Finite Group Databasebeta

← C2×#13118661 #16030670

Subgroups — C2×#13118661 #16030670

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×#88147C211yesmaximal, characteristic
3#13118661C2116yesmaximal, direct product factor
4C2×#11718647C211yesmaximal, characteristic, complemented
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718334C211yesmaximal, characteristic, complemented
7C2×#11718307C211yesmaximal, characteristic, complemented
8C2×#11718316C211yesmaximal, characteristic, complemented
9C2×#11718326C211yesmaximal, characteristic
10C2×#11718326C211yesmaximal, characteristic
11C2×#11718650C211yesmaximal, characteristic, complemented
12C2×#11718650C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718648C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#398C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88151—28no—
41C2×#88151C2218yescomplemented
42C2×#88147—28no—
43C2×#88147C2218yes—
44C13×#398C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718650C2218yescomplemented
59#11718650C2218yescomplemented
60#11718650C2218yescomplemented
61#11718648C2218yescomplemented
62#11718647C2218yescomplemented
63#11718334C2218yescomplemented
64#11718326C2218yes—
65#11718326C2218yes—
66D13×#95C2218yescomplemented
67#11718316C2218yescomplemented
68#11718307C2218yescomplemented
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×D52—24no—
85C22×D52—24no—
86C22×D52Q818yescomplemented
87C22×D52C2314yes—
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—42no—
96C22×C4×D13—42no—
97C22×C4×D13—42no—
98C22×C4×D13—42no—
99C22×C4×D13—42no—
100C22×C4×D13C2314yes—
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⋊C4—42no—
111C2×C13×C4⋊C4—42no—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C4⋊C4C2314yes—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103D418yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×C4⋊Dic13—24no—
133C2×C4⋊Dic13—24no—
134C2×C4⋊Dic13C2314yes—
135C2×C4⋊Dic13C2314yes—
136C2×#6101—24no—
137C2×#6101—42no—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—24no—
141C2×C4×Dic13C2314yes—
142#88151—232no—
143#88147—232no—
144C13×#95C2314yes—
145C13×#95C2314yes—
146C13×#95C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2450—131nomaximal, Sylow
157C24×C13C2411yescharacteristic
158C23×D13—22no—
159C23×D13—22no—
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13C2×D414yes—
169C23×D13C2×Q814yes—
170C23×D13C2×Q814yes—
171C23×D13#4114yes—
172C23×D13C2412yes—
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—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13C2×D414yes—
193C22×C4×C13C2×Q814yes—
194C22×C4×C13#4114yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
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×Dic13C2×D414yes—
219C22×Dic13#4114yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C2×D52—232no—
227C2×D52—28no—
228C2×D52—28no—
229C2×D52C2×Q8116yescomplemented
230C2×C4×D13—28no—
231C2×C4×D13—28no—
232C2×C4×D13—28no—
233C2×C4×D13—28no—
234C2×C4×D13—28no—
235C2×C4×D13—28no—
236C2×C4×D13—28no—
237C2×C4×D13—44no—
238C2×C4×D13—44no—
239C2×C4×D13—44no—
240C2×C4×D13—44no—
241C2×C4×D13—44no—
242C2×C4×D13—416no—
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×C4⋊C4—44no—
253C13×C4⋊C4—44no—
254#6103—28no—
255#6103—28no—
256#6103—28no—
257#6103—28no—
258#6103—44no—
259#6103—44no—
260#6103—44no—
261#6103C2×D4116yes—
262C4⋊Dic13—28no—
263C4⋊Dic13—28no—
264#6101—28no—
265#6101—44no—
266C4×Dic13—28no—
267C22×C22⋊Q8—131no—
268C22×C4×D4—131no—
269#2450—1316no—
270C2×#400—131no—
271C2×#398D1311yescharacteristic, complemented
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×#385—131no—
281C2×#380—131no—
282C22×#95—131no—
283C23×C13C22×D412yes—
284C23×C13C22×Q812yes—
285C23×C13C2×#4112yes—
286C23×C13C2×#4112yes—
287C23×C13C2×#4112yes—
288C23×C13H(5,𝔽2)12yes—
289C23×C13H(5,𝔽2)12yes—
290C23×C13C2511yescharacteristic
291C22×D13—28no—
292C22×D13—28no—
293C22×D13—28no—
294C22×D13—28no—
295C22×D13—28no—
296C22×D13—28no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—28no—
302C22×D13—28no—
303C22×D13—28no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—44no—
311C22×D13—44no—
312C22×D13—44no—
313C22×D13—44no—
314C22×D13C22⋊Q8116yes—
315C22×D13C22×D414yes—
316C22×D13C22×Q814yes—
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—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—44no—
341C2×C4×C13—44no—
342C2×C4×C13—44no—
343C2×C4×C13—44no—
344C2×C4×C13C22×D414yes—
345C2×C4×C13C22×Q814yes—
346C2×C4×C13C2×#4114yes—
347C2×Dic13—28no—
348C2×Dic13—28no—
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—44no—
366C2×Dic13—44no—
367C2×Dic13—44no—
368C2×Dic13—44no—
369C2×Dic13C22×D414yes—
370C2×Dic13C2×#4114yes—
371D52—232no—
372C4×D13—416no—
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×C4—131no—
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⋊C4C2×D1311yescharacteristic
392C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
402C22×C22⋊C4—131no—
403C22×C42—131no—
404#400—138no—
405#398C2×D1318yescomplemented
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#385—138no—
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—138no—
426C2×#95C2×D1311yescharacteristic
427C2×#95C2×D1311yescharacteristic
428C2×#95C2×D1311yescharacteristic
429C22×C13C2×C22⋊Q814yes—
430C22×C13#52914yes—
431C22×C13#53814yes—
432C22×C13#54614yes—
433C22×C13#54614yes—
434C22×C13#55414yes—
435C22×C13#55414yes—
436C22×C13C23×D411yescharacteristic
437C22×C13C23×Q811yescharacteristic
438C22×C13C22×#4111yescharacteristic
439C22×C13C22×#4111yescharacteristic
440C22×C13C22×#4111yescharacteristic
441C22×C13C2×H(5,𝔽2)11yescharacteristic
442C22×C13C2×H(5,𝔽2)11yescharacteristic
443C2×D13—24no—
444C2×D13—24no—
445C2×D13—24no—
446C2×D13—24no—
447C2×D13—24no—
448C2×D13—24no—
449C2×D13—232no—
450C2×D13—24no—
451C2×D13—24no—
452C2×D13—24no—
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—42no—
456C2×D13—42no—
457C2×D13—416no—
458C2×D13C2×C22⋊Q818yes—
459C4×C13—24no—
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—42no—
463C4×C13—42no—
464C4×C13—42no—
465C4×C13—42no—
466Dic13—24no—
467Dic13—24no—
468Dic13—42no—
469Dic13—42no—
470Dic13—42no—
471Dic13—42no—
472C25—131no—
473C25—131no—
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—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—131no—
488C23×C4—134no—
489C23×C4—134no—
490C23×C4—134no—
491C23×C4—134no—
492C23×C4—264no—
493C23×C4—264no—
494C23×C4—264no—
495C23×C4—264no—
496C23×C4—264no—
497C23×C4—264no—
498C23×C4—264no—
499C23×C4—522no—
500C23×C4—522no—
501C23×C4—522no—
502C23×C4—522no—
503C23×C4—522no—
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
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—42no—
516C2×C4⋊C4—42no—
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⋊C4C22×D1314yes—
526C2×C4⋊C4C22×D1314yes—
527C2×C4⋊C4C22×D1314yes—
528C2×C4⋊C4C22×D1314yes—
529C2×C22⋊C4—138no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
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—264no—
542C2×C22⋊C4—522no—
543C2×C22⋊C4—522no—
544C2×C22⋊C4—522no—
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#95C22×D1314yes—
557#95C22×D1314yes—
558#95C22×D1314yes—
559C2×C13#245018yescomplemented
560C2×C13C22×C22⋊Q811yescharacteristic
561C2×C13C2×#52911yescharacteristic
562C2×C13C2×#53811yescharacteristic
563C2×C13C2×#54611yescharacteristic
564C2×C13C2×#54611yescharacteristic
565C2×C13C2×#55411yescharacteristic
566C2×C13C2×#55411yescharacteristic
567D13—28no—
568D13—44no—
569C24—134no—
570C24—134no—
571C24—134no—
572C24—132no—
573C24—134no—
574C24—132no—
575C24—262no—
576C24—262no—
577C24—262no—
578C24—262no—
579C24—262no—
580C24—262no—
581C24—262no—
582C24—262no—
583C24—262no—
584C24—262no—
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—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—134no—
613C22×C4—134no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—268no—
621C22×C4—268no—
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—268no—
642C22×C4—268no—
643C22×C4—524no—
644C22×C4—524no—
645C22×C4—524no—
646C22×C4—524no—
647C22×C4—524no—
648C22×C4—5216no—
649C22×C4—5216no—
650C22×C4—5216no—
651C22×C4—5216no—
652C22×C4D4×D1314yes—
653C22×C4Q8×D1314yes—
654C22×C4#613114yes—
655C22×C4C23×D1312yes—
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—44no—
665C4⋊C4—44no—
666C4⋊C4—268no—
667C4⋊C4—268no—
668C4⋊C4—268no—
669C4⋊C4—524no—
670C22⋊C4—1316no—
671C22⋊C4—268no—
672C22⋊C4—268no—
673C22⋊C4—268no—
674C22⋊C4—268no—
675C22⋊C4—524no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C42—268no—
679C13C2×#245011yescharacteristic, complemented, Sylow
680C23—1316no—
681C23—134no—
682C23—134no—
683C23—134no—
684C23—134no—
685C23—268no—
686C23—268no—
687C23—268no—
688C23—268no—
689C23—262no—
690C23—262no—
691C23—262no—
692C23—262no—
693C23—268no—
694C23—268no—
695C23—268no—
696C23—268no—
697C23—262no—
698C23—262no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—262no—
703C23—268no—
704C23—524no—
705C23—524no—
706C23—524no—
707C23—524no—
708C23C2×D4×D1312yes—
709C23#8825112yes—
710C23C2×Q8×D1312yes—
711C23C2×#613112yes—
712C23#41×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—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—134no—
744C2×C4—134no—
745C2×C4—268no—
746C2×C4—268no—
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—5216no—
767C2×C4—524no—
768C2×C4—524no—
769C2×C4—524no—
770C2×C4—524no—
771C2×C4C2×D4×D1314yes—
772C2×C4C2×Q8×D1314yes—
773C2×C4C2×#613114yes—
774C22—138no—
775C22—264no—
776C22—264no—
777C22—264no—
778C22—264no—
779C22—264no—
780C22—2632no—
781C22—264no—
782C22—264no—
783C22—264no—
784C22—264no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—5216no—
789C22—522no—
790C22#1171931514yes—
791C22D13×C22⋊Q814yes—
792C22#1171933514yes—
793C22#1171936214yes—
794C22#1171939514yes—
795C22#1171939614yes—
796C22#1171943514yes—
797C22C22×D4×D1311yescharacteristic
798C22C2×#8825111yescharacteristic
799C22C22×Q8×D1311yescharacteristic
800C22C22×#613111yescharacteristic
801C22C2×#41×D1311yescharacteristic
802C22C2×#41×D1311yescharacteristic
803C22C2×#8825611yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—264no—
812C4—264no—
813C4—522no—
814C4—522no—
815C4—522no—
816C4—522no—
817C2—268no—
818C2—524no—
819C2#1311866118yesdirect product factor
820C2C2×D13×C22⋊Q811yescharacteristic
821C2C2×#1171939611yescharacteristic
822C2C2×#1171936211yescharacteristic
823C2C2×#1171931511yescharacteristic
824C2C2×#1171933511yescharacteristic
825C2C2×#1171939511yescharacteristic
826C2C2×#1171943511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#398D13
hypocenterC13C2×#2450
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
3. #13118661C2direct (N × H)
4. C2×#11718647C2semidirect
5. C2×#11718655C2semidirect
6. C2×#11718334C2semidirect
7. C2×#11718307C2semidirect
8. C2×#11718316C2semidirect
11. C2×#11718650C2semidirect
12. C2×#11718650C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718648C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#398C2semidirect
41. C2×#88151C22semidirect
44. C13×#398C22semidirect
57. #11718655C22semidirect
58. #11718650C22semidirect
59. #11718650C22semidirect
60. #11718650C22semidirect
61. #11718648C22semidirect
62. #11718647C22semidirect
63. #11718334C22semidirect
66. D13×#95C22semidirect
67. #11718316C22semidirect
68. #11718307C22semidirect
86. C22×D52Q8semidirect
229. C2×D52C2×Q8semidirect
271. C2×#398D13semidirect
405. #398C2×D13semidirect
559. C2×C13#2450semidirect
679. C13C2×#2450semidirect
819. C2#13118661direct (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×#881472
#131186612
C2×#117186472
C2×#117186552
C2×#117183342
C2×#117183072
C2×#117183162
C2×#117183262
C2×#117186502
C2×#117186482
C2×D13×#952
C2×C13×#3982
C2×#245013