Finite Group Databasebeta

← #15785325

Subgroups — #15785325

Order 3328.

1710 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic
2C2×#11718638C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic
4#13113106C212yesmaximal
5#13113102C212yesmaximal
6#13113070C212yesmaximal
7#13113067C212yesmaximal
8#13113066C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113065C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×C4×Dic26—24no—
25C2×C4×Dic26—24no—
26C2×C4×Dic26C418yescomplemented
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718638—24no—
39C4⋊C4×Dic13—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26—22no—
57C22×Dic26C2×C414yes—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4Q814yescomplemented
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13C2×C414yes—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13C2×C414yes—
75C2×C4⋊Dic13Q814yescomplemented
76C2×#6101—22no—
77C2×#6101—22no—
78C2×#6101—22no—
79C2×#6101—22no—
80C2×#6101C2×C414yes—
81C2×#6101C2×C414yes—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—42no—
86C2×C4×Dic13—42no—
87C2×C4×Dic13C2×C414yes—
88C2×C4×Dic13C2×C414yes—
89C2×C4×Dic13D414yes—
90C2×C4×Dic13D414yes—
91C4×Dic26—232no—
92C13×#95—24no—
93C13×#95—42no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—42no—
101#88071—42no—
102#88071—42no—
103#13925—131nomaximal, Sylow
104C24×C13C2411yescharacteristic
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×Q814yes—
134C22×C4×C13C2×Q812yes—
135C22×C4×C13C2×Q812yes—
136C22×C4×C13#4112yes—
137C22×C4×C13#4112yes—
138C22×C4×C13#4112yes—
139C22×C4×C13#4112yes—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13C22×C412yes—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C412yes—
175C22×Dic13C2×D412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13C2×D412yes—
179C22×Dic13C2×Q814yes—
180C22×Dic13#4112yes—
181C22×Dic13#4112yes—
182C2×Dic26—28no—
183C2×Dic26—28no—
184C2×Dic26—28no—
185C2×Dic26—28no—
186C2×Dic26—28no—
187C2×Dic26—28no—
188C2×Dic26—28no—
189C13×C4⋊C4—28no—
190C13×C4⋊C4—44no—
191C42×C13—28no—
192C4⋊Dic13—28no—
193C4⋊Dic13—28no—
194C4⋊Dic13—44no—
195#6101—28no—
196#6101—28no—
197C4×Dic13—28no—
198C4×Dic13—48no—
199C4×Dic13C22⋊C4116yes—
200C22×C4×Q8—131no—
201C2×#382—131no—
202C2×C4×C4⋊C4—131no—
203#1446—132no—
204#1445—132no—
205#1436—132no—
206#1436—132no—
207C4⋊#95—131no—
208C4⋊#95—131no—
209C4⋊#95—131no—
210C4⋊#95D1311yescharacteristic
211C23×C13C23×C411yescharacteristic
212C23×C13C22×D411yescharacteristic
213C23×C13C22×D411yescharacteristic
214C23×C13C22×Q811yescharacteristic
215C23×C13C22×Q811yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13C2×#4111yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13H(5,𝔽2)11yescharacteristic
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C132−1+411yescharacteristic
225C23×C132−1+411yescharacteristic
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13C2×C22⋊C414yes—
254C2×C4×C13#11714yes—
255C2×C4×C13C4×Q814yes—
256C2×C4×C13C4×Q814yes—
257C2×C4×C13C22⋊Q814yes—
258C2×C4×C13C22⋊Q814yes—
259C2×C4×C13#12414yes—
260C2×C4×C13C4⋊Q814yes—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13C2×C22⋊C414yes—
301C2×Dic13C2×C22⋊C414yes—
302C2×Dic13#11714yes—
303Dic26—232no—
304C23×Q8—131no—
305C2×C4×Q8—138no—
306C2×C4×Q8—264no—
307C2×C4×Q8—264no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—131no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—131no—
313C22×C4⋊C4C2×D1311yescharacteristic
314C22×C4⋊C4C2×D1311yescharacteristic
315C22×C42—131no—
316C22×C42—131no—
317C22×C42—132no—
318C22×C42C2×D1311yescharacteristic
319#382—264no—
320C4×C4⋊C4—264no—
321C2×#95—132no—
322C2×#95—132no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95—132no—
329C2×#95—132no—
330C2×#95C2×D1312yes—
331C2×#95C2×D1312yes—
332C22×C13C22×C22⋊C411yescharacteristic
333C22×C13C2×#11711yescharacteristic
334C22×C13C2×#11711yescharacteristic
335C22×C13C2×C4×Q811yescharacteristic
336C22×C13C2×C4×Q811yescharacteristic
337C22×C13#52011yescharacteristic
338C22×C13#52011yescharacteristic
339C22×C13C2×C22⋊Q811yescharacteristic
340C22×C13C2×C22⋊Q811yescharacteristic
341C22×C13#52511yescharacteristic
342C22×C13#52511yescharacteristic
343C22×C13#52511yescharacteristic
344C22×C13#52511yescharacteristic
345C22×C13C2×#12411yescharacteristic
346C22×C13C2×C4⋊Q811yescharacteristic
347C22×C13#53511yescharacteristic
348C22×C13#53611yescharacteristic
349C22×C13#53711yescharacteristic
350C22×C13#53711yescharacteristic
351C22×C13#55411yescharacteristic
352C22×C13#55411yescharacteristic
353C22×C13#55411yescharacteristic
354C22×C13#55411yescharacteristic
355C22×C13#55611yescharacteristic
356C22×C13#55611yescharacteristic
357C22×C13#55611yescharacteristic
358C22×C13#55611yescharacteristic
359C22×C13#55711yescharacteristic
360C22×C13#55711yescharacteristic
361C22×C13#55711yescharacteristic
362C22×C13#55711yescharacteristic
363C22×C13#55911yescharacteristic
364C22×C13#55911yescharacteristic
365C22×C13#55911yescharacteristic
366C22×C13#55911yescharacteristic
367C4×C13—24no—
368C4×C13—42no—
369C4×C13—44no—
370C4×C13—82no—
371C4×C13#39118yes—
372Dic13—24no—
373Dic13—24no—
374Dic13—24no—
375Dic13—42no—
376Dic13—44no—
377Dic13—82no—
378C22×Q8—134no—
379C22×Q8—262no—
380C22×Q8—262no—
381C22×Q8—262no—
382C22×Q8—262no—
383C22×Q8—262no—
384C22×Q8—262no—
385C23×C4—131no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—132no—
390C23×C4—132no—
391C23×C4C22×D1312yes—
392C23×C4C22×D1312yes—
393C23×C4C22×D1311yescharacteristic
394C23×C4C22×D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C4×Q8—2632no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—134no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—134no—
405C2×C4⋊C4—134no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—262no—
408C2×C4⋊C4—262no—
409C2×C4⋊C4—262no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—262no—
414C2×C4⋊C4—262no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4Dic2614yescomplemented
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—134no—
421C2×C42—134no—
422C2×C42—134no—
423C2×C42—134no—
424C2×C42—262no—
425C2×C42—262no—
426C2×C42—264no—
427C2×C42—522no—
428C2×C42—522no—
429C2×C42C4×D1314yes—
430#95—24no—
431#95—42no—
432#95—264no—
433#95—264no—
434#95—264no—
435#95—264no—
436#95—264no—
437#95—264no—
438#95—522no—
439#95—522no—
440#95—522no—
441C2×C13#228011yescharacteristic
442C2×C13C2×#39111yescharacteristic
443C2×C13#231111yescharacteristic
444C2×C13#235511yescharacteristic
445C2×C13#235511yescharacteristic
446C2×C13#235511yescharacteristic
447C2×C13#235511yescharacteristic
448C2×C13#258011yescharacteristic
449C2×C13#258011yescharacteristic
450C2×C13#258111yescharacteristic
451C2×C13#258111yescharacteristic
452C2×C13#258411yescharacteristic
453C2×C13#258411yescharacteristic
454C2×C13#259211yescharacteristic
455C2×C13#259211yescharacteristic
456C24C23×D1311yescharacteristic
457C2×Q8—268no—
458C2×Q8—268no—
459C2×Q8—268no—
460C2×Q8—268no—
461C2×Q8—268no—
462C2×Q8—268no—
463C2×Q8—268no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—132no—
488C22×C4—132no—
489C22×C4—132no—
490C22×C4—132no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—132no—
496C22×C4—132no—
497C22×C4—134no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4—261no—
508C22×C4—261no—
509C22×C4—261no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—261no—
518C22×C4—262no—
519C22×C4—261no—
520C22×C4—262no—
521C22×C4—261no—
522C22×C4—262no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4C2×Dic2614yes—
530C22×C4C2×Dic2612yes—
531C22×C4C2×C4×D1312yes—
532C22×C4C2×C4×D1312yes—
533C22×C4C2×C4×D1312yes—
534C22×C4#612712yes—
535C22×C4D4×D1312yes—
536C22×C4D4×D1312yes—
537C22×C4#612912yes—
538C22×C4#612912yes—
539C22×C4Q8×D1312yes—
540C22×C4#613112yes—
541C4⋊C4—28no—
542C4⋊C4—44no—
543C4⋊C4—268no—
544C4⋊C4—268no—
545C4⋊C4—268no—
546C4⋊C4—268no—
547C4⋊C4—524no—
548C42—28no—
549C42—1316no—
550C42—268no—
551C42—528no—
552C13#1392511yescharacteristic, complemented, Sylow
553C23C22×Dic2611yescharacteristic
554C23C22×C4×D1311yescharacteristic
555C23C2×#612711yescharacteristic
556C23C2×D4×D1311yescharacteristic
557C23C2×D4×D1311yescharacteristic
558C23C2×#612911yescharacteristic
559C23C2×#612911yescharacteristic
560C23#8825111yescharacteristic
561C23C2×Q8×D1311yescharacteristic
562C23C2×#613111yescharacteristic
563C23#8825411yescharacteristic
564C23#41×D1311yescharacteristic
565C23#41×D1311yescharacteristic
566C23#8825611yescharacteristic
567C23#8825711yescharacteristic
568Q8—2632no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—134no—
597C2×C4—134no—
598C2×C4—134no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—262no—
617C2×C4—264no—
618C2×C4—262no—
619C2×C4—262no—
620C2×C4—264no—
621C2×C4—262no—
622C2×C4—264no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—522no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4C4×Dic2614yes—
639C2×C4#8813214yes—
640C2×C4C22⋊C4×D1314yes—
641C2×C4#8813914yes—
642C2×C4#8814114yes—
643C2×C4#8814214yes—
644C2×C4#8814614yes—
645C2×C4#8815014yes—
646C22C2×C4×Dic2611yescharacteristic
647C22C2×#8813211yescharacteristic
648C22C2×C22⋊C4×D1311yescharacteristic
649C22C2×#8813911yescharacteristic
650C22C2×#8814111yescharacteristic
651C22C2×#8814211yescharacteristic
652C22C2×#8814611yescharacteristic
653C22#1171920911yescharacteristic
654C22C2×#8815011yescharacteristic
655C22D13×#11711yescharacteristic
656C22#1171922811yescharacteristic
657C22#1171924411yescharacteristic
658C22#1171924711yescharacteristic
659C22#1171924811yescharacteristic
660C22#1171926411yescharacteristic
661C22#1171927311yescharacteristic
662C22#1171927411yescharacteristic
663C22#1171927511yescharacteristic
664C22#1171929011yescharacteristic
665C22#1171931111yescharacteristic
666C22#1171931111yescharacteristic
667C22#1171931211yescharacteristic
668C22#1171931311yescharacteristic
669C22#1171933211yescharacteristic
670C22#1171933211yescharacteristic
671C22#1171933311yescharacteristic
672C22#1171933411yescharacteristic
673C22#1171937611yescharacteristic
674C22#1171938611yescharacteristic
675C22#1171939011yescharacteristic
676C22#1171939511yescharacteristic
677C22#1171941811yescharacteristic
678C22#1171942611yescharacteristic
679C22#1171943511yescharacteristic
680C22#1171943711yescharacteristic
681C4—24no—
682C4—44no—
683C4—42no—
684C4—82no—
685C4—264no—
686C4—264no—
687C4—264no—
688C4—524no—
689C4—522no—
690C4—1042no—
691C4#1171830718yes—
692C2#1311721811yescharacteristic
693C2C2×#1171830711yescharacteristic
694C2#1311742511yescharacteristic
695C2#1311778811yescharacteristic
696C2#1311779111yescharacteristic
697C2#1311779411yescharacteristic
698C2#1311779511yescharacteristic
699C2#1312019211yescharacteristic
700C2#1312019611yescharacteristic
701C2#1312020011yescharacteristic
702C2#1312020411yescharacteristic
703C2#1312022111yescharacteristic
704C2#1312022311yescharacteristic
705C2#1312032111yescharacteristic
706C2#1312032311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#13925
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
26. C2×C4×Dic26C4semidirect
63. C2×C13×C4⋊C4Q8semidirect
75. C2×C4⋊Dic13Q8semidirect
417. C2×C4⋊C4Dic26semidirect
552. C13#13925semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117186382
C2×C4⋊C4×Dic132
#131131062
#131131022
#131130702
#131130672
#131130662
#131130652
C13×C4⋊#952
#1392513