Finite Group Databasebeta

← C2×#20284923 #28252349

Subgroups — C2×#20284923 #28252349

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811103C211yesmaximal, characteristic
2#20284923C2116yesmaximal, direct product factor
3C2×#16810956C211yesmaximal, characteristic, complemented
4C2×#16810951C211yesmaximal, characteristic, complemented
5C2×#16810927C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810830C211yesmaximal, characteristic, complemented
8C2×#16810825C211yesmaximal, characteristic, complemented
9C2×#16810783C211yesmaximal, characteristic
10C2×#16810783C211yesmaximal, characteristic
11C2×#16810728C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×C4×#11719924C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#541C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811103—24no—
23#16811103C2218yes—
24C2×C4×Dic106C2211yescharacteristic
25C2×C4×Dic106C2211yescharacteristic
26C2×C4×D212C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C2×#13133177—21no—
29C2×#13133177—21no—
30C2×#13133175—21no—
31C22×C4⋊Dic53C2211yescharacteristic
32C2×C4⋊C4×D53—21no—
33#16810956C2218yescomplemented
34#16810951C2218yescomplemented
35#16810927C2218yescomplemented
36#16810920C2218yescomplemented
37#16810830C2218yescomplemented
38#16810825C2218yescomplemented
39#16810783C2218yes—
40#16810783C2218yes—
41#16810728C2218yescomplemented
42#16810721C2218yescomplemented
43C4×#11719925C2218yescomplemented
44C4×#11719924C2218yescomplemented
45#16810684C2218yescomplemented
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#541—24no—
65C53×#541C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#126×C53—21no—
69C2×#125×C53—21no—
70C2×#125×C53—21no—
71C2×#125×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×Q8×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×#11719925—24no—
89C2×#11719925—24no—
90C2×#11719925C2314yes—
91C2×#11719925C2314yes—
92C2×#11719924—24no—
93C2×#11719924—24no—
94C2×#11719924C2314yes—
95C2×#11719924C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C4×Dic106—22no—
101C4×Dic106—22no—
102C4×Dic106C2314yes—
103C4×Dic106C2314yes—
104C4×D212—22no—
105C4×D212—22no—
106C4×D212C2314yes—
107C4×D212C2314yes—
108#13133177—28no—
109#13133177—28no—
110#13133175—28no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53—22no—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2314yes—
116C2×#11719919—21no—
117C2×#11719919—21no—
118C4⋊C4×D53—28no—
119C2×#11719921—21no—
120C2×#11719921—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127C4⋊#88322C2314yes—
128C4⋊#88322C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133137C2314yes—
136#13133137C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139#13133128C2314yes—
140C4×#88322C2314yes—
141C22×Q8×C53C2311yescharacteristic
142C22×Q8×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C4⋊Q8×C53—22no—
145C4⋊Q8×C53C2314yes—
146#126×C53—28no—
147#126×C53—28no—
148#125×C53—28no—
149#125×C53—28no—
150#125×C53—22no—
151#125×C53C2314yes—
152C22⋊Q8×C53—22no—
153C22⋊Q8×C53—22no—
154C22⋊Q8×C53C2314yes—
155C22⋊Q8×C53C2314yes—
156C4×Q8×C53—22no—
157C4×Q8×C53—22no—
158C4×Q8×C53C2314yes—
159C4×Q8×C53C2314yes—
160#117×C53D414yes—
161#117×C53C2314yes—
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×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53D411yescharacteristic
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—28no—
207C2×C22⋊D53—24no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—24no—
212C22×Dic53—82no—
213#11719945—216no—
214#11719945—28no—
215#11719945—28no—
216C2×D212—21no—
217C2×D212—22no—
218C2×D212#4114yes—
219C2×D212C2412yes—
220C2×C4×D53—28no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—82no—
225C2×C4×D53—82no—
226C2×Dic106—21no—
227C2×Dic106—22no—
228C2×Dic106#4114yes—
229C2×Dic106C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53C2×D414yes—
241C4⋊C4×C53C2×D414yes—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53C2×D414yes—
247C22⋊C4×C53C2×D414yes—
248C42×C53—24no—
249C42×C53—24no—
250C42×C53C2×D412yes—
251C42×C53C2×D412yes—
252C42×C53C2412yes—
253C42×C53C2412yes—
254#11719925—28no—
255#11719925—28no—
256#11719924—28no—
257#11719924—28no—
258#11719921—24no—
259#11719921—24no—
260C4⋊Dic53—24no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322—22no—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—24no—
283C22×D53—22no—
284C22×D53—42no—
285C22×D53—42no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291Q8×C53—42no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—24no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C2×#4112yes—
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2511yescharacteristic
317C22⋊D53—216no—
318C2×Dic53—24no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—84no—
325D212—24no—
326D212—22no—
327D212C2×#4114yes—
328C4×D53—216no—
329C4×D53—84no—
330C4×D53—84no—
331Dic106—24no—
332Dic106—22no—
333Dic106C2×#4114yes—
334#88322—22no—
335#88322—22no—
336#88322—22no—
337#88322—22no—
338C2×#3120—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—44no—
343C22×C53#52512yes—
344C22×C53#57712yes—
345C22×C53#57812yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—24no—
348C2×D53—48no—
349C2×D53—42no—
350C2×D53—42no—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—42no—
357C4×C53—42no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53#52512yes—
361C4×C53C22×#4111yescharacteristic
362C4×C53C22×#4111yescharacteristic
363Dic53—24no—
364Dic53—42no—
365Dic53—42no—
366C2×#541D5311yescharacteristic, complemented
367C2×#520—531no—
368#3120—5316no—
369C2×#484—531no—
370C2×#483—531no—
371C2×#479—531no—
372C2×#478—531no—
373C2×#462—531no—
374C2×#461—531no—
375C2×#452—531no—
376C2×#452—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—42no—
383C2×C53#312014yescomplemented
384C2×C53C2×#52511yescharacteristic
385C2×C53C2×#57711yescharacteristic
386C2×C53C2×#57811yescharacteristic
387D53—44no—
388C22×#41—531no—
389C22×Q16—531no—
390C22×Q16—531no—
391C22×SD16—531no—
392C22×SD16—531no—
393#541—24no—
394#541C2×D5318yescomplemented
395C2×C4⋊Q8C2×D5311yescharacteristic
396C2×#126—21no—
397C2×#126—21no—
398C2×#125—21no—
399C2×#125—21no—
400C2×#125C2×D5311yescharacteristic
401C2×C22⋊Q8C2×D5311yescharacteristic
402C2×C22⋊Q8C2×D5311yescharacteristic
403#520—538no—
404#520—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8C2×D5311yescharacteristic
408C2×C4×Q8C2×D5311yescharacteristic
409C2×C4×D4—531no—
410C2×C4×D4—531no—
411C2×C4×D4—1061no—
412C2×C4×D4—1061no—
413C2×#117—1061no—
414C2×#117C2×D5311yescharacteristic
415C22×C4⋊C4—531no—
416C22×C4⋊C4—1061no—
417#484—538no—
418#483—538no—
419#479—538no—
420#478—538no—
421#462—538no—
422#461—538no—
423#452—538no—
424#452—538no—
425#441—538no—
426#440—538no—
427C4×Q16—538no—
428C4×SD16—538no—
429#433—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#106—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×#97—531no—
447C2×C4×C8—531no—
448C53C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—534no—
450C2×#41—1064no—
451C2×#41—1064no—
452C2×#41—1062no—
453C22×Q8—531no—
454C22×Q8C22×D5311yescharacteristic
455C22×Q8C22×D5311yescharacteristic
456C22×D4—531no—
457C22×D4—1061no—
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×Q16—534no—
464C2×Q16—534no—
465C2×Q16—1064no—
466C2×Q16—1064no—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—1064no—
470C2×SD16—1064no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8—531no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D5314yes—
477#126—28no—
478#126—28no—
479#125—28no—
480#125—28no—
481#125—22no—
482#125C22×D5314yes—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8C22×D5314yes—
486C22⋊Q8C22×D5314yes—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×Q8C22×D5314yes—
494C4×Q8C22×D5314yes—
495C4×D4—534no—
496C4×D4—534no—
497C4×D4—1068no—
498C4×D4—1068no—
499C4×D4—1062no—
500C4×D4—1062no—
501#117—1068no—
502#117C22⋊D5314yes—
503#117C22×D5314yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1068no—
520C2×C4⋊C4C22⋊D5311yescharacteristic
521C2×C4⋊C4C22⋊D5311yescharacteristic
522C2×C4⋊C4C22×D5311yescharacteristic
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4C22⋊D5311yescharacteristic
529C2×C22⋊C4C22⋊D5311yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42C22×D5311yescharacteristic
535C2×C42C22×D5311yescharacteristic
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540C4⋊C8—534no—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103—534no—
547#103—534no—
548#102—534no—
549#102—534no—
550C22⋊C8—534no—
551C22⋊C8—534no—
552#97—534no—
553C4×C8—534no—
554C24—1061no—
555C24C2×C22⋊D5311yescharacteristic
556#41—1068no—
557#41—1068no—
558#41—10616no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—534no—
566C2×Q8—532no—
567C2×Q8—1061no—
568C2×Q8—1062no—
569C2×Q8C23×D5312yes—
570C2×Q8C23×D5312yes—
571C2×D4—534no—
572C2×D4—532no—
573C2×D4—1068no—
574C2×D4—1064no—
575C2×D4—1061no—
576C2×D4—1062no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—1068no—
584C22×C4—1061no—
585C22×C4—1064no—
586C22×C4—1064no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—4242no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4C2×C22⋊D5312yes—
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C2×C22⋊D5311yescharacteristic
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602Q16—1068no—
603Q16—1068no—
604SD16—1068no—
605SD16—1068no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8—1062no—
613C2×C8—1062no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4C2×C22⋊D5314yes—
632C4⋊C4C2×C22⋊D5314yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4C2×C22⋊D5314yes—
640C22⋊C4C2×C22⋊D5314yes—
641C42—24no—
642C42—24no—
643C42—1064no—
644C42—1064no—
645C42C2×C22⋊D5312yes—
646C42C2×C22⋊D5312yes—
647C42C23×D5312yes—
648C42C23×D5312yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1064no—
653C23—1062no—
654C23—2122no—
655C23—2122no—
656C23C22×C22⋊D5312yes—
657C23C22×C22⋊D5311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—534no—
665Q8—1064no—
666Q8—1062no—
667D4—534no—
668D4—10616no—
669D4—1064no—
670D4—1062no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—10616no—
688C2×C4—1064no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—4244no—
693C2×C4—4244no—
694C2×C4—4244no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4C22×C22⋊D5312yes—
698C2×C4C22×C22⋊D5312yes—
699C2×C4C22×C22⋊D5312yes—
700C2×C4C22×C22⋊D5312yes—
701C2×C4C22×C22⋊D5312yes—
702C2×C4C22×C22⋊D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#41×D5312yes—
705C2×C4C24×D5311yescharacteristic
706C8—1062no—
707C8—1062no—
708C8—1062no—
709C8—1062no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—1064no—
715C22—2122no—
716C22—2122no—
717C22—2128no—
718C22#1681113012yes—
719C22#1681143112yes—
720C22#1681143812yes—
721C22C23×C22⋊D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—1064no—
732C4—2122no—
733C4—2122no—
734C4#1681113012yes—
735C4C2×#41×D5311yescharacteristic
736C4C2×#41×D5311yescharacteristic
737C2—42no—
738C2—2124no—
739C2#2028492314yesdirect product factor
740C2C2×#1681113011yescharacteristic
741C2C2×#1681143111yescharacteristic
742C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#541C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
hypercenterC2×#541D53
hypocenterC53C2×#3120
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #20284923C2direct (N × H)
3. C2×#16810956C2semidirect
4. C2×#16810951C2semidirect
5. C2×#16810927C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810830C2semidirect
8. C2×#16810825C2semidirect
11. C2×#16810728C2semidirect
12. C2×#16810721C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×C4×#11719924C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#541C2semidirect
33. #16810956C22semidirect
34. #16810951C22semidirect
35. #16810927C22semidirect
36. #16810920C22semidirect
37. #16810830C22semidirect
38. #16810825C22semidirect
41. #16810728C22semidirect
42. #16810721C22semidirect
43. C4×#11719925C22semidirect
44. C4×#11719924C22semidirect
45. #16810684C22semidirect
65. C53×#541C22semidirect
366. C2×#541D53semidirect
383. C2×C53#3120semidirect
394. #541C2×D53semidirect
448. C53C2×#3120semidirect
739. C2#20284923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111032
#202849232
C2×#168109562
C2×#168109512
C2×#168109272
C2×#168109202
C2×#168108302
C2×#168108252
C2×#168107832
C2×#168107282
C2×#168107212
C2×C4×#117199252
C2×C4×#117199242
C2×#168106842
C2×C53×#5412
C2×#312053