Finite Group Databasebeta

← #15786317

Subgroups — #15786317

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×C4×D52C211yesmaximal, characteristic
2C2×#11718649C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718329C212yesmaximal, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113082C212yesmaximal, complemented
8#13113080C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C23×C4×D13C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C2×C4×D52—24no—
29C2×C4×D52—24no—
30C2×C4×D52—24no—
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38#11718649—24no—
39#11718649C418yescomplemented
40#11718646—24no—
41C4×#6101—24no—
42#11718329—28no—
43C24×D13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
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—22no—
73C2×C13×C4⋊C4C2×C414yescomplemented
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13D414yes—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—42no—
87C2×#6103—42no—
88C2×#6103—42no—
89C2×#6103—42no—
90C2×#6103C2×C418yescomplemented
91C2×#6103C2×C418yescomplemented
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—42no—
97C2×C4⋊Dic13D414yes—
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×Dic13—22no—
109C2×C4×Dic13C2×C414yescomplemented
110C4×D52—232no—
111C13×#95—24no—
112C13×#95—42no—
113#88071—22no—
114#88071—22no—
115#88071—24no—
116#88071—24no—
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—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13C22×C414yes—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
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—22no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—22no—
190C22×Dic13—21no—
191C22×Dic13—22no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13C22×C412yes—
199C22×Dic13C22×C412yes—
200C22×Dic13C2×D414yes—
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—44no—
221C42×C13—28no—
222#6103—216no—
223#6103—216no—
224#6103—48no—
225#6103—48no—
226#6103—48no—
227C4⋊Dic13—28no—
228C4⋊Dic13—48no—
229#6101—28no—
230#6101—28no—
231C4×Dic13—28no—
232C4×Dic13—44no—
233C22×C4×D4—131no—
234C2×#390—131no—
235C2×#390—131no—
236C2×#389—131no—
237C2×#385—132no—
238C2×C4×C4⋊C4—131no—
239#1439—132no—
240#1439—132no—
241C4⋊#95—131no—
242C4⋊#95D1311yescharacteristic, complemented
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—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—24no—
301C2×C4×C13—24no—
302C2×C4×C13—24no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—42no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—41no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13C2×C4⋊C414yes—
322C2×C4×C13C4×D414yes—
323C2×C4×C13C4×D414yes—
324C2×C4×C13#12014yes—
325C2×C4×C13#12114yes—
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—24no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—24no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—24no—
346C2×Dic13—22no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—41no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362C2×Dic13—41no—
363C2×Dic13C4×D414yescomplemented
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⋊C4—132no—
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—264no—
388#385—268no—
389C4×C4⋊C4—264no—
390C2×#95—131no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—131no—
394C2×#95—132no—
395C2×#95C2×D1312yes—
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—24no—
448C4×C13—44no—
449C4×C13—42no—
450C4×C13—82no—
451C4×C13#38518yescomplemented
452Dic13—24no—
453Dic13—42no—
454Dic13—42no—
455Dic13—44no—
456Dic13—42no—
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×D1312yes—
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
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—22no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—262no—
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—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—522no—
500C2×C4⋊C4C4×D1314yescomplemented
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—134no—
519C2×C42—262no—
520C2×C42—262no—
521C2×C42—262no—
522C2×C42—262no—
523C2×C42—262no—
524C2×C42D5214yes—
525#95—24no—
526#95—42no—
527#95—264no—
528#95—264no—
529#95—262no—
530#95—262no—
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—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—134no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—2616no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—262no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—262no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—262no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—262no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—262no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—262no—
630C22×C4—528no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—528no—
636C22×C4C2×C4×D1314yes—
637C22×C4C2×C4×D1312yes—
638C22×C4C2×D5212yes—
639C22×C4C2×D5212yes—
640C22×C4C2×D5212yes—
641C22×C4#612712yes—
642C22×C4D4×D1312yes—
643C22×C4D4×D1312yes—
644C22×C4D4×D1312yes—
645C22×C4#612912yes—
646C22×C4Q8×D1312yes—
647C22×C4#613112yes—
648C4⋊C4—28no—
649C4⋊C4—44no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—528no—
654C22⋊C4—2616no—
655C22⋊C4—2616no—
656C22⋊C4—528no—
657C22⋊C4—528no—
658C22⋊C4—528no—
659C42—28no—
660C42—268no—
661C42—524no—
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
699C23C22×D5211yescharacteristic
700C23C2×#612711yescharacteristic
701C23C2×D4×D1311yescharacteristic
702C23C2×D4×D1311yescharacteristic
703C23C2×D4×D1311yescharacteristic
704C23C2×#612911yescharacteristic
705C23#8825111yescharacteristic
706C23C2×Q8×D1311yescharacteristic
707C23C2×#613111yescharacteristic
708C23#8825411yescharacteristic
709C23#41×D1311yescharacteristic
710C23#41×D1311yescharacteristic
711C23#8825611yescharacteristic
712C23#8825611yescharacteristic
713D4—2632no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—134no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—264no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—264no—
757C2×C4—262no—
758C2×C4—264no—
759C2×C4—262no—
760C2×C4—5232no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—522no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—522no—
769C2×C4—521no—
770C2×C4—521no—
771C2×C4—521no—
772C2×C4—522no—
773C2×C4—521no—
774C2×C4—521no—
775C2×C4—522no—
776C2×C4—521no—
777C2×C4C4×D5214yes—
778C2×C4#8813514yes—
779C2×C4#8813614yes—
780C2×C4#8813714yes—
781C2×C4C4⋊C4×D1314yes—
782C2×C4#8814914yes—
783C2×C4#8815014yes—
784C2×C4#8815114yes—
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×D5211yescharacteristic
801C22C2×#8813511yescharacteristic
802C22C2×#8813611yescharacteristic
803C22C2×#8813711yescharacteristic
804C22C2×C4⋊C4×D1311yescharacteristic
805C22C2×#8814911yescharacteristic
806C22C2×#8815011yescharacteristic
807C22C2×#8815111yescharacteristic
808C22#1171921511yescharacteristic
809C22#1171922911yescharacteristic
810C22#1171923011yescharacteristic
811C22C4×D4×D1311yescharacteristic
812C22#1171925011yescharacteristic
813C22#1171925311yescharacteristic
814C22#1171926711yescharacteristic
815C22C4×#613111yescharacteristic
816C22#1171927911yescharacteristic
817C22#1171928511yescharacteristic
818C22#1171928711yescharacteristic
819C22#1171930411yescharacteristic
820C22#1171931411yescharacteristic
821C22#1171931411yescharacteristic
822C22#1171931711yescharacteristic
823C22#1171933511yescharacteristic
824C22#1171933511yescharacteristic
825C22#1171933611yescharacteristic
826C22#1171933811yescharacteristic
827C22#1171938611yescharacteristic
828C22#1171938611yescharacteristic
829C22#1171939511yescharacteristic
830C22#1171939511yescharacteristic
831C22#1171942311yescharacteristic
832C22#1171943211yescharacteristic
833C22#1171943511yescharacteristic
834C22#1171943711yescharacteristic
835C4—24no—
836C4—44no—
837C4—42no—
838C4—82no—
839C4—264no—
840C4—522no—
841C4—522no—
842C4—522no—
843C4—524no—
844C4#1171832918yescomplemented
845C2—528no—
846C2C2×#1171832911yescharacteristic
847C2C4×#8814911yescharacteristic
848C2#1311753011yescharacteristic
849C2#1311773711yescharacteristic
850C2#1311774511yescharacteristic
851C2#1311789711yescharacteristic
852C2#1311791211yescharacteristic
853C2#1311818211yescharacteristic
854C2#1311819311yescharacteristic
855C2#1311860211yescharacteristic
856C2#1311862411yescharacteristic
857C2#1311868711yescharacteristic
858C2#1311870911yescharacteristic
859C2#1311975911yescharacteristic
860C2#1312019511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#14018
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718646C2semidirect
5. C2×#11718329C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113082C2semidirect
8. #13113080C2semidirect
9. #13113065C2semidirect
10. #13113057C2semidirect
11. C13×C4⋊#95C2semidirect
39. #11718649C4semidirect
73. C2×C13×C4⋊C4C2×C4semidirect
90. C2×#6103C2×C4semidirect
91. C2×#6103C2×C4semidirect
103. C2×#6101D4semidirect
109. C2×C4×Dic13C2×C4semidirect
211. C2×D52C4⋊C4semidirect
242. C4⋊#95D13semidirect
363. C2×Dic13C4×D4semidirect
451. C4×C13#385semidirect
500. C2×C4⋊C4C4×D13semidirect
662. C13#14018semidirect
844. C4#11718329semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D522
C2×#117186492
C2×#117186462
C2×#117183292
C2×C4×#61012
#131130822
#131130802
#131130652
#131130572
C13×C4⋊#952
#1401813