Finite Group Databasebeta

← C2×#20285383 #28253960

Subgroups — C2×#20285383 #28253960

Order 13568.

1906 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×#16811244C211yesmaximal, characteristic
2C2×#16811235C211yesmaximal, characteristic, complemented
3#20285383C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16811017C211yesmaximal, characteristic, complemented
6C2×#16810978C211yesmaximal, characteristic, complemented
7C2×#16810974C211yesmaximal, characteristic, complemented
8C2×#16810881C211yesmaximal, characteristic, complemented
9C2×#16810869C211yesmaximal, characteristic
10C2×#16810864C211yesmaximal, characteristic, complemented
11C2×#16810852C211yesmaximal, characteristic
12C2×#16810731C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×C4×Dic212C211yesmaximal, characteristic, complemented
15C2×C4×#11719913C211yesmaximal, characteristic, complemented
16C2×C53×#405C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21#16811244—24no—
22#16811244C2218yes—
23#16811235—24no—
24#16811235C2218yescomplemented
25C2×#13133217C2211yescharacteristic
26C2×#13133217C2211yescharacteristic
27C2×#13133212—21no—
28C2×#13133210—21no—
29C2×#13133210—21no—
30C2×#13133209C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133207—21no—
33C2×#13133205C2211yescharacteristic
34C2×#13133203—21no—
35C2×#13133199—21no—
36C2×#13133196C2211yescharacteristic
37C2×#13133196C2211yescharacteristic
38C2×#13133196C2211yescharacteristic
39C2×#13133195—21no—
40C2×#13133191C2211yescharacteristic
41C2×C4×Dic106C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×C4×Dic106C2211yescharacteristic
44C2×C4×D212C2211yescharacteristic
45#16811032C2218yescomplemented
46#16811017C2218yescomplemented
47#16810978C2218yescomplemented
48#16810974C2218yescomplemented
49#16810881C2218yescomplemented
50#16810869C2218yes—
51#16810864C2218yescomplemented
52#16810852C2218yes—
53#16810731C2218yescomplemented
54#16810725C2218yescomplemented
55C4×Dic212C2218yescomplemented
56C4×#11719913C2218yescomplemented
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×#117×C53C2211yescharacteristic
72C53×#405C2218yescomplemented
73C2×#97×C53C2211yescharacteristic
74C2×#97×C53C2211yescharacteristic
75C2×C4×C8×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C2×Dic212—24no—
85C2×Dic212—24no—
86C2×Dic212C2314yes—
87C2×Dic212C2314yes—
88C2×#11719913—24no—
89C2×#11719913—24no—
90C2×#11719913C2314yes—
91C2×#11719913C2314yes—
92#13133217—22no—
93#13133217—22no—
94#13133217C2314yes—
95#13133217C2314yes—
96#13133212—28no—
97#13133210—28no—
98#13133210—28no—
99#13133209—22no—
100#13133209C2314yes—
101#13133207—28no—
102#13133207—28no—
103#13133205—22no—
104#13133205C2314yes—
105#13133203—28no—
106#13133199—28no—
107#13133196—22no—
108#13133196—22no—
109#13133196—22no—
110#13133196C2314yes—
111#13133196C2314yes—
112#13133196C2314yes—
113#13133195—28no—
114#13133191—22no—
115#13133191C2314yes—
116C4×Dic106—22no—
117C4×Dic106—22no—
118C4×Dic106—22no—
119C4×Dic106C2314yes—
120C4×Dic106C2314yes—
121C4×Dic106C2314yes—
122C4×D212—22no—
123C4×D212C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149#13133151C2314yes—
150#13133151C2314yes—
151#13133149C2314yes—
152#13133149C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161C23×C4×C53C2311yescharacteristic
162C2×M16×C53—24no—
163C2×M16×C53C2314yes—
164C22×C8×C53—24no—
165C22×C8×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170#117×C53D414yes—
171#117×C53C2314yes—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C22⋊C4×C53D411yescharacteristic
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178#97×C53C2314yes—
179#97×C53C2314yes—
180C4×C8×C53C2314yes—
181C4×C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2412yes—
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—24no—
195C2×C22⋊D53—82no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—21no—
206C2×D212C2412yes—
207C2×C4×D53—24no—
208C2×C4×D53—82no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—22no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—21no—
216C2×Dic106—21no—
217C2×Dic106—21no—
218C2×Dic106—24no—
219C2×Dic106—82no—
220C2×Dic106C2412yes—
221C2×Dic106C2412yes—
222C2×Dic106C2412yes—
223M16×C53—28no—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53—28no—
227C2×C8×C53#4114yes—
228C2×C8×C53#4114yes—
229C2×C8×C53C2412yes—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53C2×D414yes—
234C4⋊C4×C53C2×D414yes—
235C22⋊C4×C53C2×D414yes—
236C22⋊C4×C53C2×D414yes—
237C42×C53C2×D412yes—
238C42×C53C2×D412yes—
239C42×C53C2412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270Dic212—28no—
271Dic212—28no—
272#11719913—28no—
273#11719913—28no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53C22×D412yes—
278C23×C53C22×D411yescharacteristic
279C22×D53—22no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4112yes—
298C2×C4×C53C2×#4112yes—
299C2×C4×C53C2511yescharacteristic
300C22⋊D53—84no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315D212—22no—
316D212—22no—
317D212—42no—
318C4×D53—84no—
319Dic106—22no—
320Dic106—22no—
321Dic106—22no—
322Dic106—22no—
323Dic106—22no—
324Dic106—22no—
325Dic106—42no—
326Dic106—42no—
327Dic106—42no—
328Dic106—84no—
329C8×C53—22no—
330C8×C53—22no—
331C8×C53C2×#4114yes—
332C8×C53C2×#4114yes—
333C2×#3178—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—44no—
338C22×C53#53212yes—
339C22×C53#57712yes—
340C22×C53#57812yes—
341C22×C53C23×D411yescharacteristic
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—84no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53#53212yes—
352C4×C53C22×#4111yescharacteristic
353C4×C53C22×#4111yescharacteristic
354Dic53—42no—
355Dic53—42no—
356Dic53—42no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#542—531no—
362C2×#541—531no—
363#3178—5316no—
364C2×#501—531no—
365C2×#497—531no—
366C2×#488—531no—
367C2×#487—531no—
368C2×#470—531no—
369C2×#468—531no—
370C2×#467—531no—
371C2×#465—531no—
372C2×#441—531no—
373C2×#440—531no—
374C2×C4×Q16—531no—
375C2×C4×SD16—531no—
376C2×#405D5311yescharacteristic, complemented
377C2×C53—42no—
378C2×C53#317814yescomplemented
379C2×C53C2×#53211yescharacteristic
380C2×C53C2×#57711yescharacteristic
381C2×C53C2×#57811yescharacteristic
382D53—82no—
383C22×Q16—531no—
384C22×Q16—531no—
385C22×SD16—531no—
386C22×SD16—531no—
387C22×M16C2×D5311yescharacteristic
388C23×C8C2×D5311yescharacteristic
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—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—531no—
412C2×C4×D4—531no—
413C2×#117C2×D5311yescharacteristic
414#501—538no—
415#497—538no—
416#488—538no—
417#487—538no—
418#470—538no—
419#468—538no—
420#467—538no—
421#465—538no—
422#441—538no—
423#440—538no—
424C4×Q16—538no—
425C4×SD16—538no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#106—531no—
429C2×#106—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#102—531no—
437C2×#102—531no—
438#405C2×D5318yescomplemented
439C2×#97C2×D5311yescharacteristic
440C2×#97C2×D5311yescharacteristic
441C2×C4×C8C2×D5311yescharacteristic
442C2×C4×C8C2×D5311yescharacteristic
443C53C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—531no—
445C22×Q8—531no—
446C22×Q8—531no—
447C22×Q8—1061no—
448C22×D4—531no—
449C22×D4—1061no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C2×Q16—534no—
453C2×Q16—534no—
454C2×Q16—1064no—
455C2×Q16—1064no—
456C2×SD16—534no—
457C2×SD16—534no—
458C2×SD16—1064no—
459C2×SD16—1064no—
460C2×M16—24no—
461C2×M16C22×D5314yes—
462C22×C8—24no—
463C22×C8C22×D5311yescharacteristic
464C22×C8C22×D5314yes—
465C22×C8C22×D5311yescharacteristic
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—1068no—
477#125—1068no—
478#125—1062no—
479#124—534no—
480#124—1068no—
481#124—1062no—
482#123—1068no—
483C22⋊Q8—534no—
484C22⋊Q8—534no—
485C22⋊Q8—534no—
486C22⋊Q8—1062no—
487C22⋊Q8—1062no—
488C22⋊Q8—1062no—
489C22⋊Q8—1068no—
490#121—534no—
491#121—1062no—
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#117D21214yes—
501#117C22×D5314yes—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—1061no—
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⋊C4D21211yescharacteristic
518C2×C4⋊C4D21211yescharacteristic
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4D21211yescharacteristic
527C2×C22⋊C4D21211yescharacteristic
528C2×C42—1061no—
529C2×C42—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533#107—534no—
534#107—534no—
535#106—534no—
536#106—534no—
537#103—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#102—534no—
544#102—534no—
545#97C22×D5314yes—
546#97C22×D5314yes—
547C4×C8C22×D5314yes—
548C4×C8C22×D5314yes—
549C24—1061no—
550C24C2×D21211yescharacteristic
551C2×Q8—532no—
552C2×Q8—532no—
553C2×Q8—532no—
554C2×Q8—1064no—
555C2×Q8—1061no—
556C2×Q8—1061no—
557C2×Q8—1061no—
558C2×Q8—1062no—
559C2×Q8—1062no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—1062no—
564C2×Q8—4242no—
565C2×D4—532no—
566C2×D4—1064no—
567C2×D4—1061no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—4242no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1064no—
581C22×C4—4242no—
582C22×C4C2×D21212yes—
583C22×C4C2×D21211yescharacteristic
584C22×C4C2×D21211yescharacteristic
585C22×C4C2×D21211yescharacteristic
586C22×C4C2×D21211yescharacteristic
587C22×C4C2×D21211yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590Q16—1068no—
591Q16—1068no—
592SD16—1068no—
593SD16—1068no—
594M16—28no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—28no—
598C2×C8#1171994514yes—
599C2×C8#1171994514yes—
600C2×C8C23×D5312yes—
601C2×C8C23×D5312yes—
602C2×C8C23×D5312yes—
603C2×C8C23×D5312yes—
604C4⋊C4—532no—
605C4⋊C4—532no—
606C4⋊C4—532no—
607C4⋊C4—532no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4C2×D21214yes—
624C4⋊C4C2×D21214yes—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C22⋊C4C2×D21214yes—
633C22⋊C4C2×D21214yes—
634C42—1064no—
635C42—1064no—
636C42—1064no—
637C42C2×D21212yes—
638C42C2×D21212yes—
639C42C23×D5312yes—
640C42C23×D5312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—1062no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23C22×D21212yes—
649C23C22×D21211yescharacteristic
650Q8—1062no—
651Q8—1062no—
652Q8—1062no—
653Q8—1062no—
654Q8—1062no—
655Q8—1062no—
656Q8—4244no—
657Q8—2122no—
658Q8—2122no—
659Q8—2122no—
660D4—1062no—
661D4—1062no—
662D4—4244no—
663D4—2122no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—4244no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4C22×D21212yes—
688C2×C4C22×D21212yes—
689C2×C4C22×D21212yes—
690C2×C4C22×D21212yes—
691C2×C4C22×D21212yes—
692C2×C4C22×D21211yescharacteristic
693C2×C4C2×#1171994512yes—
694C2×C4C2×#1171994512yes—
695C2×C4C24×D5311yescharacteristic
696C8—22no—
697C8—22no—
698C8C2×#1171994514yes—
699C8C2×#1171994514yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—4244no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22#1681117312yes—
709C22#1681143512yes—
710C22#1681144012yes—
711C22C23×D21211yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—2122no—
718C4—2122no—
719C4—2122no—
720C4—2122no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4#1681117312yes—
725C4C22×#1171994511yescharacteristic
726C4C22×#1171994511yescharacteristic
727C2—42no—
728C2—4242no—
729C2#2028538314yesdirect product factor
730C2C2×#1681117311yescharacteristic
731C2C2×#1681143511yescharacteristic
732C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#405C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#405D53
hypocenterC53C2×#3178
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#16811235C2semidirect
3. #20285383C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16811017C2semidirect
6. C2×#16810978C2semidirect
7. C2×#16810974C2semidirect
8. C2×#16810881C2semidirect
10. C2×#16810864C2semidirect
12. C2×#16810731C2semidirect
13. C2×#16810725C2semidirect
14. C2×C4×Dic212C2semidirect
15. C2×C4×#11719913C2semidirect
16. C2×C53×#405C2semidirect
24. #16811235C22semidirect
45. #16811032C22semidirect
46. #16811017C22semidirect
47. #16810978C22semidirect
48. #16810974C22semidirect
49. #16810881C22semidirect
51. #16810864C22semidirect
53. #16810731C22semidirect
54. #16810725C22semidirect
55. C4×Dic212C22semidirect
56. C4×#11719913C22semidirect
72. C53×#405C22semidirect
376. C2×#405D53semidirect
378. C2×C53#3178semidirect
438. #405C2×D53semidirect
443. C53C2×#3178semidirect
729. C2#20285383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
C2×#168112352
#202853832
C2×#168110322
C2×#168110172
C2×#168109782
C2×#168109742
C2×#168108812
C2×#168108692
C2×#168108642
C2×#168108522
C2×#168107312
C2×#168107252
C2×C4×Dic2122
C2×C4×#117199132
C2×C53×#4052
C2×#317853