Finite Group Databasebeta

← C2×#20286823 #28260679

Subgroups — C2×#20286823 #28260679

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×#16811334C211yesmaximal, characteristic, complemented
2C2×#16811285C211yesmaximal, characteristic
3#20286823C2116yesmaximal, direct product factor
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810955C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810846C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810780C211yesmaximal, characteristic, complemented
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810693C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#475C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811334—24no—
25#16811334C2218yescomplemented
26#16811285—24no—
27#16811285C2218yes—
28C2×#13133208—21no—
29C2×#13133205—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133197—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133197C2211yescharacteristic
34C2×#13133197C2211yescharacteristic
35C2×#13133193—21no—
36C2×#13133193—21no—
37C2×#13133192—21no—
38C2×#13133192C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×D212—21no—
41C2×C4×D212C2211yescharacteristic
42C2×#13133179—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810985C2218yescomplemented
46#16810955C2218yescomplemented
47#16810943C2218yescomplemented
48#16810882C2218yescomplemented
49#16810853C2218yescomplemented
50#16810846C2218yescomplemented
51#16810788C2218yescomplemented
52#16810780C2218yescomplemented
53#16810728C2218yescomplemented
54#16810693C2218yescomplemented
55C2×#13133148C2211yescharacteristic
56#16810623C2218yescomplemented
57C2×#13133142C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62#103×D53C2218yescomplemented
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#475C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—24no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C22×D212—21no—
89C22×D212—21no—
90C22×D212D411yescharacteristic
91C22×D212C2311yescharacteristic
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C22×C4×D53C2311yescharacteristic
98C2×Dic212—42no—
99C2×Dic212C2314yes—
100C2×#11719925—24no—
101C2×#11719925C2314yes—
102C2×#11719913—42no—
103C2×#11719913C2314yes—
104C2×#11719912—42no—
105C2×#11719912C2314yes—
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C2×C8×D53—42no—
109C2×C8×D53C2314yes—
110#13133208—28no—
111#13133205—22no—
112#13133205—28no—
113#13133205C2314yes—
114#13133197—28no—
115#13133197—22no—
116#13133197—22no—
117#13133197—22no—
118#13133197C2314yes—
119#13133197C2314yes—
120#13133197C2314yes—
121#13133193—28no—
122#13133193—28no—
123#13133192—28no—
124#13133192—22no—
125#13133192C2314yes—
126C4×Dic106—22no—
127C4×Dic106C2314yes—
128C4×D212—28no—
129C4×D212D414yes—
130C4×D212C2314yes—
131#13133179—28no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C4⋊C4×D53—22no—
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C4⋊C4×D53C2314yes—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921D411yescharacteristic
151C2×#11719921D411yescharacteristic
152C2×C4×Dic53—21no—
153#13133148C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133139C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164#13133128C2314yes—
165C22×Q8×C53—21no—
166C22×Q8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53C2311yescharacteristic
180#106×C53C2314yes—
181#106×C53C2314yes—
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—22no—
191C2×Q8×C53—82no—
192C2×Q8×C53#4114yes—
193C2×Q8×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206#11719949—28no—
207#11719949—44no—
208#11719949—48no—
209Q8×D53—28no—
210Q8×D53—44no—
211Q8×D53—48no—
212C2×D212—24no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—24no—
216C2×D212—24no—
217C2×D212—21no—
218C2×D212—44no—
219C2×D212—44no—
220C2×D212C2×D414yes—
221C2×D212C2412yes—
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—24no—
230C2×C4×D53—44no—
231C2×C4×D53—44no—
232C2×C4×D53—82no—
233C2×C4×D53—82no—
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2412yes—
237C2×C4×D53C2412yes—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—22no—
242C2×Dic106—21no—
243C2×Dic106—21no—
244C2×Dic106—24no—
245C2×Dic106—44no—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C42×C53—24no—
261C42×C53C2×D412yes—
262C42×C53C2412yes—
263#11719925—28no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921C2×D414yes—
271#11719921C2×D414yes—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53—24no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2×D414yes—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286Dic212—44no—
287#11719913—44no—
288#11719912—44no—
289C8×D53—44no—
290C23×C53C22×D411yescharacteristic
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53#13714yes—
301C22×D53C22×D412yes—
302C22×D53C22×D412yes—
303Q8×C53—24no—
304Q8×C53—22no—
305Q8×C53—84no—
306Q8×C53C2×#4114yes—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C2×#4112yes—
321C2×C4×C53H(5,𝔽2)12yes—
322C2×C4×C53C2511yescharacteristic
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333D212—28no—
334D212—22no—
335D212—22no—
336D212—48no—
337D212—48no—
338D212—42no—
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—
348C4×D53—84no—
349Dic106—22no—
350Dic106—22no—
351Dic106—22no—
352Dic106—22no—
353Dic106—48no—
354Dic106—42no—
355Dic106—42no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3316—531nomaximal, Sylow
361C22×C53#54612yes—
362C22×C53C2×#13712yes—
363C22×C53#57712yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—22no—
366C2×D53—28no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—44no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—84no—
376C2×D53C2×#13714yes—
377C4×C53—24no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53#54612yes—
384C4×C53C22×#4111yescharacteristic
385C4×C53C2×H(5,𝔽2)11yescharacteristic
386Dic53—22no—
387Dic53—22no—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391C2×#554—531no—
392C2×#548—531no—
393#3316—5316no—
394C2×#489—531no—
395C2×#481—531no—
396C2×#483—531no—
397C2×#475D5311yescharacteristic, complemented
398C2×#470—531no—
399C2×#465—531no—
400C2×#464—531no—
401C2×#452—531no—
402C2×#451—531no—
403C2×#441—531no—
404C2×#435—531no—
405C2×#417—531no—
406C22×#103—531no—
407C2×C53#331614yescomplemented
408C2×C53C2×#54611yescharacteristic
409C2×C53C22×#13711yescharacteristic
410C2×C53C2×#57711yescharacteristic
411D53—24no—
412D53—42no—
413D53—82no—
414C22×#41—531no—
415C23×Q8—531no—
416C22×Q16—531no—
417C22×Q16—531no—
418C22×SD16—531no—
419C22×M16—531no—
420C23×C8—531no—
421#554—538no—
422#554—1064no—
423#548—538no—
424#548—1064no—
425C2×C4⋊Q8C2×D5311yescharacteristic
426C2×#125—1061no—
427C2×#124—531no—
428C2×#124—1061no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C2×C22⋊Q8—1061no—
435C2×#121—531no—
436C2×#121—1061no—
437C2×C4×Q8—531no—
438C2×C4×Q8C2×D5311yescharacteristic
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1061no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444#489—538no—
445#483—538no—
446#481—538no—
447#475C2×D5318yescomplemented
448#470—538no—
449#465—538no—
450#464—538no—
451#452—538no—
452#451—538no—
453#441—538no—
454#435—538no—
455C2×#106—531no—
456C2×#106C2×D5311yescharacteristic
457C2×#106C2×D5311yescharacteristic
458C2×C4⋊C8C2×D5311yescharacteristic
459#417—538no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—538no—
466C2×#103C2×D5311yescharacteristic
467C2×#103C2×D5311yescharacteristic
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×#97—531no—
474C53C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—534no—
476C2×#41—1062no—
477C2×#41—1064no—
478C2×#41—2122no—
479C22×Q8—21no—
480C22×Q8—534no—
481C22×Q8—531no—
482C22×Q8—531no—
483C22×Q8—1061no—
484C22×Q8—1062no—
485C22×Q8—1064no—
486C22×Q8—2122no—
487C22×Q8C22×D5311yescharacteristic
488C22×D4—531no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4—1061no—
492C23×C4—531no—
493C23×C4—531no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1061no—
498C2×Q16—534no—
499C2×Q16—534no—
500C2×Q16—1064no—
501C2×Q16—2122no—
502C2×SD16—534no—
503C2×SD16—2122no—
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—22no—
513C4⋊Q8C22×D5314yes—
514#125—1068no—
515#124—534no—
516#124—1068no—
517#124—1062no—
518C22⋊Q8—534no—
519C22⋊Q8—534no—
520C22⋊Q8—534no—
521C22⋊Q8—1068no—
522C22⋊Q8—1068no—
523C22⋊Q8—1068no—
524C22⋊Q8—1062no—
525C22⋊Q8—1062no—
526C22⋊Q8—1062no—
527#121—534no—
528#121—1062no—
529#121—1068no—
530C4×Q8—22no—
531C4×Q8—534no—
532C4×Q8—1062no—
533C4×Q8C22×D5314yes—
534C4×D4—534no—
535C4×D4—534no—
536C4×D4—1068no—
537C4×D4—1068no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—534no—
543C2×C4⋊C4—534no—
544C2×C4⋊C4—1062no—
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⋊C4C22×D5311yescharacteristic
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—531no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—1061no—
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#106—534no—
567#106C22×D5314yes—
568#106C22×D5314yes—
569C4⋊C8C22×D5314yes—
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—
582#97—534no—
583C24—531no—
584C24—531no—
585C24—1061no—
586#41—1068no—
587#41—2124no—
588#41—2128no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8—532no—
594C2×Q8—532no—
595C2×Q8—1064no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×Q8—1068no—
599C2×Q8—1062no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—1062no—
603C2×Q8—2124no—
604C2×Q8—2124no—
605C2×Q8—2128no—
606C2×Q8#1171994914yes—
607C2×Q8C23×D5312yes—
608C2×D4—534no—
609C2×D4—532no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1064no—
613C2×D4—1061no—
614C2×D4—1062no—
615C2×D4—1062no—
616C2×D4—2124no—
617C2×D4—2124no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—531no—
623C22×C4—531no—
624C22×C4—532no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—532no—
628C22×C4—1064no—
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—4242no—
640C22×C4—4242no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4D4×D5311yescharacteristic
644C22×C4D4×D5311yescharacteristic
645C22×C4C23×D5311yescharacteristic
646Q16—1068no—
647Q16—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—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—534no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1061no—
672C4⋊C4—1064no—
673C4⋊C4C23×D5312yes—
674C4⋊C4C23×D5312yes—
675C4⋊C4C23×D5312yes—
676C22⋊C4—534no—
677C22⋊C4—534no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—24no—
685C42—1064no—
686C42D4×D5312yes—
687C42C23×D5312yes—
688C23—534no—
689C23—532no—
690C23—532no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—1062no—
697C23—2122no—
698C23—2122no—
699C23—2122no—
700C23C2×D4×D5311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—84no—
704Q8—1062no—
705Q8—1062no—
706Q8—1062no—
707Q8—1062no—
708Q8—2128no—
709Q8—2122no—
710Q8—2122no—
711Q8C2×#1171994914yes—
712D4—1068no—
713D4—1062no—
714D4—1062no—
715D4—2128no—
716D4—2128no—
717D4—2122no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—532no—
729C2×C4—532no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1064no—
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—4244no—
743C2×C4—2128no—
744C2×C4—2128no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4C2×D4×D5312yes—
749C2×C4C2×D4×D5312yes—
750C2×C4C2×D4×D5311yescharacteristic
751C2×C4C2×#1171994912yes—
752C2×C4#1313326312yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—534no—
759C22—1068no—
760C22—1062no—
761C22—1062no—
762C22—1062no—
763C22—1062no—
764C22—1062no—
765C22—4244no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22—2124no—
770C22#1681126412yes—
771C22#137×D5312yes—
772C22#1681142912yes—
773C22C22×D4×D5311yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—1062no—
781C4—1062no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126412yes—
786C4C22×#1171994911yescharacteristic
787C4C2×#1313326311yescharacteristic
788C2—1064no—
789C2—4242no—
790C2—2122no—
791C2#2028682314yesdirect product factor
792C2C2×#1681126411yescharacteristic
793C2C2×#137×D5311yescharacteristic
794C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#475C2
socleC23×C53C22×D4
prime radicalC2×#16811285C2
hypercenterC2×#475D53
hypocenterC53C2×#3316
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#16811334C2semidirect
3. #20286823C2direct (N × H)
4. C2×#16810985C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810955C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810846C2semidirect
10. C2×#16810788C2semidirect
11. C2×#16810780C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810693C2semidirect
14. C2×#16810623C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#475C2semidirect
25. #16811334C22semidirect
45. #16810985C22semidirect
46. #16810955C22semidirect
47. #16810943C22semidirect
48. #16810882C22semidirect
49. #16810853C22semidirect
50. #16810846C22semidirect
51. #16810788C22semidirect
52. #16810780C22semidirect
53. #16810728C22semidirect
54. #16810693C22semidirect
56. #16810623C22semidirect
62. #103×D53C22semidirect
71. C53×#475C22semidirect
397. C2×#475D53semidirect
407. C2×C53#3316semidirect
447. #475C2×D53semidirect
474. C53C2×#3316semidirect
791. C2#20286823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113342
C2×#168112852
#202868232
C2×#168109852
C2×#168109432
C2×#168109552
C2×#168108822
C2×#168108532
C2×#168108462
C2×#168107882
C2×#168107802
C2×#168107282
C2×#168106932
C2×#168106232
C2×#103×D532
C2×C53×#4752
C2×#331653