Finite Group Databasebeta

← #15786223

Subgroups — #15786223

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C211yesmaximal, characteristic, complemented
2C2×#11718594C211yesmaximal, characteristic, complemented
3C2×#11718871C211yesmaximal, characteristic
4C2×#11718873C211yesmaximal, characteristic
5#13113092C211yesmaximal, characteristic, complemented
6#13113090C211yesmaximal, characteristic, complemented
7#13113079C211yesmaximal, characteristic
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113069C211yesmaximal, characteristic, complemented
13#13113069C211yesmaximal, characteristic, complemented
14C4×#88071C211yesmaximal, characteristic, complemented
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C4×C13×C22⋊C4—24no—
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#11718594—24no—
55#11718308—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—22no—
83C2×C13×C22⋊C4Q814yes—
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—41no—
89C2×C42×C13—41no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13—41no—
100C2×C22⋊Dic13C2×C414yes—
101C2×C22⋊Dic13C2×C414yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13—41no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×#6101C2×C414yes—
119C2×#6101C2×C414yes—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13—41no—
126C13×#95—22no—
127C13×#95D414yes—
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#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071C2×C414yes—
142#88071C2×C414yes—
143#88071D414yes—
144#14011—131nomaximal, Sylow
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×C13—21no—
156C24×C13—21no—
157C24×C13C22×C412yes—
158C24×C13C2×Q812yes—
159C24×C13#4112yes—
160C24×C13C2411yescharacteristic
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×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—28no—
192C22×C4×C13—28no—
193C22×C4×C13—44no—
194C22×C4×C13—44no—
195C22×C4×C13—44no—
196C22×C4×C13—44no—
197C22×C4×C13—44no—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×Q812yes—
205C22×C4×C13C2×Q812yes—
206C22×C4×C13#4112yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
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×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13#4112yes—
265C22×Dic13#4112yes—
266C13×C22⋊C4—28no—
267C13×C22⋊C4—28no—
268C42×C13—44no—
269C42×C13—44no—
270C22⋊Dic13—28no—
271C22⋊Dic13—44no—
272C22⋊Dic13—44no—
273C22⋊Dic13—44no—
274C4⋊Dic13—44no—
275C4⋊Dic13—44no—
276#6101—28no—
277#6101—28no—
278#6101—44no—
279#6101—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#389—131no—
283C2×#387—131no—
284C2×#385—131no—
285C2×#380—131no—
286C2×C4×C22⋊C4D1311yescharacteristic
287#1442—131no—
288#1441—131no—
289#1439—131no—
290#1439—131no—
291#1437—131no—
292#1437—131no—
293#1436—131no—
294#1436—131no—
295#1436—131no—
296C4×#95—131no—
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—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
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×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13C4×Q814yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C132−1+411yescharacteristic
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—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—416no—
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×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13C4×D414yes—
388C2×C4×C13C4×D414yes—
389C2×C4×C13C22⋊Q814yes—
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—22no—
410C2×Dic13—22no—
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—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13#11714yes—
446C24×C4C2×D1311yescharacteristic
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4C2×D1311yescharacteristic
458C22×C22⋊C4C2×D1311yescharacteristic
459C22×C42—131no—
460C22×C42—131no—
461C22×C42C2×D1311yescharacteristic
462C22×C42C2×D1311yescharacteristic
463#389—264no—
464#387—264no—
465#385—138no—
466#380—264no—
467C4×C22⋊C4—24no—
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×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C2×#11711yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C2×C4×D411yescharacteristic
504C22×C13C2×C4×Q811yescharacteristic
505C22×C13C4×#4111yescharacteristic
506C22×C13#51811yescharacteristic
507C22×C13#52011yescharacteristic
508C22×C13C2×C22⋊Q811yescharacteristic
509C22×C13#52511yescharacteristic
510C22×C13#52911yescharacteristic
511C22×C13#52911yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#53211yescharacteristic
514C22×C13#53211yescharacteristic
515C22×C13#53311yescharacteristic
516C22×C13#53811yescharacteristic
517C22×C13#53911yescharacteristic
518C22×C13#54011yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13D4211yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#54811yescharacteristic
526C22×C13D4×Q811yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55211yescharacteristic
530C22×C13#55311yescharacteristic
531C22×C13#55311yescharacteristic
532C22×C13#55311yescharacteristic
533C22×C13#55411yescharacteristic
534C22×C13#55411yescharacteristic
535C22×C13#55411yescharacteristic
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—24no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542Dic13—24no—
543Dic13—42no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—81no—
549Dic13—81no—
550C25C22×D1311yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4C4×D1314yes—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—521no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—134no—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—262no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—521no—
604C2×C22⋊C4—521no—
605C2×C22⋊C4—521no—
606C2×C22⋊C4—521no—
607C2×C22⋊C4Dic2614yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—134no—
622#95—134no—
623#95—134no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95C22⋊D1314yes—
638C2×C13—44no—
639C2×C13#229311yescharacteristic
640C2×C13C4×C22⋊Q811yescharacteristic
641C2×C13#233511yescharacteristic
642C2×C13#234511yescharacteristic
643C2×C13#235211yescharacteristic
644C2×C13#235811yescharacteristic
645C2×C13#236011yescharacteristic
646C2×C13#245011yescharacteristic
647C2×C13#245211yescharacteristic
648C2×C13#246011yescharacteristic
649C2×C13#246411yescharacteristic
650C2×C13#252211yescharacteristic
651C2×C13#253011yescharacteristic
652C2×C13#255611yescharacteristic
653C2×C13#255911yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×Dic2612yes—
667C24C2×C4×D1312yes—
668C24#612712yes—
669C24C23×D1311yescharacteristic
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—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—21no—
699C22×C4—21no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
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×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4C2×Dic2612yes—
764C22×C4C2×Dic2612yes—
765C22×C4C2×C4×D1312yes—
766C22×C4C2×C4×D1312yes—
767C22×C4#612712yes—
768C22×C4#612712yes—
769C22×C4#612712yes—
770C22×C4D4×D1312yes—
771C22×C4#612912yes—
772C22×C4C2×C22⋊D1312yes—
773C22×C4C2×C22⋊D1312yes—
774C22×C4C2×C22⋊D1312yes—
775C4⋊C4—268no—
776C4⋊C4—268no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—268no—
784C22⋊C4—524no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C42—44no—
788C42—44no—
789C42—524no—
790C42—524no—
791C13#1401111yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4×Dic2614yes—
827C23C22×Dic2611yescharacteristic
828C23C22×C4×D1311yescharacteristic
829C23C2×#612711yescharacteristic
830C23C2×#612711yescharacteristic
831C23C2×#612711yescharacteristic
832C23C2×#612711yescharacteristic
833C23C2×D4×D1311yescharacteristic
834C23C2×#612911yescharacteristic
835C23#8825111yescharacteristic
836C23#8825111yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
841C23C22×C22⋊D1311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—134no—
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—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
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×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4#8813514yes—
939C2×C4#8817814yes—
940C2×C4C4×C22⋊D1314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×Dic2611yescharacteristic
957C22#1171917511yescharacteristic
958C22C4×#612711yescharacteristic
959C22#1171918411yescharacteristic
960C22C2×#8813511yescharacteristic
961C22#1171919111yescharacteristic
962C22#1171919511yescharacteristic
963C22#1171920011yescharacteristic
964C22D13×#11711yescharacteristic
965C22#1171922811yescharacteristic
966C22#1171923411yescharacteristic
967C22#1171923511yescharacteristic
968C22D4×Dic2611yescharacteristic
969C22#1171924311yescharacteristic
970C22#1171924311yescharacteristic
971C22#1171924411yescharacteristic
972C22#1171924411yescharacteristic
973C22#1171924511yescharacteristic
974C22#1171924511yescharacteristic
975C22#1171924611yescharacteristic
976C22#1171924811yescharacteristic
977C22#1171925311yescharacteristic
978C22#1171925311yescharacteristic
979C22#1171925511yescharacteristic
980C22#1171926511yescharacteristic
981C22#1171926611yescharacteristic
982C22#1171926711yescharacteristic
983C22#1171926911yescharacteristic
984C22C2×#8817811yescharacteristic
985C22C2×C4×C22⋊D1311yescharacteristic
986C22#1171949611yescharacteristic
987C22D4×C22⋊D1311yescharacteristic
988C22#1171951111yescharacteristic
989C22#1171953411yescharacteristic
990C22#1171953611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—264no—
998C4—522no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—1041no—
1004C4—1041no—
1005C2—44no—
1006C2#1311729911yescharacteristic
1007C2C4×#8817811yescharacteristic
1008C2#1311762611yescharacteristic
1009C2#1311771411yescharacteristic
1010C2#1311776611yescharacteristic
1011C2#1311781511yescharacteristic
1012C2#1311783911yescharacteristic
1013C2#1311865411yescharacteristic
1014C2#1311868011yescharacteristic
1015C2#1311878211yescharacteristic
1016C2#1311883611yescharacteristic
1017C2#1311955411yescharacteristic
1018C2#1311966811yescharacteristic
1019C2#1311992011yescharacteristic
1020C2#1311996511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#14011
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718308C2semidirect
2. C2×#11718594C2semidirect
5. #13113092C2semidirect
6. #13113090C2semidirect
11. #13113070C2semidirect
12. #13113069C2semidirect
13. #13113069C2semidirect
14. C4×#88071C2semidirect
37. #11718871C4semidirect
791. C13#14011semidirect

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×#117185942
C2×#117188712
C2×#117188732
#131130922
#131130902
#131130792
#131130732
#131130702
#131130692
C4×#880712
C2×C4×C13×C22⋊C42
#1401113