Finite Group Databasebeta

← C2×#20287542 #28263857

Subgroups — C2×#20287542 #28263857

Order 13568.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811346C211yesmaximal, characteristic, complemented
2#20287542C2116yesmaximal, direct product factor
3C2×#16810993C211yesmaximal, characteristic, complemented
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810980C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810905C211yesmaximal, characteristic, complemented
8C2×#16810920C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic
10C2×#16810838C211yesmaximal, characteristic
11C2×#16810828C211yesmaximal, characteristic, complemented
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×C4×#11719923C211yesmaximal, characteristic, complemented
16C2×C53×#554C211yesmaximal, characteristic, complemented
17C22×#11719923C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811346—24no—
21#16811346C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133212—21no—
25C2×#13133205C2211yescharacteristic
26C2×#13133205C2211yescharacteristic
27C2×#13133193—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×Dic106C2211yescharacteristic
30C2×C4×D212C2211yescharacteristic
31C2×#13133175—21no—
32#16810993C2218yescomplemented
33#16810985C2218yescomplemented
34#16810980C2218yescomplemented
35#16810927C2218yescomplemented
36#16810920C2218yescomplemented
37#16810905C2218yescomplemented
38#16810838C2218yes—
39#16810838C2218yes—
40#16810828C2218yescomplemented
41#16810754C2218yescomplemented
42#16810733C2218yes—
43#16810723C2218yescomplemented
44C4×#11719923C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×#13133140C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#554—24no—
65C53×#554C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#125×C53C2211yescharacteristic
68C2×#125×C53C2211yescharacteristic
69C2×C22⋊Q8×C53—21no—
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C4⋊C4×C53—21no—
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C4×D53—21no—
81C2×#11719923—24no—
82C2×#11719923—24no—
83C2×#11719923C2314yes—
84C2×#11719923C2314yes—
85C2×#11719922—24no—
86C2×#11719922C2314yes—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133217—22no—
92#13133217C2314yes—
93#13133212—28no—
94#13133212—28no—
95#13133205—22no—
96#13133205—22no—
97#13133205C2314yes—
98#13133205C2314yes—
99#13133193—28no—
100C4×Dic106—22no—
101C4×Dic106—22no—
102C4×Dic106C2314yes—
103C4×Dic106C2314yes—
104C4×D212—22no—
105C4×D212C2314yes—
106#13133175—28no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53—21no—
109C2×C4⋊Dic53C2311yescharacteristic
110C2×#11719919—21no—
111C2×#11719919—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133148C2314yes—
121#13133148C2314yes—
122C4⋊#88322C2314yes—
123C4⋊#88322C2314yes—
124C4⋊#88322C2314yes—
125#13133140C2314yes—
126#13133140C2314yes—
127#13133140C2314yes—
128#13133140C2314yes—
129#13133140C2314yes—
130#13133140C2314yes—
131#13133138C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133128C2314yes—
136#13133128C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53—21no—
139C22×Q8×C53D411yescharacteristic
140C22×D4×C53C2311yescharacteristic
141C23×C4×C53—21no—
142C23×C4×C53—21no—
143C23×C4×C53—21no—
144C4⋊Q8×C53—22no—
145C4⋊Q8×C53C2314yes—
146#125×C53—22no—
147#125×C53—22no—
148#125×C53C2314yes—
149#125×C53C2314yes—
150C22⋊Q8×C53—28no—
151C22⋊Q8×C53—28no—
152C22⋊Q8×C53—28no—
153C4×Q8×C53D414yes—
154C4×Q8×C53C2314yes—
155C4×D4×C53—22no—
156C4×D4×C53—22no—
157C4×D4×C53—22no—
158C4×D4×C53C2314yes—
159C4×D4×C53C2314yes—
160C4×D4×C53C2314yes—
161C2×C4⋊C4×C53—28no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C23×D53—21no—
181C2×Q8×C53—24no—
182C2×Q8×C53—42no—
183C2×Q8×C53—82no—
184C2×Q8×C53C2×D414yes—
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53#4114yes—
188C2×D4×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—24no—
194C22×C4×C53—24no—
195C22×C4×C53—44no—
196C22×C4×C53—82no—
197C22×C4×C53—82no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—21no—
211C2×D212C2412yes—
212C2×C4×D53—24no—
213C2×C4×D53—44no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—21no—
219C2×Dic106—21no—
220C2×Dic106C2412yes—
221C2×Dic106C2412yes—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2×D414yes—
231C4⋊C4×C53C2×D414yes—
232C4⋊C4×C53C2×D414yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2×D412yes—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C42×C53C2412yes—
244C42×C53C2412yes—
245#11719923—28no—
246#11719923—28no—
247#11719922—28no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53—21no—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C2×#88322—22no—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C23×C53—24no—
270C23×C53—22no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278Q8×C53—44no—
279Q8×C53—84no—
280D4×C53—24no—
281D4×C53—22no—
282D4×C53C2×#4114yes—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—48no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—84no—
297C2×C4×C53—84no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314D212—22no—
315D212—22no—
316D212—42no—
317C4×D53—48no—
318Dic106—22no—
319Dic106—22no—
320Dic106—22no—
321Dic106—22no—
322Dic106—42no—
323Dic106—42no—
324#88322—22no—
325#88322—22no—
326#88322—22no—
327#88322—22no—
328C2×#3376—531nomaximal, Sylow
329C22×C53—24no—
330C22×C53—48no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53#54812yes—
334C22×C53#57512yes—
335C22×C53#57712yes—
336C22×C53C23×D411yescharacteristic
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53#54812yes—
351C4×C53C22×#4111yescharacteristic
352C4×C53C2×2−1+411yescharacteristic
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#556—531no—
357C2×#554D5311yescharacteristic, complemented
358#3376—5316no—
359C2×#491—531no—
360C2×#489—531no—
361C2×#488—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#478—531no—
365C2×#463—531no—
366C2×#463—531no—
367C2×#461—531no—
368C2×#446—531no—
369C2×#442—531no—
370C2×#440—531no—
371C2×C4×SD16—531no—
372C2×C53—44no—
373C2×C53#337614yescomplemented
374C2×C53C2×#54811yescharacteristic
375C2×C53C2×#57511yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—82no—
378C22×SD16—531no—
379C22×SD16—531no—
380C22×D8—531no—
381#556—538no—
382#556—1064no—
383#554—24no—
384#554C2×D5318yescomplemented
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8C2×D5311yescharacteristic
387C2×#126—1061no—
388C2×#126—1061no—
389C2×#125C2×D5311yescharacteristic
390C2×#125C2×D5311yescharacteristic
391C2×#124—531no—
392C2×#124—531no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×D4—531no—
401C2×C4×D4C2×D5311yescharacteristic
402C2×C4×D4C2×D5311yescharacteristic
403C2×C4×D4C2×D5311yescharacteristic
404C2×#117—1061no—
405C22×C4⋊C4—21no—
406#491—538no—
407#489—538no—
408#488—538no—
409#479—538no—
410#478—538no—
411#475—538no—
412#463—538no—
413#463—538no—
414#461—538no—
415#446—538no—
416#442—538no—
417#440—538no—
418C4×SD16—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×C4⋊C8—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×#97—531no—
436C2×#97—531no—
437C2×C4×C8—531no—
438C53C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—531no—
441C22×Q8—531no—
442C22×Q8C22⋊D5311yescharacteristic
443C22×D4—531no—
444C22×D4C22×D5311yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—1061no—
449C2×SD16—534no—
450C2×SD16—534no—
451C2×SD16—1064no—
452C2×SD16—1064no—
453C2×D8—534no—
454C2×D8—1064no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—531no—
459C4⋊Q8—22no—
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462C4⋊Q8C22×D5314yes—
463#126—1068no—
464#126—1068no—
465#125—22no—
466#125—22no—
467#125C22×D5314yes—
468#125C22×D5314yes—
469#124—534no—
470#124—534no—
471#124—1062no—
472#124—1062no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—1068no—
477C4×Q8—534no—
478C4×Q8—534no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8C22⋊D5314yes—
482C4×Q8C22×D5314yes—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—534no—
487C4×D4—1062no—
488C4×D4C22×D5314yes—
489C4×D4C22×D5314yes—
490C4×D4C22×D5314yes—
491#117—1068no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4C22⋊D5311yescharacteristic
504C2×C4⋊C4C22⋊D5311yescharacteristic
505C2×C4⋊C4C22⋊D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42C22×D5311yescharacteristic
520C2×C42C22×D5311yescharacteristic
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8—534no—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#102—534no—
535#102—534no—
536#102—534no—
537#102—534no—
538#97—534no—
539#97—534no—
540C4×C8—534no—
541C24—21no—
542C24—1061no—
543C2×Q8—24no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—532no—
547C2×Q8—532no—
548C2×Q8—1061no—
549C2×Q8—1061no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×Q8C2×C22⋊D5314yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—532no—
558C2×D4—1061no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4#1171994914yes—
562C2×D4C23×D5312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—44no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1064no—
576C22×C4—2124no—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C2×C22⋊D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584SD16—1068no—
585SD16—1068no—
586D8—1068no—
587C2×C8—532no—
588C2×C8—532no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8—1062no—
594C2×C8—1062no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—532no—
604C4⋊C4—1061no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4C2×C22⋊D5314yes—
610C4⋊C4C2×C22⋊D5314yes—
611C4⋊C4C2×C22⋊D5314yes—
612C4⋊C4C23×D5312yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—1064no—
624C42—1064no—
625C42C2×C22⋊D5312yes—
626C42C2×C22⋊D5312yes—
627C42C2×C22⋊D5312yes—
628C42C23×D5312yes—
629C42C23×D5312yes—
630C42C23×D5312yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—1062no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23C22×C22⋊D5311yescharacteristic
640Q8—44no—
641Q8—84no—
642Q8—1062no—
643Q8—1062no—
644Q8—1062no—
645Q8—1062no—
646Q8—2122no—
647Q8—2122no—
648D4—24no—
649D4—22no—
650D4—1062no—
651D4—1062no—
652D4—2122no—
653D4C2×#1171994914yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—2128no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4C22×C22⋊D5312yes—
677C2×C4C22×C22⋊D5312yes—
678C2×C4C22×C22⋊D5312yes—
679C2×C4C22×C22⋊D5312yes—
680C2×C4C22×C22⋊D5312yes—
681C2×C4C22×C22⋊D5312yes—
682C2×C4C22×C22⋊D5311yescharacteristic
683C2×C4C2×#1171994912yes—
684C2×C4#1313326512yes—
685C2×C4C24×D5311yescharacteristic
686C8—1062no—
687C8—1062no—
688C8—1062no—
689C8—1062no—
690C22—24no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—4244no—
695C22—2122no—
696C22—2122no—
697C22—2122no—
698C22#1681128412yes—
699C22#1681142112yes—
700C22#1681143412yes—
701C22C23×C22⋊D5311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4#1681128412yes—
715C4C22×#1171994911yescharacteristic
716C4C2×#1313326511yescharacteristic
717C2—44no—
718C2—4242no—
719C2#2028754214yesdirect product factor
720C2C2×#1681128411yescharacteristic
721C2C2×#1681142111yescharacteristic
722C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#554D53
hypocenterC53C2×#3376
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16811346C2semidirect
2. #20287542C2direct (N × H)
3. C2×#16810993C2semidirect
4. C2×#16810985C2semidirect
5. C2×#16810980C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810905C2semidirect
8. C2×#16810920C2semidirect
11. C2×#16810828C2semidirect
12. C2×#16810754C2semidirect
14. C2×#16810723C2semidirect
15. C2×C4×#11719923C2semidirect
16. C2×C53×#554C2semidirect
21. #16811346C22semidirect
32. #16810993C22semidirect
33. #16810985C22semidirect
34. #16810980C22semidirect
35. #16810927C22semidirect
36. #16810920C22semidirect
37. #16810905C22semidirect
40. #16810828C22semidirect
41. #16810754C22semidirect
43. #16810723C22semidirect
44. C4×#11719923C22semidirect
65. C53×#554C22semidirect
357. C2×#554D53semidirect
373. C2×C53#3376semidirect
384. #554C2×D53semidirect
438. C53C2×#3376semidirect
719. C2#20287542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113462
#202875422
C2×#168109932
C2×#168109852
C2×#168109802
C2×#168109272
C2×#168109052
C2×#168109202
C2×#168108382
C2×#168108282
C2×#168107542
C2×#168107332
C2×#168107232
C2×C4×#117199232
C2×C53×#5542
C2×#337653