Finite Group Databasebeta

← C2×#20275075 #27385564

Subgroups — C2×#20275075 #27385564

Order 13568.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811421C211yesmaximal, characteristic
2C2×#16811390C211yesmaximal, characteristic, complemented
3C2×#16810641C211yesmaximal, characteristic, complemented
4C2×#16810589C211yesmaximal, characteristic, complemented
5#20275075C218yesmaximal, direct product factor
6C2×#16810393C211yesmaximal, characteristic, complemented
7C2×#16810388C211yesmaximal, characteristic, complemented
8C2×C53×#416C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811421—22no—
11#16811421—22no—
12#16811421C414yescomplemented
13#16811421C2214yes—
14C2×#13133248—21no—
15C2×#13133247C412yescomplemented
16C2×#13133243—21no—
17C2×#13133242C412yescomplemented
18C2×#13133237—22no—
19#16811390—22no—
20#16811390—22no—
21#16811390—22no—
22#16811390C2214yescomplemented
23C2×#13133224—22no—
24C2×#13133224—22no—
25C22×#11719917—22no—
26C22×#11719917C2211yescharacteristic
27C22×#11719917C2211yescharacteristic
28C22×#11719917C2211yescharacteristic
29#16810641—22no—
30#16810641C2214yescomplemented
31C2×#13133145—22no—
32#16810589—22no—
33#16810589C2214yescomplemented
34C2×#13133129—22no—
35#16810393C2214yescomplemented
36#16810388C2214yescomplemented
37C22×#41×C53C2211yescharacteristic
38C23×C8×C53C2211yescharacteristic
39C2×#117×C53C2211yescharacteristic
40C53×#416—22no—
41C53×#416C2214yescomplemented
42C2×#103×C53—21no—
43C2×#102×C53—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945—21no—
54C2×#11719945C2×C412yes—
55C2×#11719945C2312yes—
56C22×Dic106C2×C411yescharacteristic
57C22×D212C2×C411yescharacteristic
58C22×C22⋊D53—21no—
59C22×C4×D53—21no—
60#13133248—24no—
61#13133248—24no—
62#13133247—24no—
63#13133247C2×C418yescomplemented
64#13133243—24no—
65#13133243—24no—
66#13133242—24no—
67#13133242C2×C418yescomplemented
68#13133237—28no—
69#13133237—28no—
70C2×#11719925—22no—
71C2×#11719923—22no—
72C2×#11719924—22no—
73C2×#11719922—22no—
74#13133224—28no—
75#13133224—28no—
76#13133224—28no—
77#13133224—28no—
78C2×#11719917—24no—
79C2×#11719917—28no—
80C2×#11719917—28no—
81C2×#11719917—21no—
82C2×#11719917—21no—
83C2×#11719917—21no—
84C2×#11719917—21no—
85C2×#11719917—21no—
86C2×#11719917—21no—
87C2×#11719917—21no—
88C2×#11719917—21no—
89C2×#11719917—21no—
90C2×#11719917—21no—
91C2×#11719917C2×C412yes—
92C2×#11719917C2×C412yes—
93C2×#11719917D412yes—
94C2×#11719917D412yes—
95C2×#11719917D412yes—
96C2×#11719917C2312yes—
97C2×#11719917C2312yes—
98C2×#11719917C2312yes—
99C22×#88322—24no—
100C22×#88322—21no—
101C22×#88322—21no—
102C22×#88322D412yes—
103#13133145—28no—
104#13133129—28no—
105C2×#41×C53—21no—
106C2×#41×C53—21no—
107C2×#41×C53—21no—
108C2×#41×C53—21no—
109C2×#41×C53—21no—
110C2×#41×C53—21no—
111C2×#41×C53C2×C412yes—
112C2×#41×C53C2×C412yes—
113C2×#41×C53D412yes—
114C2×#41×C53D412yes—
115C2×#41×C53D412yes—
116C2×#41×C53C2312yes—
117C22×Q8×C53D411yescharacteristic
118C22×D4×C53—21no—
119C22×D4×C53D411yescharacteristic
120C23×C4×C53—21no—
121C23×C4×C53C2311yescharacteristic
122C22×C8×C53—21no—
123C22×C8×C53—21no—
124C22×C8×C53—21no—
125C22×C8×C53—21no—
126C22×C8×C53—21no—
127C22×C8×C53—21no—
128C22×C8×C53C2312yes—
129#117×C53—21no—
130#117×C53—21no—
131#117×C53—21no—
132#117×C53C2312yes—
133C2×C4⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C42×C53—21no—
136#103×C53—24no—
137#102×C53—24no—
138C24×C53—21no—
139C24×C53#4111yescharacteristic
140C23×D53—21no—
141#41×C53—22no—
142#41×C53—22no—
143#41×C53—22no—
144#41×C53—22no—
145#41×C53—22no—
146#41×C53—22no—
147#41×C53—22no—
148#41×C53—22no—
149#41×C53—22no—
150#41×C53—22no—
151#41×C53—22no—
152#41×C53—22no—
153#41×C53C22⋊C414yes—
154#41×C53C22⋊C414yes—
155#41×C53C22×C414yes—
156#41×C53C2×D414yes—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53—21no—
160C2×Q8×C53C22⋊C412yes—
161C2×Q8×C53C22⋊C412yes—
162C2×Q8×C53C2×D412yes—
163C2×D4×C53—22no—
164C2×D4×C53—22no—
165C2×D4×C53—22no—
166C2×D4×C53—22no—
167C2×D4×C53—22no—
168C2×D4×C53—22no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53C22⋊C412yes—
173C2×D4×C53C22⋊C412yes—
174C2×D4×C53C2×D412yes—
175C22×C4×C53—21no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—41no—
183C22×C4×C53C22×C411yescharacteristic
184C22×C4×C53C22×C411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53#4111yescharacteristic
194C22×C4×C53#4111yescharacteristic
195C22×C4×C53#4111yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—22no—
198C2×C22⋊D53—22no—
199C2×C22⋊D53—41no—
200C2×C22⋊D53—41no—
201C2×C22⋊D53—41no—
202C2×C22⋊D53—41no—
203C22×Dic53—21no—
204#11719945—22no—
205#11719945—22no—
206#11719945—22no—
207#11719945—22no—
208#11719945—22no—
209#11719945—22no—
210#11719945—22no—
211#11719945—22no—
212#11719945—41no—
213#11719945—41no—
214#11719945—41no—
215#11719945—41no—
216#11719945—41no—
217#11719945—41no—
218#11719945—41no—
219#11719945—41no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212C22×C412yes—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—41no—
229C2×C4×D53—41no—
230C2×C4×D53—41no—
231C2×C4×D53—41no—
232C2×Dic106—21no—
233C2×Dic106—21no—
234C2×Dic106—21no—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106C22×C412yes—
238C2×C8×C53—22no—
239C2×C8×C53—22no—
240C2×C8×C53—22no—
241C2×C8×C53—41no—
242C2×C8×C53—41no—
243C2×C8×C53—41no—
244C2×C8×C53—41no—
245C4⋊C4×C53—22no—
246C4⋊C4×C53—41no—
247C22⋊C4×C53—22no—
248C22⋊C4×C53—41no—
249C42×C53—22no—
250C42×C53—41no—
251#11719925—28no—
252#11719924—28no—
253#11719923—28no—
254#11719922—28no—
255#11719917—216no—
256#11719917—22no—
257#11719917—22no—
258#11719917—22no—
259#11719917—22no—
260#11719917—22no—
261#11719917—22no—
262#11719917—22no—
263#11719917—22no—
264#11719917—22no—
265#11719917—22no—
266#11719917C22×C414yes—
267#11719917C2×D414yes—
268C2×#88322—216no—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2×D414yes—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—82no—
283C23×C53C4×D411yescharacteristic
284C23×C53C4×D411yescharacteristic
285C23×C53#12111yescharacteristic
286C23×C53#12111yescharacteristic
287C23×C53#12311yescharacteristic
288C23×C53#12311yescharacteristic
289C23×C53C2×#4111yescharacteristic
290C22×D53—22no—
291C22×D53—44no—
292C22×D53—41no—
293C22×D53—41no—
294Q8×C53—22no—
295Q8×C53—22no—
296Q8×C53—22no—
297Q8×C53C2×C22⋊C414yes—
298D4×C53—24no—
299D4×C53—24no—
300D4×C53—24no—
301D4×C53—24no—
302D4×C53—22no—
303D4×C53—22no—
304D4×C53—22no—
305D4×C53C2×C22⋊C414yes—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—24no—
310C2×C4×C53—24no—
311C2×C4×C53—24no—
312C2×C4×C53—24no—
313C2×C4×C53—42no—
314C2×C4×C53—82no—
315C2×C4×C53C2×C22⋊C411yescharacteristic
316C2×C4×C53C2×C22⋊C411yescharacteristic
317C2×C4×C53C2×C22⋊C411yescharacteristic
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C4×D411yescharacteristic
320C2×C4×C53C4×D411yescharacteristic
321C2×C4×C53C4×D411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53C4×D411yescharacteristic
325C2×C4×C53#12011yescharacteristic
326C2×C4×C53#12011yescharacteristic
327C2×C4×C53#12011yescharacteristic
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12111yescharacteristic
330C2×C4×C53#12111yescharacteristic
331C2×C4×C53#12111yescharacteristic
332C2×C4×C53#12111yescharacteristic
333C2×C4×C53#12111yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12311yescharacteristic
336C2×C4×C53#12311yescharacteristic
337C2×C4×C53C23×C411yescharacteristic
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C2×#4111yescharacteristic
343C22⋊D53—42no—
344C22⋊D53—42no—
345C22⋊D53—42no—
346C22⋊D53—42no—
347C2×Dic53—22no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350D212—22no—
351D212—22no—
352D212—41no—
353D212—41no—
354C4×D53—42no—
355C4×D53—42no—
356C4×D53—42no—
357C4×D53—42no—
358Dic106—22no—
359Dic106—22no—
360Dic106—41no—
361Dic106—41no—
362C8×C53—42no—
363#88322—24no—
364#88322—24no—
365#88322—24no—
366C2×#1881—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—24no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—44no—
376C22×C53—82no—
377C22×C53—82no—
378C22×C53#38611yescharacteristic
379C22×C53#38611yescharacteristic
380C22×C53#38611yescharacteristic
381C22×C53#38611yescharacteristic
382C22×C53C2×C4×D411yescharacteristic
383C22×C53C2×#12111yescharacteristic
384C22×C53C2×#12311yescharacteristic
385C2×D53—44no—
386C2×D53—42no—
387C2×D53—82no—
388C2×D53—82no—
389C4×C53—24no—
390C4×C53—82no—
391C4×C53#38611yescharacteristic
392C4×C53#38611yescharacteristic
393C4×C53#38611yescharacteristic
394C4×C53#38611yescharacteristic
395C4×C53C22×C22⋊C411yescharacteristic
396C4×C53C2×C4×D411yescharacteristic
397C4×C53C2×#12011yescharacteristic
398C4×C53C2×#12111yescharacteristic
399Dic53—42no—
400C2×#575—531no—
401C2×#568—531no—
402C2×#421—531no—
403C2×#416D5311yescharacteristic, complemented
404C2×#408—531no—
405#1881—538no—
406C2×#344—531no—
407C2×#341—531no—
408C2×C53—21no—
409C2×C53—21no—
410C2×C53—21no—
411C2×C53—21no—
412C2×C53—21no—
413C2×C53—21no—
414C2×C53—44no—
415C2×C53#188112yescomplemented
416C2×C53C2×#38611yescharacteristic
417D53—82no—
418C22×#41—531no—
419C22×#41C2×D5311yescharacteristic
420#575—534no—
421#575—534no—
422#575—1062no—
423#575—1062no—
424C2×#137—532no—
425C2×#137—1061no—
426C2×AGL(1,ℤ/8)—532no—
427C2×AGL(1,ℤ/8)—1061no—
428C2×#135—1062no—
429#568—534no—
430#568—1062no—
431#568—1062no—
432#568—1062no—
433C2×#131—1062no—
434C2×#131—1062no—
435C22×M16—531no—
436C22×M16—531no—
437C22×M16—531no—
438C22×M16—1062no—
439C23×C8C2×D5311yescharacteristic
440C2×#117C2×D5311yescharacteristic
441#421—534no—
442#421—1062no—
443C2×#104—1062no—
444#416—22no—
445#416C2×D5314yescomplemented
446C2×#103—21no—
447C2×#102—21no—
448#408—534no—
449#408—1062no—
450C2×C22⋊C8—1062no—
451#344—534no—
452#341—534no—
453C53C2×#188111yescharacteristic, complemented, Sylow
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—532no—
461C2×#41—532no—
462C2×#41—1061no—
463C2×#41—1061no—
464C2×#41—1061no—
465C2×#41—1061no—
466C2×#41—1061no—
467C2×#41—1061no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—1061no—
471C2×#41—1061no—
472C2×#41C4×D5312yes—
473C2×#41C4×D5312yes—
474C2×#41D21212yes—
475C2×#41D21212yes—
476C2×#41C22⋊D5312yes—
477C2×#41C22×D5312yes—
478C22×Q8—531no—
479C22×Q8C22⋊D5311yescharacteristic
480C22×D4—21no—
481C22×D4—531no—
482C22×D4—1061no—
483C22×D4C22⋊D5311yescharacteristic
484C23×C4—21no—
485C23×C4—1061no—
486C23×C4C22×D5311yescharacteristic
487#137—538no—
488#137—1064no—
489#137—1064no—
490#137—1064no—
491AGL(1,ℤ/8)—538no—
492AGL(1,ℤ/8)—1064no—
493AGL(1,ℤ/8)—1064no—
494AGL(1,ℤ/8)—1064no—
495#135—1068no—
496#135—1068no—
497C2×Q16—1062no—
498C2×SD16—1062no—
499C2×SD16—1062no—
500C2×D8—1062no—
501#131—1068no—
502#131—1068no—
503#131—1068no—
504#131—1068no—
505C2×M16—532no—
506C2×M16—532no—
507C2×M16—532no—
508C2×M16—532no—
509C2×M16—532no—
510C2×M16—532no—
511C2×M16—532no—
512C2×M16—532no—
513C2×M16—1068no—
514C2×M16—1064no—
515C2×M16—1068no—
516C2×M16—1061no—
517C2×M16—1061no—
518C2×M16—1061no—
519C2×M16—1061no—
520C2×M16—1061no—
521C2×M16—1061no—
522C2×M16—1061no—
523C2×M16—1061no—
524C2×M16—1061no—
525C2×M16—1061no—
526C22×C8—21no—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—21no—
530C22×C8—21no—
531C22×C8—21no—
532C22×C8—532no—
533C22×C8—1064no—
534C22×C8—1061no—
535C22×C8—1061no—
536C22×C8C22×D5312yes—
537#117—21no—
538#117—21no—
539#117—21no—
540#117C22×D5312yes—
541C2×C4⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544#104—1068no—
545#103—24no—
546#102—24no—
547C22⋊C8—1068no—
548C24—21no—
549C24—1061no—
550C24#1171994711yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—1062no—
564#41—1062no—
565#41—1062no—
566#41—1062no—
567#41—1062no—
568#41—1062no—
569#41—1062no—
570#41—1062no—
571#41—2121no—
572#41—2121no—
573#41—2121no—
574#41—2121no—
575#41—2121no—
576#41—2121no—
577#41—2121no—
578#41—2121no—
579#41#1171992114yes—
580#41#1171992114yes—
581#41C2×C4×D5314yes—
582#41C2×D21214yes—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—532no—
587C2×Q8—1061no—
588C2×Q8—1061no—
589C2×Q8—1061no—
590C2×Q8—1061no—
591C2×Q8—1061no—
592C2×Q8#1171992112yes—
593C2×Q8#1171992112yes—
594C2×Q8C2×C22⋊D5312yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—532no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—1061no—
608C2×D4—1061no—
609C2×D4—1061no—
610C2×D4—1061no—
611C2×D4—1061no—
612C2×D4—2121no—
613C2×D4—2121no—
614C2×D4—2121no—
615C2×D4—2121no—
616C2×D4#1171992112yes—
617C2×D4#1171992112yes—
618C2×D4C2×C22⋊D5312yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—41no—
627C22×C4—1061no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—2121no—
631C22×C4—2121no—
632C22×C4—2121no—
633C22×C4—2121no—
634C22×C4C2×C4×D5311yescharacteristic
635C22×C4C2×C4×D5311yescharacteristic
636C22×C4C2×D21211yescharacteristic
637C22×C4C2×D21211yescharacteristic
638C22×C4D4×D5311yescharacteristic
639C22×C4D4×D5311yescharacteristic
640C22×C4D4×D5311yescharacteristic
641C22×C4D4×D5311yescharacteristic
642C22×C4#1171994711yescharacteristic
643C22×C4#1171994711yescharacteristic
644C22×C4#1171994711yescharacteristic
645C22×C4C2×C22⋊D5311yescharacteristic
646C22×C4C2×C22⋊D5311yescharacteristic
647C22×C4C23×D5311yescharacteristic
648Q16—1068no—
649SD16—1068no—
650SD16—1068no—
651D8—1068no—
652M16—534no—
653M16—534no—
654M16—10616no—
655M16—1062no—
656M16—1062no—
657M16—1062no—
658M16—1062no—
659M16—1062no—
660M16—1062no—
661M16—1062no—
662M16—1062no—
663M16—1062no—
664M16—1062no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—41no—
669C2×C8—41no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—534no—
673C2×C8—10616no—
674C2×C8—1062no—
675C2×C8—1062no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8—1062no—
679C2×C8—1062no—
680C2×C8—1062no—
681C2×C8—1062no—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C42—22no—
687C42—41no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—82no—
693C23—1062no—
694C23—2124no—
695C23—2121no—
696C23—2121no—
697C23#1313317711yescharacteristic
698C23#1313317711yescharacteristic
699C23#1313318911yescharacteristic
700C23#1313318911yescharacteristic
701C23#1313320111yescharacteristic
702C23#1313320111yescharacteristic
703C23C2×#1171994711yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—1062no—
708Q8—1062no—
709Q8—2121no—
710Q8—2121no—
711Q8C2×#1171992114yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—1062no—
720D4—1062no—
721D4—2122no—
722D4—2122no—
723D4—2122no—
724D4—2122no—
725D4—2121no—
726D4—2121no—
727D4C2×#1171992114yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—42no—
736C2×C4—82no—
737C2×C4—1062no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4C2×#1171992111yescharacteristic
745C2×C4C2×#1171992111yescharacteristic
746C2×C4C2×#1171992111yescharacteristic
747C2×C4C2×#1171992111yescharacteristic
748C2×C4#1313317711yescharacteristic
749C2×C4#1313317711yescharacteristic
750C2×C4#1313317711yescharacteristic
751C2×C4#1313317711yescharacteristic
752C2×C4#1313317711yescharacteristic
753C2×C4#1313317711yescharacteristic
754C2×C4#1313318711yescharacteristic
755C2×C4#1313318711yescharacteristic
756C2×C4#1313318711yescharacteristic
757C2×C4#1313318711yescharacteristic
758C2×C4#1313318911yescharacteristic
759C2×C4#1313318911yescharacteristic
760C2×C4#1313318911yescharacteristic
761C2×C4#1313318911yescharacteristic
762C2×C4#1313318911yescharacteristic
763C2×C4#1313318911yescharacteristic
764C2×C4#1313320111yescharacteristic
765C2×C4#1313320111yescharacteristic
766C2×C4C22×C4×D5311yescharacteristic
767C2×C4C2×D4×D5311yescharacteristic
768C2×C4C2×D4×D5311yescharacteristic
769C2×C4C22×C22⋊D5311yescharacteristic
770C2×C4C22×D21211yescharacteristic
771C2×C4C2×#1171994711yescharacteristic
772C8—42no—
773C8—1064no—
774C8—1064no—
775C8—1064no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—82no—
786C22—82no—
787C22—4242no—
788C22—4242no—
789C22—2124no—
790C22—2122no—
791C22#1681050011yescharacteristic
792C22#1681050011yescharacteristic
793C22#1681050011yescharacteristic
794C22#1681050011yescharacteristic
795C22C2×#1313317711yescharacteristic
796C22C2×#1313318911yescharacteristic
797C22C2×#1313320111yescharacteristic
798C4—24no—
799C4—82no—
800C4—2122no—
801C4#1681050011yescharacteristic
802C4#1681050011yescharacteristic
803C4#1681050011yescharacteristic
804C4#1681050011yescharacteristic
805C4C22×#1171992111yescharacteristic
806C4C2×#1313317711yescharacteristic
807C4C2×#1313318711yescharacteristic
808C4C2×#1313318911yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—44no—
816C2—4242no—
817C2#2027507512yesdirect product factor
818C2C2×#1681050011yescharacteristic
subgroupG/H
centerC2×C4#13133187
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#416C2
socleC22×C53#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#416D53
hypocenterC53C2×#1881
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16811390C2semidirect
3. C2×#16810641C2semidirect
4. C2×#16810589C2semidirect
5. #20275075C2direct (N × H)
6. C2×#16810393C2semidirect
7. C2×#16810388C2semidirect
8. C2×C53×#416C2semidirect
12. #16811421C4semidirect
15. C2×#13133247C4semidirect
17. C2×#13133242C4semidirect
22. #16811390C22semidirect
30. #16810641C22semidirect
33. #16810589C22semidirect
35. #16810393C22semidirect
36. #16810388C22semidirect
41. C53×#416C22semidirect
63. #13133247C2×C4semidirect
67. #13133242C2×C4semidirect
403. C2×#416D53semidirect
415. C2×C53#1881semidirect
445. #416C2×D53semidirect
453. C53C2×#1881semidirect
817. C2#20275075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168114212
C2×#168113902
C2×#168106412
C2×#168105892
#202750752
C2×#168103932
C2×#168103882
C2×C53×#4162
C2×#188153