Finite Group Databasebeta

← C2×#13124631 #16730428

Subgroups — C2×#13124631 #16730428

Order 3328.

2530 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719393C211yesmaximal, characteristic, complemented
2C2×C4×D4×D13C211yesmaximal, characteristic
3#13124631C2116yesmaximal, direct product factor
4C2×#11718508C211yesmaximal, characteristic, complemented
5C2×#11718670C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718531C211yesmaximal, characteristic, complemented
8C2×#11718422C211yesmaximal, characteristic, complemented
9C2×#11718551C211yesmaximal, characteristic, complemented
10C2×#11718420C211yesmaximal, characteristic, complemented
11C2×#11718542C211yesmaximal, characteristic, complemented
12C2×#11718522C211yesmaximal, characteristic, complemented
13C2×#11718498C211yesmaximal, characteristic, complemented
14C2×#11718431C211yesmaximal, characteristic
15C2×#11718431C211yesmaximal, characteristic
16C2×C13×#478C211yesmaximal, characteristic, complemented
17C22×D4×D13C2211yescharacteristic
18C23×C4×D13—21no—
19C2×C13×#125C2211yescharacteristic, complemented
20C2×C4×D4×C13C2211yescharacteristic
21C2×D4×Dic13C2211yescharacteristic
22C2×C4×C22⋊D13—21no—
23C22×#6094C2211yescharacteristic
24C22×#6094C2211yescharacteristic
25#11719393—24no—
26#11719393C2218yescomplemented
27C4×D4×D13—24no—
28C4×D4×D13C2218yes—
29C2×#88150—21no—
30C2×#88150—21no—
31C2×#88147C2211yescharacteristic
32C2×#88146C2211yescharacteristic
33C2×#88146C2211yescharacteristic
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×#88142C2211yescharacteristic, complemented
36C2×#88142C2211yescharacteristic, complemented
37C2×#88141—21no—
38C2×#88141—21no—
39C2×#88135—21no—
40C2×C22⋊C4×D13—21no—
41C2×C4×D52C2211yescharacteristic
42C2×C42×D13C2211yescharacteristic
43C2×#88124C2211yescharacteristic, complemented
44C13×#478C2218yescomplemented
45C2×C13×#107C2211yescharacteristic, complemented
46C2×C13×#106C2211yescharacteristic, complemented
47C2×C13×C4⋊C8C2211yescharacteristic, complemented
48C2×C13×#102C2211yescharacteristic
49C2×C13×#102C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88061C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88058C2211yescharacteristic, complemented
55C2×#88057C2211yescharacteristic, complemented
56C2×#88054C2211yescharacteristic, complemented
57C2×#88054C2211yescharacteristic, complemented
58#11718727C2218yescomplemented
59#11718670C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88048C2211yescharacteristic, complemented
63C2×#88048C2211yescharacteristic, complemented
64C2×#88047C2211yescharacteristic, complemented
65C2×#88047C2211yescharacteristic, complemented
66C2×C4⋊#1055C2211yescharacteristic, complemented
67#11718551C2218yescomplemented
68#11718542C2218yescomplemented
69#11718531C2218yescomplemented
70#11718522C2218yescomplemented
71#11718508C2218yescomplemented
72#11718498C2218yescomplemented
73#11718431C2218yes—
74#11718431C2218yes—
75#11718422C2218yescomplemented
76#11718420C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C22×C22⋊D13—21no—
81C23×Dic13—21no—
82C2×D4×D13—22no—
83C2×D4×D13—24no—
84C2×D4×D13Q818yescomplemented
85C2×D4×D13C2314yes—
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13—28no—
91C22×C4×D13—48no—
92C22×C4×D13D411yescharacteristic
93C22×C4×D13D411yescharacteristic
94C22×C4×D13C2311yescharacteristic
95C22×Dic26—21no—
96C22×Dic26—21no—
97C22×C8×C13C2311yescharacteristic
98C22×C8×C13C2311yescharacteristic
99C13×#125—22no—
100C13×#125C2314yescomplemented
101C4×D4×C13—22no—
102C4×D4×C13C2314yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C42×C13C2311yescharacteristic
110C2×C22⋊Dic13—21no—
111D4×Dic13—22no—
112D4×Dic13C2314yes—
113C4×C22⋊D13—28no—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×C4×Dic13D411yescharacteristic
129C2×C4×Dic13D411yescharacteristic
130C2×C4×Dic13C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C2×#6094—24no—
134C2×#6094—24no—
135C2×#6094C2314yes—
136C2×#6094C2314yes—
137#88150—28no—
138#88150—28no—
139#88147—22no—
140#88147C2314yes—
141#88146—22no—
142#88146—22no—
143#88146C2314yes—
144#88146C2314yes—
145C4⋊C4×D13—22no—
146C4⋊C4×D13C2314yes—
147#88142—22no—
148#88142—22no—
149#88142C2314yescomplemented
150#88142C2314yescomplemented
151#88141—28no—
152#88141—28no—
153#88135—28no—
154C22⋊C4×D13—28no—
155C4×D52—22no—
156C4×D52C2314yes—
157C42×D13D414yes—
158C42×D13C2314yes—
159#88124—22no—
160#88124C2314yescomplemented
161C13×#107C2314yescomplemented
162C13×#106C2314yescomplemented
163C13×C4⋊C8C2314yescomplemented
164C13×#102C2314yes—
165C13×#102C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168#88061C2314yes—
169#88061C2314yes—
170#88058C2314yescomplemented
171#88057C2314yescomplemented
172#88054C2314yescomplemented
173#88054C2314yescomplemented
174#88049C2314yes—
175#88049C2314yes—
176#88048C2314yescomplemented
177#88048C2314yescomplemented
178#88047C2314yescomplemented
179#88047C2314yescomplemented
180C4⋊#1055C2314yescomplemented
181C2×#3077—131nomaximal, Sylow
182C24×C13—21no—
183C23×D13—21no—
184C23×D13—28no—
185C23×D13—24no—
186C23×D13—44no—
187C23×D13—44no—
188C23×D13C2×D411yescharacteristic
189C2×D4×C13—21no—
190C2×D4×C13—22no—
191C2×D4×C13C2×Q814yes—
192C2×D4×C13C2412yes—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—24no—
197C22×C4×C13—44no—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2411yescharacteristic
201C2×C22⋊D13—28no—
202C2×C22⋊D13—24no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—24no—
207C22×Dic13—44no—
208C22×Dic13C2×D411yescharacteristic
209C22×Dic13C2×D411yescharacteristic
210C22×Dic13C2×D411yescharacteristic
211D4×D13—216no—
212D4×D13—28no—
213D4×D13C2×Q8116yescomplemented
214C2×D52—21no—
215C2×D52—22no—
216C2×D52C2×Q814yes—
217C2×D52C2412yes—
218C2×C4×D13—24no—
219C2×C4×D13—24no—
220C2×C4×D13—24no—
221C2×C4×D13—24no—
222C2×C4×D13—432no—
223C2×C4×D13—42no—
224C2×C4×D13—44no—
225C2×C4×D13—44no—
226C2×C4×D13—44no—
227C2×C4×D13C2×D414yes—
228C2×C4×D13C2×D414yes—
229C2×C4×D13C2×D412yes—
230C2×C4×D13C2×Q814yes—
231C2×C4×D13#4114yes—
232C2×C4×D13C2412yes—
233C2×Dic26—24no—
234C2×Dic26—24no—
235C2×Dic26—44no—
236C2×Dic26—44no—
237C2×C8×C13—22no—
238C2×C8×C13—22no—
239C2×C8×C13C2412yes—
240C2×C8×C13C2412yes—
241C13×C4⋊C4—24no—
242C13×C4⋊C4—24no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4—21no—
246C13×C4⋊C4C2412yes—
247C13×C4⋊C4C2412yes—
248C13×C4⋊C4C2412yes—
249C13×C22⋊C4—24no—
250C42×C13C2×D412yes—
251C42×C13C2412yes—
252C22⋊Dic13—24no—
253#6103—24no—
254#6103—24no—
255#6103—24no—
256#6103—24no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262C4⋊Dic13C2412yes—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267#6101—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C4×Dic13C2×D412yes—
271C4×Dic13C2×D414yes—
272C4×Dic13C2×D414yes—
273C4×Dic13C2412yes—
274C2×#1055—22no—
275C2×#1055—22no—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278#6094—28no—
279#6094—28no—
280C2×#533—131no—
281C22×C4×D4—131no—
282#3077—1316no—
283C2×#478—131no—
284C2×#478—131no—
285C2×#478—131no—
286C2×#478D1311yescharacteristic, complemented
287C2×#476—131no—
288C2×#476—131no—
289C2×#474—131no—
290C2×#474—131no—
291C2×#428—131no—
292C2×#428—131no—
293C2×#423—131no—
294C2×#418—131no—
295C2×#418—131no—
296C23×C13—24no—
297C23×C13—22no—
298C23×C13—42no—
299C23×C13—42no—
300C23×C13C22×D411yescharacteristic
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—24no—
304C22×D13—22no—
305C22×D13—216no—
306C22×D13—48no—
307C22×D13—432no—
308C22×D13—48no—
309C22×D13—42no—
310C22×D13—42no—
311C22×D13C22⋊Q814yes—
312C22×D13C22×D412yes—
313D4×C13—24no—
314D4×C13—22no—
315D4×C13C22×Q814yes—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—48no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D411yescharacteristic
328C2×C4×C13C22×Q812yes—
329C2×C4×C13C2×#4112yes—
330C2×C4×C13C2511yescharacteristic
331C22⋊D13—216no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—48no—
340C2×Dic13C22⋊Q814yes—
341C2×Dic13AGL(1,ℤ/8)14yes—
342C2×Dic13C22×D412yes—
343C2×Dic13C22×D412yes—
344C2×Dic13C22×D412yes—
345D52—24no—
346D52—22no—
347D52C22×Q814yes—
348C4×D13—28no—
349C4×D13—44no—
350C4×D13—48no—
351C4×D13—48no—
352C4×D13—48no—
353C4×D13C22⋊Q818yes—
354C4×D13C22×Q814yes—
355C4×D13C2×#4114yes—
356Dic26—48no—
357Dic26—48no—
358C8×C13—22no—
359C8×C13—22no—
360#1055—22no—
361#1055—22no—
362C23×D4—131no—
363C24×C4—261no—
364C22×M16—131no—
365C22×M16—131no—
366#533—138no—
367#533—264no—
368C2×C4⋊Q8—131no—
369C2×C4⋊Q8—131no—
370C2×#125—131no—
371C2×#125C2×D1311yescharacteristic, complemented
372C2×C22⋊Q8—261no—
373C2×C22⋊Q8—261no—
374C2×C4×Q8—261no—
375C2×C4×Q8—261no—
376C2×C4×D4—131no—
377C2×C4×D4—138no—
378C2×C4×D4—131no—
379C2×C4×D4—131no—
380C2×C4×D4—261no—
381C2×C4×D4—264no—
382C2×C4×D4—261no—
383C2×C4×D4C2×D1311yescharacteristic
384C2×#117—131no—
385C2×#117—131no—
386C22×C4⋊C4—131no—
387C22×C22⋊C4—261no—
388C22×C42—131no—
389#478—138no—
390#478—138no—
391#478—138no—
392#478C2×D1318yescomplemented
393#476—138no—
394#476—138no—
395#474—138no—
396#474—138no—
397#428—138no—
398#428—138no—
399C2×#107—131no—
400C2×#107—131no—
401C2×#107—131no—
402C2×#107C2×D1311yescharacteristic, complemented
403C2×#106—131no—
404C2×#106—131no—
405C2×#106—131no—
406C2×#106C2×D1311yescharacteristic, complemented
407#423—138no—
408C2×C4⋊C8—131no—
409C2×C4⋊C8—131no—
410C2×C4⋊C8—131no—
411C2×C4⋊C8C2×D1311yescharacteristic, complemented
412#418—138no—
413#418—138no—
414C2×#102—131no—
415C2×#102—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×#102—131no—
419C2×#102—131no—
420C2×#102C2×D1311yescharacteristic
421C2×#102C2×D1311yescharacteristic
422C22×C13—24no—
423C22×C13—48no—
424C22×C13—42no—
425C22×C13—42no—
426C22×C13C2×C22⋊Q812yes—
427C22×C13C2×AGL(1,ℤ/8)12yes—
428C22×C13#57512yes—
429C22×C13C23×D411yescharacteristic
430C2×D13—28no—
431C2×D13—22no—
432C2×D13—22no—
433C2×D13—24no—
434C2×D13—432no—
435C2×D13—48no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13C2×C22⋊Q814yes—
439C4×C13—22no—
440C4×C13—22no—
441C4×C13—42no—
442C4×C13—42no—
443C4×C13—42no—
444C4×C13C2×C22⋊Q812yes—
445C4×C13C23×Q811yescharacteristic
446C4×C13C22×#4111yescharacteristic
447Dic13—22no—
448Dic13—42no—
449Dic13—42no—
450Dic13—42no—
451Dic13C2×C22⋊Q814yes—
452Dic13C2×AGL(1,ℤ/8)14yes—
453C25—261no—
454C22×Q8—261no—
455C22×Q8—261no—
456C22×D4—138no—
457C22×D4—134no—
458C22×D4—131no—
459C22×D4—262no—
460C22×D4—264no—
461C22×D4—261no—
462C22×D4C22×D1311yescharacteristic
463C23×C4—21no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—261no—
468C23×C4—268no—
469C23×C4—261no—
470C23×C4—261no—
471C23×C4—261no—
472C23×C4—528no—
473C2×M16—134no—
474C2×M16—134no—
475C2×M16—264no—
476C2×M16—264no—
477C22×C8—131no—
478C22×C8—131no—
479C22×C8C22×D1311yescharacteristic
480C22×C8C22×D1311yescharacteristic
481C4⋊Q8—134no—
482C4⋊Q8—134no—
483C4⋊Q8—262no—
484C4⋊Q8—262no—
485#125—22no—
486#125—134no—
487#125—262no—
488#125C22×D1314yescomplemented
489C22⋊Q8—268no—
490C22⋊Q8—268no—
491C4×Q8—268no—
492C4×Q8—268no—
493C4×D4—22no—
494C4×D4—134no—
495C4×D4—134no—
496C4×D4—134no—
497C4×D4—268no—
498C4×D4—262no—
499C4×D4—268no—
500C4×D4—262no—
501C4×D4—262no—
502C4×D4C22×D1314yes—
503#117—134no—
504#117—134no—
505#117—262no—
506#117—262no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—131no—
510C2×C4⋊C4—131no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—262no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4C22×D1311yescharacteristic
520C2×C4⋊C4C22×D1311yescharacteristic
521C2×C4⋊C4C22×D1311yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—268no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4—261no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C42—131no—
530C2×C42—131no—
531C2×C42—131no—
532C2×C42—134no—
533C2×C42—134no—
534C2×C42—261no—
535C2×C42—261no—
536C2×C42C22×D1311yescharacteristic
537#107—134no—
538#107—134no—
539#107—134no—
540#107C22×D1314yescomplemented
541#106—134no—
542#106—134no—
543#106—134no—
544#106C22×D1314yescomplemented
545C4⋊C8—134no—
546C4⋊C8—134no—
547C4⋊C8—134no—
548C4⋊C8C22×D1314yescomplemented
549#102—134no—
550#102—134no—
551#102—134no—
552#102—134no—
553#102—134no—
554#102—134no—
555#102C22×D1314yes—
556#102C22×D1314yes—
557C2×C13—44no—
558C2×C13#307714yescomplemented
559C2×C13C22×C22⋊Q811yescharacteristic
560C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
561C2×C13C2×#57511yescharacteristic
562D13—24no—
563D13—44no—
564C24—21no—
565C24—131no—
566C24—264no—
567C24—268no—
568C24—261no—
569C24—524no—
570C24—524no—
571C2×Q8—264no—
572C2×Q8—264no—
573C2×Q8—524no—
574C2×Q8—524no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—1316no—
578C2×D4—134no—
579C2×D4—132no—
580C2×D4—2616no—
581C2×D4—268no—
582C2×D4—264no—
583C2×D4—268no—
584C2×D4—261no—
585C2×D4—262no—
586C2×D4Q8×D1314yes—
587C2×D4C23×D1312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—44no—
593C22×C4—131no—
594C22×C4—131no—
595C22×C4—132no—
596C22×C4—134no—
597C22×C4—134no—
598C22×C4—132no—
599C22×C4—131no—
600C22×C4—134no—
601C22×C4—134no—
602C22×C4—264no—
603C22×C4—264no—
604C22×C4—264no—
605C22×C4—264no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—264no—
610C22×C4—522no—
611C22×C4—524no—
612C22×C4—524no—
613C22×C4—5232no—
614C22×C4—524no—
615C22×C4—524no—
616C22×C4D4×D1311yescharacteristic
617C22×C4D4×D1311yescharacteristic
618C22×C4C23×D1311yescharacteristic
619M16—268no—
620M16—268no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—132no—
624C2×C8—132no—
625C2×C8—262no—
626C2×C8—262no—
627C2×C8C23×D1312yes—
628C2×C8C23×D1312yes—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—132no—
635C4⋊C4—132no—
636C4⋊C4—132no—
637C4⋊C4—264no—
638C4⋊C4—264no—
639C4⋊C4—264no—
640C4⋊C4—261no—
641C4⋊C4—261no—
642C4⋊C4—261no—
643C4⋊C4—264no—
644C4⋊C4—264no—
645C4⋊C4C23×D1312yes—
646C4⋊C4C23×D1312yes—
647C4⋊C4C23×D1312yes—
648C22⋊C4—24no—
649C22⋊C4—264no—
650C22⋊C4—264no—
651C22⋊C4—264no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C42—134no—
655C42—134no—
656C42—132no—
657C42—132no—
658C42—264no—
659C42—264no—
660C42D4×D1312yes—
661C42C23×D1312yes—
662C13C2×#307711yescharacteristic, complemented, Sylow
663C23—24no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—134no—
668C23—132no—
669C23—2616no—
670C23—262no—
671C23—262no—
672C23—264no—
673C23—262no—
674C23—528no—
675C23—5232no—
676C23—528no—
677C23—522no—
678C23—522no—
679C23C2×D4×D1311yescharacteristic
680Q8—528no—
681Q8—528no—
682D4—24no—
683D4—22no—
684D4—134no—
685D4—2616no—
686D4—264no—
687D4—262no—
688D4C2×Q8×D1314yes—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—134no—
699C2×C4—134no—
700C2×C4—132no—
701C2×C4—132no—
702C2×C4—138no—
703C2×C4—134no—
704C2×C4—134no—
705C2×C4—132no—
706C2×C4—268no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—524no—
712C2×C4—528no—
713C2×C4—528no—
714C2×C4—528no—
715C2×C4—528no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4C2×D4×D1312yes—
720C2×C4C2×D4×D1312yes—
721C2×C4C2×D4×D1311yescharacteristic
722C2×C4C2×Q8×D1312yes—
723C2×C4#41×D1312yes—
724C2×C4C24×D1311yescharacteristic
725C8—22no—
726C8—22no—
727C8—262no—
728C8—262no—
729C22—24no—
730C22—48no—
731C22—42no—
732C22—42no—
733C22—134no—
734C22—268no—
735C22—262no—
736C22—262no—
737C22—264no—
738C22—5232no—
739C22—528no—
740C22—522no—
741C22—522no—
742C22D13×C22⋊Q812yes—
743C22#1171947312yes—
744C22D13×AGL(1,ℤ/8)12yes—
745C22C22×D4×D1311yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—134no—
752C4—134no—
753C4—262no—
754C4—522no—
755C4—522no—
756C4—522no—
757C4D13×C22⋊Q812yes—
758C4C22×Q8×D1311yescharacteristic
759C4C2×#41×D1311yescharacteristic
760C2—44no—
761C2—264no—
762C2—524no—
763C2#1312463114yesdirect product factor
764C2C2×D13×C22⋊Q811yescharacteristic
765C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
766C2C2×#1171947311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×D4×D13C22
hypercenterC2×#478D13
hypocenterC13C2×#3077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11719393C2semidirect
3. #13124631C2direct (N × H)
4. C2×#11718508C2semidirect
5. C2×#11718670C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718531C2semidirect
8. C2×#11718422C2semidirect
9. C2×#11718551C2semidirect
10. C2×#11718420C2semidirect
11. C2×#11718542C2semidirect
12. C2×#11718522C2semidirect
13. C2×#11718498C2semidirect
16. C2×C13×#478C2semidirect
19. C2×C13×#125C22semidirect
26. #11719393C22semidirect
35. C2×#88142C22semidirect
36. C2×#88142C22semidirect
43. C2×#88124C22semidirect
44. C13×#478C22semidirect
45. C2×C13×#107C22semidirect
46. C2×C13×#106C22semidirect
47. C2×C13×C4⋊C8C22semidirect
54. C2×#88058C22semidirect
55. C2×#88057C22semidirect
56. C2×#88054C22semidirect
57. C2×#88054C22semidirect
58. #11718727C22semidirect
59. #11718670C22semidirect
62. C2×#88048C22semidirect
63. C2×#88048C22semidirect
64. C2×#88047C22semidirect
65. C2×#88047C22semidirect
66. C2×C4⋊#1055C22semidirect
67. #11718551C22semidirect
68. #11718542C22semidirect
69. #11718531C22semidirect
70. #11718522C22semidirect
71. #11718508C22semidirect
72. #11718498C22semidirect
75. #11718422C22semidirect
76. #11718420C22semidirect
84. C2×D4×D13Q8semidirect
100. C13×#125C23semidirect
149. #88142C23semidirect
150. #88142C23semidirect
160. #88124C23semidirect
161. C13×#107C23semidirect
162. C13×#106C23semidirect
163. C13×C4⋊C8C23semidirect
170. #88058C23semidirect
171. #88057C23semidirect
172. #88054C23semidirect
173. #88054C23semidirect
176. #88048C23semidirect
177. #88048C23semidirect
178. #88047C23semidirect
179. #88047C23semidirect
180. C4⋊#1055C23semidirect
213. D4×D13C2×Q8semidirect
286. C2×#478D13semidirect
371. C2×#125C2×D13semidirect
392. #478C2×D13semidirect
402. C2×#107C2×D13semidirect
406. C2×#106C2×D13semidirect
411. C2×C4⋊C8C2×D13semidirect
488. #125C22×D13semidirect
540. #107C22×D13semidirect
544. #106C22×D13semidirect
548. C4⋊C8C22×D13semidirect
558. C2×C13#3077semidirect
662. C13C2×#3077semidirect
763. C2#13124631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193932
C2×C4×D4×D132
#131246312
C2×#117185082
C2×#117186702
C2×#117187272
C2×#117185312
C2×#117184222
C2×#117185512
C2×#117184202
C2×#117185422
C2×#117185222
C2×#117184982
C2×#117184312
C2×C13×#4782
C2×#307713