Finite Group Databasebeta

← #15784486

Subgroups — #15784486

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#11718618C212yesmaximal
3C2×C4×#6101C212yesmaximal, complemented
4C2×#11718327C211yesmaximal, characteristic, complemented
5#13113074C212yesmaximal, complemented
6#13113073C212yesmaximal, complemented
7#13113064C211yesmaximal, characteristic, complemented
8#13113059C211yesmaximal, characteristic, complemented
9#13113057C211yesmaximal, characteristic, complemented
10#95×Dic13C211yesmaximal, characteristic, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C23×C22⋊D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C42×C13C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C2×C4×C22⋊D13—28no—
20C2×C4×C22⋊D13C418yescomplemented
21C22×#6103C2211yescharacteristic
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×#6101C2212yes—
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2212yes—
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2212yes—
29C4×C13×C22⋊C4—24no—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718618C4116yescomplemented
39C4×#6101—28no—
40#11718327—24no—
41C25×C13C2311yescharacteristic
42C24×D13C2311yescharacteristic
43C23×C4×C13—22no—
44C23×C4×C13—24no—
45C23×C4×C13—22no—
46C23×C4×C13—42no—
47C23×C4×C13C2×C414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C22×C22⋊D13—24no—
53C22×C22⋊D13—22no—
54C22×C22⋊D13—22no—
55C22×C22⋊D13C2×C414yes—
56C22×C22⋊D13C2×C418yes—
57C23×Dic13C2312yes—
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C22×C4×D13—22no—
63C22×C4×D13—22no—
64C22×C4×D13—24no—
65C22×C4×D13—42no—
66C22×C4×D13C2×C414yes—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—24no—
69C2×C13×C22⋊C4C2×C418yescomplemented
70C2×C42×C13—24no—
71C2×C42×C13—24no—
72C2×C42×C13—42no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—42no—
75C2×C22⋊Dic13—42no—
76C2×C22⋊Dic13C2×C414yes—
77C2×C22⋊Dic13C2×C418yescomplemented
78C4×C22⋊D13—232no—
79C2×#6103—24no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×#6103C2×C414yes—
85C2×#6103C2×C418yescomplemented
86C2×#6103C2×C418yescomplemented
87C2×#6101—24no—
88C2×#6101—24no—
89C2×#6101C2×C414yes—
90C2×#6101C2×C418yescomplemented
91C2×#6101D418yes—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—24no—
96C2×C4×Dic13—24no—
97C2×C4×Dic13—42no—
98C2×C4×Dic13C2×C414yes—
99C2×C4×Dic13C2×C418yescomplemented
100C13×#95—22no—
101C13×#95D414yescomplemented
102#88071—22no—
103#88071—24no—
104#88071—22no—
105#88071—24no—
106#88071—24no—
107#88071—42no—
108#13820—131nomaximal, Sylow
109C24×C13—22no—
110C24×C13—21no—
111C24×C13—22no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—22no—
117C24×C13—21no—
118C24×C13C22×C412yes—
119C24×C13C22×C414yes—
120C24×C13C2411yescharacteristic
121C23×D13—21no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—22no—
129C23×D13—21no—
130C23×D13C22×C412yes—
131C23×D13C22×C414yes—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—28no—
148C22×C4×C13—28no—
149C22×C4×C13—44no—
150C22×C4×C13—48no—
151C22×C4×C13—48no—
152C22×C4×C13C22×C414yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C22×C414yes—
156C22×C4×C13C2×D414yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D414yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4114yes—
161C2×C22⋊D13—28no—
162C2×C22⋊D13—28no—
163C2×C22⋊D13—216no—
164C2×C22⋊D13—216no—
165C2×C22⋊D13C42116yescomplemented
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13C22×C412yes—
186C22×Dic13C22×C414yes—
187C22×Dic13C22×C414yes—
188C22×Dic13C22×C412yes—
189C22×Dic13C22×C412yes—
190C22×Dic13C22×C414yes—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D414yes—
193C22×Dic13#4112yes—
194C22×Dic13#4112yes—
195C2×C4×D13—28no—
196C2×C4×D13—28no—
197C2×C4×D13—44no—
198C2×C4×D13—48no—
199C2×C4×D13—48no—
200C13×C22⋊C4—216no—
201C42×C13—48no—
202C22⋊Dic13—28no—
203C22⋊Dic13—48no—
204#6103—28no—
205#6103—216no—
206#6103—48no—
207#6101—216no—
208#6101C22⋊C4116yescomplemented
209C4×Dic13—28no—
210C4×Dic13—216no—
211C4×Dic13—48no—
212C22×C4×D4—131no—
213C2×#390—132no—
214C2×C4×C4⋊C4—132no—
215C2×C4×C22⋊C4—131no—
216C2×C4×C22⋊C4D1311yescharacteristic, complemented
217#1437—132no—
218#1437—132no—
219C4⋊#95—131no—
220C22⋊#95—131no—
221C22⋊#95—131no—
222C4×#95—131no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—24no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—24no—
231C23×C13—24no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—24no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—41no—
238C23×C13—42no—
239C23×C13—42no—
240C23×C13—41no—
241C23×C13—42no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—42no—
245C23×C13C2×C4214yes—
246C23×C13C23×C411yescharacteristic
247C23×C13C23×C412yes—
248C23×C13C22×D412yes—
249C23×C13C22×D411yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13C2×#4111yescharacteristic
252C23×C13C2×#4111yescharacteristic
253C23×C13C2×#4112yes—
254C23×C13H(5,𝔽2)12yes—
255C23×C13H(5,𝔽2)11yescharacteristic
256C23×C132−1+411yescharacteristic
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—24no—
260C22×D13—22no—
261C22×D13—24no—
262C22×D13—24no—
263C22×D13—22no—
264C22×D13—24no—
265C22×D13—24no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—24no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—41no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—41no—
275C22×D13—42no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—42no—
279C22×D13C2×C4214yes—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—416no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13C2×C22⋊C414yes—
303C2×C4×C13C4×D414yes—
304C2×C4×C13C4×D418yescomplemented
305C22⋊D13—232no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—24no—
309C2×Dic13—24no—
310C2×Dic13—22no—
311C2×Dic13—24no—
312C2×Dic13—24no—
313C2×Dic13—24no—
314C2×Dic13—22no—
315C2×Dic13—24no—
316C2×Dic13—24no—
317C2×Dic13—24no—
318C2×Dic13—22no—
319C2×Dic13—42no—
320C2×Dic13—42no—
321C2×Dic13—42no—
322C2×Dic13—42no—
323C2×Dic13—42no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13C2×C4214yes—
330C2×Dic13C2×C22⋊C414yes—
331C2×Dic13C2×C22⋊C414yes—
332C2×Dic13#11714yes—
333C2×Dic13C4×D418yes—
334C2×Dic13C4×D418yes—
335C4×D13—416no—
336C23×D4—131no—
337C24×C4—131no—
338C24×C4C2×D1311yescharacteristic
339C2×C4×D4—138no—
340C2×C4×D4—268no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—132no—
343C22×C22⋊C4—131no—
344C22×C22⋊C4—131no—
345C22×C22⋊C4—132no—
346C22×C22⋊C4—132no—
347C22×C22⋊C4—132no—
348C22×C22⋊C4C2×D1312yes—
349C22×C42—131no—
350C22×C42—132no—
351C22×C42—132no—
352C22×C42C2×D1312yes—
353#390—1316no—
354C4×C4⋊C4—268no—
355C4×C22⋊C4—24no—
356C4×C22⋊C4—264no—
357C2×#95—131no—
358C2×#95—132no—
359C2×#95—131no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95C2×D1311yescharacteristic
364C2×#95C2×D1311yescharacteristic
365C22×C13—24no—
366C22×C13—24no—
367C22×C13—24no—
368C22×C13—42no—
369C22×C13—42no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—44no—
373C22×C13—44no—
374C22×C13—44no—
375C22×C13—44no—
376C22×C13C22×C4211yescharacteristic
377C22×C13C22×C22⋊C411yescharacteristic
378C22×C13C2×#11711yescharacteristic
379C22×C13C2×C4×D411yescharacteristic
380C22×C13C2×C4×D412yes—
381C22×C13C2×C4×D412yes—
382C22×C13C2×C4×D412yes—
383C22×C13C4×#4111yescharacteristic
384C22×C13C4×#4112yes—
385C22×C13#51811yescharacteristic
386C22×C13#51812yes—
387C22×C13#52011yescharacteristic
388C22×C13#52012yes—
389C22×C13D4212yes—
390C22×C13#54612yes—
391C22×C13#54711yescharacteristic
392C22×C13#54812yes—
393C22×C13#55012yes—
394C22×C13#55011yescharacteristic
395C22×C13#55312yes—
396C22×C13#55511yescharacteristic
397C22×C13#55611yescharacteristic
398C22×C13#55912yes—
399C2×D13—24no—
400C2×D13—24no—
401C2×D13—24no—
402C2×D13—42no—
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—44no—
407C2×D13—44no—
408C2×D13—44no—
409C2×D13—44no—
410C4×C13—24no—
411C4×C13—24no—
412C4×C13—28no—
413C4×C13—44no—
414Dic13—24no—
415Dic13—42no—
416Dic13—44no—
417Dic13—44no—
418Dic13C4×C22⋊C418yescomplemented
419C25—131no—
420C25C22×D1311yescharacteristic
421C22×D4—134no—
422C22×D4—138no—
423C22×D4—264no—
424C22×D4—262no—
425C22×D4—262no—
426C23×C4—22no—
427C23×C4—24no—
428C23×C4—22no—
429C23×C4—42no—
430C23×C4—131no—
431C23×C4—131no—
432C23×C4—132no—
433C23×C4—132no—
434C23×C4—131no—
435C23×C4—134no—
436C23×C4—264no—
437C23×C4—262no—
438C23×C4—262no—
439C23×C4—522no—
440C23×C4C4×D1314yes—
441C23×C4C22×D1312yes—
442C23×C4C22×D1312yes—
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C4×D4—2632no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—138no—
448C2×C4⋊C4—138no—
449C2×C4⋊C4—264no—
450C2×C4⋊C4—264no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—134no—
454C2×C22⋊C4—134no—
455C2×C22⋊C4—138no—
456C2×C22⋊C4—138no—
457C2×C22⋊C4—138no—
458C2×C22⋊C4—264no—
459C2×C22⋊C4—264no—
460C2×C22⋊C4—264no—
461C2×C22⋊C4—264no—
462C2×C22⋊C4—522no—
463C2×C22⋊C4—522no—
464C2×C22⋊C4—522no—
465C2×C22⋊C4—522no—
466C2×C22⋊C4C4×D1318yescomplemented
467C2×C42—24no—
468C2×C42—24no—
469C2×C42—42no—
470C2×C42—134no—
471C2×C42—138no—
472C2×C42—264no—
473C2×C42—264no—
474C2×C42—264no—
475C2×C42—264no—
476C2×C42—264no—
477C2×C42—522no—
478#95—22no—
479#95—264no—
480#95—262no—
481#95—264no—
482#95—264no—
483#95—262no—
484#95—522no—
485#95C22⋊D1314yescomplemented
486C2×C13—44no—
487C2×C13C2×C4×C22⋊C411yescharacteristic
488C2×C13C42×D411yescharacteristic
489C2×C13#227511yescharacteristic
490C2×C13D4×C22⋊C411yescharacteristic
491C2×C13#234111yescharacteristic
492C2×C13#235411yescharacteristic
493C2×C13#235711yescharacteristic
494C2×C13#236112yes—
495C2×C13#236312yes—
496C2×C13#236612yes—
497C2×C13#236712yes—
498D13—44no—
499C24—22no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—134no—
509C24—132no—
510C24—262no—
511C24—261no—
512C24—262no—
513C24—262no—
514C24—261no—
515C24—261no—
516C24—261no—
517C24—261no—
518C24—261no—
519C24C2×C4×D1314yes—
520C24C2×C4×D1312yes—
521C24C23×D1311yescharacteristic
522C2×D4—1316no—
523C2×D4—268no—
524C2×D4—268no—
525C2×D4—2616no—
526C2×D4—2616no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—132no—
548C22×C4—134no—
549C22×C4—134no—
550C22×C4—132no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—134no—
554C22×C4—132no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—268no—
558C22×C4—261no—
559C22×C4—262no—
560C22×C4—261no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—261no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—261no—
576C22×C4—262no—
577C22×C4—268no—
578C22×C4—524no—
579C22×C4—528no—
580C22×C4—528no—
581C22×C4C2×C4×D1314yes—
582C22×C4C2×C4×D1312yes—
583C22×C4C2×C4×D1312yes—
584C22×C4C2×C4×D1314yes—
585C22×C4#612712yes—
586C22×C4#612714yes—
587C22×C4D4×D1314yes—
588C22×C4C2×C22⋊D1312yes—
589C22×C4C2×C22⋊D1314yes—
590C4⋊C4—1316no—
591C4⋊C4—2616no—
592C22⋊C4—216no—
593C22⋊C4—268no—
594C22⋊C4—268no—
595C22⋊C4—2616no—
596C22⋊C4—528no—
597C22⋊C4—528no—
598C42—48no—
599C42—268no—
600C42—2616no—
601C42—528no—
602C13#1382011yescharacteristic, complemented, Sylow
603C23—22no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23—41no—
625C23—134no—
626C23—262no—
627C23—264no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—264no—
633C23—262no—
634C23—264no—
635C23—264no—
636C23—264no—
637C23—264no—
638C23—522no—
639C23—521no—
640C23—521no—
641C23—522no—
642C23—522no—
643C23—522no—
644C23—522no—
645C23—522no—
646C23—521no—
647C23—521no—
648C23C42×D1314yes—
649C23C22×C4×D1311yescharacteristic
650C23C22×C4×D1312yes—
651C23C2×#612711yescharacteristic
652C23C2×#612712yes—
653C23C2×D4×D1312yes—
654C23#8825112yes—
655C23#41×D1311yescharacteristic
656C23#41×D1311yescharacteristic
657C23#8825611yescharacteristic
658C23#8825711yescharacteristic
659C23C22×C22⋊D1311yescharacteristic
660D4—2632no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—134no—
684C2×C4—134no—
685C2×C4—134no—
686C2×C4—138no—
687C2×C4—138no—
688C2×C4—134no—
689C2×C4—262no—
690C2×C4—264no—
691C2×C4—262no—
692C2×C4—264no—
693C2×C4—264no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—264no—
698C2×C4—264no—
699C2×C4—264no—
700C2×C4—264no—
701C2×C4—264no—
702C2×C4—5216no—
703C2×C4—522no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
708C2×C4—522no—
709C2×C4—522no—
710C2×C4—522no—
711C2×C4—522no—
712C2×C4—522no—
713C2×C4C22⋊C4×D1314yes—
714C2×C4C4×C22⋊D1314yes—
715C2×C4C4×C22⋊D1318yescomplemented
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—264no—
728C22—264no—
729C22—264no—
730C22—522no—
731C22—522no—
732C22—524no—
733C22—524no—
734C22—524no—
735C22—524no—
736C22—522no—
737C22—522no—
738C22C2×C42×D1311yescharacteristic
739C22C4×#612711yescharacteristic
740C22C4×#612712yes—
741C22C2×C22⋊C4×D1311yescharacteristic
742C22#1171919111yescharacteristic
743C22#1171919512yes—
744C22D13×#11711yescharacteristic
745C22#1171922811yescharacteristic
746C22#1171923711yescharacteristic
747C22#1171923811yescharacteristic
748C22#1171924512yes—
749C22C4×D4×D1312yes—
750C22C4×D4×D1312yes—
751C22#1171925012yes—
752C22#1171925112yes—
753C22#1171925712yes—
754C22#1171925812yes—
755C22#1171926412yes—
756C22C2×C4×C22⋊D1311yescharacteristic
757C22C2×C4×C22⋊D1312yes—
758C22D4×C22⋊D1312yes—
759C22#1171952911yescharacteristic
760C22#1171953911yescharacteristic
761C4—28no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—138no—
766C4—264no—
767C4—524no—
768C4—524no—
769C4—522no—
770C2—44no—
771C2—524no—
772C2C4×C22⋊C4×D1311yescharacteristic
773C2C42×C22⋊D1311yescharacteristic
774C2#1311719511yescharacteristic
775C2C22⋊C4×C22⋊D1311yescharacteristic
776C2#1311767611yescharacteristic
777C2#1311778611yescharacteristic
778C2#1311781011yescharacteristic
779C2#1311785312yes—
780C2#1311787512yes—
781C2#1311789812yes—
782C2#1311790812yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13820
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#6101C2semidirect
4. C2×#11718327C2semidirect
5. #13113074C2semidirect
6. #13113073C2semidirect
7. #13113064C2semidirect
8. #13113059C2semidirect
9. #13113057C2semidirect
10. #95×Dic13C2semidirect
11. C2×C4×C13×C22⋊C4C2semidirect
20. C2×C4×C22⋊D13C4semidirect
38. #11718618C4semidirect
69. C2×C13×C22⋊C4C2×C4semidirect
77. C2×C22⋊Dic13C2×C4semidirect
85. C2×#6103C2×C4semidirect
86. C2×#6103C2×C4semidirect
90. C2×#6101C2×C4semidirect
99. C2×C4×Dic13C2×C4semidirect
101. C13×#95D4semidirect
165. C2×C22⋊D13C42semidirect
208. #6101C22⋊C4semidirect
216. C2×C4×C22⋊C4D13semidirect
304. C2×C4×C13C4×D4semidirect
418. Dic13C4×C22⋊C4semidirect
466. C2×C22⋊C4C4×D13semidirect
485. #95C22⋊D13semidirect
602. C13#13820semidirect
715. C2×C4C4×C22⋊D13semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C2×#117186182
C2×C4×#61012
C2×#117183272
#131130742
#131130732
#131130642
#131130592
#131130572
#95×Dic132
C2×C4×C13×C22⋊C42
#1382013