Finite Group Databasebeta

← C2×#13126821 #16739487

Subgroups — C2×#13126821 #16739487

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719257C211yesmaximal, characteristic, complemented
2#13126821C2116yesmaximal, direct product factor
3C2×#11718750C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718628C211yesmaximal, characteristic, complemented
6C2×#11718752C211yesmaximal, characteristic, complemented
7C2×#11718703C211yesmaximal, characteristic, complemented
8C2×#11718699C211yesmaximal, characteristic, complemented
9C2×#11718677C211yesmaximal, characteristic, complemented
10C2×#11718698C211yesmaximal, characteristic, complemented
11C2×#11718701C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718627C211yesmaximal, characteristic, complemented
15C22×#88050C211yesmaximal, characteristic, complemented
16C2×C13×#547C211yesmaximal, characteristic, complemented
17C22×C13×#41—21no—
18C22×#6127C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C13×#547—24no—
21C13×#547C2218yescomplemented
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C13×#121C2211yescharacteristic
27C2×C13×#121C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C2×#88193—21no—
33C22×#6105C2211yescharacteristic
34C22×#6105C2211yescharacteristic
35C22×#6104C2211yescharacteristic
36C2×#88184C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719257—24no—
41#11719257C2218yescomplemented
42C2×#88150—21no—
43C2×#88139—21no—
44C2×#88135—21no—
45C2×#88129C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718752C2218yescomplemented
51#11718750C2218yescomplemented
52#11718703C2218yescomplemented
53#11718701C2218yescomplemented
54#11718699C2218yescomplemented
55#11718698C2218yescomplemented
56#11718679C2218yescomplemented
57#11718677C2218yescomplemented
58#11718672C2218yescomplemented
59#11718631C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88050C2218yescomplemented
67#11718628C2218yescomplemented
68#11718627C2218yescomplemented
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C2×C13×#41—28no—
78C2×C13×#41—48no—
79C22×Q8×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13—21no—
82C22×D4×C13D411yescharacteristic
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13—21no—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—21no—
90C22×C22⋊D13—21no—
91C23×Dic13—21no—
92C2×#6127—22no—
93C2×#6127—24no—
94C2×#6127—42no—
95C2×#6127C2314yes—
96C22×D52C2311yescharacteristic
97C22×C4×D13—21no—
98C22×Dic26—24no—
99C22×Dic26—21no—
100C22×Dic26—22no—
101C22×Dic26—42no—
102C22×Dic26C2311yescharacteristic
103C22×Dic26C2314yes—
104C22×Dic26C2311yescharacteristic
105C13×C4⋊Q8—22no—
106C13×C4⋊Q8C2314yes—
107C13×#123—28no—
108C13×#123—28no—
109C13×C22⋊Q8—28no—
110C13×#121—22no—
111C13×#121—22no—
112C13×#121C2314yes—
113C13×#121C2314yes—
114C4×D4×C13—22no—
115C4×D4×C13D414yes—
116C4×D4×C13C2314yes—
117C4×D4×C13C2314yes—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4D411yescharacteristic
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C4⋊C4C2311yescharacteristic
127C2×C13×C4⋊C4C2314yes—
128C2×C13×C4⋊C4C2314yes—
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×C13C2311yescharacteristic
135C2×C22⋊Dic13—21no—
136#88193—28no—
137C2×#6105—24no—
138C2×#6105—42no—
139C2×#6105C2314yes—
140C2×#6105C2314yes—
141C2×#6104—42no—
142C2×#6104C2314yes—
143#88184—22no—
144#88184C2314yes—
145C2×#6103—21no—
146C2×#6103—21no—
147C2×#6103—21no—
148C2×C4⋊Dic13C2311yescharacteristic
149#88178—22no—
150#88178C2314yes—
151C2×#6101—21no—
152C2×#6101—21no—
153C2×C4×Dic13—21no—
154C2×#6099—42no—
155C2×#6099C2314yes—
156C22×#1055—42no—
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2314yes—
162#88150—28no—
163#88139—28no—
164#88135—28no—
165#88129—22no—
166#88129C2314yes—
167C4×Dic26—22no—
168C4×Dic26C2314yes—
169#88072C2314yes—
170C22⋊#1055C2314yes—
171C22⋊#1055C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88050C2314yes—
178#88049C2314yes—
179#88049C2314yes—
180#88049C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183#88047C2314yes—
184C4⋊#1055C2314yes—
185#88043C2314yes—
186C2×#3308—131nomaximal, Sylow
187C24×C13—21no—
188C24×C13C2×D411yescharacteristic
189C24×C13C2×D411yescharacteristic
190C23×D13—21no—
191C13×#41—432no—
192C2×Q8×C13—24no—
193C2×Q8×C13—44no—
194C2×D4×C13—24no—
195C2×D4×C13—24no—
196C2×D4×C13—24no—
197C2×D4×C13—21no—
198C2×D4×C13—22no—
199C2×D4×C13—22no—
200C2×D4×C13—44no—
201C2×D4×C13—44no—
202C2×D4×C13C2×D414yes—
203C2×D4×C13C2412yes—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—24no—
212C22×C4×C13—24no—
213C22×C4×C13—24no—
214C22×C4×C13—44no—
215C22×C4×C13—44no—
216C22×C4×C13—44no—
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D412yes—
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D412yes—
223C22×C4×C13C2412yes—
224C22×C4×C13C2412yes—
225C22×C4×C13C2411yescharacteristic
226C2×C22⋊D13—24no—
227C2×C22⋊D13—24no—
228C2×C22⋊D13—44no—
229C2×C22⋊D13—44no—
230C22×Dic13—21no—
231C22×Dic13—24no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—44no—
235#6127—28no—
236#6127—44no—
237#6127—48no—
238C2×D52—22no—
239C2×D52—22no—
240C2×D52—21no—
241C2×D52C2412yes—
242C2×C4×D13—24no—
243C2×C4×D13—44no—
244C2×Dic26—21no—
245C2×Dic26—22no—
246C2×Dic26—22no—
247C2×Dic26—22no—
248C2×Dic26—28no—
249C2×Dic26—21no—
250C2×Dic26—24no—
251C2×Dic26—44no—
252C2×Dic26—48no—
253C2×Dic26—44no—
254C2×Dic26#4114yescomplemented
255C2×Dic26C2412yes—
256C2×Dic26C2412yes—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—24no—
261C13×C4⋊C4—24no—
262C13×C4⋊C4—24no—
263C13×C4⋊C4C2×D414yes—
264C13×C4⋊C4C2412yes—
265C13×C4⋊C4C2412yes—
266C13×C4⋊C4C2412yes—
267C13×C22⋊C4—24no—
268C13×C22⋊C4—24no—
269C13×C22⋊C4—24no—
270C13×C22⋊C4C2×D414yes—
271C13×C22⋊C4C2×D414yes—
272C42×C13C2×D412yes—
273C42×C13C2412yes—
274C22⋊Dic13—24no—
275#6105—28no—
276#6105—44no—
277#6104—44no—
278#6103—24no—
279#6103—24no—
280#6103—24no—
281C4⋊Dic13—21no—
282C4⋊Dic13C2412yes—
283#6101—24no—
284#6101—24no—
285C4×Dic13—24no—
286#6099—44no—
287C2×#1055—22no—
288C2×#1055—22no—
289C2×#1055—22no—
290C2×#1055—22no—
291C2×#1055—44no—
292C2×#1055C2412yes—
293C2×#1055C2412yes—
294C2×#1055C2412yes—
295C2×#1055C2412yes—
296C2×#548—131no—
297C2×#547D1311yescharacteristic, complemented
298#3308—1316no—
299C2×#489—131no—
300C2×#484—131no—
301C2×#480—131no—
302C2×#477—131no—
303C2×#468—131no—
304C2×#466—131no—
305C2×#463—131no—
306C2×#449—131no—
307C2×#448—131no—
308C2×#440—131no—
309C2×#435—131no—
310C2×#417—131no—
311C22×#103—131no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13AGL(1,ℤ/8)14yes—
322C23×C13C22×D412yes—
323C23×C13C22×D412yes—
324C23×C13C22×D411yescharacteristic
325C22×D13—22no—
326C22×D13—42no—
327C22×D13—42no—
328C22×D13—42no—
329Q8×C13—48no—
330D4×C13—28no—
331D4×C13—22no—
332D4×C13—22no—
333D4×C13—48no—
334D4×C13—48no—
335D4×C13—42no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—24no—
341C2×C4×C13—24no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—48no—
350C2×C4×C13—48no—
351C2×C4×C13—42no—
352C2×C4×C13—42no—
353C2×C4×C13—42no—
354C2×C4×C13—48no—
355C2×C4×C13C22×D412yes—
356C2×C4×C13C22×D412yes—
357C2×C4×C13C22×D412yes—
358C2×C4×C13C22×D412yes—
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C13C2×#4112yes—
361C2×C4×C13H(5,𝔽2)12yes—
362C2×C4×C13C2511yescharacteristic
363C22⋊D13—48no—
364C22⋊D13—48no—
365C2×Dic13—24no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—48no—
370C2×Dic13—42no—
371C2×Dic13—42no—
372D52—22no—
373D52—22no—
374D52—42no—
375C4×D13—48no—
376Dic26—24no—
377Dic26—22no—
378Dic26—22no—
379Dic26—22no—
380Dic26—48no—
381Dic26—42no—
382Dic26C2×#4114yescomplemented
383#1055—22no—
384#1055—22no—
385#1055—22no—
386#1055—22no—
387C22×#41—21no—
388C22×#41—131no—
389C23×Q8—131no—
390C22×SD16—131no—
391C22×SD16—131no—
392C22×D8—131no—
393C22×M16—131no—
394C23×C8—131no—
395#548—138no—
396#548—264no—
397#547—24no—
398#547C2×D1318yescomplemented
399C2×C4⋊Q8C2×D1311yescharacteristic
400C2×#124—131no—
401C2×#124—261no—
402C2×#123—21no—
403C2×#123—21no—
404C2×C22⋊Q8—21no—
405C2×C22⋊Q8—131no—
406C2×C22⋊Q8—261no—
407C2×#121—131no—
408C2×#121—261no—
409C2×#121C2×D1311yescharacteristic
410C2×#121C2×D1311yescharacteristic
411C2×C4×Q8—131no—
412C2×C4×D4—261no—
413C2×C4×D4C2×D1311yescharacteristic
414C2×C4×D4C2×D1311yescharacteristic
415C22×C4⋊C4C2×D1311yescharacteristic
416C22×C4⋊C4C2×D1311yescharacteristic
417#489—138no—
418#484—138no—
419#480—138no—
420#477—138no—
421#468—138no—
422#466—138no—
423#463—138no—
424#449—138no—
425#448—138no—
426#440—138no—
427#435—138no—
428C2×#107—131no—
429C2×#107—131no—
430C2×#107—131no—
431C2×C4⋊C8—131no—
432#417—138no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103—131no—
436C2×#103—131no—
437C2×#103—131no—
438C2×#103—131no—
439C2×#103—138no—
440C2×#102—131no—
441C2×#102—131no—
442C2×#102—131no—
443C2×#102—131no—
444C2×C22⋊C8—131no—
445C2×C22⋊C8—131no—
446C2×#97—131no—
447C22×C13—22no—
448C22×C13—28no—
449C22×C13—22no—
450C22×C13—22no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—44no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—84no—
458C22×C13#54612yes—
459C22×C13C2×AGL(1,ℤ/8)14yes—
460C22×C13C2×AGL(1,ℤ/8)12yes—
461C22×C13#57812yes—
462C22×C13C23×D411yescharacteristic
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—42no—
466C2×D13—84no—
467C4×C13—22no—
468C4×C13—22no—
469C4×C13—22no—
470C4×C13—22no—
471C4×C13—42no—
472C4×C13—42no—
473C4×C13—42no—
474C4×C13#54612yes—
475C4×C13C22×#4111yescharacteristic
476C4×C13C2×H(5,𝔽2)11yescharacteristic
477Dic13—24no—
478Dic13—42no—
479Dic13—42no—
480C2×#41—28no—
481C2×#41—48no—
482C2×#41—134no—
483C2×#41—264no—
484C2×#41—262no—
485C2×#41—522no—
486C22×Q8—21no—
487C22×Q8—131no—
488C22×Q8—131no—
489C22×Q8—134no—
490C22×Q8—264no—
491C22×Q8—261no—
492C22×Q8—262no—
493C22×Q8—522no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—131no—
497C22×D4—261no—
498C22×D4—261no—
499C22×D4C22⋊D1311yescharacteristic
500C22×D4C22×D1311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—261no—
505C23×C4—261no—
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C2×SD16—134no—
509C2×SD16—134no—
510C2×SD16—264no—
511C2×SD16—522no—
512C2×D8—134no—
513C2×D8—522no—
514C2×M16—134no—
515C2×M16—522no—
516C22×C8—131no—
517C22×C8—131no—
518C22×C8—131no—
519C22×C8—131no—
520C22×C8—134no—
521C22×C8—522no—
522C4⋊Q8—22no—
523C4⋊Q8C22×D1314yes—
524#124—134no—
525#124—268no—
526#124—262no—
527#123—28no—
528#123—28no—
529C22⋊Q8—28no—
530C22⋊Q8—134no—
531C22⋊Q8—262no—
532C22⋊Q8—268no—
533#121—22no—
534#121—22no—
535#121—134no—
536#121—268no—
537#121—262no—
538#121C22×D1314yes—
539#121C22×D1314yes—
540C4×Q8—134no—
541C4×Q8—262no—
542C4×D4—22no—
543C4×D4—268no—
544C4×D4C22⋊D1314yes—
545C4×D4C22×D1314yes—
546C4×D4C22×D1314yes—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—131no—
553C2×C4⋊C4—261no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4C22⋊D1311yescharacteristic
556C2×C4⋊C4C22×D1311yescharacteristic
557C2×C4⋊C4C22×D1311yescharacteristic
558C2×C4⋊C4C22×D1311yescharacteristic
559C2×C4⋊C4C22×D1314yes—
560C2×C4⋊C4C22×D1314yes—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—261no—
567C2×C22⋊C4—261no—
568C2×C22⋊C4C22⋊D1311yescharacteristic
569C2×C22⋊C4C22⋊D1311yescharacteristic
570C2×C42—261no—
571C2×C42C22×D1311yescharacteristic
572#107—134no—
573#107—134no—
574#107—134no—
575C4⋊C8—134no—
576#103—134no—
577#103—134no—
578#103—134no—
579#103—134no—
580#103—134no—
581#103—134no—
582#102—134no—
583#102—134no—
584#102—134no—
585#102—134no—
586C22⋊C8—134no—
587C22⋊C8—134no—
588#97—134no—
589C2×C13—24no—
590C2×C13—42no—
591C2×C13—82no—
592C2×C13#330814yescomplemented
593C2×C13C2×#54611yescharacteristic
594C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
595C2×C13C2×#57811yescharacteristic
596D13—82no—
597C24—21no—
598C24—261no—
599C24C2×C22⋊D1311yescharacteristic
600C24C2×C22⋊D1311yescharacteristic
601#41—432no—
602#41—268no—
603#41—524no—
604#41—528no—
605C2×Q8—24no—
606C2×Q8—44no—
607C2×Q8—134no—
608C2×Q8—132no—
609C2×Q8—132no—
610C2×Q8—268no—
611C2×Q8—262no—
612C2×Q8—261no—
613C2×Q8—264no—
614C2×Q8—261no—
615C2×Q8—262no—
616C2×Q8—262no—
617C2×Q8—524no—
618C2×Q8—524no—
619C2×Q8—528no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—132no—
629C2×D4—264no—
630C2×D4—264no—
631C2×D4—262no—
632C2×D4—262no—
633C2×D4—261no—
634C2×D4—524no—
635C2×D4—524no—
636C2×D4C2×C22⋊D1314yes—
637C2×D4C23×D1312yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—261no—
652C22×C4—264no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—264no—
656C22×C4—524no—
657C22×C4—524no—
658C22×C4C2×C22⋊D1312yes—
659C22×C4C2×C22⋊D1312yes—
660C22×C4C2×C22⋊D1311yescharacteristic
661C22×C4C2×C22⋊D1311yescharacteristic
662C22×C4C2×C22⋊D1311yescharacteristic
663C22×C4C2×C22⋊D1311yescharacteristic
664C22×C4C23×D1312yes—
665C22×C4C23×D1312yes—
666C22×C4C23×D1311yescharacteristic
667SD16—268no—
668SD16—524no—
669D8—524no—
670M16—524no—
671C2×C8—132no—
672C2×C8—132no—
673C2×C8—132no—
674C2×C8—132no—
675C2×C8—262no—
676C2×C8—262no—
677C2×C8—262no—
678C2×C8—262no—
679C2×C8—524no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—132no—
687C4⋊C4—261no—
688C4⋊C4—264no—
689C4⋊C4—264no—
690C4⋊C4C2×C22⋊D1314yes—
691C4⋊C4C23×D1312yes—
692C4⋊C4C23×D1312yes—
693C4⋊C4C23×D1312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—264no—
698C22⋊C4—264no—
699C22⋊C4—264no—
700C22⋊C4—264no—
701C22⋊C4C2×C22⋊D1314yes—
702C22⋊C4C2×C22⋊D1314yes—
703C42—264no—
704C42C2×C22⋊D1312yes—
705C42C23×D1312yes—
706C13C2×#330811yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—262no—
717C23—522no—
718C23—522no—
719C23—522no—
720C23#8818614yes—
721C23C22×C22⋊D1312yes—
722C23C22×C22⋊D1312yes—
723C23C22×C22⋊D1311yescharacteristic
724Q8—48no—
725Q8—134no—
726Q8—264no—
727Q8—262no—
728Q8—262no—
729Q8—262no—
730Q8—528no—
731Q8—522no—
732D4—28no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—48no—
737D4—42no—
738D4—262no—
739D4—262no—
740D4—528no—
741D4—528no—
742D4—522no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—48no—
762C2×C4—264no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—528no—
767C2×C4—528no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4#41×D1312yes—
771C2×C4#8825612yes—
772C2×C4C22×C22⋊D1312yes—
773C2×C4C22×C22⋊D1312yes—
774C2×C4C22×C22⋊D1312yes—
775C2×C4C22×C22⋊D1312yes—
776C2×C4C22×C22⋊D1311yescharacteristic
777C2×C4C24×D1311yescharacteristic
778C8—262no—
779C8—262no—
780C8—262no—
781C8—262no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—522no—
794C22—522no—
795C22—522no—
796C22—1044no—
797C22C2×#8818614yes—
798C22C2×#8818612yes—
799C22#1171953412yes—
800C22#1171954312yes—
801C22C23×C22⋊D1311yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—264no—
810C4—522no—
811C4—522no—
812C4#1171953412yes—
813C4C2×#41×D1311yescharacteristic
814C4C2×#8825611yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—1042no—
819C2#1312682114yesdirect product factor
820C2C2×#1171953411yescharacteristic
821C2C22×#8818611yescharacteristic
822C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13C2×#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11719257C2semidirect
2. #13126821C2direct (N × H)
3. C2×#11718750C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718628C2semidirect
6. C2×#11718752C2semidirect
7. C2×#11718703C2semidirect
8. C2×#11718699C2semidirect
9. C2×#11718677C2semidirect
10. C2×#11718698C2semidirect
11. C2×#11718701C2semidirect
12. C2×#11718679C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718627C2semidirect
15. C22×#88050C2semidirect
16. C2×C13×#547C2semidirect
21. C13×#547C22semidirect
41. #11719257C22semidirect
50. #11718752C22semidirect
51. #11718750C22semidirect
52. #11718703C22semidirect
53. #11718701C22semidirect
54. #11718699C22semidirect
55. #11718698C22semidirect
56. #11718679C22semidirect
57. #11718677C22semidirect
58. #11718672C22semidirect
59. #11718631C22semidirect
66. C2×#88050C22semidirect
67. #11718628C22semidirect
68. #11718627C22semidirect
254. C2×Dic26#41semidirect
297. C2×#547D13semidirect
382. Dic26C2×#41semidirect
398. #547C2×D13semidirect
592. C2×C13#3308semidirect
706. C13C2×#3308semidirect
819. C2#13126821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192572
#131268212
C2×#117187502
C2×#117186312
C2×#117186282
C2×#117187522
C2×#117187032
C2×#117186992
C2×#117186772
C2×#117186982
C2×#117187012
C2×#117186792
C2×#117186722
C2×#117186272
C22×#880502
C2×C13×#5472
C2×#330813