Finite Group Databasebeta

← C2×#20287026 #28261008

Subgroups — C2×#20287026 #28261008

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×#16811331C211yesmaximal, characteristic, complemented
2C2×#16811275C211yesmaximal, characteristic
3#20287026C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810955C211yesmaximal, characteristic, complemented
6C2×#16810951C211yesmaximal, characteristic, complemented
7C2×#16810912C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810784C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810708C211yesmaximal, characteristic, complemented
13C2×#16810699C211yesmaximal, characteristic, complemented
14C2×#16810625C211yesmaximal, characteristic, complemented
15C2×#16810623C211yesmaximal, characteristic, complemented
16C2×C53×#470C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22#16811331—24no—
23#16811331C2218yescomplemented
24#16811275—24no—
25#16811275C2218yes—
26C2×#13133216C2211yescharacteristic
27C2×#13133215C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133202—21no—
30C2×#13133199—21no—
31C2×#13133197—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133190—21no—
36C2×Q8×Dic53C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133177—21no—
40C22×C4⋊Dic53C2211yescharacteristic
41C2×C4⋊C4×D53—21no—
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810972C2218yescomplemented
44#16810955C2218yescomplemented
45#16810951C2218yescomplemented
46#16810912C2218yescomplemented
47#16810880C2218yescomplemented
48#16810831C2218yescomplemented
49#16810784C2218yescomplemented
50#16810783C2218yescomplemented
51#16810708C2218yescomplemented
52#16810699C2218yescomplemented
53C2×#13133148C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133146C2211yescharacteristic
56#16810625C2218yescomplemented
57#16810623C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#470C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719945—22no—
82C2×#11719945—24no—
83C2×#11719945—42no—
84C2×#11719945C2314yes—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53D411yescharacteristic
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719925—42no—
98C2×#11719925C2314yes—
99C2×#11719924—24no—
100C2×#11719924C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133215—22no—
108#13133215C2314yes—
109#13133207—28no—
110#13133202—28no—
111#13133199—28no—
112#13133197—28no—
113#13133197—22no—
114#13133197C2314yes—
115#13133194—28no—
116#13133193—22no—
117#13133193C2314yes—
118#13133190—28no—
119Q8×Dic53—22no—
120Q8×Dic53C2314yes—
121#13133179—22no—
122#13133179C2314yes—
123C4×C22⋊D53D414yes—
124C4×C22⋊D53C2314yes—
125#13133177—28no—
126C2×C4⋊Dic53—22no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2314yes—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C4⋊C4×D53—28no—
140C4⋊C4×D53—22no—
141C4⋊C4×D53C2314yes—
142C2×C22⋊Dic53D411yescharacteristic
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133148C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C2×Q16×C53—42no—
167C2×Q16×C53C2314yes—
168C2×M16×C53—42no—
169C2×M16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22⋊Q8×C53—22no—
173C22⋊Q8×C53—22no—
174C22⋊Q8×C53C2314yes—
175C22⋊Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182#106×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53C2412yes—
195C2×Q8×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53C2×D414yes—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—24no—
214C22×Dic53—82no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218#11719949—28no—
219#11719949—44no—
220#11719949—48no—
221#11719945—28no—
222#11719945—44no—
223#11719945—48no—
224C2×D212—21no—
225C2×D212—22no—
226C2×D212—24no—
227C2×D212—44no—
228C2×D212#4114yes—
229C2×D212C2412yes—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53—82no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2412yes—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106—24no—
246C2×Dic106—82no—
247C2×Dic106C2412yes—
248Q16×C53—44no—
249M16×C53—44no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—24no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊Dic53C2×D414yes—
263#11719925—44no—
264#11719924—28no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921C2×D414yes—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919C2×D414yes—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289#11719912—44no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53C22×D412yes—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—24no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53C22×D412yes—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—42no—
308Q8×C53—42no—
309C2×C4×C53—22no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4112yes—
324C2×C4×C53H(5,𝔽2)12yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—28no—
327C22⋊D53—48no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—84no—
337C2×Dic53#13714yes—
338C2×Dic53C22×D412yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341D212—24no—
342D212—22no—
343D212—48no—
344D212C2×#4114yes—
345C4×D53—24no—
346C4×D53—22no—
347C4×D53—22no—
348C4×D53—48no—
349C4×D53—48no—
350C4×D53—48no—
351C4×D53—84no—
352Dic106—22no—
353Dic106—22no—
354Dic106—42no—
355Dic106—84no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3331—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—44no—
365C22×C53#54612yes—
366C22×C53C2×#13712yes—
367C22×C53#57712yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—22no—
370C2×D53—24no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—44no—
374C2×D53—48no—
375C2×D53—42no—
376C2×D53—42no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
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—
390Dic53C2×#13714yes—
391C2×#554—531no—
392C2×#547—531no—
393#3331—5316no—
394C2×#487—531no—
395C2×#483—531no—
396C2×#483—531no—
397C2×#476—531no—
398C2×#470—531no—
399C2×#470D5311yescharacteristic, complemented
400C2×#462—531no—
401C2×#452—531no—
402C2×#452—531no—
403C2×C4×SD16—531no—
404C2×#436—531no—
405C2×#417—531no—
406C2×#417—531no—
407C2×C53—42no—
408C2×C53#333114yescomplemented
409C2×C53C2×#54611yescharacteristic
410C2×C53C22×#13711yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—42no—
413D53—44no—
414C22×#41—531no—
415C22×#41—531no—
416C22×Q16—531no—
417C22×Q16C2×D5311yescharacteristic
418C22×SD16—531no—
419C22×M16—531no—
420C22×M16C2×D5311yescharacteristic
421#554—538no—
422#554—1064no—
423#547—538no—
424#547—1064no—
425C2×C4⋊Q8—531no—
426C2×C4⋊Q8—531no—
427C2×#125—1061no—
428C2×#123—1061no—
429C2×#123—1061no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C2×C22⋊Q8C2×D5311yescharacteristic
435C2×C22⋊Q8C2×D5311yescharacteristic
436C2×#121—1061no—
437C2×C4×Q8—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C22×C4⋊C4—531no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—1061no—
444#487—538no—
445#483—538no—
446#483—538no—
447#476—538no—
448#470—538no—
449#470C2×D5318yescomplemented
450#462—538no—
451#452—538no—
452#452—538no—
453C4×SD16—538no—
454#436—538no—
455C2×#106—531no—
456C2×#106—531no—
457C2×#106C2×D5311yescharacteristic
458C2×C4⋊C8—531no—
459#417—538no—
460#417—538no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103C2×D5311yescharacteristic
467C2×#103C2×D5311yescharacteristic
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×C4×C8—531no—
474C53C2×#333111yescharacteristic, complemented, Sylow
475C2×#41—534no—
476C2×#41—534no—
477C2×#41—1064no—
478C2×#41—1062no—
479C2×#41—1062no—
480C2×#41—1064no—
481C2×#41—2122no—
482C2×#41—2122no—
483C22×Q8—531no—
484C22×Q8—1061no—
485C22×Q8C22×D5311yescharacteristic
486C22×Q8C22×D5311yescharacteristic
487C22×D4—531no—
488C22×D4—531no—
489C22×D4—1061no—
490C22×D4—1061no—
491C23×C4—531no—
492C23×C4—1061no—
493C23×C4—1061no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4C22×D5311yescharacteristic
498C2×Q16—42no—
499C2×Q16—534no—
500C2×Q16—2122no—
501C2×Q16C22×D5314yes—
502C2×SD16—534no—
503C2×SD16—1064no—
504C2×M16—42no—
505C2×M16—534no—
506C2×M16—2122no—
507C2×M16C22×D5314yes—
508C22×C8—531no—
509C22×C8—531no—
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5311yescharacteristic
512C4⋊Q8—534no—
513C4⋊Q8—534no—
514C4⋊Q8—1062no—
515C4⋊Q8—1062no—
516#125—1068no—
517#123—1068no—
518#123—1068no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—534no—
522C22⋊Q8—534no—
523C22⋊Q8—1068no—
524C22⋊Q8—1068no—
525C22⋊Q8—1062no—
526C22⋊Q8—1062no—
527C22⋊Q8C22×D5314yes—
528C22⋊Q8C22×D5314yes—
529#121—1068no—
530C4×Q8—534no—
531C4×Q8—1062no—
532C4×D4—534no—
533C4×D4—534no—
534C4×D4—534no—
535C4×D4—1062no—
536C4×D4—1068no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—534no—
543C2×C4⋊C4—534no—
544C2×C4⋊C4—1068no—
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⋊C4—1061no—
554C2×C4⋊C4—1062no—
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—531no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C42—531no—
565C2×C42—1061no—
566#106—534no—
567#106—534no—
568#106C22×D5314yes—
569C4⋊C8—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#103C22×D5314yes—
576#103C22×D5314yes—
577#102—534no—
578#102—534no—
579#102—534no—
580C22⋊C8—534no—
581C22⋊C8—534no—
582C4×C8—534no—
583C24—531no—
584C24—1061no—
585C24D4×D5311yescharacteristic
586#41—1068no—
587#41—1068no—
588#41—2124no—
589#41—2128no—
590#41—2124no—
591#41—2128no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—532no—
599C2×Q8—1064no—
600C2×Q8—1061no—
601C2×Q8—1062no—
602C2×Q8—1062no—
603C2×Q8—4242no—
604C2×Q8C23×D5312yes—
605C2×Q8C23×D5312yes—
606C2×D4—534no—
607C2×D4—534no—
608C2×D4—532no—
609C2×D4—1064no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1061no—
613C2×D4—1062no—
614C2×D4—2124no—
615C2×D4—2124no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—531no—
623C22×C4—531no—
624C22×C4—531no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—1064no—
628C22×C4—1064no—
629C22×C4—1064no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1064no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1064no—
637C22×C4—4242no—
638C22×C4—4242no—
639C22×C4—2124no—
640C22×C4—2124no—
641C22×C4—2124no—
642C22×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646Q16—44no—
647Q16—2124no—
648SD16—1068no—
649M16—44no—
650M16—2124no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—532no—
654C2×C8—532no—
655C2×C8—1062no—
656C2×C8—1062no—
657C2×C8C23×D5312yes—
658C2×C8C23×D5312yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—534no—
664C4⋊C4—532no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—1064no—
673C4⋊C4—1061no—
674C4⋊C4—1064no—
675C4⋊C4—1061no—
676C4⋊C4C23×D5312yes—
677C4⋊C4C23×D5312yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—534no—
681C22⋊C4—534no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C22⋊C4—1064no—
685C42—532no—
686C42—532no—
687C42—1064no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—532no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—1064no—
697C23—2122no—
698C23—2122no—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—1062no—
708Q8—1062no—
709Q8—4244no—
710Q8—2122no—
711D4—534no—
712D4—1068no—
713D4—1062no—
714D4—1064no—
715D4—2128no—
716D4—2128no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—534no—
730C2×C4—532no—
731C2×C4—532no—
732C2×C4—532no—
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—4244no—
742C2×C4—4244no—
743C2×C4—2128no—
744C2×C4—2128no—
745C2×C4—2128no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4C2×D4×D5312yes—
750C2×C4C2×D4×D5311yescharacteristic
751C2×C4#41×D5312yes—
752C2×C4#1313326212yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—1062no—
763C22—1064no—
764C22—1062no—
765C22—1062no—
766C22—2124no—
767C22—2128no—
768C22—2122no—
769C22—2122no—
770C22#1681126212yes—
771C22#137×D5312yes—
772C22#1681143212yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—534no—
780C4—1062no—
781C4—1062no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126212yes—
786C4C2×#41×D5311yescharacteristic
787C4C2×#1313326211yescharacteristic
788C2—42no—
789C2—2122no—
790C2—2124no—
791C2#2028702614yesdirect product factor
792C2C2×#1681126211yescharacteristic
793C2C2×#137×D5311yescharacteristic
794C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#470C2
socleC23×C53C22×D4
prime radicalC2×#16811275C2
hypercenterC2×#470D53
hypocenterC53C2×#3331
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#16811331C2semidirect
3. #20287026C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810955C2semidirect
6. C2×#16810951C2semidirect
7. C2×#16810912C2semidirect
8. C2×#16810880C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810784C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810708C2semidirect
13. C2×#16810699C2semidirect
14. C2×#16810625C2semidirect
15. C2×#16810623C2semidirect
16. C2×C53×#470C2semidirect
23. #16811331C22semidirect
43. #16810972C22semidirect
44. #16810955C22semidirect
45. #16810951C22semidirect
46. #16810912C22semidirect
47. #16810880C22semidirect
48. #16810831C22semidirect
49. #16810784C22semidirect
50. #16810783C22semidirect
51. #16810708C22semidirect
52. #16810699C22semidirect
56. #16810625C22semidirect
57. #16810623C22semidirect
73. C53×#470C22semidirect
399. C2×#470D53semidirect
408. C2×C53#3331semidirect
449. #470C2×D53semidirect
474. C53C2×#3331semidirect
791. C2#20287026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168112752
#202870262
C2×#168109722
C2×#168109552
C2×#168109512
C2×#168109122
C2×#168108802
C2×#168108312
C2×#168107842
C2×#168107832
C2×#168107082
C2×#168106992
C2×#168106252
C2×#168106232
C2×C53×#4702
C2×#333153