Finite Group Databasebeta

← C2×#20286119 #28256995

Subgroups — C2×#20286119 #28256995

Order 13568.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811240C211yesmaximal, characteristic, complemented
2C2×#16811226C211yesmaximal, characteristic, complemented
3#20286119C2116yesmaximal, direct product factor
4C2×#16810929C211yesmaximal, characteristic, complemented
5C2×#16810925C211yesmaximal, characteristic, complemented
6C2×#16810911C211yesmaximal, characteristic, complemented
7C2×#16810902C211yesmaximal, characteristic, complemented
8C2×#16810874C211yesmaximal, characteristic, complemented
9C2×#16810867C211yesmaximal, characteristic, complemented
10C2×#16810852C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic, complemented
12C2×#16810837C211yesmaximal, characteristic, complemented
13C2×#16810836C211yesmaximal, characteristic, complemented
14C2×#16810816C211yesmaximal, characteristic, complemented
15C2×#16810649C211yesmaximal, characteristic, complemented
16C2×C53×#466C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16811240—24no—
22#16811240C2218yescomplemented
23#16811226—24no—
24#16811226C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133213C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133204—21no—
30C2×#13133204C2211yescharacteristic
31C2×#13133201—21no—
32C2×#13133199—21no—
33C2×#13133198—21no—
34C2×#13133196C2211yescharacteristic
35C2×#13133194—21no—
36C2×#13133191C2211yescharacteristic
37C2×#13133189—21no—
38C2×#13133188—21no—
39C2×#13133182C2211yescharacteristic
40C2×D4×Dic53C2211yescharacteristic
41C2×D4×Dic53C2211yescharacteristic
42C2×#13133179C2211yescharacteristic
43C2×#13133176C2211yescharacteristic
44#16810929C2218yescomplemented
45#16810925C2218yescomplemented
46#16810911C2218yescomplemented
47#16810902C2218yescomplemented
48#16810874C2218yescomplemented
49#16810867C2218yescomplemented
50#16810852C2218yescomplemented
51#16810837C2218yescomplemented
52#16810836C2218yescomplemented
53#16810822C2218yescomplemented
54#16810816C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58#16810649C2218yescomplemented
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133138C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#466C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719913—42no—
87C2×#11719913C2314yes—
88C2×#11719923—42no—
89C2×#11719923C2314yes—
90C2×#11719922—42no—
91C2×#11719922C2314yes—
92C2×#11719917—42no—
93C2×#11719917C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133216—22no—
97#13133216C2314yes—
98#13133213—22no—
99#13133213C2314yes—
100#13133210—28no—
101#13133208—22no—
102#13133208C2314yes—
103#13133204—28no—
104#13133204—22no—
105#13133204C2314yes—
106#13133201—28no—
107#13133199—28no—
108#13133198—28no—
109#13133196—22no—
110#13133196C2314yes—
111#13133194—28no—
112#13133191—22no—
113#13133191C2314yes—
114#13133189—28no—
115#13133188—28no—
116#13133182—22no—
117#13133182C2314yes—
118D4×Dic53—22no—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121D4×Dic53C2314yes—
122#13133179—22no—
123#13133179C2314yes—
124#13133176D414yes—
125#13133176C2314yes—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53D411yescharacteristic
128C2×C4⋊Dic53D411yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
141C2×C22⋊Dic53D411yescharacteristic
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133137C2314yes—
160C22×D4×C53—21no—
161C22×D4×C53—21no—
162C22×D4×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C2×D8×C53—42no—
166C2×D8×C53C2314yes—
167C22×C8×C53—42no—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2314yes—
171#121×C53—22no—
172#121×C53—22no—
173#121×C53C2314yes—
174#121×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179#107×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53C2×D411yescharacteristic
185C23×D53—21no—
186C2×D4×C53—24no—
187C2×D4×C53—24no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—82no—
195C2×D4×C53—82no—
196C2×D4×C53C2412yes—
197C2×D4×C53C2412yes—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—82no—
210C2×C22⋊D53—82no—
211C2×C22⋊D53—82no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—24no—
216C22×Dic53—24no—
217C22×Dic53—82no—
218C22×Dic53—82no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—21no—
226C2×D212C2412yes—
227C2×C4×D53—24no—
228C2×C4×D53—82no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—21no—
232C2×Dic106—24no—
233C2×Dic106—82no—
234C2×Dic106C2412yes—
235D8×C53—44no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53—44no—
239C2×C8×C53C2412yes—
240C2×C8×C53C2412yes—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊Dic53—24no—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252C22⋊Dic53C2×D414yes—
253C22⋊Dic53C2×D414yes—
254#11719923—44no—
255#11719922—44no—
256#11719921—24no—
257#11719921—24no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53C2×D414yes—
262C4⋊Dic53C2×D414yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269C4×Dic53—24no—
270C4×Dic53C2×D412yes—
271C4×Dic53C2×D412yes—
272C4×Dic53C2412yes—
273C4×Dic53C2412yes—
274#11719917—44no—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279#11719913—44no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53C22×D412yes—
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297D4×C53—22no—
298D4×C53—22no—
299D4×C53—22no—
300D4×C53—22no—
301D4×C53—42no—
302D4×C53—42no—
303D4×C53—84no—
304D4×C53—84no—
305C2×C4×C53—22no—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53H(5,𝔽2)12yes—
316C2×C4×C532−1+412yes—
317C2×C4×C53C2511yescharacteristic
318C22⋊D53—84no—
319C22⋊D53—84no—
320C22⋊D53—84no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—84no—
332C2×Dic53—84no—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337D212—22no—
338D212—22no—
339D212—42no—
340C4×D53—84no—
341Dic106—22no—
342Dic106—22no—
343Dic106—42no—
344Dic106—84no—
345C8×C53—22no—
346C8×C53—22no—
347#88322—22no—
348#88322—22no—
349C2×#3257—531nomaximal, Sylow
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—44no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—84no—
361C22×C53—84no—
362C22×C53#53712yes—
363C22×C53#57612yes—
364C22×C53#57712yes—
365C22×C53C23×D411yescharacteristic
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—84no—
370C4×C53—22no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53#53712yes—
374C4×C53C2×H(5,𝔽2)11yescharacteristic
375C4×C53C2×2−1+411yescharacteristic
376Dic53—22no—
377Dic53—22no—
378Dic53—22no—
379Dic53—22no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383C2×#542—531no—
384C2×#540—531no—
385#3257—5316no—
386C2×#479—531no—
387C2×#478—531no—
388C2×#476—531no—
389C2×#474—531no—
390C2×#469—531no—
391C2×#468—531no—
392C2×#466D5311yescharacteristic, complemented
393C2×#465—531no—
394C2×#460—531no—
395C2×#463—531no—
396C2×#463—531no—
397C2×#459—531no—
398C2×#424—531no—
399C2×C53—42no—
400C2×C53—82no—
401C2×C53—82no—
402C2×C53#325714yescomplemented
403C2×C53C2×#53711yescharacteristic
404C2×C53C2×#57611yescharacteristic
405C2×C53C2×#57711yescharacteristic
406D53—82no—
407C22×SD16—531no—
408C22×SD16—531no—
409C22×D8—531no—
410C22×D8C2×D5311yescharacteristic
411C22×M16—531no—
412C23×C8C2×D5311yescharacteristic
413#542—538no—
414#542—1064no—
415#540—538no—
416#540—1064no—
417C2×C4⋊Q8—531no—
418C2×#127—531no—
419C2×#126—1061no—
420C2×#125—531no—
421C2×#124—531no—
422C2×#124—1061no—
423C2×#123—1061no—
424C2×#123—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—531no—
427C2×C22⋊Q8—1061no—
428C2×#121—531no—
429C2×#121—1061no—
430C2×#121—1061no—
431C2×#121C2×D5311yescharacteristic
432C2×#121C2×D5311yescharacteristic
433C2×C4×Q8—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×#117—531no—
438#479—538no—
439#478—538no—
440#476—538no—
441#474—538no—
442#469—538no—
443#468—538no—
444#466C2×D5318yescomplemented
445#465—538no—
446#463—538no—
447#463—538no—
448#460—538no—
449#459—538no—
450C2×#107—531no—
451C2×#107C2×D5311yescharacteristic
452C2×#106—531no—
453C2×#106—531no—
454#424—538no—
455C2×C4⋊C8—531no—
456C2×C4⋊C8—531no—
457C2×C4⋊C8—531no—
458C2×C4⋊C8—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102C2×D5311yescharacteristic
466C2×#102C2×D5311yescharacteristic
467C53C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—531no—
469C22×Q8—1061no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4C22×D5311yescharacteristic
477C22×D4C22×D5311yescharacteristic
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C2×SD16—534no—
483C2×SD16—534no—
484C2×SD16—2122no—
485C2×SD16—2122no—
486C2×D8—42no—
487C2×D8—534no—
488C2×D8—2122no—
489C2×D8C22×D5314yes—
490C2×M16—534no—
491C2×M16—2122no—
492C22×C8—42no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5311yescharacteristic
497C22×C8C22×D5314yes—
498C4⋊Q8—534no—
499C4⋊Q8—1062no—
500#127—534no—
501#127—1062no—
502#126—1068no—
503#125—534no—
504#125—1062no—
505#124—534no—
506#124—1062no—
507#124—1068no—
508#123—1068no—
509#123—1068no—
510#123—1068no—
511C22⋊Q8—534no—
512C22⋊Q8—1068no—
513C22⋊Q8—1062no—
514#121—22no—
515#121—22no—
516#121—534no—
517#121—1068no—
518#121—1068no—
519#121—1062no—
520#121C22×D5314yes—
521#121C22×D5314yes—
522C4×Q8—534no—
523C4×Q8—1062no—
524C4×D4—534no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4—1062no—
530#117—534no—
531#117—534no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—531no—
546C2×C22⋊C4—531no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C42—531no—
555C2×C42—531no—
556C2×C42—1061no—
557#107—534no—
558#107C22×D5314yes—
559#106—534no—
560#106—534no—
561C4⋊C8—534no—
562C4⋊C8—534no—
563C4⋊C8—534no—
564C4⋊C8—534no—
565#103—534no—
566#103—534no—
567#102—534no—
568#102—534no—
569#102—534no—
570#102—534no—
571#102C22×D5314yes—
572#102C22×D5314yes—
573C24—21no—
574C24—21no—
575C24—1061no—
576C24D4×D5311yescharacteristic
577C2×Q8—532no—
578C2×Q8—1064no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8—4242no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—82no—
592C2×D4—82no—
593C2×D4—532no—
594C2×D4—1064no—
595C2×D4—1064no—
596C2×D4—1064no—
597C2×D4—1061no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—4242no—
601C2×D4—4242no—
602C2×D4—4242no—
603C2×D4C23×D5312yes—
604C2×D4C23×D5312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—531no—
613C22×C4—1064no—
614C22×C4—1064no—
615C22×C4—1064no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—4242no—
620C22×C4—4242no—
621C22×C4—4242no—
622C22×C4D4×D5312yes—
623C22×C4D4×D5311yescharacteristic
624C22×C4C23×D5312yes—
625C22×C4C23×D5311yescharacteristic
626SD16—2124no—
627SD16—2124no—
628D8—44no—
629D8—2124no—
630M16—2124no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—1062no—
637C2×C8—1062no—
638C2×C8C23×D5312yes—
639C2×C8C23×D5312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—534no—
643C4⋊C4—534no—
644C4⋊C4—532no—
645C4⋊C4—532no—
646C4⋊C4—1064no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1064no—
653C4⋊C4C23×D5312yes—
654C4⋊C4C23×D5312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—534no—
658C22⋊C4—534no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C42—532no—
667C42—532no—
668C42—532no—
669C42—532no—
670C42—1064no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—1062no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23C2×D4×D5312yes—
687C23C2×D4×D5311yescharacteristic
688Q8—1062no—
689Q8—1062no—
690Q8—4244no—
691Q8—2122no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—1062no—
701D4—1062no—
702D4—4244no—
703D4—4244no—
704D4—4244no—
705D4—2122no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—532no—
715C2×C4—532no—
716C2×C4—532no—
717C2×C4—532no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—4244no—
726C2×C4—4244no—
727C2×C4—4244no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4C2×D4×D5312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4#1313326212yes—
734C2×C4#1313326412yes—
735C2×C4C24×D5311yescharacteristic
736C8—22no—
737C8—22no—
738C8—1062no—
739C8—1062no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—4244no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22#1681120012yes—
757C22#1681142412yes—
758C22#1681143012yes—
759C22C22×D4×D5311yescharacteristic
760C4—22no—
761C4—42no—
762C4—42no—
763C4—1062no—
764C4—1062no—
765C4—1062no—
766C4—1062no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4#1681120012yes—
771C4C2×#1313326211yescharacteristic
772C4C2×#1313326411yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—4242no—
777C2#2028611914yesdirect product factor
778C2C2×#1681120011yescharacteristic
779C2C2×#1681142411yescharacteristic
780C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#466C2
socleC23×C53C22×D4
hypercenterC2×#466D53
hypocenterC53C2×#3257
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16811240C2semidirect
2. C2×#16811226C2semidirect
3. #20286119C2direct (N × H)
4. C2×#16810929C2semidirect
5. C2×#16810925C2semidirect
6. C2×#16810911C2semidirect
7. C2×#16810902C2semidirect
8. C2×#16810874C2semidirect
9. C2×#16810867C2semidirect
10. C2×#16810852C2semidirect
11. C2×#16810822C2semidirect
12. C2×#16810837C2semidirect
13. C2×#16810836C2semidirect
14. C2×#16810816C2semidirect
15. C2×#16810649C2semidirect
16. C2×C53×#466C2semidirect
22. #16811240C22semidirect
24. #16811226C22semidirect
44. #16810929C22semidirect
45. #16810925C22semidirect
46. #16810911C22semidirect
47. #16810902C22semidirect
48. #16810874C22semidirect
49. #16810867C22semidirect
50. #16810852C22semidirect
51. #16810837C22semidirect
52. #16810836C22semidirect
53. #16810822C22semidirect
54. #16810816C22semidirect
58. #16810649C22semidirect
73. C53×#466C22semidirect
392. C2×#466D53semidirect
402. C2×C53#3257semidirect
444. #466C2×D53semidirect
467. C53C2×#3257semidirect
777. C2#20286119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112402
C2×#168112262
#202861192
C2×#168109292
C2×#168109252
C2×#168109112
C2×#168109022
C2×#168108742
C2×#168108672
C2×#168108522
C2×#168108222
C2×#168108372
C2×#168108362
C2×#168108162
C2×#168106492
C2×C53×#4662
C2×#325753