Finite Group Databasebeta

← C2×#20286890 #28260718

Subgroups — C2×#20286890 #28260718

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811325C211yesmaximal, characteristic
2C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
3#20286890C2116yesmaximal, direct product factor
4C2×#16810990C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810963C211yesmaximal, characteristic, complemented
7C2×#16810932C211yesmaximal, characteristic, complemented
8C2×#16810866C211yesmaximal, characteristic, complemented
9C2×#16810850C211yesmaximal, characteristic, complemented
10C2×#16810826C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×C53×#448C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811325—24no—
22#16811325C2218yes—
23Q8×C22⋊D53—24no—
24Q8×C22⋊D53C2218yescomplemented
25C2×#13133215—21no—
26C2×#13133215C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133201—21no—
30C2×#13133196—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133193—21no—
33C2×#13133193C2211yescharacteristic
34C2×#13133189—21no—
35C2×#13133188C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×D4×Dic53—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C22×C4⋊Dic53C2211yescharacteristic
43#16810990C2218yescomplemented
44#16810963C2218yescomplemented
45#16810959C2218yescomplemented
46#16810932C2218yescomplemented
47#16810866C2218yescomplemented
48#16810850C2218yescomplemented
49#16810826C2218yescomplemented
50#16810760C2218yescomplemented
51#16810724C2218yescomplemented
52#16810691C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810630C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2218yescomplemented
65C2×#13133140C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#448C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×Q8×D53—22no—
80C2×Q8×D53—24no—
81C2×Q8×D53—42no—
82C2×Q8×D53C2314yes—
83C22×C22⋊D53—21no—
84C22×C22⋊D53D411yescharacteristic
85C23×Dic53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719923—42no—
90C2×#11719923C2314yes—
91C2×#11719912—42no—
92C2×#11719912C2314yes—
93C22×#88322—42no—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C22×#88322C2314yes—
97#13133215—28no—
98#13133215—22no—
99#13133215C2314yes—
100#13133210—28no—
101#13133208—22no—
102#13133208C2314yes—
103#13133201—28no—
104#13133196—28no—
105#13133196—22no—
106#13133196C2314yes—
107#13133193—28no—
108#13133193—22no—
109#13133193C2314yes—
110#13133189—28no—
111#13133188—22no—
112#13133188C2314yes—
113Q8×Dic53—22no—
114Q8×Dic53C2314yes—
115D4×Dic53—28no—
116D4×Dic53—22no—
117D4×Dic53C2314yes—
118C4×C22⋊D53—28no—
119C4×C22⋊D53D414yes—
120C4×C22⋊D53C2314yes—
121#13133175—22no—
122#13133175C2314yes—
123C2×C4⋊Dic53—22no—
124C2×C4⋊Dic53—21no—
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×#11719919D411yescharacteristic
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133151C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133140C2314yes—
158#13133138C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C22×Q8×C53—22no—
162C22×Q8×C53—21no—
163C22×Q8×C53—24no—
164C22×Q8×C53—42no—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C2×SD16×C53—24no—
173C2×SD16×C53—42no—
174C2×SD16×C53C2314yes—
175C2×SD16×C53C2314yes—
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178#121×C53—22no—
179#121×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—28no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—44no—
196C2×Q8×C53—44no—
197C2×Q8×C53—48no—
198C2×Q8×C53#4114yes—
199C2×Q8×C53C2412yes—
200C2×Q8×C53C2412yes—
201C2×D4×C53—24no—
202C2×D4×C53—21no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53C2412yes—
207C22×C4×C53—21no—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—24no—
213C22×C4×C53—44no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—82no—
221C2×C22⋊D53C2×D414yes—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—24no—
228C22×Dic53—82no—
229C22×Dic53—82no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233Q8×D53—28no—
234Q8×D53—44no—
235Q8×D53—48no—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2412yes—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106—24no—
246C2×Dic106—44no—
247C2×Dic106C2412yes—
248SD16×C53—28no—
249SD16×C53—44no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53C2×D414yes—
261#11719923—44no—
262#11719921—24no—
263#11719921—24no—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53—21no—
269C4⋊Dic53—24no—
270C4⋊Dic53—24no—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273C4⋊Dic53C2412yes—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280C4×Dic53—24no—
281C4×Dic53—24no—
282C4×Dic53C2×D412yes—
283C4×Dic53C2412yes—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322—44no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289#11719912—44no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53#13714yes—
297C23×C53C22×D412yes—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53C22×D412yes—
303Q8×C53—24no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—48no—
308Q8×C53—42no—
309Q8×C53C2×#4114yes—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—48no—
313D4×C53—42no—
314C2×C4×C53—24no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—48no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4112yes—
328C2×C4×C53H(5,𝔽2)12yes—
329C2×C4×C53C2511yescharacteristic
330C22⋊D53—28no—
331C22⋊D53—84no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—84no—
344C2×Dic53—84no—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348C4×D53—24no—
349C4×D53—22no—
350C4×D53—22no—
351C4×D53—48no—
352Dic106—22no—
353Dic106—22no—
354Dic106—48no—
355Dic106—42no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3320—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—28no—
363C22×C53—22no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—84no—
368C22×C53#54612yes—
369C22×C53C2×#13714yes—
370C22×C53C2×#13712yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—44no—
377C4×C53—24no—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#54612yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C2×H(5,𝔽2)11yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391C2×#553—531no—
392C2×D4×Q8—531no—
393#3320—5316no—
394C2×#491—531no—
395C2×#484—531no—
396C2×#485—531no—
397C2×#479—531no—
398C2×#468—531no—
399C2×#465—531no—
400C2×#461—531no—
401C2×#448—531no—
402C2×#448D5311yescharacteristic, complemented
403C2×#440—531no—
404C2×#435—531no—
405C2×#419—531no—
406C22×#103—531no—
407C2×C53—24no—
408C2×C53—82no—
409C2×C53#332014yescomplemented
410C2×C53C2×#54611yescharacteristic
411C2×C53C22×#13711yescharacteristic
412C2×C53C2×#57711yescharacteristic
413D53—42no—
414C23×Q8—531no—
415C23×Q8C2×D5311yescharacteristic
416C22×SD16—531no—
417C22×SD16C2×D5311yescharacteristic
418C22×SD16C2×D5311yescharacteristic
419C22×M16—531no—
420C23×C8—531no—
421#553—538no—
422#553—1064no—
423D4×Q8—538no—
424D4×Q8—1064no—
425C2×C4⋊Q8—531no—
426C2×C4⋊Q8—1061no—
427C2×#126—1061no—
428C2×#125—531no—
429C2×#123—1061no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C2×#121—531no—
435C2×#121—1061no—
436C2×#121C2×D5311yescharacteristic
437C2×C4×Q8—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1061no—
442C2×#117—531no—
443C22×C4⋊C4—531no—
444#491—538no—
445#485—538no—
446#484—538no—
447#479—538no—
448#468—538no—
449#465—538no—
450#461—538no—
451#448—538no—
452#448C2×D5318yescomplemented
453#440—538no—
454#435—538no—
455C2×#107—531no—
456C2×#107—531no—
457C2×#106—531no—
458C2×C4⋊C8—531no—
459#419—538no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—538no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103C2×D5311yescharacteristic
469C2×#103C2×D5311yescharacteristic
470C2×#102—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8C2×D5311yescharacteristic
473C2×#97—531no—
474C53C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—534no—
480C22×Q8—531no—
481C22×Q8—1061no—
482C22×Q8—1062no—
483C22×Q8—1064no—
484C22×Q8—2122no—
485C22×Q8C22×D5311yescharacteristic
486C22×Q8C22×D5314yes—
487C22×Q8C22×D5311yescharacteristic
488C22×D4—21no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—531no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4C22×D5311yescharacteristic
498C2×SD16—24no—
499C2×SD16—42no—
500C2×SD16—534no—
501C2×SD16—2122no—
502C2×SD16C22×D5314yes—
503C2×SD16C22×D5314yes—
504C2×M16—534no—
505C2×M16—2122no—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8—534no—
509C22×C8—2122no—
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5311yescharacteristic
512C4⋊Q8—534no—
513C4⋊Q8—1062no—
514C4⋊Q8—1068no—
515#126—1068no—
516#125—534no—
517#125—1062no—
518#123—1068no—
519C22⋊Q8—534no—
520C22⋊Q8—534no—
521C22⋊Q8—1068no—
522C22⋊Q8—1068no—
523C22⋊Q8—1062no—
524C22⋊Q8—1062no—
525#121—22no—
526#121—534no—
527#121—1062no—
528#121—1068no—
529#121C22×D5314yes—
530C4×Q8—534no—
531C4×Q8—1062no—
532C4×D4—534no—
533C4×D4—534no—
534C4×D4—534no—
535C4×D4—1062no—
536C4×D4—1068no—
537C4×D4—1068no—
538#117—534no—
539#117—1062no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—534no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1062no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—531no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C42—531no—
564C2×C42—1061no—
565C2×C42—1061no—
566#107—534no—
567#107—534no—
568#106—534no—
569C4⋊C8—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#103—534no—
576#103—534no—
577#103C22×D5314yes—
578#103C22×D5314yes—
579#102—534no—
580C22⋊C8—534no—
581C22⋊C8C22×D5314yes—
582#97—534no—
583C24—21no—
584C24—531no—
585C24D4×D5311yescharacteristic
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—48no—
596C2×Q8—532no—
597C2×Q8—1064no—
598C2×Q8—1061no—
599C2×Q8—1068no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—2124no—
603C2×Q8—2124no—
604C2×Q8—2128no—
605C2×Q8#1171994714yes—
606C2×Q8C23×D5312yes—
607C2×Q8C23×D5312yes—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—534no—
614C2×D4—1064no—
615C2×D4—1064no—
616C2×D4—4242no—
617C2×D4C23×D5312yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—44no—
625C22×C4—531no—
626C22×C4—531no—
627C22×C4—531no—
628C22×C4—532no—
629C22×C4—532no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1064no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4—2124no—
642C22×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646SD16—28no—
647SD16—44no—
648SD16—2124no—
649M16—2124no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—532no—
653C2×C8—532no—
654C2×C8—1062no—
655C2×C8—1062no—
656C2×C8—2124no—
657C2×C8C23×D5312yes—
658C2×C8C23×D5312yes—
659C4⋊C4—21no—
660C4⋊C4—534no—
661C4⋊C4—532no—
662C4⋊C4—532no—
663C4⋊C4—532no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1061no—
671C4⋊C4—1061no—
672C4⋊C4—1064no—
673C4⋊C4—1061no—
674C4⋊C4—1064no—
675C4⋊C4C23×D5312yes—
676C22⋊C4—24no—
677C22⋊C4—534no—
678C22⋊C4—534no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—532no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23#1313324614yes—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—1062no—
708Q8—1062no—
709Q8—2128no—
710Q8—2122no—
711Q8C2×#1171994714yes—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—1068no—
717D4—4244no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—532no—
730C2×C4—532no—
731C2×C4—532no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1064no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—4244no—
743C2×C4—4244no—
744C2×C4—2128no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4C2×D4×D5312yes—
750C2×C4C2×D4×D5311yescharacteristic
751C2×C4C2×#1171994712yes—
752C2×C4#1313326212yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—84no—
765C22—1062no—
766C22—1062no—
767C22—1062no—
768C22—2124no—
769C22#1681126012yes—
770C22C2×#1313324614yes—
771C22C2×#1313324612yes—
772C22#1681143212yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—1062no—
779C4—1062no—
780C4—1062no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126012yes—
786C4C22×#1171994711yescharacteristic
787C4C2×#1313326211yescharacteristic
788C2—24no—
789C2—82no—
790C2—2122no—
791C2#2028689014yesdirect product factor
792C2C2×#1681126011yescharacteristic
793C2C22×#1313324611yescharacteristic
794C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#448C2
socleC23×C53C22×D4
prime radicalC2×#16811325C2
hypercenterC2×#448D53
hypocenterC53C2×#3320
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
2. C2×Q8×C22⋊D53C2semidirect
3. #20286890C2direct (N × H)
4. C2×#16810990C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810963C2semidirect
7. C2×#16810932C2semidirect
8. C2×#16810866C2semidirect
9. C2×#16810850C2semidirect
10. C2×#16810826C2semidirect
11. C2×#16810760C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810691C2semidirect
14. C2×#16810630C2semidirect
15. C22×#13133141C2semidirect
16. C2×C53×#448C2semidirect
24. Q8×C22⋊D53C22semidirect
43. #16810990C22semidirect
44. #16810963C22semidirect
45. #16810959C22semidirect
46. #16810932C22semidirect
47. #16810866C22semidirect
48. #16810850C22semidirect
49. #16810826C22semidirect
50. #16810760C22semidirect
51. #16810724C22semidirect
52. #16810691C22semidirect
57. #16810630C22semidirect
64. C2×#13133141C22semidirect
73. C53×#448C22semidirect
402. C2×#448D53semidirect
409. C2×C53#3320semidirect
452. #448C2×D53semidirect
474. C53C2×#3320semidirect
791. C2#20286890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113252
C2×Q8×C22⋊D532
#202868902
C2×#168109902
C2×#168109592
C2×#168109632
C2×#168109322
C2×#168108662
C2×#168108502
C2×#168108262
C2×#168107602
C2×#168107242
C2×#168106912
C2×#168106302
C22×#131331412
C2×C53×#4482
C2×#332053