Finite Group Databasebeta

← C2×#20288701 #28292284

Subgroups — C2×#20288701 #28292284

Order 13568.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288701C2132yesmaximal, direct product factor
2C2×#16811349C211yesmaximal, characteristic, complemented
3C2×#16811342C213yesmaximal, complemented
4C2×#16811331C213yesmaximal, complemented
5C2×#16811320C213yesmaximal, complemented
6C2×#16811313C213yesmaximal, complemented
7C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
8C2×#16811280C211yesmaximal, characteristic, complemented
9C2×#16811240C213yesmaximal, complemented
10C2×#16811233C213yesmaximal, complemented
11C2×#16811155C213yesmaximal, complemented
12C2×#16811152C213yesmaximal, complemented
13C2×#16811106C211yesmaximal, characteristic, complemented
14C2×#16811101C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18#16811349C22116yescomplemented
19#16811342C22148yescomplemented
20#16811331C22148yescomplemented
21#16811320C22148yescomplemented
22#16811313C22148yescomplemented
23Q8×C22⋊D53C22116yescomplemented
24#16811280C22116yescomplemented
25#16811240C22148yescomplemented
26#16811233C22148yescomplemented
27C2×#13133216C2213yes—
28C2×#13133215C2213yes—
29#16811155C22148yescomplemented
30#16811152C22148yescomplemented
31C2×#13133210C2213yes—
32C2×#13133210C2216yes—
33C2×#13133210C2216yes—
34C2×#13133210C2213yes—
35C2×#13133209C2213yes—
36C2×#13133208C2213yes—
37C2×#13133208C2213yes—
38C2×#13133207C2216yes—
39C2×#13133204C2213yes—
40C2×#13133204C2213yes—
41C2×#13133199C2213yes—
42C2×#13133199C2211yescharacteristic
43C2×#13133198C2216yes—
44C2×#13133197C2213yes—
45C2×#13133196C2213yes—
46C2×#13133196C2213yes—
47C2×#13133194C2216yes—
48C2×#13133193C2213yes—
49C2×#13133188C2213yes—
50C2×#13133188C2213yes—
51#16811106C22116yescomplemented
52#16811101C22116yescomplemented
53C2×Q8×Dic53C2213yes—
54C2×Q8×Dic53C2211yescharacteristic
55C2×Q8×Dic53C2211yescharacteristic
56C2×Q8×Dic53C2213yes—
57C2×Q8×Dic53C2211yescharacteristic
58C2×C4×Dic106C2213yes—
59C2×C4×Dic106C2213yes—
60C2×#13133182C2213yes—
61C4×Q8×D53C22116yescomplemented
62C2×D4×Dic53C2213yes—
63C2×D4×Dic53C2213yes—
64C2×C4×C22⋊D53C2213yes—
65C2×C4×C22⋊D53C2213yes—
66C2×#13133177C2216yes—
67C2×#13133176C2213yes—
68C2×#13133176C2213yes—
69C2×#13133176C2213yes—
70C2×#13133173C2216yes—
71C22×C4⋊Dic53C2213yes—
72C2×C4⋊C4×D53C2213yes—
73C2×C42×D53C2213yes—
74C22×#41×C53C2211yescharacteristic
75C23×Q8×C53C2211yescharacteristic
76C53×#548C22116yescomplemented
77C2×#124×C53C2213yes—
78C2×C22⋊Q8×C53C2213yes—
79C2×#121×C53C2213yes—
80C2×C4×Q8×C53C2211yescharacteristic
81C2×C4×D4×C53C2213yes—
82C22×Dic106C2313yes—
83C22×Dic106C2313yes—
84C2×Q8×D53—28no—
85C2×Q8×D53C2318yes—
86C22×C22⋊D53C2313yes—
87C22×C22⋊D53C2311yescharacteristic
88C23×Dic53C2316yes—
89C22×C4×D53C2311yescharacteristic
90C22×C4×D53C2313yes—
91C22×C4×D53C2313yes—
92#13133216C23124yes—
93#13133215C23124yes—
94#13133210C23124yes—
95#13133210C23148yes—
96#13133210C23124yes—
97#13133210C23148yes—
98#13133209C23124yes—
99#13133208C23124yes—
100#13133208C23124yes—
101#13133207C23148yes—
102#13133204C23124yes—
103#13133204C23124yes—
104#13133199C23124yes—
105#13133199C2318yes—
106#13133198C23148yes—
107#13133197C23124yes—
108#13133196C23124yes—
109#13133196C23124yes—
110#13133194C23148yes—
111#13133193C23124yes—
112#13133188C23124yes—
113#13133188C23124yes—
114Q8×Dic53C2318yes—
115Q8×Dic53C2318yes—
116Q8×Dic53C23124yes—
117Q8×Dic53C2318yes—
118Q8×Dic53C23124yes—
119C4×Dic106C23124yes—
120C4×Dic106C23124yes—
121#13133182C23124yes—
122D4×Dic53C23124yes—
123D4×Dic53C23124yes—
124C4×C22⋊D53C23124yes—
125C4×C22⋊D53C23124yes—
126#13133177C23148yes—
127#13133176C23124yes—
128#13133176C23124yes—
129#13133176C23124yes—
130#13133173C23148yes—
131C2×C4⋊Dic53C23124yes—
132C2×C4⋊Dic53C2313yes—
133C2×C4⋊Dic53C2313yes—
134C2×C4⋊Dic53C2313yes—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2313yes—
137C2×C4⋊Dic53C2313yes—
138C2×C4⋊Dic53C2313yes—
139C2×C4⋊Dic53C2313yes—
140C2×#11719919C2316yes—
141C2×#11719919C2313yes—
142C2×#11719919C2316yes—
143C2×#11719919C2316yes—
144C2×#11719919C2313yes—
145C2×#11719919C2313yes—
146C2×#11719919C2311yescharacteristic
147C4⋊C4×D53C23124yes—
148C2×C22⋊Dic53C2316yes—
149C2×C22⋊Dic53C2313yes—
150C2×C22⋊Dic53C2311yescharacteristic
151C2×C22⋊Dic53C2313yes—
152C2×C22⋊Dic53C2313yes—
153C2×C22⋊Dic53C2313yes—
154C2×C22⋊Dic53C2313yes—
155C2×#11719921C2313yes—
156C2×#11719921C2311yescharacteristic
157C2×C4×Dic53C2313yes—
158C2×C4×Dic53C2313yes—
159C2×C4×Dic53C2313yes—
160C2×C4×Dic53C2316yes—
161C2×C4×Dic53C2313yes—
162C2×C4×Dic53C2313yes—
163C42×D53C23124yes—
164C2×#41×C53—28no—
165C2×#41×C53C2318yes—
166C22×Q8×C53—28no—
167C22×Q8×C53C2318yes—
168C22×Q8×C53C2313yes—
169C22×Q8×C53C2311yescharacteristic
170C22×D4×C53C2313yes—
171C22×D4×C53C2313yes—
172C23×C4×C53C2313yes—
173C23×C4×C53C2313yes—
174#124×C53C23124yes—
175C22⋊Q8×C53C23124yes—
176#121×C53C23124yes—
177C4×Q8×C53C2318yes—
178C4×D4×C53C23124yes—
179C2×C4⋊C4×C53C2313yes—
180C2×C4⋊C4×C53C2313yes—
181C2×C22⋊C4×C53C2311yescharacteristic
182C2×C22⋊C4×C53C2313yes—
183C2×C22⋊C4×C53C2316yes—
184C2×C42×C53C2313yes—
185C24×C53C2413yes—
186C24×C53C2411yescharacteristic
187C23×D53C2411yescharacteristic
188#41×C53—232no—
189C2×Q8×C53—232no—
190C2×Q8×C53—212no—
191C2×Q8×C53#4118yes—
192C2×Q8×C53C24112yes—
193C2×Q8×C53C2414yes—
194C2×D4×C53—212no—
195C2×D4×C53—46no—
196C2×D4×C53C24112yes—
197C2×D4×C53C24112yes—
198C22×C4×C53—212no—
199C22×C4×C53—212no—
200C22×C4×C53C2411yescharacteristic
201C22×C4×C53C2413yes—
202C22×C4×C53C2413yes—
203C22×C4×C53C2411yescharacteristic
204C22×C4×C53C24112yes—
205C22×C4×C53C24112yes—
206C22×C4×C53C2413yes—
207C2×C22⋊D53—212no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53C24112yes—
210C2×C22⋊D53C2414yes—
211C22×Dic53—412no—
212C22×Dic53C2411yescharacteristic
213C22×Dic53C2413yes—
214C22×Dic53C2411yescharacteristic
215C22×Dic53C2413yes—
216C22×Dic53C2411yescharacteristic
217C22×Dic53C2413yes—
218C22×Dic53C2413yes—
219C22×Dic53C24124yes—
220Q8×D53—232no—
221C2×C4×D53—24no—
222C2×C4×D53—212no—
223C2×C4×D53—46no—
224C2×C4×D53C2414yes—
225C2×C4×D53C24112yes—
226C2×C4×D53C24112yes—
227C2×Dic106—212no—
228C2×Dic106—46no—
229C2×Dic106C24112yes—
230C2×Dic106C24112yes—
231C4⋊C4×C53C24112yes—
232C4⋊C4×C53C24112yes—
233C22⋊C4×C53C2414yes—
234C22⋊C4×C53C24112yes—
235C22⋊C4×C53C24124yes—
236C42×C53C24112yes—
237C22⋊Dic53C24124yes—
238C22⋊Dic53C24112yes—
239C22⋊Dic53C2414yes—
240C22⋊Dic53C24112yes—
241C22⋊Dic53C24112yes—
242C22⋊Dic53C24112yes—
243C22⋊Dic53C24112yes—
244#11719921C24112yes—
245#11719921C2414yes—
246C4⋊Dic53C24112yes—
247C4⋊Dic53C24112yes—
248C4⋊Dic53C24112yes—
249C4⋊Dic53C2414yes—
250C4⋊Dic53C24112yes—
251C4⋊Dic53C24112yes—
252C4⋊Dic53C24112yes—
253C4⋊Dic53C24112yes—
254#11719919C24124yes—
255#11719919C24112yes—
256#11719919C24124yes—
257#11719919C24124yes—
258#11719919C24112yes—
259#11719919C24112yes—
260#11719919C2414yes—
261C4×Dic53C24112yes—
262C4×Dic53C24112yes—
263C4×Dic53C24112yes—
264C4×Dic53C24124yes—
265C4×Dic53C24112yes—
266C4×Dic53C24112yes—
267C23×C53—22no—
268C23×C53—26no—
269C23×C53—26no—
270C23×C53—22no—
271C23×C53—26no—
272C23×C53—22no—
273C23×C53C2516yes—
274C23×C53C2512yes—
275C23×C53C2511yescharacteristic
276C22×D53—22no—
277C22×D53—22no—
278C22×D532−1+414yes—
279C22×D53C2512yes—
280Q8×C53—224no—
281Q8×C53C2×#41116yes—
282D4×C53—224no—
283D4×C53—412no—
284C2×C4×C53—22no—
285C2×C4×C53—26no—
286C2×C4×C53—22no—
287C2×C4×C53—26no—
288C2×C4×C53—224no—
289C2×C4×C53—224no—
290C2×C4×C53C2×#41112yes—
291C2×C4×C53C2516yes—
292C2×C4×C53C2512yes—
293C2×C4×C53C2512yes—
294C2×C4×C53C2516yes—
295C2×C4×C53C2516yes—
296C22⋊D53—224no—
297C22⋊D53—28no—
298C2×Dic53—26no—
299C2×Dic53—22no—
300C2×Dic53—26no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—26no—
304C2×Dic53—26no—
305C2×Dic53—424no—
306C2×Dic53C2512yes—
307C2×Dic53C2516yes—
308C2×Dic53C2516yes—
309C2×Dic53C2516yes—
310C2×Dic53C2512yes—
311C2×Dic53C2516yes—
312C2×Dic53C2512yes—
313C4×D53—28no—
314C4×D53—224no—
315C4×D53—412no—
316Dic106—224no—
317Dic106—412no—
318C2×#3516—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—26no—
321C22×C53—26no—
322C22×C53—22no—
323C22×C53—26no—
324C22×C53—22no—
325C22×C53—44no—
326C22×C53—412no—
327C22×C53C22×#4112yes—
328C22×C53C2×2−1+412yes—
329C22×C53#58512yes—
330C22×C53C2611yescharacteristic
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—28no—
334C2×D53C2×2−1+414yes—
335C4×C53—22no—
336C4×C53—26no—
337C4×C53—22no—
338C4×C53—26no—
339C4×C53C22×#41112yes—
340Dic53—26no—
341Dic53—22no—
342Dic53—26no—
343Dic53—22no—
344Dic53—22no—
345Dic53—26no—
346Dic53—26no—
347#3516—5332no—
348C2×#557—531no—
349C2×#556—533no—
350C2×#554—533no—
351C2×#553—533no—
352C2×#552—533no—
353C2×D4×Q8—531no—
354C2×#548—531no—
355C2×#548D5311yescharacteristic, complemented
356C2×#542—533no—
357C2×#541—533no—
358C2×#529—533no—
359C2×#529—533no—
360C2×#520—531no—
361C2×#519—531no—
362C22×C4×Q8—531no—
363C2×C53—42no—
364C2×C53—46no—
365C2×C53#351614yescomplemented
366C2×C53C23×#4111yescharacteristic
367C2×C53C22×2−1+411yescharacteristic
368C2×C53C2×#58511yescharacteristic
369D53—24no—
370C22×#41C2×D5311yescharacteristic
371C23×Q8—531no—
372C23×Q8C2×D5311yescharacteristic
373#557—5316no—
374#556—5348no—
375#554—5348no—
376#553—5348no—
377#552—5348no—
378D4×Q8—5316no—
379#548—5316no—
380#548C2×D53116yescomplemented
381#542—5348no—
382#541—5348no—
383C2×C4⋊Q8—533no—
384C2×C4⋊Q8—533no—
385#529—5348no—
386#529—5348no—
387C2×#126—536no—
388C2×#126—533no—
389C2×#126—533no—
390C2×#126—536no—
391C2×#125—533no—
392C2×#125—536no—
393C2×#125—533no—
394C2×#125—533no—
395C2×#124—533no—
396C2×#124—533no—
397C2×#124C2×D5313yes—
398C2×#123—536no—
399C2×#123—531no—
400C2×#123—533no—
401C2×C22⋊Q8—533no—
402C2×C22⋊Q8—533no—
403C2×C22⋊Q8—533no—
404C2×C22⋊Q8—533no—
405C2×C22⋊Q8—536no—
406C2×C22⋊Q8C2×D5313yes—
407C2×#121—533no—
408C2×#121—533no—
409C2×#121C2×D5313yes—
410#520—5316no—
411#519—5316no—
412C2×C4×Q8—531no—
413C2×C4×Q8—533no—
414C2×C4×Q8—531no—
415C2×C4×Q8—533no—
416C2×C4×Q8—531no—
417C2×C4×Q8—5316no—
418C2×C4×Q8—533no—
419C2×C4×Q8—533no—
420C2×C4×Q8—533no—
421C2×C4×Q8C2×D5311yescharacteristic
422C2×C4×D4—533no—
423C2×C4×D4—533no—
424C2×C4×D4—533no—
425C2×C4×D4—533no—
426C2×C4×D4—536no—
427C2×C4×D4C2×D5313yes—
428C2×#117—533no—
429C2×#117—533no—
430C2×#117—533no—
431C2×#117—536no—
432C22×C4⋊C4—533no—
433C22×C4⋊C4—533no—
434C22×C42—533no—
435C53C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—28no—
437C2×#41C22×D5318yes—
438C22×Q8—28no—
439C22×Q8—538no—
440C22×Q8—533no—
441C22×Q8—533no—
442C22×Q8—1068no—
443C22×Q8C22×D5313yes—
444C22×Q8C22×D5318yes—
445C22×Q8C22×D5311yescharacteristic
446C22×D4—531no—
447C22×D4—533no—
448C22×D4C22×D5313yes—
449C22×D4C22×D5313yes—
450C23×C4—536no—
451C23×C4—533no—
452C23×C4—531no—
453C23×C4—533no—
454C23×C4C22×D5313yes—
455C23×C4C22×D5313yes—
456C4⋊Q8—5324no—
457C4⋊Q8—5324no—
458#126—5348no—
459#126—5324no—
460#126—5324no—
461#126—5348no—
462#125—5324no—
463#125—5348no—
464#125—5324no—
465#125—5324no—
466#124—5324no—
467#124—5324no—
468#124C22×D53124yes—
469#123—5348no—
470#123—538no—
471#123—5324no—
472C22⋊Q8—5324no—
473C22⋊Q8—5324no—
474C22⋊Q8—5324no—
475C22⋊Q8—5324no—
476C22⋊Q8—5348no—
477C22⋊Q8C22×D53124yes—
478#121—5324no—
479#121—5324no—
480#121C22×D53124yes—
481C4×Q8—538no—
482C4×Q8—5324no—
483C4×Q8—538no—
484C4×Q8—5324no—
485C4×Q8—538no—
486C4×Q8—5324no—
487C4×Q8—5324no—
488C4×Q8—5324no—
489C4×Q8C22×D5318yes—
490C4×D4—5324no—
491C4×D4—5324no—
492C4×D4—5324no—
493C4×D4—5324no—
494C4×D4—5348no—
495C4×D4C22×D53124yes—
496#117—5324no—
497#117—5324no—
498#117—5324no—
499#117—5348no—
500C2×C4⋊C4—533no—
501C2×C4⋊C4—533no—
502C2×C4⋊C4—533no—
503C2×C4⋊C4—536no—
504C2×C4⋊C4—5324no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—533no—
507C2×C4⋊C4—533no—
508C2×C4⋊C4—533no—
509C2×C4⋊C4—533no—
510C2×C4⋊C4—536no—
511C2×C4⋊C4—533no—
512C2×C4⋊C4—536no—
513C2×C4⋊C4—533no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—533no—
516C2×C4⋊C4—5324no—
517C2×C4⋊C4C22×D5313yes—
518C2×C4⋊C4C22×D5313yes—
519C2×C22⋊C4—533no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—533no—
522C2×C22⋊C4—533no—
523C2×C22⋊C4—536no—
524C2×C22⋊C4—533no—
525C2×C22⋊C4—533no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—533no—
528C2×C22⋊C4C22×D5313yes—
529C2×C22⋊C4C22×D5316yes—
530C2×C22⋊C4C22×D5311yescharacteristic
531C2×C42—533no—
532C2×C42—536no—
533C2×C42—533no—
534C2×C42—533no—
535C2×C42—533no—
536C2×C42—533no—
537C2×C42—5324no—
538C2×C42C22×D5313yes—
539C24—531no—
540C24C23×D5311yescharacteristic
541C24C23×D5313yes—
542#41—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—5312no—
546C2×Q8—5312no—
547C2×Q8—10632no—
548C2×Q8—10612no—
549C2×Q8—2126no—
550C2×Q8#1171994718yes—
551C2×Q8C23×D53112yes—
552C2×Q8C23×D5314yes—
553C2×D4—212no—
554C2×D4—46no—
555C2×D4—534no—
556C2×D4—5312no—
557C2×D4—1064no—
558C2×D4—10612no—
559C2×D4C23×D53112yes—
560C2×D4C23×D53112yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—531no—
564C22×C4—533no—
565C22×C4—531no—
566C22×C4—533no—
567C22×C4—531no—
568C22×C4—533no—
569C22×C4—533no—
570C22×C4—5324no—
571C22×C4—534no—
572C22×C4—5312no—
573C22×C4—5312no—
574C22×C4—1064no—
575C22×C4—10612no—
576C22×C4—2126no—
577C22×C4—21212no—
578C22×C4C23×D53112yes—
579C22×C4C23×D53112yes—
580C22×C4C23×D5311yescharacteristic
581C22×C4C23×D5313yes—
582C22×C4C23×D5313yes—
583C22×C4C23×D5311yescharacteristic
584C22×C4C23×D5313yes—
585C4⋊C4—5312no—
586C4⋊C4—5312no—
587C4⋊C4—5312no—
588C4⋊C4—5324no—
589C4⋊C4—534no—
590C4⋊C4—5312no—
591C4⋊C4—5312no—
592C4⋊C4—5312no—
593C4⋊C4—5312no—
594C4⋊C4—5324no—
595C4⋊C4—5312no—
596C4⋊C4—5324no—
597C4⋊C4—5312no—
598C4⋊C4—534no—
599C4⋊C4—5312no—
600C4⋊C4C23×D53112yes—
601C4⋊C4C23×D53112yes—
602C22⋊C4—5312no—
603C22⋊C4—534no—
604C22⋊C4—5312no—
605C22⋊C4—5312no—
606C22⋊C4—5324no—
607C22⋊C4—5312no—
608C22⋊C4—5312no—
609C22⋊C4—534no—
610C22⋊C4—5312no—
611C22⋊C4C23×D53112yes—
612C22⋊C4C23×D53124yes—
613C22⋊C4C23×D5314yes—
614C42—5312no—
615C42—5312no—
616C42—5312no—
617C42—5324no—
618C42—5312no—
619C42—5312no—
620C42C23×D53112yes—
621C23—22no—
622C23—26no—
623C23—22no—
624C23—26no—
625C23—26no—
626C23—22no—
627C23—534no—
628C23—532no—
629C23—1062no—
630C23—1062no—
631C23C24×D5312yes—
632C23C24×D5316yes—
633C23C24×D5311yescharacteristic
634Q8—224no—
635Q8—10624no—
636Q8—21212no—
637Q8C2×#11719947116yes—
638D4—224no—
639D4—412no—
640D4—1068no—
641D4—10624no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—532no—
649C2×C4—536no—
650C2×C4—532no—
651C2×C4—536no—
652C2×C4—532no—
653C2×C4—536no—
654C2×C4—536no—
655C2×C4—1068no—
656C2×C4—1066no—
657C2×C4—1062no—
658C2×C4—1066no—
659C2×C4—1062no—
660C2×C4—1066no—
661C2×C4—1066no—
662C2×C4—1062no—
663C2×C4—10624no—
664C2×C4—21212no—
665C2×C4—21224no—
666C2×C4C2×#11719947112yes—
667C2×C4C24×D5312yes—
668C2×C4C24×D5316yes—
669C2×C4C24×D5316yes—
670C2×C4C24×D5312yes—
671C2×C4C24×D5316yes—
672C22—22no—
673C22—26no—
674C22—22no—
675C22—26no—
676C22—26no—
677C22—22no—
678C22—44no—
679C22—412no—
680C22—534no—
681C22—1068no—
682C22—1062no—
683C22—1062no—
684C22C22×#1171994712yes—
685C222−1+4×D5312yes—
686C22#1681145912yes—
687C22C25×D5311yescharacteristic
688C4—22no—
689C4—26no—
690C4—22no—
691C4—26no—
692C4—1066no—
693C4—1062no—
694C4—1066no—
695C4—1062no—
696C4—1066no—
697C4—1066no—
698C4—1062no—
699C4C22×#11719947112yes—
700C2—42no—
701C2—46no—
702C2—1064no—
703C2#2028870114yesdirect product factor
704C2C23×#1171994711yescharacteristic
705C2C2×2−1+4×D5311yescharacteristic
706C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3516
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #20288701C2direct (N × H)
2. C2×#16811349C2semidirect
3. C2×#16811342C2semidirect
4. C2×#16811331C2semidirect
5. C2×#16811320C2semidirect
6. C2×#16811313C2semidirect
7. C2×Q8×C22⋊D53C2semidirect
8. C2×#16811280C2semidirect
9. C2×#16811240C2semidirect
10. C2×#16811233C2semidirect
11. C2×#16811155C2semidirect
12. C2×#16811152C2semidirect
13. C2×#16811106C2semidirect
14. C2×#16811101C2semidirect
15. C2×C4×Q8×D53C2semidirect
16. C2×C53×#548C2semidirect
18. #16811349C22semidirect
19. #16811342C22semidirect
20. #16811331C22semidirect
21. #16811320C22semidirect
22. #16811313C22semidirect
23. Q8×C22⋊D53C22semidirect
24. #16811280C22semidirect
25. #16811240C22semidirect
26. #16811233C22semidirect
29. #16811155C22semidirect
30. #16811152C22semidirect
51. #16811106C22semidirect
52. #16811101C22semidirect
61. C4×Q8×D53C22semidirect
76. C53×#548C22semidirect
355. C2×#548D53semidirect
365. C2×C53#3516semidirect
380. #548C2×D53semidirect
435. C53C2×#3516semidirect
703. C2#20288701direct (N × H)

Maximal subgroups

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

subgroupindex
#202887012
C2×#168113492
C2×#168113422
C2×#168113312
C2×#168113202
C2×#168113132
C2×Q8×C22⋊D532
C2×#168112802
C2×#168112402
C2×#168112332
C2×#168111552
C2×#168111522
C2×#168111062
C2×#168111012
C2×C4×Q8×D532
C2×C53×#5482
C2×#351653