Finite Group Databasebeta

← C2×#20286891 #28260719

Subgroups — C2×#20286891 #28260719

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×#16811323C211yesmaximal, characteristic
2C2×Q8×D212C211yesmaximal, characteristic, complemented
3#20286891C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810966C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810868C211yesmaximal, characteristic, complemented
9C2×#16810851C211yesmaximal, characteristic, complemented
10C2×#16810828C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×#16810760C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811323—24no—
24#16811323C2218yes—
25Q8×D212—24no—
26Q8×D212C2218yescomplemented
27C2×#13133217—21no—
28C2×#13133217C2211yescharacteristic
29C2×#13133210—21no—
30C2×#13133209C2211yescharacteristic
31C2×#13133200—21no—
32C2×#13133197—21no—
33C2×#13133197—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133197C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133188C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×#13133175C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810992C2218yescomplemented
45#16810966C2218yescomplemented
46#16810960C2218yescomplemented
47#16810930C2218yescomplemented
48#16810868C2218yescomplemented
49#16810851C2218yescomplemented
50#16810828C2218yescomplemented
51#16810760C2218yescomplemented
52#16810760C2218yescomplemented
53#16810696C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57#16810630C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66#103×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—22no—
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53—24no—
85C2×Q8×D53—42no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C2×Q8×D53C2314yes—
89C22×D212D411yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C2×#11719923—42no—
98C2×#11719923—42no—
99C2×#11719923C2314yes—
100C2×#11719923C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C2×C8×D53—42no—
106C2×C8×D53C2314yes—
107#13133217—22no—
108#13133217—28no—
109#13133217C2314yes—
110#13133210—28no—
111#13133209—22no—
112#13133209C2314yes—
113#13133200—28no—
114#13133197—28no—
115#13133197—28no—
116#13133197—22no—
117#13133197—22no—
118#13133197C2314yes—
119#13133197C2314yes—
120#13133190—28no—
121#13133188—22no—
122#13133188—22no—
123#13133188C2314yes—
124#13133188C2314yes—
125C4×D212—28no—
126C4×D212D414yes—
127C4×D212C2314yes—
128C4×C22⋊D53—28no—
129#13133175—22no—
130#13133175C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133141C2314yes—
159#13133141C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C23×D53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53#4114yes—
191C2×Q8×C53C2412yes—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—82no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—44no—
207C2×C22⋊D53—82no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214Q8×D53—28no—
215Q8×D53—28no—
216Q8×D53—44no—
217Q8×D53—44no—
218Q8×D53—48no—
219Q8×D53—48no—
220C2×D212—24no—
221C2×D212C2×D414yes—
222C2×C4×D53—22no—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—22no—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—44no—
230C2×C4×D53—44no—
231C2×C4×D53—82no—
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2×D412yes—
234C2×C4×D53C2412yes—
235C2×C4×D53C2412yes—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106—24no—
243C2×Dic106—24no—
244C2×Dic106—44no—
245C2×Dic106—44no—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248SD16×C53—28no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C42×C53—24no—
260C42×C53C2×D412yes—
261C42×C53C2412yes—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264#11719923—44no—
265#11719923—44no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921C2×D414yes—
270#11719921C2×D414yes—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53—24no—
277C4⋊Dic53C2×D414yes—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283C4×Dic53—24no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288#11719912—44no—
289C8×D53—44no—
290C23×C53—22no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53#13714yes—
301C22×D53C22×D412yes—
302C22×D53C22×D412yes—
303Q8×C53—24no—
304Q8×C53—22no—
305Q8×C53C2×#4114yes—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—42no—
309C2×C4×C53—24no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—84no—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53H(5,𝔽2)12yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—48no—
325C22⋊D53—84no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—28no—
339C4×D53—24no—
340C4×D53—24no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—48no—
346C4×D53—48no—
347C4×D53—84no—
348Dic106—22no—
349Dic106—22no—
350Dic106—22no—
351Dic106—22no—
352Dic106—48no—
353Dic106—48no—
354Dic106—42no—
355Dic106—42no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3320—531nomaximal, Sylow
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—84no—
365C22×C53#54612yes—
366C22×C53C2×#13712yes—
367C22×C53#57712yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—22no—
370C2×D53—28no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—44no—
376C2×D53C2×#13714yes—
377C4×C53—24no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53#54612yes—
383C4×C53C22×#4111yescharacteristic
384C4×C53C2×H(5,𝔽2)11yescharacteristic
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×#448—531no—
403C2×#440D5311yescharacteristic, complemented
404C2×#435—531no—
405C2×#419—531no—
406C22×#103—531no—
407C2×C53—82no—
408C2×C53#332014yescomplemented
409C2×C53C2×#54611yescharacteristic
410C2×C53C22×#13711yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—24no—
413D53—42no—
414C23×Q8—531no—
415C23×Q8—531no—
416C22×SD16—531no—
417C22×SD16—531no—
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—531no—
436C2×#121—1061no—
437C2×C4×Q8C2×D5311yescharacteristic
438C2×C4×D4—531no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
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#448—538no—
453#440C2×D5318yescomplemented
454#435—538no—
455C2×#107—531no—
456C2×#107C2×D5311yescharacteristic
457C2×#106—531no—
458C2×C4⋊C8—531no—
459#419—538no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—538no—
469C2×#103C2×D5311yescharacteristic
470C2×#102C2×D5311yescharacteristic
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×#97C2×D5311yescharacteristic
474C53C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—534no—
476C22×Q8—534no—
477C22×Q8—531no—
478C22×Q8—531no—
479C22×Q8—1061no—
480C22×Q8—1061no—
481C22×Q8—1062no—
482C22×Q8—1062no—
483C22×Q8—1064no—
484C22×Q8—1064no—
485C22×Q8—2122no—
486C22×Q8—2122no—
487C22×Q8C22×D5311yescharacteristic
488C22×D4—531no—
489C22×D4—1061no—
490C22×D4—1061no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—531no—
494C23×C4—531no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1061no—
498C2×SD16—24no—
499C2×SD16—534no—
500C2×SD16—534no—
501C2×SD16—2122no—
502C2×SD16—2122no—
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—1068no—
514C4⋊Q8—1062no—
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—534no—
526#121—534no—
527#121—1068no—
528#121—1062no—
529#121—1062no—
530C4×Q8—22no—
531C4×Q8C22×D5314yes—
532C4×D4—22no—
533C4×D4—534no—
534C4×D4—534no—
535C4×D4—1068no—
536C4×D4—1068no—
537C4×D4C22×D5314yes—
538#117—534no—
539#117—1062no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—534no—
545C2×C4⋊C4—1062no—
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—1061no—
553C2×C4⋊C4C22×D5311yescharacteristic
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—21no—
564C2×C42—1061no—
565C2×C42C22×D5311yescharacteristic
566#107—534no—
567#107C22×D5314yes—
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#103—534no—
578#103C22×D5314yes—
579#102C22×D5314yes—
580C22⋊C8—534no—
581C22⋊C8—534no—
582#97C22×D5314yes—
583C24—21no—
584C24—531no—
585C24—531no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—532no—
589C2×Q8—532no—
590C2×Q8—1064no—
591C2×Q8—1064no—
592C2×Q8—1061no—
593C2×Q8—1061no—
594C2×Q8—1068no—
595C2×Q8—1068no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—1062no—
600C2×Q8—2124no—
601C2×Q8—2124no—
602C2×Q8—2124no—
603C2×Q8—2124no—
604C2×Q8—2128no—
605C2×Q8—2128no—
606C2×Q8#1171994514yes—
607C2×Q8C23×D5312yes—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—534no—
612C2×D4—1064no—
613C2×D4—1064no—
614C2×D4—1064no—
615C2×D4—4242no—
616C2×D4—2124no—
617C2×D4C23×D5312yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—82no—
623C22×C4—531no—
624C22×C4—531no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—532no—
628C22×C4—532no—
629C22×C4—1064no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—4242no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4D4×D5311yescharacteristic
644C22×C4D4×D5311yescharacteristic
645C22×C4C23×D5311yescharacteristic
646SD16—28no—
647SD16—2124no—
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—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—534no—
663C4⋊C4—532no—
664C4⋊C4—532no—
665C4⋊C4—1064no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1061no—
669C4⋊C4—1061no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—1064no—
673C4⋊C4—1064no—
674C4⋊C4C23×D5312yes—
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—24no—
685C42—1064no—
686C42D4×D5312yes—
687C42C23×D5312yes—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—534no—
693C23—532no—
694C23—532no—
695C23—1062no—
696C23—1062no—
697C23—1062no—
698C23—1062no—
699C23—1062no—
700C23C2×D4×D5311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—1062no—
704Q8—1062no—
705Q8—1062no—
706Q8—1062no—
707Q8—2128no—
708Q8—2128no—
709Q8—2122no—
710Q8—2122no—
711Q8C2×#1171994514yes—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—1068no—
716D4—4244no—
717D4—2128no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—532no—
728C2×C4—532no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1064no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—4244no—
742C2×C4—2128no—
743C2×C4—2128no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4C2×D4×D5312yes—
749C2×C4C2×D4×D5312yes—
750C2×C4C2×D4×D5311yescharacteristic
751C2×C4C2×#1171994512yes—
752C2×C4#1313326312yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—534no—
763C22—1062no—
764C22—1068no—
765C22—1062no—
766C22—1062no—
767C22—1062no—
768C22—1062no—
769C22—2124no—
770C22#1681126912yes—
771C22#137×D5312yes—
772C22#1681143312yes—
773C22C22×D4×D5311yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—1062no—
780C4—1062no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126912yes—
786C4C22×#1171994511yescharacteristic
787C4C2×#1313326311yescharacteristic
788C2—82no—
789C2—1064no—
790C2—2122no—
791C2#2028689114yesdirect product factor
792C2C2×#1681126911yescharacteristic
793C2C2×#137×D5311yescharacteristic
794C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#16811323C2
hypercenterC2×#440D53
hypocenterC53C2×#3320
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D212C2semidirect
3. #20286891C2direct (N × H)
4. C2×#16810992C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810966C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810868C2semidirect
9. C2×#16810851C2semidirect
10. C2×#16810828C2semidirect
11. C2×#16810760C2semidirect
12. C2×#16810760C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810630C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#440C2semidirect
26. Q8×D212C22semidirect
44. #16810992C22semidirect
45. #16810966C22semidirect
46. #16810960C22semidirect
47. #16810930C22semidirect
48. #16810868C22semidirect
49. #16810851C22semidirect
50. #16810828C22semidirect
51. #16810760C22semidirect
52. #16810760C22semidirect
53. #16810696C22semidirect
57. #16810630C22semidirect
66. #103×D53C22semidirect
72. C53×#440C22semidirect
403. C2×#440D53semidirect
408. C2×C53#3320semidirect
453. #440C2×D53semidirect
474. C53C2×#3320semidirect
791. C2#20286891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113232
C2×Q8×D2122
#202868912
C2×#168109922
C2×#168109602
C2×#168109662
C2×#168109302
C2×#168108682
C2×#168108512
C2×#168108282
C2×#168107602
C2×#168106962
C2×#168106302
C2×#103×D532
C2×C53×#4402
C2×#332053