Finite Group Databasebeta

← #15785594

Subgroups — #15785594

Order 3328.

1630 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718589C211yesmaximal, characteristic
3C2×#11718634C211yesmaximal, characteristic
4C2×#11718638C211yesmaximal, characteristic
5C2×C4⋊C4×Dic13C211yesmaximal, characteristic
6C2×C4×#6101C211yesmaximal, characteristic
7#13113100C212yesmaximal
8#13113099C212yesmaximal
9#13113065C212yesmaximal
10#13113064C212yesmaximal
11C2×C13×#389C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C13×#389—24no—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36#11718646—24no—
37#11718638—24no—
38C4⋊C4×Dic13C418yescomplemented
39#11718634—24no—
40C4×#6101—24no—
41#11718589—24no—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4C2×C414yes—
60C2×C13×C4⋊C4D414yes—
61C2×C13×C4⋊C4Q814yes—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—24no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—24no—
70C2×C4⋊Dic13—42no—
71C2×C4⋊Dic13C2×C414yes—
72C2×C4⋊Dic13D414yes—
73C2×C4⋊Dic13Q814yes—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101—22no—
78C2×#6101—22no—
79C2×#6101—22no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—24no—
84C2×#6101—42no—
85C2×#6101—42no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—42no—
90C2×C4×Dic13—42no—
91C2×C4×Dic13C2×C418yes—
92C2×C4×Dic13C2×C414yes—
93C2×C4×Dic13D414yes—
94C2×C4×Dic13Q814yes—
95C13×#95—24no—
96#88071—24no—
97#88071—24no—
98#88071—22no—
99#88071—22no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071C2×C418yes—
104#13954—131nomaximal, Sylow
105C24×C13C2411yescharacteristic
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
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×C13—22no—
129C22×C4×C13C22×C414yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×D414yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×Q814yes—
136C22×C4×C13C2×Q812yes—
137C22×C4×C13C2×Q812yes—
138C22×C4×C13C2×Q812yes—
139C22×C4×C13#4112yes—
140C22×C4×C13#4112yes—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C414yes—
174C22×Dic13C22×C412yes—
175C22×Dic13C2×D412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D414yes—
178C22×Dic13C2×Q812yes—
179C22×Dic13C2×Q812yes—
180C22×Dic13C2×Q814yes—
181C22×Dic13#4112yes—
182C22×Dic13#4112yes—
183C13×C4⋊C4—48no—
184C13×C4⋊C4—44no—
185C13×C4⋊C4C4⋊C4116yescomplemented
186C42×C13—44no—
187C4⋊Dic13—48no—
188C4⋊Dic13—44no—
189C4⋊Dic13C4⋊C4116yescomplemented
190#6101—28no—
191#6101—28no—
192#6101—48no—
193#6101—48no—
194C4×Dic13—48no—
195C4×Dic13—44no—
196C4×Dic13C4⋊C4116yescomplemented
197C2×#389—131no—
198C2×#389—131no—
199C2×#389—131no—
200C2×#389D1311yescharacteristic
201C2×#382—131no—
202C2×C4×C4⋊C4—131no—
203C2×C4×C4⋊C4—131no—
204#1444—132no—
205#1444—132no—
206C4⋊#95—132no—
207C4⋊#95—132no—
208C23×C13C23×C411yescharacteristic
209C23×C13C22×D411yescharacteristic
210C23×C13C22×D411yescharacteristic
211C23×C13C22×D411yescharacteristic
212C23×C13C22×Q811yescharacteristic
213C23×C13C22×Q811yescharacteristic
214C23×C13C22×Q811yescharacteristic
215C23×C13C2×#4111yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13C2×#4111yescharacteristic
219C23×C13H(5,𝔽2)11yescharacteristic
220C23×C13H(5,𝔽2)11yescharacteristic
221C23×C132−1+411yescharacteristic
222C23×C132−1+411yescharacteristic
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
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—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—42no—
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×C13C2×C4⋊C418yes—
251C2×C4×C13C2×C4⋊C414yes—
252C2×C4×C13C2×C4⋊C414yes—
253C2×C4×C13C2×C4⋊C414yes—
254C2×C4×C13#12714yes—
255C2×C4×C13C4⋊Q814yes—
256C2×C4×C13C4⋊Q814yes—
257C2×C4×C13C4⋊Q814yes—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
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—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13C2×C4⋊C414yes—
298C2×Dic13C2×C4⋊C414yes—
299C2×Dic13C2×C4⋊C418yes—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—131no—
304C22×C4⋊C4—132no—
305C22×C4⋊C4—132no—
306C22×C4⋊C4—132no—
307C22×C4⋊C4C2×D1311yescharacteristic
308C22×C4⋊C4C2×D1312yes—
309C22×C4⋊C4C2×D1311yescharacteristic
310C22×C42—131no—
311C22×C42—132no—
312C22×C42—131no—
313C22×C42C2×D1311yescharacteristic
314#389—24no—
315#389—264no—
316#389—264no—
317#389—264no—
318#382—264no—
319C4×C4⋊C4—138no—
320C4×C4⋊C4—264no—
321C2×#95—132no—
322C2×#95—131no—
323C2×#95—131no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95—132no—
329C2×#95C2×D1312yes—
330C22×C13C22×C4⋊C411yescharacteristic
331C22×C13C22×C4⋊C411yescharacteristic
332C22×C13C22×C4⋊C411yescharacteristic
333C22×C13C4×#4111yescharacteristic
334C22×C13C4×#4111yescharacteristic
335C22×C13#51811yescharacteristic
336C22×C13#51911yescharacteristic
337C22×C13#52511yescharacteristic
338C22×C13#52511yescharacteristic
339C22×C13C2×#12711yescharacteristic
340C22×C13C2×C4⋊Q811yescharacteristic
341C22×C13C2×C4⋊Q811yescharacteristic
342C22×C13C2×C4⋊Q811yescharacteristic
343C22×C13#53311yescharacteristic
344C22×C13#53311yescharacteristic
345C22×C13#53711yescharacteristic
346C22×C13#53711yescharacteristic
347C22×C13#54411yescharacteristic
348C22×C13#54411yescharacteristic
349C22×C13#54611yescharacteristic
350C22×C13#54611yescharacteristic
351C22×C13#54611yescharacteristic
352C22×C13#54611yescharacteristic
353C22×C13#54811yescharacteristic
354C22×C13#54811yescharacteristic
355C22×C13#54811yescharacteristic
356C22×C13#54811yescharacteristic
357C22×C13#55411yescharacteristic
358C22×C13#55411yescharacteristic
359C22×C13#55411yescharacteristic
360C22×C13#55411yescharacteristic
361C22×C13#55711yescharacteristic
362C22×C13#55711yescharacteristic
363C22×C13#55711yescharacteristic
364C22×C13#55711yescharacteristic
365C4×C13—28no—
366C4×C13—42no—
367C4×C13—42no—
368C4×C13—82no—
369C4×C13#38418yes—
370Dic13—24no—
371Dic13—28no—
372Dic13—24no—
373Dic13—42no—
374Dic13—42no—
375Dic13—82no—
376C23×C4—132no—
377C23×C4—131no—
378C23×C4—131no—
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—132no—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385C23×C4C22×D1312yes—
386C23×C4C22×D1311yescharacteristic
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—134no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—134no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—262no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4—264no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—262no—
408C2×C4⋊C4—264no—
409C2×C4⋊C4—264no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—522no—
412C2×C4⋊C4—522no—
413C2×C4⋊C4—522no—
414C2×C4⋊C4Dic2614yes—
415C2×C4⋊C4C4×D1314yes—
416C2×C4⋊C4C22⋊D1314yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—134no—
421C2×C42—134no—
422C2×C42—134no—
423C2×C42—138no—
424C2×C42—262no—
425C2×C42—262no—
426C2×C42—262no—
427C2×C42—522no—
428C2×C42—522no—
429#95—24no—
430#95—138no—
431#95—262no—
432#95—262no—
433#95—264no—
434#95—264no—
435#95—264no—
436#95—264no—
437#95—264no—
438C2×C13C2×#38411yescharacteristic
439C2×C13#229611yescharacteristic
440C2×C13#231611yescharacteristic
441C2×C13#234911yescharacteristic
442C2×C13#234911yescharacteristic
443C2×C13#235111yescharacteristic
444C2×C13#235111yescharacteristic
445C2×C13#254011yescharacteristic
446C2×C13#254011yescharacteristic
447C2×C13#255011yescharacteristic
448C2×C13#255011yescharacteristic
449C2×C13#255011yescharacteristic
450C2×C13#255011yescharacteristic
451C2×C13#258411yescharacteristic
452C2×C13#258411yescharacteristic
453C24C23×D1311yescharacteristic
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—132no—
478C22×C4—134no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—134no—
483C22×C4—132no—
484C22×C4—132no—
485C22×C4—134no—
486C22×C4—132no—
487C22×C4—132no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—262no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—262no—
497C22×C4—261no—
498C22×C4—262no—
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—261no—
511C22×C4—261no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4C2×Dic2614yes—
520C22×C4C2×Dic2612yes—
521C22×C4C2×C4×D1314yes—
522C22×C4C2×C4×D1312yes—
523C22×C4D4×D1312yes—
524C22×C4D4×D1312yes—
525C22×C4#612912yes—
526C22×C4Q8×D1312yes—
527C22×C4Q8×D1312yes—
528C22×C4#613112yes—
529C22×C4C2×C22⋊D1314yes—
530C22×C4C2×C22⋊D1312yes—
531C4⋊C4—48no—
532C4⋊C4—44no—
533C4⋊C4—1316no—
534C4⋊C4—268no—
535C4⋊C4—268no—
536C4⋊C4—528no—
537C4⋊C4—528no—
538C4⋊C4—528no—
539C4⋊C4—524no—
540C4⋊C4#6101116yescomplemented
541C42—44no—
542C42—1316no—
543C42—528no—
544C42—524no—
545C13#1395411yescharacteristic, complemented, Sylow
546C23C22×Dic2611yescharacteristic
547C23C22×C4×D1311yescharacteristic
548C23C2×D4×D1311yescharacteristic
549C23C2×D4×D1311yescharacteristic
550C23C2×#612911yescharacteristic
551C23#8825111yescharacteristic
552C23C2×Q8×D1311yescharacteristic
553C23C2×Q8×D1311yescharacteristic
554C23C2×#613111yescharacteristic
555C23#8825411yescharacteristic
556C23#41×D1311yescharacteristic
557C23#41×D1311yescharacteristic
558C23#8825611yescharacteristic
559C23#8825711yescharacteristic
560C23C22×C22⋊D1311yescharacteristic
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—134no—
589C2×C4—134no—
590C2×C4—138no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—264no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—264no—
597C2×C4—262no—
598C2×C4—264no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—264no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—264no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—264no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4#8814214yes—
631C2×C4#8814214yes—
632C2×C4C4⋊C4×D1314yes—
633C2×C4C4⋊C4×D1314yes—
634C2×C4C2×#610118yes—
635C2×C4C2×#610114yes—
636C2×C4#8819414yes—
637C2×C4#8819814yes—
638C22C2×#8814211yescharacteristic
639C22C2×#8814211yescharacteristic
640C22C2×C4⋊C4×D1311yescharacteristic
641C22C2×C4⋊C4×D1311yescharacteristic
642C22C4×#612911yescharacteristic
643C22#1171924411yescharacteristic
644C22#1171924811yescharacteristic
645C22#1171925011yescharacteristic
646C22#1171927411yescharacteristic
647C22#1171927511yescharacteristic
648C22#1171927711yescharacteristic
649C22C4×#613111yescharacteristic
650C22#1171930311yescharacteristic
651C22#1171931111yescharacteristic
652C22#1171931311yescharacteristic
653C22#1171931711yescharacteristic
654C22#1171933211yescharacteristic
655C22#1171933411yescharacteristic
656C22#1171933511yescharacteristic
657C22#1171933811yescharacteristic
658C22#1171939011yescharacteristic
659C22#1171939311yescharacteristic
660C22#1171939411yescharacteristic
661C22#1171939511yescharacteristic
662C22#1171942611yescharacteristic
663C22#1171943311yescharacteristic
664C22#1171943411yescharacteristic
665C22#1171943511yescharacteristic
666C22C22×#610111yescharacteristic
667C22C2×#8819411yescharacteristic
668C22#1171951111yescharacteristic
669C22C2×#8819811yescharacteristic
670C22#1171952211yescharacteristic
671C22#1171953411yescharacteristic
672C22#1171953611yescharacteristic
673C4—28no—
674C4—42no—
675C4—42no—
676C4—82no—
677C4—264no—
678C4—268no—
679C4—264no—
680C4—522no—
681C4—522no—
682C4—1042no—
683C4#1171863718yes—
684C2C2×#1171863711yescharacteristic
685C2#1311731711yescharacteristic
686C2#1311745111yescharacteristic
687C2#1311774111yescharacteristic
688C2#1311774511yescharacteristic
689C2#1311775411yescharacteristic
690C2#1311775511yescharacteristic
691C2#1311977211yescharacteristic
692C2#1311977411yescharacteristic
693C2#1311985311yescharacteristic
694C2#1311985511yescharacteristic
695C2#1311985911yescharacteristic
696C2#1311986011yescharacteristic
697C2#1312022111yescharacteristic
698C2#1312022311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#13954
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. C4⋊C4×Dic13C4semidirect
185. C13×C4⋊C4C4⋊C4semidirect
189. C4⋊Dic13C4⋊C4semidirect
196. C4×Dic13C4⋊C4semidirect
540. C4⋊C4#6101semidirect
545. C13#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117185892
C2×#117186342
C2×#117186382
C2×C4⋊C4×Dic132
C2×C4×#61012
#131131002
#131130992
#131130652
#131130642
C2×C13×#3892
#1395413