Finite Group Databasebeta

← #15784867

Subgroups — #15784867

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C211yesmaximal, characteristic
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718603C211yesmaximal, characteristic
4C2×#11718603C211yesmaximal, characteristic
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic13C211yesmaximal, characteristic
7#13113095C211yesmaximal, characteristic, complemented
8#13113092C211yesmaximal, characteristic, complemented
9#13113079C211yesmaximal, characteristic
10#13113079C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113064C211yesmaximal, characteristic, complemented
15C2×C13×#388C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C13×#388—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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
52#11718637—24no—
53#11718612—24no—
54#11718603—24no—
55#11718603—24no—
56C22⋊C4×Dic13C418yescomplemented
57C4×#6101—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—22no—
70C23×Dic13—22no—
71C23×Dic13C2×C414yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C13×C22⋊C4D414yes—
91C2×C13×C22⋊C4Q814yes—
92C2×C42×C13—22no—
93C2×C42×C13—22no—
94C2×C42×C13—41no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—41no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13C2×C414yes—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—41no—
107C2×#6101—22no—
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—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—41no—
122C2×#6101—41no—
123C2×#6101D414yes—
124C2×#6101D414yes—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—41no—
132C2×C4×Dic13C2×C414yes—
133C2×C4×Dic13C2×C414yes—
134C13×#95—22no—
135C13×#95—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—41no—
147#88071—41no—
148#88071C2×C414yes—
149#88071C2×C414yes—
150#13876—131nomaximal, Sylow
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×D412yes—
165C24×C13C2×Q812yes—
166C24×C13C2411yescharacteristic
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—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×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×Q812yes—
208C22×C4×C13C2×Q812yes—
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—28no—
238C22×Dic13—28no—
239C22×Dic13—28no—
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—44no—
255C22×Dic13—44no—
256C22×Dic13—44no—
257C22×Dic13—44no—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13#4112yes—
267C22×Dic13#4112yes—
268C22×Dic13#4112yes—
269C22×Dic13#4112yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C13×C4⋊C4—44no—
273C13×C22⋊C4—44no—
274C13×C22⋊C4—44no—
275C13×C22⋊C4C4⋊C4116yescomplemented
276C42×C13—44no—
277C22⋊Dic13—28no—
278C22⋊Dic13—44no—
279C22⋊Dic13—44no—
280C4⋊Dic13—44no—
281#6101—28no—
282#6101—28no—
283#6101—44no—
284#6101—44no—
285#6101—44no—
286#6101—44no—
287C4×Dic13—28no—
288C4×Dic13—28no—
289C4×Dic13—44no—
290C2×#388—131no—
291C2×#388D1311yescharacteristic
292C2×#384—131no—
293C2×#380—131no—
294C2×#380—131no—
295C2×C4×C4⋊C4—131no—
296C2×C4×C22⋊C4—131no—
297#1442—131no—
298#1442—131no—
299#1439—131no—
300#1439—131no—
301#1436—131no—
302#1436—131no—
303C4⋊#95—131no—
304C4⋊#95—131no—
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—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
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×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13C2×C4⋊C414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C132−1+411yescharacteristic
354C23×C132−1+411yescharacteristic
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—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×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13C2×C4⋊C414yes—
396C2×C4×C13C2×C4⋊C414yes—
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—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
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—416no—
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—41no—
446C2×Dic13#11714yes—
447C2×Dic13#11714yes—
448C2×Dic13C4×D414yes—
449C2×Dic13C4×D414yes—
450C2×Dic13#12114yes—
451C2×Dic13#12314yes—
452C2×Dic13#12414yes—
453C2×Dic13#12614yes—
454C24×C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4C2×D1311yescharacteristic
463C22×C22⋊C4—131no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4—131no—
466C22×C22⋊C4C2×D1311yescharacteristic
467C22×C22⋊C4C2×D1311yescharacteristic
468C22×C22⋊C4C2×D1311yescharacteristic
469C22×C42—131no—
470C22×C42—131no—
471C22×C42—131no—
472C22×C42C2×D1311yescharacteristic
473#388—24no—
474#388—264no—
475#384—264no—
476#380—264no—
477#380—264no—
478C4×C4⋊C4—264no—
479C4×C22⋊C4—138no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C22×C4⋊C411yescharacteristic
512C22×C13C2×#11711yescharacteristic
513C22×C13C2×#11711yescharacteristic
514C22×C13C2×C4×D411yescharacteristic
515C22×C13C2×C4×D411yescharacteristic
516C22×C13#52011yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13C2×#12111yescharacteristic
519C22×C13C2×#12311yescharacteristic
520C22×C13C2×#12411yescharacteristic
521C22×C13C2×#12611yescharacteristic
522C22×C13#53211yescharacteristic
523C22×C13#53211yescharacteristic
524C22×C13#53311yescharacteristic
525C22×C13#53311yescharacteristic
526C22×C13#54011yescharacteristic
527C22×C13#54111yescharacteristic
528C22×C13#54211yescharacteristic
529C22×C13#54211yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54711yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13D4×Q811yescharacteristic
538C22×C13D4×Q811yescharacteristic
539C22×C13#55011yescharacteristic
540C22×C13#55211yescharacteristic
541C22×C13#55311yescharacteristic
542C22×C13#55411yescharacteristic
543C22×C13#55411yescharacteristic
544C22×C13#55511yescharacteristic
545C22×C13#55611yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—81no—
551C4×C13—81no—
552Dic13—24no—
553Dic13—42no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—81no—
558Dic13—81no—
559Dic13#38818yescomplemented
560C25C22×D1311yescharacteristic
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—134no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—262no—
573C23×C4—262no—
574C23×C4—262no—
575C23×C4—262no—
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—521no—
604C2×C4⋊C4—521no—
605C2×C4⋊C4—521no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—134no—
613C2×C22⋊C4—262no—
614C2×C22⋊C4—262no—
615C2×C22⋊C4—262no—
616C2×C22⋊C4—262no—
617C2×C22⋊C4—262no—
618C2×C22⋊C4—262no—
619C2×C22⋊C4—521no—
620C2×C22⋊C4—521no—
621C2×C22⋊C4Dic2614yes—
622C2×C22⋊C4C4×D1314yes—
623C2×C22⋊C4C22⋊D1314yes—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—41no—
627C2×C42—134no—
628C2×C42—134no—
629C2×C42—262no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—521no—
636#95—22no—
637#95—22no—
638#95—134no—
639#95—134no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—521no—
651#95—521no—
652C2×C13—44no—
653C2×C13#228511yescharacteristic
654C2×C13C2×#38811yescharacteristic
655C2×C13#231411yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13D4×C4⋊C411yescharacteristic
658C2×C13#235211yescharacteristic
659C2×C13#235411yescharacteristic
660C2×C13#242211yescharacteristic
661C2×C13#242311yescharacteristic
662C2×C13#242811yescharacteristic
663C2×C13#242911yescharacteristic
664C2×C13#249111yescharacteristic
665C2×C13#249211yescharacteristic
666C2×C13#249611yescharacteristic
667C2×C13#249711yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Dic2612yes—
681C24C2×C4×D1312yes—
682C24C2×C22⋊D1312yes—
683C24C23×D1311yescharacteristic
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—132no—
732C22×C4—268no—
733C22×C4—268no—
734C22×C4—268no—
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×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—524no—
778C22×C4—524no—
779C22×C4—524no—
780C22×C4—524no—
781C22×C4C2×Dic2612yes—
782C22×C4C2×Dic2612yes—
783C22×C4C2×C4×D1312yes—
784C22×C4C2×C4×D1312yes—
785C22×C4D4×D1312yes—
786C22×C4D4×D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—44no—
790C4⋊C4—268no—
791C4⋊C4—268no—
792C4⋊C4—524no—
793C4⋊C4—524no—
794C4⋊C4—524no—
795C4⋊C4—524no—
796C4⋊C4—524no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—268no—
800C22⋊C4—524no—
801C22⋊C4—524no—
802C22⋊C4#6101116yescomplemented
803C42—44no—
804C42—268no—
805C42—268no—
806C42—524no—
807C13#1387611yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×#610114yes—
843C23C22×Dic2611yescharacteristic
844C23C22×C4×D1311yescharacteristic
845C23C2×D4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23#8825111yescharacteristic
848C23#8825111yescharacteristic
849C23#41×D1311yescharacteristic
850C23#41×D1311yescharacteristic
851C23#41×D1311yescharacteristic
852C23#41×D1311yescharacteristic
853C23#41×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#8825711yescharacteristic
856C23#8825711yescharacteristic
857C23C22×C22⋊D1311yescharacteristic
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—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—134no—
899C2×C4—134no—
900C2×C4—134no—
901C2×C4—134no—
902C2×C4—134no—
903C2×C4—134no—
904C2×C4—134no—
905C2×C4—134no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—5216no—
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—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4C2×#610114yes—
956C2×C4C2×#610114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#1171922211yescharacteristic
973C22#1171922211yescharacteristic
974C22D13×#11711yescharacteristic
975C22D13×#11711yescharacteristic
976C22D4×Dic2611yescharacteristic
977C22D4×Dic2611yescharacteristic
978C22#1171924411yescharacteristic
979C22#1171924411yescharacteristic
980C22C4×D4×D1311yescharacteristic
981C22C4×D4×D1311yescharacteristic
982C22#1171925111yescharacteristic
983C22#1171925111yescharacteristic
984C22#1171930411yescharacteristic
985C22D13×#12111yescharacteristic
986C22#1171931511yescharacteristic
987C22#1171932011yescharacteristic
988C22D13×#12311yescharacteristic
989C22#1171936011yescharacteristic
990C22#1171936611yescharacteristic
991C22#1171936711yescharacteristic
992C22#1171937411yescharacteristic
993C22#1171937511yescharacteristic
994C22D13×#12411yescharacteristic
995C22#1171938211yescharacteristic
996C22#1171940611yescharacteristic
997C22#1171940711yescharacteristic
998C22D13×#12611yescharacteristic
999C22#1171941311yescharacteristic
1000C22C22×#610111yescharacteristic
1001C22D4×C22⋊D1311yescharacteristic
1002C22D4×C22⋊D1311yescharacteristic
1003C22#1171952911yescharacteristic
1004C22#1171952911yescharacteristic
1005C22#1171953711yescharacteristic
1006C22#1171953711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—138no—
1014C4—264no—
1015C4—522no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—1041no—
1020C4—1041no—
1021C2—44no—
1022C2#1311723911yescharacteristic
1023C2D13×#38811yescharacteristic
1024C2#1311744011yescharacteristic
1025C2D4×#610111yescharacteristic
1026C2D4×#610111yescharacteristic
1027C2#1311776411yescharacteristic
1028C2#1311778211yescharacteristic
1029C2#1311834711yescharacteristic
1030C2#1311835811yescharacteristic
1031C2#1311842111yescharacteristic
1032C2#1311843211yescharacteristic
1033C2#1311919611yescharacteristic
1034C2#1311920711yescharacteristic
1035C2#1311925511yescharacteristic
1036C2#1311926611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
5. C2×C4×#6101C2semidirect
7. #13113095C2semidirect
8. #13113092C2semidirect
11. #13113069C2semidirect
12. #13113067C2semidirect
13. #13113064C2semidirect
14. #13113064C2semidirect
56. C22⋊C4×Dic13C4semidirect
275. C13×C22⋊C4C4⋊C4semidirect
559. Dic13#388semidirect
802. C22⋊C4#6101semidirect
807. C13#13876semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117186372
C2×#117186032
C2×C4×#61012
C2×C22⋊C4×Dic132
#131130952
#131130922
#131130792
#131130692
#131130672
#131130642
C2×C13×#3882
#1387613