Finite Group Databasebeta

← C2×#20275130 #27385740

Subgroups — C2×#20275130 #27385740

Order 13568.

1870 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811389C211yesmaximal, characteristic, complemented
2C2×#16811134C211yesmaximal, characteristic
3C2×#16810605C211yesmaximal, characteristic, complemented
4C2×#16810587C211yesmaximal, characteristic, complemented
5#20275130C218yesmaximal, direct product factor
6C2×#16810395C211yesmaximal, characteristic, complemented
7C2×#16810394C211yesmaximal, characteristic, complemented
8C2×C53×#407C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811389—22no—
11#16811389—22no—
12#16811389—22no—
13#16811389C2214yescomplemented
14C2×#13133225—22no—
15C2×#13133223—22no—
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×M16×D53—22no—
19#16811134—22no—
20#16811134—22no—
21#16811134C414yes—
22#16811134C2214yes—
23C2×#13133200C412yes—
24C2×#13133196—21no—
25C2×#13133191—21no—
26C2×#13133186C412yes—
27C2×C4×C22⋊D53—22no—
28C2×#13133176C2211yescharacteristic
29#16810605—22no—
30#16810605C2214yescomplemented
31C2×#13133135—21no—
32C2×#13133133—21no—
33#16810587—22no—
34#16810587C2214yescomplemented
35C2×C22⋊#88322—22no—
36#16810395C2214yescomplemented
37#16810394C2214yescomplemented
38C24×C4×C53C2211yescharacteristic
39C22×M16×C53C2211yescharacteristic
40C22×M16×C53C2211yescharacteristic
41C53×#407—22no—
42C53×#407C2214yescomplemented
43C2×C22⋊C8×C53—22no—
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×#11719945C2×C412yes—
53C2×#11719945D412yes—
54C2×#11719945D412yes—
55C2×#11719945C2312yes—
56C22×Dic106D411yescharacteristic
57C22×D212D411yescharacteristic
58C22×C22⋊D53—22no—
59C22×C22⋊D53C2×C412yes—
60C22×C4×D53D412yes—
61#13133225—28no—
62#13133225—28no—
63#13133223—28no—
64#13133223—28no—
65C2×#11719917—21no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917—21no—
72C2×#11719917—21no—
73C2×#11719917—21no—
74C2×#11719917D412yescomplemented
75C2×#11719917C2312yes—
76C2×#11719917C2312yes—
77C2×#11719912—24no—
78M16×D53—28no—
79M16×D53—28no—
80C22×#88322—21no—
81C22×#88322D412yescomplemented
82C2×C8×D53—24no—
83#13133200—24no—
84#13133200C2×C418yes—
85#13133196—24no—
86#13133196—24no—
87#13133191—24no—
88#13133191—24no—
89#13133186—24no—
90#13133186C2×C418yes—
91C4×C22⋊D53—28no—
92C4×C22⋊D53—28no—
93#13133176—21no—
94#13133176—21no—
95#13133176C2×C412yes—
96#13133176C2312yes—
97C2×C4⋊Dic53—21no—
98C2×#11719919—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53C2×C412yes—
101C2×#11719921—22no—
102C2×C4×Dic53—21no—
103#13133135—24no—
104#13133133—24no—
105C22⋊#88322—28no—
106C25×C53C2×C411yescharacteristic
107C23×C4×C53—21no—
108C23×C4×C53—21no—
109C23×C4×C53—21no—
110C23×C4×C53—21no—
111C23×C4×C53—21no—
112C23×C4×C53—21no—
113C23×C4×C53—21no—
114C23×C4×C53—21no—
115C23×C4×C53—21no—
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53—21no—
119C23×C4×C53C2×C411yescharacteristic
120C23×C4×C53C2×C412yes—
121C23×C4×C53C2312yes—
122C23×C4×C53C2311yescharacteristic
123C2×M16×C53—21no—
124C2×M16×C53—21no—
125C2×M16×C53—21no—
126C2×M16×C53—21no—
127C2×M16×C53—21no—
128C2×M16×C53—21no—
129C2×M16×C53—21no—
130C2×M16×C53—21no—
131C2×M16×C53—21no—
132C2×M16×C53D412yescomplemented
133C2×M16×C53C2312yes—
134C2×M16×C53C2312yes—
135C22×C8×C53—21no—
136C22×C8×C53D412yescomplemented
137C22⋊C8×C53—28no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53—21no—
143C24×C53—21no—
144C24×C53—44no—
145C24×C53C22×C412yes—
146C24×C53C22×C411yescharacteristic
147C23×D53C22⋊C412yes—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—41no—
167C22×C4×C53—41no—
168C22×C4×C53—41no—
169C22×C4×C53—41no—
170C22×C4×C53—41no—
171C22×C4×C53—41no—
172C22×C4×C53—41no—
173C22×C4×C53—41no—
174C22×C4×C53—41no—
175C22×C4×C53—41no—
176C22×C4×C53—41no—
177C22×C4×C53—41no—
178C22×C4×C53—41no—
179C22×C4×C53—41no—
180C22×C4×C53—41no—
181C22×C4×C53—41no—
182C22×C4×C53C22×C412yes—
183C22×C4×C53C22×C411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
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×C53#4111yescharacteristic
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—22no—
200C2×C22⋊D53—22no—
201C2×C22⋊D53—28no—
202C2×C22⋊D53—48no—
203C2×C22⋊D53C22⋊C414yes—
204C2×C22⋊D53C22×C414yes—
205C22×Dic53—22no—
206C22×Dic53C22⋊C412yes—
207#11719945—22no—
208#11719945—22no—
209#11719945—22no—
210#11719945—22no—
211#11719945—22no—
212#11719945—22no—
213#11719945—22no—
214#11719945—22no—
215#11719945—22no—
216#11719945—22no—
217#11719945—22no—
218#11719945—22no—
219#11719945—22no—
220#11719945—22no—
221#11719945—22no—
222#11719945—22no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—21no—
226C2×D212—21no—
227C2×D212C22⋊C412yes—
228C2×D212C2×D412yes—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—22no—
233C2×C4×D53C22⋊C414yes—
234C2×C4×D53C2×D414yes—
235C2×Dic106—21no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106C22⋊C412yes—
240C2×Dic106C2×D412yes—
241M16×C53—22no—
242M16×C53—22no—
243M16×C53—22no—
244M16×C53—22no—
245M16×C53—22no—
246M16×C53—22no—
247M16×C53—41no—
248M16×C53—41no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53—41no—
253C2×C8×C53—41no—
254C2×C8×C53C2×D414yescomplemented
255C22⋊Dic53—22no—
256C22⋊Dic53—28no—
257C22⋊Dic53C22×C414yes—
258#11719921—28no—
259C4⋊Dic53—22no—
260C4⋊Dic53—22no—
261#11719919—28no—
262C4×Dic53—22no—
263C4×Dic53—22no—
264#11719917—22no—
265#11719917—22no—
266#11719917—22no—
267#11719917—22no—
268#11719917—22no—
269#11719917—22no—
270#11719917—41no—
271#11719917—41no—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322—41no—
276C2×#88322—41no—
277C2×#88322C2×D414yescomplemented
278#11719912—216no—
279C8×D53—216no—
280C23×C53—24no—
281C23×C53—24no—
282C23×C53—24no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—44no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—44no—
292C23×C53—44no—
293C23×C53—44no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53C2×C22⋊C411yescharacteristic
299C23×C53C2×C22⋊C411yescharacteristic
300C23×C53C4×D411yescharacteristic
301C23×C53C4×D411yescharacteristic
302C23×C53C4×D411yescharacteristic
303C23×C53C4×D411yescharacteristic
304C23×C53C23×C411yescharacteristic
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—44no—
308C22×D53C2×C22⋊C414yes—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53C2×C22⋊C411yescharacteristic
325C2×C4×C53C2×C22⋊C411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C4×D411yescharacteristic
328C2×C4×C53C4×D411yescharacteristic
329C2×C4×C53C4×D411yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53#12011yescharacteristic
332C2×C4×C53#12011yescharacteristic
333C2×C4×C53#12011yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12111yescharacteristic
339C2×C4×C53#12111yescharacteristic
340C2×C4×C53#12111yescharacteristic
341C2×C4×C53#12111yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12311yescharacteristic
344C2×C4×C53#12311yescharacteristic
345C2×C4×C53#12311yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53C22×D411yescharacteristic
349C2×C4×C53C22×D411yescharacteristic
350C2×C4×C53C2×#4111yescharacteristic
351C2×C4×C53C2×#4111yescharacteristic
352C22⋊D53—24no—
353C22⋊D53—24no—
354C22⋊D53—24no—
355C22⋊D53—24no—
356C22⋊D53—416no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—24no—
360C2×Dic53—44no—
361C2×Dic53C2×C22⋊C414yes—
362D212—22no—
363D212—22no—
364D212—22no—
365D212—22no—
366C4×D53—24no—
367C4×D53—24no—
368C4×D53—24no—
369C4×D53—24no—
370Dic106—22no—
371Dic106—22no—
372Dic106—22no—
373Dic106—22no—
374C8×C53—24no—
375C8×C53—42no—
376#88322—24no—
377#88322—42no—
378C2×#1891—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—24no—
383C22×C53—24no—
384C22×C53—24no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—42no—
390C22×C53—44no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—44no—
394C22×C53—44no—
395C22×C53—44no—
396C22×C53—42no—
397C22×C53#38611yescharacteristic
398C22×C53#38611yescharacteristic
399C22×C53#38611yescharacteristic
400C22×C53#38611yescharacteristic
401C22×C53C22×C22⋊C411yescharacteristic
402C22×C53C2×C4×D411yescharacteristic
403C22×C53C2×C4×D411yescharacteristic
404C2×D53—24no—
405C2×D53—44no—
406C2×D53—44no—
407C2×D53—82no—
408C4×C53—42no—
409C4×C53#38611yescharacteristic
410C4×C53#38611yescharacteristic
411C4×C53#38611yescharacteristic
412C4×C53#38611yescharacteristic
413C4×C53C2×#12011yescharacteristic
414C4×C53C2×#12111yescharacteristic
415C4×C53C2×#12111yescharacteristic
416C4×C53C2×#12311yescharacteristic
417Dic53—24no—
418Dic53—44no—
419C2×#568—531no—
420C2×#525—531no—
421C2×#413—531no—
422C2×#407—531no—
423C2×#407D5311yescharacteristic, complemented
424#1891—538no—
425C2×#344—531no—
426C2×#344—531no—
427C2×C53—21no—
428C2×C53—21no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—21no—
432C2×C53—21no—
433C2×C53—44no—
434C2×C53#189112yescomplemented
435C2×C53C2×#38611yescharacteristic
436D53—44no—
437C22×#41—531no—
438C24×C4C2×D5311yescharacteristic
439#568—534no—
440#568—1062no—
441#568—1062no—
442#568—1062no—
443C2×#131—1062no—
444C2×#131—1062no—
445C22×M16—531no—
446C22×M16—531no—
447C22×M16—1062no—
448C22×M16C2×D5311yescharacteristic
449C22×M16C2×D5311yescharacteristic
450#525—534no—
451#525—534no—
452#525—1062no—
453#525—1062no—
454C2×#123—532no—
455C2×C22⋊Q8—1061no—
456C2×#121—1061no—
457C2×#120—532no—
458C2×C4×D4—1062no—
459C2×#117—531no—
460#413—534no—
461#413—1062no—
462C2×#101—1061no—
463C2×#100—1061no—
464#407—22no—
465#407—534no—
466#407—1062no—
467#407C2×D5314yescomplemented
468C2×C22⋊C8—22no—
469C2×C22⋊C8—1062no—
470#344—534no—
471#344—534no—
472C53C2×#189111yescharacteristic, complemented, Sylow
473C25C4×D5311yescharacteristic
474C2×#41—532no—
475C2×#41—532no—
476C2×#41—532no—
477C2×#41—532no—
478C2×#41—1061no—
479C2×#41—1061no—
480C2×#41—1061no—
481C2×#41—1061no—
482C2×#41—1061no—
483C2×#41—1061no—
484C2×#41—1061no—
485C2×#41—1061no—
486C22×Q8—531no—
487C22×D4—532no—
488C22×D4—531no—
489C22×D4—1062no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—532no—
503C23×C4C4×D5311yescharacteristic
504C23×C4C4×D5312yes—
505C23×C4C22×D5312yes—
506C23×C4C22×D5311yescharacteristic
507#131—1068no—
508#131—1068no—
509#131—1068no—
510#131—1068no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—532no—
521C2×M16—532no—
522C2×M16—532no—
523C2×M16—1064no—
524C2×M16—1068no—
525C2×M16—1068no—
526C2×M16—1061no—
527C2×M16—1061no—
528C2×M16—1061no—
529C2×M16—1061no—
530C2×M16—1061no—
531C2×M16—1061no—
532C2×M16—1061no—
533C2×M16—1061no—
534C2×M16—1061no—
535C2×M16C22⋊D5312yescomplemented
536C2×M16C22×D5312yes—
537C2×M16C22×D5312yes—
538C22×C8—21no—
539C22×C8—532no—
540C22×C8—1064no—
541C22×C8—1061no—
542C22×C8C22⋊D5312yescomplemented
543#123—538no—
544#123—1064no—
545C22⋊Q8—1064no—
546C22⋊Q8—1064no—
547#121—1064no—
548#121—1064no—
549#120—538no—
550#120—1064no—
551C4×D4—1068no—
552C4×D4—1068no—
553#117—532no—
554#117—532no—
555#117—1061no—
556#117—1061no—
557C2×C4⋊C4—1062no—
558C2×C4⋊C4—1061no—
559C2×C22⋊C4—532no—
560C2×C22⋊C4—1062no—
561C2×C22⋊C4—1062no—
562C2×C42—1061no—
563#101—1064no—
564#100—1064no—
565C22⋊C8—28no—
566C22⋊C8—1068no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24—21no—
573C24—44no—
574C24—532no—
575C24C2×C4×D5312yes—
576C24C2×C4×D5311yescharacteristic
577#41—1062no—
578#41—1062no—
579#41—1062no—
580#41—1062no—
581#41—1062no—
582#41—1062no—
583#41—1062no—
584#41—1062no—
585#41—1062no—
586#41—1062no—
587#41—1062no—
588#41—1062no—
589#41—1062no—
590#41—1062no—
591#41—1062no—
592#41—1062no—
593C2×Q8—532no—
594C2×Q8—532no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×Q8—1061no—
599C2×D4—534no—
600C2×D4—534no—
601C2×D4—532no—
602C2×D4—532no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—1068no—
608C2×D4—1061no—
609C2×D4—1061no—
610C2×D4—1061no—
611C2×D4—1061no—
612C2×D4—2128no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—532no—
648C22×C4—534no—
649C22×C4—534no—
650C22×C4—1062no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4C2×C4×D5312yes—
656C22×C4C2×C4×D5311yescharacteristic
657C22×C4#1171994511yescharacteristic
658C22×C4#1171994511yescharacteristic
659C22×C4D4×D5311yescharacteristic
660C22×C4D4×D5311yescharacteristic
661C22×C4D4×D5311yescharacteristic
662C22×C4D4×D5311yescharacteristic
663C22×C4D4×D5311yescharacteristic
664C22×C4D4×D5311yescharacteristic
665C22×C4#1171994711yescharacteristic
666C22×C4#1171994711yescharacteristic
667C22×C4C2×C22⋊D5311yescharacteristic
668C22×C4C2×C22⋊D5311yescharacteristic
669C22×C4C23×D5311yescharacteristic
670M16—22no—
671M16—22no—
672M16—22no—
673M16—22no—
674M16—22no—
675M16—22no—
676M16—41no—
677M16—41no—
678M16—10616no—
679M16—1062no—
680M16—1062no—
681M16—1062no—
682M16—1062no—
683M16—1062no—
684M16—1062no—
685M16—2121no—
686M16—2121no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—534no—
693C2×C8—10616no—
694C2×C8—1062no—
695C2×C8—1062no—
696C2×C8—1062no—
697C2×C8—2121no—
698C2×C8—2121no—
699C2×C8C2×C22⋊D5314yescomplemented
700C4⋊C4—1068no—
701C4⋊C4—1062no—
702C4⋊C4—1062no—
703C22⋊C4—534no—
704C22⋊C4—1068no—
705C22⋊C4—1068no—
706C22⋊C4—1062no—
707C42—1062no—
708C42—1062no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—42no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—534no—
728C23—1062no—
729C23—1062no—
730C23—2124no—
731C23C22⋊C4×D5311yescharacteristic
732C23C22⋊C4×D5311yescharacteristic
733C23#1313317711yescharacteristic
734C23#1313317711yescharacteristic
735C23C4×C22⋊D5311yescharacteristic
736C23C4×C22⋊D5311yescharacteristic
737C23C22×C4×D5311yescharacteristic
738Q8—1062no—
739Q8—1062no—
740Q8—1062no—
741Q8—1062no—
742D4—1064no—
743D4—1064no—
744D4—1064no—
745D4—1064no—
746D4—1062no—
747D4—1062no—
748D4—1062no—
749D4—1062no—
750D4—21216no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—534no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1064no—
770C2×C4—1064no—
771C2×C4—1064no—
772C2×C4—1064no—
773C2×C4—1064no—
774C2×C4—2124no—
775C2×C4C22⋊C4×D5311yescharacteristic
776C2×C4C22⋊C4×D5311yescharacteristic
777C2×C4#1313317711yescharacteristic
778C2×C4#1313317711yescharacteristic
779C2×C4C4×C22⋊D5311yescharacteristic
780C2×C4C4×C22⋊D5311yescharacteristic
781C2×C4#1313318511yescharacteristic
782C2×C4#1313318511yescharacteristic
783C2×C4#1313318511yescharacteristic
784C2×C4#1313318511yescharacteristic
785C2×C4#1313318811yescharacteristic
786C2×C4#1313318811yescharacteristic
787C2×C4#1313318811yescharacteristic
788C2×C4#1313318811yescharacteristic
789C2×C4#1313319011yescharacteristic
790C2×C4#1313319011yescharacteristic
791C2×C4#1313319011yescharacteristic
792C2×C4#1313319011yescharacteristic
793C2×C4#1313319911yescharacteristic
794C2×C4#1313319911yescharacteristic
795C2×C4#1313319911yescharacteristic
796C2×C4#1313319911yescharacteristic
797C2×C4C2×D4×D5311yescharacteristic
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C2×D4×D5311yescharacteristic
800C2×C4C22×C22⋊D5311yescharacteristic
801C2×C4C2×#1171994711yescharacteristic
802C2×C4C2×#1171994511yescharacteristic
803C8—24no—
804C8—42no—
805C8—1064no—
806C8—2122no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—1064no—
826C22—4242no—
827C22—2124no—
828C22—2124no—
829C22#1681049911yescharacteristic
830C22#1681049911yescharacteristic
831C22#1681049911yescharacteristic
832C22#1681049911yescharacteristic
833C22C2×C22⋊C4×D5311yescharacteristic
834C22C2×#1313317711yescharacteristic
835C22C2×C4×C22⋊D5311yescharacteristic
836C4—42no—
837C4—1064no—
838C4—2124no—
839C4#1681049911yescharacteristic
840C4#1681049911yescharacteristic
841C4#1681049911yescharacteristic
842C4#1681049911yescharacteristic
843C4C2×#1313318511yescharacteristic
844C4C2×#1313318811yescharacteristic
845C4C2×#1313319011yescharacteristic
846C4C2×#1313319911yescharacteristic
847C2—21no—
848C2—21no—
849C2—21no—
850C2—21no—
851C2—21no—
852C2—21no—
853C2—44no—
854C2—2124no—
855C2#2027513012yesdirect product factor
856C2C2×#1681049911yescharacteristic
subgroupG/H
centerC2×C4#13133185
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#407C2
socleC22×C53#386
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53C2×#1891
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16811389C2semidirect
3. C2×#16810605C2semidirect
4. C2×#16810587C2semidirect
5. #20275130C2direct (N × H)
6. C2×#16810395C2semidirect
7. C2×#16810394C2semidirect
8. C2×C53×#407C2semidirect
13. #16811389C22semidirect
30. #16810605C22semidirect
34. #16810587C22semidirect
36. #16810395C22semidirect
37. #16810394C22semidirect
42. C53×#407C22semidirect
74. C2×#11719917D4semidirect
81. C22×#88322D4semidirect
132. C2×M16×C53D4semidirect
136. C22×C8×C53D4semidirect
254. C2×C8×C53C2×D4semidirect
277. C2×#88322C2×D4semidirect
423. C2×#407D53semidirect
434. C2×C53#1891semidirect
467. #407C2×D53semidirect
472. C53C2×#1891semidirect
535. C2×M16C22⋊D53semidirect
542. C22×C8C22⋊D53semidirect
699. C2×C8C2×C22⋊D53semidirect
855. C2#20275130direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113892
C2×#168111342
C2×#168106052
C2×#168105872
#202751302
C2×#168103952
C2×#168103942
C2×C53×#4072
C2×#189153