Finite Group Databasebeta

← C2×#13118580 #16030653

Subgroups — C2×#13118580 #16030653

Order 3328.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88193C211yesmaximal, characteristic
2#13118580C2116yesmaximal, direct product factor
3C2×#11718643C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718654C211yesmaximal, characteristic, complemented
6C2×#11718620C211yesmaximal, characteristic, complemented
7C2×#11718601C211yesmaximal, characteristic, complemented
8C2×#11718594C211yesmaximal, characteristic, complemented
9C2×#11718881C211yesmaximal, characteristic, complemented
10C2×#11718874C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic, complemented
12C2×#11718619C211yesmaximal, characteristic, complemented
13C2×#11718607C211yesmaximal, characteristic, complemented
14C2×#11718872C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C2×C4×D4×C13—28no—
25C2×C4×D4×C13C2218yescomplemented
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C2×#88193—28no—
35C2×#88193C2218yes—
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44#11718881C2218yescomplemented
45#11718874C2218yescomplemented
46#11718874C2218yescomplemented
47#11718872C2218yescomplemented
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2218yescomplemented
61#11718654C2218yescomplemented
62#11718643C2218yescomplemented
63#11718620C2218yescomplemented
64#11718619C2218yescomplemented
65#11718613C2218yescomplemented
66#11718607C2218yescomplemented
67#11718601C2218yescomplemented
68#11718594C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13D418yes—
75C22×D4×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—42no—
81C23×C4×C13—42no—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2314yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13—24no—
93C22×C22⋊D13—24no—
94C22×C22⋊D13—42no—
95C22×C22⋊D13C2314yes—
96C22×C22⋊D13C2314yes—
97C23×Dic13—24no—
98C23×Dic13—24no—
99C23×Dic13—24no—
100C23×Dic13—42no—
101C23×Dic13—42no—
102C23×Dic13—42no—
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2314yes—
110C23×Dic13C2311yescharacteristic
111C23×Dic13C2314yes—
112C4×D4×C13—232no—
113C2×C13×C4⋊C4—24no—
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4C2314yes—
118C2×C13×C22⋊C4C2314yes—
119C2×C42×C13—24no—
120C2×C42×C13C2314yes—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—42no—
124C2×C22⋊Dic13—42no—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129#88193—232no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—42no—
133C2×#6103—42no—
134C2×#6103—42no—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101—42no—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2444—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13C2×D414yes—
170C24×C13C2×D414yes—
171C24×C13#4114yes—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13C2412yes—
184C2×D4×C13—232no—
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13C2×D4116yes—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—28no—
196C22×C4×C13—28no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—28no—
204C22×C4×C13—28no—
205C22×C4×C13—44no—
206C22×C4×C13—44no—
207C22×C4×C13—416no—
208C22×C4×C13—416no—
209C22×C4×C13C2×D414yes—
210C22×C4×C13#4114yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—28no—
218C2×C22⋊D13—28no—
219C2×C22⋊D13—28no—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—44no—
222C2×C22⋊D13—416no—
223C2×C22⋊D13—416no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—28no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—28no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—28no—
247C22×Dic13—44no—
248C22×Dic13—44no—
249C22×Dic13—44no—
250C22×Dic13—416no—
251C22×Dic13—416no—
252C22×Dic13#4114yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C13×C4⋊C4—28no—
261C13×C22⋊C4—28no—
262C13×C22⋊C4—28no—
263C42×C13—28no—
264C22⋊Dic13—28no—
265C22⋊Dic13—28no—
266C22⋊Dic13—44no—
267C22⋊Dic13—44no—
268#6103—28no—
269#6103—28no—
270#6103—44no—
271#6103—44no—
272#6103—44no—
273#6101—28no—
274#6101—28no—
275#6101—44no—
276C22×#121—131no—
277C22×C4×D4D1311yescharacteristic, complemented
278#2444—1316no—
279C2×#400—131no—
280C2×#397—131no—
281C2×#397—131no—
282C2×#394—131no—
283C2×#388—131no—
284C2×#387—131no—
285C2×#386—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×#385—131no—
290C2×#381—131no—
291C22×#95—131no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—28no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13#123116yes—
316C23×C13C22×D414yes—
317C23×C13C22×D414yes—
318C23×C13C22×D412yes—
319C23×C13C2×#4114yes—
320C23×C13C2×#4114yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13C2×#4112yes—
324C23×C13C2×#4112yes—
325C23×C13H(5,𝔽2)12yes—
326C23×C13H(5,𝔽2)12yes—
327C23×C13C2511yescharacteristic
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13—44no—
340C22×D13—44no—
341C22×D13—44no—
342D4×C13—232no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—416no—
359C2×C4×C13—416no—
360C2×C4×C13—44no—
361C2×C4×C13—44no—
362C2×C4×C13—44no—
363C2×C4×C13C22×D414yes—
364C2×C4×C13C2×#4114yes—
365C22⋊D13—416no—
366C22⋊D13—416no—
367C2×Dic13—28no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—416no—
389C2×Dic13—416no—
390C2×Dic13—44no—
391C2×Dic13—44no—
392C2×Dic13—44no—
393C2×Dic13—44no—
394C2×Dic13—44no—
395C2×Dic13—44no—
396C2×Dic13C2×#4114yes—
397C23×D4—131no—
398C23×D4—131no—
399C23×D4C2×D1311yescharacteristic
400C24×C4—131no—
401C24×C4—131no—
402C24×C4C2×D1311yescharacteristic
403C24×C4C2×D1311yescharacteristic
404C2×#121—138no—
405C2×#121—268no—
406C2×C4×D4—28no—
407C2×C4×D4C2×D1318yescomplemented
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4C2×D1311yescharacteristic
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#400—138no—
425#397—138no—
426#397—138no—
427#394—138no—
428#388—138no—
429#387—138no—
430#386—138no—
431#386—138no—
432#386—138no—
433#386—138no—
434#385—138no—
435#381—138no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—138no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C22×C13—24no—
450C22×C13—24no—
451C22×C13—24no—
452C22×C13—24no—
453C22×C13—232no—
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—416no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13C2×#12318yes—
465C22×C13C2×#12314yes—
466C22×C13#52914yes—
467C22×C13#53814yes—
468C22×C13#54614yes—
469C22×C13#54614yes—
470C22×C13#55314yes—
471C22×C13#55314yes—
472C22×C13C23×D411yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C22×#4111yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C22×#4111yescharacteristic
477C22×C13C2×H(5,𝔽2)11yescharacteristic
478C22×C13C2×H(5,𝔽2)11yescharacteristic
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—42no—
486C2×D13—88no—
487C4×C13—24no—
488C4×C13—24no—
489C4×C13—42no—
490C4×C13—42no—
491C4×C13—42no—
492Dic13—24no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497Dic13—42no—
498Dic13—42no—
499C25—131no—
500C25C22×D1311yescharacteristic
501C25C22×D1311yescharacteristic
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—134no—
505C22×D4—134no—
506C22×D4—264no—
507C22×D4—264no—
508C22×D4—264no—
509C22×D4—264no—
510C22×D4—264no—
511C22×D4—522no—
512C22×D4C22⋊D1318yes—
513C22×D4C22×D1314yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—42no—
519C23×C4—42no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—134no—
528C23×C4—134no—
529C23×C4—264no—
530C23×C4—264no—
531C23×C4—264no—
532C23×C4—522no—
533C23×C4—522no—
534C23×C4—522no—
535C23×C4C22×D1311yescharacteristic
536C23×C4C22×D1311yescharacteristic
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1314yes—
539C23×C4C22×D1314yes—
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542#121—2632no—
543C4×D4—232no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—134no—
546C2×C4⋊C4—134no—
547C2×C4⋊C4—134no—
548C2×C4⋊C4—264no—
549C2×C4⋊C4—264no—
550C2×C4⋊C4—522no—
551C2×C4⋊C4C22×D1314yes—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—264no—
567C2×C22⋊C4—522no—
568C2×C22⋊C4—522no—
569C2×C22⋊C4—522no—
570C2×C22⋊C4—522no—
571C2×C22⋊C4—522no—
572C2×C22⋊C4C22×D1314yes—
573C2×C22⋊C4C22×D1314yes—
574C2×C42—24no—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584#95—134no—
585#95—134no—
586#95—134no—
587#95—134no—
588C2×C13—28no—
589C2×C13—44no—
590C2×C13#244418yescomplemented
591C2×C13C22×#12311yescharacteristic
592C2×C13C2×#52911yescharacteristic
593C2×C13C2×#53811yescharacteristic
594C2×C13C2×#54611yescharacteristic
595C2×C13C2×#54611yescharacteristic
596C2×C13C2×#55311yescharacteristic
597C2×C13C2×#55311yescharacteristic
598D13—82no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—132no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24—262no—
617C24#612714yes—
618C24#612714yes—
619C24C2×C22⋊D1314yes—
620C24C2×C22⋊D1314yes—
621C24C23×D1312yes—
622C24C23×D1312yes—
623C24C23×D1311yescharacteristic
624C2×D4—232no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—268no—
628C2×D4—268no—
629C2×D4—268no—
630C2×D4—268no—
631C2×D4—268no—
632C2×D4—524no—
633C2×D4—5216no—
634C2×D4—5216no—
635C2×D4C2×C22⋊D13116yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4—134no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—268no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—268no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—268no—
688C22×C4—524no—
689C22×C4—524no—
690C22×C4—524no—
691C22×C4—5216no—
692C22×C4—5216no—
693C22×C4#612914yes—
694C22×C4C2×C22⋊D1314yes—
695C22×C4C23×D1312yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C4⋊C4—28no—
701C4⋊C4—268no—
702C4⋊C4—268no—
703C4⋊C4—524no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—268no—
707C22⋊C4—268no—
708C22⋊C4—268no—
709C22⋊C4—268no—
710C22⋊C4—524no—
711C22⋊C4—524no—
712C22⋊C4—524no—
713C22⋊C4—524no—
714C22⋊C4—524no—
715C42—28no—
716C13C2×#244411yescharacteristic, complemented, Sylow
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—262no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23—524no—
753C23—524no—
754C23#88183116yes—
755C23C2×#612714yes—
756C23C2×#612714yes—
757C23C2×#612712yes—
758C23C2×#612712yes—
759C23C2×#612912yes—
760C23#8825112yes—
761C23#41×D1312yes—
762C23#8825612yes—
763C23C22×C22⋊D1314yes—
764C23C22×C22⋊D1314yes—
765C23C22×C22⋊D1312yes—
766C23C24×D1311yescharacteristic
767D4—232no—
768D4—5216no—
769D4—5216no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—134no—
791C2×C4—268no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—262no—
812C2×C4—5216no—
813C2×C4—5216no—
814C2×C4—524no—
815C2×C4—524no—
816C2×C4—524no—
817C2×C4—524no—
818C2×C4—524no—
819C2×C4—524no—
820C2×C4C2×#612914yes—
821C2×C4C22×C22⋊D1314yes—
822C22—24no—
823C22—24no—
824C22—232no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—416no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—522no—
838C22—522no—
839C22—522no—
840C22—522no—
841C22—522no—
842C22—522no—
843C22—522no—
844C22—1048no—
845C22#1171924314yes—
846C22#1171924514yes—
847C22#1171926514yes—
848C22#1171927014yes—
849C22C2×#8818318yes—
850C22C2×#8818314yes—
851C22#1171951114yes—
852C22#1171953414yes—
853C22C22×#612711yescharacteristic
854C22C22×#612711yescharacteristic
855C22C22×#612911yescharacteristic
856C22C2×#8825111yescharacteristic
857C22C2×#41×D1311yescharacteristic
858C22C2×#8825611yescharacteristic
859C22C23×C22⋊D1311yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—264no—
866C4—522no—
867C4—522no—
868C4—522no—
869C4—522no—
870C4—522no—
871C4—522no—
872C2—28no—
873C2—44no—
874C2—1042no—
875C2#1311858018yesdirect product factor
876C2C22×#8818311yescharacteristic
877C2C2×#1171924311yescharacteristic
878C2C2×#1171926511yescharacteristic
879C2C2×#1171953411yescharacteristic
880C2C2×#1171951111yescharacteristic
881C2C2×#1171927011yescharacteristic
882C2C2×#1171924511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2444
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13118580C2direct (N × H)
3. C2×#11718643C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718654C2semidirect
6. C2×#11718620C2semidirect
7. C2×#11718601C2semidirect
8. C2×#11718594C2semidirect
9. C2×#11718881C2semidirect
10. C2×#11718874C2semidirect
11. C2×#11718874C2semidirect
12. C2×#11718619C2semidirect
13. C2×#11718607C2semidirect
14. C2×#11718872C2semidirect
15. C22×#88071C2semidirect
16. C22×C4×D4×C13C2semidirect
25. C2×C4×D4×C13C22semidirect
44. #11718881C22semidirect
45. #11718874C22semidirect
46. #11718874C22semidirect
47. #11718872C22semidirect
60. C2×#88071C22semidirect
61. #11718654C22semidirect
62. #11718643C22semidirect
63. #11718620C22semidirect
64. #11718619C22semidirect
65. #11718613C22semidirect
66. #11718607C22semidirect
67. #11718601C22semidirect
68. #11718594C22semidirect
277. C22×C4×D4D13semidirect
407. C2×C4×D4C2×D13semidirect
590. C2×C13#2444semidirect
716. C13C2×#2444semidirect
875. C2#13118580direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881932
#131185802
C2×#117186432
C2×#117186132
C2×#117186542
C2×#117186202
C2×#117186012
C2×#117185942
C2×#117188812
C2×#117188742
C2×#117186192
C2×#117186072
C2×#117188722
C22×#880712
C22×C4×D4×C132
C2×#244413