Finite Group Databasebeta

← C2×#13120677 #16029304

Subgroups — C2×#13120677 #16029304

Order 3328.

3218 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×#88183C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3#13120677C2116yesmaximal, direct product factor
4C2×#11718644C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718655C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718652C211yesmaximal, characteristic, complemented
9C2×#11718622C211yesmaximal, characteristic, complemented
10C2×#11718622C211yesmaximal, characteristic, complemented
11C2×#11718621C211yesmaximal, characteristic
12C2×#11718331C211yesmaximal, characteristic, complemented
13C2×#11718314C211yesmaximal, characteristic, complemented
14C2×#11718326C211yesmaximal, characteristic, complemented
15C2×#11718329C211yesmaximal, characteristic, complemented
16C2×C13×#380C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C2×#88183—28no—
29C2×#88183C2218yescomplemented
30C2×C4×C22⋊D13—28no—
31C2×C4×C22⋊D13C2218yescomplemented
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×C4⋊Dic13C2211yescharacteristic
43C22×C4⋊Dic13C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C13×#380C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718655C2218yescomplemented
59#11718652C2218yescomplemented
60#11718644C2218yescomplemented
61#11718622C2218yescomplemented
62#11718622C2218yescomplemented
63#11718621C2218yes—
64#11718614C2218yescomplemented
65#11718331C2218yescomplemented
66#11718329C2218yescomplemented
67#11718326C2218yescomplemented
68#11718314C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—42no—
73C23×C4×C13—42no—
74C23×C4×C13D418yescomplemented
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
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—42no—
98C22×D52—42no—
99C22×D52C2314yes—
100C22×C4×D13—24no—
101C22×C4×D13—42no—
102C22×C4×D13—42no—
103C22×C4×D13C2314yes—
104C2×C13×C4⋊C4—42no—
105C2×C13×C4⋊C4—42no—
106C2×C13×C4⋊C4C2314yes—
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4—42no—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116#88183—232no—
117C4×C22⋊D13—232no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103—42no—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×C4⋊Dic13—24no—
137C2×C4⋊Dic13—42no—
138C2×C4⋊Dic13—42no—
139C2×C4⋊Dic13C2314yes—
140C2×C4⋊Dic13C2314yes—
141C2×C4⋊Dic13C2314yes—
142C2×#6101—24no—
143C2×#6101—24no—
144C2×#6101—24no—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×C4×Dic13—24no—
149C2×C4×Dic13C2314yes—
150C13×#95C2314yes—
151C13×#95C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2630—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13C2×D414yes—
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—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×C13—22no—
200C22×C4×C13—416no—
201C22×C4×C13—44no—
202C22×C4×C13—44no—
203C22×C4×C13C2×D414yes—
204C22×C4×C13C2×D414yes—
205C22×C4×C13C2×D4116yescomplemented
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—232no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—44no—
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—44no—
246C2×D52—44no—
247C2×D52—416no—
248C2×C4×D13—28no—
249C2×C4×D13—44no—
250C2×C4×D13—44no—
251C2×C4×D13—416no—
252C13×C4⋊C4—44no—
253C13×C4⋊C4—44no—
254C13×C22⋊C4—44no—
255C13×C22⋊C4—44no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266#6103—44no—
267C4⋊Dic13—28no—
268C4⋊Dic13—44no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—28no—
272#6101—28no—
273C4×Dic13—28no—
274C22×#123—131no—
275C22×C4×D4—131no—
276#2630—1316no—
277C2×#398—131no—
278C2×#397—131no—
279C2×#396—131no—
280C2×#396—131no—
281C2×#394—131no—
282C2×#394—131no—
283C2×#394—131no—
284C2×#392—131no—
285C2×#388—131no—
286C2×#387—131no—
287C2×#386—131no—
288C2×#385—131no—
289C2×#380D1311yescharacteristic, complemented
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×D414yes—
304C23×C13C22×D412yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C132−1+412yes—
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—28no—
341C2×C4×C13—28no—
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—22no—
358C2×C4×C13—416no—
359C2×C4×C13—44no—
360C2×C4×C13—44no—
361C2×C4×C13—44no—
362C2×C4×C13—44no—
363C2×C4×C13C22×D414yes—
364C2×C4×C13C22×D414yes—
365C22⋊D13—232no—
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×C4×D4—138no—
401C2×C4×D4—268no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4C2×D1311yescharacteristic
409C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42—131no—
424#398—138no—
425#397—138no—
426#396—138no—
427#396—138no—
428#394—138no—
429#394—138no—
430#394—138no—
431#392—138no—
432#388—138no—
433#387—138no—
434#386—138no—
435#385—138no—
436#380C2×D1318yescomplemented
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95C2×D1311yescharacteristic
444C2×#95C2×D1311yescharacteristic
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—416no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13#52514yes—
454C22×C13#53414yes—
455C22×C13#53714yes—
456C22×C13#53814yes—
457C22×C13#53914yes—
458C22×C13#54014yes—
459C22×C13#54214yes—
460C22×C13C23×D411yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×H(5,𝔽2)11yescharacteristic
465C22×C13C2×H(5,𝔽2)11yescharacteristic
466C22×C13C2×2−1+411yescharacteristic
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—416no—
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—
482C2×D13—88no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—42no—
486C4×C13—42no—
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—522no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4—522no—
510C23×C4—42no—
511C23×C4—42no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—134no—
519C23×C4—264no—
520C23×C4—522no—
521C23×C4—522no—
522C23×C4D5218yescomplemented
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1314yes—
530#123—2632no—
531C4×D4—2632no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—42no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—522no—
545C2×C4⋊C4—522no—
546C2×C4⋊C4C22×D1314yes—
547C2×C4⋊C4C22×D1314yes—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
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—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—264no—
567C2×C22⋊C4—264no—
568C2×C22⋊C4—522no—
569C2×C22⋊C4—522no—
570C2×C22⋊C4—522no—
571C2×C22⋊C4—522no—
572C2×C22⋊C4C22×D1314yes—
573C2×C22⋊C4C22×D1314yes—
574C2×C42—134no—
575C2×C42—264no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95C22×D1314yes—
583#95C22×D1314yes—
584C2×C13—44no—
585C2×C13#263018yescomplemented
586C2×C13C2×#52511yescharacteristic
587C2×C13C2×#53411yescharacteristic
588C2×C13C2×#53711yescharacteristic
589C2×C13C2×#53811yescharacteristic
590C2×C13C2×#53911yescharacteristic
591C2×C13C2×#54011yescharacteristic
592C2×C13C2×#54211yescharacteristic
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—
617C24C2×D5214yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—268no—
621C2×D4—268no—
622C2×D4—268no—
623C2×D4—2632no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—5216no—
629C2×D4—524no—
630C2×D4—524no—
631C2×D4—5216no—
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—22no—
648C22×C4—416no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—134no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
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—524no—
678C22×C4—5216no—
679C22×C4C2×D5214yes—
680C22×C4C2×D5214yes—
681C22×C4C2×D52116yescomplemented
682C22×C4C23×D1312yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—268no—
693C4⋊C4—268no—
694C4⋊C4—524no—
695C4⋊C4—524no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—268no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C42—268no—
710C13C2×#263011yescharacteristic, 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—
752C23C22×D5214yes—
753C23C22×D5212yes—
754C23#8825112yes—
755C23#8825112yes—
756C23#8825112yes—
757C23#8825412yes—
758C23#41×D1312yes—
759C23#41×D1312yes—
760C23C24×D1311yescharacteristic
761D4—2632no—
762D4—5216no—
763D4—5216no—
764C2×C4—28no—
765C2×C4—28no—
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—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—134no—
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—262no—
806C2×C4—5216no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4C22×D5214yes—
813C2×C4C22×D5214yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—416no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—522no—
826C22—5216no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—1048no—
838C22#1171919814yes—
839C22#1171921514yes—
840C22#1171922914yes—
841C22#1171931814yes—
842C22#1171932014yes—
843C22#1171934314yes—
844C22#1171934514yes—
845C22C23×D5211yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C2×#8825111yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C2×#8825411yescharacteristic
850C22C2×#41×D1311yescharacteristic
851C22C2×#41×D1311yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—264no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—524no—
866C2—1042no—
867C2#1312067718yesdirect product factor
868C2C2×#1171922911yescharacteristic
869C2C2×#1171919811yescharacteristic
870C2C2×#1171921511yescharacteristic
871C2C2×#1171931811yescharacteristic
872C2C2×#1171934311yescharacteristic
873C2C2×#1171932011yescharacteristic
874C2C2×#1171934511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×#380D13
hypocenterC13C2×#2630
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88183C2semidirect
2. C22×C4×C22⋊D13C2semidirect
3. #13120677C2direct (N × H)
4. C2×#11718644C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718655C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718652C2semidirect
9. C2×#11718622C2semidirect
10. C2×#11718622C2semidirect
12. C2×#11718331C2semidirect
13. C2×#11718314C2semidirect
14. C2×#11718326C2semidirect
15. C2×#11718329C2semidirect
16. C2×C13×#380C2semidirect
29. C2×#88183C22semidirect
31. C2×C4×C22⋊D13C22semidirect
48. C13×#380C22semidirect
57. #11718655C22semidirect
58. #11718655C22semidirect
59. #11718652C22semidirect
60. #11718644C22semidirect
61. #11718622C22semidirect
62. #11718622C22semidirect
64. #11718614C22semidirect
65. #11718331C22semidirect
66. #11718329C22semidirect
67. #11718326C22semidirect
68. #11718314C22semidirect
74. C23×C4×C13D4semidirect
205. C22×C4×C13C2×D4semidirect
289. C2×#380D13semidirect
436. #380C2×D13semidirect
522. C23×C4D52semidirect
585. C2×C13#2630semidirect
681. C22×C4C2×D52semidirect
710. C13C2×#2630semidirect
867. C2#13120677direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
C22×C4×C22⋊D132
#131206772
C2×#117186442
C2×#117186142
C2×#117186552
C2×#117186522
C2×#117186222
C2×#117186212
C2×#117183312
C2×#117183142
C2×#117183262
C2×#117183292
C2×C13×#3802
C2×#263013