Finite Group Databasebeta

← C2×#13126677 #16739276

Subgroups — C2×#13126677 #16739276

Order 3328.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719347C211yesmaximal, characteristic, complemented
2C2×#11719335C211yesmaximal, characteristic
3#13126677C2116yesmaximal, direct product factor
4C2×#11718461C211yesmaximal, characteristic, complemented
5C2×#11718546C211yesmaximal, characteristic, complemented
6C2×#11718704C211yesmaximal, characteristic, complemented
7C2×#11718552C211yesmaximal, characteristic, complemented
8C2×#11718468C211yesmaximal, characteristic, complemented
9C2×#11718846C211yesmaximal, characteristic, complemented
10C2×#11718848C211yesmaximal, characteristic, complemented
11C2×#11718707C211yesmaximal, characteristic, complemented
12C2×#11718449C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
14C2×#11718465C211yesmaximal, characteristic, complemented
15C22×#88061C211yesmaximal, characteristic, complemented
16C2×C13×#467C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C22×C13×Q16C2211yescharacteristic, complemented
20C23×C8×C13C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×#88201C2211yescharacteristic
24C2×#88200C2211yescharacteristic, complemented
25C2×Q8×Dic13C2211yescharacteristic, complemented
26C22×#6106C2211yescharacteristic
27C22×#6106C2211yescharacteristic
28C2×C4×C22⋊D13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C8×D13C2211yescharacteristic, complemented
31#11719347—24no—
32#11719347C2218yescomplemented
33#11719335—24no—
34#11719335C2218yes—
35C2×#88152—21no—
36C2×#88149—21no—
37C2×#88149C2211yescharacteristic
38C2×#88148—21no—
39C2×#88147C2211yescharacteristic
40C2×#88146C2211yescharacteristic, complemented
41C2×#88144—21no—
42C2×#88144C2211yescharacteristic, complemented
43C2×#88140—21no—
44C2×#88136—21no—
45C2×C22⋊C4×D13—21no—
46C2×#88131—21no—
47C13×#467C2218yescomplemented
48C2×C13×#107C2211yescharacteristic, complemented
49C2×C13×#103C2211yescharacteristic, complemented
50C2×C13×#103C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×#88075C2211yescharacteristic, complemented
53C2×C22⋊#1055C2211yescharacteristic
54#11718848C2218yescomplemented
55#11718846C2218yescomplemented
56C2×#88061C2211yescharacteristic
57C2×#88061C2211yescharacteristic
58C2×#88061C2211yescharacteristic
59C2×#88061C2211yescharacteristic
60C2×#88061C2218yescomplemented
61C8×C22⋊D13C2218yescomplemented
62C2×#88060C2211yescharacteristic, complemented
63C2×#88054C2211yescharacteristic, complemented
64C2×C8×Dic13C2211yescharacteristic, complemented
65#11718707C2218yescomplemented
66#11718704C2218yescomplemented
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic, complemented
70C2×#88048C2211yescharacteristic, complemented
71#11718552C2218yescomplemented
72#11718546C2218yescomplemented
73#11718468C2218yescomplemented
74#11718465C2218yescomplemented
75#11718461C2218yescomplemented
76#11718449C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13D411yescharacteristic
82C23×Dic13—21no—
83C2×#6131—22no—
84C2×#6131—24no—
85C2×#6131—42no—
86C2×#6131C2314yes—
87C22×D52—24no—
88C22×D52—21no—
89C22×D52—21no—
90C22×D52—22no—
91C22×D52—21no—
92C22×D52—42no—
93C22×D52C2311yescharacteristic
94C22×D52C2314yes—
95C22×D52C2311yescharacteristic
96C22×C4×D13—21no—
97C22×C4×D13—21no—
98C22×C4×D13C2311yescharacteristic
99C2×C13×Q16—42no—
100C2×C13×Q16C2314yescomplemented
101C22×C8×C13—42no—
102C22×C8×C13C2311yescharacteristic
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2314yes—
105C13×C22⋊Q8—22no—
106C13×C22⋊Q8—22no—
107C13×C22⋊Q8C2314yes—
108C13×C22⋊Q8C2314yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C22⋊Dic13D411yescharacteristic
116#88201—22no—
117#88201C2314yes—
118#88200—22no—
119#88200C2314yescomplemented
120Q8×Dic13—22no—
121Q8×Dic13C2314yescomplemented
122C2×#6106—24no—
123C2×#6106—42no—
124C2×#6106C2314yes—
125C2×#6106C2314yes—
126C4×C22⋊D13D414yes—
127C4×C22⋊D13C2314yes—
128C2×#6103—21no—
129C2×#6103—21no—
130C2×#6103—21no—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×#6103—21no—
134C2×#6103D411yescharacteristic
135C2×C4⋊Dic13—21no—
136C2×C4⋊Dic13—22no—
137C2×C4⋊Dic13—21no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2314yes—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101D411yescharacteristic
145C2×C4×Dic13—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13C2311yescharacteristic
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C2×C8×D13—42no—
151C2×C8×D13C2314yescomplemented
152#88152—28no—
153#88149—22no—
154#88149—28no—
155#88149C2314yes—
156#88148—28no—
157#88147—22no—
158#88147C2314yes—
159#88146—22no—
160#88146C2314yescomplemented
161#88144—28no—
162#88144—22no—
163#88144C2314yescomplemented
164#88140—28no—
165#88136—28no—
166C22⋊C4×D13—28no—
167#88131—28no—
168C13×#107C2314yescomplemented
169C13×#103C2314yescomplemented
170C13×#103C2314yescomplemented
171#88075C2314yescomplemented
172#88075C2314yescomplemented
173C22⋊#1055C2314yes—
174#88061C2314yes—
175#88061C2314yes—
176#88061C2314yes—
177#88061C2314yes—
178#88060C2314yescomplemented
179#88054C2314yescomplemented
180C8×Dic13C2314yescomplemented
181#88049C2314yes—
182#88049C2314yes—
183#88048C2314yescomplemented
184#88048C2314yescomplemented
185C2×#3296—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C23×D13—21no—
188C23×D13—21no—
189C23×D13—24no—
190C23×D13—44no—
191C23×D13—44no—
192C23×D13—82no—
193C23×D13C2×D411yescharacteristic
194C2×Q8×C13—21no—
195C2×Q8×C13—21no—
196C2×Q8×C13—22no—
197C2×Q8×C13—22no—
198C2×Q8×C13—22no—
199C2×Q8×C13—22no—
200C2×Q8×C13C2412yes—
201C2×Q8×C13C2412yes—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2411yescharacteristic
212C2×C22⋊D13—24no—
213C2×C22⋊D13C2×D414yes—
214C22×Dic13—24no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—44no—
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220C22×Dic13C2×D411yescharacteristic
221#6131—28no—
222#6131—44no—
223#6131—48no—
224C2×D52—21no—
225C2×D52—22no—
226C2×D52—22no—
227C2×D52—22no—
228C2×D52—28no—
229C2×D52—24no—
230C2×D52—24no—
231C2×D52—21no—
232C2×D52—24no—
233C2×D52—44no—
234C2×D52—48no—
235C2×D52—44no—
236C2×D52—44no—
237C2×D52—82no—
238C2×D52#4114yes—
239C2×D52C2412yes—
240C2×D52C2412yes—
241C2×C4×D13—22no—
242C2×C4×D13—22no—
243C2×C4×D13—24no—
244C2×C4×D13—24no—
245C2×C4×D13—44no—
246C2×C4×D13—82no—
247C2×C4×D13C2×D412yes—
248C2×C4×D13C2412yes—
249C13×Q16—44no—
250C2×C8×C13—22no—
251C2×C8×C13—22no—
252C2×C8×C13—44no—
253C2×C8×C13C2412yes—
254C2×C8×C13C2412yes—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—24no—
259C13×C4⋊C4C2412yes—
260C13×C4⋊C4C2412yes—
261C13×C22⋊C4—24no—
262C13×C22⋊C4—24no—
263C22⋊Dic13C2×D414yes—
264#6106—28no—
265#6106—44no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271#6103—24no—
272#6103C2×D414yes—
273C4⋊Dic13—24no—
274C4⋊Dic13—21no—
275C4⋊Dic13—21no—
276C4⋊Dic13—24no—
277C4⋊Dic13—24no—
278C4⋊Dic13C2412yes—
279C4⋊Dic13C2412yes—
280#6101—24no—
281#6101—24no—
282#6101C2×D414yes—
283C4×Dic13—24no—
284C4×Dic13—24no—
285C4×Dic13C2×D412yes—
286C4×Dic13C2412yes—
287C2×#1055—22no—
288C2×#1055—22no—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C8×D13—44no—
292C2×#552—131no—
293C2×#546—131no—
294#3296—1316no—
295C2×#488—131no—
296C2×#482—131no—
297C2×#483—131no—
298C2×#478—131no—
299C2×#467D1311yescharacteristic, complemented
300C2×#465—131no—
301C2×#464—131no—
302C2×#452—131no—
303C2×#450—131no—
304C2×C4×SD16—131no—
305C2×C8×D4—131no—
306C2×#416—131no—
307C22×#102—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13#13514yes—
311C23×C13C22×D412yes—
312C23×C13C22×D411yescharacteristic
313C22×D13—22no—
314C22×D13—24no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—48no—
320C22×D13—42no—
321C22×D13—42no—
322C22×D13—42no—
323C22×D13—48no—
324C22×D13—42no—
325C22×D13—42no—
326C22×D13—84no—
327C22×D13—816no—
328C22×D13C22×D412yes—
329Q8×C13—22no—
330Q8×C13—22no—
331Q8×C13—22no—
332Q8×C13—22no—
333Q8×C13—42no—
334Q8×C13—42no—
335C2×C4×C13—22no—
336C2×C4×C13—24no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13C22×D412yes—
348C2×C4×C13C22×D411yescharacteristic
349C2×C4×C13C2×#4112yes—
350C2×C4×C13H(5,𝔽2)12yes—
351C2×C4×C13C2511yescharacteristic
352C22⋊D13—28no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—48no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13C22×D412yes—
362C2×Dic13C22×D412yes—
363C2×Dic13C22×D412yes—
364D52—24no—
365D52—22no—
366D52—22no—
367D52—22no—
368D52—48no—
369D52—48no—
370D52—42no—
371D52—84no—
372D52C2×#4114yes—
373C4×D13—24no—
374C4×D13—22no—
375C4×D13—22no—
376C4×D13—48no—
377C4×D13—84no—
378C8×C13—22no—
379C8×C13—22no—
380#1055—22no—
381#1055—22no—
382C22×#41—131no—
383C23×D4—131no—
384C22×Q16C2×D1311yescharacteristic, complemented
385C22×SD16—131no—
386C22×SD16—131no—
387C23×C8—131no—
388C23×C8C2×D1311yescharacteristic
389#552—138no—
390#552—264no—
391#546—138no—
392#546—264no—
393C2×#126—261no—
394C2×#125—131no—
395C2×#125—261no—
396C2×#124—131no—
397C2×#123—261no—
398C2×#123—261no—
399C2×C22⋊Q8—131no—
400C2×C22⋊Q8C2×D1311yescharacteristic
401C2×C22⋊Q8C2×D1311yescharacteristic
402C2×#121—131no—
403C2×#121—261no—
404C2×#120—261no—
405C2×C4×Q8—131no—
406C2×C4×D4—131no—
407C2×C4×D4—131no—
408C2×#117—131no—
409C2×#117—261no—
410C22×C4⋊C4—131no—
411C22×C22⋊C4—261no—
412#488—138no—
413#483—138no—
414#482—138no—
415#478—138no—
416#467C2×D1318yescomplemented
417#465—138no—
418#464—138no—
419#452—138no—
420#450—138no—
421C4×SD16—138no—
422C8×D4—138no—
423C2×#107C2×D1311yescharacteristic, complemented
424C2×#106—131no—
425C2×#106—131no—
426C2×C4⋊C8—131no—
427#416—138no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103C2×D1311yescharacteristic, complemented
431C2×#103C2×D1311yescharacteristic, complemented
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—138no—
437C2×#102—131no—
438C2×#102—131no—
439C2×C22⋊C8—131no—
440C2×C22⋊C8—131no—
441C2×C4×C8—131no—
442C22×C13—22no—
443C22×C13—28no—
444C22×C13—22no—
445C22×C13#54612yes—
446C22×C13C2×#13514yes—
447C22×C13C2×#13512yes—
448C22×C13#57712yes—
449C22×C13C23×D411yescharacteristic
450C2×D13—22no—
451C2×D13—24no—
452C2×D13—22no—
453C2×D13—22no—
454C2×D13—44no—
455C2×D13—48no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—816no—
462C2×D13—84no—
463C4×C13—22no—
464C4×C13—42no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#54612yes—
469C4×C13C22×#4111yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—22no—
472Dic13—22no—
473Dic13—22no—
474Dic13—42no—
475Dic13—42no—
476C25—261no—
477C2×#41—134no—
478C2×#41—262no—
479C2×#41—264no—
480C2×#41—522no—
481C22×Q8C22×D1311yescharacteristic
482C22×Q8C22×D1311yescharacteristic
483C22×D4—131no—
484C22×D4—131no—
485C22×D4—131no—
486C22×D4—134no—
487C22×D4—264no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4—261no—
491C22×D4—262no—
492C22×D4—522no—
493C23×C4—131no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4—261no—
497C23×C4C22×D1311yescharacteristic
498C2×Q16—42no—
499C2×Q16C22×D1314yescomplemented
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—264no—
503C2×SD16—522no—
504C22×C8—42no—
505C22×C8—131no—
506C22×C8—131no—
507C22×C8—134no—
508C22×C8—522no—
509C22×C8C22×D1311yescharacteristic
510C22×C8C22×D1311yescharacteristic
511C22×C8C22×D1314yes—
512#126—268no—
513#125—134no—
514#125—262no—
515#125—268no—
516#124—134no—
517#124—262no—
518#123—268no—
519#123—268no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—134no—
523C22⋊Q8—262no—
524C22⋊Q8C22×D1314yes—
525C22⋊Q8C22×D1314yes—
526#121—134no—
527#121—268no—
528#121—262no—
529#120—268no—
530C4×Q8—134no—
531C4×Q8—262no—
532C4×D4—134no—
533C4×D4—134no—
534C4×D4—134no—
535C4×D4—262no—
536#117—134no—
537#117—268no—
538#117—262no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—131no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4—261no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—131no—
556C2×C22⋊C4—131no—
557C2×C22⋊C4—268no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4—261no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C42—131no—
565C2×C42—261no—
566C2×C42—261no—
567#107C22×D1314yescomplemented
568#106—134no—
569#106—134no—
570C4⋊C8—134no—
571#103—134no—
572#103—134no—
573#103C22×D1314yescomplemented
574#103C22×D1314yescomplemented
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579#102—134no—
580#102—134no—
581C22⋊C8—134no—
582C22⋊C8—134no—
583C4×C8—134no—
584C2×C13—24no—
585C2×C13#329614yescomplemented
586C2×C13C2×#54611yescharacteristic
587C2×C13C22×#13511yescharacteristic
588C2×C13C2×#57711yescharacteristic
589D13—42no—
590D13—44no—
591D13—82no—
592C24—131no—
593C24—261no—
594C24—261no—
595C24—264no—
596C24—524no—
597C24—524no—
598C24—1042no—
599C24D4×D1311yescharacteristic
600#41—268no—
601#41—524no—
602#41—528no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8C23×D1312yes—
610C2×Q8C23×D1312yes—
611C2×D4—134no—
612C2×D4—134no—
613C2×D4—132no—
614C2×D4—132no—
615C2×D4—268no—
616C2×D4—264no—
617C2×D4—264no—
618C2×D4—264no—
619C2×D4—261no—
620C2×D4—264no—
621C2×D4—261no—
622C2×D4—262no—
623C2×D4—262no—
624C2×D4—262no—
625C2×D4—524no—
626C2×D4—528no—
627C2×D4—524no—
628C2×D4—524no—
629C2×D4—1042no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—131no—
637C22×C4—131no—
638C22×C4—131no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—264no—
642C22×C4—264no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—264no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—524no—
649C22×C4—524no—
650C22×C4—1042no—
651C22×C4D4×D1312yes—
652C22×C4D4×D1311yescharacteristic
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—44no—
656SD16—268no—
657SD16—524no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—44no—
661C2×C8—132no—
662C2×C8—132no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—524no—
666C2×C8C23×D1312yes—
667C2×C8C23×D1312yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—134no—
673C4⋊C4—132no—
674C4⋊C4—132no—
675C4⋊C4—264no—
676C4⋊C4—264no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—261no—
680C4⋊C4—261no—
681C4⋊C4—264no—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—134no—
687C22⋊C4—134no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4—264no—
694C42—132no—
695C42—132no—
696C42—264no—
697C42—264no—
698C13C2×#329611yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—132no—
702C23—262no—
703C23—262no—
704C23—262no—
705C23—264no—
706C23—262no—
707C23—262no—
708C23—528no—
709C23—522no—
710C23—522no—
711C23—528no—
712C23—522no—
713C23—522no—
714C23—522no—
715C23—1044no—
716C23—10416no—
717C23#8817314yes—
718C23C2×D4×D1312yes—
719C23C2×D4×D1311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—134no—
727D4—268no—
728D4—264no—
729D4—262no—
730D4—262no—
731D4—262no—
732D4—528no—
733D4—528no—
734D4—522no—
735D4—1044no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—132no—
749C2×C4—132no—
750C2×C4—132no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—264no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—528no—
760C2×C4—528no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—1044no—
764C2×C4C2×D4×D1312yes—
765C2×C4C2×D4×D1311yescharacteristic
766C2×C4#8825112yes—
767C2×C4#41×D1312yes—
768C2×C4C24×D1311yescharacteristic
769C8—22no—
770C8—22no—
771C8—262no—
772C8—262no—
773C22—28no—
774C22—22no—
775C22—22no—
776C22—262no—
777C22—264no—
778C22—262no—
779C22—262no—
780C22—524no—
781C22—528no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—522no—
786C22—522no—
787C22—10416no—
788C22—1044no—
789C22#1171931512yes—
790C22C2×#8817314yes—
791C22C2×#8817312yes—
792C22#1171947512yes—
793C22C22×D4×D1311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—262no—
800C4—262no—
801C4—262no—
802C4—522no—
803C4—522no—
804C4#1171931512yes—
805C4C2×#8825111yescharacteristic
806C4C2×#41×D1311yescharacteristic
807C2—24no—
808C2—522no—
809C2—524no—
810C2—1042no—
811C2#1312667714yesdirect product factor
812C2C2×#1171931511yescharacteristic
813C2C22×#8817311yescharacteristic
814C2C2×#1171947511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#467C2
socleC23×C13C22×D4
prime radicalC2×#11719335C2
hypercenterC2×#467D13
hypocenterC13C2×#3296
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#11719347C2semidirect
3. #13126677C2direct (N × H)
4. C2×#11718461C2semidirect
5. C2×#11718546C2semidirect
6. C2×#11718704C2semidirect
7. C2×#11718552C2semidirect
8. C2×#11718468C2semidirect
9. C2×#11718846C2semidirect
10. C2×#11718848C2semidirect
11. C2×#11718707C2semidirect
12. C2×#11718449C2semidirect
13. C2×C8×C22⋊D13C2semidirect
14. C2×#11718465C2semidirect
15. C22×#88061C2semidirect
16. C2×C13×#467C2semidirect
19. C22×C13×Q16C22semidirect
24. C2×#88200C22semidirect
25. C2×Q8×Dic13C22semidirect
30. C22×C8×D13C22semidirect
32. #11719347C22semidirect
40. C2×#88146C22semidirect
42. C2×#88144C22semidirect
47. C13×#467C22semidirect
48. C2×C13×#107C22semidirect
49. C2×C13×#103C22semidirect
50. C2×C13×#103C22semidirect
51. C2×#88075C22semidirect
52. C2×#88075C22semidirect
54. #11718848C22semidirect
55. #11718846C22semidirect
60. C2×#88061C22semidirect
61. C8×C22⋊D13C22semidirect
62. C2×#88060C22semidirect
63. C2×#88054C22semidirect
64. C2×C8×Dic13C22semidirect
65. #11718707C22semidirect
66. #11718704C22semidirect
69. C2×#88048C22semidirect
70. C2×#88048C22semidirect
71. #11718552C22semidirect
72. #11718546C22semidirect
73. #11718468C22semidirect
74. #11718465C22semidirect
75. #11718461C22semidirect
76. #11718449C22semidirect
100. C2×C13×Q16C23semidirect
119. #88200C23semidirect
121. Q8×Dic13C23semidirect
151. C2×C8×D13C23semidirect
160. #88146C23semidirect
163. #88144C23semidirect
168. C13×#107C23semidirect
169. C13×#103C23semidirect
170. C13×#103C23semidirect
171. #88075C23semidirect
172. #88075C23semidirect
178. #88060C23semidirect
179. #88054C23semidirect
180. C8×Dic13C23semidirect
183. #88048C23semidirect
184. #88048C23semidirect
299. C2×#467D13semidirect
384. C22×Q16C2×D13semidirect
416. #467C2×D13semidirect
423. C2×#107C2×D13semidirect
430. C2×#103C2×D13semidirect
431. C2×#103C2×D13semidirect
499. C2×Q16C22×D13semidirect
567. #107C22×D13semidirect
573. #103C22×D13semidirect
574. #103C22×D13semidirect
585. C2×C13#3296semidirect
698. C13C2×#3296semidirect
811. C2#13126677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193472
C2×#117193352
#131266772
C2×#117184612
C2×#117185462
C2×#117187042
C2×#117185522
C2×#117184682
C2×#117188462
C2×#117188482
C2×#117187072
C2×#117184492
C2×C8×C22⋊D132
C2×#117184652
C22×#880612
C2×C13×#4672
C2×#329613