Finite Group Databasebeta

← C2×#13117949 #16022600

Subgroups — C2×#13117949 #16022600

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic
2#13117949C2116yesmaximal, direct product factor
3C2×#11718308C211yesmaximal, characteristic, complemented
4C2×#11718331C211yesmaximal, characteristic
5C2×#11718330C211yesmaximal, characteristic
6C2×#11718330C211yesmaximal, characteristic
7C2×#11718314C211yesmaximal, characteristic, complemented
8C2×#11718313C211yesmaximal, characteristic, complemented
9C2×#11718650C211yesmaximal, characteristic
10C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
12C2×#11718310C211yesmaximal, characteristic, complemented
13C2×C4×#6103C211yesmaximal, characteristic
14C2×#11718327C211yesmaximal, characteristic
15C2×#11718593C211yesmaximal, characteristic, complemented
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88152C4116yescomplemented
41C2×#88152C2218yes—
42C13×#387C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718650C2218yes—
56C4⋊C4×Dic13C2218yescomplemented
57C4⋊C4×Dic13C2218yescomplemented
58C4×#6103C2218yes—
59#11718593C2218yescomplemented
60#11718331C2218yes—
61#11718330C2218yes—
62#11718330C2218yes—
63#11718327C2218yes—
64#11718314C2218yescomplemented
65#11718313C2218yescomplemented
66#11718310C2218yescomplemented
67#11718308C2218yescomplemented
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—24no—
84C22×C4×D13—24no—
85C22×C4×D13—42no—
86C22×C4×D13C2314yes—
87C2×C13×C4⋊C4—24no—
88C2×C13×C4⋊C4C2×C418yescomplemented
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C4⋊C4C2314yes—
91C2×C42×C13—24no—
92C2×C42×C13C2314yes—
93C2×#6103—24no—
94C2×#6103—24no—
95C2×#6103—42no—
96C2×#6103C2×C418yes—
97C2×#6103C2×C418yes—
98C2×#6103C2×C418yes—
99C2×#6103C2314yes—
100C2×#6103C2314yes—
101C2×#6103C2314yes—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×#6103C2314yes—
105C2×C4⋊Dic13—24no—
106C2×C4⋊Dic13C2×C418yescomplemented
107C2×C4⋊Dic13C2314yes—
108C2×C4⋊Dic13C2314yes—
109C2×#6101—24no—
110C2×#6101—24no—
111C2×#6101—42no—
112C2×#6101C2×C418yescomplemented
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×C4×Dic13—24no—
118C2×C4×Dic13—24no—
119C2×C4×Dic13—24no—
120C2×C4×Dic13—42no—
121C2×C4×Dic13—42no—
122C2×C4×Dic13—42no—
123C2×C4×Dic13C2×C418yescomplemented
124C2×C4×Dic13C2314yes—
125C2×C4×Dic13C2314yes—
126C2×C4×Dic13C2314yes—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130C2×C4×Dic13C2314yes—
131#88152C2×C4164yescomplemented
132C13×#95C2314yes—
133C13×#95C2314yes—
134C13×#95C2314yes—
135C13×#95C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2373—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×Dic13C22×C414yes—
198C22×Dic13C22×C414yes—
199C22×Dic13C22×C414yes—
200C22×Dic13#4114yes—
201C22×Dic13#4114yes—
202C22×Dic13#4114yes—
203C22×Dic13C2412yes—
204C22×Dic13C2412yes—
205C22×Dic13C2412yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C2×C4×D13—28no—
211C2×C4×D13—28no—
212C2×C4×D13—44no—
213C2×C4×D13—416no—
214C13×C4⋊C4—28no—
215C13×C4⋊C4C22×C4116yescomplemented
216C42×C13—28no—
217#6103—28no—
218#6103—28no—
219#6103—44no—
220#6103C22×C4116yes—
221#6103C22×C4116yes—
222#6103C22×C4116yes—
223C4⋊Dic13—28no—
224C4⋊Dic13C22×C4116yescomplemented
225#6101—28no—
226#6101—28no—
227#6101—44no—
228#6101C22×C4116yescomplemented
229C4×Dic13—28no—
230C4×Dic13—28no—
231C4×Dic13—28no—
232C4×Dic13—44no—
233C4×Dic13—44no—
234C4×Dic13—44no—
235C4×Dic13C22×C4116yescomplemented
236C22×#126—131no—
237#2373—1316no—
238C2×#389—131no—
239C2×#388—131no—
240C2×#388—131no—
241C2×#388—131no—
242C2×#387—131no—
243C2×#387—131no—
244C2×#387D1311yescharacteristic, complemented
245C2×#385—131no—
246C2×C4×C4⋊C4—131no—
247C2×C4×C4⋊C4—131no—
248C2×C4×C4⋊C4—131no—
249C2×C4×C22⋊C4—131no—
250C2×C4×C22⋊C4—131no—
251C2×#376—131no—
252C23×C13C23×C412yes—
253C23×C13C2×#4112yes—
254C23×C13C2×#4112yes—
255C23×C13C2×#4112yes—
256C23×C13C2×#4112yes—
257C23×C13H(5,𝔽2)12yes—
258C23×C132−1+412yes—
259C23×C13C2511yescharacteristic
260C22×D13—28no—
261C22×D13—28no—
262C22×D13—28no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—44no—
270C22×D13—44no—
271C22×D13—44no—
272C22×D13—44no—
273C22×D13C23×C414yes—
274C2×C4×C13—28no—
275C2×C4×C13—28no—
276C2×C4×C13—28no—
277C2×C4×C13—28no—
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—22no—
294C2×C4×C13—22no—
295C2×C4×C13—44no—
296C2×C4×C13—44no—
297C2×C4×C13—44no—
298C2×C4×C13C23×C414yes—
299C2×C4×C13C23×C414yes—
300C2×C4×C13C23×C414yes—
301C2×C4×C13C2×#4114yes—
302C2×Dic13—28no—
303C2×Dic13—28no—
304C2×Dic13—28no—
305C2×Dic13—28no—
306C2×Dic13—28no—
307C2×Dic13—28no—
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—44no—
324C2×Dic13C23×C414yes—
325C2×Dic13C23×C414yes—
326C2×Dic13C23×C414yes—
327C2×Dic13C2×#4114yes—
328C2×Dic13C2×#4114yes—
329C2×Dic13C2×#4114yes—
330C4×D13—416no—
331C24×C4—131no—
332C2×#126—1316no—
333C2×#126—138no—
334C22×C4⋊C4—131no—
335C22×C4⋊C4—131no—
336C22×C4⋊C4—131no—
337C22×C4⋊C4—131no—
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4C2×D1311yescharacteristic
341C22×C4⋊C4C2×D1311yescharacteristic
342C22×C22⋊C4—131no—
343C22×C22⋊C4—131no—
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4—131no—
347C22×C22⋊C4—131no—
348C22×C42—131no—
349C22×C42—131no—
350C22×C42—131no—
351C22×C42—131no—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—131no—
355C22×C42C2×D1311yescharacteristic
356#389—138no—
357#388—138no—
358#388—138no—
359#388—138no—
360#387—138no—
361#387—138no—
362#387C2×D1318yescomplemented
363#385—138no—
364C4×C4⋊C4—138no—
365C4×C4⋊C4—138no—
366C4×C4⋊C4—138no—
367C4×C22⋊C4—138no—
368C4×C22⋊C4—138no—
369#376—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×#95C2×D1311yescharacteristic
379C2×#95C2×D1311yescharacteristic
380C2×#95C2×D1311yescharacteristic
381C2×#95C2×D1311yescharacteristic
382C22×C13C4×#4114yes—
383C22×C13C4×#4114yes—
384C22×C13#52014yes—
385C22×C13#55114yes—
386C22×C13#55214yes—
387C22×C13#55314yes—
388C22×C13#55614yes—
389C22×C13C24×C411yescharacteristic
390C22×C13C22×#4111yescharacteristic
391C22×C13C22×#4111yescharacteristic
392C22×C13C22×#4111yescharacteristic
393C22×C13C22×#4111yescharacteristic
394C22×C13C2×H(5,𝔽2)11yescharacteristic
395C22×C13C2×2−1+411yescharacteristic
396C2×D13—24no—
397C2×D13—24no—
398C2×D13—24no—
399C2×D13—416no—
400C2×D13—42no—
401C2×D13—42no—
402C2×D13—42no—
403C2×D13—42no—
404C4×C13—24no—
405C4×C13—24no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13—42no—
411Dic13—24no—
412Dic13—24no—
413Dic13—24no—
414Dic13—24no—
415Dic13—24no—
416Dic13—24no—
417Dic13—42no—
418C25—131no—
419C23×C4—131no—
420C23×C4—131no—
421C23×C4—131no—
422C23×C4—131no—
423C23×C4—131no—
424C23×C4—131no—
425C23×C4—131no—
426C23×C4—134no—
427C23×C4—264no—
428C23×C4—264no—
429C23×C4—522no—
430C23×C4C22×D1311yescharacteristic
431C23×C4C22×D1311yescharacteristic
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437#126—1364no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—138no—
440C2×C4⋊C4—138no—
441C2×C4⋊C4—134no—
442C2×C4⋊C4—134no—
443C2×C4⋊C4—134no—
444C2×C4⋊C4—134no—
445C2×C4⋊C4—134no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—264no—
448C2×C4⋊C4—264no—
449C2×C4⋊C4—264no—
450C2×C4⋊C4—522no—
451C2×C4⋊C4C4×D1318yescomplemented
452C2×C4⋊C4C22×D1314yes—
453C2×C4⋊C4C22×D1314yes—
454C2×C22⋊C4—138no—
455C2×C22⋊C4—138no—
456C2×C22⋊C4—138no—
457C2×C22⋊C4—134no—
458C2×C22⋊C4—134no—
459C2×C22⋊C4—134no—
460C2×C22⋊C4—134no—
461C2×C22⋊C4—134no—
462C2×C22⋊C4—134no—
463C2×C22⋊C4—264no—
464C2×C22⋊C4—264no—
465C2×C22⋊C4—522no—
466C2×C42—24no—
467C2×C42—138no—
468C2×C42—134no—
469C2×C42—134no—
470C2×C42—134no—
471C2×C42—134no—
472C2×C42—134no—
473C2×C42—134no—
474C2×C42—134no—
475C2×C42—264no—
476C2×C42—264no—
477C2×C42—264no—
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#95C22×D1314yes—
491#95C22×D1314yes—
492#95C22×D1314yes—
493#95C22×D1314yes—
494C2×C13#237318yescomplemented
495C2×C13C2×C4×#4111yescharacteristic
496C2×C13C2×C4×#4111yescharacteristic
497C2×C13C2×#52011yescharacteristic
498C2×C13C2×#55111yescharacteristic
499C2×C13C2×#55211yescharacteristic
500C2×C13C2×#55311yescharacteristic
501C2×C13C2×#55611yescharacteristic
502D13—44no—
503C24—134no—
504C24—132no—
505C24—262no—
506C24—262no—
507C24—262no—
508C24—262no—
509C24—262no—
510C24—262no—
511C24C23×D1311yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
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—134no—
530C22×C4—134no—
531C22×C4—134no—
532C22×C4—134no—
533C22×C4—134no—
534C22×C4—134no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—268no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
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—268no—
559C22×C4—524no—
560C22×C4—5216no—
561C22×C4C2×C4×D1314yes—
562C22×C4C2×C4×D1314yes—
563C22×C4C2×C4×D1314yes—
564C22×C4#612914yes—
565C22×C4C23×D1312yes—
566C22×C4C23×D1312yes—
567C22×C4C23×D1312yes—
568C22×C4C23×D1312yes—
569C22×C4C23×D1312yes—
570C22×C4C23×D1312yes—
571C22×C4C23×D1312yes—
572C4⋊C4—28no—
573C4⋊C4—1316no—
574C4⋊C4—1316no—
575C4⋊C4—268no—
576C4⋊C4—268no—
577C4⋊C4—268no—
578C4⋊C4—524no—
579C4⋊C4C2×C4×D13116yescomplemented
580C22⋊C4—1316no—
581C22⋊C4—1316no—
582C22⋊C4—1316no—
583C22⋊C4—268no—
584C22⋊C4—268no—
585C22⋊C4—524no—
586C42—28no—
587C42—1316no—
588C42—268no—
589C42—268no—
590C42—268no—
591C42—524no—
592C42—524no—
593C42—524no—
594C13C2×#237311yescharacteristic, complemented, Sylow
595C23—134no—
596C23—268no—
597C23—268no—
598C23—268no—
599C23—262no—
600C23—262no—
601C23—262no—
602C23—262no—
603C23—262no—
604C23—262no—
605C23—524no—
606C23—524no—
607C23—524no—
608C23—524no—
609C23C22×C4×D1312yes—
610C23C2×#612912yes—
611C23#8825412yes—
612C23#41×D1312yes—
613C23#41×D1312yes—
614C23#41×D1312yes—
615C23#8825612yes—
616C23C24×D1311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
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—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—134no—
642C2×C4—134no—
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—268no—
664C2×C4—268no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—5216no—
669C2×C4—524no—
670C2×C4C22×C4×D1314yes—
671C2×C4C22×C4×D1314yes—
672C2×C4C22×C4×D1314yes—
673C2×C4C2×#612914yes—
674C22—264no—
675C22—264no—
676C22—264no—
677C22—522no—
678C22—522no—
679C22—522no—
680C22—522no—
681C22—5216no—
682C22#1171922714yes—
683C22C4×#612914yes—
684C22#1171927914yes—
685C22#1171934614yes—
686C22#1171936314yes—
687C22#1171939814yes—
688C22#1171941414yes—
689C22C23×C4×D1311yescharacteristic
690C22C22×#612911yescharacteristic
691C22C2×#8825411yescharacteristic
692C22C2×#41×D1311yescharacteristic
693C22C2×#41×D1311yescharacteristic
694C22C2×#41×D1311yescharacteristic
695C22C2×#8825611yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—264no—
704C4—264no—
705C4—264no—
706C4—264no—
707C4—264no—
708C4—264no—
709C4—522no—
710C2—524no—
711C2#1311794918yesdirect product factor
712C2C2×C4×#612911yescharacteristic
713C2C2×#1171922711yescharacteristic
714C2C2×#1171927911yescharacteristic
715C2C2×#1171936311yescharacteristic
716C2C2×#1171939811yescharacteristic
717C2C2×#1171941411yescharacteristic
718C2C2×#1171934611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C2×#2373
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13117949C2direct (N × H)
3. C2×#11718308C2semidirect
7. C2×#11718314C2semidirect
8. C2×#11718313C2semidirect
10. C2×C4⋊C4×Dic13C2semidirect
11. C2×C4⋊C4×Dic13C2semidirect
12. C2×#11718310C2semidirect
15. C2×#11718593C2semidirect
16. C2×C13×#387C2semidirect
40. C2×#88152C4semidirect
42. C13×#387C22semidirect
56. C4⋊C4×Dic13C22semidirect
57. C4⋊C4×Dic13C22semidirect
59. #11718593C22semidirect
64. #11718314C22semidirect
65. #11718313C22semidirect
66. #11718310C22semidirect
67. #11718308C22semidirect
88. C2×C13×C4⋊C4C2×C4semidirect
106. C2×C4⋊Dic13C2×C4semidirect
112. C2×#6101C2×C4semidirect
123. C2×C4×Dic13C2×C4semidirect
131. #88152C2×C4semidirect
215. C13×C4⋊C4C22×C4semidirect
224. C4⋊Dic13C22×C4semidirect
228. #6101C22×C4semidirect
235. C4×Dic13C22×C4semidirect
244. C2×#387D13semidirect
362. #387C2×D13semidirect
451. C2×C4⋊C4C4×D13semidirect
494. C2×C13#2373semidirect
579. C4⋊C4C2×C4×D13semidirect
594. C13C2×#2373semidirect
711. C2#13117949direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
#131179492
C2×#117183082
C2×#117183312
C2×#117183302
C2×#117183142
C2×#117183132
C2×#117186502
C2×C4⋊C4×Dic132
C2×#117183102
C2×C4×#61032
C2×#117183272
C2×#117185932
C2×C13×#3872
C2×#237313