Finite Group Databasebeta

← C2×#13117989 #16025512

Subgroups — C2×#13117989 #16025512

Order 3328.

3302 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×#88138C211yesmaximal, characteristic
2#13117989C2116yesmaximal, direct product factor
3C2×#11718600C211yesmaximal, characteristic, complemented
4C2×#11718618C211yesmaximal, characteristic, complemented
5C2×#11718331C211yesmaximal, characteristic, complemented
6C2×#11718316C211yesmaximal, characteristic, complemented
7C2×#11718594C211yesmaximal, characteristic, complemented
8C2×#11718326C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic, complemented
10C2×#11718619C211yesmaximal, characteristic, complemented
11C2×#11718617C211yesmaximal, characteristic, complemented
12C2×#11718611C211yesmaximal, characteristic, complemented
13C2×#11718650C211yesmaximal, characteristic, complemented
14C2×#11718325C211yesmaximal, characteristic, complemented
15C2×#11718648C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88138C4116yescomplemented
43C2×#88138C2218yes—
44C13×#388C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718650C2218yescomplemented
56#11718648C2218yescomplemented
57#11718619C2218yescomplemented
58#11718619C2218yescomplemented
59#11718618C2218yescomplemented
60#11718617C2218yescomplemented
61#11718611C2218yescomplemented
62#11718600C2218yescomplemented
63#11718594C2218yescomplemented
64#11718331C2218yescomplemented
65#11718326C2218yescomplemented
66#11718325C2218yescomplemented
67#11718316C2218yescomplemented
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13—42no—
78C22×C22⋊D13—42no—
79C22×C22⋊D13—42no—
80C22×C22⋊D13—42no—
81C22×C22⋊D13C2×C418yes—
82C22×C22⋊D13C2×C418yescomplemented
83C22×C22⋊D13C2314yes—
84C22×C22⋊D13C2314yes—
85C23×Dic13—42no—
86C23×Dic13—42no—
87C23×Dic13—42no—
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C22×D52—42no—
96C22×D52—42no—
97C22×D52C2×C418yescomplemented
98C22×D52C2314yes—
99C22×C4×D13—42no—
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13—42no—
103C22×C4×D13—42no—
104C22×C4×D13C2×C418yescomplemented
105C22×C4×D13C2314yes—
106C22×C4×D13C2314yes—
107C2×C13×C4⋊C4—42no—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4—42no—
111C2×C13×C22⋊C4C2×C418yescomplemented
112C2×C13×C22⋊C4C2314yes—
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C42×C13—42no—
116C2×C42×C13C2314yes—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13C2314yes—
119C2×#6103—42no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103C2×C418yescomplemented
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×C4⋊Dic13—42no—
136C2×C4⋊Dic13—42no—
137C2×C4⋊Dic13C2314yes—
138C2×C4⋊Dic13C2314yes—
139C2×#6101—42no—
140C2×#6101C2×C418yescomplemented
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—42no—
144C2×C4×Dic13C2314yes—
145#88138C2×C4164yescomplemented
146C13×#95C2314yes—
147C13×#95C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C2×#2377—131nomaximal, Sylow
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13C22×C414yes—
164C24×C13C2412yes—
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×D13C22×C414yes—
179C23×D13C22×C414yes—
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×C13C22×C414yes—
199C22×C4×C13C22×C414yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C2×C22⋊D13—416no—
207C2×C22⋊D13—416no—
208C2×C22⋊D13—44no—
209C2×C22⋊D13—44no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13C22×C4116yes—
213C2×C22⋊D13C22×C4116yescomplemented
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×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—44no—
231C22×Dic13—44no—
232C22×Dic13—44no—
233C22×Dic13—416no—
234C22×Dic13C22×C414yes—
235C22×Dic13C22×C414yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C2×D52—416no—
243C2×D52—44no—
244C2×D52—44no—
245C2×D52C22×C4116yescomplemented
246C2×C4×D13—416no—
247C2×C4×D13—44no—
248C2×C4×D13—44no—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—44no—
252C2×C4×D13—416no—
253C2×C4×D13C22×C4116yescomplemented
254C13×C4⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4C22×C4116yescomplemented
258C42×C13—44no—
259C22⋊Dic13—44no—
260#6103—44no—
261#6103—44no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267#6103C22×C4116yescomplemented
268C4⋊Dic13—44no—
269C4⋊Dic13—44no—
270#6101—44no—
271#6101C22×C4116yescomplemented
272C4×Dic13—44no—
273C22×#121—131no—
274#2377—1316no—
275C2×#390—131no—
276C2×#390—131no—
277C2×#388—131no—
278C2×#388D1311yescharacteristic, complemented
279C2×#387—131no—
280C2×#387—131no—
281C2×#386—131no—
282C2×#386—131no—
283C2×#386—131no—
284C2×#386—131no—
285C2×#385—131no—
286C2×#385—131no—
287C2×#381—131no—
288C2×#380—131no—
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13C23×C414yes—
303C23×C13C23×C412yes—
304C23×C13H(5,𝔽2)12yes—
305C23×C13H(5,𝔽2)12yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C132−1+412yes—
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—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13C23×C414yes—
338C22×D13C23×C414yes—
339C2×C4×C13—28no—
340C2×C4×C13—28no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
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—44no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13—44no—
361C2×C4×C13C23×C414yes—
362C2×C4×C13C23×C414yes—
363C22⋊D13—416no—
364C22⋊D13—416no—
365C2×Dic13—28no—
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—416no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13C23×C414yes—
389C2×Dic13C23×C414yes—
390D52—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⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
416C22×C22⋊C4C2×D1311yescharacteristic
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C42—131no—
419C22×C42C2×D1311yescharacteristic
420#390—138no—
421#390—138no—
422#388—138no—
423#388C2×D1318yescomplemented
424#387—138no—
425#387—138no—
426#386—138no—
427#386—138no—
428#386—138no—
429#386—138no—
430#385—138no—
431#385—138no—
432#381—138no—
433#380—138no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95C2×D1311yescharacteristic
443C2×#95C2×D1311yescharacteristic
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—416no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13#51814yes—
453C22×C13#51814yes—
454C22×C13#52014yes—
455C22×C13#56014yes—
456C22×C13#56014yes—
457C22×C13#56214yes—
458C22×C13#56214yes—
459C22×C13C24×C411yescharacteristic
460C22×C13C2×H(5,𝔽2)11yescharacteristic
461C22×C13C2×H(5,𝔽2)11yescharacteristic
462C22×C13C2×H(5,𝔽2)11yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×H(5,𝔽2)11yescharacteristic
465C22×C13C2×2−1+411yescharacteristic
466C2×D13—24no—
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—24no—
471C2×D13—24no—
472C2×D13—416no—
473C2×D13—416no—
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—42no—
485C4×C13—42no—
486C4×C13—42no—
487C4×C13—42no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494C25—131no—
495C25—131no—
496C25C22×D1311yescharacteristic
497C22×D4—138no—
498C22×D4—138no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—138no—
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—131no—
517C23×C4—134no—
518C23×C4—134no—
519C23×C4—522no—
520C23×C4—522no—
521C23×C4—522no—
522C23×C4—522no—
523C23×C4—522no—
524C23×C4—522no—
525C23×C4—522no—
526C23×C4—522no—
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—138no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—522no—
541C2×C4⋊C4—522no—
542C2×C4⋊C4—522no—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—138no—
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—522no—
557C2×C22⋊C4—522no—
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×C22⋊C4C4×D1318yescomplemented
565C2×C22⋊C4C22×D1314yes—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—42no—
569C2×C42—134no—
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#95—134no—
579#95—134no—
580#95C22×D1314yes—
581#95C22×D1314yes—
582C2×C13—44no—
583C2×C13#237718yescomplemented
584C2×C13C2×#51811yescharacteristic
585C2×C13C2×#51811yescharacteristic
586C2×C13C2×#52011yescharacteristic
587C2×C13C2×#56011yescharacteristic
588C2×C13C2×#56011yescharacteristic
589C2×C13C2×#56211yescharacteristic
590C2×C13C2×#56211yescharacteristic
591D13—44no—
592D13—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—134no—
600C24—134no—
601C24—132no—
602C24—132no—
603C24—262no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24C2×C4×D1314yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—1316no—
619C2×D4—1316no—
620C2×D4—1316no—
621C2×D4—5216no—
622C2×D4—524no—
623C2×D4—524no—
624C2×D4—5216no—
625C2×D4—5216no—
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—134no—
647C22×C4—134no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—1316no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—262no—
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—262no—
670C22×C4—262no—
671C22×C4—5216no—
672C22×C4—524no—
673C22×C4—524no—
674C22×C4—524no—
675C22×C4—524no—
676C22×C4—524no—
677C22×C4—5216no—
678C22×C4—524no—
679C22×C4—524no—
680C22×C4—524no—
681C22×C4—5216no—
682C22×C4C2×C4×D1314yes—
683C22×C4C2×C4×D1314yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C22×C4C23×D1312yes—
689C22×C4C23×D1312yes—
690C4⋊C4—44no—
691C4⋊C4—1316no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—1316no—
698C22⋊C4—524no—
699C22⋊C4—524no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4C2×C4×D13116yescomplemented
707C42—44no—
708C42—524no—
709C13C2×#237711yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—134no—
724C23—134no—
725C23—268no—
726C23—268no—
727C23—268no—
728C23—268no—
729C23—268no—
730C23—268no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23C22×C4×D1314yes—
752C23C22×C4×D1312yes—
753C23#8825112yes—
754C23#8825112yes—
755C23#8825612yes—
756C23#8825612yes—
757C23#8825612yes—
758C23#8825712yes—
759C23C24×D1311yescharacteristic
760D4—5216no—
761D4—5216no—
762D4—5216no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
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—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—134no—
786C2×C4—134no—
787C2×C4—268no—
788C2×C4—268no—
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—5216no—
806C2×C4—5216no—
807C2×C4—5216no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4C22×C4×D1314yes—
813C2×C4C22×C4×D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—416no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—264no—
826C22—264no—
827C22—264no—
828C22—522no—
829C22—522no—
830C22—5216no—
831C22—5216no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22#1171922814yes—
839C22#1171925014yes—
840C22#1171925014yes—
841C22#1171932514yes—
842C22#1171937214yes—
843C22#1171938914yes—
844C22#1171941614yes—
845C22C23×C4×D1311yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C2×#8825111yescharacteristic
848C22C2×#8825611yescharacteristic
849C22C2×#8825611yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C2×#8825711yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—264no—
859C4—264no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—524no—
866C2—524no—
867C2#1311798918yesdirect product factor
868C2C2×#1171925011yescharacteristic
869C2C2×#1171925011yescharacteristic
870C2C2×#1171922811yescharacteristic
871C2C2×#1171932511yescharacteristic
872C2C2×#1171941611yescharacteristic
873C2C2×#1171938911yescharacteristic
874C2C2×#1171937211yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC22×#88138C2
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2377
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #13117989C2direct (N × H)
3. C2×#11718600C2semidirect
4. C2×#11718618C2semidirect
5. C2×#11718331C2semidirect
6. C2×#11718316C2semidirect
7. C2×#11718594C2semidirect
8. C2×#11718326C2semidirect
9. C2×#11718619C2semidirect
10. C2×#11718619C2semidirect
11. C2×#11718617C2semidirect
12. C2×#11718611C2semidirect
13. C2×#11718650C2semidirect
14. C2×#11718325C2semidirect
15. C2×#11718648C2semidirect
16. C2×C13×#388C2semidirect
42. C2×#88138C4semidirect
44. C13×#388C22semidirect
55. #11718650C22semidirect
56. #11718648C22semidirect
57. #11718619C22semidirect
58. #11718619C22semidirect
59. #11718618C22semidirect
60. #11718617C22semidirect
61. #11718611C22semidirect
62. #11718600C22semidirect
63. #11718594C22semidirect
64. #11718331C22semidirect
65. #11718326C22semidirect
66. #11718325C22semidirect
67. #11718316C22semidirect
82. C22×C22⋊D13C2×C4semidirect
97. C22×D52C2×C4semidirect
104. C22×C4×D13C2×C4semidirect
111. C2×C13×C22⋊C4C2×C4semidirect
126. C2×#6103C2×C4semidirect
140. C2×#6101C2×C4semidirect
145. #88138C2×C4semidirect
213. C2×C22⋊D13C22×C4semidirect
245. C2×D52C22×C4semidirect
253. C2×C4×D13C22×C4semidirect
257. C13×C22⋊C4C22×C4semidirect
267. #6103C22×C4semidirect
271. #6101C22×C4semidirect
278. C2×#388D13semidirect
423. #388C2×D13semidirect
564. C2×C22⋊C4C4×D13semidirect
583. C2×C13#2377semidirect
706. C22⋊C4C2×C4×D13semidirect
709. C13C2×#2377semidirect
867. C2#13117989direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881382
#131179892
C2×#117186002
C2×#117186182
C2×#117183312
C2×#117183162
C2×#117185942
C2×#117183262
C2×#117186192
C2×#117186172
C2×#117186112
C2×#117186502
C2×#117183252
C2×#117186482
C2×C13×#3882
C2×#237713