Finite Group Databasebeta

← C2×#20286266 #28259117

Subgroups — C2×#20286266 #28259117

Order 13568.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133247C211yesmaximal, characteristic, complemented
2C22×#13133237C211yesmaximal, characteristic, complemented
3C2×#16811282C211yesmaximal, characteristic, complemented
4#20286266C2116yesmaximal, direct product factor
5C2×#16811015C211yesmaximal, characteristic, complemented
6C2×#16810871C211yesmaximal, characteristic, complemented
7C2×#16810862C211yesmaximal, characteristic, complemented
8C2×#16810830C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810778C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×#16810695C211yesmaximal, characteristic, complemented
16C2×C53×#547C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C2×#13133247—28no—
20C2×#13133247C2218yescomplemented
21C2×#13133237—28no—
22C2×#13133237C2218yescomplemented
23C22×#11719925C2211yescharacteristic
24C22×#11719925C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719923C2211yescharacteristic
28C22×#11719923C2211yescharacteristic
29C22×#11719924C2211yescharacteristic
30C22×#11719924C2211yescharacteristic
31C22×#11719922C2211yescharacteristic
32C22×#11719917C2211yescharacteristic
33C23×#88322C2211yescharacteristic
34#16811282—24no—
35#16811282C2218yescomplemented
36C2×#13133205C2211yescharacteristic
37C2×#13133203—21no—
38C2×#13133196C2211yescharacteristic
39C2×#13133195—21no—
40C2×#13133191C2211yescharacteristic
41C2×#13133189—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133177—21no—
44#16811015C2218yescomplemented
45#16810871C2218yescomplemented
46#16810862C2218yescomplemented
47#16810838C2218yescomplemented
48#16810830C2218yescomplemented
49#16810785C2218yescomplemented
50#16810783C2218yescomplemented
51#16810778C2218yescomplemented
52#16810768C2218yescomplemented
53#16810723C2218yescomplemented
54#16810695C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×C22⋊#88322C2211yescharacteristic
64C2×C22⋊#88322C2211yescharacteristic
65C2×#13133128C2211yescharacteristic
66C22×#41×C53C2211yescharacteristic
67C22×#41×C53C2211yescharacteristic
68C53×#547—24no—
69C53×#547C2218yescomplemented
70C2×C4⋊Q8×C53C2211yescharacteristic
71C2×#123×C53—21no—
72C2×#123×C53—21no—
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C2×#121×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C2×C4×D4×C53C2211yescharacteristic
78C22×C4⋊C4×C53—21no—
79C2×#11719945—22no—
80C2×#11719945—24no—
81C2×#11719945—42no—
82C2×#11719945C2314yes—
83C22×Dic106—24no—
84C22×Dic106—22no—
85C22×Dic106—21no—
86C22×Dic106—42no—
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2314yes—
89C22×Dic106C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95#13133247—232no—
96#13133237—232no—
97C2×#11719925—24no—
98C2×#11719925—24no—
99C2×#11719925—24no—
100C2×#11719925—42no—
101C2×#11719925C2314yes—
102C2×#11719925C2314yes—
103C2×#11719925C2314yes—
104C2×#11719925C2314yes—
105C2×#11719923—24no—
106C2×#11719923D418yescomplemented
107C2×#11719923C2314yes—
108C2×#11719923C2314yes—
109C2×#11719924—24no—
110C2×#11719924—42no—
111C2×#11719924C2314yes—
112C2×#11719924C2314yes—
113C2×#11719922—24no—
114C2×#11719922C2314yes—
115C2×#11719917—24no—
116C2×#11719917C2314yes—
117C22×#88322—24no—
118C22×#88322C2311yescharacteristic
119C22×#88322C2311yescharacteristic
120C22×#88322C2311yescharacteristic
121C22×#88322C2314yes—
122C22×#88322C2311yescharacteristic
123#13133205—22no—
124#13133205C2314yes—
125#13133203—28no—
126#13133196—22no—
127#13133196C2314yes—
128#13133195—28no—
129#13133191—22no—
130#13133191C2314yes—
131#13133189—28no—
132C4×Dic106—22no—
133C4×Dic106C2314yes—
134#13133177—28no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143#13133150C2314yes—
144C4⋊#88322C2314yes—
145#13133141C2314yes—
146#13133141C2314yes—
147#13133140C2314yes—
148#13133140C2314yes—
149#13133138C2314yes—
150#13133137C2314yes—
151C22⋊#88322C2314yes—
152C22⋊#88322C2314yes—
153#13133128C2314yes—
154C2×#41×C53—22no—
155C2×#41×C53—22no—
156C2×#41×C53—24no—
157C2×#41×C53—24no—
158C2×#41×C53—42no—
159C2×#41×C53—42no—
160C2×#41×C53C2314yes—
161C2×#41×C53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53—21no—
165C22×D4×C53—21no—
166C22×D4×C53D411yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C23×C4×C53—21no—
169C23×C4×C53—21no—
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C23×C4×C53C2311yescharacteristic
173C4⋊Q8×C53—22no—
174C4⋊Q8×C53C2314yes—
175#123×C53—28no—
176#123×C53—28no—
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53—22no—
179C22⋊Q8×C53C2314yes—
180C22⋊Q8×C53C2314yes—
181#121×C53—28no—
182C4×D4×C53—22no—
183C4×D4×C53D414yes—
184C4×D4×C53C2314yes—
185C4×D4×C53C2314yes—
186C2×C4⋊C4×C53—28no—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53—21no—
190C2×C4⋊C4×C53—21no—
191C2×C4⋊C4×C53D411yescharacteristic
192C2×C4⋊C4×C53C2311yescharacteristic
193C2×C22⋊C4×C53—21no—
194C2×C22⋊C4×C53—21no—
195C2×C22⋊C4×C53—21no—
196C2×C22⋊C4×C53D411yescharacteristic
197C2×C22⋊C4×C53D411yescharacteristic
198C2×C42×C53C2311yescharacteristic
199C24×C53—21no—
200C24×C53C2×D411yescharacteristic
201C24×C53C2×D411yescharacteristic
202C23×D53—21no—
203#41×C53—28no—
204#41×C53—28no—
205#41×C53—44no—
206#41×C53—44no—
207#41×C53—48no—
208#41×C53—48no—
209C2×Q8×C53—21no—
210C2×Q8×C53—21no—
211C2×Q8×C53—22no—
212C2×Q8×C53—22no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53C2412yes—
216C2×Q8×C53C2412yes—
217C2×D4×C53—24no—
218C2×D4×C53—24no—
219C2×D4×C53—21no—
220C2×D4×C53—22no—
221C2×D4×C53—42no—
222C2×D4×C53—44no—
223C2×D4×C53—44no—
224C2×D4×C53C2×D414yes—
225C2×D4×C53C2×D414yes—
226C2×D4×C53C2412yes—
227C22×C4×C53—22no—
228C22×C4×C53—22no—
229C22×C4×C53—22no—
230C22×C4×C53—22no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—24no—
235C22×C4×C53—24no—
236C22×C4×C53—24no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53—44no—
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D411yescharacteristic
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2412yes—
247C22×C4×C53C2412yes—
248C22×C4×C53C2411yescharacteristic
249C2×C22⋊D53—24no—
250C2×C22⋊D53—24no—
251C2×C22⋊D53—44no—
252C2×C22⋊D53—44no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—24no—
257C22×Dic53—44no—
258#11719945—28no—
259#11719945—44no—
260#11719945—48no—
261C2×D212—22no—
262C2×D212—22no—
263C2×D212—21no—
264C2×D212C2412yes—
265C2×C4×D53—24no—
266C2×C4×D53—44no—
267C2×Dic106—21no—
268C2×Dic106—22no—
269C2×Dic106—22no—
270C2×Dic106—22no—
271C2×Dic106—28no—
272C2×Dic106—24no—
273C2×Dic106—21no—
274C2×Dic106—44no—
275C2×Dic106—48no—
276C2×Dic106—44no—
277C2×Dic106C2×D414yes—
278C2×Dic106C2412yes—
279C2×Dic106C2412yes—
280C4⋊C4×C53—24no—
281C4⋊C4×C53—24no—
282C4⋊C4×C53—24no—
283C4⋊C4×C53—24no—
284C4⋊C4×C53—21no—
285C4⋊C4×C53C2×D414yes—
286C4⋊C4×C53C2412yes—
287C22⋊C4×C53—24no—
288C22⋊C4×C53—24no—
289C22⋊C4×C53—24no—
290C22⋊C4×C53C2×D414yes—
291C22⋊C4×C53C2×D414yes—
292C42×C53C2×D412yes—
293C42×C53C2412yes—
294C22⋊Dic53—24no—
295#11719925—28no—
296#11719925—28no—
297#11719925—28no—
298#11719925—44no—
299#11719924—28no—
300#11719924—44no—
301#11719923—28no—
302#11719923C2×D4116yescomplemented
303#11719922—28no—
304#11719921—24no—
305#11719921—24no—
306#11719921—24no—
307C4⋊Dic53—21no—
308C4⋊Dic53C2412yes—
309#11719919—24no—
310#11719919—24no—
311C4×Dic53—24no—
312#11719917—28no—
313C2×#88322—22no—
314C2×#88322—22no—
315C2×#88322—22no—
316C2×#88322—28no—
317C2×#88322C2×D414yes—
318C2×#88322C2412yes—
319C2×#88322C2412yes—
320C2×#88322C2412yes—
321C2×#88322C2412yes—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—24no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—42no—
331C23×C53—42no—
332C23×C53C22×D412yes—
333C23×C53C22×D412yes—
334C23×C53C22×D411yescharacteristic
335C22×D53—22no—
336C22×D53—42no—
337C22×D53—42no—
338C22×D53—42no—
339Q8×C53—22no—
340Q8×C53—22no—
341Q8×C53—22no—
342Q8×C53—22no—
343Q8×C53—42no—
344Q8×C53—42no—
345D4×C53—24no—
346D4×C53—22no—
347D4×C53—44no—
348D4×C53—48no—
349D4×C53—48no—
350D4×C53C22×D414yes—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—48no—
365C2×C4×C53—48no—
366C2×C4×C53—48no—
367C2×C4×C53—42no—
368C2×C4×C53—42no—
369C2×C4×C53—42no—
370C2×C4×C53C22×D412yes—
371C2×C4×C53C22×D412yes—
372C2×C4×C53C22×D412yes—
373C2×C4×C53C22×D412yes—
374C2×C4×C53C22×D412yes—
375C2×C4×C53C22×D411yescharacteristic
376C2×C4×C53H(5,𝔽2)12yes—
377C2×C4×C53C2511yescharacteristic
378C22⋊D53—48no—
379C22⋊D53—48no—
380C2×Dic53—24no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—48no—
385C2×Dic53—42no—
386C2×Dic53—42no—
387D212—22no—
388D212—22no—
389D212—42no—
390C4×D53—48no—
391Dic106—24no—
392Dic106—22no—
393Dic106—22no—
394Dic106—22no—
395Dic106—48no—
396Dic106—42no—
397Dic106C22×D414yes—
398#88322—22no—
399#88322—22no—
400#88322—22no—
401#88322C22×D414yes—
402C2×#3269—531nomaximal, Sylow
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—24no—
406C22×C53—22no—
407C22×C53—22no—
408C22×C53—22no—
409C22×C53—22no—
410C22×C53—44no—
411C22×C53—44no—
412C22×C53—48no—
413C22×C53—42no—
414C22×C53—42no—
415C22×C53D4212yes—
416C22×C53#57512yes—
417C22×C53#57812yes—
418C22×C53C23×D411yescharacteristic
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—84no—
423C4×C53—22no—
424C4×C53—22no—
425C4×C53—22no—
426C4×C53—22no—
427C4×C53—42no—
428C4×C53—42no—
429C4×C53—42no—
430C4×C53D4212yes—
431C4×C53C23×D411yescharacteristic
432C4×C53C2×H(5,𝔽2)11yescharacteristic
433Dic53—24no—
434Dic53—42no—
435Dic53—42no—
436C22×#137—531no—
437C22×#135—531no—
438C2×#548—531no—
439C2×#547D5311yescharacteristic, complemented
440#3269—5316no—
441C2×#497—531no—
442C2×#468—531no—
443C2×#467—531no—
444C2×#462—531no—
445C2×#463—531no—
446C2×#452—531no—
447C2×#452—531no—
448C2×#449—531no—
449C2×#451—531no—
450C2×#440—531no—
451C2×#435—531no—
452C2×C53—42no—
453C2×C53—42no—
454C2×C53—44no—
455C2×C53#326914yescomplemented
456C2×C53C2×D4211yescharacteristic
457C2×C53C2×#57511yescharacteristic
458C2×C53C2×#57811yescharacteristic
459D53—82no—
460C22×#41—531no—
461C22×#41C2×D5311yescharacteristic
462C22×#41C2×D5311yescharacteristic
463C23×Q8—531no—
464C2×#137—538no—
465C2×#137—1068no—
466C2×#135—538no—
467C2×#135—1068no—
468C22×Q16—531no—
469C22×Q16—531no—
470C22×Q16—531no—
471C22×Q16—531no—
472C22×SD16—531no—
473C22×SD16—531no—
474C22×SD16—531no—
475C22×SD16—531no—
476C22×D8—531no—
477C22×M16—531no—
478C23×C8—531no—
479#548—538no—
480#548—1064no—
481#547—24no—
482#547C2×D5318yescomplemented
483C2×C4⋊Q8C2×D5311yescharacteristic
484C2×#124—531no—
485C2×#124—1061no—
486C2×#123—21no—
487C2×#123—21no—
488C2×C22⋊Q8—531no—
489C2×C22⋊Q8—1061no—
490C2×C22⋊Q8C2×D5311yescharacteristic
491C2×C22⋊Q8C2×D5311yescharacteristic
492C2×#121—21no—
493C2×#121—531no—
494C2×#121—1061no—
495C2×C4×Q8—531no—
496C2×C4×D4—1061no—
497C2×C4×D4C2×D5311yescharacteristic
498C2×C4×D4C2×D5311yescharacteristic
499C22×C4⋊C4—21no—
500#497—538no—
501#468—538no—
502#467—538no—
503#463—538no—
504#462—538no—
505#452—538no—
506#452—538no—
507#451—538no—
508#449—538no—
509#440—538no—
510#435—538no—
511C2×#107—531no—
512C2×C4⋊C8—531no—
513C2×#103—531no—
514C2×#103—531no—
515C2×#103—531no—
516C2×#103—531no—
517C2×#102—531no—
518C2×#102—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×#97—531no—
522C53C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41—534no—
530C2×#41—1064no—
531C2×#41—1062no—
532C2×#41—2122no—
533C2×#41C22×D5314yes—
534C2×#41C22×D5314yes—
535C22×Q8—531no—
536C22×Q8—531no—
537C22×Q8—534no—
538C22×Q8—1064no—
539C22×Q8—1061no—
540C22×Q8—1062no—
541C22×Q8—2122no—
542C22×Q8C22×D5311yescharacteristic
543C22×Q8C22×D5311yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—531no—
547C22×D4—1061no—
548C22×D4—1061no—
549C22×D4C22⋊D5311yescharacteristic
550C22×D4C22×D5311yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—1061no—
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C23×C4C22×D5311yescharacteristic
558#137—10632no—
559#135—10632no—
560C2×Q16—534no—
561C2×Q16—534no—
562C2×Q16—534no—
563C2×Q16—534no—
564C2×Q16—1064no—
565C2×Q16—1064no—
566C2×Q16—1064no—
567C2×Q16—2122no—
568C2×SD16—538no—
569C2×SD16—534no—
570C2×SD16—534no—
571C2×SD16—534no—
572C2×SD16—534no—
573C2×SD16—1064no—
574C2×SD16—1064no—
575C2×SD16—2122no—
576C2×D8—534no—
577C2×D8—1064no—
578C2×M16—534no—
579C2×M16—1064no—
580C22×C8—531no—
581C22×C8—531no—
582C22×C8—534no—
583C22×C8—531no—
584C22×C8—531no—
585C22×C8—1064no—
586C4⋊Q8—22no—
587C4⋊Q8C22×D5314yes—
588#124—534no—
589#124—1068no—
590#124—1062no—
591#123—28no—
592#123—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—534no—
596C22⋊Q8—1062no—
597C22⋊Q8—1068no—
598C22⋊Q8C22×D5314yes—
599C22⋊Q8C22×D5314yes—
600#121—28no—
601#121—534no—
602#121—1068no—
603#121—1062no—
604C4×Q8—534no—
605C4×Q8—1062no—
606C4×D4—22no—
607C4×D4—1068no—
608C4×D4C22⋊D5314yes—
609C4×D4C22×D5314yes—
610C4×D4C22×D5314yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—531no—
617C2×C4⋊C4—1061no—
618C2×C4⋊C4—1061no—
619C2×C4⋊C4C22⋊D5311yescharacteristic
620C2×C4⋊C4C22×D5311yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C22⋊C4—1061no—
627C2×C22⋊C4—1061no—
628C2×C22⋊C4C22⋊D5311yescharacteristic
629C2×C22⋊C4C22⋊D5311yescharacteristic
630C2×C42—1061no—
631C2×C42C22×D5311yescharacteristic
632#107—534no—
633C4⋊C8—534no—
634#103—534no—
635#103—534no—
636#103—534no—
637#103—534no—
638#102—534no—
639#102—534no—
640C22⋊C8—534no—
641C22⋊C8—534no—
642#97—534no—
643C24—21no—
644C24—1061no—
645C24C2×C22⋊D5311yescharacteristic
646C24C2×C22⋊D5311yescharacteristic
647#41—28no—
648#41—28no—
649#41—44no—
650#41—44no—
651#41—48no—
652#41—48no—
653#41—1068no—
654#41—2124no—
655#41—2128no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—534no—
663C2×Q8—532no—
664C2×Q8—532no—
665C2×Q8—1068no—
666C2×Q8—1061no—
667C2×Q8—1064no—
668C2×Q8—1061no—
669C2×Q8—1062no—
670C2×Q8—1062no—
671C2×Q8—1062no—
672C2×Q8—2124no—
673C2×Q8—2124no—
674C2×Q8—2128no—
675C2×Q8C23×D5312yes—
676C2×Q8C23×D5312yes—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—42no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—532no—
685C2×D4—1064no—
686C2×D4—1064no—
687C2×D4—1062no—
688C2×D4—1061no—
689C2×D4—1062no—
690C2×D4—2124no—
691C2×D4—2124no—
692C2×D4D4×D5314yes—
693C2×D4C2×C22⋊D5314yes—
694C2×D4C23×D5312yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—1061no—
709C22×C4—1064no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1064no—
713C22×C4—2124no—
714C22×C4—2124no—
715C22×C4C2×C22⋊D5312yes—
716C22×C4C2×C22⋊D5312yes—
717C22×C4C2×C22⋊D5311yescharacteristic
718C22×C4C2×C22⋊D5311yescharacteristic
719C22×C4C2×C22⋊D5311yescharacteristic
720C22×C4C2×C22⋊D5311yescharacteristic
721C22×C4C23×D5312yes—
722C22×C4C23×D5312yes—
723C22×C4C23×D5311yescharacteristic
724Q16—1068no—
725Q16—1068no—
726Q16—1068no—
727Q16—2124no—
728SD16—5316no—
729SD16—1068no—
730SD16—1068no—
731SD16—2124no—
732D8—1068no—
733M16—1068no—
734C2×C8—534no—
735C2×C8—532no—
736C2×C8—532no—
737C2×C8—532no—
738C2×C8—532no—
739C2×C8—1068no—
740C2×C8—1062no—
741C2×C8—1062no—
742C2×C8—1062no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—21no—
748C4⋊C4—532no—
749C4⋊C4—1061no—
750C4⋊C4—1064no—
751C4⋊C4—1064no—
752C4⋊C4C2×C22⋊D5314yes—
753C4⋊C4C23×D5312yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1064no—
758C22⋊C4—1064no—
759C22⋊C4—1064no—
760C22⋊C4—1064no—
761C22⋊C4C2×C22⋊D5314yes—
762C22⋊C4C2×C22⋊D5314yes—
763C42—1064no—
764C42C2×C22⋊D5312yes—
765C42C23×D5312yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—42no—
775C23—42no—
776C23—1062no—
777C23—2122no—
778C23—2122no—
779C23—2122no—
780C23C22×C22⋊D5312yes—
781C23C22×C22⋊D5312yes—
782C23C22×C22⋊D5311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—42no—
789Q8—534no—
790Q8—1062no—
791Q8—1064no—
792Q8—1062no—
793Q8—1062no—
794Q8—2128no—
795Q8—2122no—
796D4—22no—
797D4—24no—
798D4—44no—
799D4—48no—
800D4—48no—
801D4—1062no—
802D4—1062no—
803D4—2128no—
804D4—2128no—
805D4—2122no—
806D4C2×D4×D5314yes—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—48no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—1062no—
827C2×C4—1064no—
828C2×C4—1062no—
829C2×C4—1062no—
830C2×C4—2128no—
831C2×C4—2128no—
832C2×C4—2122no—
833C2×C4—2122no—
834C2×C4C2×D4×D5312yes—
835C2×C4C22×C22⋊D5312yes—
836C2×C4C22×C22⋊D5312yes—
837C2×C4C22×C22⋊D5312yes—
838C2×C4C22×C22⋊D5312yes—
839C2×C4C22×C22⋊D5311yescharacteristic
840C2×C4#1313326212yes—
841C2×C4C24×D5311yescharacteristic
842C8—534no—
843C8—1062no—
844C8—1062no—
845C8—1062no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—44no—
854C22—44no—
855C22—48no—
856C22—42no—
857C22—42no—
858C22—4244no—
859C22—2122no—
860C22—2122no—
861C22—2122no—
862C22D4×C22⋊D5312yes—
863C22#1681142112yes—
864C22#1681143812yes—
865C22C23×C22⋊D5311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—1064no—
874C4—2122no—
875C4—2122no—
876C4D4×C22⋊D5312yes—
877C4C22×D4×D5311yescharacteristic
878C4C2×#1313326211yescharacteristic
879C2—42no—
880C2—42no—
881C2—44no—
882C2—4242no—
883C2#2028626614yesdirect product factor
884C2C2×D4×C22⋊D5311yescharacteristic
885C2C2×#1681142111yescharacteristic
886C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#547C2
socleC23×C53C22×D4
hypercenterC2×#547D53
hypocenterC53C2×#3269
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#13133247C2semidirect
2. C22×#13133237C2semidirect
3. C2×#16811282C2semidirect
4. #20286266C2direct (N × H)
5. C2×#16811015C2semidirect
6. C2×#16810871C2semidirect
7. C2×#16810862C2semidirect
8. C2×#16810830C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810778C2semidirect
14. C2×#16810723C2semidirect
15. C2×#16810695C2semidirect
16. C2×C53×#547C2semidirect
20. C2×#13133247C22semidirect
22. C2×#13133237C22semidirect
35. #16811282C22semidirect
44. #16811015C22semidirect
45. #16810871C22semidirect
46. #16810862C22semidirect
47. #16810838C22semidirect
48. #16810830C22semidirect
49. #16810785C22semidirect
50. #16810783C22semidirect
51. #16810778C22semidirect
52. #16810768C22semidirect
53. #16810723C22semidirect
54. #16810695C22semidirect
69. C53×#547C22semidirect
106. C2×#11719923D4semidirect
302. #11719923C2×D4semidirect
439. C2×#547D53semidirect
455. C2×C53#3269semidirect
482. #547C2×D53semidirect
522. C53C2×#3269semidirect
883. C2#20286266direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332472
C22×#131332372
C2×#168112822
#202862662
C2×#168110152
C2×#168108712
C2×#168108622
C2×#168108302
C2×#168108382
C2×#168107852
C2×#168107832
C2×#168107682
C2×#168107782
C2×#168107232
C2×#168106952
C2×C53×#5472
C2×#326953