Finite Group Databasebeta

← #15785709

Subgroups — #15785709

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×#88178C211yesmaximal, characteristic
2C22×#88141C211yesmaximal, characteristic, complemented
3C2×#11718635C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113087C212yesmaximal, complemented
6#13113079C212yesmaximal
7#13113073C212yesmaximal
8#13113067C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C23×Dic26C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88178—24no—
22C2×#88178—24no—
23C2×#88178C418yescomplemented
24C22×#6101C2212yes—
25C22×#6101C2212yes—
26C22×C4×Dic13C2212yes—
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×#88141—24no—
30C2×#88141—24no—
31C2×#88141—24no—
32C13×#380—24no—
33C2×C13×#95C2212yes—
34C4×C22⋊Dic13—24no—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43#11718635—24no—
44C25×C13C2311yescharacteristic
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13C2×C414yes—
52C23×C4×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2312yes—
61C23×Dic13C2311yescharacteristic
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⋊C4D414yes—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—42no—
78C2×C22⋊Dic13—22no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13C2×C418yes—
86C2×C22⋊Dic13Q814yescomplemented
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13C2×C414yes—
90#88178—232no—
91C2×#6101—24no—
92C2×#6101—24no—
93C2×#6101—24no—
94C2×#6101—24no—
95C2×#6101—24no—
96C2×#6101C2×C418yes—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—24no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13D414yes—
106#88141—232no—
107C13×#95—24no—
108#88071—22no—
109#88071—22no—
110#88071—24no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—42no—
115#88071—42no—
116#13969—131nomaximal, Sylow
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13—21no—
126C24×C13—21no—
127C24×C13—21no—
128C24×C13—21no—
129C24×C13C22×C412yes—
130C24×C13C2×Q812yes—
131C24×C13#4112yes—
132C24×C13C2411yescharacteristic
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
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—22no—
144C22×C4×C13—22no—
145C22×C4×C13—28no—
146C22×C4×C13—28no—
147C22×C4×C13—28no—
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—44no—
156C22×C4×C13—44no—
157C22×C4×C13—44no—
158C22×C4×C13—44no—
159C22×C4×C13C22×C412yes—
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×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
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—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—22no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—22no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13C22×C414yes—
201C22×Dic13C22×C414yes—
202C22×Dic13C2×D412yes—
203C22×Dic13C2×D414yes—
204C22×Dic13C2×D414yes—
205C22×Dic13C2×D412yes—
206C22×Dic13C2×Q812yes—
207C22×Dic13C2×Q812yes—
208C22×Dic13#4112yes—
209C22×Dic13#4112yes—
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—
219C13×C22⋊C4—48no—
220C22⋊Dic13—28no—
221C22⋊Dic13—216no—
222C22⋊Dic13—28no—
223C4⋊Dic13—28no—
224#6101—216no—
225#6101—216no—
226C4×Dic13—216no—
227C4×Dic13—28no—
228C4×Dic13—44no—
229C22×C22⋊Q8—131no—
230C22×C4×Q8—131no—
231C2×#391—131no—
232C2×#380D1311yescharacteristic
233C2×C4×C22⋊C4—131no—
234#1441—132no—
235#1439—132no—
236#1437—132no—
237#1436—132no—
238C4⋊#95—131no—
239C4⋊#95—131no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13C4×Q814yescomplemented
275C23×C13C23×C411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×D411yescharacteristic
279C23×C13C22×D411yescharacteristic
280C23×C13C22×Q811yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C132−1+411yescharacteristic
288C23×C132−1+411yescharacteristic
289C23×C132−1+411yescharacteristic
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—416no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13C2×C22⋊C414yes—
313C2×C4×C13C4×D414yes—
314C2×C4×C13C4×D414yes—
315C2×C4×C13#12014yes—
316C2×C4×C13#12114yes—
317C2×C4×C13#12114yes—
318C2×C4×C13#12314yes—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—22no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—24no—
325C2×Dic13—24no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—24no—
332C2×Dic13—24no—
333C2×Dic13—24no—
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—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13C2×C22⋊C418yes—
360C2×Dic13C22⋊Q814yescomplemented
361Dic26—232no—
362C23×Q8—131no—
363C24×C4C2×D1311yescharacteristic
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—132no—
371C22×C4⋊C4—131no—
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⋊C4C2×D1312yes—
379C22×C42—131no—
380C22×C42—132no—
381C22×C42—131no—
382#391—264no—
383#380—24no—
384C4×C22⋊C4—264no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—131no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—131no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95C2×D1312yes—
394C22×C13—24no—
395C22×C13—24no—
396C22×C13—24no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13C22×C22⋊C411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C2×C4×D411yescharacteristic
412C22×C13C2×C4×Q811yescharacteristic
413C22×C13C4×#4111yescharacteristic
414C22×C13#51911yescharacteristic
415C22×C13#52011yescharacteristic
416C22×C13C2×#12011yescharacteristic
417C22×C13C2×#12111yescharacteristic
418C22×C13C2×#12111yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13C2×#12311yescharacteristic
421C22×C13#52511yescharacteristic
422C22×C13#52911yescharacteristic
423C22×C13#53311yescharacteristic
424C22×C13#53611yescharacteristic
425C22×C13#53711yescharacteristic
426C22×C13#54111yescharacteristic
427C22×C13#54211yescharacteristic
428C22×C13#54611yescharacteristic
429C22×C13#54711yescharacteristic
430C22×C13#54811yescharacteristic
431C22×C13#54811yescharacteristic
432C22×C13#54811yescharacteristic
433C22×C13#54811yescharacteristic
434C22×C13#54811yescharacteristic
435C22×C13D4×Q811yescharacteristic
436C22×C13D4×Q811yescharacteristic
437C22×C13D4×Q811yescharacteristic
438C22×C13#55011yescharacteristic
439C22×C13#55011yescharacteristic
440C22×C13#55211yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55411yescharacteristic
443C22×C13#55611yescharacteristic
444C4×C13—44no—
445C4×C13—42no—
446C4×C13—82no—
447C4×C13#38618yes—
448Dic13—24no—
449Dic13—28no—
450Dic13—44no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454C25C22×D1311yescharacteristic
455C22×Q8—134no—
456C22×Q8—134no—
457C22×Q8—134no—
458C22×Q8—262no—
459C22×Q8—262no—
460C22×Q8—262no—
461C22×Q8—262no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—132no—
469C23×C4—131no—
470C23×C4—132no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4C4×D1314yes—
475C23×C4C22×D1312yes—
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1312yes—
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—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4C22⋊D1314yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—138no—
500C2×C22⋊C4—134no—
501C2×C22⋊C4—264no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—262no—
505C2×C22⋊C4—262no—
506C2×C22⋊C4—262no—
507C2×C22⋊C4—262no—
508C2×C42—134no—
509C2×C42—264no—
510C2×C42—264no—
511C2×C42—262no—
512C2×C42—264no—
513C2×C42—262no—
514C2×C42—262no—
515C2×C42—262no—
516C2×C42—262no—
517#95—24no—
518#95—264no—
519#95—264no—
520#95—262no—
521#95—262no—
522#95—264no—
523#95—264no—
524#95—522no—
525#95—522no—
526C2×C13—44no—
527C2×C13C2×#38611yescharacteristic
528C2×C13C4×C22⋊Q811yescharacteristic
529C2×C13#232311yescharacteristic
530C2×C13Q8×C22⋊C411yescharacteristic
531C2×C13#234111yescharacteristic
532C2×C13#236011yescharacteristic
533C2×C13#236211yescharacteristic
534C2×C13#240711yescharacteristic
535C2×C13#240911yescharacteristic
536C2×C13#242111yescharacteristic
537C2×C13#242311yescharacteristic
538C2×C13#242611yescharacteristic
539C2×C13#242911yescharacteristic
540C2×C13#253611yescharacteristic
541C2×C13#253811yescharacteristic
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24C2×C4×D1312yes—
555C24#612912yes—
556C24Q8×D1312yes—
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—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—134no—
592C22×C4—134no—
593C22×C4—132no—
594C22×C4—134no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—134no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—262no—
602C22×C4—261no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—262no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—262no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—262no—
624C22×C4—261no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—261no—
633C22×C4C2×C4×D1312yes—
634C22×C4C2×C4×D1312yes—
635C22×C4#612712yes—
636C22×C4D4×D1312yes—
637C22×C4D4×D1312yes—
638C22×C4D4×D1312yes—
639C22×C4#612912yes—
640C22×C4C2×C22⋊D1314yes—
641C22×C4C2×C22⋊D1312yes—
642C4⋊C4—28no—
643C4⋊C4—44no—
644C4⋊C4—2616no—
645C4⋊C4—2616no—
646C4⋊C4—268no—
647C22⋊C4—48no—
648C22⋊C4—2616no—
649C22⋊C4—268no—
650C22⋊C4—268no—
651C42—2616no—
652C42—268no—
653C42—524no—
654C13#1396911yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#8814114yescomplemented
690C23C22×C4×D1311yescharacteristic
691C23C2×#612711yescharacteristic
692C23C2×D4×D1311yescharacteristic
693C23C2×D4×D1311yescharacteristic
694C23C2×D4×D1311yescharacteristic
695C23C2×#612911yescharacteristic
696C23C2×#612911yescharacteristic
697C23#8825111yescharacteristic
698C23C2×Q8×D1311yescharacteristic
699C23#8825411yescharacteristic
700C23#41×D1311yescharacteristic
701C23#41×D1311yescharacteristic
702C23#8825711yescharacteristic
703C23#8825711yescharacteristic
704C23C22×C22⋊D1311yescharacteristic
705Q8—2632no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—138no—
729C2×C4—134no—
730C2×C4—264no—
731C2×C4—264no—
732C2×C4—264no—
733C2×C4—264no—
734C2×C4—262no—
735C2×C4—264no—
736C2×C4—264no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—264no—
743C2×C4—264no—
744C2×C4—262no—
745C2×C4—264no—
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—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4C22⋊C4×D1314yes—
771C2×C4#8813514yes—
772C2×C4#8813714yes—
773C2×C4#8813814yes—
774C2×C4C4×C22⋊D1314yes—
775C2×C4#8819114yes—
776C2×C4#8819214yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×C22⋊C4×D1311yescharacteristic
793C22C2×#8813511yescharacteristic
794C22C2×#8813711yescharacteristic
795C22C2×#8813811yescharacteristic
796C22C2×#8814111yescharacteristic
797C22#1171920911yescharacteristic
798C22#1171921611yescharacteristic
799C22#1171921811yescharacteristic
800C22#1171922111yescharacteristic
801C22#1171922711yescharacteristic
802C22#1171923411yescharacteristic
803C22#1171923811yescharacteristic
804C22#1171930311yescharacteristic
805C22#1171930311yescharacteristic
806C22#1171930411yescharacteristic
807C22#1171930411yescharacteristic
808C22#1171930511yescharacteristic
809C22#1171930811yescharacteristic
810C22#1171931111yescharacteristic
811C22#1171931311yescharacteristic
812C22#1171932711yescharacteristic
813C22#1171933011yescharacteristic
814C22D13×C22⋊Q811yescharacteristic
815C22#1171933311yescharacteristic
816C22#1171933711yescharacteristic
817C22#1171933711yescharacteristic
818C22#1171933811yescharacteristic
819C22#1171933811yescharacteristic
820C22C2×C4×C22⋊D1311yescharacteristic
821C22C2×#8819111yescharacteristic
822C22C2×#8819211yescharacteristic
823C22#1171951111yescharacteristic
824C22Q8×C22⋊D1311yescharacteristic
825C22#1171952911yescharacteristic
826C22#1171953611yescharacteristic
827C4—42no—
828C4—44no—
829C4—82no—
830C4—268no—
831C4—264no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—524no—
836C4#1171861718yes—
837C2—44no—
838C2C2×#1171861711yescharacteristic
839C2#1311736411yescharacteristic
840C2#1311751411yescharacteristic
841C2#1311766811yescharacteristic
842C2#1311767311yescharacteristic
843C2#1311784111yescharacteristic
844C2#1311786311yescharacteristic
845C2#1311817711yescharacteristic
846C2#1311819711yescharacteristic
847C2#1311834111yescharacteristic
848C2#1311836311yescharacteristic
849C2#1311839811yescharacteristic
850C2#1311843111yescharacteristic
851C2#1311974711yescharacteristic
852C2#1311976011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13969
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#88141C2semidirect
3. C2×#11718635C2semidirect
5. #13113087C2semidirect
8. #13113067C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
23. C2×#88178C4semidirect
86. C2×C22⋊Dic13Q8semidirect
216. C2×Dic26C22⋊C4semidirect
274. C23×C13C4×Q8semidirect
360. C2×Dic13C22⋊Q8semidirect
654. C13#13969semidirect
689. C23#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881782
C22×#881412
C2×#117186352
C2×C4×C22⋊Dic132
#131130872
#131130792
#131130732
#131130672
#131130652
C2×C13×#3802
#1396913