Finite Group Databasebeta

← C2×#13117588 #16021772

Subgroups — C2×#13117588 #16021772

Order 3328.

2678 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×#88151C211yesmaximal, characteristic
2#13117588C2116yesmaximal, direct product factor
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718307C211yesmaximal, characteristic, complemented
5C2×#11718331C211yesmaximal, characteristic
6C2×#11718601C211yesmaximal, characteristic
7C2×#11718651C211yesmaximal, characteristic
8C2×#11718330C211yesmaximal, characteristic
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718314C211yesmaximal, characteristic, complemented
11C2×#11718315C211yesmaximal, characteristic, complemented
12C2×#11718325C211yesmaximal, characteristic
13C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
15C2×#11718327C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88151C4116yescomplemented
39C2×#88151C2218yes—
40C13×#387C2218yescomplemented
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718651C2218yes—
56#11718642C2218yescomplemented
57C4⋊C4×Dic13C2218yescomplemented
58#11718601C2218yes—
59C4×C4⋊Dic13C2218yescomplemented
60#11718331C2218yes—
61#11718330C2218yes—
62#11718327C2218yes—
63#11718325C2218yes—
64#11718315C2218yescomplemented
65#11718314C2218yescomplemented
66#11718307C2218yescomplemented
67#11718307C2218yescomplemented
68C24×D13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C22×C4×D13—42no—
84C22×C4×D13—42no—
85C22×C4×D13C2×C418yes—
86C22×C4×D13C2314yes—
87C22×Dic26—42no—
88C22×Dic26—42no—
89C22×Dic26C2×C418yes—
90C22×Dic26C2314yes—
91C2×C13×C4⋊C4—24no—
92C2×C13×C4⋊C4C2×C418yes—
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C4⋊C4C2314yes—
95C2×C42×C13—24no—
96C2×C42×C13C2314yes—
97C2×#6103—24no—
98C2×#6103—24no—
99C2×#6103—42no—
100C2×#6103—42no—
101C2×#6103C2×C418yes—
102C2×#6103C2×C418yes—
103C2×#6103C2314yes—
104C2×#6103C2314yes—
105C2×#6103C2314yes—
106C2×#6103C2314yes—
107C2×#6103C2314yes—
108C2×#6103C2314yes—
109C2×C4⋊Dic13—24no—
110C2×C4⋊Dic13C2×C418yes—
111C2×C4⋊Dic13C2×C418yes—
112C2×C4⋊Dic13C2314yes—
113C2×C4⋊Dic13C2314yes—
114C2×C4⋊Dic13C2314yes—
115C2×#6101—42no—
116C2×#6101—42no—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×C4×Dic13—24no—
120C2×C4×Dic13—42no—
121C2×C4×Dic13—42no—
122C2×C4×Dic13—42no—
123C2×C4×Dic13—42no—
124C2×C4×Dic13C2314yes—
125C2×C4×Dic13C2314yes—
126C2×C4×Dic13C2314yes—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129#88151C2×C4164yescomplemented
130C13×#95C2314yes—
131C13×#95C2314yes—
132C13×#95C2314yes—
133C13×#95C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2332—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—22no—
147C23×D13—22no—
148C23×D13—22no—
149C23×D13—22no—
150C23×D13—22no—
151C23×D13—22no—
152C23×D13C22×C414yes—
153C23×D13C2412yes—
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×C13—22no—
171C22×C4×C13C22×C414yes—
172C22×C4×C13C22×C414yes—
173C22×C4×C13C22×C414yes—
174C22×C4×C13#4114yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
178C22×C4×C13C2412yes—
179C22×C4×C13C2412yes—
180C22×C4×C13C2412yes—
181C22×C4×C13C2412yes—
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—22no—
199C22×Dic13C22×C414yes—
200C22×Dic13C22×C414yes—
201C22×Dic13C22×C414yes—
202C22×Dic13#4114yes—
203C22×Dic13C2412yes—
204C22×Dic13C2412yes—
205C22×Dic13C2412yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C2×C4×D13—416no—
211C2×C4×D13—44no—
212C2×C4×D13—44no—
213C2×C4×D13C22×C4116yes—
214C2×Dic26—416no—
215C2×Dic26—44no—
216C2×Dic26—44no—
217C2×Dic26C22×C4116yes—
218C13×C4⋊C4—28no—
219C13×C4⋊C4C22×C4116yes—
220C42×C13—28no—
221#6103—28no—
222#6103—28no—
223#6103—44no—
224#6103—44no—
225#6103C22×C4116yes—
226#6103C22×C4116yes—
227C4⋊Dic13—28no—
228C4⋊Dic13C22×C4116yes—
229C4⋊Dic13C22×C4116yes—
230#6101—44no—
231#6101—44no—
232C4×Dic13—28no—
233C4×Dic13—44no—
234C4×Dic13—44no—
235C4×Dic13—44no—
236C4×Dic13—44no—
237C22×C22⋊Q8—131no—
238#2332—1316no—
239C2×#391—131no—
240C2×#391—131no—
241C2×#388—131no—
242C2×#388—131no—
243C2×#388—131no—
244C2×#388—131no—
245C2×#387—131no—
246C2×#387—131no—
247C2×#387—131no—
248C2×#387D1311yescharacteristic, complemented
249C2×#381—131no—
250C2×C4×C4⋊C4—131no—
251C2×C4×C4⋊C4—131no—
252C2×C4×C22⋊C4—131no—
253C23×C13C23×C412yes—
254C23×C13C2×#4112yes—
255C23×C13C2×#4112yes—
256C23×C13H(5,𝔽2)12yes—
257C23×C13H(5,𝔽2)12yes—
258C23×C132−1+412yes—
259C23×C132−1+412yes—
260C23×C13C2511yescharacteristic
261C22×D13—28no—
262C22×D13—28no—
263C22×D13—28no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—44no—
271C22×D13—44no—
272C22×D13—44no—
273C22×D13—44no—
274C22×D13C23×C414yes—
275C2×C4×C13—28no—
276C2×C4×C13—28no—
277C2×C4×C13—28no—
278C2×C4×C13—28no—
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—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—44no—
297C2×C4×C13—44no—
298C2×C4×C13—44no—
299C2×C4×C13C23×C414yes—
300C2×C4×C13C23×C414yes—
301C2×C4×C13C23×C414yes—
302C2×C4×C13C2×#4114yes—
303C2×Dic13—28no—
304C2×Dic13—28no—
305C2×Dic13—28no—
306C2×Dic13—28no—
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—22no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13C23×C414yes—
328C2×Dic13C23×C414yes—
329C2×Dic13C23×C414yes—
330C2×Dic13C2×#4114yes—
331C4×D13—416no—
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⋊C4C2×D1311yescharacteristic
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4—131no—
347C22×C22⋊C4—131no—
348C22×C22⋊C4—131no—
349C22×C22⋊C4—131no—
350C22×C42—131no—
351C22×C42—131no—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—131no—
355C22×C42C2×D1311yescharacteristic
356#391—138no—
357#391—138no—
358#388—138no—
359#388—138no—
360#388—138no—
361#388—138no—
362#387—138no—
363#387—138no—
364#387—138no—
365#387C2×D1318yescomplemented
366#381—138no—
367C4×C4⋊C4—138no—
368C4×C4⋊C4—138no—
369C4×C22⋊C4—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×#95C2×D1311yescharacteristic
381C2×#95C2×D1311yescharacteristic
382C2×#95C2×D1311yescharacteristic
383C2×#95C2×D1311yescharacteristic
384C22×C13C4×#4114yes—
385C22×C13#51814yes—
386C22×C13#51914yes—
387C22×C13#53914yes—
388C22×C13#53914yes—
389C22×C13#54214yes—
390C22×C13#54214yes—
391C22×C13C24×C411yescharacteristic
392C22×C13C22×#4111yescharacteristic
393C22×C13C22×#4111yescharacteristic
394C22×C13C2×H(5,𝔽2)11yescharacteristic
395C22×C13C2×H(5,𝔽2)11yescharacteristic
396C22×C13C2×2−1+411yescharacteristic
397C22×C13C2×2−1+411yescharacteristic
398C2×D13—24no—
399C2×D13—24no—
400C2×D13—24no—
401C2×D13—416no—
402C2×D13—42no—
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—24no—
409C4×C13—24no—
410C4×C13—42no—
411C4×C13—42no—
412C4×C13—42no—
413Dic13—24no—
414Dic13—24no—
415Dic13—24no—
416Dic13—24no—
417Dic13—42no—
418Dic13—42no—
419Dic13—42no—
420C25—131no—
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—522no—
435C23×C4—522no—
436C23×C4C22×D1311yescharacteristic
437C23×C4C22×D1311yescharacteristic
438C23×C4C22×D1311yescharacteristic
439C23×C4C22×D1311yescharacteristic
440C23×C4C22×D1311yescharacteristic
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C22⋊Q8—1364no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—138no—
446C2×C4⋊C4—138no—
447C2×C4⋊C4—134no—
448C2×C4⋊C4—134no—
449C2×C4⋊C4—134no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—522no—
454C2×C4⋊C4—522no—
455C2×C4⋊C4C4×D1318yes—
456C2×C4⋊C4C22×D1314yes—
457C2×C4⋊C4C22×D1314yes—
458C2×C22⋊C4—138no—
459C2×C22⋊C4—138no—
460C2×C22⋊C4—134no—
461C2×C22⋊C4—134no—
462C2×C22⋊C4—134no—
463C2×C22⋊C4—134no—
464C2×C22⋊C4—134no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—264no—
468C2×C22⋊C4—522no—
469C2×C22⋊C4—522no—
470C2×C42—24no—
471C2×C42—134no—
472C2×C42—134no—
473C2×C42—134no—
474C2×C42—134no—
475C2×C42—134no—
476C2×C42—264no—
477C2×C42—522no—
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#95C22×D1314yes—
493#95C22×D1314yes—
494#95C22×D1314yes—
495#95C22×D1314yes—
496C2×C13#233218yescomplemented
497C2×C13C2×C4×#4111yescharacteristic
498C2×C13C2×#51811yescharacteristic
499C2×C13C2×#51911yescharacteristic
500C2×C13C2×#53911yescharacteristic
501C2×C13C2×#53911yescharacteristic
502C2×C13C2×#54211yescharacteristic
503C2×C13C2×#54211yescharacteristic
504D13—44no—
505C24—134no—
506C24—132no—
507C24—262no—
508C24—262no—
509C24—262no—
510C24—262no—
511C24—262no—
512C24—262no—
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—22no—
535C22×C4—134no—
536C22×C4—134no—
537C22×C4—134no—
538C22×C4—134no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—132no—
543C22×C4—1316no—
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—5216no—
565C22×C4—524no—
566C22×C4—524no—
567C22×C4C2×C4×D1314yes—
568C22×C4C2×C4×D1314yes—
569C22×C4C2×C4×D1314yes—
570C22×C4#612914yes—
571C22×C4C23×D1312yes—
572C22×C4C23×D1312yes—
573C22×C4C23×D1312yes—
574C22×C4C23×D1312yes—
575C22×C4C23×D1312yes—
576C22×C4C23×D1312yes—
577C22×C4C23×D1312yes—
578C4⋊C4—28no—
579C4⋊C4—1316no—
580C4⋊C4—1316no—
581C4⋊C4—268no—
582C4⋊C4—524no—
583C4⋊C4—524no—
584C4⋊C4C2×C4×D13116yes—
585C22⋊C4—1316no—
586C22⋊C4—1316no—
587C22⋊C4—268no—
588C22⋊C4—268no—
589C22⋊C4—524no—
590C22⋊C4—524no—
591C42—28no—
592C42—268no—
593C42—524no—
594C42—524no—
595C42—524no—
596C42—524no—
597C13C2×#233211yescharacteristic, complemented, Sylow
598C23—134no—
599C23—268no—
600C23—268no—
601C23—268no—
602C23—262no—
603C23—262no—
604C23—262no—
605C23—262no—
606C23—262no—
607C23—262no—
608C23—524no—
609C23—524no—
610C23—524no—
611C23—524no—
612C23C22×C4×D1312yes—
613C23C2×#612912yes—
614C23#8825412yes—
615C23#41×D1312yes—
616C23#8825612yes—
617C23#8825612yes—
618C23#8825712yes—
619C23C24×D1311yescharacteristic
620Q8—5216no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
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—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—134no—
646C2×C4—134no—
647C2×C4—134no—
648C2×C4—134no—
649C2×C4—268no—
650C2×C4—268no—
651C2×C4—268no—
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—268no—
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—5216no—
671C2×C4—524no—
672C2×C4—524no—
673C2×C4—524no—
674C2×C4C22×C4×D1314yes—
675C2×C4C22×C4×D1314yes—
676C2×C4C22×C4×D1314yes—
677C2×C4C2×#612914yes—
678C22—264no—
679C22—264no—
680C22—264no—
681C22—522no—
682C22—522no—
683C22—5216no—
684C22—522no—
685C22—522no—
686C22#1171922614yes—
687C22C4×#612914yes—
688C22#1171927714yes—
689C22#1171934814yes—
690C22#1171937014yes—
691C22#1171939714yes—
692C22#1171941514yes—
693C22C23×C4×D1311yescharacteristic
694C22C22×#612911yescharacteristic
695C22C2×#8825411yescharacteristic
696C22C2×#41×D1311yescharacteristic
697C22C2×#8825611yescharacteristic
698C22C2×#8825611yescharacteristic
699C22C2×#8825711yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—264no—
708C4—264no—
709C4—264no—
710C4—264no—
711C4—522no—
712C4—522no—
713C4—522no—
714C2—524no—
715C2#1311758818yesdirect product factor
716C2C2×C4×#612911yescharacteristic
717C2C2×#1171922611yescharacteristic
718C2C2×#1171927711yescharacteristic
719C2C2×#1171937011yescharacteristic
720C2C2×#1171939711yescharacteristic
721C2C2×#1171941511yescharacteristic
722C2C2×#1171934811yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C2×#2332
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13117588C2direct (N × H)
3. C2×#11718307C2semidirect
4. C2×#11718307C2semidirect
9. C2×#11718642C2semidirect
10. C2×#11718314C2semidirect
11. C2×#11718315C2semidirect
13. C2×C4⋊C4×Dic13C2semidirect
14. C2×C4×C4⋊Dic13C2semidirect
16. C2×C13×#387C2semidirect
38. C2×#88151C4semidirect
40. C13×#387C22semidirect
56. #11718642C22semidirect
57. C4⋊C4×Dic13C22semidirect
59. C4×C4⋊Dic13C22semidirect
64. #11718315C22semidirect
65. #11718314C22semidirect
66. #11718307C22semidirect
67. #11718307C22semidirect
129. #88151C2×C4semidirect
248. C2×#387D13semidirect
365. #387C2×D13semidirect
496. C2×C13#2332semidirect
597. C13C2×#2332semidirect
715. C2#13117588direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
#131175882
C2×#117183072
C2×#117183312
C2×#117186012
C2×#117186512
C2×#117183302
C2×#117186422
C2×#117183142
C2×#117183152
C2×#117183252
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
C2×#117183272
C2×C13×#3872
C2×#233213