Finite Group Databasebeta

← C2×#13117880 #16022496

Subgroups — C2×#13117880 #16022496

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×#88138C211yesmaximal, characteristic
2C22×#88147C211yesmaximal, characteristic, complemented
3C22×#88135C211yesmaximal, characteristic, complemented
4#13117880C2116yesmaximal, direct product factor
5C2×#11718330C211yesmaximal, characteristic, complemented
6C2×#11718313C211yesmaximal, characteristic, complemented
7C2×#11718639C211yesmaximal, characteristic, complemented
8C2×#11718326C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic, complemented
10C2×#11718617C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
13C2×C4×#6103C211yesmaximal, characteristic, complemented
14C2×C4×#6103C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88147—28no—
43C2×#88147C2218yescomplemented
44C2×#88138C4116yescomplemented
45C2×#88138C2218yes—
46C2×#88135—28no—
47C2×#88135C2218yescomplemented
48C13×#388C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718639C2218yescomplemented
60#11718619C2218yescomplemented
61#11718617C2218yescomplemented
62#11718617C2218yescomplemented
63C22⋊C4×Dic13C2218yescomplemented
64C4×#6103C2218yescomplemented
65C4×#6103C2218yescomplemented
66#11718330C2218yescomplemented
67#11718326C2218yescomplemented
68D13×#95C2218yescomplemented
69#11718313C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—24no—
80C22×C22⋊D13—24no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13C2×C418yescomplemented
84C22×C22⋊D13C2×C418yescomplemented
85C22×C22⋊D13C2314yes—
86C22×C22⋊D13C2314yes—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2314yes—
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C22×D52—24no—
98C22×D52—24no—
99C22×D52C2×C418yescomplemented
100C22×D52C2314yes—
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—24no—
106C22×C4×D13—24no—
107C22×C4×D13—42no—
108C22×C4×D13—42no—
109C22×C4×D13—42no—
110C22×C4×D13—42no—
111C22×C4×D13—42no—
112C22×C4×D13C2×C418yescomplemented
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C22×C4×D13C2314yes—
116C22×C4×D13C2314yes—
117C2×C13×C4⋊C4—24no—
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C22⋊C4—24no—
120C2×C13×C22⋊C4—42no—
121C2×C13×C22⋊C4C2×C418yescomplemented
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C42×C13—42no—
126C2×C42×C13C2314yes—
127C2×C22⋊Dic13—24no—
128C2×C22⋊Dic13C2314yes—
129C2×#6103—24no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—42no—
133C2×#6103C2×C418yescomplemented
134C2×#6103D418yescomplemented
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6101—24no—
142C2×#6101C2×C418yescomplemented
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×C4×Dic13—24no—
146C2×C4×Dic13—24no—
147C2×C4×Dic13—42no—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151#88147—232no—
152#88138C2×C4164yescomplemented
153#88135—232no—
154C13×#95C2314yes—
155C13×#95C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2364—131nomaximal, Sylow
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C22×C414yes—
172C24×C13C2412yes—
173C24×C13C2411yescharacteristic
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×D13—22no—
183C23×D13—22no—
184C23×D13C22×C414yes—
185C23×D13C22×C414yes—
186C23×D13C2×D414yes—
187C23×D13#4114yes—
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×C13C22×C414yes—
206C22×C4×C13C22×C414yes—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C2×C22⋊D13—232no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—416no—
218C2×C22⋊D13—44no—
219C2×C22⋊D13—44no—
220C2×C22⋊D13C22×C4116yescomplemented
221C2×C22⋊D13C22×C4116yescomplemented
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×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—28no—
236C22×Dic13—28no—
237C22×Dic13—44no—
238C22×Dic13—416no—
239C22×Dic13C22×C414yes—
240C22×Dic13C22×C414yes—
241C22×Dic13C2×D414yes—
242C22×Dic13#4114yes—
243C22×Dic13#4114yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×D52—232no—
251C2×D52—28no—
252C2×D52—28no—
253C2×D52C22×C4116yescomplemented
254C2×C4×D13—28no—
255C2×C4×D13—28no—
256C2×C4×D13—28no—
257C2×C4×D13—28no—
258C2×C4×D13—28no—
259C2×C4×D13—28no—
260C2×C4×D13—416no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C2×C4×D13—416no—
267C2×C4×D13—416no—
268C2×C4×D13—416no—
269C2×C4×D13C22×C4116yescomplemented
270C13×C4⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—44no—
273C13×C22⋊C4C22×C4116yescomplemented
274C42×C13—44no—
275C22⋊Dic13—28no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—44no—
280#6103C22×C4116yescomplemented
281#6103C2×D4116yescomplemented
282#6101—28no—
283#6101C22×C4116yescomplemented
284C4×Dic13—28no—
285C4×Dic13—28no—
286C4×Dic13—44no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4—131no—
290#2364—1316no—
291C2×#388—131no—
292C2×#388D1311yescharacteristic, complemented
293C2×#387—131no—
294C2×#387—131no—
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×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C23×C414yes—
317C23×C13C23×C412yes—
318C23×C13C22×D412yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13C2511yescharacteristic
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—28no—
336C22×D13—28no—
337C22×D13—28no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13C4×D4116yes—
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—22no—
357C2×C4×C13—22no—
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—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13C23×C414yes—
375C2×C4×C13C23×C414yes—
376C2×C4×C13C22×D414yes—
377C22⋊D13—232no—
378C22⋊D13—416no—
379C2×Dic13—28no—
380C2×Dic13—28no—
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—22no—
397C2×Dic13—416no—
398C2×Dic13—44no—
399C2×Dic13C23×C414yes—
400C2×Dic13C23×C414yes—
401C2×Dic13C22×D414yes—
402C2×Dic13C2×#4114yes—
403C2×Dic13C2×#4114yes—
404D52—232no—
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⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
434C22×C22⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C42—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42C2×D1311yescharacteristic
440#388—138no—
441#388C2×D1318yescomplemented
442#387—138no—
443#387—138no—
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—131no—
458C2×#95—131no—
459C2×#95—138no—
460C2×#95C2×D1311yescharacteristic
461C2×#95C2×D1311yescharacteristic
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—416no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13C2×C4×D414yes—
471C22×C13C4×#4114yes—
472C22×C13#51814yes—
473C22×C13#54614yes—
474C22×C13#54614yes—
475C22×C13#55314yes—
476C22×C13#55314yes—
477C22×C13C24×C411yescharacteristic
478C22×C13C23×D411yescharacteristic
479C22×C13C22×#4111yescharacteristic
480C22×C13C22×#4111yescharacteristic
481C22×C13C22×#4111yescharacteristic
482C22×C13C2×H(5,𝔽2)11yescharacteristic
483C22×C13C2×H(5,𝔽2)11yescharacteristic
484C2×D13—232no—
485C2×D13—24no—
486C2×D13—24no—
487C2×D13—24no—
488C2×D13—24no—
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—416no—
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—42no—
504C4×C13—42no—
505C4×C13—42no—
506Dic13—24no—
507Dic13—24no—
508Dic13—24no—
509Dic13—24no—
510Dic13—24no—
511Dic13—42no—
512C25—131no—
513C25—131no—
514C25C22×D1311yescharacteristic
515C22×D4—138no—
516C22×D4—134no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—138no—
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—131no—
531C23×C4—131no—
532C23×C4—138no—
533C23×C4—134no—
534C23×C4—131no—
535C23×C4—134no—
536C23×C4—134no—
537C23×C4—134no—
538C23×C4—134no—
539C23×C4—264no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—522no—
548C23×C4—522no—
549C23×C4—522no—
550C23×C4—522no—
551C23×C4—522no—
552C23×C4—522no—
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—138no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—138no—
571C2×C22⋊C4—138no—
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—264no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—522no—
584C2×C22⋊C4C4×D1318yescomplemented
585C2×C22⋊C4C22×D1314yes—
586C2×C22⋊C4C22×D1314yes—
587C2×C22⋊C4C22×D1314yes—
588C2×C42—42no—
589C2×C42—134no—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—264no—
593C2×C42—264no—
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#95—134no—
603#95—134no—
604#95C22×D1314yes—
605#95C22×D1314yes—
606C2×C13—44no—
607C2×C13#236418yescomplemented
608C2×C13C22×C4×D411yescharacteristic
609C2×C13C2×C4×#4111yescharacteristic
610C2×C13C2×#51811yescharacteristic
611C2×C13C2×#54611yescharacteristic
612C2×C13C2×#54611yescharacteristic
613C2×C13C2×#55311yescharacteristic
614C2×C13C2×#55311yescharacteristic
615D13—28no—
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—134no—
624C24—134no—
625C24—134no—
626C24—132no—
627C24—134no—
628C24—132no—
629C24—262no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24C2×C4×D1314yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—1316no—
643C2×D4—1316no—
644C2×D4—1316no—
645C2×D4—268no—
646C2×D4—2632no—
647C2×D4—268no—
648C2×D4—268no—
649C2×D4—2632no—
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—134no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—134no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—1316no—
680C22×C4—132no—
681C22×C4—268no—
682C22×C4—268no—
683C22×C4—268no—
684C22×C4—268no—
685C22×C4—268no—
686C22×C4—268no—
687C22×C4—268no—
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—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—268no—
702C22×C4—5216no—
703C22×C4—524no—
704C22×C4—524no—
705C22×C4—524no—
706C22×C4—524no—
707C22×C4—524no—
708C22×C4—5216no—
709C22×C4—5216no—
710C22×C4—5216no—
711C22×C4—524no—
712C22×C4—5216no—
713C22×C4C2×C4×D1314yes—
714C22×C4C2×C4×D1314yes—
715C22×C4D4×D1314yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1312yes—
722C4⋊C4—28no—
723C4⋊C4—1316no—
724C4⋊C4—268no—
725C22⋊C4—28no—
726C22⋊C4—44no—
727C22⋊C4—1316no—
728C22⋊C4—1316no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—524no—
734C22⋊C4C2×C4×D13116yescomplemented
735C42—44no—
736C42—268no—
737C42—268no—
738C42—524no—
739C13C2×#236411yescharacteristic, complemented, Sylow
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—1316no—
754C23—134no—
755C23—134no—
756C23—134no—
757C23—134no—
758C23—268no—
759C23—268no—
760C23—268no—
761C23—268no—
762C23—268no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—268no—
768C23—268no—
769C23—268no—
770C23—268no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—262no—
775C23—262no—
776C23—262no—
777C23—524no—
778C23—524no—
779C23—524no—
780C23—524no—
781C23C22×C4×D1314yes—
782C23C22×C4×D1312yes—
783C23C2×D4×D1312yes—
784C23#8825112yes—
785C23#41×D1312yes—
786C23#41×D1312yes—
787C23#41×D1312yes—
788C23#8825612yes—
789C23C24×D1311yescharacteristic
790D4—2632no—
791D4—2632no—
792D4—5216no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
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—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—134no—
819C2×C4—268no—
820C2×C4—268no—
821C2×C4—268no—
822C2×C4—268no—
823C2×C4—268no—
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—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—5216no—
840C2×C4—5216no—
841C2×C4—5216no—
842C2×C4—524no—
843C2×C4C22×C4×D1314yes—
844C2×C4C22×C4×D1314yes—
845C2×C4C2×D4×D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—138no—
855C22—264no—
856C22—264no—
857C22—264no—
858C22—264no—
859C22—264no—
860C22—264no—
861C22—2632no—
862C22—264no—
863C22—264no—
864C22—264no—
865C22—522no—
866C22—522no—
867C22—522no—
868C22—522no—
869C22—5216no—
870C22#1171922714yes—
871C22C4×D4×D1314yes—
872C22#1171925014yes—
873C22#1171931514yes—
874C22#1171936614yes—
875C22#1171938114yes—
876C22#1171941414yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×D4×D1311yescharacteristic
879C22C2×#8825111yescharacteristic
880C22C2×#41×D1311yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#41×D1311yescharacteristic
883C22C2×#8825611yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—264no—
894C4—264no—
895C4—522no—
896C2—44no—
897C2—268no—
898C2—524no—
899C2#1311788018yesdirect product factor
900C2C2×C4×D4×D1311yescharacteristic
901C2C2×#1171922711yescharacteristic
902C2C2×#1171925011yescharacteristic
903C2C2×#1171931511yescharacteristic
904C2C2×#1171938111yescharacteristic
905C2C2×#1171936611yescharacteristic
906C2C2×#1171941411yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2364
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#88147C2semidirect
3. C22×#88135C2semidirect
4. #13117880C2direct (N × H)
5. C2×#11718330C2semidirect
6. C2×#11718313C2semidirect
7. C2×#11718639C2semidirect
8. C2×#11718326C2semidirect
9. C2×#11718619C2semidirect
10. C2×#11718617C2semidirect
11. C2×#11718617C2semidirect
12. C2×C22⋊C4×Dic13C2semidirect
13. C2×C4×#6103C2semidirect
14. C2×C4×#6103C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#388C2semidirect
43. C2×#88147C22semidirect
44. C2×#88138C4semidirect
47. C2×#88135C22semidirect
48. C13×#388C22semidirect
59. #11718639C22semidirect
60. #11718619C22semidirect
61. #11718617C22semidirect
62. #11718617C22semidirect
63. C22⋊C4×Dic13C22semidirect
64. C4×#6103C22semidirect
65. C4×#6103C22semidirect
66. #11718330C22semidirect
67. #11718326C22semidirect
68. D13×#95C22semidirect
69. #11718313C22semidirect
83. C22×C22⋊D13C2×C4semidirect
84. C22×C22⋊D13C2×C4semidirect
99. C22×D52C2×C4semidirect
112. C22×C4×D13C2×C4semidirect
121. C2×C13×C22⋊C4C2×C4semidirect
133. C2×#6103C2×C4semidirect
134. C2×#6103D4semidirect
142. C2×#6101C2×C4semidirect
152. #88138C2×C4semidirect
220. C2×C22⋊D13C22×C4semidirect
221. C2×C22⋊D13C22×C4semidirect
253. C2×D52C22×C4semidirect
269. C2×C4×D13C22×C4semidirect
273. C13×C22⋊C4C22×C4semidirect
280. #6103C22×C4semidirect
281. #6103C2×D4semidirect
283. #6101C22×C4semidirect
292. C2×#388D13semidirect
441. #388C2×D13semidirect
584. C2×C22⋊C4C4×D13semidirect
607. C2×C13#2364semidirect
734. C22⋊C4C2×C4×D13semidirect
739. C13C2×#2364semidirect
899. C2#13117880direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
C22×#881472
C22×#881352
#131178802
C2×#117183302
C2×#117183132
C2×#117186392
C2×#117183262
C2×#117186192
C2×#117186172
C2×C22⋊C4×Dic132
C2×C4×#61032
C2×D13×#952
C2×C13×#3882
C2×#236413