Finite Group Databasebeta

← C2×#13118941 #16031489

Subgroups — C2×#13118941 #16031489

Order 3328.

3330 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×#88148C211yesmaximal, characteristic, complemented
2#13118941C2116yesmaximal, direct product factor
3C2×#11718653C211yesmaximal, characteristic, complemented
4C2×#11718654C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718621C211yesmaximal, characteristic
7C2×#11718600C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic, complemented
9C2×#11718601C211yesmaximal, characteristic, complemented
10C2×#11718642C211yesmaximal, characteristic, complemented
11C2×#11718594C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718617C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C22×C13×#117C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C2×C13×#117—28no—
23C2×C13×#117C2218yescomplemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88148—28no—
47C2×#88148C2218yescomplemented
48#11718874C2218yescomplemented
49#11718874C2218yescomplemented
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718654C2218yescomplemented
59#11718653C2218yescomplemented
60#11718642C2218yescomplemented
61#11718621C2218yes—
62#11718618C2218yescomplemented
63#11718617C2218yescomplemented
64#11718609C2218yescomplemented
65#11718601C2218yescomplemented
66#11718600C2218yescomplemented
67C4×#6103C2218yescomplemented
68#11718594C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—24no—
74C23×C4×C13—24no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2314yes—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—24no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13C2314yes—
89C22×C22⋊D13C2314yes—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C22×D52—24no—
97C22×D52—24no—
98C22×D52—42no—
99C22×D52C2314yes—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—42no—
103C22×C4×D13C2314yes—
104C13×#117—232no—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4D418yescomplemented
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4C2314yes—
112C2×C13×C22⋊C4C2314yes—
113C2×C42×C13—24no—
114C2×C42×C13—24no—
115C2×C42×C13C2314yes—
116C2×C42×C13C2314yes—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—42no—
128C2×#6103—42no—
129C2×#6103—42no—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×C4⋊Dic13—42no—
140C2×C4⋊Dic13C2314yes—
141C2×#6101—24no—
142C2×#6101—24no—
143C2×#6101—42no—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×C4×Dic13—42no—
148C2×C4×Dic13C2314yes—
149#88148—232no—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2471—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13#4114yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
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#4114yes—
182C23×D13C2412yes—
183C23×D13C2412yes—
184C22×C4×C13—232no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—28no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—28no—
195C22×C4×C13—28no—
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×C13C2×D414yes—
203C22×C4×C13C2×D414yes—
204C22×C4×C13C2×D414yes—
205C22×C4×C13#4114yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—416no—
219C2×C22⋊D13—416no—
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—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13#4114yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×D52—28no—
245C2×D52—28no—
246C2×D52—44no—
247C2×D52—416no—
248C2×C4×D13—28no—
249C2×C4×D13—28no—
250C2×C4×D13—44no—
251C2×C4×D13—416no—
252C13×C4⋊C4—28no—
253C13×C4⋊C4C2×D4116yescomplemented
254C13×C22⋊C4—28no—
255C13×C22⋊C4—28no—
256C42×C13—28no—
257C42×C13—28no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—44no—
267#6103—44no—
268#6103—44no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—28no—
272#6101—44no—
273C4×Dic13—44no—
274C22×#123—131no—
275C22×#117D1311yescharacteristic, complemented
276#2471—1316no—
277C2×#399—131no—
278C2×#397—131no—
279C2×#396—131no—
280C2×#392—131no—
281C2×#390—131no—
282C2×#390—131no—
283C2×#388—131no—
284C2×#387—131no—
285C2×#387—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×C4×C22⋊C4—131no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13C22×D412yes—
304C23×C13C2×#4114yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13C2×#4112yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C13C2511yescharacteristic
312C22×D13—28no—
313C22×D13—28no—
314C22×D13—28no—
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—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
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×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13C2×#4114yes—
340C2×C4×C13—232no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
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—44no—
360C2×C4×C13—44no—
361C2×C4×C13C22×D414yes—
362C2×C4×C13C22×D414yes—
363C2×C4×C13C22×D414yes—
364C2×C4×C13C2×#4114yes—
365C22⋊D13—416no—
366C22⋊D13—416no—
367C2×Dic13—28no—
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—22no—
384C2×Dic13—22no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13C2×#4114yes—
391D52—416no—
392C4×D13—416no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4—131no—
396C24×C4—131no—
397C24×C4C2×D1311yescharacteristic
398C2×#123—138no—
399C2×#123—268no—
400C2×#117—28no—
401C2×#117C2×D1318yescomplemented
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4C2×D1311yescharacteristic
407C22×C4⋊C4C2×D1311yescharacteristic
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×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#399—138no—
425#397—138no—
426#396—138no—
427#392—138no—
428#390—138no—
429#390—138no—
430#388—138no—
431#387—138no—
432#387—138no—
433#386—138no—
434#386—138no—
435#386—138no—
436C4×C22⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—416no—
453C22×C13#52514yes—
454C22×C13#52914yes—
455C22×C13#54014yes—
456C22×C13#54614yes—
457C22×C13#55014yes—
458C22×C13#55114yes—
459C22×C13#55114yes—
460C22×C13C23×D411yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C22×#4111yescharacteristic
464C22×C13C22×#4111yescharacteristic
465C22×C13C2×H(5,𝔽2)11yescharacteristic
466C22×C13C2×H(5,𝔽2)11yescharacteristic
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—416no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—88no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—24no—
487C4×C13—42no—
488C4×C13—42no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25—131no—
496C25—131no—
497C25C22×D1311yescharacteristic
498C22×D4—134no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—264no—
502C22×D4—264no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—264no—
506C22×D4—264no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4—522no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—134no—
520C23×C4—264no—
521C23×C4—264no—
522C23×C4—522no—
523C23×C4C22×D1314yes—
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530#123—2632no—
531#117—232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—264no—
538C2×C4⋊C4—264no—
539C2×C4⋊C4—522no—
540C2×C4⋊C4—522no—
541C2×C4⋊C4C22⋊D1318yescomplemented
542C2×C4⋊C4C22×D1314yes—
543C2×C4⋊C4C22×D1314yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
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—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4—522no—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—134no—
573C2×C42—522no—
574C2×C42C22×D1314yes—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584C2×C13—44no—
585C2×C13#247118yescomplemented
586C2×C13C2×#52511yescharacteristic
587C2×C13C2×#52911yescharacteristic
588C2×C13C2×#54011yescharacteristic
589C2×C13C2×#54611yescharacteristic
590C2×C13C2×#55011yescharacteristic
591C2×C13C2×#55111yescharacteristic
592C2×C13C2×#55111yescharacteristic
593D13—44no—
594D13—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—134no—
602C24—132no—
603C24—132no—
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—
617C24#612714yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—268no—
621C2×D4—268no—
622C2×D4—268no—
623C2×D4—268no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—524no—
627C2×D4—5216no—
628C2×D4—524no—
629C2×D4—524no—
630C2×D4—5216no—
631C2×D4—5216no—
632C22×C4—232no—
633C22×C4—28no—
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—28no—
643C22×C4—28no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—134no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—268no—
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—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—268no—
676C22×C4—524no—
677C22×C4—5216no—
678C22×C4#612714yes—
679C22×C4C2×C22⋊D1314yes—
680C22×C4C2×C22⋊D1314yes—
681C22×C4C2×C22⋊D1314yes—
682C22×C4C23×D1312yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—28no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C4⋊C4C2×C22⋊D13116yescomplemented
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C42—28no—
708C42—28no—
709C42—524no—
710C13C2×#247111yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—134no—
725C23—268no—
726C23—268no—
727C23—268no—
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—262no—
741C23—524no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23C2×#612714yes—
753C23C2×#612712yes—
754C23C2×#612712yes—
755C23#41×D1312yes—
756C23#41×D1312yes—
757C23#8825612yes—
758C23#8825612yes—
759C23C22×C22⋊D1312yes—
760C23C24×D1311yescharacteristic
761D4—5216no—
762D4—5216no—
763D4—5216no—
764C2×C4—232no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
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—44no—
784C2×C4—44no—
785C2×C4—134no—
786C2×C4—268no—
787C2×C4—262no—
788C2×C4—262no—
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—5216no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4C2×#612714yes—
811C2×C4C22×C22⋊D1314yes—
812C2×C4C22×C22⋊D1314yes—
813C2×C4C22×C22⋊D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—522no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—5216no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—1048no—
838C22#1171923214yes—
839C22#1171923214yes—
840C22#1171923314yes—
841C22#1171924014yes—
842C22#1171949614yes—
843C22#1171953414yes—
844C22#1171953914yes—
845C22C22×#612711yescharacteristic
846C22C22×#612711yescharacteristic
847C22C2×#41×D1311yescharacteristic
848C22C2×#41×D1311yescharacteristic
849C22C2×#8825611yescharacteristic
850C22C2×#8825611yescharacteristic
851C22C23×C22⋊D1311yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—264no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—524no—
866C2—1042no—
867C2#1311894118yesdirect product factor
868C2C2×#1171949611yescharacteristic
869C2C2×#1171923311yescharacteristic
870C2C2×#1171924011yescharacteristic
871C2C2×#1171953411yescharacteristic
872C2C2×#1171953911yescharacteristic
873C2C2×#1171923211yescharacteristic
874C2C2×#1171923211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#117C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC22×#117D13
hypocenterC13C2×#2471
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#88148C2semidirect
2. #13118941C2direct (N × H)
3. C2×#11718653C2semidirect
4. C2×#11718654C2semidirect
5. C2×#11718609C2semidirect
7. C2×#11718600C2semidirect
8. C2×#11718618C2semidirect
9. C2×#11718601C2semidirect
10. C2×#11718642C2semidirect
11. C2×#11718594C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718617C2semidirect
15. C2×C4×#6103C2semidirect
16. C22×C13×#117C2semidirect
23. C2×C13×#117C22semidirect
47. C2×#88148C22semidirect
48. #11718874C22semidirect
49. #11718874C22semidirect
58. #11718654C22semidirect
59. #11718653C22semidirect
60. #11718642C22semidirect
62. #11718618C22semidirect
63. #11718617C22semidirect
64. #11718609C22semidirect
65. #11718601C22semidirect
66. #11718600C22semidirect
67. C4×#6103C22semidirect
68. #11718594C22semidirect
106. C2×C13×C4⋊C4D4semidirect
253. C13×C4⋊C4C2×D4semidirect
275. C22×#117D13semidirect
401. C2×#117C2×D13semidirect
541. C2×C4⋊C4C22⋊D13semidirect
585. C2×C13#2471semidirect
693. C4⋊C4C2×C22⋊D13semidirect
710. C13C2×#2471semidirect
867. C2#13118941direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881482
#131189412
C2×#117186532
C2×#117186542
C2×#117186092
C2×#117186212
C2×#117186002
C2×#117186182
C2×#117186012
C2×#117186422
C2×#117185942
C2×#117188742
C2×#117186172
C2×C4×#61032
C22×C13×#1172
C2×#247113