Finite Group Databasebeta

← C2×#20287202 #28262673

Subgroups — C2×#20287202 #28262673

Order 13568.

1942 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×#16811330C211yesmaximal, characteristic, complemented
2C2×#16811319C211yesmaximal, characteristic
3#20287202C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810942C211yesmaximal, characteristic, complemented
7C2×#16810965C211yesmaximal, characteristic, complemented
8C2×#16810937C211yesmaximal, characteristic, complemented
9C2×#16810931C211yesmaximal, characteristic, complemented
10C2×#16810904C211yesmaximal, characteristic, complemented
11C2×#16810869C211yesmaximal, characteristic, complemented
12C2×#16810852C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C22×#13133151C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18#16811330—24no—
19#16811330C2218yescomplemented
20#16811319—24no—
21#16811319C2218yes—
22C2×#13133217C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133208—21no—
26C2×#13133199—21no—
27C2×#13133196C2211yescharacteristic
28C2×#13133196C2211yescharacteristic
29C2×#13133194—21no—
30C2×#13133194—21no—
31C2×#13133191C2211yescharacteristic
32C2×#13133191C2211yescharacteristic
33C2×#13133189—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×D4×Dic53—21no—
37C2×#13133177—21no—
38C2×#13133176C2211yescharacteristic
39C22×C4⋊Dic53C2211yescharacteristic
40C22×C4⋊Dic53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16810965C2218yescomplemented
44#16810959C2218yescomplemented
45#16810942C2218yescomplemented
46#16810937C2218yescomplemented
47#16810931C2218yescomplemented
48#16810904C2218yescomplemented
49#16810869C2218yescomplemented
50#16810852C2218yescomplemented
51#16810725C2218yescomplemented
52#16810665C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133151C2218yescomplemented
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133149C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C23×Dic53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719913—24no—
87C2×#11719913C2314yes—
88#13133217—22no—
89#13133217C2314yes—
90#13133212—28no—
91#13133209—22no—
92#13133209C2314yes—
93#13133208—28no—
94#13133199—28no—
95#13133196—22no—
96#13133196—22no—
97#13133196C2314yes—
98#13133196C2314yes—
99#13133194—28no—
100#13133194—28no—
101#13133191—22no—
102#13133191—22no—
103#13133191C2314yes—
104#13133191C2314yes—
105#13133189—28no—
106C4×Dic106—22no—
107C4×Dic106C2314yes—
108C4×D212—22no—
109C4×D212C2314yes—
110D4×Dic53—28no—
111#13133177—28no—
112#13133176—22no—
113#13133176C2314yes—
114C2×C4⋊Dic53—22no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—22no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2314yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2314yes—
124C2×C4⋊Dic53C2314yes—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
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×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133151C2314yes—
147#13133151C2314yes—
148#13133151C2314yes—
149#13133149C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158C22×D4×C53D411yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C2×M16×C53—24no—
162C2×M16×C53C2314yes—
163C22×C8×C53—24no—
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53D414yes—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C4⋊C8×C53C2314yes—
176C22⋊C8×C53C2314yes—
177C22⋊C8×C53C2314yes—
178#97×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C2×D4×C53—24no—
183C2×D4×C53C2×D414yes—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—44no—
200C2×C22⋊D53—82no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—24no—
210C22×Dic53—24no—
211C22×Dic53—82no—
212C22×Dic53—82no—
213C22×Dic53—82no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—21no—
217C2×D212C2412yes—
218C2×C4×D53—24no—
219C2×C4×D53—82no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—21no—
223C2×Dic106—24no—
224C2×Dic106—82no—
225C2×Dic106C2412yes—
226M16×C53—28no—
227C2×C8×C53—22no—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53—28no—
231C2×C8×C53#4114yes—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C4⋊C4×C53C2×D414yes—
237C22⋊C4×C53C2×D414yes—
238C22⋊C4×C53C2×D414yes—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—21no—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270#11719913—28no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53#13714yes—
277C23×C53C22×D412yes—
278C23×C53C22×D412yes—
279C23×C53C22×D411yescharacteristic
280C22×D53—22no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284D4×C53—28no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C22⋊D53—48no—
304C22⋊D53—84no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—84no—
320C2×Dic53—84no—
321C2×Dic53—84no—
322D212—22no—
323D212—22no—
324D212—42no—
325C4×D53—84no—
326Dic106—22no—
327Dic106—22no—
328Dic106—42no—
329Dic106—84no—
330C8×C53—22no—
331C8×C53—22no—
332C8×C53—22no—
333C8×C53C2×#4114yes—
334C2×#3346—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—44no—
342C22×C53#54712yes—
343C22×C53C2×#13714yes—
344C22×C53C2×#13712yes—
345C22×C53#57612yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—84no—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53#54712yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C2×2−1+411yescharacteristic
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#554—531no—
366C2×#553—531no—
367#3346—5316no—
368C2×#501—531no—
369C2×#484—531no—
370C2×#481—531no—
371C2×#485—531no—
372C2×#480—531no—
373C2×#479—531no—
374C2×#474—531no—
375C2×#468—531no—
376C2×#465—531no—
377C2×#440—531no—
378C2×#435D5311yescharacteristic, complemented
379C2×#428—531no—
380C22×#107—531no—
381C2×C53—24no—
382C2×C53—42no—
383C2×C53#334614yescomplemented
384C2×C53C2×#54711yescharacteristic
385C2×C53C22×#13711yescharacteristic
386C2×C53C2×#57611yescharacteristic
387D53—82no—
388C22×SD16—531no—
389C22×M16C2×D5311yescharacteristic
390C23×C8C2×D5311yescharacteristic
391#554—538no—
392#554—1064no—
393#553—538no—
394#553—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#125—531no—
398C2×#125—1061no—
399C2×#123—1061no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8—1061no—
404C2×#121—531no—
405C2×#121—531no—
406C2×#121—1061no—
407C2×C4×Q8—531no—
408C2×C4×D4—531no—
409C2×C4×D4—1061no—
410C2×C4×D4—1061no—
411C2×C4×D4C2×D5311yescharacteristic
412C2×#117—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416#501—538no—
417#485—538no—
418#484—538no—
419#481—538no—
420#480—538no—
421#479—538no—
422#474—538no—
423#468—538no—
424#465—538no—
425#440—538no—
426#435C2×D5318yescomplemented
427#428—538no—
428C2×#107—531no—
429C2×#107—531no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—538no—
433C2×#107—531no—
434C2×#107—531no—
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×C4⋊C8C2×D5311yescharacteristic
439C2×#103—531no—
440C2×#103—531no—
441C2×#103—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×C22⋊C8C2×D5311yescharacteristic
446C2×C22⋊C8C2×D5311yescharacteristic
447C2×#97C2×D5311yescharacteristic
448C53C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—531no—
450C22×Q8—1061no—
451C22×D4—531no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4D21211yescharacteristic
455C23×C4—1061no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C2×SD16—534no—
462C2×SD16—1064no—
463C2×M16—24no—
464C2×M16C22×D5314yes—
465C22×C8—24no—
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5314yes—
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#126—1068no—
474#125—534no—
475#125—1068no—
476#125—1062no—
477#123—1068no—
478C22⋊Q8—534no—
479C22⋊Q8—534no—
480C22⋊Q8—1062no—
481C22⋊Q8—1062no—
482C22⋊Q8—1068no—
483C22⋊Q8—1068no—
484#121—534no—
485#121—534no—
486#121—1068no—
487#121—1062no—
488#121—1062no—
489C4×Q8—534no—
490C4×Q8—1062no—
491C4×D4—534no—
492C4×D4—1068no—
493C4×D4—1068no—
494C4×D4—1062no—
495C4×D4D21214yes—
496C4×D4C22×D5314yes—
497#117—534no—
498#117—1062no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—534no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1062no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4D21211yescharacteristic
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4D21211yescharacteristic
528C2×C22⋊C4D21211yescharacteristic
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532#107—534no—
533#107—534no—
534#107—534no—
535#107—534no—
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540#106—534no—
541C4⋊C8C22×D5314yes—
542#103—534no—
543#103—534no—
544#103—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548C22⋊C8C22×D5314yes—
549C22⋊C8C22×D5314yes—
550#97C22×D5314yes—
551C24—1061no—
552C24C2×D21211yescharacteristic
553C24C2×D21211yescharacteristic
554C2×Q8—532no—
555C2×Q8—1064no—
556C2×Q8—1061no—
557C2×Q8—1062no—
558C2×Q8—1062no—
559C2×Q8—4242no—
560C2×D4—24no—
561C2×D4—532no—
562C2×D4—1064no—
563C2×D4—1064no—
564C2×D4—1061no—
565C2×D4—1062no—
566C2×D4—1062no—
567C2×D4—4242no—
568C2×D4—2124no—
569C2×D4C2×D21214yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—1064no—
575C22×C4—1064no—
576C22×C4—1064no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1064no—
585C22×C4—4242no—
586C22×C4—4242no—
587C22×C4—4242no—
588C22×C4—4242no—
589C22×C4C2×D21212yes—
590C22×C4C2×D21212yes—
591C22×C4C2×D21211yescharacteristic
592C22×C4C2×D21211yescharacteristic
593C22×C4C2×D21211yescharacteristic
594C22×C4C2×D21211yescharacteristic
595C22×C4C23×D5312yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5311yescharacteristic
598SD16—1068no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1171994714yes—
605C2×C8C23×D5312yes—
606C2×C8C23×D5312yes—
607C2×C8C23×D5312yes—
608C2×C8C23×D5312yes—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—532no—
612C4⋊C4—532no—
613C4⋊C4—532no—
614C4⋊C4—532no—
615C4⋊C4—1061no—
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1064no—
623C4⋊C4—1061no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4C2×D21214yes—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4C2×D21214yes—
638C22⋊C4C2×D21214yes—
639C42—1064no—
640C42—1064no—
641C42C2×D21212yes—
642C42C23×D5312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—1062no—
649C23—2122no—
650C23—2122no—
651C23—2122no—
652C23#1313325014yes—
653C23C22×D21212yes—
654C23C22×D21212yes—
655C23C22×D21211yescharacteristic
656Q8—1062no—
657Q8—1062no—
658Q8—4244no—
659Q8—2122no—
660D4—28no—
661D4—1062no—
662D4—1062no—
663D4—4244no—
664D4—2128no—
665D4—2122no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—4244no—
684C2×C4—4244no—
685C2×C4—4244no—
686C2×C4—4244no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4C22×D21212yes—
695C2×C4C22×D21212yes—
696C2×C4C22×D21212yes—
697C2×C4C22×D21212yes—
698C2×C4C22×D21211yescharacteristic
699C2×C4C2×#1171994712yes—
700C2×C4#1313326412yes—
701C2×C4C24×D5311yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1171994714yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—4244no—
714C22—2122no—
715C22—2122no—
716C22—2122no—
717C22#1681127712yes—
718C22C2×#1313325014yes—
719C22C2×#1313325012yes—
720C22#1681142812yes—
721C22C23×D21211yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—2122no—
727C4—2122no—
728C4—2122no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681127712yes—
734C4C22×#1171994711yescharacteristic
735C4C2×#1313326411yescharacteristic
736C2—24no—
737C2—42no—
738C2—4242no—
739C2#2028720214yesdirect product factor
740C2C2×#1681127711yescharacteristic
741C2C22×#1313325011yescharacteristic
742C2C2×#1681142811yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811319C2
hypercenterC2×#435D53
hypocenterC53C2×#3346
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16811330C2semidirect
3. #20287202C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810942C2semidirect
7. C2×#16810965C2semidirect
8. C2×#16810937C2semidirect
9. C2×#16810931C2semidirect
10. C2×#16810904C2semidirect
11. C2×#16810869C2semidirect
12. C2×#16810852C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810665C2semidirect
15. C22×#13133151C2semidirect
16. C2×C53×#435C2semidirect
19. #16811330C22semidirect
42. #16811032C22semidirect
43. #16810965C22semidirect
44. #16810959C22semidirect
45. #16810942C22semidirect
46. #16810937C22semidirect
47. #16810931C22semidirect
48. #16810904C22semidirect
49. #16810869C22semidirect
50. #16810852C22semidirect
51. #16810725C22semidirect
52. #16810665C22semidirect
59. C2×#13133151C22semidirect
72. C53×#435C22semidirect
378. C2×#435D53semidirect
383. C2×C53#3346semidirect
426. #435C2×D53semidirect
448. C53C2×#3346semidirect
739. C2#20287202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113302
C2×#168113192
#202872022
C2×#168110322
C2×#168109592
C2×#168109422
C2×#168109652
C2×#168109372
C2×#168109312
C2×#168109042
C2×#168108692
C2×#168108522
C2×#168107252
C2×#168106652
C22×#131331512
C2×C53×#4352
C2×#334653