Finite Group Databasebeta

← C2×#20287790 #28265108

Subgroups — C2×#20287790 #28265108

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×#16811346C211yesmaximal, characteristic, complemented
2#20287790C2116yesmaximal, direct product factor
3C2×#16811018C211yesmaximal, characteristic, complemented
4C2×#16811015C211yesmaximal, characteristic, complemented
5C2×#16811005C211yesmaximal, characteristic
6C2×#16810845C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810833C211yesmaximal, characteristic, complemented
9C2×#16810830C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic
11C2×#16810835C211yesmaximal, characteristic
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810723C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×C4×#11719925C211yesmaximal, characteristic, complemented
16C2×C53×#556C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719923C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26#16811346—24no—
27#16811346C2218yescomplemented
28C2×#13133217C2211yescharacteristic
29C2×#13133212—21no—
30C2×#13133212—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133205C2211yescharacteristic
33C2×#13133193—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133175—21no—
38#16811018C2218yescomplemented
39#16811015C2218yescomplemented
40#16811005C2218yes—
41#16810845C2218yescomplemented
42#16810842C2218yescomplemented
43#16810838C2218yes—
44#16810835C2218yes—
45#16810833C2218yescomplemented
46#16810830C2218yescomplemented
47#16810754C2218yescomplemented
48#16810723C2218yescomplemented
49#16810721C2218yescomplemented
50C4×#11719925C2218yescomplemented
51C2×#13133150C2211yescharacteristic
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#556—24no—
65C53×#556C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#126×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53—21no—
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C4×D53—21no—
81C2×#11719925—24no—
82C2×#11719925—42no—
83C2×#11719925—42no—
84C2×#11719925—42no—
85C2×#11719925C2314yes—
86C2×#11719925C2314yes—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C2×#11719923—24no—
90C2×#11719923—42no—
91C2×#11719923C2314yes—
92C2×#11719923C2314yes—
93C2×#11719924—24no—
94C2×#11719924—42no—
95C2×#11719924C2314yes—
96C2×#11719924C2314yes—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133217—22no—
104#13133217C2314yes—
105#13133212—28no—
106#13133212—28no—
107#13133205—22no—
108#13133205—22no—
109#13133205C2314yes—
110#13133205C2314yes—
111#13133193—28no—
112C4×Dic106—22no—
113C4×Dic106—22no—
114C4×Dic106C2314yes—
115C4×Dic106C2314yes—
116C4×D212—22no—
117C4×D212C2314yes—
118#13133175—28no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×#11719921—21no—
127C2×#11719921—21no—
128C2×#11719921—21no—
129C2×C4×Dic53—21no—
130C2×C4×Dic53—21no—
131#13133150C2314yes—
132C4⋊#88322C2314yes—
133C4⋊#88322C2314yes—
134C4⋊#88322C2314yes—
135#13133141C2314yes—
136#13133141C2314yes—
137#13133140C2314yes—
138#13133140C2314yes—
139#13133138C2314yes—
140#13133137C2314yes—
141#13133128C2314yes—
142#13133128C2314yes—
143C4×#88322C2314yes—
144C22×Q8×C53D411yescharacteristic
145C22×Q8×C53C2311yescharacteristic
146C22×Q8×C53C2311yescharacteristic
147C22×D4×C53C2311yescharacteristic
148C23×C4×C53—21no—
149C4⋊Q8×C53—22no—
150C4⋊Q8×C53C2314yes—
151#126×C53—28no—
152#126×C53—28no—
153#124×C53—22no—
154#124×C53—22no—
155#124×C53C2314yes—
156#124×C53C2314yes—
157C22⋊Q8×C53—28no—
158C4×Q8×C53—22no—
159C4×Q8×C53—22no—
160C4×Q8×C53D414yes—
161C4×Q8×C53C2314yes—
162C4×Q8×C53C2314yes—
163C4×Q8×C53C2314yes—
164C4×D4×C53—22no—
165C4×D4×C53C2314yes—
166#117×C53—28no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181C2×C42×C53—21no—
182C2×C42×C53C2311yescharacteristic
183C2×C42×C53C2311yescharacteristic
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C23×D53—21no—
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—42no—
194C2×Q8×C53C2×D414yes—
195C2×Q8×C53C2412yes—
196C2×Q8×C53C2412yes—
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—44no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2411yescharacteristic
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—44no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106—21no—
228C2×Dic106C2412yes—
229C2×Dic106C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2×D414yes—
236C4⋊C4×C53C2×D414yes—
237C4⋊C4×C53C2×D414yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊C4×C53—24no—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C42×C53—24no—
245C42×C53—24no—
246C42×C53C2×D412yes—
247C42×C53C2×D412yes—
248C42×C53C2×D412yes—
249C42×C53C2412yes—
250C42×C53C2412yes—
251C42×C53C2412yes—
252#11719925—28no—
253#11719925—44no—
254#11719925—44no—
255#11719925—44no—
256#11719924—28no—
257#11719924—44no—
258#11719923—28no—
259#11719923—44no—
260#11719922—44no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266C4⋊Dic53—24no—
267C4⋊Dic53—24no—
268C4⋊Dic53—21no—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272C4×Dic53—24no—
273C4×Dic53—24no—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322#4114yes—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281C2×#88322C2412yes—
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—22no—
294Q8×C53—22no—
295Q8×C53—44no—
296Q8×C53—42no—
297Q8×C53—42no—
298D4×C53—22no—
299D4×C53—22no—
300D4×C53—42no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—48no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53H(5,𝔽2)12yes—
323C2×C4×C53C2511yescharacteristic
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330D212—22no—
331D212—22no—
332D212—42no—
333C4×D53—48no—
334Dic106—22no—
335Dic106—22no—
336Dic106—22no—
337Dic106—22no—
338Dic106—42no—
339Dic106—42no—
340#88322—22no—
341#88322—22no—
342#88322—22no—
343#88322C2×#4114yes—
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—22no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53#55012yes—
367C4×C53C22×#4111yescharacteristic
368C4×C53C2×H(5,𝔽2)11yescharacteristic
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#556—531no—
373C2×#556D5311yescharacteristic, complemented
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×#440—531no—
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×SD16—531no—
402C22×D8—531no—
403#556—24no—
404#556—538no—
405#556—1064no—
406#556C2×D5318yescomplemented
407C2×C4⋊Q8—531no—
408C2×C4⋊Q8C2×D5311yescharacteristic
409C2×#126—21no—
410C2×#126—21no—
411C2×#126—1061no—
412C2×#126—1061no—
413C2×#124—531no—
414C2×#124—531no—
415C2×#124C2×D5311yescharacteristic
416C2×#124C2×D5311yescharacteristic
417C2×C22⋊Q8—21no—
418C2×C22⋊Q8—1061no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×Q8C2×D5311yescharacteristic
422C2×C4×Q8C2×D5311yescharacteristic
423C2×C4×Q8C2×D5311yescharacteristic
424C2×C4×D4—531no—
425C2×C4×D4C2×D5311yescharacteristic
426C2×#117—21no—
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#440—538no—
440C4×Q16—538no—
441C2×#107—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#103—531no—
448C2×#103—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#97—531no—
452C2×#97—531no—
453C2×C4×C8—531no—
454C53C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—531no—
456C22×Q8—531no—
457C22×Q8C22⋊D5311yescharacteristic
458C22×Q8C22×D5311yescharacteristic
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—534no—
473C2×SD16—534no—
474C2×SD16—534no—
475C2×SD16—534no—
476C2×SD16—1064no—
477C2×SD16—1064no—
478C2×SD16—2122no—
479C2×SD16—2122no—
480C2×D8—534no—
481C2×D8—2122no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8—531no—
485C22×C8—531no—
486C4⋊Q8—22no—
487C4⋊Q8—534no—
488C4⋊Q8—1062no—
489C4⋊Q8C22×D5314yes—
490#126—28no—
491#126—28no—
492#126—1068no—
493#126—1068no—
494#124—22no—
495#124—22no—
496#124—534no—
497#124—534no—
498#124—1062no—
499#124—1062no—
500#124C22×D5314yes—
501#124C22×D5314yes—
502C22⋊Q8—28no—
503C22⋊Q8—1068no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—534no—
507C4×Q8—534no—
508C4×Q8—1062no—
509C4×Q8—1062no—
510C4×Q8C22⋊D5314yes—
511C4×Q8C22×D5314yes—
512C4×Q8C22×D5314yes—
513C4×Q8C22×D5314yes—
514C4×D4—22no—
515C4×D4—534no—
516C4×D4—1062no—
517C4×D4C22×D5314yes—
518#117—28no—
519#117—1068no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4C22⋊D5311yescharacteristic
530C2×C4⋊C4C22⋊D5311yescharacteristic
531C2×C4⋊C4C22⋊D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
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—21no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42C22×D5311yescharacteristic
548C2×C42C22×D5311yescharacteristic
549C2×C42C22×D5311yescharacteristic
550#107—534no—
551C4⋊C8—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103—534no—
558#102—534no—
559#102—534no—
560#97—534no—
561#97—534no—
562C4×C8—534no—
563C24—21no—
564C24—1061no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—532no—
573C2×Q8—532no—
574C2×Q8—1061no—
575C2×Q8—1061no—
576C2×Q8—1062no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×Q8C2×C22⋊D5314yes—
581C2×Q8C23×D5312yes—
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—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1064no—
600C22×C4—2124no—
601C22×C4C2×C22⋊D5311yescharacteristic
602C22×C4C2×C22⋊D5311yescharacteristic
603C22×C4C2×C22⋊D5311yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C2×C22⋊D5311yescharacteristic
606C22×C4C2×C22⋊D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—1068no—
609Q16—2124no—
610Q16—2124no—
611Q16—2124no—
612SD16—1068no—
613SD16—1068no—
614SD16—2124no—
615SD16—2124no—
616D8—2124no—
617C2×C8—534no—
618C2×C8—532no—
619C2×C8—532no—
620C2×C8—532no—
621C2×C8—532no—
622C2×C8—1062no—
623C2×C8—1062no—
624C2×C8—1062no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—532no—
631C4⋊C4—1061no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4C2×C22⋊D5314yes—
637C4⋊C4C2×C22⋊D5314yes—
638C4⋊C4C2×C22⋊D5314yes—
639C4⋊C4C23×D5312yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—24no—
651C42—24no—
652C42—1064no—
653C42—1064no—
654C42C2×C22⋊D5312yes—
655C42C2×C22⋊D5312yes—
656C42C2×C22⋊D5312yes—
657C42C23×D5312yes—
658C42C23×D5312yes—
659C42C23×D5312yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C22×C22⋊D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—1062no—
677Q8—1062no—
678Q8—1062no—
679Q8—1062no—
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—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—2128no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4C22×C22⋊D5312yes—
709C2×C4C22×C22⋊D5312yes—
710C2×C4C22×C22⋊D5312yes—
711C2×C4C22×C22⋊D5312yes—
712C2×C4C22×C22⋊D5312yes—
713C2×C4C22×C22⋊D5312yes—
714C2×C4C22×C22⋊D5311yescharacteristic
715C2×C4#41×D5312yes—
716C2×C4#1313326312yes—
717C2×C4C24×D5311yescharacteristic
718C8—534no—
719C8—1062no—
720C8—1062no—
721C8—1062no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4244no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22#1681129212yes—
731C22#1681142112yes—
732C22#1681143812yes—
733C22C23×C22⋊D5311yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2122no—
744C4—2122no—
745C4—2122no—
746C4#1681129212yes—
747C4C2×#41×D5311yescharacteristic
748C4C2×#1313326311yescharacteristic
749C2—82no—
750C2—4242no—
751C2#2028779014yesdirect product factor
752C2C2×#1681129211yescharacteristic
753C2C2×#1681142111yescharacteristic
754C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#556C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#556D53
hypocenterC53C2×#3402
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16811346C2semidirect
2. #20287790C2direct (N × H)
3. C2×#16811018C2semidirect
4. C2×#16811015C2semidirect
6. C2×#16810845C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810833C2semidirect
9. C2×#16810830C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810723C2semidirect
14. C2×#16810721C2semidirect
15. C2×C4×#11719925C2semidirect
16. C2×C53×#556C2semidirect
27. #16811346C22semidirect
38. #16811018C22semidirect
39. #16811015C22semidirect
41. #16810845C22semidirect
42. #16810842C22semidirect
45. #16810833C22semidirect
46. #16810830C22semidirect
47. #16810754C22semidirect
48. #16810723C22semidirect
49. #16810721C22semidirect
50. C4×#11719925C22semidirect
65. C53×#556C22semidirect
373. C2×#556D53semidirect
389. C2×C53#3402semidirect
406. #556C2×D53semidirect
454. C53C2×#3402semidirect
751. C2#20287790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113462
#202877902
C2×#168110182
C2×#168110152
C2×#168110052
C2×#168108452
C2×#168108422
C2×#168108332
C2×#168108302
C2×#168108382
C2×#168108352
C2×#168107542
C2×#168107232
C2×#168107212
C2×C4×#117199252
C2×C53×#5562
C2×#340253