Finite Group Databasebeta

← #15868262

Subgroups — #15868262

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2#13117219C211yesmaximal, characteristic, complemented
3#13115821C212yesmaximal, complemented
4#13115672C212yesmaximal, complemented
5#13115289C214yesmaximal, complemented
6C4×#88046C214yesmaximal, complemented
7C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C22×C13×C22⋊C4C2212yes—
11C22×C42×C13—21no—
12C2×#88207C2212yes—
13#11719496—21no—
14#11719496—21no—
15#11719496—21no—
16#11719496—21no—
17#11719496—21no—
18#11719496—21no—
19#11719496—21no—
20#11719496—21no—
21C2×#88184C411yescharacteristic, complemented
22C2×#88184C2211yescharacteristic
23C2×#88183C412yescomplemented
24C2×C4×C22⋊D13C412yescomplemented
25C2×C4×C22⋊D13C2212yes—
26C2×#88180—21no—
27C2×#88180C411yescharacteristic, complemented
28C2×#88178C411yescharacteristic, complemented
29C2×#88178C2211yescharacteristic
30C4×C13×C22⋊C4—21no—
31C4×C13×C22⋊C4—21no—
32C4×C13×C22⋊C4C2212yes—
33C4×C13×C22⋊C4C2212yes—
34C2×C13×#95—21no—
35#11718908C2212yes—
36#11718873—21no—
37#11718873C2212yes—
38#11718872—21no—
39C4×C22⋊Dic13—21no—
40C4×C22⋊Dic13C2212yes—
41C2×#88046C2218yes—
42#11718119C2218yes—
43C25×C13C2311yescharacteristic
44C23×C4×C13—22no—
45C23×C4×C13—44no—
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×C4×C13C2×C411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D411yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13C2×C412yes—
61C22×C22⋊D13C2×C412yes—
62C22×C22⋊D13C2312yes—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—21no—
66C2×#6127—21no—
67C2×#6127—44no—
68C22×D52C2×C411yescharacteristic, complemented
69C22×C4×D13C2×C412yescomplemented
70C22×Dic26C2×C411yescharacteristic, complemented
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—28no—
73C2×C13×C22⋊C4C2314yes—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13—44no—
77#88207—22no—
78#88207—22no—
79#88207—22no—
80#88207—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13C2×C412yes—
84C2×C22⋊Dic13C2×C412yes—
85C2×C22⋊Dic13C2314yes—
86C2×C22⋊Dic13C2312yes—
87#88184—21no—
88#88184—21no—
89#88184—21no—
90#88184—21no—
91#88184—21no—
92#88184—21no—
93#88184—21no—
94#88184—21no—
95#88183—22no—
96#88183—22no—
97#88183—22no—
98#88183—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C4×C22⋊D13—22no—
104C4×C22⋊D13—22no—
105C4×C22⋊D13—22no—
106C4×C22⋊D13—22no—
107C2×#6103C2×C412yescomplemented
108C2×#6103C2×C412yescomplemented
109#88180—21no—
110#88180—21no—
111#88180—21no—
112#88180—21no—
113#88180—44no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13C2×C411yescharacteristic, complemented
116C2×C4⋊Dic13C2×C411yescharacteristic, complemented
117#88178—21no—
118#88178—21no—
119#88178—21no—
120#88178—21no—
121#88178—21no—
122#88178—21no—
123#88178—21no—
124#88178—21no—
125C2×#6101C2×C412yescomplemented
126C2×#6101C2×C412yescomplemented
127C2×C4×Dic13—22no—
128C2×C4×Dic13C2×C412yescomplemented
129C13×#95—22no—
130C13×#95—22no—
131#88071—22no—
132#88071—22no—
133#88046—216no—
134#21420—131nomaximal, Sylow
135C24×C13—24no—
136C24×C13—42no—
137C24×C13—42no—
138C24×C13C22×C411yescharacteristic
139C24×C13C22×C411yescharacteristic
140C24×C13C2×D411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C24×C13C2411yescharacteristic
145C23×D13C22×C412yes—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
149C22×C4×C13—28no—
150C22×C4×C13—24no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13—42no—
159C22×C4×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—44no—
163C22×C4×C13—44no—
164C22×C4×C13C22⋊C411yescharacteristic
165C22×C4×C13C22⋊C411yescharacteristic
166C22×C4×C13C22⋊C411yescharacteristic
167C22×C4×C13C22⋊C411yescharacteristic
168C22×C4×C13C22⋊C411yescharacteristic
169C22×C4×C13C22⋊C411yescharacteristic
170C22×C4×C13C22⋊C411yescharacteristic
171C22×C4×C13C22⋊C411yescharacteristic
172C22×C4×C13C22⋊C411yescharacteristic
173C22×C4×C13C22⋊C411yescharacteristic
174C22×C4×C13C22⋊C411yescharacteristic
175C22×C4×C13C22⋊C411yescharacteristic
176C22×C4×C13C22⋊C411yescharacteristic
177C22×C4×C13C22⋊C411yescharacteristic
178C22×C4×C13C22⋊C411yescharacteristic
179C22×C4×C13C22⋊C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C22×C411yescharacteristic
182C22×C4×C13C22×C411yescharacteristic
183C22×C4×C13C22×C411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C2×C22⋊D13—22no—
193C2×C22⋊D13—22no—
194C2×C22⋊D13—22no—
195C2×C22⋊D13—22no—
196C2×C22⋊D13—22no—
197C2×C22⋊D13—22no—
198C2×C22⋊D13—28no—
199C2×C22⋊D13—44no—
200C2×C22⋊D13—44no—
201C22×Dic13—24no—
202C22×Dic13C22×C412yes—
203C22×Dic13C22×C412yes—
204C22×Dic13C22×C412yes—
205#6127—44no—
206#6127—44no—
207#6127—44no—
208#6127—44no—
209C2×D52—21no—
210C2×D52—21no—
211C2×D52—42no—
212C2×C4×D13—22no—
213C2×C4×D13—22no—
214C2×C4×D13—44no—
215C2×Dic26—21no—
216C2×Dic26—21no—
217C2×Dic26—42no—
218C13×C22⋊C4—28no—
219C13×C22⋊C4—24no—
220C13×C22⋊C4#4118yescomplemented
221C42×C13—44no—
222C42×C13—44no—
223C22⋊Dic13—22no—
224C22⋊Dic13—22no—
225C22⋊Dic13—22no—
226C22⋊Dic13—22no—
227C22⋊Dic13—22no—
228C22⋊Dic13—22no—
229C22⋊Dic13—28no—
230C22⋊Dic13—44no—
231C22⋊Dic13—44no—
232#6103—22no—
233#6103—22no—
234#6103—22no—
235#6103—22no—
236C4⋊Dic13—21no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13—44no—
241#6101—22no—
242#6101—22no—
243#6101—22no—
244#6101—22no—
245C4×Dic13—22no—
246C4×Dic13—22no—
247C4×Dic13—44no—
248C2×#525—131no—
249#2280—131no—
250C2×C4×C22⋊C4D1311yescharacteristic, complemented
251#1996—132no—
252#1964—132no—
253#1898—134no—
254C4×#99—134no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—416no—
276C23×C13C2×C22⋊C411yescharacteristic
277C23×C13C2×C22⋊C411yescharacteristic
278C23×C13C2×C22⋊C411yescharacteristic
279C23×C13C2×C22⋊C411yescharacteristic
280C23×C13C23×C411yescharacteristic
281C23×C13C22×D411yescharacteristic
282C23×C13C22×D411yescharacteristic
283C23×C13C2×#4114yes—
284C22×D13—22no—
285C22×D13—24no—
286C22×D13—42no—
287C22×D13—42no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—28no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—44no—
317C2×C4×C13—416no—
318C2×C4×C13—44no—
319C2×C4×C13#9914yescomplemented
320C2×C4×C13C2×C22⋊C411yescharacteristic
321C2×C4×C13C2×C22⋊C411yescharacteristic
322C2×C4×C13C2×C22⋊C411yescharacteristic
323C2×C4×C13C2×C22⋊C411yescharacteristic
324C2×C4×C13C2×C22⋊C411yescharacteristic
325C2×C4×C13C2×C22⋊C411yescharacteristic
326C2×C4×C13C2×C22⋊C411yescharacteristic
327C2×C4×C13C2×C22⋊C411yescharacteristic
328C22⋊D13—44no—
329C22⋊D13—44no—
330C22⋊D13—44no—
331C22⋊D13—44no—
332C22⋊D13—44no—
333C22⋊D13—44no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—24no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—44no—
341C2×Dic13—44no—
342C2×Dic13—44no—
343D52—42no—
344D52—42no—
345C4×D13—44no—
346C4×D13—44no—
347Dic26—42no—
348Dic26—42no—
349C22×#41—131no—
350C24×C4C2×D1311yescharacteristic
351#525—261no—
352#525—261no—
353#525—261no—
354#525—261no—
355#525—261no—
356#525—261no—
357#525—261no—
358#525—261no—
359C2×#123—132no—
360C2×C22⋊Q8—131no—
361C2×C22⋊Q8—131no—
362C2×#121—131no—
363C2×#121—131no—
364C2×#120—132no—
365C2×C4×D4—132no—
366C2×C4×D4—132no—
367C2×#117—131no—
368C2×#117—261no—
369C22×C22⋊C4C2×D1312yes—
370C22×C42—21no—
371C2×#99—138no—
372#381—261no—
373#380—132no—
374#380—261no—
375#379—132no—
376C4×C22⋊C4—21no—
377C4×C22⋊C4—21no—
378C4×C22⋊C4—132no—
379C4×C22⋊C4—261no—
380C4×C22⋊C4C2×D1312yes—
381C4×C22⋊C4C2×D1312yes—
382C2×#95—21no—
383#342—138no—
384C22×C13—28no—
385C22×C13—21no—
386C22×C13—21no—
387C22×C13—21no—
388C22×C13—21no—
389C22×C13—21no—
390C22×C13—21no—
391C22×C13—21no—
392C22×C13—21no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13—21no—
396C22×C13—21no—
397C22×C13—21no—
398C22×C13—21no—
399C22×C13—21no—
400C22×C13—21no—
401C22×C13—44no—
402C22×C13—44no—
403C22×C13—44no—
404C22×C13—44no—
405C22×C13—44no—
406C22×C13—44no—
407C22×C13C2×#9912yes—
408C22×C13#41012yes—
409C22×C13C22×C22⋊C411yescharacteristic
410C22×C13C4×#4112yes—
411C22×C13#52512yes—
412C22×C13#53212yes—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—84no—
417C4×C13—21no—
418C4×C13—21no—
419C4×C13—21no—
420C4×C13—21no—
421C4×C13—21no—
422C4×C13—21no—
423C4×C13—48no—
424C4×C13C2×#9912yes—
425C4×C13C2×#9912yes—
426Dic13—42no—
427Dic13—42no—
428Dic13—42no—
429Dic13—84no—
430C25C22×D1311yescharacteristic
431C2×#41—261no—
432C2×#41—261no—
433C2×#41—261no—
434C2×#41—261no—
435C2×#41—524no—
436C22×Q8—131no—
437C22×D4—132no—
438C22×D4—132no—
439C22×D4—132no—
440C22×D4—131no—
441C23×C4—22no—
442C23×C4—44no—
443C23×C4—132no—
444C23×C4C4×D1311yescharacteristic
445C23×C4C4×D1311yescharacteristic
446C23×C4C4×D1311yescharacteristic
447C23×C4C4×D1311yescharacteristic
448C23×C4D5211yescharacteristic
449C23×C4D5211yescharacteristic
450C23×C4D5211yescharacteristic
451C23×C4D5211yescharacteristic
452C23×C4C22⋊D1311yescharacteristic
453C23×C4C22⋊D1311yescharacteristic
454C23×C4C22⋊D1311yescharacteristic
455C23×C4C22⋊D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458#123—262no—
459#123—262no—
460#123—262no—
461#123—262no—
462C22⋊Q8—261no—
463C22⋊Q8—261no—
464C22⋊Q8—261no—
465C22⋊Q8—261no—
466C22⋊Q8—261no—
467C22⋊Q8—261no—
468C22⋊Q8—261no—
469C22⋊Q8—261no—
470#121—261no—
471#121—261no—
472#121—261no—
473#121—261no—
474#121—261no—
475#121—261no—
476#121—261no—
477#121—261no—
478#120—262no—
479#120—262no—
480#120—262no—
481#120—262no—
482C4×D4—262no—
483C4×D4—262no—
484C4×D4—262no—
485C4×D4—262no—
486C4×D4—262no—
487C4×D4—262no—
488C4×D4—262no—
489C4×D4—262no—
490#117—261no—
491#117—261no—
492#117—261no—
493#117—261no—
494#117—524no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—132no—
498C2×C4⋊C4—132no—
499C2×C4⋊C4—262no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—132no—
503C2×C22⋊C4—132no—
504C2×C22⋊C4—132no—
505C2×C22⋊C4—132no—
506C2×C22⋊C4—132no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—262no—
509C2×C22⋊C4—262no—
510C2×C22⋊C4C22×D1314yes—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—44no—
514C2×C42—132no—
515C2×C42—262no—
516#99—2616no—
517#95—22no—
518#95—22no—
519#95—262no—
520#95—262no—
521C2×C13—22no—
522C2×C13—22no—
523C2×C13—22no—
524C2×C13—22no—
525C2×C13—22no—
526C2×C13—41no—
527C2×C13—41no—
528C2×C13#229711yescharacteristic
529C2×C13C22×#9911yescharacteristic
530C2×C13C2×#41011yescharacteristic
531D13—82no—
532C24—24no—
533C24—42no—
534C24—42no—
535C24—132no—
536C24C2×C4×D1311yescharacteristic
537C24C2×C4×D1311yescharacteristic
538C24C2×D5211yescharacteristic
539C24C2×D5211yescharacteristic
540C24C2×C22⋊D1311yescharacteristic
541C24C2×C22⋊D1311yescharacteristic
542C24C23×D1311yescharacteristic
543#41—524no—
544#41—524no—
545#41—524no—
546#41—524no—
547C2×Q8—261no—
548C2×Q8—261no—
549C2×Q8—522no—
550C2×D4—262no—
551C2×D4—262no—
552C2×D4—262no—
553C2×D4—262no—
554C2×D4—262no—
555C2×D4—268no—
556C2×D4—262no—
557C2×D4—261no—
558C2×D4—261no—
559C2×D4—522no—
560C2×D4—524no—
561C2×D4—524no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—132no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—264no—
586C22×C4—524no—
587C22×C4#610311yescharacteristic
588C22×C4#610311yescharacteristic
589C22×C4#610311yescharacteristic
590C22×C4#610311yescharacteristic
591C22×C4#610311yescharacteristic
592C22×C4#610311yescharacteristic
593C22×C4#610311yescharacteristic
594C22×C4#610311yescharacteristic
595C22×C4#610311yescharacteristic
596C22×C4#610311yescharacteristic
597C22×C4#610311yescharacteristic
598C22×C4#610311yescharacteristic
599C22×C4#610311yescharacteristic
600C22×C4#610311yescharacteristic
601C22×C4#610311yescharacteristic
602C22×C4#610311yescharacteristic
603C22×C4C2×C4×D1311yescharacteristic
604C22×C4C2×C4×D1311yescharacteristic
605C22×C4C2×C4×D1311yescharacteristic
606C22×C4C2×C4×D1311yescharacteristic
607C22×C4C2×D5211yescharacteristic
608C22×C4C2×D5211yescharacteristic
609C22×C4C2×D5211yescharacteristic
610C22×C4C2×D5211yescharacteristic
611C22×C4C2×C22⋊D1311yescharacteristic
612C22×C4C2×C22⋊D1311yescharacteristic
613C22×C4C2×C22⋊D1311yescharacteristic
614C22×C4C2×C22⋊D1311yescharacteristic
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—261no—
618C4⋊C4—261no—
619C4⋊C4—262no—
620C4⋊C4—262no—
621C4⋊C4—262no—
622C4⋊C4—262no—
623C4⋊C4—524no—
624C22⋊C4—28no—
625C22⋊C4—24no—
626C22⋊C4—262no—
627C22⋊C4—262no—
628C22⋊C4—262no—
629C22⋊C4—262no—
630C22⋊C4—262no—
631C22⋊C4—262no—
632C22⋊C4—262no—
633C22⋊C4—262no—
634C22⋊C4—262no—
635C22⋊C4—262no—
636C22⋊C4—268no—
637C22⋊C4—524no—
638C22⋊C4—524no—
639C22⋊C4#612718yescomplemented
640C42—44no—
641C42—44no—
642C42—262no—
643C42—262no—
644C42—524no—
645C13#2142011yescharacteristic, complemented, Sylow
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—262no—
668C23—264no—
669C23—522no—
670C23—522no—
671C23C2×#610311yescharacteristic
672C23C2×#610311yescharacteristic
673C23C2×#610311yescharacteristic
674C23C2×#610311yescharacteristic
675C23C22×C4×D1311yescharacteristic
676C23C22×D5211yescharacteristic
677C23C2×#612714yes—
678C23C22×C22⋊D1311yescharacteristic
679Q8—522no—
680Q8—522no—
681D4—522no—
682D4—524no—
683D4—524no—
684D4—524no—
685D4—524no—
686D4—524no—
687D4—524no—
688D4—522no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—264no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—524no—
725C2×C4—524no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—524no—
729C2×C4—524no—
730C2×C4—524no—
731C2×C4#8804614yescomplemented
732C2×C4C2×#610311yescharacteristic
733C2×C4C2×#610311yescharacteristic
734C2×C4C2×#610311yescharacteristic
735C2×C4C2×#610311yescharacteristic
736C2×C4C2×#610311yescharacteristic
737C2×C4C2×#610311yescharacteristic
738C2×C4C2×#610311yescharacteristic
739C2×C4C2×#610311yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—522no—
764C22—522no—
765C22—522no—
766C22—1044no—
767C22C2×#8804612yes—
768C22#1171866712yes—
769C22C4×#612712yes—
770C22#1171918212yes—
771C22C22×#610311yescharacteristic
772C22#1171949612yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—522no—
781C4—522no—
782C4—522no—
783C4—1044no—
784C4C2×#8804612yes—
785C4C2×#8804612yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—1042no—
794C2#1311732611yescharacteristic
795C2C22×#8804611yescharacteristic
796C2C2×#1171866711yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719496C2
cosocleC24×C13C24
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#21420
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13117219C2semidirect
3. #13115821C2semidirect
4. #13115672C2semidirect
5. #13115289C2semidirect
6. C4×#88046C2semidirect
7. C2×C4×C13×C22⋊C4C2semidirect
9. C22×#6127C4semidirect
21. C2×#88184C4semidirect
23. C2×#88183C4semidirect
24. C2×C4×C22⋊D13C4semidirect
27. C2×#88180C4semidirect
28. C2×#88178C4semidirect
68. C22×D52C2×C4semidirect
69. C22×C4×D13C2×C4semidirect
70. C22×Dic26C2×C4semidirect
107. C2×#6103C2×C4semidirect
108. C2×#6103C2×C4semidirect
115. C2×C4⋊Dic13C2×C4semidirect
116. C2×C4⋊Dic13C2×C4semidirect
125. C2×#6101C2×C4semidirect
126. C2×#6101C2×C4semidirect
128. C2×C4×Dic13C2×C4semidirect
220. C13×C22⋊C4#41semidirect
250. C2×C4×C22⋊C4D13semidirect
319. C2×C4×C13#99semidirect
639. C22⋊C4#6127semidirect
645. C13#21420semidirect
731. C2×C4#88046semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
#131172192
#131158212
#131156722
#131152892
C4×#880462
C2×C4×C13×C22⋊C42
#2142013