Finite Group Databasebeta

← #15786620

Subgroups — #15786620

Order 3328.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C2×#11718633C211yesmaximal, characteristic, complemented
3C2×#11718650C211yesmaximal, characteristic
4C2×#11718650C211yesmaximal, characteristic
5C2×#11718650C211yesmaximal, characteristic
6C2×C4×#6103C211yesmaximal, characteristic
7#13113100C211yesmaximal, characteristic, complemented
8#13113099C211yesmaximal, characteristic, complemented
9#13113089C211yesmaximal, characteristic, complemented
10#13113087C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C2×C13×#389C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×C4⋊C4×D13—24no—
36C2×C4⋊C4×D13—24no—
37C2×C4⋊C4×D13—24no—
38C13×#389—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718650—24no—
56#11718650—24no—
57#11718650C418yescomplemented
58#11718633—24no—
59C4×#6103—24no—
60C24×D13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C22×C4×D13—22no—
76C22×C4×D13—22no—
77C22×C4×D13—22no—
78C22×C4×D13—22no—
79C22×C4×D13—22no—
80C22×C4×D13—22no—
81C22×C4×D13—22no—
82C22×C4×D13—22no—
83C22×C4×D13—22no—
84C22×C4×D13—22no—
85C22×C4×D13—22no—
86C22×C4×D13—22no—
87C22×C4×D13—22no—
88C22×C4×D13—22no—
89C22×C4×D13—22no—
90C22×C4×D13—41no—
91C22×C4×D13—41no—
92C22×C4×D13—41no—
93C22×C4×D13—41no—
94C22×C4×D13C2×C414yes—
95C22×C4×D13D414yes—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4C2×C414yescomplemented
107C2×C13×C4⋊C4D414yes—
108C2×C42×C13—22no—
109C2×C42×C13—22no—
110C2×C42×C13—41no—
111C2×#6103—22no—
112C2×#6103—22no—
113C2×#6103—22no—
114C2×#6103—22no—
115C2×#6103—22no—
116C2×#6103—22no—
117C2×#6103—22no—
118C2×#6103C2×C414yes—
119C2×#6103C2×C414yes—
120C2×#6103D414yes—
121C2×#6103Q814yes—
122C2×#6103Q814yes—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13—22no—
126C2×#6101—22no—
127C2×#6101—22no—
128C2×#6101—22no—
129C2×#6101—22no—
130C2×#6101—22no—
131C2×#6101—22no—
132C2×#6101—22no—
133C2×#6101—22no—
134C2×#6101—22no—
135C2×#6101—22no—
136C2×#6101—41no—
137C2×#6101—41no—
138C2×#6101—41no—
139C2×#6101C2×C414yescomplemented
140C2×#6101D414yes—
141C2×C4×Dic13—22no—
142C2×C4×Dic13—22no—
143C2×C4×Dic13—41no—
144C4⋊C4×D13—232no—
145C13×#95—22no—
146C13×#95—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—22no—
156#88071—22no—
157#88071—41no—
158#88071—41no—
159#88071C2×C414yescomplemented
160#88071C2×C414yescomplemented
161#14043—131nomaximal, Sylow
162C24×C13C2411yescharacteristic
163C23×D13—21no—
164C23×D13—21no—
165C23×D13—21no—
166C23×D13—21no—
167C23×D13—21no—
168C23×D13—21no—
169C23×D13—21no—
170C23×D13—21no—
171C23×D13C22×C412yes—
172C23×D13C2×D412yes—
173C23×D13C2×D412yes—
174C23×D13C2×Q812yes—
175C23×D13C2×Q812yes—
176C23×D13#4112yes—
177C23×D13#4112yes—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C22×C412yes—
217C22×C4×C13C22×C412yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13C2×D412yes—
221C22×C4×C13C2×D412yes—
222C22×C4×C13C2×D412yes—
223C22×C4×C13C2×D412yes—
224C22×C4×C13C2×Q812yes—
225C22×C4×C13C2×Q812yes—
226C22×C4×C13#4112yes—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13—21no—
264C22×Dic13—21no—
265C22×Dic13—21no—
266C22×Dic13C22×C412yes—
267C22×Dic13C22×C412yes—
268C22×Dic13C22×C412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×D412yes—
271C22×Dic13C2×D412yes—
272C22×Dic13C2×D412yes—
273C22×Dic13C2×Q812yes—
274C22×Dic13C2×Q812yes—
275C22×Dic13#4112yes—
276C2×C4×D13—28no—
277C2×C4×D13—28no—
278C2×C4×D13—28no—
279C2×C4×D13—28no—
280C2×C4×D13—28no—
281C2×C4×D13—28no—
282C2×C4×D13—28no—
283C2×C4×D13—28no—
284C2×C4×D13—28no—
285C2×C4×D13—28no—
286C2×C4×D13—44no—
287C2×C4×D13—44no—
288C2×C4×D13—44no—
289C2×C4×D13—44no—
290C2×C4×D13—44no—
291C2×C4×D13—44no—
292C2×C4×D13—44no—
293C2×C4×D13—44no—
294C2×C4×D13—44no—
295C2×C4×D13—44no—
296C2×C4×D13—44no—
297C13×C4⋊C4—28no—
298C13×C4⋊C4—28no—
299C13×C4⋊C4—44no—
300C13×C4⋊C4—44no—
301C42×C13—44no—
302#6103—28no—
303#6103—28no—
304#6103—44no—
305#6103C4⋊C4116yescomplemented
306C4⋊Dic13—28no—
307#6101—28no—
308#6101—28no—
309#6101—28no—
310#6101—44no—
311#6101—44no—
312C4×Dic13—44no—
313C23×C4⋊C4—131no—
314C2×#389—131no—
315C2×#389D1311yescharacteristic, complemented
316C2×#385—131no—
317C2×#385—131no—
318C2×#385—131no—
319C2×C4×C22⋊C4—131no—
320#1444—131no—
321#1444—131no—
322#1441—131no—
323#1441—131no—
324#1436—131no—
325#1436—131no—
326C22⋊#95—131no—
327C22⋊#95—131no—
328C23×C13C23×C411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C22×D411yescharacteristic
331C23×C13C22×D411yescharacteristic
332C23×C13C22×D411yescharacteristic
333C23×C13C22×Q811yescharacteristic
334C23×C13C22×Q811yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C132−1+411yescharacteristic
342C23×C132−1+411yescharacteristic
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—22no—
349C22×D13—22no—
350C22×D13—22no—
351C22×D13—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—22no—
361C22×D13—22no—
362C22×D13—22no—
363C22×D13—22no—
364C22×D13—22no—
365C22×D13—22no—
366C22×D13—22no—
367C22×D13—22no—
368C22×D13—22no—
369C22×D13—22no—
370C22×D13—22no—
371C22×D13C2×C4⋊C414yes—
372C22×D13C4×D414yes—
373C22×D13C4×Q814yes—
374C22×D13#12114yes—
375C22×D13C22⋊Q814yes—
376C22×D13#12514yes—
377C22×D13C4⋊Q814yes—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13C2×C4⋊C414yescomplemented
425C2×C4×C13C4×D414yes—
426C2×C4×C13#12014yes—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
434C2×Dic13—22no—
435C2×Dic13—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—22no—
440C2×Dic13—22no—
441C2×Dic13—22no—
442C2×Dic13—22no—
443C2×Dic13—22no—
444C2×Dic13—22no—
445C2×Dic13—22no—
446C2×Dic13—22no—
447C2×Dic13—22no—
448C2×Dic13—22no—
449C2×Dic13—22no—
450C2×Dic13—22no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13—41no—
461C2×Dic13—41no—
462C2×Dic13—41no—
463C2×Dic13—41no—
464C2×Dic13—41no—
465C2×Dic13—41no—
466C2×Dic13—41no—
467C2×Dic13—41no—
468C2×Dic13—41no—
469C2×Dic13—41no—
470C2×Dic13—41no—
471C2×Dic13—41no—
472C2×Dic13—41no—
473C2×Dic13—41no—
474C2×Dic13C2×C4⋊C414yescomplemented
475C2×Dic13C4×D414yes—
476C4×D13—232no—
477C4×D13—416no—
478C4×D13—416no—
479C24×C4—131no—
480C24×C4—131no—
481C24×C4—131no—
482C22×C4⋊C4—131no—
483C22×C4⋊C4—131no—
484C22×C4⋊C4—131no—
485C22×C4⋊C4—131no—
486C22×C4⋊C4—131no—
487C22×C4⋊C4—131no—
488C22×C4⋊C4—264no—
489C22×C4⋊C4—264no—
490C22×C4⋊C4—264no—
491C22×C4⋊C4C2×D1311yescharacteristic
492C22×C4⋊C4C2×D1311yescharacteristic
493C22×C4⋊C4C2×D1311yescharacteristic
494C22×C4⋊C4C2×D1311yescharacteristic
495C22×C22⋊C4—131no—
496C22×C22⋊C4—131no—
497C22×C22⋊C4—131no—
498C22×C22⋊C4—131no—
499C22×C42—131no—
500C22×C42C2×D1311yescharacteristic
501#389—24no—
502#389—264no—
503#385—138no—
504#385—264no—
505#385—264no—
506C4×C22⋊C4—264no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95—131no—
510C2×#95—131no—
511C2×#95—131no—
512C2×#95—131no—
513C2×#95—131no—
514C2×#95—131no—
515C2×#95—131no—
516C2×#95—131no—
517C2×#95—131no—
518C2×#95—131no—
519C2×#95—131no—
520C2×#95—131no—
521C2×#95C2×D1311yescharacteristic
522C2×#95C2×D1311yescharacteristic
523C22×C13C22×C4⋊C411yescharacteristic
524C22×C13C2×C4×D411yescharacteristic
525C22×C13C2×C4×D411yescharacteristic
526C22×C13C2×C4×D411yescharacteristic
527C22×C13C2×C4×Q811yescharacteristic
528C22×C13#52011yescharacteristic
529C22×C13#52011yescharacteristic
530C22×C13C2×#12011yescharacteristic
531C22×C13C2×#12111yescharacteristic
532C22×C13C2×C22⋊Q811yescharacteristic
533C22×C13#52511yescharacteristic
534C22×C13#52511yescharacteristic
535C22×C13#52511yescharacteristic
536C22×C13C2×#12511yescharacteristic
537C22×C13C2×C4⋊Q811yescharacteristic
538C22×C13#53411yescharacteristic
539C22×C13#53611yescharacteristic
540C22×C13#53911yescharacteristic
541C22×C13#53911yescharacteristic
542C22×C13D4211yescharacteristic
543C22×C13D4211yescharacteristic
544C22×C13#54611yescharacteristic
545C22×C13#54611yescharacteristic
546C22×C13#54711yescharacteristic
547C22×C13#54711yescharacteristic
548C22×C13D4×Q811yescharacteristic
549C22×C13D4×Q811yescharacteristic
550C22×C13D4×Q811yescharacteristic
551C22×C13D4×Q811yescharacteristic
552C22×C13#55211yescharacteristic
553C22×C13#55211yescharacteristic
554C22×C13#55411yescharacteristic
555C22×C13#55411yescharacteristic
556C22×C13#55411yescharacteristic
557C22×C13#55411yescharacteristic
558C2×D13—24no—
559C2×D13—24no—
560C2×D13—24no—
561C2×D13—24no—
562C2×D13—24no—
563C2×D13—24no—
564C2×D13—24no—
565C2×D13—24no—
566C2×D13—24no—
567C2×D13—24no—
568C2×D13—24no—
569C2×D13—24no—
570C2×D13—24no—
571C2×D13—24no—
572C2×D13#38918yescomplemented
573C4×C13—24no—
574C4×C13—24no—
575C4×C13—24no—
576C4×C13—42no—
577C4×C13—42no—
578C4×C13—42no—
579C4×C13—81no—
580Dic13—24no—
581Dic13—24no—
582Dic13—42no—
583Dic13—42no—
584Dic13—42no—
585Dic13—42no—
586Dic13—81no—
587C25—131no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—131no—
591C23×C4—131no—
592C23×C4—131no—
593C23×C4—131no—
594C23×C4—134no—
595C23×C4—134no—
596C23×C4—131no—
597C23×C4—262no—
598C23×C4—262no—
599C23×C4—262no—
600C23×C4—262no—
601C23×C4—262no—
602C23×C4—262no—
603C23×C4—262no—
604C23×C4—262no—
605C23×C4—262no—
606C23×C4—262no—
607C23×C4—262no—
608C23×C4—262no—
609C23×C4—262no—
610C23×C4—262no—
611C23×C4—262no—
612C23×C4—521no—
613C23×C4—521no—
614C23×C4—521no—
615C23×C4—521no—
616C23×C4C22×D1311yescharacteristic
617C23×C4C22×D1311yescharacteristic
618C23×C4C22×D1311yescharacteristic
619C23×C4C22×D1311yescharacteristic
620C23×C4C22×D1311yescharacteristic
621C23×C4C22×D1311yescharacteristic
622C23×C4C22×D1311yescharacteristic
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4—134no—
635C2×C4⋊C4—2632no—
636C2×C4⋊C4—262no—
637C2×C4⋊C4—262no—
638C2×C4⋊C4—262no—
639C2×C4⋊C4—262no—
640C2×C4⋊C4—262no—
641C2×C4⋊C4—262no—
642C2×C4⋊C4—262no—
643C2×C4⋊C4—262no—
644C2×C4⋊C4—262no—
645C2×C4⋊C4—262no—
646C2×C4⋊C4—262no—
647C2×C4⋊C4—262no—
648C2×C4⋊C4—262no—
649C2×C4⋊C4—521no—
650C2×C4⋊C4—521no—
651C2×C4⋊C4—521no—
652C2×C4⋊C4C4×D1314yescomplemented
653C2×C4⋊C4C22⋊D1314yes—
654C2×C22⋊C4—134no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—134no—
657C2×C22⋊C4—134no—
658C2×C22⋊C4—134no—
659C2×C22⋊C4—262no—
660C2×C22⋊C4—262no—
661C2×C22⋊C4—262no—
662C2×C22⋊C4—262no—
663C2×C22⋊C4—262no—
664C2×C22⋊C4—262no—
665C2×C22⋊C4—262no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—41no—
669C2×C42—262no—
670C2×C42—262no—
671C2×C42—521no—
672#95—22no—
673#95—22no—
674#95—134no—
675#95—134no—
676#95—262no—
677#95—262no—
678#95—262no—
679#95—262no—
680#95—262no—
681#95—262no—
682#95—262no—
683#95—262no—
684#95—262no—
685#95—262no—
686#95—521no—
687#95—521no—
688C2×C13C2×#38911yescharacteristic
689C2×C13C4×#12011yescharacteristic
690C2×C13#232211yescharacteristic
691C2×C13D4×C4⋊C411yescharacteristic
692C2×C13D4×C4⋊C411yescharacteristic
693C2×C13#236011yescharacteristic
694C2×C13#236011yescharacteristic
695C2×C13#241011yescharacteristic
696C2×C13#241311yescharacteristic
697C2×C13#243411yescharacteristic
698C2×C13#244911yescharacteristic
699C2×C13#244911yescharacteristic
700C2×C13#247311yescharacteristic
701C2×C13#247311yescharacteristic
702C2×C13#258311yescharacteristic
703D13—28no—
704C24—132no—
705C24—132no—
706C24—132no—
707C24—132no—
708C24—132no—
709C24—132no—
710C24—132no—
711C24—261no—
712C24—261no—
713C24—261no—
714C24—261no—
715C24—261no—
716C24—261no—
717C24—261no—
718C24—261no—
719C24C23×D1311yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—132no—
762C22×C4—132no—
763C22×C4—132no—
764C22×C4—132no—
765C22×C4—132no—
766C22×C4—132no—
767C22×C4—268no—
768C22×C4—268no—
769C22×C4—268no—
770C22×C4—268no—
771C22×C4—268no—
772C22×C4—268no—
773C22×C4—268no—
774C22×C4—268no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—268no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—261no—
807C22×C4—261no—
808C22×C4—268no—
809C22×C4—261no—
810C22×C4—261no—
811C22×C4—261no—
812C22×C4—261no—
813C22×C4—261no—
814C22×C4—261no—
815C22×C4—261no—
816C22×C4—524no—
817C22×C4—524no—
818C22×C4—524no—
819C22×C4—524no—
820C22×C4—524no—
821C22×C4—524no—
822C22×C4—524no—
823C22×C4—524no—
824C22×C4—524no—
825C22×C4—524no—
826C22×C4—524no—
827C22×C4C2×C4×D1312yes—
828C22×C4C2×C4×D1312yes—
829C22×C4C2×C4×D1312yes—
830C22×C4#612712yes—
831C22×C4D4×D1312yes—
832C22×C4D4×D1312yes—
833C22×C4D4×D1312yes—
834C22×C4Q8×D1312yes—
835C22×C4Q8×D1312yes—
836C22×C4C2×C22⋊D1312yes—
837C22×C4C2×C22⋊D1312yes—
838C22×C4C2×C22⋊D1312yes—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—268no—
844C4⋊C4—268no—
845C4⋊C4—268no—
846C4⋊C4—268no—
847C4⋊C4—524no—
848C4⋊C4—524no—
849C22⋊C4—1316no—
850C22⋊C4—268no—
851C22⋊C4—268no—
852C22⋊C4—524no—
853C42—44no—
854C42—524no—
855C13#1404311yescharacteristic, complemented, Sylow
856C23—134no—
857C23—134no—
858C23—134no—
859C23—134no—
860C23—134no—
861C23—134no—
862C23—134no—
863C23—262no—
864C23—262no—
865C23—262no—
866C23—262no—
867C23—262no—
868C23—262no—
869C23—262no—
870C23—262no—
871C23—262no—
872C23—262no—
873C23—262no—
874C23—262no—
875C23—262no—
876C23—262no—
877C23—262no—
878C23—262no—
879C23—262no—
880C23—262no—
881C23—262no—
882C23—262no—
883C23—262no—
884C23—262no—
885C23—262no—
886C23—262no—
887C23—262no—
888C23—262no—
889C23—262no—
890C23—262no—
891C23C22×C4×D1311yescharacteristic
892C23C2×#612711yescharacteristic
893C23C2×D4×D1311yescharacteristic
894C23C2×D4×D1311yescharacteristic
895C23C2×D4×D1311yescharacteristic
896C23#8825111yescharacteristic
897C23C2×Q8×D1311yescharacteristic
898C23C2×Q8×D1311yescharacteristic
899C23#8825411yescharacteristic
900C23#8825411yescharacteristic
901C23#41×D1311yescharacteristic
902C23#41×D1311yescharacteristic
903C23#41×D1311yescharacteristic
904C23#8825611yescharacteristic
905C23C22×C22⋊D1311yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—134no—
953C2×C4—134no—
954C2×C4—2632no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—262no—
958C2×C4—262no—
959C2×C4—262no—
960C2×C4—262no—
961C2×C4—262no—
962C2×C4—262no—
963C2×C4—262no—
964C2×C4—262no—
965C2×C4—262no—
966C2×C4—262no—
967C2×C4—262no—
968C2×C4—262no—
969C2×C4—262no—
970C2×C4—262no—
971C2×C4—262no—
972C2×C4—262no—
973C2×C4—262no—
974C2×C4—262no—
975C2×C4—262no—
976C2×C4—262no—
977C2×C4—262no—
978C2×C4—262no—
979C2×C4—5216no—
980C2×C4—5216no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4—521no—
985C2×C4—521no—
986C2×C4—521no—
987C2×C4—521no—
988C2×C4—521no—
989C2×C4—521no—
990C2×C4—521no—
991C2×C4—521no—
992C2×C4—521no—
993C2×C4—521no—
994C2×C4—521no—
995C2×C4—521no—
996C2×C4—521no—
997C2×C4—521no—
998C2×C4—521no—
999C2×C4—521no—
1000C2×C4—521no—
1001C2×C4—521no—
1002C2×C4—521no—
1003C2×C4—521no—
1004C2×C4C4⋊C4×D1314yescomplemented
1005C2×C4C4×C22⋊D1314yes—
1006C2×C4#8819114yes—
1007C22—138no—
1008C22—264no—
1009C22—264no—
1010C22—264no—
1011C22—264no—
1012C22—264no—
1013C22—264no—
1014C22—264no—
1015C22—264no—
1016C22—264no—
1017C22—264no—
1018C22—264no—
1019C22—264no—
1020C22—264no—
1021C22—264no—
1022C22C2×C4⋊C4×D1311yescharacteristic
1023C22#1171920911yescharacteristic
1024C22#1171921211yescharacteristic
1025C22#1171921611yescharacteristic
1026C22C4×D4×D1311yescharacteristic
1027C22C4×D4×D1311yescharacteristic
1028C22#1171925211yescharacteristic
1029C22#1171925211yescharacteristic
1030C22C4×Q8×D1311yescharacteristic
1031C22#1171927911yescharacteristic
1032C22#1171928411yescharacteristic
1033C22#1171928611yescharacteristic
1034C22D13×#12111yescharacteristic
1035C22#1171931011yescharacteristic
1036C22#1171931411yescharacteristic
1037C22#1171931511yescharacteristic
1038C22D13×C22⋊Q811yescharacteristic
1039C22#1171933611yescharacteristic
1040C22#1171934111yescharacteristic
1041C22#1171934311yescharacteristic
1042C22D13×#12511yescharacteristic
1043C22#1171939511yescharacteristic
1044C22#1171939711yescharacteristic
1045C22#1171939811yescharacteristic
1046C22D13×C4⋊Q811yescharacteristic
1047C22#1171942911yescharacteristic
1048C22#1171943211yescharacteristic
1049C22#1171943211yescharacteristic
1050C22C2×C4×C22⋊D1311yescharacteristic
1051C22C2×#8819111yescharacteristic
1052C22D4×C22⋊D1311yescharacteristic
1053C22Q8×C22⋊D1311yescharacteristic
1054C22Q8×C22⋊D1311yescharacteristic
1055C22#1171953311yescharacteristic
1056C22#1171953411yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—264no—
1065C4—264no—
1066C4—522no—
1067C4—522no—
1068C4—522no—
1069C4—522no—
1070C4—1041no—
1071C2—268no—
1072C2D13×#38911yescharacteristic
1073C2C4×#8819111yescharacteristic
1074C2#1311750011yescharacteristic
1075C2C4⋊C4×C22⋊D1311yescharacteristic
1076C2#1311773711yescharacteristic
1077C2#1311783711yescharacteristic
1078C2#1311783811yescharacteristic
1079C2#1311820711yescharacteristic
1080C2#1311824011yescharacteristic
1081C2#1311847711yescharacteristic
1082C2#1311864211yescharacteristic
1083C2#1311865211yescharacteristic
1084C2#1311897311yescharacteristic
1085C2#1311898311yescharacteristic
1086C2#1312021411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#14043
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718633C2semidirect
7. #13113100C2semidirect
8. #13113099C2semidirect
9. #13113089C2semidirect
10. #13113087C2semidirect
11. #13113069C2semidirect
12. #13113068C2semidirect
15. C2×C13×#389C2semidirect
57. #11718650C4semidirect
106. C2×C13×C4⋊C4C2×C4semidirect
139. C2×#6101C2×C4semidirect
159. #88071C2×C4semidirect
160. #88071C2×C4semidirect
305. #6103C4⋊C4semidirect
315. C2×#389D13semidirect
424. C2×C4×C13C2×C4⋊C4semidirect
474. C2×Dic13C2×C4⋊C4semidirect
572. C2×D13#389semidirect
652. C2×C4⋊C4C4×D13semidirect
855. C13#14043semidirect
1004. C2×C4C4⋊C4×D13semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C2×#117186332
C2×#117186502
C2×C4×#61032
#131131002
#131130992
#131130892
#131130872
#131130692
#131130682
#131130572
C2×C13×#3892
#1404313