—
428C22×#41—531no—
429C22×#41—1061no—
430C22×#41C2×D5311yescharacteristic
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16—531no—
435C22×M16C2×D5311yescharacteristic
436#547—538no—
437#547—538no—
438#547—1064no—
439#547—1064no—
440C2×C4⋊Q8—531no—
441C2×C4⋊Q8—531no—
442C2×#123—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×#123—1061no—
446C2×C22⋊Q8—531no—
447C2×C22⋊Q8—531no—
448C2×C22⋊Q8—1061no—
449C2×#121—531no—
450C2×#121—531no—
451C2×#121—1061no—
452C2×C4×D4—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C22×C4⋊C4—531no—
456C22×C4⋊C4—1061no—
457C22×C4⋊C4C2×D5311yescharacteristic
458#487—538no—
459#484—538no—
460#484—538no—
461#474—538no—
462#468—538no—
463#468—538no—
464#461—538no—
465#449—538no—
466#449—538no—
467C4×D8—538no—
468#436—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107—531no—
472C2×C4⋊C8—531no—
473#417—538no—
474#417C2×D5318yescomplemented
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103C2×D5311yescharacteristic
480C2×#103C2×D5311yescharacteristic
481C2×#102—531no—
482C2×#102—531no—
483C2×#102C2×D5311yescharacteristic
484C2×#102C2×D5311yescharacteristic
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×C4×C8—531no—
488C53C2×#333011yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—534no—
493C2×#41—1068no—
494C2×#41—1062no—
495C2×#41—1064no—
496C2×#41—2128no—
497C2×#41—2122no—
498C2×#41C22×D5314yes—
499C22×Q8—531no—
500C22×Q8—1061no—
501C22×Q8C22×D5311yescharacteristic
502C22×D4—21no—
503C22×D4—531no—
504C22×D4—531no—
505C22×D4—1061no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4C22×D5311yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—531no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4C22×D5311yescharacteristic
517C2×SD16—534no—
518C2×SD16—534no—
519C2×SD16—2122no—
520C2×SD16—2122no—
521C2×D8—534no—
522C2×D8—1064no—
523C2×M16—42no—
524C2×M16—534no—
525C2×M16—2122no—
526C2×M16C22×D5314yes—
527C22×C8—531no—
528C22×C8—531no—
529C22×C8C22×D5311yescharacteristic
530C22×C8C22×D5311yescharacteristic
531C4⋊Q8—534no—
532C4⋊Q8—534no—
533C4⋊Q8—1062no—
534C4⋊Q8—1062no—
535#123—1068no—
536#123—1068no—
537#123—1068no—
538#123—1068no—
539C22⋊Q8—534no—
540C22⋊Q8—534no—
541C22⋊Q8—1068no—
542C22⋊Q8—1062no—
543C22⋊Q8—1062no—
544#121—534no—
545#121—534no—
546#121—1062no—
547#121—1068no—
548#121—1062no—
549C4×D4—534no—
550C4×D4—534no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—1062no—
554C4×D4—1062no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—534no—
561C2×C4⋊C4—1062no—
562C2×C4⋊C4—1068no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4C22×D5311yescharacteristic
570C2×C4⋊C4C22×D5311yescharacteristic
571C2×C4⋊C4C22×D5314yes—
572C2×C22⋊C4—531no—
573C2×C22⋊C4—531no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C42—531no—
581#107—534no—
582#107—534no—
583#107—534no—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103C22×D5314yes—
590#103C22×D5314yes—
591#102—534no—
592#102—534no—
593#102C22×D5314yes—
594#102C22×D5314yes—
595C22⋊C8—534no—
596C22⋊C8—534no—
597C4×C8—534no—
598C24—21no—
599C24—531no—
600C24—1061no—
601C24D4×D5311yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—1068no—
606#41—21232no—
607#41—2124no—
608#41—2128no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—532no—
613C2×Q8—1064no—
614C2×Q8—1061no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—2124no—
618C2×Q8C23×D5312yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—534no—
624C2×D4—532no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1064no—
629C2×D4—1061no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—2124no—
633C2×D4—2124no—
634C2×D4—2124no—
635C2×D4#1171994514yescomplemented
636C2×D4C23×D5312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—531no—
649C22×C4—532no—
650C22×C4—532no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—1064no—
654C22×C4—1064no—
655C22×C4—1062no—
656C22×C4—1062no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—2124no—
661C22×C4—2124no—
662C22×C4—2124no—
663C22×C4—2124no—
664C22×C4D4×D5312yes—
665C22×C4D4×D5311yescharacteristic
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—2124no—
669SD16—2124no—
670D8—1068no—
671M16—44no—
672M16—2124no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—532no—
676C2×C8—532no—
677C2×C8—1062no—
678C2×C8—1062no—
679C2×C8C23×D5312yes—
680C2×C8C23×D5312yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—534no—
685C4⋊C4—532no—
686C4⋊C4—532no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4—1064no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1064no—
695C4⋊C4C23×D5312yes—
696C4⋊C4C23×D5312yes—
697C22⋊C4—534no—
698C22⋊C4—534no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C42—532no—
706C42—532no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—42no—
713C23—42no—
714C23—532no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—1062no—
719C23—2122no—
720C23—2122no—
721C23—2122no—
722C23C2×D4×D5312yes—
723C23C2×D4×D5311yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—42no—
727Q8—1062no—
728Q8—1062no—
729Q8—2128no—
730Q8—2122no—
731D4—22no—
732D4—24no—
733D4—48no—
734D4—1068no—
735D4—1062no—
736D4—1062no—
737D4—2128no—
738D4—2128no—
739D4—2128no—
740D4—2122no—
741D4C2×#1171994514yescomplemented
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
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—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1064no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—2128no—
767C2×C4—2128no—
768C2×C4—2128no—
769C2×C4—2128no—
770C2×C4—2122no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4C2×#1171994512yes—
776C2×C4#1313326212yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1062no—
781C8—1062no—
782C22—22no—
783C22—24no—
784C22—22no—
785C22—22no—
786C22—44no—
787C22—48no—
788C22—42no—
789C22—42no—
790C22—1062no—
791C22—1062no—
792C22—1062no—
793C22—4244no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2124no—
798C22#1681126312yes—
799C22AGL(1,ℤ/8)×D5312yes—
800C22#1681143912yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—534no—
807C4—1062no—
808C4—1062no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126312yes—
813C4C22×#1171994511yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—42no—
816C2—44no—
817C2—4242no—
818C2—2122no—
819C2#2028701614yesdirect product factor
820C2C2×#1681126311yescharacteristic
821C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
822C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#417C2
socleC23×C53C22×D4
hypercenterC2×#417D53
hypocenterC53C2×#3330
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16811274C2semidirect
2. C2×#16811272C2semidirect
3. #20287016C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810958C2semidirect
6. C2×#16810957C2semidirect
7. C2×#16810901C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810869C2semidirect
10. C2×#16810827C2semidirect
11. C2×#16810769C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810703C2semidirect
14. C2×#16810699C2semidirect
15. C2×#16810621C2semidirect
16. C2×C53×#417C2semidirect
24. #16811274C22semidirect
26. #16811272C22semidirect
44. #16810972C22semidirect
45. #16810958C22semidirect
46. #16810957C22semidirect
47. #16810901C22semidirect
48. #16810872C22semidirect
49. #16810869C22semidirect
50. #16810827C22semidirect
51. #16810769C22semidirect
52. #16810768C22semidirect
53. #16810703C22semidirect
54. #16810699C22semidirect
59. #16810621C22semidirect
72. C53×#417C22semidirect
201. C2×D4×C53#41semidirect
318. D4×C53C2×#41semidirect
419. C2×#417D53semidirect
422. C2×C53#3330semidirect
474. #417C2×D53semidirect
488. C53C2×#3330semidirect
635. C2×D4#11719945semidirect
741. D4C2×#11719945semidirect
819. C2#20287016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112742
C2×#168112722
#202870162
C2×#168109722
C2×#168109582
C2×#168109572
C2×#168109012
C2×#168108722
C2×#168108692
C2×#168108272
C2×#168107692
C2×#168107682
C2×#168107032
C2×#168106992
C2×#168106212
C2×C53×#4172
C2×#333053