Finite Group Databasebeta

← #15785194

Subgroups — #15785194

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 714 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×#11718637C212yesmaximal
5C2×#11718637C211yesmaximal, characteristic
6C2×C4⋊C4×Dic13C211yesmaximal, characteristic
7C2×C4×#6101C211yesmaximal, characteristic
8#13113100C212yesmaximal
9#13113099C212yesmaximal
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×#6101C2212yes—
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2212yes—
27C22×C4×Dic13C2211yescharacteristic
28C13×#389—24no—
29C2×C13×#95C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718646—24no—
37#11718637—28no—
38#11718637—24no—
39C4⋊C4×Dic13C418yescomplemented
40#11718634—24no—
41C4×#6101—24no—
42#11718589—24no—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4C2×C414yes—
61C2×C13×C4⋊C4D414yes—
62C2×C13×C4⋊C4Q814yes—
63C2×C42×C13—22no—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—24no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—24no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13C2×C414yes—
73C2×C4⋊Dic13D414yes—
74C2×C4⋊Dic13Q814yes—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101—22no—
78C2×#6101—22no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—24no—
84C2×#6101—24no—
85C2×#6101—24no—
86C2×#6101—24no—
87C2×#6101—42no—
88C2×#6101—42no—
89C2×#6101—42no—
90C2×#6101—42no—
91C2×#6101D414yes—
92C2×#6101Q814yes—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2×C418yes—
99C2×C4×Dic13C2×C414yes—
100C2×C4×Dic13D414yes—
101C2×C4×Dic13Q814yes—
102C13×#95—24no—
103#88071—24no—
104#88071—24no—
105#88071—22no—
106#88071—22no—
107#88071—24no—
108#88071C2×C418yes—
109#13910—131nomaximal, Sylow
110C24×C13C2411yescharacteristic
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
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—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D414yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×Q814yes—
142C22×C4×C13C2×Q812yes—
143C22×C4×C13C2×Q812yes—
144C22×C4×C13C2×Q812yes—
145C22×C4×C13C2×Q812yes—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—22no—
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—21no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C414yes—
175C22×Dic13C22×C412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13C2×D414yes—
179C22×Dic13C2×D412yes—
180C22×Dic13C2×D412yes—
181C22×Dic13C2×Q812yes—
182C22×Dic13C2×Q812yes—
183C22×Dic13C2×Q814yes—
184C22×Dic13C2×Q812yes—
185C22×Dic13C2×Q812yes—
186C22×Dic13#4112yes—
187C22×Dic13#4112yes—
188C13×C4⋊C4—48no—
189C13×C4⋊C4—44no—
190C13×C4⋊C4C4⋊C4116yescomplemented
191C42×C13—44no—
192C4⋊Dic13—48no—
193C4⋊Dic13—44no—
194C4⋊Dic13C4⋊C4116yescomplemented
195#6101—28no—
196#6101—28no—
197#6101—48no—
198#6101—48no—
199#6101—48no—
200#6101—48no—
201C4×Dic13—216no—
202C4×Dic13—44no—
203C4×Dic13C4⋊C4116yescomplemented
204C2×#389—131no—
205C2×#389—131no—
206C2×#389—131no—
207C2×#389D1311yescharacteristic
208C2×#384—132no—
209C2×#384—131no—
210C2×C4×C4⋊C4—131no—
211C2×C4×C4⋊C4—131no—
212#1444—132no—
213#1444—132no—
214C4⋊#95—132no—
215C23×C13C23×C411yescharacteristic
216C23×C13C22×D411yescharacteristic
217C23×C13C22×D411yescharacteristic
218C23×C13C22×D411yescharacteristic
219C23×C13C22×D411yescharacteristic
220C23×C13C22×Q811yescharacteristic
221C23×C13C22×Q811yescharacteristic
222C23×C13C22×Q811yescharacteristic
223C23×C13C22×Q811yescharacteristic
224C23×C13C2×#4111yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13H(5,𝔽2)11yescharacteristic
227C23×C13H(5,𝔽2)11yescharacteristic
228C23×C132−1+411yescharacteristic
229C23×C132−1+411yescharacteristic
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13C2×C4⋊C418yes—
258C2×C4×C13C2×C4⋊C414yes—
259C2×C4×C13C2×C4⋊C414yes—
260C2×C4×C13C2×C4⋊C414yes—
261C2×C4×C13#12714yes—
262C2×C4×C13C4⋊Q814yes—
263C2×C4×C13C4⋊Q814yes—
264C2×C4×C13C4⋊Q814yes—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
299C2×Dic13C2×C4⋊C418yes—
300C2×Dic13C2×C4⋊C414yes—
301C2×Dic13C4×D414yes—
302C2×Dic13C4×Q814yes—
303C2×Dic13#12114yes—
304C2×Dic13C22⋊Q814yes—
305C2×Dic13#12514yes—
306C2×Dic13C4⋊Q814yes—
307C22×C4⋊C4—131no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—131no—
310C22×C4⋊C4—132no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—132no—
313C22×C4⋊C4—132no—
314C22×C4⋊C4—132no—
315C22×C4⋊C4—132no—
316C22×C4⋊C4C2×D1311yescharacteristic
317C22×C4⋊C4C2×D1312yes—
318C22×C4⋊C4C2×D1311yescharacteristic
319C22×C42—131no—
320C22×C42—132no—
321C22×C42—131no—
322C22×C42C2×D1311yescharacteristic
323#389—24no—
324#389—264no—
325#389—264no—
326#389—264no—
327#384—264no—
328#384—268no—
329C4×C4⋊C4—138no—
330C4×C4⋊C4—264no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—132no—
334C2×#95—132no—
335C2×#95—131no—
336C2×#95—131no—
337C2×#95C2×D1312yes—
338C22×C13C22×C4⋊C411yescharacteristic
339C22×C13C22×C4⋊C411yescharacteristic
340C22×C13C22×C4⋊C411yescharacteristic
341C22×C13C2×C4×D411yescharacteristic
342C22×C13C2×C4×Q811yescharacteristic
343C22×C13#52011yescharacteristic
344C22×C13#52011yescharacteristic
345C22×C13C2×#12111yescharacteristic
346C22×C13C2×C22⋊Q811yescharacteristic
347C22×C13C2×#12511yescharacteristic
348C22×C13C2×#12711yescharacteristic
349C22×C13C2×C4⋊Q811yescharacteristic
350C22×C13C2×C4⋊Q811yescharacteristic
351C22×C13C2×C4⋊Q811yescharacteristic
352C22×C13C2×C4⋊Q811yescharacteristic
353C22×C13#53511yescharacteristic
354C22×C13#53611yescharacteristic
355C22×C13#54411yescharacteristic
356C22×C13#54411yescharacteristic
357C22×C13D4211yescharacteristic
358C22×C13D4211yescharacteristic
359C22×C13#54711yescharacteristic
360C22×C13#54711yescharacteristic
361C22×C13D4×Q811yescharacteristic
362C22×C13D4×Q811yescharacteristic
363C22×C13D4×Q811yescharacteristic
364C22×C13D4×Q811yescharacteristic
365C22×C13#55011yescharacteristic
366C22×C13#55011yescharacteristic
367C22×C13#55411yescharacteristic
368C22×C13#55411yescharacteristic
369C22×C13#55711yescharacteristic
370C22×C13#55711yescharacteristic
371C22×C13Q8211yescharacteristic
372C22×C13Q8211yescharacteristic
373C4×C13—28no—
374C4×C13—42no—
375C4×C13—42no—
376C4×C13—82no—
377C4×C13#38418yescomplemented
378Dic13—24no—
379Dic13—28no—
380Dic13—42no—
381Dic13—42no—
382Dic13—82no—
383Dic13#38918yescomplemented
384C23×C4—131no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—132no—
390C23×C4C22×D1312yes—
391C23×C4C22×D1311yescharacteristic
392C23×C4C22×D1311yescharacteristic
393C23×C4C22×D1312yes—
394C23×C4C22×D1311yescharacteristic
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—134no—
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—264no—
411C2×C4⋊C4—264no—
412C2×C4⋊C4—264no—
413C2×C4⋊C4—264no—
414C2×C4⋊C4—264no—
415C2×C4⋊C4—264no—
416C2×C4⋊C4—264no—
417C2×C4⋊C4—264no—
418C2×C4⋊C4—264no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—264no—
422C2×C4⋊C4—262no—
423C2×C4⋊C4—522no—
424C2×C4⋊C4—522no—
425C2×C4⋊C4—522no—
426C2×C4⋊C4—522no—
427C2×C4⋊C4—522no—
428C2×C4⋊C4Dic2614yes—
429C2×C4⋊C4C4×D1314yes—
430C2×C4⋊C4C22⋊D1314yes—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—134no—
435C2×C42—134no—
436C2×C42—134no—
437C2×C42—138no—
438C2×C42—264no—
439C2×C42—264no—
440C2×C42—262no—
441C2×C42—262no—
442C2×C42—262no—
443#95—24no—
444#95—138no—
445#95—262no—
446#95—262no—
447#95—264no—
448#95—264no—
449#95—264no—
450C2×C13C2×#38411yescharacteristic
451C2×C13C2×#38911yescharacteristic
452C2×C13#231711yescharacteristic
453C2×C13D4×C4⋊C411yescharacteristic
454C2×C13D4×C4⋊C411yescharacteristic
455C2×C13Q8×C4⋊C411yescharacteristic
456C2×C13Q8×C4⋊C411yescharacteristic
457C2×C13#254111yescharacteristic
458C2×C13#254211yescharacteristic
459C2×C13#254611yescharacteristic
460C2×C13#255111yescharacteristic
461C2×C13#255111yescharacteristic
462C2×C13#255211yescharacteristic
463C2×C13#255211yescharacteristic
464C2×C13#256711yescharacteristic
465C24C23×D1311yescharacteristic
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
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—132no—
499C22×C4—134no—
500C22×C4—132no—
501C22×C4—134no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—262no—
505C22×C4—261no—
506C22×C4—262no—
507C22×C4—261no—
508C22×C4—262no—
509C22×C4—261no—
510C22×C4—262no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4C2×Dic2614yes—
532C22×C4C2×Dic2612yes—
533C22×C4C2×C4×D1314yes—
534C22×C4C2×C4×D1312yes—
535C22×C4D4×D1312yes—
536C22×C4D4×D1312yes—
537C22×C4D4×D1312yes—
538C22×C4Q8×D1312yes—
539C22×C4Q8×D1312yes—
540C22×C4Q8×D1312yes—
541C22×C4C2×C22⋊D1314yes—
542C22×C4C2×C22⋊D1312yes—
543C4⋊C4—48no—
544C4⋊C4—44no—
545C4⋊C4—1316no—
546C4⋊C4—268no—
547C4⋊C4—268no—
548C4⋊C4—528no—
549C4⋊C4—528no—
550C4⋊C4—528no—
551C4⋊C4—528no—
552C4⋊C4—528no—
553C4⋊C4—524no—
554C4⋊C4#6101116yescomplemented
555C42—44no—
556C42—1316no—
557C42—2616no—
558C42—524no—
559C13#1391011yescharacteristic, complemented, Sylow
560C23C22×Dic2611yescharacteristic
561C23C22×C4×D1311yescharacteristic
562C23C2×D4×D1311yescharacteristic
563C23C2×D4×D1311yescharacteristic
564C23C2×D4×D1311yescharacteristic
565C23#8825111yescharacteristic
566C23C2×Q8×D1311yescharacteristic
567C23C2×Q8×D1311yescharacteristic
568C23C2×Q8×D1311yescharacteristic
569C23#8825411yescharacteristic
570C23#41×D1311yescharacteristic
571C23#41×D1311yescharacteristic
572C23#8825611yescharacteristic
573C23#8825711yescharacteristic
574C23C22×C22⋊D1311yescharacteristic
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—134no—
603C2×C4—134no—
604C2×C4—134no—
605C2×C4—134no—
606C2×C4—134no—
607C2×C4—134no—
608C2×C4—134no—
609C2×C4—134no—
610C2×C4—138no—
611C2×C4—264no—
612C2×C4—262no—
613C2×C4—264no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—264no—
617C2×C4—262no—
618C2×C4—264no—
619C2×C4—262no—
620C2×C4—264no—
621C2×C4—262no—
622C2×C4—264no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4—522no—
641C2×C4—522no—
642C2×C4—522no—
643C2×C4—522no—
644C2×C4#8814214yes—
645C2×C4#8814214yes—
646C2×C4C4⋊C4×D1314yes—
647C2×C4C4⋊C4×D1314yes—
648C2×C4C2×#610118yes—
649C2×C4C2×#610114yes—
650C2×C4#8819414yes—
651C2×C4#8819814yes—
652C22C2×#8814211yescharacteristic
653C22C2×#8814211yescharacteristic
654C22C2×C4⋊C4×D1311yescharacteristic
655C22C2×C4⋊C4×D1311yescharacteristic
656C22D4×Dic2611yescharacteristic
657C22#1171924411yescharacteristic
658C22C4×D4×D1311yescharacteristic
659C22#1171925111yescharacteristic
660C22Q8×Dic2611yescharacteristic
661C22#1171927411yescharacteristic
662C22C4×Q8×D1311yescharacteristic
663C22#1171927911yescharacteristic
664C22#1171930411yescharacteristic
665C22D13×#12111yescharacteristic
666C22#1171931211yescharacteristic
667C22#1171931411yescharacteristic
668C22D13×C22⋊Q811yescharacteristic
669C22#1171933311yescharacteristic
670C22#1171933611yescharacteristic
671C22#1171933711yescharacteristic
672C22#1171939011yescharacteristic
673C22D13×#12511yescharacteristic
674C22#1171939411yescharacteristic
675C22#1171939511yescharacteristic
676C22#1171942711yescharacteristic
677C22D13×C4⋊Q811yescharacteristic
678C22#1171943211yescharacteristic
679C22#1171943411yescharacteristic
680C22C22×#610111yescharacteristic
681C22D4×C22⋊D1311yescharacteristic
682C22C2×#8819411yescharacteristic
683C22C2×#8819811yescharacteristic
684C22Q8×C22⋊D1311yescharacteristic
685C22#1171952911yescharacteristic
686C22#1171953911yescharacteristic
687C4—28no—
688C4—42no—
689C4—42no—
690C4—82no—
691C4—138no—
692C4—264no—
693C4—268no—
694C4—522no—
695C4—522no—
696C4—1042no—
697C4#1171863718yescomplemented
698C2C2×#1171863711yescharacteristic
699C2D13×#38911yescharacteristic
700C2#1311745811yescharacteristic
701C2D4×#610111yescharacteristic
702C2#1311773711yescharacteristic
703C2Q8×#610111yescharacteristic
704C2#1311775011yescharacteristic
705C2#1311977911yescharacteristic
706C2#1311978611yescharacteristic
707C2#1311982311yescharacteristic
708C2#1311986311yescharacteristic
709C2#1311986411yescharacteristic
710C2#1311986811yescharacteristic
711C2#1311987311yescharacteristic
712C2#1312004311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#13910
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
39. C4⋊C4×Dic13C4semidirect
190. C13×C4⋊C4C4⋊C4semidirect
194. C4⋊Dic13C4⋊C4semidirect
203. C4×Dic13C4⋊C4semidirect
377. C4×C13#384semidirect
383. Dic13#389semidirect
554. C4⋊C4#6101semidirect
559. C13#13910semidirect
697. C4#11718637semidirect

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×#117186372
C2×C4⋊C4×Dic132
C2×C4×#61012
#131131002
#131130992
#131130642
C2×C13×#3892
#1391013