Finite Group Databasebeta

← C2×#13118767 #16030557

Subgroups — C2×#13118767 #16030557

Order 3328.

3394 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88139C211yesmaximal, characteristic, complemented
2#13118767C2116yesmaximal, direct product factor
3C2×#11718622C211yesmaximal, characteristic, complemented
4C2×#11718883C211yesmaximal, characteristic, complemented
5C2×#11718608C211yesmaximal, characteristic, complemented
6C2×#11718884C211yesmaximal, characteristic
7C2×#11718590C211yesmaximal, characteristic, complemented
8C2×#11718612C211yesmaximal, characteristic, complemented
9C2×#11718601C211yesmaximal, characteristic, complemented
10C2×#11718651C211yesmaximal, characteristic, complemented
11C2×#11718639C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718872C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C2×C4×D4×C13—28no—
24C2×C4×D4×C13C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88139—28no—
45C2×#88139C2218yescomplemented
46#11718884C2218yes—
47#11718883C2218yescomplemented
48#11718874C2218yescomplemented
49#11718874C2218yescomplemented
50#11718872C2218yescomplemented
51C4×C22⋊Dic13C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718651C2218yescomplemented
63#11718639C2218yescomplemented
64#11718622C2218yescomplemented
65#11718612C2218yescomplemented
66#11718608C2218yescomplemented
67#11718601C2218yescomplemented
68#11718590C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
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×C13C2314yes—
84C23×C4×C13C2314yes—
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13—42no—
93C22×C22⋊D13—42no—
94C22×C22⋊D13—42no—
95C22×C22⋊D13C2314yes—
96C22×C22⋊D13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C22×Dic26—24no—
105C22×Dic26—24no—
106C22×Dic26—42no—
107C22×Dic26C2314yes—
108C4×D4×C13—232no—
109C2×C13×C4⋊C4—24no—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4D418yescomplemented
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C42×C13—24no—
116C2×C42×C13C2314yes—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—24no—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13—42no—
122C2×C22⋊Dic13—42no—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—42no—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×C4⋊Dic13—42no—
140C2×C4⋊Dic13C2314yes—
141C2×#6101—24no—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—42no—
145C2×C4×Dic13C2314yes—
146C2×C4×Dic13C2314yes—
147#88139—232no—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2459—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×C13—22no—
170C24×C13—22no—
171C24×C13C2×D414yes—
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×C13—28no—
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—22no—
196C22×C4×C13—22no—
197C22×C4×C13—28no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—28no—
201C22×C4×C13—28no—
202C22×C4×C13—28no—
203C22×C4×C13—44no—
204C22×C4×C13—44no—
205C22×C4×C13—416no—
206C22×C4×C13—416no—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2×D414yes—
209C22×C4×C13#4114yes—
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—44no—
220C2×C22⋊D13—44no—
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—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
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#4114yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C2×Dic26—28no—
253C2×Dic26—28no—
254C2×Dic26—44no—
255C2×Dic26—416no—
256C13×C4⋊C4—28no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4C2×D4116yescomplemented
259C42×C13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262C22⋊Dic13—28no—
263C22⋊Dic13—44no—
264C22⋊Dic13—44no—
265C22⋊Dic13—44no—
266#6103—28no—
267#6103—28no—
268#6103—28no—
269#6103—28no—
270#6103—44no—
271C4⋊Dic13—44no—
272#6101—28no—
273C4×Dic13—28no—
274C4×Dic13—44no—
275C22×#124—131no—
276C22×C4×D4D1311yescharacteristic, complemented
277#2459—1316no—
278C2×#394—131no—
279C2×#394—131no—
280C2×#393—131no—
281C2×#392—131no—
282C2×#391—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#388—131no—
286C2×#387—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×#381—131no—
290C2×C4×C22⋊C4—131no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13C22×D414yes—
318C23×C13C22×D412yes—
319C23×C13C2×#4114yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13C2×#4112yes—
323C23×C13C2×#4112yes—
324C23×C13H(5,𝔽2)12yes—
325C23×C13H(5,𝔽2)12yes—
326C23×C13C2511yescharacteristic
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13—44no—
340C22×D13—44no—
341D4×C13—232no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
345C2×C4×C13—28no—
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—416no—
358C2×C4×C13—416no—
359C2×C4×C13—44no—
360C2×C4×C13C22×D414yes—
361C2×C4×C13C22×D414yes—
362C2×C4×C13C2×#4114yes—
363C2×C4×C13C2×#4114yes—
364C22⋊D13—416no—
365C22⋊D13—416no—
366C2×Dic13—28no—
367C2×Dic13—22no—
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—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13—44no—
391C2×Dic13—44no—
392C2×Dic13—44no—
393C2×Dic13C2×#4114yes—
394Dic26—416no—
395C23×Q8—131no—
396C23×D4—131no—
397C23×D4—131no—
398C23×D4C2×D1311yescharacteristic
399C24×C4C2×D1311yescharacteristic
400C24×C4C2×D1311yescharacteristic
401C2×#124—138no—
402C2×#124—268no—
403C2×C4×D4—28no—
404C2×C4×D4C2×D1318yescomplemented
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4C2×D1311yescharacteristic
408C22×C22⋊C4—131no—
409C22×C22⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42C2×D1311yescharacteristic
424#394—138no—
425#394—138no—
426#393—138no—
427#392—138no—
428#391—138no—
429#388—138no—
430#388—138no—
431#388—138no—
432#387—138no—
433#386—138no—
434#386—138no—
435#381—138no—
436C4×C22⋊C4—138no—
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—131no—
446C2×#95—131no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13—24no—
451C22×C13—24no—
452C22×C13—24no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—416no—
462C22×C13—416no—
463C22×C13#52514yes—
464C22×C13#52914yes—
465C22×C13#53814yes—
466C22×C13#54614yes—
467C22×C13#54614yes—
468C22×C13#55514yes—
469C22×C13#55914yes—
470C22×C13C23×D411yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C22×#4111yescharacteristic
475C22×C13C2×H(5,𝔽2)11yescharacteristic
476C22×C13C2×H(5,𝔽2)11yescharacteristic
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—88no—
485C4×C13—24no—
486C4×C13—24no—
487C4×C13—24no—
488C4×C13—24no—
489C4×C13—42no—
490Dic13—24no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497C25—131no—
498C25C22×D1311yescharacteristic
499C25C22×D1311yescharacteristic
500C22×Q8—134no—
501C22×Q8—264no—
502C22×Q8—264no—
503C22×Q8—522no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—134no—
508C22×D4—134no—
509C22×D4—264no—
510C22×D4—264no—
511C22×D4—264no—
512C22×D4—522no—
513C22×D4—522no—
514C22×D4—522no—
515C22×D4C22×D1314yes—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1314yes—
531C23×C4C22×D1314yes—
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C23×C4C22×D1311yescharacteristic
535C23×C4C22×D1311yescharacteristic
536#124—2632no—
537C4×D4—232no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—134no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—264no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22⋊D1318yescomplemented
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—24no—
571C2×C42—134no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42—522no—
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—
586C2×C13—44no—
587C2×C13—44no—
588C2×C13#245918yescomplemented
589C2×C13C2×#52511yescharacteristic
590C2×C13C2×#52911yescharacteristic
591C2×C13C2×#53811yescharacteristic
592C2×C13C2×#54611yescharacteristic
593C2×C13C2×#54611yescharacteristic
594C2×C13C2×#55511yescharacteristic
595C2×C13C2×#55911yescharacteristic
596D13—82no—
597C24—22no—
598C24—22no—
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—
618C24C2×C22⋊D1314yes—
619C24C23×D1312yes—
620C24C23×D1312yes—
621C24C23×D1311yescharacteristic
622C2×Q8—268no—
623C2×Q8—268no—
624C2×Q8—524no—
625C2×Q8—5216no—
626C2×D4—232no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—268no—
631C2×D4—268no—
632C2×D4—268no—
633C2×D4—524no—
634C2×D4—524no—
635C2×D4—524no—
636C2×D4—5216no—
637C2×D4—5216no—
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—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
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#612714yes—
686C22×C4#612914yes—
687C22×C4C2×C22⋊D1314yes—
688C22×C4C2×C22⋊D1314yes—
689C22×C4C23×D1312yes—
690C22×C4C23×D1312yes—
691C22×C4C23×D1312yes—
692C22×C4C23×D1312yes—
693C22×C4C23×D1312yes—
694C4⋊C4—28no—
695C4⋊C4—268no—
696C4⋊C4—524no—
697C22⋊C4—28no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—268no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C22⋊C4C2×C22⋊D13116yescomplemented
710C42—28no—
711C42—268no—
712C42—524no—
713C13C2×#245911yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
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—
754C23C2×#612714yes—
755C23C2×#612712yes—
756C23C2×#612712yes—
757C23C2×#612912yes—
758C23#8825112yes—
759C23#41×D1312yes—
760C23#8825612yes—
761C23C22×C22⋊D1314yes—
762C23C22×C22⋊D1312yes—
763C23C24×D1311yescharacteristic
764Q8—5216no—
765D4—232no—
766D4—5216no—
767D4—5216no—
768C2×C4—28no—
769C2×C4—28no—
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—416no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—134no—
787C2×C4—268no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
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—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4—524no—
813C2×C4—524no—
814C2×C4C2×#612714yes—
815C2×C4C2×#612914yes—
816C2×C4C22×C22⋊D1314yes—
817C2×C4C22×C22⋊D1314yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22—522no—
839C22—522no—
840C22—522no—
841C22—1048no—
842C22#1171924314yes—
843C22#1171926414yes—
844C22#1171926514yes—
845C22#1171926814yes—
846C22#1171949614yes—
847C22#1171951114yes—
848C22#1171953414yes—
849C22C22×#612711yescharacteristic
850C22C22×#612711yescharacteristic
851C22C22×#612911yescharacteristic
852C22C2×#8825111yescharacteristic
853C22C2×#41×D1311yescharacteristic
854C22C2×#8825611yescharacteristic
855C22C23×C22⋊D1311yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—264no—
862C4—522no—
863C4—522no—
864C4—522no—
865C4—522no—
866C4—522no—
867C4—522no—
868C2—44no—
869C2—44no—
870C2—1042no—
871C2#1311876718yesdirect product factor
872C2C2×#1171949611yescharacteristic
873C2C2×#1171924311yescharacteristic
874C2C2×#1171926511yescharacteristic
875C2C2×#1171953411yescharacteristic
876C2C2×#1171951111yescharacteristic
877C2C2×#1171926811yescharacteristic
878C2C2×#1171926411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2459
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88139C2semidirect
2. #13118767C2direct (N × H)
3. C2×#11718622C2semidirect
4. C2×#11718883C2semidirect
5. C2×#11718608C2semidirect
7. C2×#11718590C2semidirect
8. C2×#11718612C2semidirect
9. C2×#11718601C2semidirect
10. C2×#11718651C2semidirect
11. C2×#11718639C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718872C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C22×C4×D4×C13C2semidirect
24. C2×C4×D4×C13C22semidirect
45. C2×#88139C22semidirect
47. #11718883C22semidirect
48. #11718874C22semidirect
49. #11718874C22semidirect
50. #11718872C22semidirect
51. C4×C22⋊Dic13C22semidirect
62. #11718651C22semidirect
63. #11718639C22semidirect
64. #11718622C22semidirect
65. #11718612C22semidirect
66. #11718608C22semidirect
67. #11718601C22semidirect
68. #11718590C22semidirect
112. C2×C13×C22⋊C4D4semidirect
258. C13×C22⋊C4C2×D4semidirect
276. C22×C4×D4D13semidirect
404. C2×C4×D4C2×D13semidirect
567. C2×C22⋊C4C22⋊D13semidirect
588. C2×C13#2459semidirect
709. C22⋊C4C2×C22⋊D13semidirect
713. C13C2×#2459semidirect
871. C2#13118767direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881392
#131187672
C2×#117186222
C2×#117188832
C2×#117186082
C2×#117188842
C2×#117185902
C2×#117186122
C2×#117186012
C2×#117186512
C2×#117186392
C2×#117188742
C2×#117188722
C2×C4×C22⋊Dic132
C22×C4×D4×C132
C2×#245913