Finite Group Databasebeta

← C2×#13117882 #16022498

Subgroups — C2×#13117882 #16022498

Order 3328.

4262 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88149C211yesmaximal, characteristic
2C22×C4×D52C211yesmaximal, characteristic, complemented
3C22×#88147C211yesmaximal, characteristic, complemented
4#13117882C2116yesmaximal, direct product factor
5C2×#11718331C211yesmaximal, characteristic, complemented
6C2×#11718651C211yesmaximal, characteristic, complemented
7C2×#11718642C211yesmaximal, characteristic, complemented
8C2×#11718326C211yesmaximal, characteristic, complemented
9C2×#11718326C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic, complemented
11C2×#11718326C211yesmaximal, characteristic, complemented
12C2×C4×#6103C211yesmaximal, characteristic, complemented
13C2×#11718327C211yesmaximal, characteristic, complemented
14C2×#11718327C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C23×D52C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88149C4116yescomplemented
43C2×#88149C2218yes—
44C2×#88147—28no—
45C2×#88147C2218yescomplemented
46C2×C4×D52—28no—
47C2×C4×D52C2218yescomplemented
48C13×#387C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718651C2218yescomplemented
60#11718642C2218yescomplemented
61C4×#6103C2218yescomplemented
62#11718331C2218yescomplemented
63#11718327C2218yescomplemented
64#11718327C2218yescomplemented
65#11718326C2218yescomplemented
66#11718326C2218yescomplemented
67#11718326C2218yescomplemented
68#11718326C2218yescomplemented
69D13×#95C2218yescomplemented
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C22×D52—24no—
86C22×D52—24no—
87C22×D52—24no—
88C22×D52—24no—
89C22×D52—42no—
90C22×D52—42no—
91C22×D52C2×C418yescomplemented
92C22×D52C2×C418yescomplemented
93C22×D52C2×C418yescomplemented
94C22×D52C2314yes—
95C22×D52C2314yes—
96C22×D52C2314yes—
97C22×C4×D13—24no—
98C22×C4×D13—24no—
99C22×C4×D13—24no—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—42no—
106C22×C4×D13—42no—
107C22×C4×D13—42no—
108C22×C4×D13—42no—
109C22×C4×D13—42no—
110C22×C4×D13—42no—
111C22×C4×D13C2×C418yescomplemented
112C22×C4×D13C2314yes—
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C22×C4×D13C2314yes—
116C22×C4×D13C2314yes—
117C2×C13×C4⋊C4—24no—
118C2×C13×C4⋊C4C2×C418yescomplemented
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C4⋊C4C2314yes—
121C2×C42×C13—24no—
122C2×C42×C13C2314yes—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—42no—
129C2×#6103—42no—
130C2×#6103C2×C418yescomplemented
131C2×#6103C2×C418yescomplemented
132C2×#6103D418yescomplemented
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×#6103C2314yes—
143C2×C4⋊Dic13—24no—
144C2×C4⋊Dic13C2314yes—
145C2×C4×Dic13—24no—
146C2×C4×Dic13—42no—
147C2×C4×Dic13—42no—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151#88149C2×C4164yescomplemented
152#88147—232no—
153C4×D52—232no—
154C13×#95C2314yes—
155C13×#95C2314yes—
156C13×#95C2314yes—
157C13×#95C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2364—131nomaximal, Sylow
165C24×C13C2411yescharacteristic
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13C22×C414yes—
183C23×D13C22×C414yes—
184C23×D13C22×C414yes—
185C23×D13C2×D414yes—
186C23×D13#4114yes—
187C23×D13C2412yes—
188C23×D13C2412yes—
189C23×D13C2412yes—
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—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13C22×C414yes—
207C22×C4×C13C22×C414yes—
208C22×C4×C13C22×C414yes—
209C22×C4×C13C2×D414yes—
210C22×C4×C13#4114yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13C22×C414yes—
231C22×Dic13C2×D414yes—
232C22×Dic13#4114yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C2×D52—232no—
239C2×D52—232no—
240C2×D52—28no—
241C2×D52—28no—
242C2×D52—28no—
243C2×D52—28no—
244C2×D52—416no—
245C2×D52—44no—
246C2×D52—44no—
247C2×D52C22×C4116yescomplemented
248C2×D52C22×C4116yescomplemented
249C2×D52C22×C4116yescomplemented
250C2×C4×D13—28no—
251C2×C4×D13—28no—
252C2×C4×D13—28no—
253C2×C4×D13—28no—
254C2×C4×D13—28no—
255C2×C4×D13—28no—
256C2×C4×D13—28no—
257C2×C4×D13—28no—
258C2×C4×D13—416no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—416no—
266C2×C4×D13—416no—
267C2×C4×D13—416no—
268C2×C4×D13—416no—
269C2×C4×D13C22×C4116yescomplemented
270C13×C4⋊C4—28no—
271C13×C4⋊C4C22×C4116yescomplemented
272C42×C13—28no—
273#6103—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278#6103—44no—
279#6103—44no—
280#6103C22×C4116yescomplemented
281#6103C22×C4116yescomplemented
282#6103C2×D4116yescomplemented
283C4⋊Dic13—28no—
284C4×Dic13—28no—
285C4×Dic13—44no—
286C4×Dic13—44no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4—131no—
290#2364—1316no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#387—131no—
294C2×#387D1311yescharacteristic, complemented
295C2×#386—131no—
296C2×#386—131no—
297C2×#386—131no—
298C2×#386—131no—
299C2×C4×C22⋊C4—131no—
300C2×C4×C22⋊C4—131no—
301C2×C4×C22⋊C4—131no—
302C22×#95—131no—
303C23×C13C23×C412yes—
304C23×C13C22×D412yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13C2511yescharacteristic
311C22×D13—28no—
312C22×D13—28no—
313C22×D13—28no—
314C22×D13—28no—
315C22×D13—28no—
316C22×D13—28no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—28no—
322C22×D13—28no—
323C22×D13—28no—
324C22×D13—28no—
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—44no—
340C22×D13—44no—
341C22×D13—44no—
342C22×D13—44no—
343C22×D13—44no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13C4×D4116yes—
348C22×D13C23×C414yes—
349C22×D13C23×C414yes—
350C22×D13C23×C414yes—
351C22×D13C22×D414yes—
352C22×D13C2×#4114yes—
353C2×C4×C13—28no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—28no—
357C2×C4×C13—28no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—44no—
375C2×C4×C13—44no—
376C2×C4×C13C23×C414yes—
377C2×C4×C13C23×C414yes—
378C2×C4×C13C23×C414yes—
379C2×C4×C13C22×D414yes—
380C2×C4×C13C2×#4114yes—
381C2×Dic13—28no—
382C2×Dic13—28no—
383C2×Dic13—28no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13C23×C414yes—
399C2×Dic13C22×D414yes—
400C2×Dic13C2×#4114yes—
401D52—232no—
402D52—232no—
403D52—416no—
404C4×D13—416no—
405C4×D13—416no—
406C4×D13—416no—
407C4×D13—416no—
408C4×D13—416no—
409C23×D4—131no—
410C23×D4—131no—
411C23×D4—131no—
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4—131no—
416C24×C4—131no—
417C2×#121—1316no—
418C2×#121—138no—
419C2×C4×D4—138no—
420C2×C4×D4—138no—
421C2×C4×D4—268no—
422C2×C4×D4—268no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4C2×D1311yescharacteristic
425C22×C4⋊C4C2×D1311yescharacteristic
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C42—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42C2×D1311yescharacteristic
440#388—138no—
441#388—138no—
442#387—138no—
443#387C2×D1318yescomplemented
444#386—138no—
445#386—138no—
446#386—138no—
447#386—138no—
448C4×C22⋊C4—138no—
449C4×C22⋊C4—138no—
450C4×C22⋊C4—138no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—138no—
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C2×#95C2×D1311yescharacteristic
461C2×#95C2×D1311yescharacteristic
462C22×C13C2×C4×D414yes—
463C22×C13C4×#4114yes—
464C22×C13#51814yes—
465C22×C13#54614yes—
466C22×C13#54614yes—
467C22×C13#55314yes—
468C22×C13#55314yes—
469C22×C13C24×C411yescharacteristic
470C22×C13C23×D411yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C2×H(5,𝔽2)11yescharacteristic
475C22×C13C2×H(5,𝔽2)11yescharacteristic
476C2×D13—232no—
477C2×D13—24no—
478C2×D13—24no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—24no—
483C2×D13—24no—
484C2×D13—24no—
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—24no—
489C2×D13—416no—
490C2×D13—416no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C2×D13C2×C4×D418yes—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—42no—
506C4×C13—42no—
507Dic13—24no—
508Dic13—24no—
509Dic13—24no—
510Dic13—42no—
511Dic13—42no—
512C25—131no—
513C25—131no—
514C25—131no—
515C22×D4—138no—
516C22×D4—138no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—134no—
520C22×D4—134no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—522no—
526C22×D4—522no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—138no—
531C23×C4—134no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—134no—
535C23×C4—134no—
536C23×C4—134no—
537C23×C4—134no—
538C23×C4—264no—
539C23×C4—264no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—522no—
547C23×C4—522no—
548C23×C4—522no—
549C23×C4—522no—
550C23×C4—522no—
551C23×C4—522no—
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C23×C4C22×D1311yescharacteristic
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1311yescharacteristic
559#121—1364no—
560C4×D4—2632no—
561C4×D4—2632no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4C4×D1318yescomplemented
566C2×C4⋊C4C22×D1314yes—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—138no—
569C2×C22⋊C4—138no—
570C2×C22⋊C4—138no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—264no—
586C2×C22⋊C4—522no—
587C2×C22⋊C4—522no—
588C2×C42—24no—
589C2×C42—134no—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—264no—
593C2×C42—522no—
594C2×C42—522no—
595C2×C42C22×D1314yes—
596#95—134no—
597#95—134no—
598#95—134no—
599#95—134no—
600#95—134no—
601#95—134no—
602#95C22×D1314yes—
603#95C22×D1314yes—
604#95C22×D1314yes—
605#95C22×D1314yes—
606C2×C13#236418yescomplemented
607C2×C13C22×C4×D411yescharacteristic
608C2×C13C2×C4×#4111yescharacteristic
609C2×C13C2×#51811yescharacteristic
610C2×C13C2×#54611yescharacteristic
611C2×C13C2×#54611yescharacteristic
612C2×C13C2×#55311yescharacteristic
613C2×C13C2×#55311yescharacteristic
614D13—28no—
615D13—44no—
616D13—44no—
617C24—134no—
618C24—134no—
619C24—134no—
620C24—132no—
621C24—134no—
622C24—134no—
623C24—132no—
624C24—132no—
625C24—262no—
626C24—262no—
627C24—262no—
628C24—262no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24—262no—
640C24—262no—
641C24C23×D1311yescharacteristic
642C2×D4—1316no—
643C2×D4—1316no—
644C2×D4—1316no—
645C2×D4—268no—
646C2×D4—268no—
647C2×D4—2632no—
648C2×D4—2632no—
649C2×D4—268no—
650C2×D4—268no—
651C2×D4—5216no—
652C2×D4—524no—
653C2×D4—524no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—1316no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—268no—
680C22×C4—268no—
681C22×C4—268no—
682C22×C4—268no—
683C22×C4—268no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—268no—
697C22×C4—268no—
698C22×C4—268no—
699C22×C4—5216no—
700C22×C4—524no—
701C22×C4—524no—
702C22×C4—524no—
703C22×C4—524no—
704C22×C4—524no—
705C22×C4—524no—
706C22×C4—5216no—
707C22×C4—5216no—
708C22×C4—5216no—
709C22×C4—5216no—
710C22×C4C2×C4×D1314yes—
711C22×C4C2×C4×D1314yes—
712C22×C4C2×C4×D1314yes—
713C22×C4D4×D1314yes—
714C22×C4#613114yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1312yes—
722C4⋊C4—28no—
723C4⋊C4—268no—
724C4⋊C4C2×C4×D13116yescomplemented
725C22⋊C4—1316no—
726C22⋊C4—1316no—
727C22⋊C4—1316no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C42—28no—
736C42—268no—
737C42—524no—
738C42—524no—
739C13C2×#236411yescharacteristic, complemented, Sylow
740C23—1316no—
741C23—134no—
742C23—134no—
743C23—134no—
744C23—134no—
745C23—134no—
746C23—268no—
747C23—268no—
748C23—268no—
749C23—268no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—268no—
755C23—268no—
756C23—268no—
757C23—268no—
758C23—268no—
759C23—268no—
760C23—268no—
761C23—268no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23—524no—
779C23—524no—
780C23—524no—
781C23—524no—
782C23C22×C4×D1312yes—
783C23C2×D4×D1312yes—
784C23C2×#613112yes—
785C23#41×D1312yes—
786C23#41×D1312yes—
787C23#8825612yes—
788C23#8825612yes—
789C23C24×D1311yescharacteristic
790D4—2632no—
791D4—2632no—
792D4—5216no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—134no—
819C2×C4—268no—
820C2×C4—268no—
821C2×C4—268no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—5216no—
835C2×C4—5216no—
836C2×C4—5216no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4C22×C4×D1314yes—
842C2×C4C22×C4×D1314yes—
843C2×C4C22×C4×D1314yes—
844C2×C4C2×D4×D1314yes—
845C2×C4C2×#613114yes—
846C22—138no—
847C22—264no—
848C22—264no—
849C22—264no—
850C22—264no—
851C22—264no—
852C22—264no—
853C22—2632no—
854C22—264no—
855C22—264no—
856C22—264no—
857C22—264no—
858C22—264no—
859C22—264no—
860C22—522no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—5216no—
869C22—5216no—
870C22#1171922614yes—
871C22C4×D4×D1314yes—
872C22C4×#613114yes—
873C22#1171933514yes—
874C22#1171935914yes—
875C22#1171940014yes—
876C22#1171941414yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×D4×D1311yescharacteristic
879C22C22×#613111yescharacteristic
880C22C2×#41×D1311yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#8825611yescharacteristic
883C22C2×#8825611yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—42no—
891C4—264no—
892C4—264no—
893C4—264no—
894C4—522no—
895C4—522no—
896C2—268no—
897C2—524no—
898C2—524no—
899C2#1311788218yesdirect product factor
900C2C2×C4×D4×D1311yescharacteristic
901C2C2×C4×#613111yescharacteristic
902C2C2×#1171922611yescharacteristic
903C2C2×#1171933511yescharacteristic
904C2C2×#1171935911yescharacteristic
905C2C2×#1171941411yescharacteristic
906C2C2×#1171940011yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC22×#88149C2
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C2×#2364
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×D52C2semidirect
3. C22×#88147C2semidirect
4. #13117882C2direct (N × H)
5. C2×#11718331C2semidirect
6. C2×#11718651C2semidirect
7. C2×#11718642C2semidirect
8. C2×#11718326C2semidirect
9. C2×#11718326C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718326C2semidirect
12. C2×C4×#6103C2semidirect
13. C2×#11718327C2semidirect
14. C2×#11718327C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#387C2semidirect
42. C2×#88149C4semidirect
45. C2×#88147C22semidirect
47. C2×C4×D52C22semidirect
48. C13×#387C22semidirect
59. #11718651C22semidirect
60. #11718642C22semidirect
61. C4×#6103C22semidirect
62. #11718331C22semidirect
63. #11718327C22semidirect
64. #11718327C22semidirect
65. #11718326C22semidirect
66. #11718326C22semidirect
67. #11718326C22semidirect
68. #11718326C22semidirect
69. D13×#95C22semidirect
91. C22×D52C2×C4semidirect
92. C22×D52C2×C4semidirect
93. C22×D52C2×C4semidirect
111. C22×C4×D13C2×C4semidirect
118. C2×C13×C4⋊C4C2×C4semidirect
130. C2×#6103C2×C4semidirect
131. C2×#6103C2×C4semidirect
132. C2×#6103D4semidirect
151. #88149C2×C4semidirect
247. C2×D52C22×C4semidirect
248. C2×D52C22×C4semidirect
249. C2×D52C22×C4semidirect
269. C2×C4×D13C22×C4semidirect
271. C13×C4⋊C4C22×C4semidirect
280. #6103C22×C4semidirect
281. #6103C22×C4semidirect
282. #6103C2×D4semidirect
294. C2×#387D13semidirect
443. #387C2×D13semidirect
565. C2×C4⋊C4C4×D13semidirect
606. C2×C13#2364semidirect
724. C4⋊C4C2×C4×D13semidirect
739. C13C2×#2364semidirect
899. C2#13117882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881492
C22×C4×D522
C22×#881472
#131178822
C2×#117183312
C2×#117186512
C2×#117186422
C2×#117183262
C2×C4×#61032
C2×#117183272
C2×D13×#952
C2×C13×#3872
C2×#236413