Finite Group Databasebeta

← #15784872

Subgroups — #15784872

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718606C212yesmaximal
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic13C211yesmaximal, characteristic
6#13113094C212yesmaximal, complemented
7#13113079C212yesmaximal
8#13113071C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C13×#380—24no—
27C2×C13×#95C2212yes—
28#11718873—24no—
29C4×C22⋊Dic13C418yescomplemented
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38#11718637—24no—
39C4⋊C4×Dic13—24no—
40#11718606—28no—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13C2×C414yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×Dic13C2312yes—
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2312yes—
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4D414yes—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—42no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13C2×C414yes—
74C2×C22⋊Dic13C2×C414yes—
75C2×C22⋊Dic13D414yes—
76C2×C22⋊Dic13Q814yes—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13D414yes—
83C2×#6101—24no—
84C2×#6101—24no—
85C2×#6101—24no—
86C2×#6101—24no—
87C2×#6101—42no—
88C2×#6101—42no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—42no—
96C2×C4×Dic13C2×C414yes—
97C2×C4×Dic13C2×C414yes—
98C13×#95—24no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—42no—
105#88071C2×C414yes—
106#88071C2×C414yes—
107#13876—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13C22×C412yes—
121C24×C13C2×D412yes—
122C24×C13C2×Q812yes—
123C24×C13C2411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—28no—
137C22×C4×C13—28no—
138C22×C4×C13—28no—
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—44no—
147C22×C4×C13—44no—
148C22×C4×C13—44no—
149C22×C4×C13—44no—
150C22×C4×C13C22×C412yes—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D414yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13C22×C412yes—
191C22×Dic13C22×C412yes—
192C22×Dic13C22×C412yes—
193C22×Dic13C22×C412yes—
194C22×Dic13C2×D414yes—
195C22×Dic13C2×D412yes—
196C22×Dic13C2×D412yes—
197C22×Dic13C2×Q812yes—
198C22×Dic13C2×Q812yes—
199C22×Dic13#4112yes—
200C22×Dic13#4112yes—
201C13×C4⋊C4—28no—
202C13×C4⋊C4—44no—
203C13×C22⋊C4—48no—
204C22⋊Dic13—28no—
205C22⋊Dic13—48no—
206C22⋊Dic13C4⋊C4116yescomplemented
207C4⋊Dic13—28no—
208C4⋊Dic13—44no—
209#6101—48no—
210#6101—48no—
211C4×Dic13—28no—
212C4×Dic13—28no—
213C4×Dic13—48no—
214C2×#388—132no—
215C2×#384—131no—
216C2×#380—131no—
217C2×#380D1311yescharacteristic
218C2×C4×C4⋊C4—131no—
219C2×C4×C22⋊C4—131no—
220#1442—132no—
221#1439—132no—
222#1436—132no—
223C4⋊#95—131no—
224C4⋊#95—131no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13C2×C4⋊C414yes—
260C23×C13C23×C411yescharacteristic
261C23×C13C22×D411yescharacteristic
262C23×C13C22×D411yescharacteristic
263C23×C13C22×D411yescharacteristic
264C23×C13C22×Q811yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4111yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13H(5,𝔽2)11yescharacteristic
272C23×C13H(5,𝔽2)11yescharacteristic
273C23×C132−1+411yescharacteristic
274C23×C132−1+411yescharacteristic
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—416no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13#11714yes—
298C2×C4×C13C4×D414yes—
299C2×C4×C13C4×D414yes—
300C2×C4×C13#12114yes—
301C2×C4×C13#12314yes—
302C2×C4×C13#12414yes—
303C2×C4×C13#12614yes—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—24no—
326C2×Dic13—24no—
327C2×Dic13—24no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—41no—
331C2×Dic13—42no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13C2×C4⋊C414yes—
344C2×Dic13C2×C4⋊C414yes—
345C2×Dic13#11714yes—
346C24×C4C2×D1311yescharacteristic
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—132no—
350C22×C4⋊C4—132no—
351C22×C4⋊C4C2×D1311yescharacteristic
352C22×C4⋊C4C2×D1311yescharacteristic
353C22×C22⋊C4—131no—
354C22×C22⋊C4—131no—
355C22×C22⋊C4—132no—
356C22×C22⋊C4C2×D1312yes—
357C22×C42—131no—
358C22×C42—131no—
359C22×C42—132no—
360#388—268no—
361#384—264no—
362#380—24no—
363#380—264no—
364C4×C4⋊C4—264no—
365C4×C22⋊C4—138no—
366C2×#95—131no—
367C2×#95—131no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95C2×D1312yes—
375C22×C13—24no—
376C22×C13—24no—
377C22×C13—24no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13C22×C4⋊C411yescharacteristic
391C22×C13C2×#11711yescharacteristic
392C22×C13C2×#11711yescharacteristic
393C22×C13C2×C4×D411yescharacteristic
394C22×C13C2×C4×D411yescharacteristic
395C22×C13#52011yescharacteristic
396C22×C13#52011yescharacteristic
397C22×C13C2×#12111yescharacteristic
398C22×C13C2×#12311yescharacteristic
399C22×C13C2×#12411yescharacteristic
400C22×C13C2×#12611yescharacteristic
401C22×C13#53211yescharacteristic
402C22×C13#53211yescharacteristic
403C22×C13#53311yescharacteristic
404C22×C13#53311yescharacteristic
405C22×C13#54011yescharacteristic
406C22×C13#54111yescharacteristic
407C22×C13#54211yescharacteristic
408C22×C13#54211yescharacteristic
409C22×C13D4211yescharacteristic
410C22×C13D4211yescharacteristic
411C22×C13#54611yescharacteristic
412C22×C13#54711yescharacteristic
413C22×C13#54711yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#54811yescharacteristic
416C22×C13D4×Q811yescharacteristic
417C22×C13D4×Q811yescharacteristic
418C22×C13#55011yescharacteristic
419C22×C13#55211yescharacteristic
420C22×C13#55311yescharacteristic
421C22×C13#55411yescharacteristic
422C22×C13#55411yescharacteristic
423C22×C13#55511yescharacteristic
424C22×C13#55611yescharacteristic
425C4×C13—44no—
426C4×C13—42no—
427C4×C13—82no—
428C4×C13#38818yescomplemented
429Dic13—24no—
430Dic13—24no—
431Dic13—24no—
432Dic13—42no—
433Dic13—44no—
434Dic13—82no—
435C25C22×D1311yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—132no—
446C23×C4—131no—
447C23×C4—132no—
448C23×C4C4×D1314yes—
449C23×C4C22×D1312yes—
450C23×C4C22×D1311yescharacteristic
451C23×C4C22×D1312yes—
452C23×C4C22×D1311yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—134no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—264no—
462C2×C4⋊C4—264no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—264no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—522no—
469C2×C4⋊C4—522no—
470C2×C4⋊C4C22⋊D1314yes—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—134no—
475C2×C22⋊C4—134no—
476C2×C22⋊C4—134no—
477C2×C22⋊C4—134no—
478C2×C22⋊C4—262no—
479C2×C22⋊C4—262no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—522no—
483C2×C42—134no—
484C2×C42—134no—
485C2×C42—262no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—262no—
489C2×C42—264no—
490C2×C42—264no—
491C2×C42—522no—
492#95—24no—
493#95—134no—
494#95—134no—
495#95—264no—
496#95—264no—
497#95—264no—
498#95—264no—
499#95—264no—
500#95—522no—
501C2×C13—44no—
502C2×C13#228511yescharacteristic
503C2×C13C2×#38811yescharacteristic
504C2×C13#231411yescharacteristic
505C2×C13D4×C4⋊C411yescharacteristic
506C2×C13D4×C4⋊C411yescharacteristic
507C2×C13#235211yescharacteristic
508C2×C13#235411yescharacteristic
509C2×C13#242211yescharacteristic
510C2×C13#242311yescharacteristic
511C2×C13#242811yescharacteristic
512C2×C13#242911yescharacteristic
513C2×C13#249111yescharacteristic
514C2×C13#249211yescharacteristic
515C2×C13#249611yescharacteristic
516C2×C13#249711yescharacteristic
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24C2×C4×D1312yes—
530C24D4×D1312yes—
531C24Q8×D1312yes—
532C24C23×D1311yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—134no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—262no—
585C22×C4—261no—
586C22×C4—262no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4C2×C4×D1312yes—
602C22×C4C2×C4×D1312yes—
603C22×C4#612712yes—
604C22×C4D4×D1312yes—
605C22×C4#612912yes—
606C22×C4#612912yes—
607C22×C4#612912yes—
608C22×C4C2×C22⋊D1314yes—
609C22×C4C2×C22⋊D1312yes—
610C4⋊C4—28no—
611C4⋊C4—44no—
612C4⋊C4—268no—
613C4⋊C4—528no—
614C4⋊C4—528no—
615C4⋊C4—524no—
616C22⋊C4—48no—
617C22⋊C4—1316no—
618C22⋊C4—268no—
619C22⋊C4—528no—
620C42—268no—
621C42—268no—
622C42—528no—
623C13#1387611yescharacteristic, complemented, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4⋊C4×D1314yes—
659C23C22×C4×D1311yescharacteristic
660C23C2×#612711yescharacteristic
661C23C2×D4×D1311yescharacteristic
662C23C2×D4×D1311yescharacteristic
663C23C2×#612911yescharacteristic
664C23C2×#612911yescharacteristic
665C23C2×#612911yescharacteristic
666C23#8825111yescharacteristic
667C23C2×Q8×D1311yescharacteristic
668C23#8825411yescharacteristic
669C23#41×D1311yescharacteristic
670C23#41×D1311yescharacteristic
671C23#8825611yescharacteristic
672C23#8825711yescharacteristic
673C23C22×C22⋊D1311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—134no—
697C2×C4—134no—
698C2×C4—134no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—264no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—264no—
722C2×C4—264no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4#8813114yes—
739C2×C4#8813314yes—
740C2×C4#8813514yes—
741C2×C4#8813714yes—
742C2×C4C4×C22⋊D1314yes—
743C2×C4#8819014yes—
744C2×C4#8819314yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×#8813111yescharacteristic
761C22C2×#8813311yescharacteristic
762C22C2×#8813511yescharacteristic
763C22C2×#8813711yescharacteristic
764C22C2×C4⋊C4×D1311yescharacteristic
765C22#1171920911yescharacteristic
766C22#1171921211yescharacteristic
767C22#1171921611yescharacteristic
768C22D13×#11711yescharacteristic
769C22#1171922811yescharacteristic
770C22#1171923411yescharacteristic
771C22#1171923511yescharacteristic
772C22#1171930111yescharacteristic
773C22#1171930111yescharacteristic
774C22#1171930411yescharacteristic
775C22#1171930811yescharacteristic
776C22#1171931411yescharacteristic
777C22#1171931611yescharacteristic
778C22#1171932111yescharacteristic
779C22#1171932411yescharacteristic
780C22#1171932711yescharacteristic
781C22#1171932711yescharacteristic
782C22#1171933011yescharacteristic
783C22#1171933611yescharacteristic
784C22#1171933711yescharacteristic
785C22#1171934011yescharacteristic
786C22#1171934611yescharacteristic
787C22#1171934811yescharacteristic
788C22C2×C4×C22⋊D1311yescharacteristic
789C22C2×#8819011yescharacteristic
790C22D4×C22⋊D1311yescharacteristic
791C22C2×#8819311yescharacteristic
792C22Q8×C22⋊D1311yescharacteristic
793C22#1171953411yescharacteristic
794C22#1171953611yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—264no—
799C4—264no—
800C4—264no—
801C4—522no—
802C4—524no—
803C4—1042no—
804C4#1171860618yescomplemented
805C2—44no—
806C2#1311723811yescharacteristic
807C2C2×#1171860611yescharacteristic
808C2#1311744311yescharacteristic
809C2#1311773211yescharacteristic
810C2C4⋊C4×C22⋊D1311yescharacteristic
811C2#1311776611yescharacteristic
812C2#1311778011yescharacteristic
813C2#1311835211yescharacteristic
814C2#1311836311yescharacteristic
815C2#1311842611yescharacteristic
816C2#1311843711yescharacteristic
817C2#1311920111yescharacteristic
818C2#1311921211yescharacteristic
819C2#1311926011yescharacteristic
820C2#1311927111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
4. C2×C4⋊C4×Dic13C2semidirect
6. #13113094C2semidirect
8. #13113071C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
29. C4×C22⋊Dic13C4semidirect
206. C22⋊Dic13C4⋊C4semidirect
428. C4×C13#388semidirect
623. C13#13876semidirect
804. C4#11718606semidirect

Maximal subgroups

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

subgroupindex
C2×#117186062
C2×#117186372
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130942
#131130792
#131130712
#131130652
C2×C13×#3802
#1387613