Finite Group Databasebeta

← C2×#20286708 #28260668

Subgroups — C2×#20286708 #28260668

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811282C211yesmaximal, characteristic, complemented
2C2×#16811277C211yesmaximal, characteristic, complemented
3#20286708C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810937C211yesmaximal, characteristic, complemented
7C2×#16810919C211yesmaximal, characteristic, complemented
8C2×#16810869C211yesmaximal, characteristic, complemented
9C2×#16810859C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810764C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810625C211yesmaximal, characteristic, complemented
15C22×#13133142C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947—21no—
19C23×Dic106C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×D424C2211yescharacteristic
23#16811282—24no—
24#16811282C2218yescomplemented
25#16811277—24no—
26#16811277C2218yescomplemented
27C2×#13133217C2211yescharacteristic
28C2×#13133205C2211yescharacteristic
29C2×#13133203—21no—
30C2×#13133201—21no—
31C2×#13133201—21no—
32C2×#13133197—21no—
33C2×#13133196C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic
37C2×#13133191C2211yescharacteristic
38C2×#13133189—21no—
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×#13133177—21no—
42C22×C4⋊Dic53C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic
44#16810983C2218yescomplemented
45#16810959C2218yescomplemented
46#16810937C2218yescomplemented
47#16810919C2218yescomplemented
48#16810869C2218yescomplemented
49#16810859C2218yescomplemented
50#16810839C2218yescomplemented
51#16810770C2218yescomplemented
52#16810764C2218yescomplemented
53#16810725C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57#16810625C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2218yescomplemented
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C2×#11719947—28no—
82C2×#11719947—48no—
83C22×Dic106—24no—
84C22×Dic106—22no—
85C22×Dic106—21no—
86C22×Dic106—21no—
87C22×Dic106—42no—
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2314yes—
90C22×Dic106C2311yescharacteristic
91C22×D212C2311yescharacteristic
92C22×D212C2311yescharacteristic
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C23×Dic53—21no—
98C23×Dic53—21no—
99C23×Dic53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C2×#11719913—24no—
103C2×#11719913—42no—
104C2×#11719913C2314yes—
105C2×#11719913C2314yes—
106C2×D424—42no—
107C2×D424C2314yes—
108#13133217—22no—
109#13133217C2314yes—
110#13133205—22no—
111#13133205C2314yes—
112#13133203—28no—
113#13133201—28no—
114#13133201—28no—
115#13133197—28no—
116#13133196—22no—
117#13133196C2314yes—
118#13133195—28no—
119#13133191—22no—
120#13133191—22no—
121#13133191—22no—
122#13133191C2314yes—
123#13133191C2314yes—
124#13133191C2314yes—
125#13133189—28no—
126C4×Dic106—22no—
127C4×Dic106C2314yes—
128C4×D212—22no—
129C4×D212C2314yes—
130#13133177—28no—
131C2×C4⋊Dic53—22no—
132C2×C4⋊Dic53—22no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53C2314yes—
137C2×C4⋊Dic53C2314yes—
138C2×C4⋊Dic53C2311yescharacteristic
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×C4⋊Dic53C2311yescharacteristic
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×C4×Dic53—21no—
152#13133151C2314yes—
153#13133151C2314yes—
154#13133151C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133142C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yes—
164#13133139C2314yes—
165C22×D4×C53D411yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C23×C4×C53C2311yescharacteristic
168C2×M16×C53—42no—
169C2×M16×C53C2314yes—
170C22×C8×C53—42no—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2314yes—
176C4×D4×C53D414yes—
177C4×D4×C53C2314yes—
178C2×C4⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C22⋊C4×C53D411yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184C22⋊C8×C53C2314yes—
185#97×C53C2314yes—
186C24×C53C2×D411yescharacteristic
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53—21no—
190C2×D4×C53—24no—
191C2×D4×C53C2×D414yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—24no—
220C22×Dic53—24no—
221C22×Dic53—24no—
222C22×Dic53—44no—
223C22×Dic53—44no—
224C22×Dic53—44no—
225#11719947—432no—
226#11719945—28no—
227#11719945—44no—
228#11719945—48no—
229C2×D212—22no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—21no—
234C2×D212—21no—
235C2×D212C2412yes—
236C2×D212C2412yes—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53—44no—
241C2×Dic106—21no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—28no—
246C2×Dic106—24no—
247C2×Dic106—21no—
248C2×Dic106—24no—
249C2×Dic106—44no—
250C2×Dic106—48no—
251C2×Dic106—44no—
252C2×Dic106—44no—
253C2×Dic106#4114yescomplemented
254C2×Dic106C2412yes—
255C2×Dic106C2412yes—
256M16×C53—44no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C2×C8×C53—22no—
261C2×C8×C53—44no—
262C2×C8×C53C2412yes—
263C2×C8×C53C2412yes—
264C2×C8×C53C2412yes—
265C2×C8×C53C2412yes—
266C4⋊C4×C53C2×D414yes—
267C22⋊C4×C53C2×D414yes—
268C22⋊C4×C53C2×D414yes—
269C42×C53C2×D412yes—
270C42×C53C2412yes—
271C22⋊Dic53—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53—24no—
282C4⋊Dic53—24no—
283C4⋊Dic53—24no—
284C4⋊Dic53—21no—
285C4⋊Dic53C2412yes—
286C4⋊Dic53C2412yes—
287C4⋊Dic53C2412yes—
288C4⋊Dic53C2412yes—
289#11719919—24no—
290#11719919—24no—
291C4×Dic53—24no—
292D424—44no—
293#11719913—28no—
294#11719913—44no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53AGL(1,ℤ/8)14yes—
301C23×C53C22×D412yes—
302C23×C53C22×D412yes—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—42no—
312D4×C53—28no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C2×#4112yes—
329C2×C4×C53H(5,𝔽2)12yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—48no—
332C22⋊D53—48no—
333C22⋊D53—48no—
334C22⋊D53—48no—
335C2×Dic53—24no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—48no—
343C2×Dic53—48no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—48no—
349C2×Dic53—42no—
350D212—22no—
351D212—22no—
352D212—22no—
353D212—22no—
354D212—42no—
355D212—42no—
356C4×D53—48no—
357C4×D53—48no—
358Dic106—24no—
359Dic106—22no—
360Dic106—22no—
361Dic106—22no—
362Dic106—48no—
363Dic106—48no—
364Dic106—42no—
365Dic106C2×#4114yescomplemented
366C8×C53—22no—
367C8×C53—22no—
368C8×C53—22no—
369C8×C53—22no—
370C2×#3308—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—28no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—44no—
378C22×C53#54612yes—
379C22×C53C2×AGL(1,ℤ/8)14yes—
380C22×C53C2×AGL(1,ℤ/8)12yes—
381C22×C53#57812yes—
382C22×C53C23×D411yescharacteristic
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—84no—
390C2×D53—84no—
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—22no—
394C4×C53—22no—
395C4×C53#54612yes—
396C4×C53C22×#4111yescharacteristic
397C4×C53C2×H(5,𝔽2)11yescharacteristic
398Dic53—24no—
399Dic53—42no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#548—531no—
405C2×#547—531no—
406#3308—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480—531no—
410C2×#477—531no—
411C2×#468—531no—
412C2×#466—531no—
413C2×#463—531no—
414C2×#449—531no—
415C2×#448—531no—
416C2×#440—531no—
417C2×#435D5311yescharacteristic, complemented
418C2×#417—531no—
419C22×#103—531no—
420C2×C53—24no—
421C2×C53—42no—
422C2×C53#330814yescomplemented
423C2×C53C2×#54611yescharacteristic
424C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C53C2×#57811yescharacteristic
426D53—82no—
427D53—82no—
428C22×#41—531no—
429C22×#41—1061no—
430C23×Q8—531no—
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16C2×D5311yescharacteristic
435C23×C8C2×D5311yescharacteristic
436#548—538no—
437#548—1064no—
438#547—538no—
439#547—1064no—
440C2×C4⋊Q8—531no—
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8—1061no—
448C2×#121—531no—
449C2×#121—531no—
450C2×#121—531no—
451C2×#121—1061no—
452C2×C4×Q8—531no—
453C2×C4×D4—531no—
454C2×C4×D4—1061no—
455C2×C4×D4C2×D5311yescharacteristic
456C22×C4⋊C4—531no—
457C22×C4⋊C4—531no—
458#489—538no—
459#484—538no—
460#480—538no—
461#477—538no—
462#468—538no—
463#466—538no—
464#463—538no—
465#449—538no—
466#448—538no—
467#440—538no—
468#435C2×D5318yescomplemented
469C2×#107—531no—
470C2×#107—531no—
471C2×#107—531no—
472C2×C4⋊C8C2×D5311yescharacteristic
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#103—538no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×C22⋊C8C2×D5311yescharacteristic
486C2×C22⋊C8C2×D5311yescharacteristic
487C2×#97C2×D5311yescharacteristic
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—534no—
490C2×#41—1064no—
491C2×#41—1068no—
492C2×#41—1062no—
493C2×#41—2122no—
494C2×#41—2128no—
495C22×Q8—531no—
496C22×Q8—531no—
497C22×Q8—534no—
498C22×Q8—1064no—
499C22×Q8—1061no—
500C22×Q8—1061no—
501C22×Q8—1062no—
502C22×Q8—2122no—
503C22×D4—531no—
504C22×D4—531no—
505C22×D4—1061no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4D21211yescharacteristic
510C23×C4—1061no—
511C23×C4—1061no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4C22×D5311yescharacteristic
516C23×C4C22×D5311yescharacteristic
517C2×SD16—534no—
518C2×SD16—534no—
519C2×SD16—1064no—
520C2×SD16—2122no—
521C2×D8—534no—
522C2×D8—2122no—
523C2×M16—42no—
524C2×M16C22×D5314yes—
525C22×C8—42no—
526C22×C8C22×D5311yescharacteristic
527C22×C8C22×D5311yescharacteristic
528C22×C8C22×D5311yescharacteristic
529C22×C8C22×D5311yescharacteristic
530C22×C8C22×D5314yes—
531C4⋊Q8—534no—
532C4⋊Q8—1062no—
533#124—534no—
534#124—1068no—
535#124—1062no—
536#123—1068no—
537#123—1068no—
538C22⋊Q8—534no—
539C22⋊Q8—1062no—
540C22⋊Q8—1068no—
541C22⋊Q8—1068no—
542#121—534no—
543#121—534no—
544#121—534no—
545#121—1068no—
546#121—1062no—
547#121—1062no—
548#121—1062no—
549C4×Q8—534no—
550C4×Q8—1062no—
551C4×D4—534no—
552C4×D4—1068no—
553C4×D4—1062no—
554C4×D4D21214yes—
555C4×D4C22×D5314yes—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—534no—
560C2×C4⋊C4—534no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1062no—
565C2×C4⋊C4—1062no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4D21211yescharacteristic
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4D21211yescharacteristic
578C2×C22⋊C4D21211yescharacteristic
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581#107—534no—
582#107—534no—
583#107—534no—
584C4⋊C8C22×D5314yes—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103—534no—
590#103—534no—
591#102—534no—
592#102—534no—
593#102—534no—
594#102—534no—
595C22⋊C8C22×D5314yes—
596C22⋊C8C22×D5314yes—
597#97C22×D5314yes—
598C24—1061no—
599C24—1061no—
600C24C2×D21211yescharacteristic
601C24C2×D21211yescharacteristic
602#41—1068no—
603#41—2124no—
604#41—2128no—
605#41—21232no—
606C2×Q8—534no—
607C2×Q8—532no—
608C2×Q8—532no—
609C2×Q8—1068no—
610C2×Q8—1061no—
611C2×Q8—1064no—
612C2×Q8—1061no—
613C2×Q8—1064no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—2124no—
618C2×Q8—2124no—
619C2×Q8—2128no—
620C2×Q8—2124no—
621C2×D4—24no—
622C2×D4—532no—
623C2×D4—532no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1061no—
629C2×D4—1061no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—2124no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4—2124no—
638C2×D4C2×D21214yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—1061no—
644C22×C4—1064no—
645C22×C4—1064no—
646C22×C4—1064no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—1061no—
651C22×C4—1061no—
652C22×C4—1064no—
653C22×C4—1064no—
654C22×C4—2124no—
655C22×C4—2124no—
656C22×C4—2124no—
657C22×C4—2124no—
658C22×C4—2124no—
659C22×C4C2×D21212yes—
660C22×C4C2×D21212yes—
661C22×C4C2×D21211yescharacteristic
662C22×C4C2×D21211yescharacteristic
663C22×C4C2×D21211yescharacteristic
664C22×C4C2×D21211yescharacteristic
665C22×C4C23×D5312yes—
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—1068no—
669SD16—2124no—
670D8—2124no—
671M16—44no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8C23×D5312yes—
678C2×C8C23×D5312yes—
679C2×C8C23×D5312yes—
680C2×C8C23×D5312yes—
681C4⋊C4—532no—
682C4⋊C4—532no—
683C4⋊C4—532no—
684C4⋊C4—532no—
685C4⋊C4—1061no—
686C4⋊C4—1061no—
687C4⋊C4—1061no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1061no—
691C4⋊C4—1064no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4C2×D21214yes—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4C2×D21214yes—
703C22⋊C4C2×D21214yes—
704C42—1064no—
705C42C2×D21212yes—
706C42C23×D5312yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—1062no—
713C23—1062no—
714C23—2122no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23—2122no—
719C23—2122no—
720C23#1313324514yes—
721C23C22×D21212yes—
722C23C22×D21212yes—
723C23C22×D21211yescharacteristic
724Q8—534no—
725Q8—1064no—
726Q8—1062no—
727Q8—1062no—
728Q8—1062no—
729Q8—2128no—
730Q8—2128no—
731Q8—2122no—
732D4—28no—
733D4—1062no—
734D4—1062no—
735D4—1062no—
736D4—1062no—
737D4—2128no—
738D4—2128no—
739D4—2128no—
740D4—2128no—
741D4—2122no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—1064no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—2128no—
761C2×C4—2128no—
762C2×C4—2128no—
763C2×C4—2128no—
764C2×C4—2122no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2128no—
769C2×C4—2122no—
770C2×C4C22×D21212yes—
771C2×C4C22×D21212yes—
772C2×C4C22×D21212yes—
773C2×C4C22×D21212yes—
774C2×C4C22×D21211yescharacteristic
775C2×C4#41×D5312yes—
776C2×C4#1313326212yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—22no—
781C8—22no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—4244no—
790C22—4244no—
791C22—2122no—
792C22—2122no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22#1681126812yes—
798C22C2×#1313324514yes—
799C22C2×#1313324512yes—
800C22#1681144012yes—
801C22C23×D21211yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—1064no—
807C4—2122no—
808C4—2122no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126812yes—
813C4C2×#41×D5311yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—24no—
816C2—42no—
817C2—4242no—
818C2—4242no—
819C2#2028670814yesdirect product factor
820C2C2×#1681126811yescharacteristic
821C2C22×#1313324511yescharacteristic
822C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
hypercenterC2×#435D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16811282C2semidirect
2. C2×#16811277C2semidirect
3. #20286708C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810937C2semidirect
7. C2×#16810919C2semidirect
8. C2×#16810869C2semidirect
9. C2×#16810859C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810764C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810625C2semidirect
15. C22×#13133142C2semidirect
16. C2×C53×#435C2semidirect
24. #16811282C22semidirect
26. #16811277C22semidirect
44. #16810983C22semidirect
45. #16810959C22semidirect
46. #16810937C22semidirect
47. #16810919C22semidirect
48. #16810869C22semidirect
49. #16810859C22semidirect
50. #16810839C22semidirect
51. #16810770C22semidirect
52. #16810764C22semidirect
53. #16810725C22semidirect
57. #16810625C22semidirect
64. C2×#13133142C22semidirect
72. C53×#435C22semidirect
253. C2×Dic106#41semidirect
365. Dic106C2×#41semidirect
417. C2×#435D53semidirect
422. C2×C53#3308semidirect
468. #435C2×D53semidirect
488. C53C2×#3308semidirect
819. C2#20286708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112822
C2×#168112772
#202867082
C2×#168109832
C2×#168109592
C2×#168109372
C2×#168109192
C2×#168108692
C2×#168108592
C2×#168108392
C2×#168107702
C2×#168107642
C2×#168107252
C2×#168106252
C22×#131331422
C2×C53×#4352
C2×#330853