Finite Group Databasebeta

← C2×#13117600 #16021785

Subgroups — C2×#13117600 #16021785

Order 3328.

3414 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88149C211yesmaximal, characteristic
2#13117600C2116yesmaximal, direct product factor
3C2×#11718600C211yesmaximal, characteristic, complemented
4C2×#11718649C211yesmaximal, characteristic, complemented
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×#11718325C211yesmaximal, characteristic, complemented
13C2×C4×#6103C211yesmaximal, characteristic, complemented
14C2×#11718327C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic, complemented
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×D52C2211yescharacteristic
19C23×D52C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
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—
44C13×#387C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718651C2218yescomplemented
56#11718649C2218yescomplemented
57#11718642C2218yescomplemented
58#11718600C2218yescomplemented
59C4×#6103C2218yescomplemented
60#11718331C2218yescomplemented
61#11718327C2218yescomplemented
62#11718327C2218yescomplemented
63#11718326C2218yescomplemented
64#11718326C2218yescomplemented
65#11718326C2218yescomplemented
66#11718326C2218yescomplemented
67#11718325C2218yescomplemented
68C24×D13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C22×D52—42no—
84C22×D52—42no—
85C22×D52—42no—
86C22×D52—42no—
87C22×D52—42no—
88C22×D52—42no—
89C22×D52C2×C418yes—
90C22×D52C2×C418yescomplemented
91C22×D52C2×C418yescomplemented
92C22×D52C2314yes—
93C22×D52C2314yes—
94C22×D52C2314yes—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13—42no—
98C22×C4×D13—42no—
99C22×C4×D13—42no—
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13—42no—
103C22×C4×D13C2×C418yescomplemented
104C22×C4×D13C2314yes—
105C22×C4×D13C2314yes—
106C22×C4×D13C2314yes—
107C2×C13×C4⋊C4—42no—
108C2×C13×C4⋊C4C2×C418yescomplemented
109C2×C13×C4⋊C4C2314yes—
110C2×C13×C4⋊C4C2314yes—
111C2×C42×C13—42no—
112C2×C42×C13C2314yes—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—24no—
116C2×#6103—24no—
117C2×#6103—42no—
118C2×#6103—42no—
119C2×#6103—42no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103C2×C418yescomplemented
124C2×#6103C2×C418yescomplemented
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×C4⋊Dic13—42no—
138C2×C4⋊Dic13C2314yes—
139C2×C4×Dic13—42no—
140C2×C4×Dic13—42no—
141C2×C4×Dic13—42no—
142C2×C4×Dic13C2314yes—
143C2×C4×Dic13C2314yes—
144C2×C4×Dic13C2314yes—
145#88149C2×C4164yescomplemented
146C13×#95C2314yes—
147C13×#95C2314yes—
148C13×#95C2314yes—
149C13×#95C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2333—131nomaximal, Sylow
157C24×C13C2411yescharacteristic
158C23×D13—22no—
159C23×D13—22no—
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
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×D13C22×C414yes—
177C23×D13C22×C414yes—
178C23×D13C22×C414yes—
179C23×D13C2412yes—
180C23×D13C2412yes—
181C23×D13C2412yes—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
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—22no—
198C22×C4×C13—22no—
199C22×C4×C13C22×C414yes—
200C22×C4×C13C22×C414yes—
201C22×C4×C13C22×C414yes—
202C22×C4×C13#4114yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13C22×C414yes—
224C22×Dic13#4114yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C2×D52—416no—
231C2×D52—416no—
232C2×D52—416no—
233C2×D52—44no—
234C2×D52—44no—
235C2×D52—44no—
236C2×D52—44no—
237C2×D52—44no—
238C2×D52—44no—
239C2×D52C22×C4116yes—
240C2×D52C22×C4116yescomplemented
241C2×D52C22×C4116yescomplemented
242C2×C4×D13—28no—
243C2×C4×D13—28no—
244C2×C4×D13—416no—
245C2×C4×D13—44no—
246C2×C4×D13—44no—
247C2×C4×D13—44no—
248C2×C4×D13—44no—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—416no—
252C2×C4×D13—416no—
253C2×C4×D13C22×C4116yescomplemented
254C13×C4⋊C4—44no—
255C13×C4⋊C4C22×C4116yescomplemented
256C42×C13—44no—
257#6103—28no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6103C22×C4116yescomplemented
268#6103C22×C4116yescomplemented
269C4⋊Dic13—44no—
270C4×Dic13—44no—
271C4×Dic13—44no—
272C4×Dic13—44no—
273C22×#121—131no—
274#2333—1316no—
275C2×#390—131no—
276C2×#390—131no—
277C2×#388—131no—
278C2×#388—131no—
279C2×#387—131no—
280C2×#387D1311yescharacteristic, complemented
281C2×#386—131no—
282C2×#386—131no—
283C2×#386—131no—
284C2×#386—131no—
285C2×#381—131no—
286C2×C4×C22⋊C4—131no—
287C2×C4×C22⋊C4—131no—
288C2×C4×C22⋊C4—131no—
289C23×C13C23×C412yes—
290C23×C13C2×#4112yes—
291C23×C13C2×#4112yes—
292C23×C13H(5,𝔽2)12yes—
293C23×C13H(5,𝔽2)12yes—
294C23×C13H(5,𝔽2)12yes—
295C23×C13H(5,𝔽2)12yes—
296C23×C13C2511yescharacteristic
297C22×D13—28no—
298C22×D13—28no—
299C22×D13—28no—
300C22×D13—28no—
301C22×D13—28no—
302C22×D13—28no—
303C22×D13—28no—
304C22×D13—28no—
305C22×D13—28no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—44no—
325C22×D13—44no—
326C22×D13—44no—
327C22×D13—44no—
328C22×D13—44no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13C23×C414yes—
337C22×D13C23×C414yes—
338C22×D13C23×C414yes—
339C2×C4×C13—28no—
340C2×C4×C13—28no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
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—22no—
359C2×C4×C13—22no—
360C2×C4×C13—44no—
361C2×C4×C13—44no—
362C2×C4×C13—44no—
363C2×C4×C13C23×C414yes—
364C2×C4×C13C23×C414yes—
365C2×C4×C13C23×C414yes—
366C2×C4×C13C2×#4114yes—
367C2×Dic13—28no—
368C2×Dic13—28no—
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—44no—
383C2×Dic13—44no—
384C2×Dic13—44no—
385C2×Dic13C23×C414yes—
386C2×Dic13C2×#4114yes—
387D52—416no—
388D52—416no—
389D52—416no—
390C4×D13—416no—
391C4×D13—416no—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4—131no—
396C24×C4—131no—
397C24×C4—131no—
398C24×C4—131no—
399C2×#121—1316no—
400C2×#121—138no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4C2×D1311yescharacteristic
403C22×C4⋊C4C2×D1311yescharacteristic
404C22×C22⋊C4—131no—
405C22×C22⋊C4—131no—
406C22×C22⋊C4—131no—
407C22×C22⋊C4—131no—
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×C42—131no—
417C22×C42—131no—
418C22×C42—131no—
419C22×C42C2×D1311yescharacteristic
420#390—138no—
421#390—138no—
422#388—138no—
423#388—138no—
424#387—138no—
425#387C2×D1318yescomplemented
426#386—138no—
427#386—138no—
428#386—138no—
429#386—138no—
430#381—138no—
431C4×C22⋊C4—138no—
432C4×C22⋊C4—138no—
433C4×C22⋊C4—138no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95C2×D1311yescharacteristic
441C2×#95C2×D1311yescharacteristic
442C2×#95C2×D1311yescharacteristic
443C2×#95C2×D1311yescharacteristic
444C22×C13C4×#4114yes—
445C22×C13#51814yes—
446C22×C13#51814yes—
447C22×C13#53814yes—
448C22×C13#53814yes—
449C22×C13#54014yes—
450C22×C13#54014yes—
451C22×C13C24×C411yescharacteristic
452C22×C13C22×#4111yescharacteristic
453C22×C13C22×#4111yescharacteristic
454C22×C13C2×H(5,𝔽2)11yescharacteristic
455C22×C13C2×H(5,𝔽2)11yescharacteristic
456C22×C13C2×H(5,𝔽2)11yescharacteristic
457C22×C13C2×H(5,𝔽2)11yescharacteristic
458C2×D13—24no—
459C2×D13—24no—
460C2×D13—24no—
461C2×D13—24no—
462C2×D13—24no—
463C2×D13—24no—
464C2×D13—24no—
465C2×D13—24no—
466C2×D13—24no—
467C2×D13—416no—
468C2×D13—416no—
469C2×D13—416no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C4×C13—24no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—42no—
487C4×C13—42no—
488C4×C13—42no—
489Dic13—24no—
490Dic13—24no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494C25—131no—
495C25—131no—
496C25—131no—
497C22×D4—138no—
498C22×D4—138no—
499C22×D4—138no—
500C22×D4—134no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—522no—
504C22×D4—522no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4—522no—
508C22×D4—522no—
509C23×C4—131no—
510C23×C4—131no—
511C23×C4—138no—
512C23×C4—134no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—134no—
517C23×C4—134no—
518C23×C4—264no—
519C23×C4—264no—
520C23×C4—522no—
521C23×C4—522no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533#121—1364no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—522no—
537C2×C4⋊C4C4×D1318yescomplemented
538C2×C4⋊C4C22×D1314yes—
539C2×C4⋊C4C22×D1314yes—
540C2×C22⋊C4—138no—
541C2×C22⋊C4—138no—
542C2×C22⋊C4—134no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
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—264no—
555C2×C22⋊C4—264no—
556C2×C22⋊C4—264no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—522no—
559C2×C22⋊C4—522no—
560C2×C22⋊C4—522no—
561C2×C22⋊C4—522no—
562C2×C22⋊C4—522no—
563C2×C22⋊C4—522no—
564C2×C42—42no—
565C2×C42—134no—
566C2×C42—134no—
567C2×C42—134no—
568C2×C42—522no—
569C2×C42—522no—
570C2×C42—522no—
571C2×C42C22×D1314yes—
572#95—134no—
573#95—134no—
574#95—134no—
575#95—134no—
576#95—134no—
577#95—134no—
578#95C22×D1314yes—
579#95C22×D1314yes—
580#95C22×D1314yes—
581#95C22×D1314yes—
582C2×C13#233318yescomplemented
583C2×C13C2×C4×#4111yescharacteristic
584C2×C13C2×#51811yescharacteristic
585C2×C13C2×#51811yescharacteristic
586C2×C13C2×#53811yescharacteristic
587C2×C13C2×#53811yescharacteristic
588C2×C13C2×#54011yescharacteristic
589C2×C13C2×#54011yescharacteristic
590D13—44no—
591D13—44no—
592D13—44no—
593C24—134no—
594C24—134no—
595C24—134no—
596C24—132no—
597C24—132no—
598C24—132no—
599C24—262no—
600C24—262no—
601C24—262no—
602C24—262no—
603C24—262no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24—262no—
617C24C23×D1311yescharacteristic
618C2×D4—1316no—
619C2×D4—1316no—
620C2×D4—1316no—
621C2×D4—5216no—
622C2×D4—5216no—
623C2×D4—5216no—
624C2×D4—524no—
625C2×D4—524no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—524no—
629C2×D4—524no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
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—134no—
648C22×C4—134no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—1316no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—268no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—268no—
670C22×C4—5216no—
671C22×C4—524no—
672C22×C4—524no—
673C22×C4—524no—
674C22×C4—524no—
675C22×C4—524no—
676C22×C4—524no—
677C22×C4—5216no—
678C22×C4—5216no—
679C22×C4C2×C4×D1314yes—
680C22×C4C2×C4×D1314yes—
681C22×C4C2×C4×D1314yes—
682C22×C4#613114yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C22×C4C23×D1312yes—
689C22×C4C23×D1312yes—
690C4⋊C4—44no—
691C4⋊C4—524no—
692C4⋊C4C2×C4×D13116yescomplemented
693C22⋊C4—1316no—
694C22⋊C4—1316no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—524no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C42—44no—
706C42—524no—
707C42—524no—
708C42—524no—
709C13C2×#233311yescharacteristic, complemented, Sylow
710C23—134no—
711C23—134no—
712C23—134no—
713C23—268no—
714C23—268no—
715C23—268no—
716C23—268no—
717C23—268no—
718C23—268no—
719C23—268no—
720C23—268no—
721C23—268no—
722C23—262no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—524no—
741C23—524no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23C22×C4×D1312yes—
753C23#8825112yes—
754C23C2×#613112yes—
755C23#41×D1312yes—
756C23#8825612yes—
757C23#8825612yes—
758C23#8825612yes—
759C23C24×D1311yescharacteristic
760D4—5216no—
761D4—5216no—
762D4—5216no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
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—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—134no—
788C2×C4—134no—
789C2×C4—268no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—268no—
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—5216no—
805C2×C4—5216no—
806C2×C4—5216no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4C22×C4×D1314yes—
811C2×C4C22×C4×D1314yes—
812C2×C4C22×C4×D1314yes—
813C2×C4C2×#613114yes—
814C22—264no—
815C22—264no—
816C22—264no—
817C22—264no—
818C22—264no—
819C22—264no—
820C22—264no—
821C22—264no—
822C22—264no—
823C22—522no—
824C22—522no—
825C22—522no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—5216no—
830C22—5216no—
831C22—5216no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22#1171922614yes—
839C22#1171925014yes—
840C22C4×#613114yes—
841C22#1171934914yes—
842C22#1171936814yes—
843C22#1171940314yes—
844C22#1171940914yes—
845C22C23×C4×D1311yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C22×#613111yescharacteristic
848C22C2×#41×D1311yescharacteristic
849C22C2×#8825611yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C2×#8825611yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—264no—
860C4—264no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—524no—
865C2—524no—
866C2—524no—
867C2#1311760018yesdirect product factor
868C2C2×C4×#613111yescharacteristic
869C2C2×#1171925011yescharacteristic
870C2C2×#1171922611yescharacteristic
871C2C2×#1171940911yescharacteristic
872C2C2×#1171934911yescharacteristic
873C2C2×#1171936811yescharacteristic
874C2C2×#1171940311yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC22×#88149C2
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C2×#2333
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13117600C2direct (N × H)
3. C2×#11718600C2semidirect
4. C2×#11718649C2semidirect
5. C2×#11718331C2semidirect
6. C2×#11718651C2semidirect
7. C2×#11718642C2semidirect
8. C2×#11718326C2semidirect
9. C2×#11718326C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718326C2semidirect
12. C2×#11718325C2semidirect
13. C2×C4×#6103C2semidirect
14. C2×#11718327C2semidirect
15. C2×#11718327C2semidirect
16. C2×C13×#387C2semidirect
42. C2×#88149C4semidirect
44. C13×#387C22semidirect
55. #11718651C22semidirect
56. #11718649C22semidirect
57. #11718642C22semidirect
58. #11718600C22semidirect
59. C4×#6103C22semidirect
60. #11718331C22semidirect
61. #11718327C22semidirect
62. #11718327C22semidirect
63. #11718326C22semidirect
64. #11718326C22semidirect
65. #11718326C22semidirect
66. #11718326C22semidirect
67. #11718325C22semidirect
90. C22×D52C2×C4semidirect
91. C22×D52C2×C4semidirect
103. C22×C4×D13C2×C4semidirect
108. C2×C13×C4⋊C4C2×C4semidirect
123. C2×#6103C2×C4semidirect
124. C2×#6103C2×C4semidirect
145. #88149C2×C4semidirect
240. C2×D52C22×C4semidirect
241. C2×D52C22×C4semidirect
253. C2×C4×D13C22×C4semidirect
255. C13×C4⋊C4C22×C4semidirect
267. #6103C22×C4semidirect
268. #6103C22×C4semidirect
280. C2×#387D13semidirect
425. #387C2×D13semidirect
537. C2×C4⋊C4C4×D13semidirect
582. C2×C13#2333semidirect
692. C4⋊C4C2×C4×D13semidirect
709. C13C2×#2333semidirect
867. C2#13117600direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881492
#131176002
C2×#117186002
C2×#117186492
C2×#117183312
C2×#117186512
C2×#117186422
C2×#117183262
C2×#117183252
C2×C4×#61032
C2×#117183272
C2×C13×#3872
C2×#233313