Finite Group Databasebeta

← C2×#13117533 #16021691

Subgroups — C2×#13117533 #16021691

Order 3328.

4150 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×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13117533C2116yesmaximal, direct product factor
5C2×#11718612C211yesmaximal, characteristic, complemented
6C2×#11718331C211yesmaximal, characteristic, complemented
7C2×#11718313C211yesmaximal, characteristic, complemented
8C2×#11718639C211yesmaximal, characteristic, complemented
9C2×#11718874C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×#11718617C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718648C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C23×C4×D13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C2×C4×C22⋊D13—28no—
32C2×C4×C22⋊D13C2218yescomplemented
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88147—28no—
45C2×#88147C2218yescomplemented
46C2×#88138C4116yescomplemented
47C2×#88138C2218yes—
48C13×#385C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51#11718874C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718650C2218yescomplemented
61#11718648C2218yescomplemented
62#11718639C2218yescomplemented
63#11718617C2218yescomplemented
64#11718617C2218yescomplemented
65#11718612C2218yescomplemented
66#11718331C2218yescomplemented
67#11718326C2218yescomplemented
68D13×#95C2218yescomplemented
69#11718313C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13—24no—
74C23×C4×C13—42no—
75C23×C4×C13—42no—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13C2×C418yescomplemented
88C22×C22⋊D13C2×C418yescomplemented
89C22×C22⋊D13C2314yes—
90C22×C22⋊D13C2314yes—
91C23×Dic13C2311yescharacteristic
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—42no—
104C22×C4×D13—42no—
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×D13D418yescomplemented
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C22×C4×D13C2314yes—
116C22×C4×D13C2314yes—
117C2×C13×C4⋊C4—24no—
118C2×C13×C4⋊C4—42no—
119C2×C13×C4⋊C4C2314yes—
120C2×C13×C4⋊C4C2314yes—
121C2×C13×C22⋊C4—42no—
122C2×C13×C22⋊C4C2×C418yescomplemented
123C2×C13×C22⋊C4C2314yes—
124C2×C13×C22⋊C4C2314yes—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13—42no—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C4×C22⋊D13—232no—
130C2×#6103—24no—
131C2×#6103—24no—
132C2×#6103—24no—
133C2×#6103—42no—
134C2×#6103—42no—
135C2×#6103C2×C418yescomplemented
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×C4⋊Dic13—42no—
143C2×C4⋊Dic13C2314yes—
144C2×#6101—24no—
145C2×#6101C2×C418yescomplemented
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×C4×Dic13—24no—
149C2×C4×Dic13—24no—
150C2×C4×Dic13C2314yes—
151C2×C4×Dic13C2314yes—
152#88147—232no—
153#88138C2×C4164yescomplemented
154C13×#95C2314yes—
155C13×#95C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164C2×#2325—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×C13—28no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13—416no—
209C22×C4×C13C22×C414yes—
210C22×C4×C13C22×C414yes—
211C22×C4×C13C2×D414yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C2×C22⋊D13—232no—
219C2×C22⋊D13—28no—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—416no—
222C2×C22⋊D13—44no—
223C2×C22⋊D13—44no—
224C2×C22⋊D13C22×C4116yescomplemented
225C2×C22⋊D13C22×C4116yescomplemented
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×Dic13C22×C414yes—
242C22×Dic13C22×C414yes—
243C22×Dic13C2×D414yes—
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—416no—
257C2×C4×D13—416no—
258C2×C4×D13—44no—
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—44no—
266C2×C4×D13—416no—
267C2×C4×D13—416no—
268C2×C4×D13C22×C4116yescomplemented
269C2×C4×D13C2×D4116yescomplemented
270C13×C4⋊C4—28no—
271C13×C4⋊C4—44no—
272C13×C22⋊C4—44no—
273C13×C22⋊C4C22×C4116yescomplemented
274C22⋊Dic13—28no—
275C22⋊Dic13—44no—
276#6103—28no—
277#6103—28no—
278#6103—28no—
279#6103—44no—
280#6103—44no—
281#6103C22×C4116yescomplemented
282C4⋊Dic13—44no—
283#6101—28no—
284#6101C22×C4116yescomplemented
285C4×Dic13—28no—
286C4×Dic13—28no—
287C22×#121—131no—
288C22×C4×D4—131no—
289C22×C4×D4—131no—
290#2325—1316no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#387—131no—
294C2×#387—131no—
295C2×#386—131no—
296C2×#386—131no—
297C2×#386—131no—
298C2×#386—131no—
299C2×#385—131no—
300C2×#385D1311yescharacteristic, complemented
301C2×#380—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×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C132−1+412yes—
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—416no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13C23×C414yes—
376C2×C4×C13C23×C414yes—
377C2×C4×C13C22×D414yes—
378C22⋊D13—232no—
379C22⋊D13—416no—
380C2×Dic13—28no—
381C2×Dic13—28no—
382C2×Dic13—28no—
383C2×Dic13—22no—
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—22no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13—44no—
401C2×Dic13C23×C414yes—
402C2×Dic13C23×C414yes—
403C2×Dic13C22×D414yes—
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×C4C2×D1311yescharacteristic
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⋊C4—131no—
426C22×C4⋊C4C2×D1311yescharacteristic
427C22×C4⋊C4C2×D1311yescharacteristic
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×C22⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4C2×D1311yescharacteristic
438C22×C42—131no—
439C22×C42—131no—
440#388—138no—
441#388—138no—
442#387—138no—
443#387—138no—
444#386—138no—
445#386—138no—
446#386—138no—
447#386—138no—
448#385—138no—
449#385C2×D1318yescomplemented
450#380—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×C13#51814yes—
472C22×C13#52014yes—
473C22×C13#53414yes—
474C22×C13#53714yes—
475C22×C13#53814yes—
476C22×C13#53914yes—
477C22×C13C24×C411yescharacteristic
478C22×C13C23×D411yescharacteristic
479C22×C13C22×#4111yescharacteristic
480C22×C13C2×H(5,𝔽2)11yescharacteristic
481C22×C13C2×H(5,𝔽2)11yescharacteristic
482C22×C13C2×H(5,𝔽2)11yescharacteristic
483C22×C13C2×2−1+411yescharacteristic
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—42no—
510Dic13—42no—
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—24no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—138no—
534C23×C4—138no—
535C23×C4—134no—
536C23×C4—134no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—134no—
541C23×C4—134no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—522no—
545C23×C4—522no—
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×D1314yes—
559#121—1364no—
560C4×D4—2632no—
561C4×D4—2632no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—42no—
564C2×C4⋊C4—138no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—522no—
570C2×C4⋊C4C22×D1314yes—
571C2×C4⋊C4C22×D1314yes—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—138no—
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—134no—
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×C22⋊C4—522no—
589C2×C22⋊C4C4×D1318yescomplemented
590C2×C22⋊C4C22×D1314yes—
591C2×C22⋊C4C22×D1314yes—
592C2×C42—134no—
593C2×C42—134no—
594C2×C42—264no—
595C2×C42—264no—
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#232518yescomplemented
608C2×C13C22×C4×D411yescharacteristic
609C2×C13C2×#51811yescharacteristic
610C2×C13C2×#52011yescharacteristic
611C2×C13C2×#53411yescharacteristic
612C2×C13C2×#53711yescharacteristic
613C2×C13C2×#53811yescharacteristic
614C2×C13C2×#53911yescharacteristic
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—28no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—416no—
673C22×C4—134no—
674C22×C4—134no—
675C22×C4—134no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—1316no—
680C22×C4—1316no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—268no—
685C22×C4—268no—
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—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—5216no—
702C22×C4—5216no—
703C22×C4—524no—
704C22×C4—524no—
705C22×C4—524no—
706C22×C4—524no—
707C22×C4—524no—
708C22×C4—524no—
709C22×C4—524no—
710C22×C4—524no—
711C22×C4—5216no—
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—44no—
724C4⋊C4—1316no—
725C4⋊C4—268no—
726C4⋊C4—524no—
727C22⋊C4—44no—
728C22⋊C4—1316no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C22⋊C4—524no—
736C22⋊C4C2×C4×D13116yescomplemented
737C42—268no—
738C42—268no—
739C13C2×#232511yescharacteristic, 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—268no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
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#8825112yes—
786C23#8825412yes—
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—416no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—268no—
819C2×C4—268no—
820C2×C4—268no—
821C2×C4—262no—
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—262no—
835C2×C4—262no—
836C2×C4—5216no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—5216no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4—524no—
843C2×C4C22×C4×D1314yes—
844C2×C4C22×C4×D1314yes—
845C2×C4C2×D4×D1314yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—138no—
855C22—264no—
856C22—2632no—
857C22—264no—
858C22—264no—
859C22—264no—
860C22—264no—
861C22—264no—
862C22—264no—
863C22—264no—
864C22—264no—
865C22—5216no—
866C22—522no—
867C22—522no—
868C22—522no—
869C22—522no—
870C22#1171920914yes—
871C22C4×D4×D1314yes—
872C22#1171925014yes—
873C22#1171929414yes—
874C22#1171933414yes—
875C22#1171934314yes—
876C22#1171936214yes—
877C22C23×C4×D1311yescharacteristic
878C22C22×D4×D1311yescharacteristic
879C22C2×#8825111yescharacteristic
880C22C2×#8825111yescharacteristic
881C22C2×#8825411yescharacteristic
882C22C2×#41×D1311yescharacteristic
883C22C2×#8825611yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—44no—
897C2—268no—
898C2—524no—
899C2#1311753318yesdirect product factor
900C2C2×C4×D4×D1311yescharacteristic
901C2C2×#1171925011yescharacteristic
902C2C2×#1171920911yescharacteristic
903C2C2×#1171929411yescharacteristic
904C2C2×#1171933411yescharacteristic
905C2C2×#1171936211yescharacteristic
906C2C2×#1171934311yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×#2325
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#88147C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13117533C2direct (N × H)
5. C2×#11718612C2semidirect
6. C2×#11718331C2semidirect
7. C2×#11718313C2semidirect
8. C2×#11718639C2semidirect
9. C2×#11718874C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718617C2semidirect
12. C2×#11718617C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718648C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#385C2semidirect
32. C2×C4×C22⋊D13C22semidirect
45. C2×#88147C22semidirect
46. C2×#88138C4semidirect
48. C13×#385C22semidirect
51. #11718874C22semidirect
60. #11718650C22semidirect
61. #11718648C22semidirect
62. #11718639C22semidirect
63. #11718617C22semidirect
64. #11718617C22semidirect
65. #11718612C22semidirect
66. #11718331C22semidirect
67. #11718326C22semidirect
68. D13×#95C22semidirect
69. #11718313C22semidirect
87. C22×C22⋊D13C2×C4semidirect
88. C22×C22⋊D13C2×C4semidirect
99. C22×D52C2×C4semidirect
111. C22×C4×D13C2×C4semidirect
112. C22×C4×D13D4semidirect
122. C2×C13×C22⋊C4C2×C4semidirect
135. C2×#6103C2×C4semidirect
145. C2×#6101C2×C4semidirect
153. #88138C2×C4semidirect
224. C2×C22⋊D13C22×C4semidirect
225. C2×C22⋊D13C22×C4semidirect
253. C2×D52C22×C4semidirect
268. C2×C4×D13C22×C4semidirect
269. C2×C4×D13C2×D4semidirect
273. C13×C22⋊C4C22×C4semidirect
281. #6103C22×C4semidirect
284. #6101C22×C4semidirect
300. C2×#385D13semidirect
449. #385C2×D13semidirect
589. C2×C22⋊C4C4×D13semidirect
607. C2×C13#2325semidirect
736. C22⋊C4C2×C4×D13semidirect
739. C13C2×#2325semidirect
899. C2#13117533direct (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×C4×C22⋊D132
#131175332
C2×#117186122
C2×#117183312
C2×#117183132
C2×#117186392
C2×#117188742
C2×#117183262
C2×#117186172
C2×#117186502
C2×#117186482
C2×D13×#952
C2×C13×#3852
C2×#232513