Finite Group Databasebeta

← C2×#20287747 #28265061

Subgroups — C2×#20287747 #28265061

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811351C211yesmaximal, characteristic, complemented
2C2×#16811345C211yesmaximal, characteristic
3#20287747C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic
5C2×#16811016C211yesmaximal, characteristic
6C2×#16811001C211yesmaximal, characteristic, complemented
7C2×#16810848C211yesmaximal, characteristic
8C2×#16810845C211yesmaximal, characteristic
9C2×#16810833C211yesmaximal, characteristic, complemented
10C2×#16810832C211yesmaximal, characteristic, complemented
11C2×#16810832C211yesmaximal, characteristic, complemented
12C2×#16810827C211yesmaximal, characteristic
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810729C211yesmaximal, characteristic, complemented
15C2×#16810710C211yesmaximal, characteristic
16C2×C53×#441C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25#16811351—24no—
26#16811351C2218yescomplemented
27#16811345—24no—
28#16811345C2218yes—
29C2×#13133217C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133215C2211yescharacteristic
32C2×#13133215C2211yescharacteristic
33C2×#13133212—21no—
34C2×#13133211—21no—
35C2×#13133209—21no—
36C2×#13133207—21no—
37C2×#13133207—21no—
38C2×#13133206C2211yescharacteristic
39C2×#13133205C2211yescharacteristic
40C2×#13133195—21no—
41C2×C4×Dic106—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133182C2211yescharacteristic
46C2×#13133179C2211yescharacteristic
47C2×#13133174—21no—
48#16811017C2218yes—
49#16811016C2218yes—
50#16811001C2218yescomplemented
51#16810848C2218yes—
52#16810845C2218yes—
53#16810833C2218yescomplemented
54#16810832C2218yescomplemented
55#16810832C2218yescomplemented
56#16810827C2218yes—
57#16810751C2218yescomplemented
58#16810729C2218yescomplemented
59#16810710C2218yes—
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C53×#441C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C2×Dic212—24no—
84C2×Dic212—42no—
85C2×Dic212C2314yes—
86C2×Dic212C2314yes—
87C2×#11719925—42no—
88C2×#11719925—42no—
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C2×#11719925C2314yes—
92C2×#11719925C2314yes—
93C2×#11719913—24no—
94C2×#11719913—42no—
95C2×#11719913C2314yes—
96C2×#11719913C2314yes—
97C2×#11719924—42no—
98C2×#11719924C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133217—22no—
102#13133217C2314yes—
103#13133215—22no—
104#13133215—22no—
105#13133215—22no—
106#13133215C2314yes—
107#13133215C2314yes—
108#13133215C2314yes—
109#13133212—28no—
110#13133211—28no—
111#13133209—28no—
112#13133207—28no—
113#13133207—28no—
114#13133206—22no—
115#13133206C2314yes—
116#13133205—22no—
117#13133205C2314yes—
118#13133195—28no—
119C4×Dic106—28no—
120C4×Dic106D414yes—
121C4×Dic106C2314yes—
122#13133182—22no—
123#13133182—22no—
124#13133182—22no—
125#13133182C2314yes—
126#13133182C2314yes—
127#13133182C2314yes—
128#13133179—22no—
129#13133179C2314yes—
130#13133174—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53D411yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919D411yescharacteristic
144C2×#11719919D411yescharacteristic
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yes—
156#13133146C2314yes—
157#13133146C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133137C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C2×Q16×C53—24no—
167C2×Q16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4×Q8×C53—22no—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×Q8×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#106×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184#97×C53C2314yes—
185C23×D53—21no—
186C2×Q8×C53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×Q8×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—21no—
211C2×D212C2412yes—
212C2×C4×D53—24no—
213C2×C4×D53—44no—
214C2×Dic106—24no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106C2×D414yes—
225C2×Dic106C2412yes—
226C2×Dic106C2412yes—
227C2×Dic106C2412yes—
228Q16×C53—28no—
229C2×C8×C53—22no—
230C2×C8×C53#4114yes—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C42×C53—24no—
240C42×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243#11719925—44no—
244#11719925—44no—
245#11719925—44no—
246#11719924—44no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2×D414yes—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919C2×D414yes—
265#11719919C2×D414yes—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D412yes—
271C4×Dic53C2412yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277Dic212—28no—
278Dic212—44no—
279#11719913—28no—
280#11719913—44no—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291Q8×C53—42no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C53H(5,𝔽2)12yes—
307C2×C4×C53C2511yescharacteristic
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53#13714yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322D212—22no—
323D212—22no—
324D212—42no—
325C4×D53—48no—
326Dic106—28no—
327Dic106—22no—
328Dic106—22no—
329Dic106—22no—
330Dic106—22no—
331Dic106—22no—
332Dic106—22no—
333Dic106—42no—
334Dic106—42no—
335Dic106—42no—
336C8×C53—22no—
337C8×C53C2×#4114yes—
338#88322—22no—
339#88322—22no—
340C2×#3398—531nomaximal, Sylow
341C22×C53#55012yes—
342C22×C53C2×#13712yes—
343C22×C53#57812yes—
344C22×C53C23×D411yescharacteristic
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—84no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#55012yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C2×H(5,𝔽2)11yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×#13714yes—
365C2×#557—531no—
366C2×#556—531no—
367#3398—5316no—
368C2×#497—531no—
369C2×#497—531no—
370C2×#494—531no—
371C2×#464—531no—
372C2×#464—531no—
373C2×#462—531no—
374C2×#462—531no—
375C2×#462—531no—
376C2×#461—531no—
377C2×#446—531no—
378C2×#441—531no—
379C2×#441D5311yescharacteristic, complemented
380C2×C4×SD16—531no—
381C2×C53#339814yescomplemented
382C2×C53C2×#55011yescharacteristic
383C2×C53C22×#13711yescharacteristic
384C2×C53C2×#57811yescharacteristic
385D53—82no—
386C22×Q16—531no—
387C22×Q16—531no—
388C22×Q16—531no—
389C22×Q16—531no—
390C22×Q16—531no—
391C22×Q16C2×D5311yescharacteristic
392C22×SD16—531no—
393C22×SD16—531no—
394C22×SD16—531no—
395#557—538no—
396#557—1064no—
397#556—538no—
398#556—1064no—
399C2×C4⋊Q8—531no—
400C2×C4⋊Q8—531no—
401C2×C4⋊Q8—531no—
402C2×C4⋊Q8—531no—
403C2×#126—1061no—
404C2×#126—1061no—
405C2×#125—1061no—
406C2×#125—1061no—
407C2×#125—1061no—
408C2×#124—531no—
409C2×#124—531no—
410C2×C22⋊Q8—1061no—
411C2×C4×Q8—531no—
412C2×C4×Q8—531no—
413C2×C4×Q8—531no—
414C2×C4×Q8—531no—
415C2×C4×Q8—1061no—
416C2×C4×Q8C2×D5311yescharacteristic
417C2×C4×Q8C2×D5311yescharacteristic
418C2×C4×D4—531no—
419C2×#117—1061no—
420#497—538no—
421#497—538no—
422#494—538no—
423#464—538no—
424#464—538no—
425#462—538no—
426#462—538no—
427#462—538no—
428#461—538no—
429#446—538no—
430#441—538no—
431#441C2×D5318yescomplemented
432C4×SD16—538no—
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#97—531no—
444C2×#97C2×D5311yescharacteristic
445C2×C4×C8—531no—
446C53C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—531no—
448C22×Q8—531no—
449C22×Q8—531no—
450C22×Q8—531no—
451C22×Q8C22×D5311yescharacteristic
452C22×Q8C22×D5311yescharacteristic
453C22×D4—531no—
454C23×C4—1061no—
455C2×Q16—24no—
456C2×Q16—534no—
457C2×Q16—534no—
458C2×Q16—534no—
459C2×Q16—534no—
460C2×Q16—534no—
461C2×Q16—1064no—
462C2×Q16—2122no—
463C2×Q16—2122no—
464C2×Q16—2122no—
465C2×Q16—2122no—
466C2×Q16C22×D5314yes—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—534no—
470C2×SD16—1064no—
471C2×SD16—2122no—
472C2×SD16—2122no—
473C22×C8—531no—
474C22×C8—531no—
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5311yescharacteristic
477C4⋊Q8—534no—
478C4⋊Q8—534no—
479C4⋊Q8—534no—
480C4⋊Q8—534no—
481C4⋊Q8—1062no—
482C4⋊Q8—1062no—
483C4⋊Q8—1062no—
484C4⋊Q8—1062no—
485#126—1068no—
486#126—1068no—
487#125—1068no—
488#125—1068no—
489#125—1068no—
490#124—534no—
491#124—534no—
492#124—1062no—
493#124—1062no—
494C22⋊Q8—1068no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—534no—
498C4×Q8—534no—
499C4×Q8—534no—
500C4×Q8—534no—
501C4×Q8—534no—
502C4×Q8—1068no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×Q8C22×D5314yes—
507C4×Q8C22×D5314yes—
508C4×D4—534no—
509C4×D4—1062no—
510#117—1068no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—531no—
537C2×C42—531no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—1061no—
541C2×C42C22×D5311yescharacteristic
542#106C22×D5314yes—
543C4⋊C8—534no—
544C4⋊C8—534no—
545C4⋊C8—534no—
546#103—534no—
547#103—534no—
548#103—534no—
549#103C22×D5314yes—
550#103C22×D5314yes—
551#102—534no—
552#97—534no—
553#97C22×D5314yes—
554C4×C8—534no—
555C24—1061no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—534no—
563C2×Q8—532no—
564C2×Q8—532no—
565C2×Q8—532no—
566C2×Q8—1064no—
567C2×Q8—1061no—
568C2×Q8—1061no—
569C2×Q8—1061no—
570C2×Q8—1062no—
571C2×Q8—1062no—
572C2×Q8—1062no—
573C2×Q8—1062no—
574C2×Q8—1062no—
575C2×Q8—1062no—
576C2×Q8C23×D5312yes—
577C2×Q8C23×D5312yes—
578C2×D4—532no—
579C2×D4—1061no—
580C2×D4—1062no—
581C2×D4—1062no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—1064no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—2124no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598Q16—28no—
599Q16—1068no—
600Q16—2124no—
601Q16—2124no—
602Q16—2124no—
603Q16—2124no—
604SD16—1068no—
605SD16—2124no—
606SD16—2124no—
607C2×C8—22no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8#1171994514yes—
613C2×C8C23×D5312yes—
614C2×C8C23×D5312yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—534no—
620C4⋊C4—534no—
621C4⋊C4—534no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C42—24no—
641C42—24no—
642C42—532no—
643C42—532no—
644C42—532no—
645C42—532no—
646C42—1064no—
647C42—1064no—
648C42—1064no—
649C42D4×D5312yes—
650C42C23×D5312yes—
651C23—1062no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1068no—
663Q8—1062no—
664Q8—1062no—
665Q8—1062no—
666Q8—1062no—
667Q8—1062no—
668Q8—1062no—
669Q8—2122no—
670Q8—2122no—
671Q8—2122no—
672D4—1062no—
673D4—1062no—
674D4—2122no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—534no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—532no—
689C2×C4—532no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—2128no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994512yes—
704C2×C4#1313326312yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—1062no—
708C8—1062no—
709C8C2×#1171994514yes—
710C22—4244no—
711C22—2122no—
712C22—2122no—
713C22—2122no—
714C22#1681129412yes—
715C22#137×D5312yes—
716C22#1681143912yes—
717C22C22×D4×D5311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—534no—
725C4—1062no—
726C4—1062no—
727C4—1062no—
728C4—2122no—
729C4—2122no—
730C4—2122no—
731C4#1681129412yes—
732C4C22×#1171994511yescharacteristic
733C4C2×#1313326311yescharacteristic
734C2—4242no—
735C2#2028774714yesdirect product factor
736C2C2×#1681129411yescharacteristic
737C2C2×#137×D5311yescharacteristic
738C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#441C2
socleC23×C53C22×D4
prime radicalC22×D212C23
hypercenterC2×#441D53
hypocenterC53C2×#3398
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#16811351C2semidirect
3. #20287747C2direct (N × H)
6. C2×#16811001C2semidirect
9. C2×#16810833C2semidirect
10. C2×#16810832C2semidirect
11. C2×#16810832C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810729C2semidirect
16. C2×C53×#441C2semidirect
26. #16811351C22semidirect
50. #16811001C22semidirect
53. #16810833C22semidirect
54. #16810832C22semidirect
55. #16810832C22semidirect
57. #16810751C22semidirect
58. #16810729C22semidirect
72. C53×#441C22semidirect
379. C2×#441D53semidirect
381. C2×C53#3398semidirect
431. #441C2×D53semidirect
446. C53C2×#3398semidirect
735. C2#20287747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113512
C2×#168113452
#202877472
C2×#168110172
C2×#168110162
C2×#168110012
C2×#168108482
C2×#168108452
C2×#168108332
C2×#168108322
C2×#168108272
C2×#168107512
C2×#168107292
C2×#168107102
C2×C53×#4412
C2×#339853