Finite Group Databasebeta

← #15790547

Subgroups — #15790547

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718605C211yesmaximal, characteristic
2C2×#11718316C211yesmaximal, characteristic, complemented
3C2×#11718871C211yesmaximal, characteristic
4C2×#11718873C211yesmaximal, characteristic
5#13113100C211yesmaximal, characteristic, complemented
6#13113096C211yesmaximal, characteristic, complemented
7#13113091C211yesmaximal, characteristic, complemented
8#13113090C211yesmaximal, characteristic, complemented
9#13113083C211yesmaximal, characteristic
10#13113079C211yesmaximal, characteristic
11#13113073C211yesmaximal, characteristic
12#13113070C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113064C211yesmaximal, characteristic, complemented
15C2×C13×#381C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#381—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36#11718873—24no—
37#11718871C418yescomplemented
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
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718605—24no—
55#11718316—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—41no—
62C23×C4×C13—41no—
63C23×C4×C13C2×C414yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—41no—
83C2×C13×C22⋊C4—41no—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13—41no—
91C2×C22⋊Dic13—41no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13C2×C414yes—
94C2×C22⋊Dic13C2×C414yes—
95C2×C22⋊Dic13D414yes—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13—41no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101—41no—
112C2×#6101C2×C414yes—
113C2×#6101C2×C414yes—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95D414yes—
124#88071—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—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071C2×C414yes—
139#88071C2×C414yes—
140#14381—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×C13C22×C412yes—
154C24×C13C2×D412yes—
155C24×C13#4112yes—
156C24×C13C2411yescharacteristic
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—28no—
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—28no—
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—44no—
196C22×C4×C13—44no—
197C22×C4×C13—44no—
198C22×C4×C13—44no—
199C22×C4×C13—44no—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13#4112yes—
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×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×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13#4112yes—
261C22×Dic13#4112yes—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C22⋊Dic13—28no—
265C22⋊Dic13—28no—
266C22⋊Dic13—44no—
267C22⋊Dic13—44no—
268C4⋊Dic13—44no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—44no—
272#6101—44no—
273#6101—44no—
274C4×Dic13—44no—
275C4×Dic13—44no—
276C2×#388—131no—
277C2×#387—131no—
278C2×#385—131no—
279C2×#381D1311yescharacteristic
280C2×#380—131no—
281#1444—131no—
282#1443—131no—
283#1442—131no—
284#1441—131no—
285#1440—131no—
286#1439—131no—
287#1437—131no—
288#1436—131no—
289#1436—131no—
290C4⋊#95—131no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
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×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13C4×D414yes—
326C23×C13C23×C411yescharacteristic
327C23×C13C22×D411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13H(5,𝔽2)11yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C132−1+411yescharacteristic
338C23×C132−1+411yescharacteristic
339C23×C132−1+411yescharacteristic
340C23×C132−1+411yescharacteristic
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—416no—
357C2×C4×C13—41no—
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×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13C4×D414yes—
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—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
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—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13#11714yes—
440C24×C4C2×D1311yescharacteristic
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—131no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4C2×D1311yescharacteristic
452C22×C22⋊C4C2×D1311yescharacteristic
453C22×C42—131no—
454C22×C42—131no—
455#388—264no—
456#387—264no—
457#385—138no—
458#381—24no—
459#380—264no—
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×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95C2×D1311yescharacteristic
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C22×C13—24no—
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13C2×#11711yescharacteristic
496C22×C13C2×C4×D411yescharacteristic
497C22×C13C2×C4×D411yescharacteristic
498C22×C13#51811yescharacteristic
499C22×C13#51911yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#53411yescharacteristic
503C22×C13#53611yescharacteristic
504C22×C13#53611yescharacteristic
505C22×C13#53711yescharacteristic
506C22×C13#53811yescharacteristic
507C22×C13#53811yescharacteristic
508C22×C13#53911yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#53911yescharacteristic
511C22×C13#53911yescharacteristic
512C22×C13#54111yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13D4211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#55011yescharacteristic
521C22×C13#55111yescharacteristic
522C22×C13#55211yescharacteristic
523C22×C13#55211yescharacteristic
524C22×C13#55511yescharacteristic
525C22×C13#55611yescharacteristic
526C22×C13#56211yescharacteristic
527C22×C13#56211yescharacteristic
528C22×C13#56311yescharacteristic
529C22×C13#56311yescharacteristic
530C4×C13—24no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—81no—
535C4×C13—81no—
536Dic13—24no—
537Dic13—42no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—81no—
543Dic13—81no—
544C25C22×D1311yescharacteristic
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4C4×D1314yes—
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C4⋊C4—262no—
573C2×C4⋊C4—262no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—521no—
577C2×C4⋊C4—521no—
578C2×C4⋊C4—521no—
579C2×C4⋊C4—521no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4—521no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—262no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—521no—
599C2×C22⋊C4—521no—
600C2×C22⋊C4—521no—
601C2×C22⋊C4—521no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—521no—
606C2×C42—521no—
607C2×C42—521no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—134no—
612#95—134no—
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—521no—
623#95—521no—
624#95—521no—
625#95—521no—
626#95—521no—
627#95C22⋊D1314yes—
628C2×C13—44no—
629C2×C13#231811yescharacteristic
630C2×C13#232211yescharacteristic
631C2×C13#232311yescharacteristic
632C2×C13#234411yescharacteristic
633C2×C13#235411yescharacteristic
634C2×C13#235811yescharacteristic
635C2×C13#237811yescharacteristic
636C2×C13#268011yescharacteristic
637C2×C13#268211yescharacteristic
638C2×C13#268611yescharacteristic
639C2×C13#268911yescharacteristic
640C2×C13#269411yescharacteristic
641C2×C13#269511yescharacteristic
642C2×C13#274411yescharacteristic
643C2×C13#274511yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1312yes—
657C24D4×D1312yes—
658C24#612912yes—
659C24C23×D1311yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—28no—
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—28no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
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×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4C2×C4×D1312yes—
760C22×C4C2×C4×D1312yes—
761C22×C4#612712yes—
762C22×C4C2×C22⋊D1312yes—
763C22×C4C2×C22⋊D1312yes—
764C22×C4C2×C22⋊D1312yes—
765C4⋊C4—268no—
766C4⋊C4—524no—
767C4⋊C4—524no—
768C4⋊C4—524no—
769C4⋊C4—524no—
770C4⋊C4—524no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—268no—
774C22⋊C4—268no—
775C22⋊C4—524no—
776C22⋊C4—524no—
777C42—524no—
778C42—524no—
779C13#1438111yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23#8813514yes—
815C23C22×C4×D1311yescharacteristic
816C23C2×#612711yescharacteristic
817C23C2×D4×D1311yescharacteristic
818C23C2×#612911yescharacteristic
819C23#8825111yescharacteristic
820C23#8825111yescharacteristic
821C23#41×D1311yescharacteristic
822C23#41×D1311yescharacteristic
823C23#8825611yescharacteristic
824C23#8825611yescharacteristic
825C23#8825711yescharacteristic
826C23#8825711yescharacteristic
827C23#8825711yescharacteristic
828C23#8825711yescharacteristic
829C23C22×C22⋊D1311yescharacteristic
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—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—416no—
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—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—134no—
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—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4C4×C22⋊D1314yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×#8813511yescharacteristic
945C22#1171919111yescharacteristic
946C22#1171919511yescharacteristic
947C22#1171920011yescharacteristic
948C22#1171922111yescharacteristic
949C22#1171922311yescharacteristic
950C22D13×#11711yescharacteristic
951C22#1171922811yescharacteristic
952C22#1171922811yescharacteristic
953C22#1171923711yescharacteristic
954C22#1171923811yescharacteristic
955C22#1171923911yescharacteristic
956C22#1171935311yescharacteristic
957C22#1171935511yescharacteristic
958C22#1171935511yescharacteristic
959C22#1171935611yescharacteristic
960C22#1171935611yescharacteristic
961C22#1171935811yescharacteristic
962C22#1171936011yescharacteristic
963C22#1171936011yescharacteristic
964C22#1171936211yescharacteristic
965C22#1171936211yescharacteristic
966C22#1171936511yescharacteristic
967C22#1171936511yescharacteristic
968C22#1171937011yescharacteristic
969C22#1171937011yescharacteristic
970C22#1171937211yescharacteristic
971C22#1171937211yescharacteristic
972C22C2×C4×C22⋊D1311yescharacteristic
973C22D4×C22⋊D1311yescharacteristic
974C22#1171951111yescharacteristic
975C22#1171952911yescharacteristic
976C22#1171953011yescharacteristic
977C22#1171953811yescharacteristic
978C22#1171953911yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—264no—
986C4—522no—
987C4—522no—
988C4—522no—
989C4—522no—
990C4—522no—
991C4—1041no—
992C4—1041no—
993C2—44no—
994C2#1311746511yescharacteristic
995C2#1311750211yescharacteristic
996C2#1311751811yescharacteristic
997C2#1311770011yescharacteristic
998C2#1311778611yescharacteristic
999C2#1311781511yescharacteristic
1000C2#1311800411yescharacteristic
1001C2#1312117311yescharacteristic
1002C2#1312120111yescharacteristic
1003C2#1312124211yescharacteristic
1004C2#1312128711yescharacteristic
1005C2#1312135211yescharacteristic
1006C2#1312136711yescharacteristic
1007C2#1312199011yescharacteristic
1008C2#1312200511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#381C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#381D13
hypocenterC13#14381
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C2×#11718316C2semidirect
5. #13113100C2semidirect
6. #13113096C2semidirect
7. #13113091C2semidirect
8. #13113090C2semidirect
12. #13113070C2semidirect
13. #13113067C2semidirect
14. #13113064C2semidirect
37. #11718871C4semidirect
779. C13#14381semidirect

Maximal subgroups

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

subgroupindex
C2×#117186052
C2×#117183162
C2×#117188712
C2×#117188732
#131131002
#131130962
#131130912
#131130902
#131130832
#131130792
#131130732
#131130702
#131130672
#131130642
C2×C13×#3812
#1438113