Finite Group Databasebeta

← #15794205

Subgroups — #15794205

Order 3328.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718606C211yesmaximal, characteristic
2C2×#11718612C211yesmaximal, characteristic
3C2×#11718605C211yesmaximal, characteristic
4C2×#11718316C211yesmaximal, characteristic, complemented
5C2×C42×Dic13C211yesmaximal, characteristic, complemented
6#13113073C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113071C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718612—24no—
52#11718606—24no—
53#11718605C418yescomplemented
54C42×Dic13—24no—
55#11718316—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4C2×C414yes—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13C2×C414yes—
94C2×C22⋊Dic13C2×C414yes—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101C2×C414yes—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13C2×C414yes—
120C2×C4×Dic13D414yes—
121C2×C4×Dic13D414yes—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071C2×C414yes—
139#88071C2×C414yes—
140#14701—131nomaximal, Sylow
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13C22×C412yes—
156C24×C13C2411yescharacteristic
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
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×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13#4112yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
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×Dic13C22×C412yes—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C2×D412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13C2×D412yes—
249C22×Dic13#4112yes—
250C22×Dic13#4112yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C42×C13—28no—
259C22⋊Dic13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C4⋊Dic13—44no—
264#6101—28no—
265#6101—44no—
266C4×Dic13—28no—
267C4×Dic13—28no—
268C4×Dic13—28no—
269C4×Dic13—28no—
270C4×Dic13—28no—
271C4×Dic13—28no—
272C2×#388—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×#387—131no—
276C2×C43—131no—
277#1437—131no—
278#1437—131no—
279#1437—131no—
280#1437D1311yescharacteristic
281#1436—131no—
282#1436—131no—
283#1436—131no—
284#1436—131no—
285#1434—131no—
286#1434—131no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13C23×C411yescharacteristic
323C23×C13C22×D411yescharacteristic
324C23×C13C22×D411yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13C4×D414yes—
377C2×C4×C13#12414yes—
378C2×C4×C13#12614yes—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13#11714yes—
432C2×Dic13C4×D414yes—
433C2×Dic13#12114yes—
434C2×Dic13#12314yes—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C4⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C22⋊C4C2×D1311yescharacteristic
444C22×C22⋊C4C2×D1311yescharacteristic
445C22×C42—131no—
446C22×C42—131no—
447C22×C42—131no—
448C22×C42—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42C2×D1311yescharacteristic
452#388—138no—
453#388—264no—
454#388—264no—
455#387—264no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95C2×D1311yescharacteristic
472C2×#95C2×D1311yescharacteristic
473C2×#95C2×D1311yescharacteristic
474C43—264no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—81no—
483C22×C13—81no—
484C22×C13—81no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13—81no—
488C22×C13—81no—
489C22×C13—81no—
490C22×C13C2×#11711yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13C4×#4111yescharacteristic
496C22×C13C4×#4111yescharacteristic
497C22×C13C2×#12111yescharacteristic
498C22×C13C2×#12311yescharacteristic
499C22×C13#52511yescharacteristic
500C22×C13#52511yescharacteristic
501C22×C13#52511yescharacteristic
502C22×C13#52511yescharacteristic
503C22×C13C2×#12411yescharacteristic
504C22×C13C2×#12611yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#52911yescharacteristic
509C22×C13#52911yescharacteristic
510C22×C13#52911yescharacteristic
511C22×C13#52911yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#52911yescharacteristic
515C22×C13#52911yescharacteristic
516C22×C13#52911yescharacteristic
517C22×C13#52911yescharacteristic
518C22×C13#52911yescharacteristic
519C22×C13#52911yescharacteristic
520C22×C13#52911yescharacteristic
521C22×C13#53211yescharacteristic
522C22×C13#53211yescharacteristic
523C22×C13#53211yescharacteristic
524C22×C13#53211yescharacteristic
525C4×C13—24no—
526C4×C13—24no—
527C4×C13—24no—
528C4×C13—42no—
529C4×C13—81no—
530C4×C13—81no—
531Dic13—24no—
532Dic13—24no—
533Dic13—24no—
534Dic13—24no—
535Dic13—42no—
536Dic13—42no—
537Dic13—81no—
538Dic13—81no—
539C25C22×D1311yescharacteristic
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C2×C4⋊C4—134no—
555C2×C4⋊C4—262no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4C4×D1314yes—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—134no—
588C2×C42—134no—
589C2×C42—134no—
590C2×C42—262no—
591C2×C42—262no—
592C2×C42—262no—
593C2×C42—262no—
594C2×C42—262no—
595C2×C42—262no—
596C2×C42—262no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—134no—
609#95—134no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623C2×C13—82no—
624C2×C13#229011yescharacteristic
625C2×C13#229311yescharacteristic
626C2×C13#229811yescharacteristic
627C2×C13C4×#12111yescharacteristic
628C2×C13C4×#12311yescharacteristic
629C2×C13C4×#12411yescharacteristic
630C2×C13C4×#12611yescharacteristic
631C2×C13#285011yescharacteristic
632C2×C13#285211yescharacteristic
633C2×C13#285311yescharacteristic
634C2×C13#285411yescharacteristic
635C2×C13#286011yescharacteristic
636C2×C13#286111yescharacteristic
637C2×C13#286511yescharacteristic
638C2×C13#286611yescharacteristic
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D1312yes—
654C24C23×D1311yescharacteristic
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4C2×C4×D1312yes—
744C22×C4C2×C4×D1312yes—
745C22×C4#612712yes—
746C22×C4#612712yes—
747C22×C4D4×D1312yes—
748C22×C4D4×D1312yes—
749C22×C4#612912yes—
750C22×C4#612912yes—
751C22×C4#612912yes—
752C22×C4#612912yes—
753C4⋊C4—268no—
754C4⋊C4—524no—
755C4⋊C4—524no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—268no—
760C22⋊C4—268no—
761C22⋊C4—524no—
762C22⋊C4—524no—
763C42—28no—
764C42—268no—
765C42—268no—
766C42—268no—
767C42—268no—
768C42—268no—
769C42—268no—
770C13#1470111yescharacteristic, complemented, Sylow
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C22×C4×D1311yescharacteristic
807C23C2×#612711yescharacteristic
808C23C2×#612711yescharacteristic
809C23C2×D4×D1311yescharacteristic
810C23C2×D4×D1311yescharacteristic
811C23C2×#612911yescharacteristic
812C23C2×#612911yescharacteristic
813C23C2×#612911yescharacteristic
814C23C2×#612911yescharacteristic
815C23#41×D1311yescharacteristic
816C23#41×D1311yescharacteristic
817C23#41×D1311yescharacteristic
818C23#41×D1311yescharacteristic
819C23#41×D1311yescharacteristic
820C23#41×D1311yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—134no—
861C2×C4—134no—
862C2×C4—134no—
863C2×C4—134no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4#8813314yes—
917C2×C4#8813514yes—
918C2×C4#8813914yes—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22C4×#612711yescharacteristic
935C22C2×#8813311yescharacteristic
936C22C2×#8813511yescharacteristic
937C22C2×#8813911yescharacteristic
938C22D13×#11711yescharacteristic
939C22#1171923311yescharacteristic
940C22#1171923311yescharacteristic
941C22C4×#612911yescharacteristic
942C22C4×#612911yescharacteristic
943C22C4×#612911yescharacteristic
944C22#1171924311yescharacteristic
945C22#1171924311yescharacteristic
946C22C4×D4×D1311yescharacteristic
947C22#1171925211yescharacteristic
948C22#1171925211yescharacteristic
949C22#1171925311yescharacteristic
950C22#1171926211yescharacteristic
951C22#1171926211yescharacteristic
952C22#1171926211yescharacteristic
953C22#1171929111yescharacteristic
954C22#1171930111yescharacteristic
955C22#1171930511yescharacteristic
956C22#1171930511yescharacteristic
957C22#1171930511yescharacteristic
958C22D13×#12111yescharacteristic
959C22#1171931111yescharacteristic
960C22#1171935411yescharacteristic
961C22#1171935411yescharacteristic
962C22D13×#12311yescharacteristic
963C22#1171937311yescharacteristic
964C22#1171938511yescharacteristic
965C22#1171938511yescharacteristic
966C22#1171941111yescharacteristic
967C22#1171941111yescharacteristic
968C22#1171942111yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—264no—
976C4—264no—
977C4—264no—
978C4—264no—
979C4—522no—
980C4—522no—
981C4—1041no—
982C4—1041no—
983C2—82no—
984C2#1311728211yescharacteristic
985C2#1311729611yescharacteristic
986C2#1311733011yescharacteristic
987C2#1311735211yescharacteristic
988C2#1311736111yescharacteristic
989C2C4×#8813911yescharacteristic
990C2C4×#8813311yescharacteristic
991C2#1312313311yescharacteristic
992C2#1312314911yescharacteristic
993C2#1312315611yescharacteristic
994C2#1312316311yescharacteristic
995C2#1312320011yescharacteristic
996C2#1312320711yescharacteristic
997C2#1312322411yescharacteristic
998C2#1312322711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#14701
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#11718316C2semidirect
5. C2×C42×Dic13C2semidirect
9. #13113071C2semidirect
10. #13113070C2semidirect
11. #13113069C2semidirect
12. #13113067C2semidirect
13. #13113061C2semidirect
14. #13113060C2semidirect
53. #11718605C4semidirect
770. C13#14701semidirect

Maximal subgroups

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

subgroupindex
C2×#117186062
C2×#117186122
C2×#117186052
C2×#117183162
C2×C42×Dic132
#131130732
#131130712
#131130702
#131130692
#131130672
#131130612
#131130602
C13×#14372
#1470113