Finite Group Databasebeta

← C2×#13125090 #16731225

Subgroups — C2×#13125090 #16731225

Order 3328.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719402C211yesmaximal, characteristic, complemented
2C2×#11719250C211yesmaximal, characteristic
3#13125090C2116yesmaximal, direct product factor
4C2×#11718528C211yesmaximal, characteristic, complemented
5C2×#11718549C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718502C211yesmaximal, characteristic, complemented
8C2×#11718680C211yesmaximal, characteristic, complemented
9C2×#11718437C211yesmaximal, characteristic
10C2×#11718437C211yesmaximal, characteristic
11C2×#11718550C211yesmaximal, characteristic, complemented
12C2×#11718418C211yesmaximal, characteristic, complemented
13C2×#11718419C211yesmaximal, characteristic, complemented
14C2×#11718513C211yesmaximal, characteristic, complemented
15C2×#11718501C211yesmaximal, characteristic, complemented
16C2×C13×#478C211yesmaximal, characteristic, complemented
17C22×D4×D13C2211yescharacteristic
18C2×C13×#125C2211yescharacteristic, complemented
19C2×C4×D4×C13C2211yescharacteristic
20C2×D4×Dic13C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C22×#6105C2211yescharacteristic
23C2×C4×C22⋊D13—21no—
24C22×#6103—21no—
25C22×#6095C2211yescharacteristic
26C22×#6095C2211yescharacteristic
27#11719402—24no—
28#11719402C2218yescomplemented
29#11719250—24no—
30#11719250C2218yes—
31C2×#88152—21no—
32C2×#88152—21no—
33C2×#88151C2211yescharacteristic
34C2×#88151C2211yescharacteristic
35C2×#88147C2211yescharacteristic
36C2×#88146C2211yescharacteristic
37C2×#88144—21no—
38C2×#88144—21no—
39C2×#88141C2211yescharacteristic, complemented
40C2×#88141C2211yescharacteristic, complemented
41C2×#88135—21no—
42C2×C22⋊C4×D13—21no—
43C2×C4×D52C2211yescharacteristic
44C2×#88126C2211yescharacteristic
45C2×#88123C2211yescharacteristic, complemented
46C13×#478C2218yescomplemented
47C2×C13×#107C2211yescharacteristic, complemented
48C2×C13×#106C2211yescharacteristic, complemented
49C2×C13×C4⋊C8C2211yescharacteristic, complemented
50C2×C13×#102C2211yescharacteristic
51C2×C13×#102C2211yescharacteristic
52C2×#88060C2211yescharacteristic
53C2×#88060C2211yescharacteristic
54C2×#88056C2211yescharacteristic, complemented
55C2×#88056C2211yescharacteristic, complemented
56C2×#88055C2211yescharacteristic, complemented
57C2×C8×Dic13C2211yescharacteristic, complemented
58#11718727C2218yescomplemented
59#11718680C2218yescomplemented
60C2×#88050C2211yescharacteristic, complemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88048C2211yescharacteristic, complemented
65C2×#88047C2211yescharacteristic, complemented
66C2×C4⋊#1055C2211yescharacteristic, complemented
67#11718550C2218yescomplemented
68#11718549C2218yescomplemented
69#11718528C2218yescomplemented
70#11718513C2218yescomplemented
71#11718502C2218yescomplemented
72#11718501C2218yescomplemented
73#11718437C2218yes—
74#11718437C2218yes—
75#11718419C2218yescomplemented
76#11718418C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C22×C22⋊D13—21no—
81C23×Dic13—21no—
82C2×D4×D13—24no—
83C2×D4×D13—24no—
84C2×D4×D13—22no—
85C2×D4×D13C2314yes—
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13C2311yescharacteristic
90C22×Dic26C2311yescharacteristic
91C22×Dic26C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C13×#125—22no—
95C13×#125C2314yescomplemented
96C4×D4×C13—22no—
97C4×D4×C13C2314yes—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C22⋊C4—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106D4×Dic13—22no—
107D4×Dic13C2314yes—
108C2×#6105—24no—
109C2×#6105—24no—
110C2×#6105C2314yes—
111C2×#6105C2314yes—
112C4×C22⋊D13—28no—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—28no—
119C2×#6103D411yescharacteristic
120C2×#6103D411yescharacteristic
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101D411yescharacteristic
129C2×#6101D411yescharacteristic
130C2×C4×Dic13—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13C2311yescharacteristic
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C2×#6095—24no—
137C2×#6095—24no—
138C2×#6095C2314yes—
139C2×#6095C2314yes—
140#88152—28no—
141#88152—28no—
142#88151—22no—
143#88151—22no—
144#88151C2314yes—
145#88151C2314yes—
146#88147—22no—
147#88147C2314yes—
148#88146—22no—
149#88146C2314yes—
150#88144—28no—
151#88144—28no—
152#88141—22no—
153#88141—22no—
154#88141C2314yescomplemented
155#88141C2314yescomplemented
156#88135—28no—
157C22⋊C4×D13—28no—
158C4×D52—22no—
159C4×D52C2314yes—
160#88126D414yes—
161#88126C2314yes—
162#88123—22no—
163#88123C2314yescomplemented
164C13×#107C2314yescomplemented
165C13×#106C2314yescomplemented
166C13×C4⋊C8C2314yescomplemented
167C13×#102C2314yes—
168C13×#102C2314yes—
169#88060C2314yes—
170#88060C2314yes—
171#88056C2314yescomplemented
172#88056C2314yescomplemented
173#88055C2314yescomplemented
174C8×Dic13C2314yescomplemented
175#88050C2314yescomplemented
176#88050C2314yescomplemented
177#88049C2314yes—
178#88049C2314yes—
179#88048C2314yescomplemented
180#88047C2314yescomplemented
181C4⋊#1055C2314yescomplemented
182C2×#3123—131nomaximal, Sylow
183C24×C13—21no—
184C23×D13—21no—
185C23×D13—28no—
186C23×D13—24no—
187C23×D13—82no—
188C23×D13—82no—
189C23×D13C2×D411yescharacteristic
190C2×D4×C13—21no—
191C2×D4×C13—22no—
192C2×D4×C13#4114yes—
193C2×D4×C13C2412yes—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—24no—
198C22×C4×C13—82no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—28no—
203C2×C22⋊D13—24no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—24no—
208C22×Dic13—82no—
209C22×Dic13C2×D411yescharacteristic
210C22×Dic13C2×D411yescharacteristic
211C22×Dic13C2×D411yescharacteristic
212D4×D13—216no—
213D4×D13—28no—
214D4×D13—28no—
215C2×D52—21no—
216C2×D52—22no—
217C2×D52#4114yes—
218C2×D52C2412yes—
219C2×C4×D13—22no—
220C2×C4×D13—22no—
221C2×C4×D13—24no—
222C2×C4×D13—24no—
223C2×C4×D13—82no—
224C2×C4×D13—82no—
225C2×C4×D13C2×D412yes—
226C2×C4×D13C2412yes—
227C2×Dic26—22no—
228C2×Dic26—22no—
229C2×Dic26—22no—
230C2×Dic26—22no—
231C2×Dic26—21no—
232C2×Dic26—21no—
233C2×Dic26C2412yes—
234C2×Dic26C2412yes—
235C2×C8×C13—22no—
236C2×C8×C13—22no—
237C2×C8×C13C2412yes—
238C2×C8×C13C2412yes—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—24no—
242C13×C4⋊C4—24no—
243C13×C4⋊C4—21no—
244C13×C4⋊C4C2412yes—
245C13×C4⋊C4C2412yes—
246C13×C4⋊C4C2412yes—
247C13×C22⋊C4—24no—
248C42×C13C2×D412yes—
249C42×C13C2412yes—
250C22⋊Dic13—24no—
251#6105—28no—
252#6105—28no—
253#6103—24no—
254#6103—24no—
255#6103—24no—
256#6103—24no—
257#6103—24no—
258#6103C2×D414yes—
259#6103C2×D414yes—
260C4⋊Dic13—24no—
261C4⋊Dic13—24no—
262C4⋊Dic13—21no—
263C4⋊Dic13—24no—
264C4⋊Dic13—24no—
265C4⋊Dic13C2412yes—
266#6101—24no—
267#6101—24no—
268#6101C2×D414yes—
269#6101C2×D414yes—
270C4×Dic13—24no—
271C4×Dic13—24no—
272C4×Dic13—24no—
273C4×Dic13C2×D412yes—
274C4×Dic13C2412yes—
275C2×#1055—22no—
276C2×#1055—22no—
277C2×#1055C2412yes—
278C2×#1055C2412yes—
279#6095—28no—
280#6095—28no—
281C2×#541—131no—
282C2×#518—131no—
283#3123—1316no—
284C2×#485—131no—
285C2×#485—131no—
286C2×#478—131no—
287C2×#478D1311yescharacteristic, complemented
288C2×#461—131no—
289C2×#461—131no—
290C2×#450—131no—
291C2×#450—131no—
292C2×#440—131no—
293C2×#440—131no—
294C2×C4×SD16—131no—
295C2×C4×SD16—131no—
296C2×#433—131no—
297C23×C13—24no—
298C23×C13—22no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13C22×D411yescharacteristic
302C22×D13—22no—
303C22×D13—24no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—216no—
308C22×D13—42no—
309C22×D13—42no—
310C22×D13—84no—
311C22×D13—84no—
312C22×D13—816no—
313C22×D13C22×D412yes—
314D4×C13—24no—
315D4×C13—22no—
316D4×C13C2×#4114yes—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—84no—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D411yescharacteristic
329C2×C4×C13C2×#4112yes—
330C2×C4×C13C2×#4112yes—
331C2×C4×C13C2511yescharacteristic
332C22⋊D13—216no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—84no—
343C2×Dic13C22×D412yes—
344C2×Dic13C22×D412yes—
345C2×Dic13C22×D412yes—
346D52—24no—
347D52—22no—
348D52C2×#4114yes—
349C4×D13—24no—
350C4×D13—22no—
351C4×D13—22no—
352C4×D13—84no—
353C4×D13—84no—
354Dic26—22no—
355Dic26—22no—
356Dic26—22no—
357Dic26—22no—
358Dic26—42no—
359Dic26—42no—
360C8×C13—22no—
361C8×C13—22no—
362#1055—22no—
363#1055—22no—
364C23×D4—131no—
365C22×SD16—131no—
366C22×SD16—131no—
367C22×SD16—131no—
368C22×SD16—131no—
369#541—138no—
370#541—264no—
371C2×C4⋊Q8—131no—
372C2×#126—261no—
373C2×#126—261no—
374C2×#125—261no—
375C2×#125—261no—
376C2×#125C2×D1311yescharacteristic, complemented
377C2×C22⋊Q8—131no—
378C2×C22⋊Q8—131no—
379#518—138no—
380#518—264no—
381C2×C4×Q8—131no—
382C2×C4×Q8—131no—
383C2×C4×D4—131no—
384C2×C4×D4—131no—
385C2×C4×D4—131no—
386C2×C4×D4—261no—
387C2×C4×D4—261no—
388C2×C4×D4C2×D1311yescharacteristic
389C2×#117—131no—
390C2×#117—131no—
391C22×C22⋊C4—261no—
392C22×C22⋊C4—261no—
393#485—138no—
394#485—138no—
395#478—138no—
396#478C2×D1318yescomplemented
397#461—138no—
398#461—138no—
399#450—138no—
400#450—138no—
401#440—138no—
402#440—138no—
403C4×SD16—138no—
404C4×SD16—138no—
405#433—138no—
406C2×#107—131no—
407C2×#107C2×D1311yescharacteristic, complemented
408C2×#106—131no—
409C2×#106C2×D1311yescharacteristic, complemented
410C2×C4⋊C8—131no—
411C2×C4⋊C8C2×D1311yescharacteristic, complemented
412C2×#103—131no—
413C2×#103—131no—
414C2×#103—131no—
415C2×#103—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×#102C2×D1311yescharacteristic
419C2×#102C2×D1311yescharacteristic
420C2×C22⋊C8—131no—
421C2×C22⋊C8—131no—
422C2×#97—131no—
423C2×C4×C8—131no—
424C22×C13—24no—
425C22×C13—48no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13#52512yes—
429C22×C13#57712yes—
430C22×C13#57712yes—
431C22×C13C23×D411yescharacteristic
432C2×D13—22no—
433C2×D13—24no—
434C2×D13—22no—
435C2×D13—22no—
436C2×D13—44no—
437C2×D13—48no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—816no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13—42no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13#52512yes—
447C4×C13C22×#4111yescharacteristic
448C4×C13C22×#4111yescharacteristic
449Dic13—22no—
450Dic13—22no—
451Dic13—22no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455C25—261no—
456C22×Q8—131no—
457C22×Q8—131no—
458C22×D4—134no—
459C22×D4—131no—
460C22×D4—262no—
461C22×D4—261no—
462C22×D4—264no—
463C22×D4—264no—
464C22×D4C22×D1311yescharacteristic
465C23×C4—21no—
466C23×C4—131no—
467C23×C4—261no—
468C23×C4—261no—
469C23×C4—261no—
470C2×SD16—134no—
471C2×SD16—134no—
472C2×SD16—134no—
473C2×SD16—134no—
474C2×SD16—264no—
475C2×SD16—264no—
476C2×SD16—264no—
477C2×SD16—264no—
478C22×C8—131no—
479C22×C8—131no—
480C22×C8C22×D1311yescharacteristic
481C22×C8C22×D1311yescharacteristic
482C4⋊Q8—134no—
483C4⋊Q8—262no—
484#126—268no—
485#126—268no—
486#125—22no—
487#125—268no—
488#125—268no—
489#125C22×D1314yescomplemented
490C22⋊Q8—134no—
491C22⋊Q8—134no—
492C22⋊Q8—262no—
493C22⋊Q8—262no—
494C4×Q8—134no—
495C4×Q8—134no—
496C4×Q8—262no—
497C4×Q8—262no—
498C4×D4—22no—
499C4×D4—134no—
500C4×D4—134no—
501C4×D4—134no—
502C4×D4—262no—
503C4×D4—262no—
504C4×D4—268no—
505C4×D4—268no—
506C4×D4—262no—
507C4×D4C22×D1314yes—
508#117—134no—
509#117—134no—
510#117—134no—
511#117—262no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—131no—
515C2×C4⋊C4—131no—
516C2×C4⋊C4—131no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4—261no—
522C2×C4⋊C4—261no—
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C4⋊C4C22×D1311yescharacteristic
525C2×C4⋊C4C22×D1311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—131no—
528C2×C22⋊C4—131no—
529C2×C22⋊C4—268no—
530C2×C22⋊C4—268no—
531C2×C22⋊C4—261no—
532C2×C22⋊C4—261no—
533C2×C22⋊C4—261no—
534C2×C22⋊C4—261no—
535C2×C22⋊C4—261no—
536C2×C22⋊C4—261no—
537C2×C42—131no—
538C2×C42—261no—
539C2×C42—261no—
540C2×C42—261no—
541C2×C42C22×D1311yescharacteristic
542#107—134no—
543#107C22×D1314yescomplemented
544#106—134no—
545#106C22×D1314yescomplemented
546C4⋊C8—134no—
547C4⋊C8C22×D1314yescomplemented
548#103—134no—
549#103—134no—
550#103—134no—
551#103—134no—
552#102—134no—
553#102—134no—
554#102C22×D1314yes—
555#102C22×D1314yes—
556C22⋊C8—134no—
557C22⋊C8—134no—
558#97—134no—
559C4×C8—134no—
560C2×C13—44no—
561C2×C13#312314yescomplemented
562C2×C13C2×#52511yescharacteristic
563C2×C13C2×#57711yescharacteristic
564C2×C13C2×#57711yescharacteristic
565D13—42no—
566D13—44no—
567C24—21no—
568C24—131no—
569C24—264no—
570C24—268no—
571C24—261no—
572C24—1042no—
573C24—1042no—
574C2×Q8—132no—
575C2×Q8—132no—
576C2×Q8—261no—
577C2×Q8—261no—
578C2×Q8—262no—
579C2×Q8—262no—
580C2×Q8—262no—
581C2×Q8—262no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—134no—
585C2×D4—132no—
586C2×D4—264no—
587C2×D4—268no—
588C2×D4—2616no—
589C2×D4—268no—
590C2×D4—268no—
591C2×D4—261no—
592C2×D4—262no—
593C2×D4#613114yes—
594C2×D4C23×D1312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—131no—
601C22×C4—131no—
602C22×C4—131no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—264no—
606C22×C4—264no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—264no—
613C22×C4—1042no—
614C22×C4—1042no—
615C22×C4—1042no—
616C22×C4D4×D1311yescharacteristic
617C22×C4D4×D1311yescharacteristic
618C22×C4C23×D1311yescharacteristic
619SD16—268no—
620SD16—268no—
621SD16—268no—
622SD16—268no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—132no—
626C2×C8—132no—
627C2×C8—262no—
628C2×C8—262no—
629C2×C8C23×D1312yes—
630C2×C8C23×D1312yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—134no—
637C4⋊C4—134no—
638C4⋊C4—132no—
639C4⋊C4—264no—
640C4⋊C4—264no—
641C4⋊C4—264no—
642C4⋊C4—264no—
643C4⋊C4—261no—
644C4⋊C4—264no—
645C4⋊C4—264no—
646C4⋊C4C23×D1312yes—
647C4⋊C4C23×D1312yes—
648C4⋊C4C23×D1312yes—
649C22⋊C4—24no—
650C22⋊C4—134no—
651C22⋊C4—134no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C22⋊C4—264no—
655C22⋊C4—264no—
656C22⋊C4—264no—
657C22⋊C4—264no—
658C42—132no—
659C42—132no—
660C42—264no—
661C42—264no—
662C42—264no—
663C42D4×D1312yes—
664C42C23×D1312yes—
665C13C2×#312311yescharacteristic, complemented, Sylow
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—132no—
671C23—2616no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—264no—
676C23—262no—
677C23—522no—
678C23—522no—
679C23—1044no—
680C23—1044no—
681C23—10416no—
682C23C2×D4×D1311yescharacteristic
683Q8—262no—
684Q8—262no—
685Q8—262no—
686Q8—262no—
687Q8—522no—
688Q8—522no—
689D4—24no—
690D4—22no—
691D4—134no—
692D4—2616no—
693D4—264no—
694D4—262no—
695D4C2×#613114yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—132no—
706C2×C4—132no—
707C2×C4—132no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—264no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—1044no—
721C2×C4—1044no—
722C2×C4—1044no—
723C2×C4C2×D4×D1312yes—
724C2×C4C2×D4×D1312yes—
725C2×C4C2×D4×D1311yescharacteristic
726C2×C4C2×#613112yes—
727C2×C4#41×D1312yes—
728C2×C4C24×D1311yescharacteristic
729C8—22no—
730C8—22no—
731C8—262no—
732C8—262no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—262no—
738C22—262no—
739C22—262no—
740C22—264no—
741C22—522no—
742C22—522no—
743C22—524no—
744C22—528no—
745C22—10416no—
746C22#1171933212yes—
747C22#1171947512yes—
748C22#1171948012yes—
749C22C22×D4×D1311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—262no—
756C4—262no—
757C4—262no—
758C4—522no—
759C4—522no—
760C4—522no—
761C4#1171933212yes—
762C4C22×#613111yescharacteristic
763C4C2×#41×D1311yescharacteristic
764C2—44no—
765C2—522no—
766C2—524no—
767C2#1312509014yesdirect product factor
768C2C2×#1171933211yescharacteristic
769C2C2×#1171947511yescharacteristic
770C2C2×#1171948011yescharacteristic
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×#3123
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×#11719402C2semidirect
3. #13125090C2direct (N × H)
4. C2×#11718528C2semidirect
5. C2×#11718549C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718502C2semidirect
8. C2×#11718680C2semidirect
11. C2×#11718550C2semidirect
12. C2×#11718418C2semidirect
13. C2×#11718419C2semidirect
14. C2×#11718513C2semidirect
15. C2×#11718501C2semidirect
16. C2×C13×#478C2semidirect
18. C2×C13×#125C22semidirect
28. #11719402C22semidirect
39. C2×#88141C22semidirect
40. C2×#88141C22semidirect
45. C2×#88123C22semidirect
46. C13×#478C22semidirect
47. C2×C13×#107C22semidirect
48. C2×C13×#106C22semidirect
49. C2×C13×C4⋊C8C22semidirect
54. C2×#88056C22semidirect
55. C2×#88056C22semidirect
56. C2×#88055C22semidirect
57. C2×C8×Dic13C22semidirect
58. #11718727C22semidirect
59. #11718680C22semidirect
60. C2×#88050C22semidirect
61. C2×#88050C22semidirect
64. C2×#88048C22semidirect
65. C2×#88047C22semidirect
66. C2×C4⋊#1055C22semidirect
67. #11718550C22semidirect
68. #11718549C22semidirect
69. #11718528C22semidirect
70. #11718513C22semidirect
71. #11718502C22semidirect
72. #11718501C22semidirect
75. #11718419C22semidirect
76. #11718418C22semidirect
95. C13×#125C23semidirect
154. #88141C23semidirect
155. #88141C23semidirect
163. #88123C23semidirect
164. C13×#107C23semidirect
165. C13×#106C23semidirect
166. C13×C4⋊C8C23semidirect
171. #88056C23semidirect
172. #88056C23semidirect
173. #88055C23semidirect
174. C8×Dic13C23semidirect
175. #88050C23semidirect
176. #88050C23semidirect
179. #88048C23semidirect
180. #88047C23semidirect
181. C4⋊#1055C23semidirect
287. C2×#478D13semidirect
376. C2×#125C2×D13semidirect
396. #478C2×D13semidirect
407. C2×#107C2×D13semidirect
409. C2×#106C2×D13semidirect
411. C2×C4⋊C8C2×D13semidirect
489. #125C22×D13semidirect
543. #107C22×D13semidirect
545. #106C22×D13semidirect
547. C4⋊C8C22×D13semidirect
561. C2×C13#3123semidirect
665. C13C2×#3123semidirect
767. C2#13125090direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194022
C2×#117192502
#131250902
C2×#117185282
C2×#117185492
C2×#117187272
C2×#117185022
C2×#117186802
C2×#117184372
C2×#117185502
C2×#117184182
C2×#117184192
C2×#117185132
C2×#117185012
C2×C13×#4782
C2×#312313