Finite Group Databasebeta

← C2×#20284938 #28252365

Subgroups — C2×#20284938 #28252365

Order 13568.

2058 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×#16811100C211yesmaximal, characteristic, complemented
2#20284938C2116yesmaximal, direct product factor
3C2×#16810961C211yesmaximal, characteristic, complemented
4C2×#16810944C211yesmaximal, characteristic
5C2×#16810915C211yesmaximal, characteristic, complemented
6C2×#16810905C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810778C211yesmaximal, characteristic, complemented
10C2×#16810761C211yesmaximal, characteristic
11C2×#16810728C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×C4×#11719923C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#542C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22#16811100—24no—
23#16811100C2218yescomplemented
24C2×C4×Dic106C2211yescharacteristic
25C2×C4×Dic106C2211yescharacteristic
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×Dic106C2211yescharacteristic
28C2×#13133182—21no—
29C2×#13133182—21no—
30C2×#13133176C2211yescharacteristic
31C2×#13133173—21no—
32C2×#13133173—21no—
33#16810961C2218yescomplemented
34#16810944C2218yes—
35#16810915C2218yescomplemented
36#16810905C2218yescomplemented
37#16810842C2218yescomplemented
38#16810842C2218yescomplemented
39#16810778C2218yescomplemented
40#16810761C2218yes—
41#16810728C2218yescomplemented
42#16810723C2218yescomplemented
43C4×#11719925C2218yescomplemented
44C4×#11719923C2218yescomplemented
45#16810684C2218yescomplemented
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#542—24no—
65C53×#542C2218yes—
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#123×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—22no—
79C22×Dic106—24no—
80C22×Dic106—24no—
81C22×Dic106C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C23×Dic53—21no—
85C2×#11719925—24no—
86C2×#11719925—24no—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C2×#11719923—24no—
90C2×#11719923—24no—
91C2×#11719923C2314yes—
92C2×#11719923C2314yes—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C4×Dic106—22no—
98C4×Dic106—22no—
99C4×Dic106—22no—
100C4×Dic106—22no—
101C4×Dic106C2314yes—
102C4×Dic106C2314yes—
103C4×Dic106C2314yes—
104C4×Dic106C2314yes—
105#13133182—28no—
106#13133182—28no—
107#13133176—22no—
108#13133176C2314yes—
109#13133173—28no—
110#13133173—28no—
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×#11719919—21no—
117C2×C22⋊Dic53—21no—
118C2×C4×Dic53—21no—
119C2×C4×Dic53—21no—
120C2×C4×Dic53—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#13133140C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139#13133128C2314yes—
140C4×#88322C2314yes—
141C22×Q8×C53—21no—
142C22×Q8×C53C2311yescharacteristic
143C22×D4×C53—21no—
144C22×D4×C53C2311yescharacteristic
145C23×C4×C53—21no—
146C23×C4×C53C2311yescharacteristic
147C4⋊Q8×C53—22no—
148C4⋊Q8×C53C2314yes—
149#126×C53—28no—
150#124×C53—28no—
151#124×C53—22no—
152#124×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—28no—
155C22⋊Q8×C53—22no—
156C22⋊Q8×C53C2314yes—
157#121×C53—22no—
158#121×C53C2314yes—
159C4×Q8×C53—22no—
160C4×Q8×C53C2314yes—
161C4×D4×C53—22no—
162C4×D4×C53C2314yes—
163#117×C53D414yes—
164#117×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—24no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—82no—
189C2×Q8×C53C2412yes—
190C2×D4×C53—24no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—82no—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—82no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2411yescharacteristic
211C22×Dic53—28no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C2×Dic106—28no—
218C2×Dic106—216no—
219C2×Dic106—24no—
220C2×Dic106—21no—
221C2×Dic106—21no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—28no—
225C2×Dic106—28no—
226C2×Dic106#4114yes—
227C2×Dic106#4114yes—
228C2×Dic106C2412yes—
229C2×Dic106C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2×D414yes—
236C4⋊C4×C53C2×D414yes—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊C4×C53—24no—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C22⋊C4×C53C2×D414yes—
245C22⋊C4×C53C2×D414yes—
246C42×C53—24no—
247C42×C53C2×D412yes—
248C42×C53C2×D412yes—
249C42×C53C2412yes—
250C42×C53C2412yes—
251C22⋊Dic53—24no—
252#11719925—28no—
253#11719925—28no—
254#11719923—28no—
255#11719923—28no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—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×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D412yes—
285C23×C53C22×D411yescharacteristic
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—42no—
289Q8×C53—84no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293D4×C53—84no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—24no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—84no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2×#4112yes—
317C2×C4×C53C2511yescharacteristic
318C2×Dic53—216no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327Dic106—216no—
328Dic106—24no—
329Dic106—24no—
330Dic106—22no—
331Dic106—22no—
332Dic106C2×#4114yes—
333Dic106C2×#4114yes—
334#88322—22no—
335#88322—22no—
336#88322—22no—
337#88322—22no—
338C2×#3121—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—44no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—84no—
347C22×C53#52512yes—
348C22×C53#57712yes—
349C22×C53#57812yes—
350C22×C53C23×D411yescharacteristic
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#52512yes—
360C4×C53C22×#4111yescharacteristic
361C4×C53C22×#4111yescharacteristic
362Dic53—24no—
363Dic53—24no—
364Dic53—42no—
365Dic53—42no—
366C2×#542D5311yescharacteristic
367C2×#519—531no—
368#3121—5316no—
369C2×#485—531no—
370C2×#482—531no—
371C2×#477—531no—
372C2×#475—531no—
373C2×#464—531no—
374C2×#464—531no—
375C2×#451—531no—
376C2×#448—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16—531no—
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53—42no—
383C2×C53—82no—
384C2×C53#312114yescomplemented
385C2×C53C2×#52511yescharacteristic
386C2×C53C2×#57711yescharacteristic
387C2×C53C2×#57811yescharacteristic
388C23×Q8—531no—
389C22×Q16—531no—
390C22×Q16—531no—
391C22×SD16—531no—
392C22×SD16—531no—
393#542—24no—
394#542C2×D5318yes—
395C2×C4⋊Q8C2×D5311yescharacteristic
396C2×#126—21no—
397C2×#124—21no—
398C2×#124C2×D5311yescharacteristic
399C2×#123—21no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8C2×D5311yescharacteristic
402C2×#121C2×D5311yescharacteristic
403#519—538no—
404#519—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×Q8—1061no—
410C2×C4×Q8—1061no—
411C2×C4×Q8C2×D5311yescharacteristic
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C2×#117—1061no—
415C2×#117—1061no—
416C2×#117C2×D5311yescharacteristic
417#485—538no—
418#482—538no—
419#477—538no—
420#475—538no—
421#464—538no—
422#464—538no—
423#451—538no—
424#448—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×#312111yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—531no—
451C22×Q8—531no—
452C22×Q8—534no—
453C22×Q8—1064no—
454C22×Q8—1064no—
455C22×Q8—1061no—
456C22×Q8—1062no—
457C22×Q8C22×D5311yescharacteristic
458C22×D4—21no—
459C22×D4C22×D5311yescharacteristic
460C23×C4—21no—
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#124—28no—
479#124—22no—
480#124C22×D5314yes—
481#123—28no—
482C22⋊Q8—22no—
483C22⋊Q8—28no—
484C22⋊Q8C22×D5314yes—
485#121—22no—
486#121C22×D5314yes—
487C4×Q8—22no—
488C4×Q8—534no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—534no—
492C4×Q8—1068no—
493C4×Q8—1068no—
494C4×Q8—1062no—
495C4×Q8—1062no—
496C4×Q8—1062no—
497C4×Q8—1062no—
498C4×Q8C22×D5314yes—
499C4×D4—22no—
500C4×D4C22×D5314yes—
501#117—534no—
502#117—1062no—
503#117—1068no—
504#117—1068no—
505#117C22⋊D5314yes—
506#117C22×D5314yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4C22⋊D5311yescharacteristic
517C2×C4⋊C4C22⋊D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4C22⋊D5311yescharacteristic
527C2×C22⋊C4C22⋊D5311yescharacteristic
528C2×C42—21no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42—1061no—
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—21no—
555C24C2×C22⋊D5311yescharacteristic
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—82no—
561C2×Q8—534no—
562C2×Q8—534no—
563C2×Q8—532no—
564C2×Q8—532no—
565C2×Q8—1068no—
566C2×Q8—1068no—
567C2×Q8—1068no—
568C2×Q8—10616no—
569C2×Q8—1064no—
570C2×Q8—1061no—
571C2×Q8—1061no—
572C2×Q8—1062no—
573C2×Q8—1062no—
574C2×Q8C23×D5312yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D5312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—1068no—
589C22×C4—1064no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
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—21no—
618C4⋊C4—21no—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4C2×C22⋊D5314yes—
628C4⋊C4C2×C22⋊D5314yes—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1064no—
637C22⋊C4C2×C22⋊D5314yes—
638C22⋊C4C2×C22⋊D5314yes—
639C42—24no—
640C42—1064no—
641C42—1064no—
642C42—1064no—
643C42—1064no—
644C42—1064no—
645C42C2×C22⋊D5312yes—
646C42C2×C22⋊D5312yes—
647C42C23×D5312yes—
648C42C23×D5312yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D5312yes—
657C23C22×C22⋊D5311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—84no—
662Q8—534no—
663Q8—534no—
664Q8—10616no—
665Q8—1064no—
666Q8—1064no—
667Q8—1062no—
668Q8—1062no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—10616no—
689C2×C4—1064no—
690C2×C4—1064no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
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—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1681113012yes—
719C22#1681143412yes—
720C22#1681143812yes—
721C22C23×C22⋊D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1064no—
731C4—1064no—
732C4—2122no—
733C4—2122no—
734C4#1681113012yes—
735C4C2×#41×D5311yescharacteristic
736C4C2×#41×D5311yescharacteristic
737C2—42no—
738C2—82no—
739C2#2028493814yesdirect product factor
740C2C2×#1681113011yescharacteristic
741C2C2×#1681143411yescharacteristic
742C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
hypercenterC2×#542D53
hypocenterC53C2×#3121
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16811100C2semidirect
2. #20284938C2direct (N × H)
3. C2×#16810961C2semidirect
5. C2×#16810915C2semidirect
6. C2×#16810905C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810778C2semidirect
11. C2×#16810728C2semidirect
12. C2×#16810723C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810684C2semidirect
23. #16811100C22semidirect
33. #16810961C22semidirect
35. #16810915C22semidirect
36. #16810905C22semidirect
37. #16810842C22semidirect
38. #16810842C22semidirect
39. #16810778C22semidirect
41. #16810728C22semidirect
42. #16810723C22semidirect
43. C4×#11719925C22semidirect
44. C4×#11719923C22semidirect
45. #16810684C22semidirect
384. C2×C53#3121semidirect
448. C53C2×#3121semidirect
739. C2#20284938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111002
#202849382
C2×#168109612
C2×#168109442
C2×#168109152
C2×#168109052
C2×#168108422
C2×#168107782
C2×#168107612
C2×#168107282
C2×#168107232
C2×C4×#117199252
C2×C4×#117199232
C2×#168106842
C2×C53×#5422
C2×#312153