Finite Group Databasebeta

← C2×#20286573 #28260468

Subgroups — C2×#20286573 #28260468

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic
3#20286573C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810954C211yesmaximal, characteristic, complemented
6C2×#16810952C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810850C211yesmaximal, characteristic, complemented
9C2×#16810849C211yesmaximal, characteristic, complemented
10C2×#16810826C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×SD16×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C22×#13133141C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#448C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×Q8×D53C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22Q8×C22⋊D53—24no—
23Q8×C22⋊D53C2218yescomplemented
24#16811273—24no—
25#16811273C2218yes—
26C2×#13133216C2211yescharacteristic
27C2×#13133215—21no—
28C2×#13133215C2211yescharacteristic
29C2×#13133199—21no—
30C2×#13133198—21no—
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133193—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810972C2218yescomplemented
44#16810954C2218yescomplemented
45#16810952C2218yescomplemented
46#16810906C2218yescomplemented
47#16810850C2218yescomplemented
48#16810849C2218yescomplemented
49#16810826C2218yescomplemented
50#16810760C2218yescomplemented
51SD16×Dic53C2218yescomplemented
52#16810686C2218yescomplemented
53C2×#13133149C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133142C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2218yescomplemented
64C2×#13133140C2211yescharacteristic
65#103×D53C2218yescomplemented
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#448C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106C2311yescharacteristic
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53—42no—
85C2×Q8×D53C2314yes—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C23×Dic53—21no—
89C23×Dic53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53C2311yescharacteristic
93C2×#11719923—42no—
94C2×#11719923C2314yes—
95C22×#88322—42no—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2314yes—
99C2×C8×D53—42no—
100C2×C8×D53C2314yes—
101#13133216—22no—
102#13133216C2314yes—
103#13133215—28no—
104#13133215—22no—
105#13133215C2314yes—
106#13133199—28no—
107#13133198—28no—
108#13133196—28no—
109#13133196—22no—
110#13133196C2314yes—
111#13133194—28no—
112#13133193—28no—
113#13133193—22no—
114#13133193C2314yes—
115#13133188—22no—
116#13133188C2314yes—
117Q8×Dic53—22no—
118Q8×Dic53C2314yes—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121C4×C22⋊D53—28no—
122C4×C22⋊D53D414yes—
123C4×C22⋊D53C2314yes—
124C2×C4⋊Dic53—22no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2314yes—
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919D411yescharacteristic
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148#13133149C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133138C2314yes—
160#13133129C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53—22no—
163C22×Q8×C53—21no—
164C22×Q8×C53—24no—
165C22×Q8×C53—42no—
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×D4×C53—21no—
170C22×D4×C53C2311yescharacteristic
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C2×SD16×C53—24no—
174C2×SD16×C53—42no—
175C2×SD16×C53C2314yes—
176C2×SD16×C53C2314yes—
177C22×C8×C53C2311yescharacteristic
178C22×C8×C53C2311yescharacteristic
179#121×C53—22no—
180#121×C53C2314yes—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C22⋊C4×C53—21no—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—24no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—28no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—44no—
197C2×Q8×C53—44no—
198C2×Q8×C53—48no—
199C2×Q8×C53#4114yescomplemented
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—21no—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
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—44no—
221C2×C22⋊D53SD1618yescomplemented
222C2×C22⋊D53C2×D414yes—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—24no—
228C22×Dic53—24no—
229C22×Dic53—44no—
230C22×Dic53—44no—
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234Q8×D53—28no—
235Q8×D53—44no—
236Q8×D53—48no—
237#11719947—432no—
238C2×C4×D53—22no—
239C2×C4×D53—22no—
240C2×C4×D53—24no—
241C2×C4×D53—24no—
242C2×C4×D53—44no—
243C2×C4×D53—44no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106—24no—
250C2×Dic106—24no—
251C2×Dic106—44no—
252C2×Dic106—44no—
253C2×Dic106C2412yes—
254SD16×C53—28no—
255SD16×C53—44no—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C4⋊C4×C53—21no—
261C4⋊C4×C53C2412yes—
262C22⋊C4×C53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53C2×D414yes—
267#11719923—44no—
268#11719921—24no—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53—21no—
274C4⋊Dic53—24no—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284#11719919C2×D414yes—
285C4×Dic53—24no—
286C4×Dic53C2×D412yes—
287C4×Dic53C2412yes—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322—44no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293C8×D53—44no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53C2×SD1614yes—
301C23×C53C22×D412yes—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53C2×SD1614yes—
306C22×D53C22×D412yes—
307Q8×C53—24no—
308Q8×C53—22no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—48no—
312Q8×C53—42no—
313Q8×C53C2×#4114yescomplemented
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—48no—
317D4×C53—42no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—24no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—48no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—48no—
335C22⋊D53C2×SD16116yescomplemented
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—48no—
346C2×Dic53—42no—
347C2×Dic53—48no—
348C2×Dic53C2×SD1614yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351C2×Dic53C22×D412yes—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—48no—
356C4×D53—48no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—42no—
361Dic106—48no—
362C8×C53—22no—
363C8×C53—22no—
364#88322—22no—
365#88322—22no—
366C2×#3298—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—28no—
369C22×C53—22no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—84no—
374C22×C53#54612yes—
375C22×C53C22×SD1614yes—
376C22×C53C22×SD1612yes—
377C22×C53#57812yes—
378C22×C53C23×D411yescharacteristic
379C2×D53—22no—
380C2×D53—28no—
381C2×D53—22no—
382C2×D53C22×SD1614yes—
383C4×C53—24no—
384C4×C53—22no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53#54612yes—
388C4×C53C22×#4111yescharacteristic
389C4×C53C2×H(5,𝔽2)11yescharacteristic
390Dic53—22no—
391Dic53—22no—
392Dic53—42no—
393Dic53—42no—
394Dic53—42no—
395Dic53—42no—
396Dic53C22×SD1614yes—
397C2×D4×Q8—531no—
398C2×#547—531no—
399#3298—5316no—
400C2×#487—531no—
401C2×#483—531no—
402C2×#483—531no—
403C2×#475—531no—
404C2×#465—531no—
405C2×#465—531no—
406C2×#461—531no—
407C2×#448—531no—
408C2×#448D5311yescharacteristic, complemented
409C2×C4×SD16—531no—
410C2×C8×D4—531no—
411C22×#103—531no—
412C22×#103—531no—
413C2×C53—24no—
414C2×C53—82no—
415C2×C53#329814yescomplemented
416C2×C53C2×#54611yescharacteristic
417C2×C53C23×SD1611yescharacteristic
418C2×C53C2×#57811yescharacteristic
419D53—24no—
420C22×#41—1061no—
421C23×Q8—531no—
422C23×Q8C2×D5311yescharacteristic
423C22×SD16—531no—
424C22×SD16C2×D5311yescharacteristic
425C22×SD16C2×D5311yescharacteristic
426C23×C8—531no—
427C23×C8—531no—
428D4×Q8—538no—
429D4×Q8—1064no—
430#547—538no—
431#547—1064no—
432C2×C4⋊Q8—531no—
433C2×C4⋊Q8—531no—
434C2×C4⋊Q8—1061no—
435C2×#123—1061no—
436C2×#123—1061no—
437C2×C22⋊Q8—531no—
438C2×C22⋊Q8—531no—
439C2×C22⋊Q8—1061no—
440C2×C22⋊Q8—1061no—
441C2×C22⋊Q8—1061no—
442C2×#121—531no—
443C2×#121C2×D5311yescharacteristic
444C2×C4×Q8—531no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—1061no—
448C22×C4⋊C4—531no—
449C22×C4⋊C4—531no—
450#487—538no—
451#483—538no—
452#483—538no—
453#475—538no—
454#465—538no—
455#465—538no—
456#461—538no—
457#448—538no—
458#448C2×D5318yescomplemented
459C4×SD16—538no—
460C8×D4—538no—
461C2×#106—531no—
462C2×#106—531no—
463C2×#106—531no—
464C2×C4⋊C8—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—531no—
469C2×#103—538no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—538no—
474C2×#103C2×D5311yescharacteristic
475C2×#103C2×D5311yescharacteristic
476C2×#102—531no—
477C2×C22⋊C8—531no—
478C2×C22⋊C8C2×D5311yescharacteristic
479C2×C4×C8—531no—
480C53C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—1068no—
482C2×#41—2128no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—24no—
486C22×Q8—42no—
487C22×Q8—534no—
488C22×Q8—531no—
489C22×Q8—1061no—
490C22×Q8—1061no—
491C22×Q8—1062no—
492C22×Q8—1064no—
493C22×Q8—2122no—
494C22×Q8C22×D5311yescharacteristic
495C22×Q8C22×D5314yes—
496C22×Q8C22×D5311yescharacteristic
497C22×D4—21no—
498C22×D4—531no—
499C22×D4—1061no—
500C22×D4C22×D5311yescharacteristic
501C23×C4—21no—
502C23×C4—531no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C23×C4C22×D5311yescharacteristic
508C2×SD16—24no—
509C2×SD16—42no—
510C2×SD16—534no—
511C2×SD16—2122no—
512C2×SD16C22×D5314yes—
513C2×SD16C22×D5314yes—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—534no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8—2122no—
520C22×C8C22×D5311yescharacteristic
521C22×C8C22×D5311yescharacteristic
522C4⋊Q8—534no—
523C4⋊Q8—534no—
524C4⋊Q8—1062no—
525C4⋊Q8—1062no—
526C4⋊Q8—1068no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—534no—
530C22⋊Q8—534no—
531C22⋊Q8—1068no—
532C22⋊Q8—1068no—
533C22⋊Q8—1068no—
534C22⋊Q8—1062no—
535C22⋊Q8—1062no—
536#121—22no—
537#121—534no—
538#121—1062no—
539#121C22×D5314yes—
540C4×Q8—534no—
541C4×Q8—1062no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1062no—
546C4×D4—1068no—
547C2×C4⋊C4—531no—
548C2×C4⋊C4—531no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—534no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—1062no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1062no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4C22×D5311yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—531no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—531no—
572C2×C42—1061no—
573#106—534no—
574#106—534no—
575#106—534no—
576C4⋊C8—534no—
577#103—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#103C22×D5314yes—
585#103C22×D5314yes—
586#102—534no—
587C22⋊C8—534no—
588C22⋊C8C22×D5314yes—
589C4×C8—534no—
590C24—21no—
591C24—531no—
592C24D4×D5311yescharacteristic
593#41—21232no—
594C2×Q8—21no—
595C2×Q8—24no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—28no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—48no—
604C2×Q8—532no—
605C2×Q8—1064no—
606C2×Q8—1064no—
607C2×Q8—1061no—
608C2×Q8—1068no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8—2124no—
612C2×Q8—2124no—
613C2×Q8—2124no—
614C2×Q8—2128no—
615C2×Q8#1171994714yescomplemented
616C2×Q8C23×D5312yes—
617C2×Q8C23×D5312yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—538no—
624C2×D4—534no—
625C2×D4—1064no—
626C2×D4—2124no—
627C2×D4C23×D5312yes—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—44no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—1064no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1064no—
646C22×C4—1061no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4—2124no—
654C22×C4D4×D5312yes—
655C22×C4D4×D5311yescharacteristic
656C22×C4C23×D5312yes—
657C22×C4C23×D5311yescharacteristic
658SD16—28no—
659SD16—44no—
660SD16—2124no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—532no—
664C2×C8—532no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—2124no—
668C2×C8—2124no—
669C2×C8C23×D5312yes—
670C2×C8C23×D5312yes—
671C4⋊C4—21no—
672C4⋊C4—534no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—532no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1061no—
683C4⋊C4—1061no—
684C4⋊C4—1064no—
685C4⋊C4—1061no—
686C4⋊C4—1064no—
687C4⋊C4C23×D5312yes—
688C22⋊C4—24no—
689C22⋊C4—534no—
690C22⋊C4—534no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C42—532no—
696C42—532no—
697C42—1064no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—534no—
705C23—532no—
706C23—1062no—
707C23—1062no—
708C23SD16×D5314yes—
709C23C2×D4×D5312yes—
710C23C2×D4×D5311yescharacteristic
711Q8—22no—
712Q8—24no—
713Q8—22no—
714Q8—22no—
715Q8—48no—
716Q8—42no—
717Q8—1062no—
718Q8—1062no—
719Q8—2128no—
720Q8—2128no—
721Q8—2122no—
722Q8C2×#1171994714yescomplemented
723D4—22no—
724D4—22no—
725D4—48no—
726D4—42no—
727D4—5316no—
728D4—2128no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—534no—
741C2×C4—532no—
742C2×C4—532no—
743C2×C4—532no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1064no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—2128no—
754C2×C4—2128no—
755C2×C4—2128no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4C2×#1171994712yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—534no—
778C22—1068no—
779C22—1062no—
780C22—1062no—
781C22#1681126012yes—
782C22C2×SD16×D5314yes—
783C22C2×SD16×D5312yes—
784C22#1681143912yes—
785C22C22×D4×D5311yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—534no—
791C4—1062no—
792C4—1062no—
793C4—2122no—
794C4—2122no—
795C4—2122no—
796C4—2122no—
797C4#1681126012yes—
798C4C22×#1171994711yescharacteristic
799C4C2×#1313326211yescharacteristic
800C2—24no—
801C2—82no—
802C2—1064no—
803C2#2028657314yesdirect product factor
804C2C2×#1681126011yescharacteristic
805C2C22×SD16×D5311yescharacteristic
806C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#448C2
socleC23×C53C22×D4
prime radicalC2×#16811273C2
hypercenterC2×#448D53
hypocenterC53C2×#3298
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D53C2semidirect
3. #20286573C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810954C2semidirect
6. C2×#16810952C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810850C2semidirect
9. C2×#16810849C2semidirect
10. C2×#16810826C2semidirect
11. C2×#16810760C2semidirect
12. C2×SD16×Dic53C2semidirect
13. C2×#16810686C2semidirect
14. C22×#13133141C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#448C2semidirect
23. Q8×C22⋊D53C22semidirect
43. #16810972C22semidirect
44. #16810954C22semidirect
45. #16810952C22semidirect
46. #16810906C22semidirect
47. #16810850C22semidirect
48. #16810849C22semidirect
49. #16810826C22semidirect
50. #16810760C22semidirect
51. SD16×Dic53C22semidirect
52. #16810686C22semidirect
63. C2×#13133141C22semidirect
65. #103×D53C22semidirect
73. C53×#448C22semidirect
199. C2×Q8×C53#41semidirect
221. C2×C22⋊D53SD16semidirect
313. Q8×C53C2×#41semidirect
335. C22⋊D53C2×SD16semidirect
408. C2×#448D53semidirect
415. C2×C53#3298semidirect
458. #448C2×D53semidirect
480. C53C2×#3298semidirect
615. C2×Q8#11719947semidirect
722. Q8C2×#11719947semidirect
803. C2#20286573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D532
C2×#168112732
#202865732
C2×#168109722
C2×#168109542
C2×#168109522
C2×#168109062
C2×#168108502
C2×#168108492
C2×#168108262
C2×#168107602
C2×SD16×Dic532
C2×#168106862
C22×#131331412
C2×#103×D532
C2×C53×#4482
C2×#329853