Finite Group Databasebeta

← C2×#20287157 #28262625

Subgroups — C2×#20287157 #28262625

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic, complemented
2C2×#16811277C211yesmaximal, characteristic
3#20287157C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810948C211yesmaximal, characteristic, complemented
7C2×#16810954C211yesmaximal, characteristic, complemented
8C2×#16810937C211yesmaximal, characteristic, complemented
9C2×#16810919C211yesmaximal, characteristic, complemented
10C2×#16810924C211yesmaximal, characteristic, complemented
11C2×#16810869C211yesmaximal, characteristic, complemented
12C2×#16810852C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C22×#13133151C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719913C2211yescharacteristic
19#16811313—24no—
20#16811313C2218yescomplemented
21#16811277—24no—
22#16811277C2218yes—
23C2×#13133217C2211yescharacteristic
24C2×#13133210—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133201—21no—
28C2×#13133201—21no—
29C2×#13133198—21no—
30C2×#13133197—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133196C2211yescharacteristic
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133176C2211yescharacteristic
38C2×#13133173—21no—
39C22×C4⋊Dic53C2211yescharacteristic
40C22×C4⋊Dic53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16810959C2218yescomplemented
44#16810954C2218yescomplemented
45#16810948C2218yescomplemented
46#16810937C2218yescomplemented
47#16810924C2218yescomplemented
48#16810919C2218yescomplemented
49#16810869C2218yescomplemented
50#16810852C2218yescomplemented
51#16810725C2218yescomplemented
52#16810665C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133151C2218yescomplemented
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133149C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
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×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90#13133217—22no—
91#13133217C2314yes—
92#13133210—28no—
93#13133209—22no—
94#13133209C2314yes—
95#13133207—28no—
96#13133201—28no—
97#13133201—28no—
98#13133198—28no—
99#13133197—28no—
100#13133196—22no—
101#13133196—22no—
102#13133196C2314yes—
103#13133196C2314yes—
104#13133191—22no—
105#13133191—22no—
106#13133191C2314yes—
107#13133191C2314yes—
108C4×Dic106—22no—
109C4×Dic106C2314yes—
110C4×D212—22no—
111C4×D212C2314yes—
112#13133176—22no—
113#13133176C2314yes—
114#13133173—28no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—22no—
117C2×C4⋊Dic53—22no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2314yes—
123C2×C4⋊Dic53C2314yes—
124C2×C4⋊Dic53C2314yes—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133151C2314yes—
147#13133151C2314yes—
148#13133151C2314yes—
149#13133151C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133149C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159C22×D4×C53D411yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C2×M16×C53—24no—
163C2×M16×C53C2314yes—
164C22×C8×C53—24no—
165C22×C8×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4×D4×C53D414yes—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C22⋊C4×C53D411yescharacteristic
175C2×C42×C53C2311yescharacteristic
176C4⋊C8×C53C2314yes—
177C22⋊C8×C53C2314yes—
178C22⋊C8×C53C2314yes—
179#97×C53C2314yes—
180C24×C53C2×D411yescharacteristic
181C24×C53C2×D411yescharacteristic
182C23×D53—21no—
183C2×D4×C53—24no—
184C2×D4×C53C2×D414yes—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—44no—
201C2×C22⋊D53—44no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—44no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215#11719947—432no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—44no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—21no—
225C2×Dic106—24no—
226C2×Dic106—44no—
227C2×Dic106C2412yes—
228M16×C53—28no—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53—28no—
233C2×C8×C53#4114yescomplemented
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53C2×D414yes—
239C22⋊C4×C53C2×D414yes—
240C22⋊C4×C53C2×D414yes—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—21no—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272#11719913—28no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53AGL(1,ℤ/8)14yes—
279C23×C53C22×D412yes—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286D4×C53—28no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4112yes—
303C2×C4×C532−1+412yes—
304C2×C4×C53C2511yescharacteristic
305C22⋊D53—48no—
306C22⋊D53—48no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—48no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—48no—
320C2×Dic53—48no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324D212—22no—
325D212—22no—
326D212—42no—
327C4×D53—48no—
328Dic106—22no—
329Dic106—22no—
330Dic106—48no—
331Dic106—42no—
332C8×C53—22no—
333C8×C53—22no—
334C8×C53—22no—
335C8×C53C2×#4114yescomplemented
336C2×#3343—531nomaximal, Sylow
337C22×C53—28no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—44no—
344C22×C53#54712yes—
345C22×C53C2×AGL(1,ℤ/8)14yes—
346C22×C53C2×AGL(1,ℤ/8)12yes—
347C22×C53#57812yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—84no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53#54712yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C2×2−1+411yescharacteristic
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#552—531no—
368C2×#547—531no—
369#3343—5316no—
370C2×#501—531no—
371C2×#484—531no—
372C2×#482—531no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#477—531no—
376C2×#478—531no—
377C2×#468—531no—
378C2×#465—531no—
379C2×#440—531no—
380C2×#435D5311yescharacteristic, complemented
381C2×#428—531no—
382C22×#107—531no—
383C2×C53—24no—
384C2×C53—42no—
385C2×C53#334314yescomplemented
386C2×C53C2×#54711yescharacteristic
387C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C53C2×#57811yescharacteristic
389D53—82no—
390C22×#41—1061no—
391C22×SD16—531no—
392C22×M16C2×D5311yescharacteristic
393C23×C8C2×D5311yescharacteristic
394#552—538no—
395#552—1064no—
396#547—538no—
397#547—1064no—
398C2×C4⋊Q8—531no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#125—1061no—
402C2×#123—1061no—
403C2×#123—1061no—
404C2×#123—1061no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×#121—531no—
410C2×C4×Q8—531no—
411C2×C4×D4—531no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C2×#117—1061no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418#501—538no—
419#484—538no—
420#483—538no—
421#482—538no—
422#480—538no—
423#478—538no—
424#477—538no—
425#468—538no—
426#465—538no—
427#440—538no—
428#435C2×D5318yescomplemented
429#428—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107—531no—
434C2×#107—538no—
435C2×#107—531no—
436C2×#107—531no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#106—531no—
440C2×C4⋊C8C2×D5311yescharacteristic
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×C22⋊C8C2×D5311yescharacteristic
448C2×C22⋊C8C2×D5311yescharacteristic
449C2×#97C2×D5311yescharacteristic
450C53C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1068no—
452C2×#41—2128no—
453C22×Q8—531no—
454C22×Q8—1061no—
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4D21211yescharacteristic
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C2×SD16—534no—
466C2×SD16—1064no—
467C2×M16—24no—
468C2×M16C22×D5314yes—
469C22×C8—24no—
470C22×C8C22×D5311yescharacteristic
471C22×C8C22×D5314yes—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#125—534no—
479#125—1068no—
480#125—1062no—
481#123—1068no—
482#123—1068no—
483#123—1068no—
484C22⋊Q8—534no—
485C22⋊Q8—534no—
486C22⋊Q8—1062no—
487C22⋊Q8—1062no—
488C22⋊Q8—1068no—
489#121—534no—
490#121—534no—
491#121—1062no—
492#121—1062no—
493C4×Q8—534no—
494C4×Q8—1062no—
495C4×D4—534no—
496C4×D4—1062no—
497C4×D4D21214yes—
498C4×D4C22×D5314yes—
499#117—534no—
500#117—1062no—
501#117—1068no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—534no—
509C2×C4⋊C4—534no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1062no—
515C2×C4⋊C4—1062no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4D21211yescharacteristic
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4D21211yescharacteristic
531C2×C22⋊C4D21211yescharacteristic
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42C22×D5311yescharacteristic
535#107—534no—
536#107—534no—
537#107—534no—
538#107—534no—
539#107—534no—
540#107—534no—
541#106—534no—
542#106—534no—
543#106—534no—
544C4⋊C8C22×D5314yes—
545#103—534no—
546#103—534no—
547#103—534no—
548#102—534no—
549#102—534no—
550#102—534no—
551C22⋊C8C22×D5314yes—
552C22⋊C8C22×D5314yes—
553#97C22×D5314yes—
554C24—1061no—
555C24C2×D21211yescharacteristic
556C24C2×D21211yescharacteristic
557#41—21232no—
558C2×Q8—532no—
559C2×Q8—1061no—
560C2×Q8—1064no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—2124no—
564C2×D4—24no—
565C2×D4—532no—
566C2×D4—1064no—
567C2×D4—1064no—
568C2×D4—1061no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—2124no—
572C2×D4—2124no—
573C2×D4C2×D21214yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—1064no—
579C22×C4—1064no—
580C22×C4—1064no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1064no—
589C22×C4—2124no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4C2×D21212yes—
594C22×C4C2×D21212yes—
595C22×C4C2×D21211yescharacteristic
596C22×C4C2×D21211yescharacteristic
597C22×C4C2×D21211yescharacteristic
598C22×C4C2×D21211yescharacteristic
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1171994714yescomplemented
609C2×C8C23×D5312yes—
610C2×C8C23×D5312yes—
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—532no—
614C4⋊C4—532no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—532no—
618C4⋊C4—532no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1061no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4C2×D21214yes—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4C2×D21214yes—
642C22⋊C4C2×D21214yes—
643C42—1064no—
644C42—1064no—
645C42C2×D21212yes—
646C42C23×D5312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1062no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23#1313324514yes—
657C23C22×D21212yes—
658C23C22×D21212yes—
659C23C22×D21211yescharacteristic
660Q8—1062no—
661Q8—1062no—
662Q8—2128no—
663Q8—2122no—
664D4—28no—
665D4—1062no—
666D4—1062no—
667D4—2128no—
668D4—2128no—
669D4—2122no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—2128no—
688C2×C4—2128no—
689C2×C4—2122no—
690C2×C4—2128no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2128no—
697C2×C4—2122no—
698C2×C4C22×D21212yes—
699C2×C4C22×D21212yes—
700C2×C4C22×D21212yes—
701C2×C4C22×D21212yes—
702C2×C4C22×D21211yescharacteristic
703C2×C4C2×#1171994712yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1171994714yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—4244no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22#1681127712yes—
722C22C2×#1313324514yes—
723C22C2×#1313324512yes—
724C22#1681144012yes—
725C22C23×D21211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127712yes—
738C4C22×#1171994711yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—24no—
741C2—42no—
742C2—4242no—
743C2#2028715714yesdirect product factor
744C2C2×#1681127711yescharacteristic
745C2C22×#1313324511yescharacteristic
746C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811277C2
hypercenterC2×#435D53
hypocenterC53C2×#3343
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×#16811313C2semidirect
3. #20287157C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810948C2semidirect
7. C2×#16810954C2semidirect
8. C2×#16810937C2semidirect
9. C2×#16810919C2semidirect
10. C2×#16810924C2semidirect
11. C2×#16810869C2semidirect
12. C2×#16810852C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810665C2semidirect
15. C22×#13133151C2semidirect
16. C2×C53×#435C2semidirect
20. #16811313C22semidirect
42. #16811032C22semidirect
43. #16810959C22semidirect
44. #16810954C22semidirect
45. #16810948C22semidirect
46. #16810937C22semidirect
47. #16810924C22semidirect
48. #16810919C22semidirect
49. #16810869C22semidirect
50. #16810852C22semidirect
51. #16810725C22semidirect
52. #16810665C22semidirect
59. C2×#13133151C22semidirect
72. C53×#435C22semidirect
233. C2×C8×C53#41semidirect
335. C8×C53C2×#41semidirect
380. C2×#435D53semidirect
385. C2×C53#3343semidirect
428. #435C2×D53semidirect
450. C53C2×#3343semidirect
608. C2×C8#11719947semidirect
709. C8C2×#11719947semidirect
743. C2#20287157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113132
C2×#168112772
#202871572
C2×#168110322
C2×#168109592
C2×#168109482
C2×#168109542
C2×#168109372
C2×#168109192
C2×#168109242
C2×#168108692
C2×#168108522
C2×#168107252
C2×#168106652
C22×#131331512
C2×C53×#4352
C2×#334353