Finite Group Databasebeta

← C2×#20286827 #28260683

Subgroups — C2×#20286827 #28260683

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×#16811328C211yesmaximal, characteristic, complemented
2C2×#16811280C211yesmaximal, characteristic
3#20286827C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810953C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810881C211yesmaximal, characteristic, complemented
9C2×#16810851C211yesmaximal, characteristic, complemented
10C2×#16810844C211yesmaximal, characteristic, complemented
11C2×#16810785C211yesmaximal, characteristic, complemented
12C2×#16810780C211yesmaximal, characteristic, complemented
13C2×#16810727C211yesmaximal, characteristic, complemented
14C2×#16810692C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#417C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811328—24no—
23#16811328C2218yescomplemented
24#16811280—24no—
25#16811280C2218yes—
26C2×#13133216C2211yescharacteristic
27C2×#13133207—21no—
28C2×#13133204—21no—
29C2×#13133204C2211yescharacteristic
30C2×#13133197C2211yescharacteristic
31C2×#13133196—21no—
32C2×#13133196—21no—
33C2×#13133196C2211yescharacteristic
34C2×#13133196C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133188—21no—
37C2×#13133188C2211yescharacteristic
38C2×Q8×Dic53C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×C4×C22⋊D53—21no—
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810981C2218yescomplemented
45#16810953C2218yescomplemented
46#16810940C2218yescomplemented
47#16810906C2218yescomplemented
48#16810881C2218yescomplemented
49#16810851C2218yescomplemented
50#16810844C2218yescomplemented
51#16810785C2218yescomplemented
52#16810780C2218yescomplemented
53#16810727C2218yescomplemented
54#16810692C2218yescomplemented
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64#103×D53C2218yescomplemented
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C53×#417C2218yescomplemented
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53—42no—
84C2×Q8×D53C2314yes—
85C22×C22⋊D53—21no—
86C22×C22⋊D53D411yescharacteristic
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53C2311yescharacteristic
90C2×Dic212—42no—
91C2×Dic212C2314yes—
92C2×#11719925—24no—
93C2×#11719925C2314yes—
94C2×#11719923—42no—
95C2×#11719923C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C2×C8×D53—42no—
99C2×C8×D53C2314yes—
100#13133216—22no—
101#13133216C2314yes—
102#13133207—28no—
103#13133204—28no—
104#13133204—22no—
105#13133204C2314yes—
106#13133197—22no—
107#13133197C2314yes—
108#13133196—28no—
109#13133196—28no—
110#13133196—22no—
111#13133196—22no—
112#13133196C2314yes—
113#13133196C2314yes—
114#13133195—28no—
115#13133188—28no—
116#13133188—22no—
117#13133188C2314yes—
118Q8×Dic53—22no—
119Q8×Dic53C2314yes—
120#13133182—22no—
121#13133182C2314yes—
122C4×C22⋊D53—28no—
123C4×C22⋊D53—28no—
124C4×C22⋊D53D414yes—
125C4×C22⋊D53C2314yes—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C4⋊C4×D53—22no—
137C4⋊C4×D53C2314yes—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
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×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133149C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133138C2314yes—
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161#13133127C2314yes—
162C2×#41×C53—22no—
163C2×#41×C53—24no—
164C2×#41×C53—42no—
165C2×#41×C53C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C2×M16×C53—42no—
173C2×M16×C53C2314yes—
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2311yescharacteristic
176C2×C4⋊C4×C53—22no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181#103×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188#41×C53—28no—
189#41×C53—44no—
190#41×C53—48no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53#4114yes—
194C2×Q8×C53C2412yes—
195C2×D4×C53—24no—
196C2×D4×C53—21no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—44no—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—24no—
207C22×C4×C53—24no—
208C22×C4×C53—44no—
209C22×C4×C53—82no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53C2×D414yes—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225Q8×D53—28no—
226Q8×D53—44no—
227Q8×D53—48no—
228C2×C4×D53—22no—
229C2×C4×D53—22no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—44no—
233C2×C4×D53—82no—
234C2×C4×D53C2×D412yes—
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—82no—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248M16×C53—44no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53C2×D414yes—
264#11719925—28no—
265#11719923—44no—
266#11719921—24no—
267#11719921C2×D414yes—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—24no—
271C4⋊Dic53—24no—
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×#88322C2412yes—
287C2×#88322C2412yes—
288Dic212—44no—
289C8×D53—44no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53C22×D412yes—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—22no—
301C22×D53#13714yes—
302C22×D53C22×D412yes—
303Q8×C53—24no—
304Q8×C53—22no—
305Q8×C53C2×#4114yes—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—48no—
309D4×C53—42no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—24no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—48no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—84no—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—28no—
328C22⋊D53—48no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343C4×D53—24no—
344C4×D53—22no—
345C4×D53—22no—
346C4×D53—48no—
347C4×D53—84no—
348Dic106—22no—
349Dic106—22no—
350Dic106—22no—
351Dic106—22no—
352Dic106—48no—
353Dic106—42no—
354Dic106—42no—
355Dic106—84no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3316—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—44no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—84no—
369C22×C53#54612yes—
370C22×C53C2×#13712yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—22no—
374C2×D53—28no—
375C2×D53—22no—
376C2×D53C2×#13714yes—
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×#554—531no—
392C2×#548—531no—
393#3316—5316no—
394C2×#489—531no—
395C2×#481—531no—
396C2×#483—531no—
397C2×#475—531no—
398C2×#470—531no—
399C2×#465—531no—
400C2×#464—531no—
401C2×#452—531no—
402C2×#451—531no—
403C2×#441—531no—
404C2×#435—531no—
405C2×#417D5311yescharacteristic, complemented
406C22×#103—531no—
407C2×C53—42no—
408C2×C53—82no—
409C2×C53#331614yescomplemented
410C2×C53C2×#54611yescharacteristic
411C2×C53C22×#13711yescharacteristic
412C2×C53C2×#57711yescharacteristic
413D53—24no—
414C22×#41C2×D5311yescharacteristic
415C23×Q8—531no—
416C22×Q16—531no—
417C22×Q16—531no—
418C22×SD16—531no—
419C22×M16C2×D5311yescharacteristic
420C23×C8—531no—
421#554—538no—
422#554—1064no—
423#548—538no—
424#548—1064no—
425C2×C4⋊Q8—531no—
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×Q8—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1061no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4C2×D5311yescharacteristic
444#489—538no—
445#483—538no—
446#481—538no—
447#475—538no—
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×#106—531no—
457C2×#106—531no—
458C2×C4⋊C8—531no—
459#417C2×D5318yescomplemented
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×#102C2×D5311yescharacteristic
470C2×#102C2×D5311yescharacteristic
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×#97—531no—
474C53C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D5314yes—
479C22×Q8—534no—
480C22×Q8—531no—
481C22×Q8—531no—
482C22×Q8—1061no—
483C22×Q8—1061no—
484C22×Q8—1062no—
485C22×Q8—1064no—
486C22×Q8—2122no—
487C22×Q8C22×D5311yescharacteristic
488C22×D4—21no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—531no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4C22×D5311yescharacteristic
498C2×Q16—534no—
499C2×Q16—534no—
500C2×Q16—1064no—
501C2×Q16—2122no—
502C2×SD16—534no—
503C2×SD16—2122no—
504C2×M16—42no—
505C2×M16C22×D5314yes—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8—534no—
509C22×C8—2122no—
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5311yescharacteristic
512C4⋊Q8—534no—
513C4⋊Q8—1062no—
514#125—1068no—
515#124—534no—
516#124—1062no—
517#124—1068no—
518C22⋊Q8—534no—
519C22⋊Q8—534no—
520C22⋊Q8—534no—
521C22⋊Q8—1068no—
522C22⋊Q8—1068no—
523C22⋊Q8—1062no—
524C22⋊Q8—1068no—
525C22⋊Q8—1062no—
526C22⋊Q8—1062no—
527#121—534no—
528#121—1062no—
529#121—1068no—
530C4×Q8—534no—
531C4×Q8—534no—
532C4×Q8—1062no—
533C4×Q8—1062no—
534C4×D4—534no—
535C4×D4—534no—
536C4×D4—1068no—
537C4×D4—1068no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—534no—
544C2×C4⋊C4—1062no—
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⋊C4C22×D5311yescharacteristic
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C4⋊C4C22×D5314yes—
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—531no—
564C2×C42—1061no—
565C2×C42—1061no—
566#106—534no—
567#106—534no—
568#106—534no—
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#102C22×D5314yes—
579#102C22×D5314yes—
580C22⋊C8—534no—
581C22⋊C8—534no—
582#97—534no—
583C24—21no—
584C24—531no—
585C24D4×D5311yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—532no—
592C2×Q8—532no—
593C2×Q8—1064no—
594C2×Q8—1064no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1068no—
598C2×Q8—1062no—
599C2×Q8—1062no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—4242no—
603C2×Q8—2124no—
604C2×Q8—2124no—
605C2×Q8—2128no—
606C2×Q8#1171994514yes—
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—2124no—
617C2×D4C23×D5312yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—44no—
626C22×C4—82no—
627C22×C4—531no—
628C22×C4—531no—
629C22×C4—531no—
630C22×C4—532no—
631C22×C4—532no—
632C22×C4—1064no—
633C22×C4—1064no—
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×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646Q16—1068no—
647Q16—2124no—
648SD16—2124no—
649M16—44no—
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—24no—
661C4⋊C4—21no—
662C4⋊C4—534no—
663C4⋊C4—532no—
664C4⋊C4—532no—
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—1064no—
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—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—534no—
696C23—532no—
697C23—1062no—
698C23—1062no—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—1062no—
704Q8—1062no—
705Q8—1062no—
706Q8—1062no—
707Q8—4244no—
708Q8—2128no—
709Q8—2122no—
710Q8—2122no—
711Q8C2×#1171994514yes—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—1068no—
717D4—2128no—
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—84no—
730C2×C4—532no—
731C2×C4—532no—
732C2×C4—532no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1064no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
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×#1171994512yes—
752C2×C4#1313326212yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—534no—
767C22—1068no—
768C22—1062no—
769C22—1062no—
770C22#1681126312yes—
771C22#137×D5312yes—
772C22#1681143312yes—
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#1681126312yes—
786C4C22×#1171994511yescharacteristic
787C4C2×#1313326211yescharacteristic
788C2—42no—
789C2—82no—
790C2—1064no—
791C2#2028682714yesdirect product factor
792C2C2×#1681126311yescharacteristic
793C2C2×#137×D5311yescharacteristic
794C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#417C2
socleC23×C53C22×D4
prime radicalC2×#16811280C2
hypercenterC2×#417D53
hypocenterC53C2×#3316
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16811328C2semidirect
3. #20286827C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810953C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810881C2semidirect
9. C2×#16810851C2semidirect
10. C2×#16810844C2semidirect
11. C2×#16810785C2semidirect
12. C2×#16810780C2semidirect
13. C2×#16810727C2semidirect
14. C2×#16810692C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#417C2semidirect
23. #16811328C22semidirect
44. #16810981C22semidirect
45. #16810953C22semidirect
46. #16810940C22semidirect
47. #16810906C22semidirect
48. #16810881C22semidirect
49. #16810851C22semidirect
50. #16810844C22semidirect
51. #16810785C22semidirect
52. #16810780C22semidirect
53. #16810727C22semidirect
54. #16810692C22semidirect
64. #103×D53C22semidirect
72. C53×#417C22semidirect
405. C2×#417D53semidirect
409. C2×C53#3316semidirect
459. #417C2×D53semidirect
474. C53C2×#3316semidirect
791. C2#20286827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112802
#202868272
C2×#168109812
C2×#168109402
C2×#168109532
C2×#168109062
C2×#168108812
C2×#168108512
C2×#168108442
C2×#168107852
C2×#168107802
C2×#168107272
C2×#168106922
C2×#103×D532
C2×C53×#4172
C2×#331653