Finite Group Databasebeta

← C2×#13118003 #16025527

Subgroups — C2×#13118003 #16025527

Order 3328.

2566 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2#13118003C2116yesmaximal, direct product factor
3C2×#11718590C211yesmaximal, characteristic, complemented
4C2×#11718307C211yesmaximal, characteristic, complemented
5C2×#11718308C211yesmaximal, characteristic, complemented
6C2×#11718634C211yesmaximal, characteristic, complemented
7C2×#11718606C211yesmaximal, characteristic
8C2×#11718606C211yesmaximal, characteristic
9C2×#11718612C211yesmaximal, characteristic
10C2×#11718314C211yesmaximal, characteristic, complemented
11C2×#11718594C211yesmaximal, characteristic, complemented
12C2×#11718313C211yesmaximal, characteristic, complemented
13C2×#11718639C211yesmaximal, characteristic, complemented
14C2×#11718604C211yesmaximal, characteristic
15C2×#11718603C211yesmaximal, characteristic
16C2×C13×#388C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88132C4116yescomplemented
39C2×#88132C2218yes—
40C13×#388C2218yes—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718639C2218yescomplemented
56#11718634C2218yescomplemented
57#11718612C2218yes—
58#11718606C2218yes—
59#11718606C2218yes—
60#11718604C2218yes—
61#11718603C2218yes—
62#11718594C2218yescomplemented
63#11718590C2218yescomplemented
64#11718314C2218yescomplemented
65#11718313C2218yescomplemented
66#11718308C2218yescomplemented
67#11718307C2218yescomplemented
68C25×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×Dic13—42no—
76C23×Dic13—42no—
77C23×Dic13C2×C418yes—
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2314yes—
87C22×Dic26—42no—
88C22×Dic26—42no—
89C22×Dic26C2×C418yes—
90C22×Dic26C2314yes—
91C2×C13×C4⋊C4—42no—
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C22⋊C4—42no—
94C2×C13×C22⋊C4—42no—
95C2×C13×C22⋊C4C2×C418yes—
96C2×C13×C22⋊C4C2314yes—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C42×C13—42no—
100C2×C42×C13C2314yes—
101C2×C22⋊Dic13—42no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13C2×C418yes—
104C2×C22⋊Dic13C2314yes—
105C2×C22⋊Dic13C2314yes—
106C2×C22⋊Dic13C2314yes—
107C2×C4⋊Dic13—42no—
108C2×C4⋊Dic13C2×C418yes—
109C2×C4⋊Dic13C2314yes—
110C2×C4⋊Dic13C2314yes—
111C2×#6101—42no—
112C2×#6101—42no—
113C2×#6101—42no—
114C2×#6101—42no—
115C2×#6101C2×C418yes—
116C2×#6101C2×C418yes—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×C4×Dic13—42no—
124C2×C4×Dic13—42no—
125C2×C4×Dic13—42no—
126C2×C4×Dic13C2314yes—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129#88132C2×C4164yescomplemented
130C13×#95C2314yes—
131C13×#95C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2378—131nomaximal, Sylow
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13C22×C414yes—
152C24×C13C2412yes—
153C24×C13C2411yescharacteristic
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13C22×C414yes—
171C22×C4×C13C22×C414yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2412yes—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—416no—
199C22×Dic13—44no—
200C22×Dic13—44no—
201C22×Dic13C22×C414yes—
202C22×Dic13C22×C414yes—
203C22×Dic13C22×C414yes—
204C22×Dic13C22×C414yes—
205C22×Dic13C22×C4116yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C2×Dic26—416no—
215C2×Dic26—44no—
216C2×Dic26—44no—
217C2×Dic26C22×C4116yes—
218C13×C4⋊C4—44no—
219C13×C22⋊C4—44no—
220C13×C22⋊C4—44no—
221C13×C22⋊C4C22×C4116yes—
222C42×C13—44no—
223C22⋊Dic13—44no—
224C22⋊Dic13—44no—
225C22⋊Dic13C22×C4116yes—
226C4⋊Dic13—44no—
227C4⋊Dic13C22×C4116yes—
228#6101—44no—
229#6101—44no—
230#6101—44no—
231#6101—44no—
232#6101C22×C4116yes—
233#6101C22×C4116yes—
234C4×Dic13—44no—
235C4×Dic13—44no—
236C4×Dic13—44no—
237C22×C22⋊Q8—131no—
238#2378—1316no—
239C2×#391—131no—
240C2×#391—131no—
241C2×#389—131no—
242C2×#389—131no—
243C2×#388—131no—
244C2×#388—131no—
245C2×#388—131no—
246C2×#388D1311yescharacteristic
247C2×#387—131no—
248C2×#387—131no—
249C2×#387—131no—
250C2×#387—131no—
251C2×#381—131no—
252C2×#380—131no—
253C23×C13—28no—
254C23×C13—28no—
255C23×C13—28no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—44no—
263C23×C13—44no—
264C23×C13—44no—
265C23×C13—44no—
266C23×C13C23×C414yes—
267C23×C13C23×C412yes—
268C23×C13H(5,𝔽2)12yes—
269C23×C13H(5,𝔽2)12yes—
270C23×C13H(5,𝔽2)12yes—
271C23×C132−1+412yes—
272C23×C132−1+412yes—
273C23×C132−1+412yes—
274C23×C13C2511yescharacteristic
275C2×C4×C13—28no—
276C2×C4×C13—28no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—44no—
294C2×C4×C13—44no—
295C2×C4×C13—44no—
296C2×C4×C13—44no—
297C2×C4×C13C23×C414yes—
298C2×C4×C13C23×C414yes—
299C2×Dic13—28no—
300C2×Dic13—28no—
301C2×Dic13—28no—
302C2×Dic13—28no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—416no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13—44no—
328C2×Dic13C23×C414yes—
329C2×Dic13C23×C414yes—
330C2×Dic13C23×C414yes—
331C2×Dic13C23×C414yes—
332Dic26—416no—
333C23×Q8—131no—
334C24×C4—131no—
335C2×C22⋊Q8—1316no—
336C2×C22⋊Q8—138no—
337C22×C4⋊C4—131no—
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—131no—
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4C2×D1311yescharacteristic
346C22×C22⋊C4—131no—
347C22×C22⋊C4—131no—
348C22×C22⋊C4—131no—
349C22×C22⋊C4C2×D1311yescharacteristic
350C22×C22⋊C4C2×D1311yescharacteristic
351C22×C22⋊C4C2×D1311yescharacteristic
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—131no—
355C22×C42C2×D1311yescharacteristic
356#391—138no—
357#391—138no—
358#389—138no—
359#389—138no—
360#388—138no—
361#388—138no—
362#388—138no—
363#388C2×D1318yes—
364#387—138no—
365#387—138no—
366#387—138no—
367#387—138no—
368#381—138no—
369#380—138no—
370C2×#95—131no—
371C2×#95—131no—
372C2×#95—131no—
373C2×#95—131no—
374C2×#95—131no—
375C2×#95—131no—
376C2×#95—131no—
377C2×#95—131no—
378C2×#95—131no—
379C2×#95—131no—
380C2×#95—131no—
381C2×#95—131no—
382C2×#95C2×D1311yescharacteristic
383C2×#95C2×D1311yescharacteristic
384C22×C13—24no—
385C22×C13—24no—
386C22×C13—24no—
387C22×C13—416no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13#51814yes—
393C22×C13#51914yes—
394C22×C13#52014yes—
395C22×C13#56214yes—
396C22×C13#56214yes—
397C22×C13#56314yes—
398C22×C13#56314yes—
399C22×C13C24×C411yescharacteristic
400C22×C13C2×H(5,𝔽2)11yescharacteristic
401C22×C13C2×H(5,𝔽2)11yescharacteristic
402C22×C13C2×H(5,𝔽2)11yescharacteristic
403C22×C13C2×2−1+411yescharacteristic
404C22×C13C2×2−1+411yescharacteristic
405C22×C13C2×2−1+411yescharacteristic
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13—42no—
411C4×C13—42no—
412Dic13—24no—
413Dic13—24no—
414Dic13—24no—
415Dic13—24no—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419Dic13—42no—
420C25C22×D1311yescharacteristic
421C22×Q8—138no—
422C22×Q8—134no—
423C22×Q8—522no—
424C22×Q8—522no—
425C23×C4—131no—
426C23×C4—131no—
427C23×C4—131no—
428C23×C4—131no—
429C23×C4—138no—
430C23×C4—134no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4—131no—
435C23×C4—522no—
436C23×C4—522no—
437C23×C4C22×D1311yescharacteristic
438C23×C4C22×D1311yescharacteristic
439C23×C4C22×D1311yescharacteristic
440C23×C4C22×D1311yescharacteristic
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C22⋊Q8—1364no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—138no—
446C2×C4⋊C4—138no—
447C2×C4⋊C4—138no—
448C2×C4⋊C4—134no—
449C2×C4⋊C4—134no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—134no—
456C2×C4⋊C4—522no—
457C2×C4⋊C4—522no—
458C2×C4⋊C4—522no—
459C2×C4⋊C4—522no—
460C2×C4⋊C4—522no—
461C2×C4⋊C4C22×D1314yes—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—138no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—134no—
468C2×C22⋊C4—522no—
469C2×C22⋊C4—522no—
470C2×C22⋊C4C4×D1318yes—
471C2×C22⋊C4C22×D1314yes—
472C2×C22⋊C4C22×D1314yes—
473C2×C22⋊C4C22×D1314yes—
474C2×C42—42no—
475C2×C42—134no—
476C2×C42—134no—
477C2×C42—134no—
478C2×C42—522no—
479C2×C42—522no—
480C2×C42—522no—
481C2×C42C22×D1314yes—
482#95—134no—
483#95—134no—
484#95—134no—
485#95—134no—
486#95—134no—
487#95—134no—
488#95—134no—
489#95—134no—
490#95—134no—
491#95—134no—
492#95—134no—
493#95—134no—
494#95C22×D1314yes—
495#95C22×D1314yes—
496C2×C13—44no—
497C2×C13#237818yescomplemented
498C2×C13C2×#51811yescharacteristic
499C2×C13C2×#51911yescharacteristic
500C2×C13C2×#52011yescharacteristic
501C2×C13C2×#56211yescharacteristic
502C2×C13C2×#56211yescharacteristic
503C2×C13C2×#56311yescharacteristic
504C2×C13C2×#56311yescharacteristic
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24C2×C4×D1314yes—
512C24C23×D1312yes—
513C24C23×D1311yescharacteristic
514C2×Q8—1316no—
515C2×Q8—5216no—
516C2×Q8—524no—
517C2×Q8—524no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—134no—
535C22×C4—134no—
536C22×C4—134no—
537C22×C4—134no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—1316no—
543C22×C4—132no—
544C22×C4—132no—
545C22×C4—132no—
546C22×C4—132no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—5216no—
568C22×C4—524no—
569C22×C4—524no—
570C22×C4C2×C4×D1314yes—
571C22×C4C2×C4×D1314yes—
572C22×C4C23×D1312yes—
573C22×C4C23×D1312yes—
574C22×C4C23×D1312yes—
575C22×C4C23×D1312yes—
576C22×C4C23×D1312yes—
577C22×C4C23×D1312yes—
578C4⋊C4—44no—
579C4⋊C4—1316no—
580C4⋊C4—1316no—
581C4⋊C4—1316no—
582C4⋊C4—524no—
583C4⋊C4—524no—
584C4⋊C4—524no—
585C4⋊C4—524no—
586C4⋊C4—524no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—1316no—
590C22⋊C4—524no—
591C22⋊C4—524no—
592C22⋊C4C2×C4×D13116yes—
593C42—44no—
594C42—524no—
595C42—524no—
596C42—524no—
597C13C2×#237811yescharacteristic, complemented, Sylow
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23C22×C4×D1314yes—
612C23C22×C4×D1312yes—
613C23#8825112yes—
614C23#8825112yes—
615C23#8825612yes—
616C23#8825712yes—
617C23#8825712yes—
618C23#8825712yes—
619C23C24×D1311yescharacteristic
620Q8—5216no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—134no—
644C2×C4—134no—
645C2×C4—134no—
646C2×C4—134no—
647C2×C4—268no—
648C2×C4—268no—
649C2×C4—268no—
650C2×C4—268no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—262no—
654C2×C4—262no—
655C2×C4—262no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—262no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—5216no—
672C2×C4—524no—
673C2×C4—524no—
674C2×C4—524no—
675C2×C4—524no—
676C2×C4C22×C4×D1314yes—
677C2×C4C22×C4×D1314yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—416no—
685C22—42no—
686C22#1171922114yes—
687C22#1171925014yes—
688C22#1171925114yes—
689C22#1171932614yes—
690C22#1171935614yes—
691C22#1171938914yes—
692C22#1171941714yes—
693C22C23×C4×D1311yescharacteristic
694C22C2×#8825111yescharacteristic
695C22C2×#8825111yescharacteristic
696C22C2×#8825611yescharacteristic
697C22C2×#8825711yescharacteristic
698C22C2×#8825711yescharacteristic
699C22C2×#8825711yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—264no—
707C4—264no—
708C4—264no—
709C4—264no—
710C4—522no—
711C4—522no—
712C4—522no—
713C4—522no—
714C2—44no—
715C2#1311800318yesdirect product factor
716C2C2×#1171925011yescharacteristic
717C2C2×#1171922111yescharacteristic
718C2C2×#1171925111yescharacteristic
719C2C2×#1171938911yescharacteristic
720C2C2×#1171932611yescharacteristic
721C2C2×#1171941711yescharacteristic
722C2C2×#1171935611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC2×#388D13
hypocenterC13C2×#2378
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #13118003C2direct (N × H)
3. C2×#11718590C2semidirect
4. C2×#11718307C2semidirect
5. C2×#11718308C2semidirect
6. C2×#11718634C2semidirect
10. C2×#11718314C2semidirect
11. C2×#11718594C2semidirect
12. C2×#11718313C2semidirect
13. C2×#11718639C2semidirect
38. C2×#88132C4semidirect
55. #11718639C22semidirect
56. #11718634C22semidirect
62. #11718594C22semidirect
63. #11718590C22semidirect
64. #11718314C22semidirect
65. #11718313C22semidirect
66. #11718308C22semidirect
67. #11718307C22semidirect
129. #88132C2×C4semidirect
497. C2×C13#2378semidirect
597. C13C2×#2378semidirect
715. C2#13118003direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
#131180032
C2×#117185902
C2×#117183072
C2×#117183082
C2×#117186342
C2×#117186062
C2×#117186122
C2×#117183142
C2×#117185942
C2×#117183132
C2×#117186392
C2×#117186042
C2×#117186032
C2×C13×#3882
C2×#237813