Finite Group Databasebeta

← C2×#13118500 #16030345

Subgroups — C2×#13118500 #16030345

Order 3328.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic, complemented
3C23×#6103C211yesmaximal, characteristic
4C22×C22⋊C4×D13C211yesmaximal, characteristic
5#13118500C2116yesmaximal, direct product factor
6C2×#11718338C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic, complemented
9C2×#11718334C211yesmaximal, characteristic, complemented
10C2×#11718611C211yesmaximal, characteristic, complemented
11C2×#11718329C211yesmaximal, characteristic, complemented
12C2×#11718329C211yesmaximal, characteristic, complemented
13C2×#11718873C211yesmaximal, characteristic, complemented
14C2×#11718648C211yesmaximal, characteristic, complemented
15C2×#11718616C211yesmaximal, characteristic
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic, complemented
23C22×C13×C4⋊C4C2211yescharacteristic, complemented
24C22×C13×C4⋊C4C2211yescharacteristic, complemented
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103—28no—
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2218yes—
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic, complemented
42C22×C4⋊Dic13C2211yescharacteristic, complemented
43C22×C4⋊Dic13C2211yescharacteristic, complemented
44C22×C4⋊Dic13C2211yescharacteristic, complemented
45C22×C4⋊Dic13C2211yescharacteristic, complemented
46C22×#6101C2211yescharacteristic, complemented
47C22×#6101C2211yescharacteristic, complemented
48C2×#88151—28no—
49C2×#88151C2218yescomplemented
50C2×C22⋊C4×D13—28no—
51C2×C22⋊C4×D13C2218yes—
52C2×#88132—28no—
53C2×#88132C2218yescomplemented
54C13×#385C2218yescomplemented
55C2×C13×#95C2211yescharacteristic, complemented
56C2×C13×#95C2211yescharacteristic, complemented
57#11718873C2218yescomplemented
58C2×#88071C2211yescharacteristic, complemented
59C2×#88071C2211yescharacteristic, complemented
60C2×#88071C2211yescharacteristic, complemented
61C2×#88071C2211yescharacteristic, complemented
62#11718655C2218yescomplemented
63#11718655C2218yescomplemented
64#11718648C2218yescomplemented
65#11718616C2218yes—
66#11718611C2218yescomplemented
67#11718338C2218yescomplemented
68#11718334C2218yescomplemented
69#11718329C2218yescomplemented
70#11718329C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13—24no—
73C24×D13—24no—
74C24×D13—24no—
75C24×D13—24no—
76C24×D13—42no—
77C24×D13—42no—
78C24×D13Q818yescomplemented
79C24×D13C2311yescharacteristic
80C24×D13C2314yes—
81C24×D13C2311yescharacteristic
82C23×C4×C13—24no—
83C23×C4×C13—24no—
84C23×C4×C13—42no—
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2314yes—
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×Dic13—24no—
93C23×Dic13—24no—
94C23×Dic13—42no—
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2314yes—
101C23×Dic13C2311yescharacteristic
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—24no—
106C22×C4×D13—42no—
107C22×C4×D13—42no—
108C22×C4×D13C2314yes—
109C22×C4×D13C2314yes—
110C22×Dic26—24no—
111C22×Dic26—24no—
112C22×Dic26—42no—
113C22×Dic26C2314yescomplemented
114C2×C13×C4⋊C4—24no—
115C2×C13×C4⋊C4—42no—
116C2×C13×C4⋊C4C2314yescomplemented
117C2×C13×C4⋊C4C2314yescomplemented
118C2×C13×C22⋊C4—24no—
119C2×C13×C22⋊C4D418yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C13×C22⋊C4C2314yes—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—24no—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—232no—
134C2×#6103—42no—
135C2×#6103—42no—
136C2×#6103D418yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×#6103C2314yes—
144C2×#6103C2314yes—
145C2×#6103C2314yes—
146C2×#6103C2314yes—
147C2×C4⋊Dic13—24no—
148C2×C4⋊Dic13—24no—
149C2×C4⋊Dic13—24no—
150C2×C4⋊Dic13—42no—
151C2×C4⋊Dic13—42no—
152C2×C4⋊Dic13C2314yescomplemented
153C2×C4⋊Dic13C2314yescomplemented
154C2×C4⋊Dic13C2314yescomplemented
155C2×C4⋊Dic13C2314yescomplemented
156C2×C4⋊Dic13C2314yescomplemented
157C2×#6101—24no—
158C2×#6101—24no—
159C2×#6101C2314yescomplemented
160C2×#6101C2314yescomplemented
161#88151—232no—
162C22⋊C4×D13—232no—
163#88132—232no—
164C13×#95C2314yescomplemented
165C13×#95C2314yescomplemented
166#88071C2314yescomplemented
167#88071C2314yescomplemented
168#88071C2314yescomplemented
169#88071C2314yescomplemented
170C2×#2437—131nomaximal, Sylow
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13C2×D414yes—
176C24×C13C2×Q814yes—
177C24×C13#4114yes—
178C24×C13C2412yes—
179C24×C13C2411yescharacteristic
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13—22no—
184C23×D13—232no—
185C23×D13—28no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—28no—
189C23×D13—22no—
190C23×D13—22no—
191C23×D13—22no—
192C23×D13—22no—
193C23×D13—232no—
194C23×D13—28no—
195C23×D13—28no—
196C23×D13—416no—
197C23×D13—44no—
198C23×D13—44no—
199C23×D13—416no—
200C23×D13—416no—
201C23×D13—416no—
202C23×D13—416no—
203C23×D13C2×D414yes—
204C23×D13C2×Q814yes—
205C23×D13C2×Q814yes—
206C23×D13C2×Q8116yescomplemented
207C23×D13#4114yes—
208C23×D13C2412yes—
209C23×D13C2412yes—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—28no—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—28no—
227C22×C4×C13—44no—
228C22×C4×C13—416no—
229C22×C4×C13C2×D414yes—
230C22×C4×C13C2×D414yes—
231C22×C4×C13C2×D414yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2412yes—
234C22×C4×C13C2412yes—
235C22×C4×C13C2412yes—
236C22×C4×C13C2412yes—
237C22×C4×C13C2412yes—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—28no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13—22no—
254C22×Dic13—22no—
255C22×Dic13—22no—
256C22×Dic13—28no—
257C22×Dic13—44no—
258C22×Dic13—416no—
259C22×Dic13C2×D414yes—
260C22×Dic13C2412yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C2×C4×D13—28no—
267C2×C4×D13—28no—
268C2×C4×D13—28no—
269C2×C4×D13—28no—
270C2×C4×D13—44no—
271C2×C4×D13—44no—
272C2×C4×D13—416no—
273C2×C4×D13—416no—
274C2×Dic26—28no—
275C2×Dic26—28no—
276C2×Dic26—44no—
277C2×Dic26—416no—
278C13×C4⋊C4—28no—
279C13×C4⋊C4—44no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4C2×D4116yes—
282C22⋊Dic13—28no—
283C22⋊Dic13—28no—
284#6103—28no—
285#6103—28no—
286#6103—28no—
287#6103—28no—
288#6103—28no—
289#6103—28no—
290#6103—28no—
291#6103—44no—
292#6103—44no—
293#6103C2×D4116yes—
294C4⋊Dic13—28no—
295C4⋊Dic13—28no—
296C4⋊Dic13—28no—
297C4⋊Dic13—44no—
298C4⋊Dic13—44no—
299#6101—28no—
300#6101—28no—
301C22×C22⋊Q8—131no—
302C22×C22⋊Q8—131no—
303C23×C22⋊C4—131no—
304C23×C22⋊C4—131no—
305#2437—1316no—
306C2×#399—131no—
307C2×#396—131no—
308C2×#396—131no—
309C2×#393—131no—
310C2×#385—131no—
311C2×#385—131no—
312C2×#385—131no—
313C2×#385D1311yescharacteristic, complemented
314C2×#380—131no—
315C2×#380—131no—
316C2×#379—131no—
317C23×C13—28no—
318C23×C13—28no—
319C23×C13—28no—
320C23×C13—28no—
321C23×C13—28no—
322C23×C13—28no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13C22⋊Q8116yescomplemented
328C23×C13C22×D414yes—
329C23×C13C22×D412yes—
330C23×C13C22×D412yes—
331C23×C13C22×Q814yes—
332C23×C13C22×Q812yes—
333C23×C13C2×#4114yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—28no—
343C22×D13—28no—
344C22×D13—28no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—22no—
349C22×D13—28no—
350C22×D13—28no—
351C22×D13—232no—
352C22×D13—28no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—232no—
360C22×D13—416no—
361C22×D13—4128no—
362C22×D13—416no—
363C22×D13—416no—
364C22×D13—416no—
365C22×D13—416no—
366C22×D13—44no—
367C22×D13—44no—
368C22×D13—44no—
369C22×D13—44no—
370C22×D13C22⋊Q8116yescomplemented
371C22×D13C22×D414yes—
372C22×D13C22×Q814yes—
373C22×D13C22×Q814yes—
374C22×D13C2×#4114yes—
375C2×C4×C13—28no—
376C2×C4×C13—28no—
377C2×C4×C13—28no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—416no—
394C2×C4×C13—44no—
395C2×C4×C13—44no—
396C2×C4×C13—44no—
397C2×C4×C13C22×D414yes—
398C2×C4×C13C22×D414yes—
399C2×C4×C13C22×D414yes—
400C2×Dic13—28no—
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—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—416no—
419C2×Dic13—44no—
420C2×Dic13—44no—
421C2×Dic13—44no—
422C2×Dic13—44no—
423C2×Dic13—44no—
424C2×Dic13C22×D414yes—
425C4×D13—416no—
426C4×D13—416no—
427Dic26—416no—
428C26—131no—
429C23×Q8—131no—
430C24×C4—131no—
431C24×C4—131no—
432C24×C4—131no—
433C24×C4C2×D1311yescharacteristic
434C2×C22⋊Q8—138no—
435C2×C22⋊Q8—138no—
436C2×C22⋊Q8—268no—
437C2×C22⋊Q8—268no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—131no—
445C22×C4⋊C4C2×D1311yescharacteristic, complemented
446C22×C4⋊C4C2×D1311yescharacteristic, complemented
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—138no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—138no—
461C22×C22⋊C4—268no—
462C22×C22⋊C4—268no—
463C22×C22⋊C4C2×D1311yescharacteristic
464C22×C22⋊C4C2×D1311yescharacteristic
465#399—138no—
466#396—138no—
467#396—138no—
468#393—138no—
469#385—138no—
470#385—138no—
471#385—138no—
472#385C2×D1318yescomplemented
473#380—138no—
474#380—138no—
475#379—138no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95C2×D1311yescharacteristic, complemented
481C2×#95C2×D1311yescharacteristic, complemented
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—232no—
485C22×C13—24no—
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13C2×C22⋊Q814yes—
490C22×C13C2×C22⋊Q814yes—
491C22×C13C2×C22⋊Q818yescomplemented
492C22×C13#54314yes—
493C22×C13D4214yes—
494C22×C13#54614yes—
495C22×C13#54614yes—
496C22×C13#55114yes—
497C22×C13C23×D411yescharacteristic
498C22×C13C23×D411yescharacteristic
499C22×C13C23×Q811yescharacteristic
500C22×C13C22×#4111yescharacteristic
501C22×C13C22×#4111yescharacteristic
502C22×C13C2×H(5,𝔽2)11yescharacteristic
503C22×C13C2×H(5,𝔽2)11yescharacteristic
504C2×D13—24no—
505C2×D13—24no—
506C2×D13—232no—
507C2×D13—24no—
508C2×D13—24no—
509C2×D13—24no—
510C2×D13—24no—
511C2×D13—24no—
512C2×D13—24no—
513C2×D13—24no—
514C2×D13—464no—
515C2×D13—416no—
516C2×D13—42no—
517C2×D13—42no—
518C2×D13—42no—
519C2×D13—42no—
520C2×D13C2×C22⋊Q818yescomplemented
521C4×C13—24no—
522C4×C13—24no—
523C4×C13—24no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—42no—
527Dic13—24no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—42no—
533C25—131no—
534C25—131no—
535C25—138no—
536C25—134no—
537C25—264no—
538C25—264no—
539C25—264no—
540C25—264no—
541C25—522no—
542C25—522no—
543C25C22×D1311yescharacteristic
544C22×Q8—134no—
545C22×Q8—264no—
546C22×Q8—264no—
547C22×Q8—522no—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—42no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—134no—
558C23×C4—134no—
559C23×C4—134no—
560C23×C4—264no—
561C23×C4—264no—
562C23×C4—264no—
563C23×C4—264no—
564C23×C4—264no—
565C23×C4—264no—
566C23×C4—522no—
567C23×C4—522no—
568C23×C4—522no—
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1314yes—
573C23×C4C22×D1311yescharacteristic
574C23×C4C22×D1311yescharacteristic
575C23×C4C22×D1311yescharacteristic
576C22⋊Q8—2632no—
577C22⋊Q8—2632no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—42no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—264no—
588C2×C4⋊C4—264no—
589C2×C4⋊C4—264no—
590C2×C4⋊C4—264no—
591C2×C4⋊C4—264no—
592C2×C4⋊C4—522no—
593C2×C4⋊C4—522no—
594C2×C4⋊C4C22×D1314yescomplemented
595C2×C4⋊C4C22×D1314yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—138no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—134no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—134no—
610C2×C22⋊C4—2632no—
611C2×C22⋊C4—264no—
612C2×C22⋊C4—264no—
613C2×C22⋊C4—264no—
614C2×C22⋊C4—264no—
615C2×C22⋊C4—264no—
616C2×C22⋊C4—264no—
617C2×C22⋊C4—264no—
618C2×C22⋊C4—264no—
619C2×C22⋊C4—264no—
620C2×C22⋊C4—2632no—
621C2×C22⋊C4—522no—
622C2×C22⋊C4—522no—
623C2×C22⋊C4D5218yes—
624C2×C22⋊C4C22×D1314yes—
625C2×C22⋊C4C22×D1314yes—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95C22×D1314yescomplemented
631#95C22×D1314yescomplemented
632C2×C13—28no—
633C2×C13#243718yescomplemented
634C2×C13C22×C22⋊Q811yescharacteristic
635C2×C13C22×C22⋊Q811yescharacteristic
636C2×C13C2×#54311yescharacteristic
637C2×C13C2×D4211yescharacteristic
638C2×C13C2×#54611yescharacteristic
639C2×C13C2×#54611yescharacteristic
640C2×C13C2×#55111yescharacteristic
641D13—28no—
642D13—44no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—134no—
648C24—134no—
649C24—134no—
650C24—132no—
651C24—134no—
652C24—132no—
653C24—1316no—
654C24—268no—
655C24—2632no—
656C24—268no—
657C24—262no—
658C24—262no—
659C24—262no—
660C24—262no—
661C24—2632no—
662C24—268no—
663C24—262no—
664C24—262no—
665C24—268no—
666C24—262no—
667C24—262no—
668C24—262no—
669C24—262no—
670C24—5216no—
671C24—524no—
672C24—524no—
673C24—5216no—
674C24—5216no—
675C24—5216no—
676C24—5216no—
677C24C2×D5214yes—
678C24#612914yes—
679C24Q8×D1314yes—
680C24C23×D1312yes—
681C24C23×D1311yescharacteristic
682C2×Q8—268no—
683C2×Q8—268no—
684C2×Q8—524no—
685C2×Q8—5216no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—28no—
703C22×C4—44no—
704C22×C4—416no—
705C22×C4—134no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—268no—
713C22×C4—268no—
714C22×C4—268no—
715C22×C4—262no—
716C22×C4—262no—
717C22×C4—262no—
718C22×C4—262no—
719C22×C4—262no—
720C22×C4—262no—
721C22×C4—262no—
722C22×C4—268no—
723C22×C4—262no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—262no—
728C22×C4—262no—
729C22×C4—262no—
730C22×C4—262no—
731C22×C4—262no—
732C22×C4—262no—
733C22×C4—268no—
734C22×C4—268no—
735C22×C4—524no—
736C22×C4—524no—
737C22×C4—5216no—
738C22×C4—5216no—
739C22×C4—524no—
740C22×C4—5216no—
741C22×C4C2×D5214yes—
742C22×C4C2×D5214yes—
743C22×C4D4×D1314yes—
744C22×C4C23×D1312yes—
745C22×C4C23×D1312yes—
746C22×C4C23×D1312yes—
747C22×C4C23×D1312yes—
748C22×C4C23×D1312yes—
749C22×C4C23×D1312yes—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—268no—
753C4⋊C4—268no—
754C4⋊C4—268no—
755C4⋊C4—268no—
756C4⋊C4—268no—
757C4⋊C4—524no—
758C4⋊C4—524no—
759C22⋊C4—28no—
760C22⋊C4—1316no—
761C22⋊C4—268no—
762C22⋊C4—268no—
763C22⋊C4—268no—
764C22⋊C4—268no—
765C22⋊C4—268no—
766C22⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—268no—
769C22⋊C4—268no—
770C22⋊C4—524no—
771C22⋊C4—524no—
772C22⋊C4C2×D52116yes—
773C13C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—1316no—
785C23—134no—
786C23—134no—
787C23—134no—
788C23—134no—
789C23—2632no—
790C23—268no—
791C23—268no—
792C23—268no—
793C23—268no—
794C23—268no—
795C23—268no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—268no—
801C23—2632no—
802C23—268no—
803C23—268no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—5216no—
811C23—52128no—
812C23—5216no—
813C23—5216no—
814C23—5216no—
815C23—5216no—
816C23—524no—
817C23—524no—
818C23—524no—
819C23—524no—
820C23#88151116yescomplemented
821C23C22×D5214yes—
822C23C22×D5212yes—
823C23C2×D4×D1312yes—
824C23C2×#612914yes—
825C23C2×#612912yes—
826C23#8825112yes—
827C23C2×Q8×D1314yes—
828C23C2×Q8×D1312yes—
829C23#41×D1312yes—
830C23#8825612yes—
831C23C24×D1311yescharacteristic
832Q8—5216no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
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—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—134no—
856C2×C4—268no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—5216no—
875C2×C4—5216no—
876C2×C4—5216no—
877C2×C4—524no—
878C2×C4—524no—
879C2×C4—524no—
880C2×C4—524no—
881C2×C4—524no—
882C2×C4C22×D5214yes—
883C2×C4C22×D5214yes—
884C2×C4C2×D4×D1314yes—
885C22—232no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—138no—
893C22—2632no—
894C22—264no—
895C22—264no—
896C22—264no—
897C22—264no—
898C22—264no—
899C22—264no—
900C22—264no—
901C22—264no—
902C22—264no—
903C22—5264no—
904C22—5216no—
905C22—522no—
906C22—522no—
907C22—522no—
908C22—522no—
909C22C2×#8815114yes—
910C22C2×#8815118yescomplemented
911C22D4×D5214yes—
912C22#1171925914yes—
913C22#1171929614yes—
914C22D13×C22⋊Q814yes—
915C22#1171933914yes—
916C22#1171936314yes—
917C22C23×D5211yescharacteristic
918C22C22×D4×D1311yescharacteristic
919C22C22×#612911yescharacteristic
920C22C2×#8825111yescharacteristic
921C22C22×Q8×D1311yescharacteristic
922C22C2×#41×D1311yescharacteristic
923C22C2×#8825611yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—264no—
931C4—522no—
932C4—522no—
933C4—522no—
934C4—522no—
935C4—522no—
936C2—28no—
937C2—268no—
938C2—524no—
939C2#1311850018yesdirect product factor
940C2C2×D13×C22⋊Q811yescharacteristic
941C2C22×#8815111yescharacteristic
942C2C2×#1171933911yescharacteristic
943C2C2×D4×D5211yescharacteristic
944C2C2×#1171929611yescharacteristic
945C2C2×#1171925911yescharacteristic
946C2C2×#1171936311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#385D13
hypocenterC13C2×#2437
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
2. C22×#88132C2semidirect
5. #13118500C2direct (N × H)
6. C2×#11718338C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718655C2semidirect
9. C2×#11718334C2semidirect
10. C2×#11718611C2semidirect
11. C2×#11718329C2semidirect
12. C2×#11718329C2semidirect
13. C2×#11718873C2semidirect
14. C2×#11718648C2semidirect
16. C2×C13×#385C2semidirect
22. C23×Dic26C22semidirect
23. C22×C13×C4⋊C4C22semidirect
24. C22×C13×C4⋊C4C22semidirect
41. C22×C4⋊Dic13C22semidirect
42. C22×C4⋊Dic13C22semidirect
43. C22×C4⋊Dic13C22semidirect
44. C22×C4⋊Dic13C22semidirect
45. C22×C4⋊Dic13C22semidirect
46. C22×#6101C22semidirect
47. C22×#6101C22semidirect
49. C2×#88151C22semidirect
53. C2×#88132C22semidirect
54. C13×#385C22semidirect
55. C2×C13×#95C22semidirect
56. C2×C13×#95C22semidirect
57. #11718873C22semidirect
58. C2×#88071C22semidirect
59. C2×#88071C22semidirect
60. C2×#88071C22semidirect
61. C2×#88071C22semidirect
62. #11718655C22semidirect
63. #11718655C22semidirect
64. #11718648C22semidirect
66. #11718611C22semidirect
67. #11718338C22semidirect
68. #11718334C22semidirect
69. #11718329C22semidirect
70. #11718329C22semidirect
78. C24×D13Q8semidirect
113. C22×Dic26C23semidirect
116. C2×C13×C4⋊C4C23semidirect
117. C2×C13×C4⋊C4C23semidirect
152. C2×C4⋊Dic13C23semidirect
153. C2×C4⋊Dic13C23semidirect
154. C2×C4⋊Dic13C23semidirect
155. C2×C4⋊Dic13C23semidirect
156. C2×C4⋊Dic13C23semidirect
159. C2×#6101C23semidirect
160. C2×#6101C23semidirect
164. C13×#95C23semidirect
165. C13×#95C23semidirect
166. #88071C23semidirect
167. #88071C23semidirect
168. #88071C23semidirect
169. #88071C23semidirect
206. C23×D13C2×Q8semidirect
313. C2×#385D13semidirect
327. C23×C13C22⋊Q8semidirect
370. C22×D13C22⋊Q8semidirect
445. C22×C4⋊C4C2×D13semidirect
446. C22×C4⋊C4C2×D13semidirect
472. #385C2×D13semidirect
480. C2×#95C2×D13semidirect
481. C2×#95C2×D13semidirect
491. C22×C13C2×C22⋊Q8semidirect
520. C2×D13C2×C22⋊Q8semidirect
594. C2×C4⋊C4C22×D13semidirect
595. C2×C4⋊C4C22×D13semidirect
630. #95C22×D13semidirect
631. #95C22×D13semidirect
633. C2×C13#2437semidirect
773. C13C2×#2437semidirect
820. C23#88151semidirect
910. C22C2×#88151semidirect
939. C2#13118500direct (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×#881322
C23×#61032
C22×C22⋊C4×D132
#131185002
C2×#117183382
C2×#117186552
C2×#117183342
C2×#117186112
C2×#117183292
C2×#117188732
C2×#117186482
C2×#117186162
C2×C13×#3852
C2×#243713