Finite Group Databasebeta

← C2×#13118665 #16030671

Subgroups — C2×#13118665 #16030671

Order 3328.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3#13118665C2116yesmaximal, direct product factor
4C2×#11718320C211yesmaximal, characteristic, complemented
5C2×#11718645C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718608C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718617C211yesmaximal, characteristic
11C2×#11718617C211yesmaximal, characteristic
12C2×#11718329C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718873C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C2×C4×C22⋊D13—28no—
31C2×C4×C22⋊D13C2218yes—
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88151—28no—
43C2×#88151C2218yescomplemented
44C13×#385C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718873C2218yescomplemented
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718650C2218yescomplemented
59#11718645C2218yescomplemented
60#11718642C2218yescomplemented
61#11718617C2218yes—
62#11718617C2218yes—
63#11718609C2218yescomplemented
64#11718608C2218yescomplemented
65#11718329C2218yescomplemented
66D13×#95C2218yescomplemented
67#11718320C2218yescomplemented
68#11718307C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—24no—
73C23×C4×C13—42no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2314yes—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—24no—
82C22×C22⋊D13—24no—
83C22×C22⋊D13Q818yescomplemented
84C22×C22⋊D13C2314yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13—42no—
98C22×C4×D13—42no—
99C22×C4×D13—42no—
100C22×C4×D13—42no—
101C22×C4×D13C2314yes—
102C22×C4×D13C2314yes—
103C22×C4×D13C2314yes—
104C22×Dic26—24no—
105C22×Dic26—24no—
106C22×Dic26—42no—
107C22×Dic26C2314yes—
108C2×C13×C4⋊C4—24no—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2314yes—
112C2×C13×C22⋊C4—24no—
113C2×C13×C22⋊C4—42no—
114C2×C13×C22⋊C4C2314yes—
115C2×C13×C22⋊C4C2314yes—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C4×C22⋊D13—232no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103D418yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×C4⋊Dic13—24no—
130C2×C4⋊Dic13—24no—
131C2×C4⋊Dic13—42no—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134C2×C4⋊Dic13C2314yes—
135C2×#6101—24no—
136C2×#6101—42no—
137C2×#6101—42no—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×C4×Dic13—24no—
142C2×C4×Dic13C2314yes—
143#88151—232no—
144C13×#95C2314yes—
145C13×#95C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2450—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C2×Q814yes—
164C24×C13C2412yes—
165C24×C13C2411yescharacteristic
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13—22no—
170C23×D13C2×D414yes—
171C23×D13C2×Q814yes—
172C23×D13#4114yes—
173C23×D13C2412yes—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—28no—
190C22×C4×C13—28no—
191C22×C4×C13—44no—
192C22×C4×C13—416no—
193C22×C4×C13C2×D414yes—
194C22×C4×C13#4114yes—
195C22×C4×C13#4114yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C2×C22⋊D13—232no—
203C2×C22⋊D13—28no—
204C2×C22⋊D13—28no—
205C2×C22⋊D13C2×Q8116yescomplemented
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13C2×D414yes—
226C22×Dic13C2×Q814yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C2×C4×D13—28no—
235C2×C4×D13—28no—
236C2×C4×D13—28no—
237C2×C4×D13—28no—
238C2×C4×D13—28no—
239C2×C4×D13—44no—
240C2×C4×D13—44no—
241C2×C4×D13—44no—
242C2×C4×D13—44no—
243C2×C4×D13—416no—
244C2×C4×D13—416no—
245C2×C4×D13—416no—
246C2×Dic26—28no—
247C2×Dic26—28no—
248C2×Dic26—44no—
249C2×Dic26—416no—
250C13×C4⋊C4—28no—
251C13×C4⋊C4—28no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—44no—
254C22⋊Dic13—28no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257#6103—28no—
258#6103—28no—
259#6103C2×D4116yes—
260C4⋊Dic13—28no—
261C4⋊Dic13—28no—
262C4⋊Dic13—44no—
263#6101—28no—
264#6101—44no—
265#6101—44no—
266C4×Dic13—28no—
267C22×C22⋊Q8—131no—
268C22×C4×D4—131no—
269#2450—1316no—
270C2×#400—131no—
271C2×#398—131no—
272C2×#396—131no—
273C2×#393—131no—
274C2×#391—131no—
275C2×#387—131no—
276C2×#386—131no—
277C2×#386—131no—
278C2×#385—131no—
279C2×#385—131no—
280C2×#385D1311yescharacteristic, complemented
281C2×#380—131no—
282C22×#95—131no—
283C23×C13—28no—
284C23×C13—28no—
285C23×C13—28no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13C22×D412yes—
297C23×C13C22×Q814yes—
298C23×C13C22×Q812yes—
299C23×C13C2×#4112yes—
300C23×C13C2×#4112yes—
301C23×C13C2×#4112yes—
302C23×C13H(5,𝔽2)12yes—
303C23×C13H(5,𝔽2)12yes—
304C23×C13C2511yescharacteristic
305C22×D13—28no—
306C22×D13—28no—
307C22×D13—28no—
308C22×D13—28no—
309C22×D13—28no—
310C22×D13—28no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13C22⋊Q8116yes—
316C22×D13C22×D414yes—
317C22×D13C22×Q814yes—
318C22×D13C2×#4114yes—
319C2×C4×C13—28no—
320C2×C4×C13—28no—
321C2×C4×C13—28no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—416no—
338C2×C4×C13—44no—
339C2×C4×C13—44no—
340C2×C4×C13—44no—
341C2×C4×C13C22×D414yes—
342C2×C4×C13C2×#4114yes—
343C2×C4×C13C2×#4114yes—
344C22⋊D13—232no—
345C2×Dic13—28no—
346C2×Dic13—28no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—44no—
367C2×Dic13—44no—
368C2×Dic13—44no—
369C2×Dic13—44no—
370C2×Dic13—44no—
371C2×Dic13C22×D414yes—
372C2×Dic13C22×Q814yes—
373C4×D13—416no—
374C4×D13—416no—
375C4×D13—416no—
376Dic26—416no—
377C23×Q8—131no—
378C23×D4—131no—
379C24×C4—131no—
380C24×C4—131no—
381C24×C4—131no—
382C24×C4C2×D1311yescharacteristic
383C2×C22⋊Q8—138no—
384C2×C22⋊Q8—268no—
385C2×C4×D4—138no—
386C2×C4×D4—268no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4C2×D1311yescharacteristic
394C22×C4⋊C4C2×D1311yescharacteristic
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4—131no—
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C42—131no—
404#400—138no—
405#398—138no—
406#396—138no—
407#393—138no—
408#391—138no—
409#387—138no—
410#386—138no—
411#386—138no—
412#385—138no—
413#385—138no—
414#385C2×D1318yescomplemented
415#380—138no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—138no—
427C2×#95C2×D1311yescharacteristic
428C2×#95C2×D1311yescharacteristic
429C22×C13—24no—
430C22×C13—24no—
431C22×C13—24no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—416no—
437C22×C13C2×C22⋊Q814yes—
438C22×C13#52914yes—
439C22×C13#53814yes—
440C22×C13#54614yes—
441C22×C13#54614yes—
442C22×C13#55414yes—
443C22×C13#55414yes—
444C22×C13C23×D411yescharacteristic
445C22×C13C23×Q811yescharacteristic
446C22×C13C22×#4111yescharacteristic
447C22×C13C22×#4111yescharacteristic
448C22×C13C22×#4111yescharacteristic
449C22×C13C2×H(5,𝔽2)11yescharacteristic
450C22×C13C2×H(5,𝔽2)11yescharacteristic
451C2×D13—24no—
452C2×D13—24no—
453C2×D13—24no—
454C2×D13—24no—
455C2×D13—24no—
456C2×D13—24no—
457C2×D13—232no—
458C2×D13C2×C22⋊Q818yes—
459C4×C13—24no—
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—42no—
463C4×C13—42no—
464C4×C13—42no—
465Dic13—24no—
466Dic13—24no—
467Dic13—42no—
468Dic13—42no—
469Dic13—42no—
470Dic13—42no—
471Dic13—42no—
472C25—131no—
473C25C22×D1311yescharacteristic
474C22×Q8—134no—
475C22×Q8—264no—
476C22×Q8—264no—
477C22×Q8—522no—
478C22×D4—138no—
479C22×D4—134no—
480C22×D4—264no—
481C22×D4—264no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—42no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—131no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—134no—
493C23×C4—134no—
494C23×C4—134no—
495C23×C4—264no—
496C23×C4—264no—
497C23×C4—264no—
498C23×C4—264no—
499C23×C4—264no—
500C23×C4—522no—
501C23×C4—522no—
502C23×C4—522no—
503C23×C4—522no—
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1314yes—
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
510C23×C4C22×D1311yescharacteristic
511C22⋊Q8—2632no—
512C4×D4—2632no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—134no—
521C2×C4⋊C4—264no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—522no—
525C2×C4⋊C4—522no—
526C2×C4⋊C4—522no—
527C2×C4⋊C4C22×D1314yes—
528C2×C4⋊C4C22×D1314yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—138no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—264no—
539C2×C22⋊C4—264no—
540C2×C22⋊C4—264no—
541C2×C22⋊C4—522no—
542C2×C22⋊C4—522no—
543C2×C22⋊C4C22×D1314yes—
544C2×C22⋊C4C22×D1314yes—
545C2×C42—134no—
546C2×C42—264no—
547#95—134no—
548#95—134no—
549#95—134no—
550#95—134no—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95C22×D1314yes—
558#95C22×D1314yes—
559C2×C13—44no—
560C2×C13#245018yescomplemented
561C2×C13C22×C22⋊Q811yescharacteristic
562C2×C13C2×#52911yescharacteristic
563C2×C13C2×#53811yescharacteristic
564C2×C13C2×#54611yescharacteristic
565C2×C13C2×#54611yescharacteristic
566C2×C13C2×#55411yescharacteristic
567C2×C13C2×#55411yescharacteristic
568D13—28no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—134no—
576C24—134no—
577C24—134no—
578C24—132no—
579C24—262no—
580C24—262no—
581C24—262no—
582C24—262no—
583C24Q8×D1314yes—
584C24C23×D1312yes—
585C24C23×D1311yescharacteristic
586C2×Q8—268no—
587C2×Q8—268no—
588C2×Q8—524no—
589C2×Q8—5216no—
590C2×D4—1316no—
591C2×D4—268no—
592C2×D4—2632no—
593C2×D4—268no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—134no—
614C22×C4—134no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—268no—
623C22×C4—268no—
624C22×C4—268no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—268no—
645C22×C4—268no—
646C22×C4—524no—
647C22×C4—524no—
648C22×C4—524no—
649C22×C4—524no—
650C22×C4—5216no—
651C22×C4—5216no—
652C22×C4—5216no—
653C22×C4#612714yes—
654C22×C4D4×D1314yes—
655C22×C4#612914yes—
656C22×C4C23×D1312yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—268no—
665C4⋊C4—268no—
666C4⋊C4—268no—
667C4⋊C4—524no—
668C4⋊C4—524no—
669C4⋊C4—524no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—1316no—
673C22⋊C4—268no—
674C22⋊C4—268no—
675C22⋊C4—268no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C42—268no—
679C13C2×#245011yescharacteristic, complemented, Sylow
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—1316no—
694C23—134no—
695C23—134no—
696C23—134no—
697C23—268no—
698C23—268no—
699C23—268no—
700C23—268no—
701C23—268no—
702C23—268no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23C2×#612712yes—
708C23C2×D4×D1312yes—
709C23C2×#612912yes—
710C23#8825112yes—
711C23C2×Q8×D1314yes—
712C23C2×Q8×D1312yes—
713C23#41×D1312yes—
714C23#8825612yes—
715C23C24×D1311yescharacteristic
716Q8—5216no—
717D4—2632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—134no—
741C2×C4—134no—
742C2×C4—268no—
743C2×C4—268no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—5216no—
764C2×C4—5216no—
765C2×C4—5216no—
766C2×C4—524no—
767C2×C4—524no—
768C2×C4—524no—
769C2×C4—524no—
770C2×C4—524no—
771C2×C4C2×#612714yes—
772C2×C4C2×D4×D1314yes—
773C2×C4C2×#612914yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—416no—
781C22—42no—
782C22—138no—
783C22—264no—
784C22—264no—
785C22—264no—
786C22—264no—
787C22—264no—
788C22—2632no—
789C22—264no—
790C22#1171921614yes—
791C22#1171925514yes—
792C22#1171926214yes—
793C22#1171929614yes—
794C22D13×C22⋊Q814yes—
795C22#1171934014yes—
796C22#1171936214yes—
797C22C22×#612711yescharacteristic
798C22C22×D4×D1311yescharacteristic
799C22C22×#612911yescharacteristic
800C22C2×#8825111yescharacteristic
801C22C22×Q8×D1311yescharacteristic
802C22C2×#41×D1311yescharacteristic
803C22C2×#8825611yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—264no—
811C4—264no—
812C4—522no—
813C4—522no—
814C4—522no—
815C4—522no—
816C4—522no—
817C2—44no—
818C2—268no—
819C2#1311866518yesdirect product factor
820C2C2×D13×C22⋊Q811yescharacteristic
821C2C2×#1171926211yescharacteristic
822C2C2×#1171936211yescharacteristic
823C2C2×#1171929611yescharacteristic
824C2C2×#1171925511yescharacteristic
825C2C2×#1171921611yescharacteristic
826C2C2×#1171934011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#385D13
hypocenterC13C2×#2450
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
3. #13118665C2direct (N × H)
4. C2×#11718320C2semidirect
5. C2×#11718645C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718608C2semidirect
8. C2×#11718307C2semidirect
9. C2×#11718642C2semidirect
12. C2×#11718329C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718873C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#385C2semidirect
43. C2×#88151C22semidirect
44. C13×#385C22semidirect
47. #11718873C22semidirect
58. #11718650C22semidirect
59. #11718645C22semidirect
60. #11718642C22semidirect
63. #11718609C22semidirect
64. #11718608C22semidirect
65. #11718329C22semidirect
66. D13×#95C22semidirect
67. #11718320C22semidirect
68. #11718307C22semidirect
83. C22×C22⋊D13Q8semidirect
205. C2×C22⋊D13C2×Q8semidirect
280. C2×#385D13semidirect
414. #385C2×D13semidirect
560. C2×C13#2450semidirect
679. C13C2×#2450semidirect
819. C2#13118665direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C4×C22⋊D132
#131186652
C2×#117183202
C2×#117186452
C2×#117186092
C2×#117186082
C2×#117183072
C2×#117186422
C2×#117186172
C2×#117183292
C2×#117186502
C2×#117188732
C2×D13×#952
C2×C13×#3852
C2×#245013