Finite Group Databasebeta

← C2×#13126956 #16739631

Subgroups — C2×#13126956 #16739631

Order 3328.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719258C211yesmaximal, characteristic
2#13126956C2116yesmaximal, direct product factor
3C2×#11718728C211yesmaximal, characteristic, complemented
4C2×#11718629C211yesmaximal, characteristic, complemented
5C2×#11718664C211yesmaximal, characteristic, complemented
6C2×#11718724C211yesmaximal, characteristic, complemented
7C2×#11718710C211yesmaximal, characteristic, complemented
8C2×#11718709C211yesmaximal, characteristic, complemented
9C2×#11718688C211yesmaximal, characteristic, complemented
10C2×#11718708C211yesmaximal, characteristic, complemented
11C2×#11718708C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718627C211yesmaximal, characteristic, complemented
15C2×#11718663C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C22×#6127C2211yescharacteristic
19C13×#552—24no—
20C13×#552C2218yescomplemented
21C2×C13×#126—21no—
22C2×C13×#125—21no—
23C2×C13×#125C2211yescharacteristic
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6106C2211yescharacteristic
34C22×#6106C2211yescharacteristic
35C2×#88194—21no—
36C2×#88184C2211yescharacteristic
37C2×#88184C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719258—24no—
41#11719258C2218yes—
42C2×#88147—21no—
43C2×#88138—21no—
44C2×#88138—21no—
45C2×#88128C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718728C2218yescomplemented
51#11718724C2218yescomplemented
52#11718710C2218yescomplemented
53#11718709C2218yescomplemented
54#11718708C2218yescomplemented
55#11718708C2218yescomplemented
56#11718691C2218yescomplemented
57#11718688C2218yescomplemented
58#11718672C2218yescomplemented
59#11718664C2218yescomplemented
60#11718663C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64#11718629C2218yescomplemented
65#11718627C2218yescomplemented
66C2×#88049C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13D411yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C22×C22⋊D13—21no—
85C22×C22⋊D13—21no—
86C2×#6127—22no—
87C2×#6127—22no—
88C2×#6127—24no—
89C2×#6127—24no—
90C2×#6127—42no—
91C2×#6127—42no—
92C2×#6127C2314yes—
93C2×#6127C2314yes—
94C22×D52—21no—
95C22×D52—21no—
96C22×D52C2311yescharacteristic
97C22×D52C2311yescharacteristic
98C22×C4×D13—21no—
99C22×C4×D13—21no—
100C22×Dic26C2311yescharacteristic
101C13×#126—28no—
102C13×#125—28no—
103C13×#125—22no—
104C13×#125C2314yes—
105C13×#123—28no—
106C13×C22⋊Q8—22no—
107C13×C22⋊Q8—22no—
108C13×C22⋊Q8C2314yes—
109C13×C22⋊Q8C2314yes—
110C4×Q8×C13—22no—
111C4×Q8×C13C2314yes—
112C4×D4×C13D414yes—
113C4×D4×C13C2314yes—
114C13×#117—22no—
115C13×#117—28no—
116C13×#117C2314yes—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4D411yescharacteristic
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C4⋊C4C2311yescharacteristic
127C2×C13×C4⋊C4C2314yes—
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4—21no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4D411yescharacteristic
133C2×C13×C22⋊C4D411yescharacteristic
134C2×C42×C13—21no—
135C2×C42×C13—21no—
136C2×C42×C13C2311yescharacteristic
137C2×#6107—24no—
138C2×#6107C2314yes—
139C2×#6106—42no—
140C2×#6106—42no—
141C2×#6106C2314yes—
142C2×#6106C2314yes—
143#88194—28no—
144#88184—22no—
145#88184—22no—
146#88184C2314yes—
147#88184C2314yes—
148C2×#6103—21no—
149C2×#6103—21no—
150C2×C4⋊Dic13C2311yescharacteristic
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88147—28no—
162#88138—28no—
163#88138—28no—
164#88128—22no—
165#88128C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88049C2314yes—
175#88049C2314yes—
176#88049C2314yes—
177#88049C2314yes—
178#88049C2314yes—
179#88049C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3317—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C23×D13—21no—
190C2×Q8×C13—21no—
191C2×Q8×C13—22no—
192C2×Q8×C13—22no—
193C2×Q8×C13C2412yes—
194C2×D4×C13—42no—
195C2×D4×C13C2×D414yes—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—24no—
205C22×C4×C13—44no—
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2411yescharacteristic
215C2×C22⋊D13—24no—
216C2×C22⋊D13—24no—
217C2×C22⋊D13—24no—
218C2×C22⋊D13—24no—
219C2×C22⋊D13—44no—
220C2×C22⋊D13—44no—
221C2×C22⋊D13—82no—
222C2×C22⋊D13—82no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225#6127—28no—
226#6127—28no—
227#6127—44no—
228#6127—44no—
229#6127—48no—
230#6127—48no—
231C2×D52—22no—
232C2×D52—22no—
233C2×D52—22no—
234C2×D52—22no—
235C2×D52—21no—
236C2×D52—21no—
237C2×D52—24no—
238C2×D52—24no—
239C2×D52—44no—
240C2×D52—82no—
241C2×D52C2412yes—
242C2×D52C2412yes—
243C2×C4×D13—24no—
244C2×C4×D13—24no—
245C2×C4×D13—44no—
246C2×C4×D13—44no—
247C2×Dic26—21no—
248C2×Dic26—22no—
249C2×Dic26#4114yes—
250C2×Dic26C2412yes—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—24no—
255C13×C4⋊C4—24no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—24no—
258C13×C4⋊C4—24no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4C2×D414yes—
261C13×C4⋊C4C2412yes—
262C13×C4⋊C4C2412yes—
263C13×C4⋊C4C2412yes—
264C13×C22⋊C4—24no—
265C13×C22⋊C4—24no—
266C13×C22⋊C4—24no—
267C13×C22⋊C4C2×D414yes—
268C13×C22⋊C4C2×D414yes—
269C42×C13—24no—
270C42×C13—24no—
271C42×C13C2×D412yes—
272C42×C13C2412yes—
273#6107—28no—
274#6106—44no—
275#6106—44no—
276#6103—24no—
277#6103—24no—
278C4⋊Dic13—21no—
279C4⋊Dic13C2412yes—
280#6101—24no—
281C4×Dic13—24no—
282#6099—44no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—22no—
287C2×#1055—44no—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#1055C2412yes—
292C2×#552D1311yescharacteristic, complemented
293C2×#550—131no—
294#3317—1316no—
295C2×#490—131no—
296C2×#481—131no—
297C2×#482—131no—
298C2×#479—131no—
299C2×#468—131no—
300C2×#465—131no—
301C2×#460—131no—
302C2×#452—131no—
303C2×#452—131no—
304C2×#441—131no—
305C2×#435—131no—
306C2×#417—131no—
307C2×#416—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13C22×D412yes—
315C23×C13C22×D412yes—
316C23×C13C22×D411yescharacteristic
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—42no—
320C22×D13—42no—
321C22×D13—42no—
322C22×D13—42no—
323C22×D13—42no—
324C22×D13—42no—
325Q8×C13—22no—
326Q8×C13—22no—
327Q8×C13—42no—
328D4×C13—44no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—24no—
334C2×C4×C13—24no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
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—48no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13C22×D412yes—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D411yescharacteristic
353C2×C4×C13C2×#4112yes—
354C2×C4×C13H(5,𝔽2)12yes—
355C2×C4×C13C2511yescharacteristic
356C22⋊D13—48no—
357C22⋊D13—48no—
358C22⋊D13—84no—
359C22⋊D13—84no—
360C2×Dic13—24no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—42no—
364D52—22no—
365D52—22no—
366D52—22no—
367D52—22no—
368D52—48no—
369D52—42no—
370D52—42no—
371D52—84no—
372C4×D13—48no—
373C4×D13—48no—
374Dic26—24no—
375Dic26—22no—
376Dic26C2×#4114yes—
377#1055—22no—
378#1055—22no—
379#1055—22no—
380#1055—22no—
381C22×#41—131no—
382C22×#41—131no—
383C22×Q16—131no—
384C22×SD16—131no—
385C22×SD16—131no—
386C22×M16—131no—
387C23×C8—131no—
388#552—24no—
389#552C2×D1318yescomplemented
390#550—138no—
391#550—264no—
392C2×#127—131no—
393C2×#127—261no—
394C2×#126—21no—
395C2×#125—21no—
396C2×#125C2×D1311yescharacteristic
397C2×#123—21no—
398C2×C22⋊Q8C2×D1311yescharacteristic
399C2×C22⋊Q8C2×D1311yescharacteristic
400C2×#121—131no—
401C2×#121—131no—
402C2×#121—261no—
403C2×#121—261no—
404C2×C4×Q8—131no—
405C2×C4×Q8C2×D1311yescharacteristic
406C2×C4×D4—261no—
407C2×C4×D4C2×D1311yescharacteristic
408C2×#117—21no—
409C2×#117C2×D1311yescharacteristic
410C22×C4⋊C4C2×D1311yescharacteristic
411#490—138no—
412#482—138no—
413#481—138no—
414#479—138no—
415#468—138no—
416#465—138no—
417#460—138no—
418#452—138no—
419#452—138no—
420#441—138no—
421#435—138no—
422C2×#107—131no—
423C2×#106—131no—
424C2×#106—131no—
425C2×C4⋊C8—131no—
426#417—138no—
427#416—138no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×C22⋊C8—131no—
439C2×C22⋊C8—131no—
440C2×#97—131no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—44no—
448C22×C13—44no—
449C22×C13#54612yes—
450C22×C13#57512yes—
451C22×C13#57712yes—
452C22×C13C23×D411yescharacteristic
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—42no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—84no—
460C2×D13—84no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13#54612yes—
470C4×C13C22×#4111yescharacteristic
471C4×C13C2×H(5,𝔽2)11yescharacteristic
472Dic13—24no—
473Dic13—42no—
474C2×#41—134no—
475C2×#41—134no—
476C2×#41—264no—
477C2×#41—264no—
478C2×#41—262no—
479C2×#41—262no—
480C2×#41—522no—
481C2×#41—522no—
482C22×Q8—131no—
483C22×Q8C22×D1311yescharacteristic
484C22×D4—131no—
485C22×D4—131no—
486C22×D4—261no—
487C22×D4—261no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4—261no—
491C22×D4—261no—
492C22×D4C22⋊D1311yescharacteristic
493C23×C4—21no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×Q16—134no—
499C2×Q16—264no—
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—522no—
503C2×SD16—522no—
504C2×M16—134no—
505C2×M16—522no—
506C22×C8—131no—
507C22×C8—131no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—134no—
511C22×C8—522no—
512#127—134no—
513#127—268no—
514#127—262no—
515#126—28no—
516#125—28no—
517#125—22no—
518#125C22×D1314yes—
519#123—28no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8C22×D1314yes—
523C22⋊Q8C22×D1314yes—
524#121—134no—
525#121—134no—
526#121—262no—
527#121—262no—
528#121—268no—
529#121—268no—
530C4×Q8—22no—
531C4×Q8—134no—
532C4×Q8—262no—
533C4×Q8C22×D1314yes—
534C4×D4—268no—
535C4×D4C22⋊D1314yes—
536C4×D4C22×D1314yes—
537#117—22no—
538#117—28no—
539#117C22×D1314yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—131no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4C22⋊D1311yescharacteristic
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1314yes—
553C2×C4⋊C4C22×D1311yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4C22⋊D1311yescharacteristic
560C2×C22⋊C4C22⋊D1311yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42—261no—
564C2×C42C22×D1311yescharacteristic
565#107—134no—
566#106—134no—
567#106—134no—
568C4⋊C8—134no—
569#103—134no—
570#103—134no—
571#103—134no—
572#103—134no—
573#102—134no—
574#102—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579C22⋊C8—134no—
580C22⋊C8—134no—
581#97—134no—
582C2×C13—42no—
583C2×C13—42no—
584C2×C13#331714yescomplemented
585C2×C13C2×#54611yescharacteristic
586C2×C13C2×#57511yescharacteristic
587C2×C13C2×#57711yescharacteristic
588D13—82no—
589D13—82no—
590C24—261no—
591C24—261no—
592C24C2×C22⋊D1311yescharacteristic
593C24C2×C22⋊D1311yescharacteristic
594#41—268no—
595#41—268no—
596#41—524no—
597#41—524no—
598#41—528no—
599#41—528no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—134no—
604C2×Q8—132no—
605C2×Q8—262no—
606C2×Q8—261no—
607C2×Q8C23×D1312yes—
608C2×D4—42no—
609C2×D4—132no—
610C2×D4—132no—
611C2×D4—264no—
612C2×D4—264no—
613C2×D4—264no—
614C2×D4—264no—
615C2×D4—262no—
616C2×D4—262no—
617C2×D4—262no—
618C2×D4—262no—
619C2×D4—264no—
620C2×D4—261no—
621C2×D4—261no—
622C2×D4—264no—
623C2×D4—524no—
624C2×D4—524no—
625C2×D4—524no—
626C2×D4—1042no—
627C2×D4—1042no—
628C2×D4—1042no—
629C2×D4C2×C22⋊D1314yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—44no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—264no—
643C22×C4—264no—
644C22×C4—524no—
645C22×C4—524no—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—268no—
656SD16—524no—
657SD16—524no—
658M16—524no—
659C2×C8—132no—
660C2×C8—132no—
661C2×C8—132no—
662C2×C8—132no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—262no—
667C2×C8—524no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—132no—
678C4⋊C4—261no—
679C4⋊C4—264no—
680C4⋊C4C2×C22⋊D1314yes—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4C2×C22⋊D1314yes—
690C22⋊C4C2×C22⋊D1314yes—
691C42—24no—
692C42—24no—
693C42—264no—
694C42C2×C22⋊D1312yes—
695C42C23×D1312yes—
696C13C2×#331711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—262no—
704C23—262no—
705C23—522no—
706C23—522no—
707C23—522no—
708C23—522no—
709C23—522no—
710C23—522no—
711C23C22×C22⋊D1312yes—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—134no—
718Q8—264no—
719Q8—262no—
720D4—44no—
721D4—262no—
722D4—262no—
723D4—262no—
724D4—262no—
725D4—528no—
726D4—528no—
727D4—528no—
728D4—522no—
729D4—522no—
730D4—1044no—
731D4—1044no—
732D4—1044no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—264no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—528no—
756C2×C4—528no—
757C2×C4—522no—
758C2×C4#41×D1312yes—
759C2×C4#8825612yes—
760C2×C4C22×C22⋊D1312yes—
761C2×C4C22×C22⋊D1312yes—
762C2×C4C22×C22⋊D1312yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1311yescharacteristic
765C2×C4C24×D1311yescharacteristic
766C8—262no—
767C8—262no—
768C8—262no—
769C8—262no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—1044no—
785C22—1044no—
786C22#1171952712yes—
787C22#1171953412yes—
788C22#1171954212yes—
789C22C23×C22⋊D1311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—264no—
799C4—522no—
800C4#1171953412yes—
801C4C2×#41×D1311yescharacteristic
802C4C2×#8825611yescharacteristic
803C2—42no—
804C2—42no—
805C2—1042no—
806C2—1042no—
807C2#1312695614yesdirect product factor
808C2C2×#1171953411yescharacteristic
809C2C2×#1171952711yescharacteristic
810C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC2×#11719258C2
hypercenterC2×#552D13
hypocenterC13C2×#3317
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13126956C2direct (N × H)
3. C2×#11718728C2semidirect
4. C2×#11718629C2semidirect
5. C2×#11718664C2semidirect
6. C2×#11718724C2semidirect
7. C2×#11718710C2semidirect
8. C2×#11718709C2semidirect
9. C2×#11718688C2semidirect
10. C2×#11718708C2semidirect
11. C2×#11718708C2semidirect
12. C2×#11718691C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718627C2semidirect
15. C2×#11718663C2semidirect
16. C2×C13×#552C2semidirect
20. C13×#552C22semidirect
50. #11718728C22semidirect
51. #11718724C22semidirect
52. #11718710C22semidirect
53. #11718709C22semidirect
54. #11718708C22semidirect
55. #11718708C22semidirect
56. #11718691C22semidirect
57. #11718688C22semidirect
58. #11718672C22semidirect
59. #11718664C22semidirect
60. #11718663C22semidirect
64. #11718629C22semidirect
65. #11718627C22semidirect
292. C2×#552D13semidirect
389. #552C2×D13semidirect
584. C2×C13#3317semidirect
696. C13C2×#3317semidirect
807. C2#13126956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192582
#131269562
C2×#117187282
C2×#117186292
C2×#117186642
C2×#117187242
C2×#117187102
C2×#117187092
C2×#117186882
C2×#117187082
C2×#117186912
C2×#117186722
C2×#117186272
C2×#117186632
C2×C13×#5522
C2×#331713