Finite Group Databasebeta

← #15784870

Subgroups — #15784870

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C212yesmaximal
2C2×#11718596C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4C2×#11718873C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6#13113093C212yesmaximal, complemented
7#13113081C212yesmaximal
8#13113070C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113066C211yesmaximal, characteristic, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2212yes—
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C4×C13×C22⋊C4C418yescomplemented
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29#11718873—24no—
30#11718873—24no—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718612—28no—
39#11718596—24no—
40C4×C4⋊Dic13—24no—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13C2×C414yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×Dic13C2312yes—
56C23×Dic13C2312yes—
57C23×Dic13C2312yes—
58C23×Dic13C2312yes—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4C2×C414yes—
62C2×C13×C22⋊C4C2×C414yes—
63C2×C13×C22⋊C4D414yes—
64C2×C13×C22⋊C4Q814yes—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13C2×C414yes—
70C2×C42×C13C2×C414yes—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—42no—
76C2×C22⋊Dic13—42no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—24no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—24no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—42no—
92C2×C4⋊Dic13—42no—
93C2×C4⋊Dic13D414yes—
94C2×C4⋊Dic13D414yes—
95C2×C4×Dic13—24no—
96C2×C4×Dic13—24no—
97C2×C4×Dic13—42no—
98C13×#95C2×C414yes—
99C13×#95C2×C414yes—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—24no—
105#88071—24no—
106#88071—42no—
107#13876—131nomaximal, Sylow
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13C22×C412yes—
121C24×C13C2×D412yes—
122C24×C13C2×Q812yes—
123C24×C13C2411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—28no—
149C22×C4×C13—28no—
150C22×C4×C13—28no—
151C22×C4×C13—44no—
152C22×C4×C13—44no—
153C22×C4×C13—44no—
154C22×C4×C13—44no—
155C22×C4×C13C22×C412yes—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C22×C412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×Q812yes—
166C22×C4×C13C2×Q812yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×C4×C13#4112yes—
171C22×C4×C13#4112yes—
172C22×C4×C13#4112yes—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13C2×D414yes—
200C22×Dic13C2×D414yes—
201C13×C22⋊C4—28no—
202C13×C22⋊C4C4⋊C4116yescomplemented
203C42×C13—28no—
204C42×C13—28no—
205C22⋊Dic13—48no—
206C22⋊Dic13—48no—
207C4⋊Dic13—28no—
208C4⋊Dic13—28no—
209C4⋊Dic13—48no—
210C4⋊Dic13—48no—
211C4⋊Dic13—44no—
212C4⋊Dic13—44no—
213C4×Dic13—48no—
214C2×#388—132no—
215C2×#384—131no—
216C2×#380—131no—
217C2×#380—131no—
218C2×C4×C4⋊C4—131no—
219C2×C4×C22⋊C4D1311yescharacteristic
220#1442—132no—
221#1439—132no—
222#1436—132no—
223C4⋊#95—131no—
224C4⋊#95—131no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13C2×C4⋊C414yes—
260C23×C13C23×C411yescharacteristic
261C23×C13C22×D411yescharacteristic
262C23×C13C22×D411yescharacteristic
263C23×C13C22×D411yescharacteristic
264C23×C13C22×Q811yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4111yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13H(5,𝔽2)11yescharacteristic
272C23×C13H(5,𝔽2)11yescharacteristic
273C23×C132−1+411yescharacteristic
274C23×C132−1+411yescharacteristic
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—416no—
308C2×C4×C13C2×C4⋊C414yes—
309C2×C4×C13C2×C4⋊C414yes—
310C2×C4×C13#11714yes—
311C2×C4×C13#11714yes—
312C2×C4×C13C4×D414yes—
313C2×C4×C13C4×D414yes—
314C2×C4×C13#12114yes—
315C2×C4×C13#12314yes—
316C2×C4×C13#12414yes—
317C2×C4×C13#12614yes—
318C2×Dic13—24no—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C24×C4C2×D1311yescharacteristic
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—132no—
352C22×C4⋊C4—132no—
353C22×C22⋊C4—132no—
354C22×C22⋊C4—132no—
355C22×C22⋊C4C2×D1311yescharacteristic
356C22×C22⋊C4C2×D1311yescharacteristic
357C22×C42—132no—
358C22×C42C2×D1311yescharacteristic
359C22×C42C2×D1311yescharacteristic
360#388—268no—
361#384—264no—
362#380—264no—
363#380—264no—
364C4×C4⋊C4—264no—
365C4×C22⋊C4Dic1318yescomplemented
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95C2×D1311yescharacteristic
374C2×#95C2×D1311yescharacteristic
375C22×C13—24no—
376C22×C13—24no—
377C22×C13—24no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13C22×C4⋊C411yescharacteristic
391C22×C13C2×#11711yescharacteristic
392C22×C13C2×#11711yescharacteristic
393C22×C13C2×C4×D411yescharacteristic
394C22×C13C2×C4×D411yescharacteristic
395C22×C13#52011yescharacteristic
396C22×C13#52011yescharacteristic
397C22×C13C2×#12111yescharacteristic
398C22×C13C2×#12311yescharacteristic
399C22×C13C2×#12411yescharacteristic
400C22×C13C2×#12611yescharacteristic
401C22×C13#53211yescharacteristic
402C22×C13#53211yescharacteristic
403C22×C13#53311yescharacteristic
404C22×C13#53311yescharacteristic
405C22×C13#54011yescharacteristic
406C22×C13#54111yescharacteristic
407C22×C13#54211yescharacteristic
408C22×C13#54211yescharacteristic
409C22×C13D4211yescharacteristic
410C22×C13D4211yescharacteristic
411C22×C13#54611yescharacteristic
412C22×C13#54711yescharacteristic
413C22×C13#54711yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#54811yescharacteristic
416C22×C13D4×Q811yescharacteristic
417C22×C13D4×Q811yescharacteristic
418C22×C13#55011yescharacteristic
419C22×C13#55211yescharacteristic
420C22×C13#55311yescharacteristic
421C22×C13#55411yescharacteristic
422C22×C13#55411yescharacteristic
423C22×C13#55511yescharacteristic
424C22×C13#55611yescharacteristic
425C4×C13—24no—
426C4×C13—24no—
427C4×C13—24no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13#38818yescomplemented
431Dic13—44no—
432Dic13—44no—
433Dic13—82no—
434Dic13—82no—
435C25C22×D1311yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—132no—
443C23×C4—132no—
444C23×C4—132no—
445C23×C4—132no—
446C23×C4C2×Dic1314yes—
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1311yescharacteristic
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—264no—
461C2×C4⋊C4—264no—
462C2×C4⋊C4—264no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—522no—
470C2×C4⋊C4—522no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—264no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—522no—
478C2×C22⋊C4—522no—
479C2×C22⋊C4Dic2614yes—
480C2×C22⋊C4D5214yes—
481C2×C22⋊C4C2×Dic1314yes—
482C2×C22⋊C4C2×Dic1314yes—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—264no—
488C2×C42—264no—
489C2×C42—522no—
490C2×C42C2×Dic1314yes—
491C2×C42C2×Dic1314yes—
492#95—264no—
493#95—264no—
494#95—264no—
495#95—264no—
496#95—264no—
497#95—264no—
498#95—522no—
499#95C2×Dic1314yes—
500#95C2×Dic1314yes—
501C2×C13—44no—
502C2×C13#228511yescharacteristic
503C2×C13C2×#38811yescharacteristic
504C2×C13#231411yescharacteristic
505C2×C13D4×C4⋊C411yescharacteristic
506C2×C13D4×C4⋊C411yescharacteristic
507C2×C13#235211yescharacteristic
508C2×C13#235411yescharacteristic
509C2×C13#242211yescharacteristic
510C2×C13#242311yescharacteristic
511C2×C13#242811yescharacteristic
512C2×C13#242911yescharacteristic
513C2×C13#249111yescharacteristic
514C2×C13#249211yescharacteristic
515C2×C13#249611yescharacteristic
516C2×C13#249711yescharacteristic
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24C2×Dic2612yes—
530C24C2×D5212yes—
531C24C22×Dic1312yes—
532C24C23×D1311yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—134no—
565C22×C4—134no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4C2×Dic2612yes—
593C22×C4C2×Dic2612yes—
594C22×C4C2×D5212yes—
595C22×C4C2×D5212yes—
596C22×C4#612712yes—
597C22×C4#612712yes—
598C22×C4#612712yes—
599C22×C4#612712yes—
600C22×C4D4×D1312yes—
601C22×C4D4×D1312yes—
602C22×C4#612912yes—
603C22×C4#612912yes—
604C22×C4C22×Dic1312yes—
605C22×C4C22×Dic1312yes—
606C22×C4C22×Dic1312yes—
607C22×C4C22×Dic1312yes—
608C22×C4C22×Dic1312yes—
609C22×C4C22×Dic1312yes—
610C4⋊C4—268no—
611C4⋊C4—268no—
612C4⋊C4—528no—
613C4⋊C4—528no—
614C4⋊C4—524no—
615C4⋊C4—524no—
616C22⋊C4—28no—
617C22⋊C4—528no—
618C22⋊C4—528no—
619C22⋊C4C4⋊Dic13116yescomplemented
620C42—28no—
621C42—28no—
622C42—528no—
623C13#1387611yescharacteristic, complemented, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊Dic1314yes—
659C23C22×Dic2611yescharacteristic
660C23C22×D5211yescharacteristic
661C23C2×#612711yescharacteristic
662C23C2×#612711yescharacteristic
663C23C2×#612711yescharacteristic
664C23C2×#612711yescharacteristic
665C23C2×D4×D1311yescharacteristic
666C23C2×D4×D1311yescharacteristic
667C23C2×#612911yescharacteristic
668C23C2×#612911yescharacteristic
669C23#8825611yescharacteristic
670C23#8825611yescharacteristic
671C23#8825711yescharacteristic
672C23#8825711yescharacteristic
673C23C23×Dic1311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—264no—
708C2×C4—264no—
709C2×C4—264no—
710C2×C4—264no—
711C2×C4—264no—
712C2×C4—264no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4#8813314yes—
736C2×C4#8813714yes—
737C2×C4#8813814yes—
738C2×C4#8813914yes—
739C2×C4C2×C4⋊Dic1314yes—
740C2×C4C2×C4⋊Dic1314yes—
741C2×C4#8818014yes—
742C2×C4#8818014yes—
743C2×C4D4×Dic1314yes—
744C2×C4D4×Dic1314yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22#1171917511yescharacteristic
761C22#1171917511yescharacteristic
762C22#1171918211yescharacteristic
763C22#1171918211yescharacteristic
764C22C2×#8813311yescharacteristic
765C22C2×#8813711yescharacteristic
766C22C2×#8813811yescharacteristic
767C22C2×#8813911yescharacteristic
768C22#1171922311yescharacteristic
769C22#1171923911yescharacteristic
770C22#1171923911yescharacteristic
771C22#1171924011yescharacteristic
772C22D4×Dic2611yescharacteristic
773C22D4×Dic2611yescharacteristic
774C22#1171924611yescharacteristic
775C22#1171924711yescharacteristic
776C22#1171924811yescharacteristic
777C22#1171924811yescharacteristic
778C22D4×D5211yescharacteristic
779C22D4×D5211yescharacteristic
780C22#1171925511yescharacteristic
781C22#1171925611yescharacteristic
782C22#1171925711yescharacteristic
783C22#1171925811yescharacteristic
784C22#1171926011yescharacteristic
785C22#1171926011yescharacteristic
786C22#1171926811yescharacteristic
787C22#1171927011yescharacteristic
788C22C22×C4⋊Dic1311yescharacteristic
789C22C2×#8818011yescharacteristic
790C22C2×#8818011yescharacteristic
791C22C2×D4×Dic1311yescharacteristic
792C22C2×D4×Dic1311yescharacteristic
793C22#1171953211yescharacteristic
794C22#1171953211yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—524no—
801C4—524no—
802C4—1042no—
803C4—1042no—
804C4#1171861218yescomplemented
805C2—44no—
806C2#1311724311yescharacteristic
807C2C2×#1171861211yescharacteristic
808C2#1311744511yescharacteristic
809C2D4×C4⋊Dic1311yescharacteristic
810C2D4×C4⋊Dic1311yescharacteristic
811C2#1311776511yescharacteristic
812C2#1311778511yescharacteristic
813C2#1311835011yescharacteristic
814C2#1311836111yescharacteristic
815C2#1311842411yescharacteristic
816C2#1311843511yescharacteristic
817C2#1311919911yescharacteristic
818C2#1311921011yescharacteristic
819C2#1311925811yescharacteristic
820C2#1311926911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718596C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
6. #13113093C2semidirect
8. #13113070C2semidirect
9. #13113066C2semidirect
10. #13113066C2semidirect
26. C4×C13×C22⋊C4C4semidirect
202. C13×C22⋊C4C4⋊C4semidirect
365. C4×C22⋊C4Dic13semidirect
430. C4×C13#388semidirect
619. C22⋊C4C4⋊Dic13semidirect
623. C13#13876semidirect
804. C4#11718612semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117185962
C2×#117188732
C2×C4×C4⋊Dic132
#131130932
#131130812
#131130702
#131130662
C2×C4×C13×C22⋊C42
#1387613