Finite Group Databasebeta

← #15786314

Subgroups — #15786314

Order 3328.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88147C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718650C212yesmaximal, complemented
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6#13113080C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C23×C4×D13C2212yes—
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C2×#88147—24no—
29C2×#88147—24no—
30C2×#88147—24no—
31C13×#389—24no—
32C2×C13×#95C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39#11718650—28no—
40#11718649C418yescomplemented
41#11718600—24no—
42C4×#6101—24no—
43C24×D13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52C2×C414yes—
59C22×D52D414yes—
60C22×D52Q814yes—
61C22×C4×D13—24no—
62C22×C4×D13—24no—
63C22×C4×D13—24no—
64C22×C4×D13—24no—
65C22×C4×D13—24no—
66C22×C4×D13—42no—
67C22×C4×D13—42no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—42no—
75C2×C13×C4⋊C4C2×C414yescomplemented
76C2×C13×C4⋊C4D414yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—24no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—42no—
90C2×#6103—42no—
91C2×#6103—42no—
92C2×#6103—42no—
93C2×#6103C2×C418yescomplemented
94C2×#6103C2×C418yescomplemented
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101D414yescomplemented
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13C2×C414yescomplemented
109C2×C4×Dic13D414yes—
110#88147—232no—
111C13×#95—24no—
112#88071—22no—
113#88071—22no—
114#88071—24no—
115#88071—24no—
116#88071—42no—
117#88071—42no—
118#14018—131nomaximal, Sylow
119C24×C13C2411yescharacteristic
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13—22no—
131C23×D13—22no—
132C23×D13C22×C414yes—
133C23×D13C2×D414yes—
134C23×D13C2×Q814yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13C22×C414yes—
160C22×C4×C13C22×C412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D414yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×Q812yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13C22×C412yes—
198C22×Dic13C22×C412yes—
199C22×Dic13C2×D412yes—
200C22×Dic13C2×D412yes—
201C22×Dic13C2×D412yes—
202C22×Dic13C2×D412yes—
203C22×Dic13#4112yes—
204C22×Dic13#4112yes—
205C2×D52—28no—
206C2×D52—28no—
207C2×D52—28no—
208C2×D52—28no—
209C2×D52—28no—
210C2×D52—28no—
211C2×D52C4⋊C4116yescomplemented
212C2×C4×D13—216no—
213C2×C4×D13—48no—
214C2×C4×D13—48no—
215C2×C4×D13—48no—
216C2×C4×D13—48no—
217C2×C4×D13—48no—
218C2×C4×D13—48no—
219C13×C4⋊C4—28no—
220C13×C4⋊C4—28no—
221C13×C4⋊C4—48no—
222C42×C13—44no—
223#6103—216no—
224#6103—216no—
225#6103—48no—
226#6103—48no—
227#6103—48no—
228C4⋊Dic13—44no—
229#6101—28no—
230#6101—28no—
231C4×Dic13—28no—
232C4×Dic13—28no—
233C22×C4×D4—131no—
234C2×#390—131no—
235C2×#390—131no—
236C2×#389D1311yescharacteristic, complemented
237C2×#385—132no—
238C2×C4×C4⋊C4—131no—
239#1439—132no—
240#1439—132no—
241C4⋊#95—131no—
242C4⋊#95—131no—
243C22⋊#95—132no—
244C23×C13C23×C411yescharacteristic
245C23×C13C22×D411yescharacteristic
246C23×C13C22×D411yescharacteristic
247C23×C13C22×D411yescharacteristic
248C23×C13C22×D411yescharacteristic
249C23×C13C22×Q811yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13C2×#4111yescharacteristic
252C23×C13C2×#4111yescharacteristic
253C23×C13C2×#4111yescharacteristic
254C23×C13C2×#4111yescharacteristic
255C23×C13H(5,𝔽2)11yescharacteristic
256C23×C13H(5,𝔽2)11yescharacteristic
257C23×C13H(5,𝔽2)11yescharacteristic
258C23×C132−1+411yescharacteristic
259C22×D13—24no—
260C22×D13—24no—
261C22×D13—24no—
262C22×D13—24no—
263C22×D13—24no—
264C22×D13—24no—
265C22×D13—24no—
266C22×D13—24no—
267C22×D13—24no—
268C22×D13—24no—
269C22×D13—24no—
270C22×D13—24no—
271C22×D13—24no—
272C22×D13—24no—
273C22×D13—24no—
274C22×D13—24no—
275C22×D13—24no—
276C22×D13—24no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
284C22×D13—42no—
285C22×D13—42no—
286C22×D13—42no—
287C22×D13—42no—
288C22×D13—42no—
289C22×D13—42no—
290C22×D13—42no—
291C22×D13—42no—
292C22×D13—42no—
293C22×D13C2×C4⋊C418yes—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—24no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—24no—
303C2×C4×C13—22no—
304C2×C4×C13—24no—
305C2×C4×C13—22no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—41no—
321C2×C4×C13—42no—
322C2×C4×C13C2×C4⋊C414yes—
323C2×C4×C13C4×D414yes—
324C2×C4×C13C4×D414yes—
325C2×C4×C13#12014yes—
326C2×C4×C13C22⋊Q814yes—
327C2×C4×C13C22⋊Q814yes—
328C2×C4×C13#12314yes—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13C4×D414yescomplemented
363C2×Dic13#12114yes—
364D52—232no—
365C4×D13—432no—
366C23×D4—131no—
367C24×C4—132no—
368C2×C4×D4—264no—
369C2×C4×D4—264no—
370C2×C4×D4—264no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4C2×D1312yes—
375C22×C4⋊C4C2×D1311yescharacteristic
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C22⋊C4—132no—
378C22×C22⋊C4—132no—
379C22×C22⋊C4—132no—
380C22×C22⋊C4—132no—
381C22×C22⋊C4—132no—
382C22×C42—131no—
383C22×C42—131no—
384C22×C42C2×D1311yescharacteristic
385#390—138no—
386#390—264no—
387#389—24no—
388#385—268no—
389C4×C4⋊C4—264no—
390C2×#95—131no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—131no—
394C2×#95—132no—
395C2×#95—132no—
396C2×#95C2×D1312yes—
397C22×C13C22×C4⋊C411yescharacteristic
398C22×C13C2×C4×D411yescharacteristic
399C22×C13C2×C4×D411yescharacteristic
400C22×C13C2×C4×D411yescharacteristic
401C22×C13C4×#4111yescharacteristic
402C22×C13#51811yescharacteristic
403C22×C13#52011yescharacteristic
404C22×C13C2×#12011yescharacteristic
405C22×C13C2×#12111yescharacteristic
406C22×C13C2×C22⋊Q811yescharacteristic
407C22×C13C2×C22⋊Q811yescharacteristic
408C22×C13C2×#12311yescharacteristic
409C22×C13#52511yescharacteristic
410C22×C13#52911yescharacteristic
411C22×C13#53211yescharacteristic
412C22×C13#53511yescharacteristic
413C22×C13#53711yescharacteristic
414C22×C13#54011yescharacteristic
415C22×C13#54211yescharacteristic
416C22×C13D4211yescharacteristic
417C22×C13D4211yescharacteristic
418C22×C13#54611yescharacteristic
419C22×C13#54611yescharacteristic
420C22×C13#54611yescharacteristic
421C22×C13#54711yescharacteristic
422C22×C13#54811yescharacteristic
423C22×C13D4×Q811yescharacteristic
424C22×C13#55011yescharacteristic
425C22×C13#55011yescharacteristic
426C22×C13#55411yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55411yescharacteristic
429C22×C13#55611yescharacteristic
430C22×C13#55911yescharacteristic
431C22×C13#55911yescharacteristic
432C2×D13—28no—
433C2×D13—28no—
434C2×D13—28no—
435C2×D13—44no—
436C2×D13—44no—
437C2×D13—44no—
438C2×D13—44no—
439C2×D13—44no—
440C2×D13—44no—
441C2×D13—44no—
442C2×D13—44no—
443C2×D13—44no—
444C2×D13—44no—
445C2×D13—44no—
446C2×D13—44no—
447C4×C13—44no—
448C4×C13—42no—
449C4×C13—44no—
450C4×C13—42no—
451C4×C13#38518yescomplemented
452Dic13—24no—
453Dic13—24no—
454Dic13—42no—
455Dic13—42no—
456Dic13—82no—
457C25—132no—
458C22×D4—134no—
459C22×D4—134no—
460C22×D4—134no—
461C22×D4—262no—
462C22×D4—262no—
463C22×D4—262no—
464C22×D4—262no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—132no—
470C23×C4—264no—
471C23×C4—264no—
472C23×C4—264no—
473C23×C4—264no—
474C23×C4—264no—
475C23×C4—522no—
476C23×C4—522no—
477C23×C4C22×D1312yes—
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1312yes—
481C23×C4C22×D1311yescharacteristic
482C4×D4—2632no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4—262no—
496C2×C4⋊C4—262no—
497C2×C4⋊C4—262no—
498C2×C4⋊C4—262no—
499C2×C4⋊C4C4×D1314yescomplemented
500C2×C4⋊C4C22⋊D1314yes—
501C2×C22⋊C4—138no—
502C2×C22⋊C4—138no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—264no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—522no—
513C2×C22⋊C4—522no—
514C2×C22⋊C4—522no—
515C2×C22⋊C4—522no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—262no—
522C2×C42—262no—
523C2×C42—262no—
524C2×C42—262no—
525#95—24no—
526#95—262no—
527#95—262no—
528#95—264no—
529#95—264no—
530#95—522no—
531#95—522no—
532C2×C13C2×#38511yescharacteristic
533C2×C13C4×#12111yescharacteristic
534C2×C13#232411yescharacteristic
535C2×C13D4×C4⋊C411yescharacteristic
536C2×C13#234911yescharacteristic
537C2×C13#236611yescharacteristic
538C2×C13#236711yescharacteristic
539C2×C13#240711yescharacteristic
540C2×C13#240811yescharacteristic
541C2×C13#244511yescharacteristic
542C2×C13#244711yescharacteristic
543C2×C13#245211yescharacteristic
544C2×C13#245411yescharacteristic
545C2×C13#253811yescharacteristic
546C2×C13#258011yescharacteristic
547D13—48no—
548C24—134no—
549C24—134no—
550C24—134no—
551C24—262no—
552C24—262no—
553C24—262no—
554C24—262no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24C23×D1311yescharacteristic
564C2×D4—1316no—
565C2×D4—268no—
566C2×D4—268no—
567C2×D4—268no—
568C2×D4—268no—
569C2×D4—268no—
570C2×D4—268no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—2616no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—528no—
636C22×C4—528no—
637C22×C4C2×C4×D1314yes—
638C22×C4C2×C4×D1312yes—
639C22×C4#612712yes—
640C22×C4D4×D1312yes—
641C22×C4D4×D1312yes—
642C22×C4D4×D1312yes—
643C22×C4Q8×D1312yes—
644C22×C4#613112yes—
645C22×C4#613112yes—
646C22×C4C2×C22⋊D1314yes—
647C22×C4C2×C22⋊D1312yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—48no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—524no—
654C22⋊C4—2616no—
655C22⋊C4—2616no—
656C22⋊C4—528no—
657C22⋊C4—528no—
658C22⋊C4—528no—
659C42—44no—
660C42—268no—
661C42—268no—
662C13#1401811yescharacteristic, complemented, Sylow
663C23—138no—
664C23—264no—
665C23—264no—
666C23—264no—
667C23—264no—
668C23—264no—
669C23—264no—
670C23—264no—
671C23—264no—
672C23—264no—
673C23—264no—
674C23—264no—
675C23—264no—
676C23—264no—
677C23—264no—
678C23—264no—
679C23—264no—
680C23—264no—
681C23—264no—
682C23—522no—
683C23—522no—
684C23—522no—
685C23—522no—
686C23—522no—
687C23—522no—
688C23—522no—
689C23—522no—
690C23—522no—
691C23—522no—
692C23—522no—
693C23—522no—
694C23—522no—
695C23—522no—
696C23—522no—
697C23—522no—
698C23C22×C4×D1311yescharacteristic
699C23C2×#612711yescharacteristic
700C23C2×D4×D1311yescharacteristic
701C23C2×D4×D1311yescharacteristic
702C23C2×D4×D1311yescharacteristic
703C23#8825111yescharacteristic
704C23C2×Q8×D1311yescharacteristic
705C23C2×#613111yescharacteristic
706C23C2×#613111yescharacteristic
707C23#8825411yescharacteristic
708C23#41×D1311yescharacteristic
709C23#41×D1311yescharacteristic
710C23#8825611yescharacteristic
711C23#8825611yescharacteristic
712C23C22×C22⋊D1311yescharacteristic
713D4—2632no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—134no—
743C2×C4—134no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—5232no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—521no—
769C2×C4—521no—
770C2×C4—521no—
771C2×C4—522no—
772C2×C4—522no—
773C2×C4—522no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4—522no—
777C2×C4—522no—
778C2×C4C4⋊C4×D1314yes—
779C2×C4#8814714yes—
780C2×C4#8814814yes—
781C2×C4#8815014yes—
782C2×C4C4×C22⋊D1314yes—
783C2×C4#8819114yes—
784C2×C4#8820014yes—
785C22—268no—
786C22—268no—
787C22—268no—
788C22—524no—
789C22—524no—
790C22—524no—
791C22—524no—
792C22—524no—
793C22—524no—
794C22—524no—
795C22—524no—
796C22—524no—
797C22—524no—
798C22—524no—
799C22—524no—
800C22C2×C4⋊C4×D1311yescharacteristic
801C22C2×#8814711yescharacteristic
802C22C2×#8814811yescharacteristic
803C22C2×#8815011yescharacteristic
804C22C4×D4×D1311yescharacteristic
805C22#1171925011yescharacteristic
806C22#1171925811yescharacteristic
807C22#1171926411yescharacteristic
808C22#1171927311yescharacteristic
809C22C4×#613111yescharacteristic
810C22#1171927911yescharacteristic
811C22#1171929011yescharacteristic
812C22D13×#12111yescharacteristic
813C22#1171931211yescharacteristic
814C22#1171931411yescharacteristic
815C22#1171931711yescharacteristic
816C22#1171933211yescharacteristic
817C22#1171933411yescharacteristic
818C22#1171933511yescharacteristic
819C22#1171933611yescharacteristic
820C22#1171939511yescharacteristic
821C22#1171939511yescharacteristic
822C22#1171939611yescharacteristic
823C22#1171940311yescharacteristic
824C22#1171943011yescharacteristic
825C22#1171943211yescharacteristic
826C22#1171943511yescharacteristic
827C22#1171943811yescharacteristic
828C22C2×C4×C22⋊D1311yescharacteristic
829C22C2×#8819111yescharacteristic
830C22D4×C22⋊D1311yescharacteristic
831C22C2×#8820011yescharacteristic
832C22#1171952211yescharacteristic
833C22#1171953411yescharacteristic
834C22#1171953911yescharacteristic
835C4—44no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—264no—
840C4—264no—
841C4—522no—
842C4—522no—
843C4—1042no—
844C4#1171865018yescomplemented
845C2—528no—
846C2C2×#1171865011yescharacteristic
847C2#1311734411yescharacteristic
848C2#1311752711yescharacteristic
849C2#1311773711yescharacteristic
850C2#1311774511yescharacteristic
851C2#1311789811yescharacteristic
852C2#1311790311yescharacteristic
853C2#1311818311yescharacteristic
854C2#1311818811yescharacteristic
855C2#1311860311yescharacteristic
856C2#1311862511yescharacteristic
857C2#1311868211yescharacteristic
858C2#1311870411yescharacteristic
859C2#1311975711yescharacteristic
860C2#1312019611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#14018
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#11718650C2semidirect
5. C2×C4×#6101C2semidirect
6. #13113080C2semidirect
7. #13113078C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113057C2semidirect
11. C2×C13×#389C2semidirect
40. #11718649C4semidirect
75. C2×C13×C4⋊C4C2×C4semidirect
93. C2×#6103C2×C4semidirect
94. C2×#6103C2×C4semidirect
103. C2×#6101D4semidirect
108. C2×C4×Dic13C2×C4semidirect
211. C2×D52C4⋊C4semidirect
236. C2×#389D13semidirect
362. C2×Dic13C4×D4semidirect
451. C4×C13#385semidirect
499. C2×C4⋊C4C4×D13semidirect
662. C13#14018semidirect
844. C4#11718650semidirect

Maximal subgroups

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

subgroupindex
C22×#881472
C2×#117186002
C2×#117186492
C2×#117186502
C2×C4×#61012
#131130802
#131130782
#131130652
#131130572
C2×C13×#3892
#1401813