Finite Group Databasebeta

← #15785714

Subgroups — #15785714

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3C2×#11718635C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113088C212yesmaximal, complemented
7#13113080C212yesmaximal
8#13113072C212yesmaximal
9#13113070C212yesmaximal, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C23×Dic26C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2212yes—
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×#88151—24no—
27C2×#88151—24no—
28C2×#88151C418yescomplemented
29C2×C4×Dic26—24no—
30C2×C4×Dic26—24no—
31C2×C4×Dic26—24no—
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40C2×#88071C2212yes—
41#11718648—24no—
42#11718635—24no—
43C4×#6103—24no—
44C24×D13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2312yes—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—22no—
61C22×C4×D13C2×C414yes—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—22no—
66C22×Dic26C2×C414yes—
67C22×Dic26D414yes—
68C22×Dic26D414yes—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13D414yes—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—22no—
85C2×#6103—24no—
86C2×#6103—24no—
87C2×#6103—42no—
88C2×#6103C2×C418yes—
89C2×#6103Q814yescomplemented
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2×C418yes—
95C2×C4⋊Dic13D414yes—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105#88151—232no—
106C4×Dic26—232no—
107C13×#95—24no—
108C13×#95—42no—
109#88071—22no—
110#88071—22no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—24no—
115#88071—42no—
116#13969—131nomaximal, Sylow
117C24×C13C2411yescharacteristic
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13—21no—
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—21no—
129C23×D13—21no—
130C23×D13C22×C412yes—
131C23×D13C2×Q812yes—
132C23×D13#4112yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
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—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
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—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13C22×C414yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×Q812yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13C22×C412yes—
197C22×Dic13C22×C414yes—
198C22×Dic13C2×D414yes—
199C22×Dic13C2×D414yes—
200C22×Dic13C2×D414yes—
201C22×Dic13C2×Q812yes—
202C22×Dic13#4112yes—
203C2×C4×D13—28no—
204C2×C4×D13—28no—
205C2×C4×D13—28no—
206C2×C4×D13—44no—
207C2×C4×D13—44no—
208C2×C4×D13—44no—
209C2×C4×D13—44no—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—28no—
213C2×Dic26—28no—
214C2×Dic26—28no—
215C2×Dic26—28no—
216C2×Dic26C22⋊C4116yescomplemented
217C13×C4⋊C4—28no—
218C13×C4⋊C4—44no—
219C42×C13—28no—
220#6103—28no—
221#6103—28no—
222#6103—216no—
223#6103—48no—
224C4⋊Dic13—28no—
225C4⋊Dic13—216no—
226#6101—216no—
227C4×Dic13—216no—
228C4×Dic13—44no—
229C22×C22⋊Q8—131no—
230C22×C4×Q8—131no—
231C2×#391—131no—
232C2×#380—131no—
233C2×C4×C22⋊C4—131no—
234#1441—132no—
235#1439—132no—
236#1437—132no—
237#1436—132no—
238C4⋊#95—131no—
239C4⋊#95D1311yescharacteristic, complemented
240C23×C13C23×C411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D411yescharacteristic
244C23×C13C22×D411yescharacteristic
245C23×C13C22×Q811yescharacteristic
246C23×C13C2×#4111yescharacteristic
247C23×C13C2×#4111yescharacteristic
248C23×C13C2×#4111yescharacteristic
249C23×C13C2×#4111yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13H(5,𝔽2)11yescharacteristic
252C23×C132−1+411yescharacteristic
253C23×C132−1+411yescharacteristic
254C23×C132−1+411yescharacteristic
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288C22×D13—41no—
289C22×D13C4×Q814yescomplemented
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—24no—
297C2×C4×C13—24no—
298C2×C4×C13—24no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—41no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—41no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13C2×C22⋊C414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13C4×D414yes—
320C2×C4×C13#12014yes—
321C2×C4×C13#12114yes—
322C2×C4×C13#12114yes—
323C2×C4×C13C22⋊Q814yescomplemented
324C2×C4×C13#12314yes—
325C2×Dic13—24no—
326C2×Dic13—24no—
327C2×Dic13—24no—
328C2×Dic13—24no—
329C2×Dic13—24no—
330C2×Dic13—24no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—24no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—24no—
338C2×Dic13—24no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—42no—
352C2×Dic13—41no—
353C2×Dic13—42no—
354C2×Dic13—41no—
355C2×Dic13—42no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13C2×C22⋊C418yes—
360C4×D13—416no—
361Dic26—232no—
362C23×Q8—131no—
363C24×C4—131no—
364C2×C22⋊Q8—138no—
365C2×C22⋊Q8—264no—
366C2×C22⋊Q8—264no—
367C2×C4×Q8—264no—
368C2×C4×Q8—264no—
369C2×C4×Q8—264no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—132no—
372C22×C4⋊C4—132no—
373C22×C4⋊C4C2×D1311yescharacteristic
374C22×C4⋊C4C2×D1311yescharacteristic
375C22×C22⋊C4—132no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—132no—
379C22×C42—132no—
380C22×C42—131no—
381C22×C42C2×D1311yescharacteristic
382#391—264no—
383#380—264no—
384C4×C22⋊C4—264no—
385C2×#95—132no—
386C2×#95—131no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—131no—
391C2×#95—132no—
392C2×#95C2×D1312yes—
393C2×#95C2×D1312yes—
394C22×C13C22×C22⋊C411yescharacteristic
395C22×C13C2×C4×D411yescharacteristic
396C22×C13C2×C4×D411yescharacteristic
397C22×C13C2×C4×Q811yescharacteristic
398C22×C13C4×#4111yescharacteristic
399C22×C13#51911yescharacteristic
400C22×C13#52011yescharacteristic
401C22×C13C2×#12011yescharacteristic
402C22×C13C2×#12111yescharacteristic
403C22×C13C2×#12111yescharacteristic
404C22×C13C2×C22⋊Q811yescharacteristic
405C22×C13C2×#12311yescharacteristic
406C22×C13#52511yescharacteristic
407C22×C13#52911yescharacteristic
408C22×C13#53311yescharacteristic
409C22×C13#53611yescharacteristic
410C22×C13#53711yescharacteristic
411C22×C13#54111yescharacteristic
412C22×C13#54211yescharacteristic
413C22×C13#54611yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#54811yescharacteristic
416C22×C13#54811yescharacteristic
417C22×C13#54811yescharacteristic
418C22×C13#54811yescharacteristic
419C22×C13#54811yescharacteristic
420C22×C13D4×Q811yescharacteristic
421C22×C13D4×Q811yescharacteristic
422C22×C13D4×Q811yescharacteristic
423C22×C13#55011yescharacteristic
424C22×C13#55011yescharacteristic
425C22×C13#55211yescharacteristic
426C22×C13#55211yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55611yescharacteristic
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C4×C13—24no—
445C4×C13—44no—
446C4×C13—42no—
447C4×C13—82no—
448C4×C13#38618yes—
449Dic13—28no—
450Dic13—44no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454C25—131no—
455C22×Q8—134no—
456C22×Q8—134no—
457C22×Q8—134no—
458C22×Q8—262no—
459C22×Q8—262no—
460C22×Q8—262no—
461C22×Q8—262no—
462C23×C4—132no—
463C23×C4—132no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—134no—
468C23×C4—262no—
469C23×C4—262no—
470C23×C4—262no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4—262no—
474C23×C4C22×D1312yes—
475C23×C4C22×D1312yes—
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C22⋊Q8—2632no—
480C4×Q8—2632no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—138no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—264no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—264no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4C4×D1314yes—
496C2×C22⋊C4—138no—
497C2×C22⋊C4—134no—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—264no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—262no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—522no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—264no—
511C2×C42—264no—
512C2×C42—264no—
513C2×C42—262no—
514C2×C42—262no—
515C2×C42—262no—
516C2×C42D5214yes—
517#95—24no—
518#95—42no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—264no—
523#95—262no—
524#95—262no—
525#95—522no—
526C2×C13C2×#38611yescharacteristic
527C2×C13C4×C22⋊Q811yescharacteristic
528C2×C13#232311yescharacteristic
529C2×C13Q8×C22⋊C411yescharacteristic
530C2×C13#234111yescharacteristic
531C2×C13#236011yescharacteristic
532C2×C13#236211yescharacteristic
533C2×C13#240711yescharacteristic
534C2×C13#240911yescharacteristic
535C2×C13#242111yescharacteristic
536C2×C13#242311yescharacteristic
537C2×C13#242611yescharacteristic
538C2×C13#242911yescharacteristic
539C2×C13#253611yescharacteristic
540C2×C13#253811yescharacteristic
541D13—44no—
542C24—132no—
543C24—132no—
544C24—132no—
545C24—261no—
546C24—261no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24—261no—
555C24—261no—
556C24—261no—
557C24C23×D1311yescharacteristic
558C2×Q8—1316no—
559C2×Q8—268no—
560C2×Q8—268no—
561C2×Q8—268no—
562C2×Q8—268no—
563C2×Q8—268no—
564C2×Q8—268no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—134no—
589C22×C4—134no—
590C22×C4—134no—
591C22×C4—132no—
592C22×C4—134no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—262no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—262no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—262no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—261no—
620C22×C4—262no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—268no—
624C22×C4—268no—
625C22×C4—268no—
626C22×C4—524no—
627C22×C4—524no—
628C22×C4—524no—
629C22×C4—524no—
630C22×C4C2×C4×D1314yes—
631C22×C4C2×C4×D1312yes—
632C22×C4C2×D5212yes—
633C22×C4C2×D5212yes—
634C22×C4C2×D5212yes—
635C22×C4#612712yes—
636C22×C4D4×D1312yes—
637C22×C4D4×D1312yes—
638C22×C4D4×D1312yes—
639C22×C4#612912yes—
640C22×C4Q8×D1312yes—
641C22×C4#613112yes—
642C4⋊C4—28no—
643C4⋊C4—44no—
644C4⋊C4—2616no—
645C4⋊C4—2616no—
646C4⋊C4—268no—
647C22⋊C4—2616no—
648C22⋊C4—268no—
649C22⋊C4—268no—
650C22⋊C4—528no—
651C42—28no—
652C42—2616no—
653C42—524no—
654C13#1396911yescharacteristic, complemented, Sylow
655C23—134no—
656C23—262no—
657C23—262no—
658C23—262no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—521no—
675C23—521no—
676C23—521no—
677C23—521no—
678C23—521no—
679C23—521no—
680C23—521no—
681C23—521no—
682C23—521no—
683C23—521no—
684C23—521no—
685C23—521no—
686C23—521no—
687C23—521no—
688C23—521no—
689C23—521no—
690C23C22×C4×D1311yescharacteristic
691C23C22×D5211yescharacteristic
692C23C2×#612711yescharacteristic
693C23C2×D4×D1311yescharacteristic
694C23C2×D4×D1311yescharacteristic
695C23C2×D4×D1311yescharacteristic
696C23C2×#612911yescharacteristic
697C23#8825111yescharacteristic
698C23C2×Q8×D1311yescharacteristic
699C23C2×#613111yescharacteristic
700C23#8825411yescharacteristic
701C23#41×D1311yescharacteristic
702C23#41×D1311yescharacteristic
703C23#8825711yescharacteristic
704C23#8825711yescharacteristic
705Q8—2632no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—138no—
734C2×C4—264no—
735C2×C4—264no—
736C2×C4—264no—
737C2×C4—264no—
738C2×C4—264no—
739C2×C4—264no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—264no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—264no—
749C2×C4—264no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—521no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—5216no—
769C2×C4C4×D5214yes—
770C2×C4C22⋊C4×D1314yes—
771C2×C4#8813614yes—
772C2×C4#8813814yes—
773C2×C4#8814714yes—
774C2×C4#8814814yes—
775C2×C4#8814914yes—
776C2×C4#8815114yescomplemented
777C22—264no—
778C22—264no—
779C22—264no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—522no—
789C22—522no—
790C22—522no—
791C22—522no—
792C22C2×C4×D5211yescharacteristic
793C22C2×C22⋊C4×D1311yescharacteristic
794C22C2×#8813611yescharacteristic
795C22C2×#8813811yescharacteristic
796C22C2×#8814711yescharacteristic
797C22C2×#8814811yescharacteristic
798C22C2×#8814911yescharacteristic
799C22C2×#8815111yescharacteristic
800C22#1171921511yescharacteristic
801C22#1171922911yescharacteristic
802C22#1171923111yescharacteristic
803C22C4×#612911yescharacteristic
804C22#1171925111yescharacteristic
805C22#1171926211yescharacteristic
806C22#1171926611yescharacteristic
807C22C4×Q8×D1311yescharacteristic
808C22#1171927711yescharacteristic
809C22#1171928311yescharacteristic
810C22#1171928811yescharacteristic
811C22#1171930311yescharacteristic
812C22#1171930311yescharacteristic
813C22#1171930411yescharacteristic
814C22#1171931711yescharacteristic
815C22#1171933611yescharacteristic
816C22#1171933711yescharacteristic
817C22#1171933711yescharacteristic
818C22#1171933811yescharacteristic
819C22#1171938211yescharacteristic
820C22#1171938211yescharacteristic
821C22#1171939911yescharacteristic
822C22#1171939911yescharacteristic
823C22#1171942311yescharacteristic
824C22#1171943211yescharacteristic
825C22#1171943511yescharacteristic
826C22#1171943711yescharacteristic
827C4—24no—
828C4—42no—
829C4—44no—
830C4—82no—
831C4—268no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—524no—
836C4#1171832618yes—
837C2—524no—
838C2C2×#1171832611yescharacteristic
839C2C4×#8815111yescharacteristic
840C2#1311751911yescharacteristic
841C2#1311767011yescharacteristic
842C2#1311767511yescharacteristic
843C2#1311784011yescharacteristic
844C2#1311786211yescharacteristic
845C2#1311818211yescharacteristic
846C2#1311820211yescharacteristic
847C2#1311834011yescharacteristic
848C2#1311836211yescharacteristic
849C2#1311840311yescharacteristic
850C2#1311843611yescharacteristic
851C2#1311974611yescharacteristic
852C2#1311975911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13969
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic26C2semidirect
3. C2×#11718635C2semidirect
6. #13113088C2semidirect
9. #13113070C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
28. C2×#88151C4semidirect
89. C2×#6103Q8semidirect
216. C2×Dic26C22⋊C4semidirect
239. C4⋊#95D13semidirect
289. C22×D13C4×Q8semidirect
323. C2×C4×C13C22⋊Q8semidirect
654. C13#13969semidirect
776. C2×C4#88151semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C4×Dic262
C2×#117186352
C2×#117186482
C2×C4×#61032
#131130882
#131130802
#131130722
#131130702
#131130652
C13×C4⋊#952
#1396913