Finite Group Databasebeta

← C2×#20286228 #28259076

Subgroups — C2×#20286228 #28259076

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133248C211yesmaximal, characteristic, complemented
2C22×SD16×D53C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
4C2×#16811270C211yesmaximal, characteristic
5#20286228C2116yesmaximal, direct product factor
6C2×#16811014C211yesmaximal, characteristic, complemented
7C2×#16810867C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810843C211yesmaximal, characteristic, complemented
10C2×#16810827C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810780C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810726C211yesmaximal, characteristic, complemented
15C2×#16810697C211yesmaximal, characteristic, complemented
16C2×C53×#448C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C2×#13133248—28no—
21C2×#13133248C2218yescomplemented
22C22×Dic212C2211yescharacteristic, complemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719925C2211yescharacteristic, complemented
25C22×#11719913C2211yescharacteristic
26C22×#11719923C2211yescharacteristic
27C22×#11719924C2211yescharacteristic
28C22×#11719924C2211yescharacteristic
29C2×SD16×D53—28no—
30C2×SD16×D53C2218yescomplemented
31C22×#11719917C2211yescharacteristic, complemented
32C22×C8×D53C2211yescharacteristic
33Q8×C22⋊D53—24no—
34Q8×C22⋊D53C2218yescomplemented
35#16811270—24no—
36#16811270C2218yes—
37C2×#13133215—21no—
38C2×#13133215C2211yescharacteristic, complemented
39C2×#13133204C2211yescharacteristic
40C2×#13133199—21no—
41C2×#13133197C2211yescharacteristic
42C2×#13133196—21no—
43C2×#13133196C2211yescharacteristic, complemented
44C2×#13133193—21no—
45C2×#13133193C2211yescharacteristic
46C2×#13133188—21no—
47C2×#13133185—21no—
48C2×Q8×Dic53C2211yescharacteristic, complemented
49C2×#13133179C2211yescharacteristic
50C2×C4×C22⋊D53—21no—
51C2×C4×C22⋊D53C2211yescharacteristic
52C2×C22⋊C4×D53—21no—
53#16811014C2218yescomplemented
54#16810867C2218yescomplemented
55#16810863C2218yescomplemented
56#16810843C2218yescomplemented
57#16810827C2218yescomplemented
58#16810787C2218yescomplemented
59#16810780C2218yescomplemented
60#16810772C2218yescomplemented
61#16810726C2218yescomplemented
62#16810697C2218yescomplemented
63C2×#13133150C2211yescharacteristic, complemented
64C2×#13133146C2211yescharacteristic, complemented
65C2×#13133142C2211yescharacteristic, complemented
66C2×#13133140C2211yescharacteristic, complemented
67C2×#13133139C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C2×#13133129C2211yescharacteristic
70C2×#13133127C2211yescharacteristic, complemented
71C23×Q8×C53C2211yescharacteristic, complemented
72C22×SD16×C53C2211yescharacteristic
73C22×SD16×C53C2211yescharacteristic
74C2×#121×C53C2211yescharacteristic
75C53×#448C2218yescomplemented
76C2×#103×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×C22⋊C8×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719945—22no—
81C2×#11719945—24no—
82C2×#11719945—42no—
83C2×#11719945C2314yes—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C2×Q8×D53—22no—
88C2×Q8×D53—24no—
89C2×Q8×D53—42no—
90C2×Q8×D53C2314yes—
91C22×D212C2311yescharacteristic
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53D411yescharacteristic
95C2×D4×D53—24no—
96C2×D4×D53—22no—
97C2×D4×D53—42no—
98C2×D4×D53C2314yes—
99C22×C4×D53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C22×C4×D53C2311yescharacteristic
103#13133248—232no—
104C2×Dic212—42no—
105C2×Dic212C2314yescomplemented
106C2×#11719925—24no—
107C2×#11719925—24no—
108C2×#11719925C2314yescomplemented
109C2×#11719925C2314yescomplemented
110C2×#11719913—24no—
111C2×#11719913C2314yes—
112C2×#11719923—24no—
113C2×#11719923C2314yes—
114C2×#11719924—24no—
115C2×#11719924D418yescomplemented
116C2×#11719924C2314yes—
117C2×#11719924C2314yes—
118SD16×D53—232no—
119C2×#11719917—24no—
120C2×#11719917C2314yescomplemented
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C2×C8×D53—24no—
124C2×C8×D53C2314yes—
125#13133215—28no—
126#13133215—22no—
127#13133215C2314yescomplemented
128#13133204—22no—
129#13133204C2314yes—
130#13133199—28no—
131#13133197—22no—
132#13133197C2314yes—
133#13133196—28no—
134#13133196—22no—
135#13133196C2314yescomplemented
136#13133193—28no—
137#13133193—22no—
138#13133193C2314yes—
139#13133188—28no—
140#13133185—28no—
141Q8×Dic53—22no—
142Q8×Dic53C2314yescomplemented
143#13133179—22no—
144#13133179C2314yes—
145C4×C22⋊D53—28no—
146C4×C22⋊D53D414yes—
147C4×C22⋊D53C2314yes—
148C2×C4⋊Dic53—21no—
149C2×C4⋊Dic53—21no—
150C2×C4⋊Dic53C2311yescharacteristic
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919—21no—
154C2×#11719919—21no—
155C2×#11719919D411yescharacteristic
156C2×C22⋊Dic53—21no—
157C2×C22⋊Dic53—21no—
158C2×C22⋊Dic53—21no—
159C2×C22⋊Dic53D411yescharacteristic
160C2×#11719921—21no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C2×#11719921D411yescharacteristic
164C22⋊C4×D53—28no—
165C2×C4×Dic53—21no—
166C2×C4×Dic53C2311yescharacteristic
167#13133150C2314yescomplemented
168#13133146C2314yescomplemented
169#13133142C2314yescomplemented
170#13133140C2314yescomplemented
171#13133139C2314yes—
172#13133138C2314yes—
173#13133129C2314yes—
174#13133127C2314yescomplemented
175C22×Q8×C53—22no—
176C22×Q8×C53—21no—
177C22×Q8×C53—24no—
178C22×Q8×C53—42no—
179C22×Q8×C53C2311yescharacteristic
180C22×Q8×C53C2311yescharacteristic
181C22×Q8×C53C2314yescomplemented
182C22×D4×C53—21no—
183C22×D4×C53C2311yescharacteristic
184C23×C4×C53—21no—
185C23×C4×C53C2311yescharacteristic
186C2×SD16×C53—24no—
187C2×SD16×C53—42no—
188C2×SD16×C53C2314yes—
189C2×SD16×C53C2314yes—
190C22×C8×C53C2311yescharacteristic
191C22×C8×C53C2311yescharacteristic
192#121×C53—22no—
193#121×C53C2314yes—
194C2×C4⋊C4×C53C2311yescharacteristic
195C2×C22⋊C4×C53—21no—
196#103×C53C2314yescomplemented
197#103×C53C2314yescomplemented
198C22⋊C8×C53C2314yescomplemented
199C24×C53—21no—
200C24×C53C2×D411yescharacteristic
201C23×D53—21no—
202C23×D53—24no—
203C23×D53—44no—
204C23×D53—44no—
205C23×D53—82no—
206C23×D53C2×D411yescharacteristic
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53—24no—
210C2×Q8×C53—22no—
211C2×Q8×C53—28no—
212C2×Q8×C53—22no—
213C2×Q8×C53—22no—
214C2×Q8×C53—44no—
215C2×Q8×C53—44no—
216C2×Q8×C53—48no—
217C2×Q8×C53C2×D414yes—
218C2×Q8×C53C2412yes—
219C2×Q8×C53C2412yes—
220C2×D4×C53—24no—
221C2×D4×C53—22no—
222C2×D4×C53—21no—
223C2×D4×C53—22no—
224C2×D4×C53—82no—
225C2×D4×C53C2412yes—
226C22×C4×C53—21no—
227C22×C4×C53—22no—
228C22×C4×C53—22no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—24no—
232C22×C4×C53—44no—
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2412yes—
236C22×C4×C53C2411yescharacteristic
237C2×C22⋊D53—24no—
238C2×C22⋊D53—24no—
239C2×C22⋊D53—24no—
240C2×C22⋊D53—44no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53C2×D414yes—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53C2×D411yescharacteristic
247C22×Dic53C2×D411yescharacteristic
248C22×Dic53C2×D411yescharacteristic
249Q8×D53—28no—
250Q8×D53—44no—
251Q8×D53—48no—
252D4×D53—28no—
253D4×D53—44no—
254D4×D53—48no—
255#11719945—28no—
256#11719945—44no—
257#11719945—48no—
258C2×D212—21no—
259C2×D212—22no—
260C2×D212C2×D414yes—
261C2×D212C2412yes—
262C2×C4×D53—22no—
263C2×C4×D53—22no—
264C2×C4×D53—24no—
265C2×C4×D53—24no—
266C2×C4×D53—24no—
267C2×C4×D53—44no—
268C2×C4×D53—44no—
269C2×C4×D53—82no—
270C2×C4×D53C2×D412yes—
271C2×C4×D53C2412yes—
272C2×Dic106—22no—
273C2×Dic106—22no—
274C2×Dic106—22no—
275C2×Dic106—22no—
276C2×Dic106—21no—
277C2×Dic106—21no—
278C2×Dic106—24no—
279C2×Dic106—44no—
280C2×Dic106C2412yes—
281C2×Dic106C2412yes—
282SD16×C53—28no—
283SD16×C53—44no—
284C2×C8×C53—22no—
285C2×C8×C53—22no—
286C2×C8×C53C2412yes—
287C2×C8×C53C2412yes—
288C4⋊C4×C53—21no—
289C4⋊C4×C53C2412yes—
290C22⋊C4×C53—24no—
291C22⋊Dic53—24no—
292C22⋊Dic53—24no—
293C22⋊Dic53—24no—
294C22⋊Dic53C2×D414yes—
295#11719925—28no—
296#11719925—28no—
297#11719924—28no—
298#11719924C2×D4116yescomplemented
299#11719923—28no—
300#11719921—24no—
301#11719921—24no—
302#11719921—24no—
303#11719921C2×D414yes—
304C4⋊Dic53—21no—
305C4⋊Dic53—24no—
306C4⋊Dic53—24no—
307C4⋊Dic53C2412yes—
308#11719919—24no—
309#11719919—24no—
310#11719919—24no—
311#11719919—24no—
312#11719919C2×D414yes—
313C4×Dic53—24no—
314C4×Dic53C2×D412yes—
315C4×Dic53C2412yes—
316#11719917—28no—
317C2×#88322—22no—
318C2×#88322C2×D414yes—
319C2×#88322C2412yes—
320C2×#88322C2412yes—
321Dic212—44no—
322#11719913—28no—
323C8×D53—28no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—42no—
329C23×C53—42no—
330C23×C53—42no—
331C23×C53C22×D412yes—
332C23×C53C22×D411yescharacteristic
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—24no—
336C22×D53—22no—
337C22×D53—48no—
338C22×D53—42no—
339C22×D53—42no—
340C22×D53—48no—
341C22×D53—84no—
342C22×D53—816no—
343C22×D53#13714yescomplemented
344C22×D53C22×D412yes—
345Q8×C53—24no—
346Q8×C53—22no—
347Q8×C53—22no—
348Q8×C53—22no—
349Q8×C53—48no—
350Q8×C53—42no—
351Q8×C53C22×D414yes—
352D4×C53—22no—
353D4×C53—22no—
354D4×C53—42no—
355D4×C53—84no—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—24no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—48no—
365C2×C4×C53—42no—
366C2×C4×C53—42no—
367C2×C4×C53C22×D412yes—
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C22×D412yes—
370C2×C4×C53H(5,𝔽2)12yes—
371C2×C4×C53C2511yescharacteristic
372C22⋊D53—28no—
373C22⋊D53—48no—
374C22⋊D53—48no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—42no—
382C2×Dic53—42no—
383C2×Dic53—42no—
384C2×Dic53C22×D412yes—
385C2×Dic53C22×D412yes—
386C2×Dic53C22×D412yes—
387D212—24no—
388D212—22no—
389D212C22×D414yes—
390C4×D53—24no—
391C4×D53—22no—
392C4×D53—22no—
393C4×D53—48no—
394C4×D53—48no—
395C4×D53—84no—
396Dic106—22no—
397Dic106—22no—
398Dic106—22no—
399Dic106—22no—
400Dic106—48no—
401Dic106—42no—
402Dic106—42no—
403C8×C53—22no—
404C8×C53—22no—
405#88322—22no—
406#88322C22×D414yes—
407C2×#3266—531nomaximal, Sylow
408C22×C53—22no—
409C22×C53—22no—
410C22×C53—22no—
411C22×C53—44no—
412C22×C53—42no—
413C22×C53—42no—
414C22×C53—42no—
415C22×C53—84no—
416C22×C53D4212yes—
417C22×C53C2×#13712yes—
418C22×C53#57712yes—
419C22×C53C23×D411yescharacteristic
420C2×D53—22no—
421C2×D53—28no—
422C2×D53—22no—
423C2×D53—24no—
424C2×D53—48no—
425C2×D53—42no—
426C2×D53—42no—
427C2×D53—816no—
428C2×D53C2×#13714yescomplemented
429C4×C53—24no—
430C4×C53—22no—
431C4×C53—42no—
432C4×C53—42no—
433C4×C53D4212yes—
434C4×C53C23×D411yescharacteristic
435C4×C53C2×H(5,𝔽2)11yescharacteristic
436Dic53—22no—
437Dic53—22no—
438Dic53—22no—
439Dic53—42no—
440Dic53—42no—
441Dic53—42no—
442C22×#137—531no—
443C23×SD16—531no—
444C2×D4×Q8—531no—
445C2×#546—531no—
446#3266—5316no—
447C2×#497—531no—
448C2×#468—531no—
449C2×#467—531no—
450C2×#464—531no—
451C2×#461—531no—
452C2×#452—531no—
453C2×#451—531no—
454C2×#448D5311yescharacteristic, complemented
455C2×#450—531no—
456C2×#440—531no—
457C2×#435—531no—
458C2×C53—42no—
459C2×C53—82no—
460C2×C53#326614yescomplemented
461C2×C53C2×D4211yescharacteristic
462C2×C53C22×#13711yescharacteristic
463C2×C53C2×#57711yescharacteristic
464D53—24no—
465D53—44no—
466C22×#41—531no—
467C23×Q8—531no—
468C23×Q8C2×D5311yescharacteristic, complemented
469C23×D4—531no—
470C2×#137—538no—
471C2×#137—1068no—
472C22×Q16—531no—
473C22×Q16—531no—
474C22×Q16—531no—
475C22×SD16—531no—
476C22×SD16—531no—
477C22×SD16—531no—
478C22×SD16—538no—
479C22×SD16—531no—
480C22×SD16—1068no—
481C22×SD16C2×D5311yescharacteristic
482C22×SD16C2×D5311yescharacteristic
483C22×M16—531no—
484C23×C8—531no—
485D4×Q8—538no—
486D4×Q8—1064no—
487#546—538no—
488#546—1064no—
489C2×C4⋊Q8—531no—
490C2×C4⋊Q8—1061no—
491C2×#124—531no—
492C2×#123—1061no—
493C2×C22⋊Q8—531no—
494C2×C22⋊Q8—531no—
495C2×C22⋊Q8—531no—
496C2×C22⋊Q8—1061no—
497C2×C22⋊Q8—1061no—
498C2×#121—1061no—
499C2×#121C2×D5311yescharacteristic
500C2×#120—1061no—
501C2×C4×Q8—531no—
502C2×C4×D4—531no—
503C2×C4×D4—531no—
504C2×C4×D4—1061no—
505C22×C22⋊C4—1061no—
506#497—538no—
507#468—538no—
508#467—538no—
509#464—538no—
510#461—538no—
511#452—538no—
512#451—538no—
513#450—538no—
514#448C2×D5318yescomplemented
515#440—538no—
516#435—538no—
517C2×#107—531no—
518C2×C4⋊C8—531no—
519C2×#103—531no—
520C2×#103—531no—
521C2×#103C2×D5311yescharacteristic, complemented
522C2×#103C2×D5311yescharacteristic, complemented
523C2×#102—531no—
524C2×#102—531no—
525C2×C22⋊C8—531no—
526C2×C22⋊C8C2×D5311yescharacteristic, complemented
527C2×#97—531no—
528C53C2×#326611yescharacteristic, complemented, Sylow
529C25—1061no—
530C2×#41—534no—
531C2×#41—1064no—
532C2×#41—1062no—
533C2×#41—2122no—
534C22×Q8—21no—
535C22×Q8—22no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—534no—
539C22×Q8—531no—
540C22×Q8—531no—
541C22×Q8—1061no—
542C22×Q8—1062no—
543C22×Q8—1064no—
544C22×Q8—2122no—
545C22×Q8C22×D5311yescharacteristic
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5314yescomplemented
548C22×D4—21no—
549C22×D4—531no—
550C22×D4—534no—
551C22×D4—531no—
552C22×D4—1062no—
553C22×D4—1061no—
554C22×D4—1064no—
555C22×D4—1061no—
556C22×D4—2122no—
557C22×D4C22×D5311yescharacteristic
558C23×C4—21no—
559C23×C4—531no—
560C23×C4—1061no—
561C23×C4—1061no—
562C23×C4—1061no—
563C23×C4C22×D5311yescharacteristic
564#137—10632no—
565C2×Q16—534no—
566C2×Q16—534no—
567C2×Q16—534no—
568C2×Q16—1064no—
569C2×Q16—1064no—
570C2×Q16—2122no—
571C2×SD16—24no—
572C2×SD16—42no—
573C2×SD16—538no—
574C2×SD16—534no—
575C2×SD16—534no—
576C2×SD16—534no—
577C2×SD16—534no—
578C2×SD16—1064no—
579C2×SD16—1064no—
580C2×SD16—10632no—
581C2×SD16—1064no—
582C2×SD16C22×D5314yes—
583C2×SD16C22×D5314yes—
584C2×M16—534no—
585C2×M16—1064no—
586C22×C8—531no—
587C22×C8—531no—
588C22×C8—534no—
589C22×C8—1064no—
590C22×C8C22×D5311yescharacteristic
591C22×C8C22×D5311yescharacteristic
592C4⋊Q8—534no—
593C4⋊Q8—1062no—
594C4⋊Q8—1068no—
595#124—534no—
596#124—1062no—
597#123—1068no—
598C22⋊Q8—534no—
599C22⋊Q8—534no—
600C22⋊Q8—534no—
601C22⋊Q8—1068no—
602C22⋊Q8—1068no—
603C22⋊Q8—1062no—
604C22⋊Q8—1062no—
605C22⋊Q8—1062no—
606#121—22no—
607#121—1068no—
608#121C22×D5314yes—
609#120—1068no—
610C4×Q8—534no—
611C4×Q8—1062no—
612C4×D4—534no—
613C4×D4—534no—
614C4×D4—534no—
615C4×D4—1062no—
616C4×D4—1068no—
617C2×C4⋊C4—531no—
618C2×C4⋊C4—531no—
619C2×C4⋊C4—1061no—
620C2×C4⋊C4—1061no—
621C2×C4⋊C4—1061no—
622C2×C4⋊C4—1061no—
623C2×C4⋊C4—1061no—
624C2×C4⋊C4—1061no—
625C2×C4⋊C4C22×D5311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—531no—
628C2×C22⋊C4—531no—
629C2×C22⋊C4—1068no—
630C2×C22⋊C4—1061no—
631C2×C22⋊C4—1061no—
632C2×C22⋊C4—1061no—
633C2×C22⋊C4—1061no—
634C2×C22⋊C4—1061no—
635C2×C22⋊C4—1061no—
636C2×C42—531no—
637C2×C42—1061no—
638#107—534no—
639C4⋊C8—534no—
640#103—534no—
641#103—534no—
642#103C22×D5314yescomplemented
643#103C22×D5314yescomplemented
644#102—534no—
645#102—534no—
646C22⋊C8—534no—
647C22⋊C8C22×D5314yescomplemented
648#97—534no—
649C24—21no—
650C24—531no—
651C24—1064no—
652C24—1061no—
653C24—4242no—
654C24—2124no—
655C24—2124no—
656C24D4×D5311yescharacteristic
657#41—1068no—
658#41—2124no—
659#41—2128no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—22no—
664C2×Q8—28no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—48no—
670C2×Q8—532no—
671C2×Q8—532no—
672C2×Q8—1064no—
673C2×Q8—1061no—
674C2×Q8—1061no—
675C2×Q8—1068no—
676C2×Q8—1062no—
677C2×Q8—1062no—
678C2×Q8—1062no—
679C2×Q8—1062no—
680C2×Q8—2124no—
681C2×Q8—2124no—
682C2×Q8—2128no—
683C2×Q8D4×D5314yes—
684C2×Q8C23×D5312yes—
685C2×Q8C23×D5312yes—
686C2×D4—24no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—82no—
691C2×D4—534no—
692C2×D4—534no—
693C2×D4—532no—
694C2×D4—1064no—
695C2×D4—1068no—
696C2×D4—1064no—
697C2×D4—1064no—
698C2×D4—1061no—
699C2×D4—1062no—
700C2×D4—2124no—
701C2×D4—2128no—
702C2×D4—2124no—
703C2×D4—2124no—
704C2×D4C23×D5312yes—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—44no—
712C22×C4—531no—
713C22×C4—531no—
714C22×C4—531no—
715C22×C4—532no—
716C22×C4—532no—
717C22×C4—1064no—
718C22×C4—1064no—
719C22×C4—1062no—
720C22×C4—1062no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1064no—
725C22×C4—4242no—
726C22×C4—2124no—
727C22×C4—2124no—
728C22×C4D4×D5312yes—
729C22×C4D4×D5311yescharacteristic
730C22×C4C23×D5312yes—
731C22×C4C23×D5311yescharacteristic
732Q16—1068no—
733Q16—1068no—
734Q16—2124no—
735SD16—28no—
736SD16—44no—
737SD16—5316no—
738SD16—1068no—
739SD16—1068no—
740SD16—1068no—
741M16—1068no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—534no—
745C2×C8—532no—
746C2×C8—532no—
747C2×C8—1068no—
748C2×C8—1062no—
749C2×C8C23×D5312yes—
750C2×C8C23×D5312yes—
751C4⋊C4—21no—
752C4⋊C4—534no—
753C4⋊C4—532no—
754C4⋊C4—1064no—
755C4⋊C4—1064no—
756C4⋊C4—1064no—
757C4⋊C4—1064no—
758C4⋊C4—1064no—
759C4⋊C4—1061no—
760C4⋊C4—1064no—
761C4⋊C4C23×D5312yes—
762C22⋊C4—24no—
763C22⋊C4—534no—
764C22⋊C4—534no—
765C22⋊C4—1064no—
766C22⋊C4—1064no—
767C22⋊C4—1064no—
768C22⋊C4—1064no—
769C22⋊C4—1064no—
770C22⋊C4—1064no—
771C42—532no—
772C42—532no—
773C42—1064no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—534no—
782C23—532no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—1064no—
787C23—4244no—
788C23—42416no—
789C23—2128no—
790C23—2128no—
791C23—2122no—
792C23—2122no—
793C23C2×D4×D5312yes—
794C23C2×D4×D5311yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—22no—
798Q8—22no—
799Q8—48no—
800Q8—42no—
801Q8—1062no—
802Q8—1062no—
803Q8—1062no—
804Q8—1062no—
805Q8—2128no—
806Q8—2122no—
807Q8—2122no—
808Q8C2×D4×D5314yes—
809D4—22no—
810D4—22no—
811D4—42no—
812D4—84no—
813D4—534no—
814D4—1068no—
815D4—1062no—
816D4—1064no—
817D4—2128no—
818D4—2128no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—48no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—532no—
831C2×C4—532no—
832C2×C4—532no—
833C2×C4—1062no—
834C2×C4—1062no—
835C2×C4—1062no—
836C2×C4—1062no—
837C2×C4—1062no—
838C2×C4—1064no—
839C2×C4—1062no—
840C2×C4—1062no—
841C2×C4—1062no—
842C2×C4—4244no—
843C2×C4—2128no—
844C2×C4—2128no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4—2122no—
848C2×C4C2×D4×D5312yes—
849C2×C4C2×D4×D5312yes—
850C2×C4C2×D4×D5311yescharacteristic
851C2×C4#1313326212yes—
852C2×C4C24×D5311yescharacteristic
853C8—22no—
854C8—22no—
855C8—534no—
856C8—1062no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—84no—
865C22—534no—
866C22—1068no—
867C22—1062no—
868C22—1062no—
869C22—1064no—
870C22—42416no—
871C22—2128no—
872C22—2122no—
873C22—2122no—
874C22#1681125512yes—
875C22#137×D5312yes—
876C22#1681142912yes—
877C22C22×D4×D5311yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—1062no—
883C4—1062no—
884C4—1062no—
885C4—2122no—
886C4—2122no—
887C4—2122no—
888C4#1681125512yes—
889C4C22×D4×D5311yescharacteristic
890C4C2×#1313326211yescharacteristic
891C2—42no—
892C2—82no—
893C2—1064no—
894C2—2124no—
895C2#2028622814yesdirect product factor
896C2C2×#1681125511yescharacteristic
897C2C2×#137×D5311yescharacteristic
898C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#448C2
socleC23×C53C22×D4
prime radicalC2×#16811270C2
hypercenterC2×#448D53
hypocenterC53C2×#3266
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
1. C22×#13133248C2semidirect
2. C22×SD16×D53C2semidirect
3. C2×Q8×C22⋊D53C2semidirect
5. #20286228C2direct (N × H)
6. C2×#16811014C2semidirect
7. C2×#16810867C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810843C2semidirect
10. C2×#16810827C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810780C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810726C2semidirect
15. C2×#16810697C2semidirect
16. C2×C53×#448C2semidirect
21. C2×#13133248C22semidirect
22. C22×Dic212C22semidirect
23. C22×#11719925C22semidirect
24. C22×#11719925C22semidirect
30. C2×SD16×D53C22semidirect
31. C22×#11719917C22semidirect
34. Q8×C22⋊D53C22semidirect
38. C2×#13133215C22semidirect
43. C2×#13133196C22semidirect
48. C2×Q8×Dic53C22semidirect
53. #16811014C22semidirect
54. #16810867C22semidirect
55. #16810863C22semidirect
56. #16810843C22semidirect
57. #16810827C22semidirect
58. #16810787C22semidirect
59. #16810780C22semidirect
60. #16810772C22semidirect
61. #16810726C22semidirect
62. #16810697C22semidirect
63. C2×#13133150C22semidirect
64. C2×#13133146C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133140C22semidirect
70. C2×#13133127C22semidirect
71. C23×Q8×C53C22semidirect
75. C53×#448C22semidirect
76. C2×#103×C53C22semidirect
77. C2×#103×C53C22semidirect
78. C2×C22⋊C8×C53C22semidirect
105. C2×Dic212C23semidirect
108. C2×#11719925C23semidirect
109. C2×#11719925C23semidirect
115. C2×#11719924D4semidirect
120. C2×#11719917C23semidirect
127. #13133215C23semidirect
135. #13133196C23semidirect
142. Q8×Dic53C23semidirect
167. #13133150C23semidirect
168. #13133146C23semidirect
169. #13133142C23semidirect
170. #13133140C23semidirect
174. #13133127C23semidirect
181. C22×Q8×C53C23semidirect
196. #103×C53C23semidirect
197. #103×C53C23semidirect
198. C22⋊C8×C53C23semidirect
298. #11719924C2×D4semidirect
343. C22×D53#137semidirect
428. C2×D53C2×#137semidirect
454. C2×#448D53semidirect
460. C2×C53#3266semidirect
468. C23×Q8C2×D53semidirect
514. #448C2×D53semidirect
521. C2×#103C2×D53semidirect
522. C2×#103C2×D53semidirect
526. C2×C22⋊C8C2×D53semidirect
528. C53C2×#3266semidirect
547. C22×Q8C22×D53semidirect
642. #103C22×D53semidirect
643. #103C22×D53semidirect
647. C22⋊C8C22×D53semidirect
895. C2#20286228direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332482
C22×SD16×D532
C2×Q8×C22⋊D532
C2×#168112702
#202862282
C2×#168110142
C2×#168108672
C2×#168108632
C2×#168108432
C2×#168108272
C2×#168107872
C2×#168107802
C2×#168107722
C2×#168107262
C2×#168106972
C2×C53×#4482
C2×#326653