Finite Group Databasebeta

← C2×#20286142 #28257019

Subgroups — C2×#20286142 #28257019

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811240C211yesmaximal, characteristic
2C2×#16811233C211yesmaximal, characteristic, complemented
3#20286142C2116yesmaximal, direct product factor
4C2×#16810929C211yesmaximal, characteristic, complemented
5C2×#16810917C211yesmaximal, characteristic, complemented
6C2×#16810906C211yesmaximal, characteristic, complemented
7C2×#16810925C211yesmaximal, characteristic, complemented
8C2×#16810881C211yesmaximal, characteristic, complemented
9C2×#16810862C211yesmaximal, characteristic, complemented
10C2×#16810850C211yesmaximal, characteristic
11C2×#16810844C211yesmaximal, characteristic, complemented
12C2×#16810843C211yesmaximal, characteristic, complemented
13C2×#16810832C211yesmaximal, characteristic, complemented
14C2×#16810826C211yesmaximal, characteristic, complemented
15C2×#16810651C211yesmaximal, characteristic, complemented
16C2×C53×#468C211yesmaximal, characteristic
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811240—24no—
22#16811240C2218yes—
23#16811233—24no—
24#16811233C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133215C2211yescharacteristic
27C2×#13133210—21no—
28C2×#13133210—21no—
29C2×#13133210—21no—
30C2×#13133208—21no—
31C2×#13133208C2211yescharacteristic
32C2×#13133207—21no—
33C2×#13133204—21no—
34C2×#13133204C2211yescharacteristic
35C2×#13133198—21no—
36C2×#13133196C2211yescharacteristic
37C2×#13133196C2211yescharacteristic
38C2×#13133194—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×#13133182C2211yescharacteristic
42C2×D4×Dic53C2211yescharacteristic
43C2×#13133176C2211yescharacteristic
44#16810929C2218yescomplemented
45#16810925C2218yescomplemented
46#16810917C2218yescomplemented
47#16810906C2218yescomplemented
48#16810881C2218yescomplemented
49#16810862C2218yescomplemented
50#16810850C2218yes—
51#16810844C2218yescomplemented
52#16810843C2218yescomplemented
53#16810832C2218yescomplemented
54#16810826C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58#16810651C2218yescomplemented
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#468C2218yes—
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C23×Dic53—21no—
81C2×Dic212—42no—
82C2×Dic212C2314yes—
83C2×#11719925—42no—
84C2×#11719925C2314yes—
85C2×#11719923—42no—
86C2×#11719923C2314yes—
87C22×#88322—42no—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2314yes—
91#13133216—22no—
92#13133216C2314yes—
93#13133215—22no—
94#13133215C2314yes—
95#13133210—28no—
96#13133210—28no—
97#13133210—28no—
98#13133208—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133204—28no—
103#13133204—22no—
104#13133204C2314yes—
105#13133198—28no—
106#13133196—22no—
107#13133196—22no—
108#13133196C2314yes—
109#13133196C2314yes—
110#13133194—28no—
111Q8×Dic53—22no—
112Q8×Dic53C2314yes—
113#13133182—22no—
114#13133182—22no—
115#13133182C2314yes—
116#13133182C2314yes—
117D4×Dic53—22no—
118D4×Dic53C2314yes—
119#13133176D414yes—
120#13133176C2314yes—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53D411yescharacteristic
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
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×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
141C2×C22⋊Dic53D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133138C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×D4×C53—21no—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C2×SD16×C53—42no—
165C2×SD16×C53C2314yes—
166C2×M16×C53—42no—
167C2×M16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172#121×C53—22no—
173#121×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179#107×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C2×D4×C53—24no—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—82no—
193C2×D4×C53C2412yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—82no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—21no—
218C2×Dic106—21no—
219C2×Dic106—24no—
220C2×Dic106—82no—
221C2×Dic106C2412yes—
222C2×Dic106C2412yes—
223SD16×C53—44no—
224M16×C53—44no—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C22⋊C4×C53—24no—
235C22⋊C4×C53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53C2×D414yes—
242C22⋊Dic53C2×D414yes—
243#11719925—44no—
244#11719923—44no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53C2×D414yes—
250C4⋊Dic53C2×D414yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2×D412yes—
266C4×Dic53C2412yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322—44no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273Dic212—44no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D412yes—
282C23×C53C22×D411yescharacteristic
283Q8×C53—22no—
284Q8×C53—22no—
285Q8×C53—42no—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—42no—
289D4×C53—84no—
290C2×C4×C53—22no—
291C2×C4×C53—24no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53H(5,𝔽2)12yes—
303C2×C4×C532−1+412yes—
304C2×C4×C53C2511yescharacteristic
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—84no—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322Dic106—22no—
323Dic106—22no—
324Dic106—22no—
325Dic106—22no—
326Dic106—42no—
327Dic106—42no—
328Dic106—84no—
329C8×C53—22no—
330C8×C53—22no—
331#88322—22no—
332#88322—22no—
333C2×#3258—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—44no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—84no—
342C22×C53#53712yes—
343C22×C53#57712yes—
344C22×C53#57812yes—
345C22×C53C23×D411yescharacteristic
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53#53712yes—
351C4×C53C2×H(5,𝔽2)11yescharacteristic
352C4×C53C2×2−1+411yescharacteristic
353Dic53—22no—
354Dic53—22no—
355Dic53—22no—
356Dic53—22no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#542—531no—
362C2×#541—531no—
363#3258—5316no—
364C2×#479—531no—
365C2×#477—531no—
366C2×#475—531no—
367C2×#478—531no—
368C2×#470—531no—
369C2×#468D5311yescharacteristic
370C2×#467—531no—
371C2×#465—531no—
372C2×#464—531no—
373C2×#464—531no—
374C2×#462—531no—
375C2×#461—531no—
376C2×#424—531no—
377C2×C53—42no—
378C2×C53—82no—
379C2×C53#325814yescomplemented
380C2×C53C2×#53711yescharacteristic
381C2×C53C2×#57711yescharacteristic
382C2×C53C2×#57811yescharacteristic
383C22×Q16—531no—
384C22×Q16—531no—
385C22×SD16—531no—
386C22×SD16C2×D5311yescharacteristic
387C22×M16C2×D5311yescharacteristic
388C23×C8—531no—
389#542—538no—
390#542—1064no—
391#541—538no—
392#541—1064no—
393C2×C4⋊Q8—531no—
394C2×C4⋊Q8—531no—
395C2×#126—1061no—
396C2×#126—1061no—
397C2×#126—1061no—
398C2×#125—531no—
399C2×#125—1061no—
400C2×#125—1061no—
401C2×#124—531no—
402C2×#124—1061no—
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—1061no—
407C2×C22⋊Q8C2×D5311yescharacteristic
408C2×#121C2×D5311yescharacteristic
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—531no—
412C2×C4×D4—531no—
413C2×#117—531no—
414#479—538no—
415#478—538no—
416#477—538no—
417#475—538no—
418#470—538no—
419#468C2×D5318yes—
420#467—538no—
421#465—538no—
422#464—538no—
423#464—538no—
424#462—538no—
425#461—538no—
426C2×#107—531no—
427C2×#107C2×D5311yescharacteristic
428C2×#106—531no—
429C2×#106—531no—
430#424—538no—
431C2×C4⋊C8—531no—
432C2×C4⋊C8—531no—
433C2×C4⋊C8—531no—
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#102—531no—
442C2×#102C2×D5311yescharacteristic
443C53C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—531no—
445C22×Q8—531no—
446C22×Q8—1061no—
447C22×Q8C22×D5311yescharacteristic
448C22×D4—21no—
449C22×D4C22×D5311yescharacteristic
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C2×Q16—534no—
453C2×Q16—534no—
454C2×Q16—2122no—
455C2×Q16—2122no—
456C2×SD16—42no—
457C2×SD16—534no—
458C2×SD16—2122no—
459C2×SD16C22×D5314yes—
460C2×M16—42no—
461C2×M16C22×D5314yes—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—534no—
465C22×C8—2122no—
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C4⋊Q8—534no—
469C4⋊Q8—534no—
470C4⋊Q8—1062no—
471C4⋊Q8—1062no—
472#126—1068no—
473#126—1068no—
474#126—1068no—
475#125—534no—
476#125—1062no—
477#125—1068no—
478#125—1068no—
479#124—534no—
480#124—1062no—
481#124—1068no—
482#123—1068no—
483C22⋊Q8—22no—
484C22⋊Q8—534no—
485C22⋊Q8—534no—
486C22⋊Q8—1068no—
487C22⋊Q8—1062no—
488C22⋊Q8—1062no—
489C22⋊Q8C22×D5314yes—
490#121—22no—
491#121C22×D5314yes—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×Q8—1062no—
497C4×Q8—1062no—
498C4×D4—534no—
499C4×D4—1062no—
500#117—534no—
501#117—534no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—1061no—
531C2×C42—1061no—
532C2×C42—1061no—
533#107—534no—
534#107C22×D5314yes—
535#106—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8—534no—
540C4⋊C8—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103C22×D5314yes—
547#102—534no—
548#102C22×D5314yes—
549C24—21no—
550C24D4×D5311yescharacteristic
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—532no—
555C2×Q8—532no—
556C2×Q8—1064no—
557C2×Q8—1061no—
558C2×Q8—1061no—
559C2×Q8—1062no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—4242no—
564C2×Q8C23×D5312yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D5312yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—531no—
577C22×C4—531no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—1064no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—4242no—
586C22×C4D4×D5312yes—
587C22×C4D4×D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590Q16—2124no—
591Q16—2124no—
592SD16—44no—
593SD16—2124no—
594M16—44no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—532no—
598C2×C8—532no—
599C2×C8—1062no—
600C2×C8—1062no—
601C2×C8—2124no—
602C2×C8C23×D5312yes—
603C2×C8C23×D5312yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—534no—
608C4⋊C4—534no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4C23×D5312yes—
624C4⋊C4C23×D5312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—534no—
628C22⋊C4—534no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C42—532no—
635C42—532no—
636C42—532no—
637C42—532no—
638C42—1064no—
639C42—1064no—
640C42—1064no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1062no—
654Q8—1062no—
655Q8—1062no—
656Q8—1062no—
657Q8—4244no—
658Q8—2122no—
659Q8—2122no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—4244no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4C2×D4×D5312yes—
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#1313326212yes—
694C2×C4#1313326412yes—
695C2×C4C24×D5311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1062no—
699C8—1062no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1681120012yes—
709C22#1681143312yes—
710C22#1681143912yes—
711C22C22×D4×D5311yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—1062no—
717C4—1062no—
718C4—1062no—
719C4—1062no—
720C4—2122no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4#1681120012yes—
725C4C2×#1313326211yescharacteristic
726C4C2×#1313326411yescharacteristic
727C2—42no—
728C2—82no—
729C2#2028614214yesdirect product factor
730C2C2×#1681120011yescharacteristic
731C2C2×#1681143311yescharacteristic
732C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#468C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
hypercenterC2×#468D53
hypocenterC53C2×#3258
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#16811233C2semidirect
3. #20286142C2direct (N × H)
4. C2×#16810929C2semidirect
5. C2×#16810917C2semidirect
6. C2×#16810906C2semidirect
7. C2×#16810925C2semidirect
8. C2×#16810881C2semidirect
9. C2×#16810862C2semidirect
11. C2×#16810844C2semidirect
12. C2×#16810843C2semidirect
13. C2×#16810832C2semidirect
14. C2×#16810826C2semidirect
15. C2×#16810651C2semidirect
24. #16811233C22semidirect
44. #16810929C22semidirect
45. #16810925C22semidirect
46. #16810917C22semidirect
47. #16810906C22semidirect
48. #16810881C22semidirect
49. #16810862C22semidirect
51. #16810844C22semidirect
52. #16810843C22semidirect
53. #16810832C22semidirect
54. #16810826C22semidirect
58. #16810651C22semidirect
379. C2×C53#3258semidirect
443. C53C2×#3258semidirect
729. C2#20286142direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112402
C2×#168112332
#202861422
C2×#168109292
C2×#168109172
C2×#168109062
C2×#168109252
C2×#168108812
C2×#168108622
C2×#168108502
C2×#168108442
C2×#168108432
C2×#168108322
C2×#168108262
C2×#168106512
C2×C53×#4682
C2×#325853