Finite Group Databasebeta

← C2×#20287795 #28265113

Subgroups — C2×#20287795 #28265113

Order 13568.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811345C211yesmaximal, characteristic, complemented
2C2×#16811343C211yesmaximal, characteristic, complemented
3#20287795C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic, complemented
5C2×#16811014C211yesmaximal, characteristic, complemented
6C2×#16811004C211yesmaximal, characteristic
7C2×#16810848C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810833C211yesmaximal, characteristic, complemented
10C2×#16810832C211yesmaximal, characteristic, complemented
11C2×#16810838C211yesmaximal, characteristic
12C2×#16810837C211yesmaximal, characteristic
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×#16810717C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719922C2211yescharacteristic
25#16811345—24no—
26#16811345C2218yescomplemented
27#16811343—24no—
28#16811343C2218yescomplemented
29C2×#13133217C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133212—21no—
32C2×#13133211—21no—
33C2×#13133210—21no—
34C2×#13133210—21no—
35C2×#13133206C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133204C2211yescharacteristic
38C2×#13133204C2211yescharacteristic
39C2×#13133196—21no—
40C2×#13133195—21no—
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133179C2211yescharacteristic
46C2×#13133176—21no—
47C2×#13133174—21no—
48#16811017C2218yescomplemented
49#16811014C2218yescomplemented
50#16811004C2218yes—
51#16810848C2218yescomplemented
52#16810844C2218yescomplemented
53#16810838C2218yes—
54#16810837C2218yes—
55#16810833C2218yescomplemented
56#16810832C2218yescomplemented
57#16810751C2218yescomplemented
58#16810722C2218yescomplemented
59#16810717C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×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×#11719925C2314yes—
90C2×#11719925C2314yes—
91C2×#11719913—24no—
92C2×#11719913—42no—
93C2×#11719913C2314yes—
94C2×#11719913C2314yes—
95C2×#11719923—42no—
96C2×#11719923C2314yes—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133217—22no—
102#13133217C2314yes—
103#13133215—22no—
104#13133215C2314yes—
105#13133212—28no—
106#13133211—28no—
107#13133210—28no—
108#13133210—28no—
109#13133206—22no—
110#13133206C2314yes—
111#13133205—22no—
112#13133205C2314yes—
113#13133204—22no—
114#13133204—22no—
115#13133204C2314yes—
116#13133204C2314yes—
117#13133196—28no—
118#13133195—28no—
119C4×Dic106D414yes—
120C4×Dic106C2314yes—
121#13133182—22no—
122#13133182—22no—
123#13133182—22no—
124#13133182C2314yes—
125#13133182C2314yes—
126#13133182C2314yes—
127#13133179—22no—
128#13133179C2314yes—
129#13133176—28no—
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×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
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×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C23×D53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—21no—
213C2×D212C2412yes—
214C2×C4×D53—24no—
215C2×C4×D53—44no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—42no—
226C2×Dic106C2×D414yes—
227C2×Dic106C2412yes—
228C2×Dic106C2412yes—
229C2×Dic106C2412yes—
230SD16×C53—28no—
231C2×C8×C53—22no—
232C2×C8×C53#4114yes—
233C2×C8×C53C2412yes—
234C2×C8×C53C2412yes—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247C22⋊Dic53—24no—
248#11719925—44no—
249#11719925—44no—
250#11719923—44no—
251#11719922—44no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2×D414yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53C2×D412yes—
271C4×Dic53C2×D412yes—
272C4×Dic53C2412yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278Dic212—28no—
279Dic212—44no—
280#11719913—28no—
281#11719913—44no—
282C23×C53—22no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53C22×D411yescharacteristic
287C22×D53—22no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291Q8×C53—22no—
292Q8×C53—22no—
293Q8×C53—42no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—48no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C53H(5,𝔽2)12yes—
311C2×C4×C53C2511yescharacteristic
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326D212—22no—
327D212—22no—
328D212—42no—
329C4×D53—48no—
330Dic106—22no—
331Dic106—22no—
332Dic106—22no—
333Dic106—22no—
334Dic106—22no—
335Dic106—22no—
336Dic106—44no—
337Dic106—42no—
338Dic106—42no—
339Dic106—42no—
340C8×C53—22no—
341C8×C53C2×#4114yes—
342#88322—22no—
343#88322—22no—
344C2×#3402—531nomaximal, Sylow
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—84no—
349C22×C53#55012yes—
350C22×C53#57512yes—
351C22×C53#57812yes—
352C22×C53C23×D411yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—84no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#55012yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C2×H(5,𝔽2)11yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#556—531no—
373C2×#556—531no—
374#3402—5316no—
375C2×#497—531no—
376C2×#497—531no—
377C2×#495—531no—
378C2×#464—531no—
379C2×#464—531no—
380C2×#462—531no—
381C2×#462—531no—
382C2×#463—531no—
383C2×#463—531no—
384C2×#446—531no—
385C2×#440—531no—
386C2×#440D5311yescharacteristic, complemented
387C2×C4×Q16—531no—
388C2×C53—82no—
389C2×C53#340214yescomplemented
390C2×C53C2×#55011yescharacteristic
391C2×C53C2×#57511yescharacteristic
392C2×C53C2×#57811yescharacteristic
393D53—82no—
394C22×Q16—531no—
395C22×Q16—531no—
396C22×Q16—531no—
397C22×Q16—531no—
398C22×SD16—531no—
399C22×SD16—531no—
400C22×SD16—531no—
401C22×SD16C2×D5311yescharacteristic
402C22×D8—531no—
403#556—538no—
404#556—538no—
405#556—1064no—
406#556—1064no—
407C2×C4⋊Q8—531no—
408C2×C4⋊Q8—531no—
409C2×#126—1061no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#126—1061no—
413C2×#124—531no—
414C2×#124—531no—
415C2×#124—531no—
416C2×#124—531no—
417C2×C22⋊Q8—1061no—
418C2×C22⋊Q8—1061no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×Q8—531no—
422C2×C4×Q8—531no—
423C2×C4×Q8C2×D5311yescharacteristic
424C2×C4×D4—531no—
425C2×C4×D4C2×D5311yescharacteristic
426C2×#117—1061no—
427C2×#117—1061no—
428#497—538no—
429#497—538no—
430#495—538no—
431#464—538no—
432#464—538no—
433#463—538no—
434#463—538no—
435#462—538no—
436#462—538no—
437#446—538no—
438#440—538no—
439#440C2×D5318yescomplemented
440C4×Q16—538no—
441C2×#107C2×D5311yescharacteristic
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#103—531no—
448C2×#103C2×D5311yescharacteristic
449C2×#102—531no—
450C2×#102C2×D5311yescharacteristic
451C2×#97—531no—
452C2×#97C2×D5311yescharacteristic
453C2×C4×C8—531no—
454C53C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—531no—
456C22×Q8—531no—
457C22×Q8—531no—
458C22×Q8—531no—
459C22×Q8C22×D5311yescharacteristic
460C22×D4—531no—
461C22×D4C22×D5311yescharacteristic
462C23×C4—21no—
463C23×C4—1061no—
464C2×Q16—534no—
465C2×Q16—534no—
466C2×Q16—534no—
467C2×Q16—534no—
468C2×Q16—1064no—
469C2×Q16—2122no—
470C2×Q16—2122no—
471C2×Q16—2122no—
472C2×SD16—24no—
473C2×SD16—534no—
474C2×SD16—534no—
475C2×SD16—534no—
476C2×SD16—1064no—
477C2×SD16—2122no—
478C2×SD16—2122no—
479C2×SD16C22×D5314yes—
480C2×D8—534no—
481C2×D8—2122no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8C22×D5311yescharacteristic
485C22×C8C22×D5311yescharacteristic
486C4⋊Q8—534no—
487C4⋊Q8—534no—
488C4⋊Q8—1062no—
489C4⋊Q8—1062no—
490#126—1068no—
491#126—1068no—
492#126—1068no—
493#126—1068no—
494#124—534no—
495#124—534no—
496#124—534no—
497#124—534no—
498#124—1062no—
499#124—1062no—
500#124—1062no—
501#124—1062no—
502C22⋊Q8—1068no—
503C22⋊Q8—1068no—
504C4×Q8—22no—
505C4×Q8—534no—
506C4×Q8—534no—
507C4×Q8—534no—
508C4×Q8—534no—
509C4×Q8—534no—
510C4×Q8—1062no—
511C4×Q8—1062no—
512C4×Q8—1062no—
513C4×Q8C22×D5314yes—
514C4×D4—22no—
515C4×D4—534no—
516C4×D4—1062no—
517C4×D4C22×D5314yes—
518#117—1068no—
519#117—1068no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4C22×D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C42—21no—
544C2×C42—531no—
545C2×C42—531no—
546C2×C42—1061no—
547C2×C42—1061no—
548C2×C42—1061no—
549C2×C42C22×D5311yescharacteristic
550#107C22×D5314yes—
551C4⋊C8—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103C22×D5314yes—
558#102—534no—
559#102C22×D5314yes—
560#97—534no—
561#97C22×D5314yes—
562C4×C8—534no—
563C24—21no—
564C24—1061no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—534no—
569C2×Q8—532no—
570C2×Q8—532no—
571C2×Q8—532no—
572C2×Q8—1061no—
573C2×Q8—1061no—
574C2×Q8—1061no—
575C2×Q8—1062no—
576C2×Q8—1062no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×Q8—1062no—
581C2×Q8—2122no—
582C2×Q8C23×D5312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—532no—
587C2×D4—1061no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4C23×D5312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—1064no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—2124no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—1068no—
609Q16—2124no—
610Q16—2124no—
611Q16—2124no—
612SD16—28no—
613SD16—1068no—
614SD16—2124no—
615SD16—2124no—
616D8—2124no—
617C2×C8—22no—
618C2×C8—532no—
619C2×C8—532no—
620C2×C8—1062no—
621C2×C8—1062no—
622C2×C8#1171994514yes—
623C2×C8C23×D5312yes—
624C2×C8C23×D5312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—534no—
629C4⋊C4—534no—
630C4⋊C4—534no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1064no—
638C4⋊C4C23×D5312yes—
639C4⋊C4C23×D5312yes—
640C22⋊C4—24no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—24no—
651C42—532no—
652C42—532no—
653C42—532no—
654C42—532no—
655C42—1064no—
656C42—1064no—
657C42—1064no—
658C42D4×D5312yes—
659C42C23×D5312yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1062no—
673Q8—1062no—
674Q8—1062no—
675Q8—1062no—
676Q8—1062no—
677Q8—1062no—
678Q8—2124no—
679Q8—2122no—
680Q8—2122no—
681Q8—2122no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1062no—
686D4—1062no—
687D4—2122no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—532no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—2128no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×D4×D5312yes—
713C2×C4C2×D4×D5312yes—
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4C2×#1171994512yes—
716C2×C4#1313326312yes—
717C2×C4C24×D5311yescharacteristic
718C8—22no—
719C8—1062no—
720C8—1062no—
721C8C2×#1171994514yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4244no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22#1681129412yes—
731C22#1681141912yes—
732C22#1681143912yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—1062no—
740C4—1062no—
741C4—1062no—
742C4—1062no—
743C4—2122no—
744C4—2122no—
745C4—2122no—
746C4#1681129412yes—
747C4C22×#1171994511yescharacteristic
748C4C2×#1313326311yescharacteristic
749C2—82no—
750C2—4242no—
751C2#2028779514yesdirect product factor
752C2C2×#1681129411yescharacteristic
753C2C2×#1681141911yescharacteristic
754C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#440D53
hypocenterC53C2×#3402
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811345C2semidirect
2. C2×#16811343C2semidirect
3. #20287795C2direct (N × H)
4. C2×#16811017C2semidirect
5. C2×#16811014C2semidirect
7. C2×#16810848C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810833C2semidirect
10. C2×#16810832C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810722C2semidirect
15. C2×#16810717C2semidirect
16. C2×C53×#440C2semidirect
26. #16811345C22semidirect
28. #16811343C22semidirect
48. #16811017C22semidirect
49. #16811014C22semidirect
51. #16810848C22semidirect
52. #16810844C22semidirect
55. #16810833C22semidirect
56. #16810832C22semidirect
57. #16810751C22semidirect
58. #16810722C22semidirect
59. #16810717C22semidirect
72. C53×#440C22semidirect
386. C2×#440D53semidirect
389. C2×C53#3402semidirect
439. #440C2×D53semidirect
454. C53C2×#3402semidirect
751. C2#20287795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113452
C2×#168113432
#202877952
C2×#168110172
C2×#168110142
C2×#168110042
C2×#168108482
C2×#168108442
C2×#168108332
C2×#168108322
C2×#168108382
C2×#168108372
C2×#168107512
C2×#168107222
C2×#168107172
C2×C53×#4402
C2×#340253