Finite Group Databasebeta

← C2×#13117957 #16022608

Subgroups — C2×#13117957 #16022608

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×#88133C211yesmaximal, characteristic
2#13117957C2116yesmaximal, direct product factor
3C2×#11718589C211yesmaximal, characteristic, complemented
4C2×#11718606C211yesmaximal, characteristic
5C2×#11718606C211yesmaximal, characteristic
6C2×#11718612C211yesmaximal, characteristic
7C2×#11718316C211yesmaximal, characteristic, complemented
8C2×#11718314C211yesmaximal, characteristic, complemented
9C2×#11718594C211yesmaximal, characteristic, complemented
10C2×#11718871C211yesmaximal, characteristic
11C2×C4×#6101C211yesmaximal, characteristic, complemented
12C2×#11718310C211yesmaximal, characteristic, complemented
13C2×#11718310C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic13C211yesmaximal, characteristic
15C2×#11718593C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
17C24×C4×C13C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88133C4116yescomplemented
41C2×#88133C2218yes—
42C4×C13×C22⋊C4C2218yes—
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45#11718871C2218yes—
46C4×C22⋊Dic13C2218yes—
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718612C2218yes—
58#11718606C2218yes—
59#11718606C2218yes—
60#11718594C2218yescomplemented
61#11718593C2218yescomplemented
62C4×#6101C2218yescomplemented
63#11718589C2218yescomplemented
64#11718316C2218yescomplemented
65#11718314C2218yescomplemented
66#11718310C2218yescomplemented
67#11718310C2218yescomplemented
68C25×C13C2311yescharacteristic
69C23×C4×C13—24no—
70C23×C4×C13—24no—
71C23×C4×C13—42no—
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2314yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C2×C13×C22⋊C4—24no—
88C2×C13×C22⋊C4C2×C418yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2314yes—
91C2×C42×C13—24no—
92C2×C42×C13—42no—
93C2×C42×C13C2314yes—
94C2×C42×C13C2314yes—
95C2×C22⋊Dic13—24no—
96C2×C22⋊Dic13—42no—
97C2×C22⋊Dic13C2×C418yes—
98C2×C22⋊Dic13C2×C418yes—
99C2×C22⋊Dic13C2314yes—
100C2×C22⋊Dic13C2314yes—
101C2×C22⋊Dic13C2314yes—
102C2×C22⋊Dic13C2314yes—
103C2×C4⋊Dic13—42no—
104C2×C4⋊Dic13C2×C418yescomplemented
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2314yes—
107C2×#6101—24no—
108C2×#6101—24no—
109C2×#6101—24no—
110C2×#6101—24no—
111C2×#6101C2×C418yescomplemented
112C2×#6101C2×C418yescomplemented
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×C4×Dic13—24no—
120C2×C4×Dic13—24no—
121C2×C4×Dic13—24no—
122C2×C4×Dic13—42no—
123C2×C4×Dic13—42no—
124C2×C4×Dic13C2×C418yescomplemented
125C2×C4×Dic13C2314yes—
126C2×C4×Dic13C2314yes—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130C2×C4×Dic13C2314yes—
131#88133C2×C4164yescomplemented
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×#2373—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—28no—
168C22×C4×C13—28no—
169C22×C4×C13—44no—
170C22×C4×C13—416no—
171C22×C4×C13C22×C414yes—
172C22×C4×C13C22×C414yes—
173C22×C4×C13#4114yes—
174C22×C4×C13#4114yes—
175C22×C4×C13#4114yes—
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×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13C22×C414yes—
202C22×Dic13C22×C414yes—
203C22×Dic13C22×C414yes—
204C22×Dic13C22×C414yes—
205C22×Dic13#4114yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C13×C22⋊C4—28no—
215C13×C22⋊C4C22×C4116yes—
216C42×C13—28no—
217C42×C13—44no—
218C22⋊Dic13—28no—
219C22⋊Dic13—44no—
220C22⋊Dic13C22×C4116yes—
221C22⋊Dic13C22×C4116yes—
222C4⋊Dic13—44no—
223C4⋊Dic13C22×C4116yescomplemented
224#6101—28no—
225#6101—28no—
226#6101—28no—
227#6101—28no—
228#6101C22×C4116yescomplemented
229#6101C22×C4116yescomplemented
230C4×Dic13—28no—
231C4×Dic13—28no—
232C4×Dic13—28no—
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×#387—131no—
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⋊C4D1311yescharacteristic
251C2×#376—131no—
252C23×C13—28no—
253C23×C13—28no—
254C23×C13—28no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—44no—
262C23×C13—44no—
263C23×C13—44no—
264C23×C13—44no—
265C23×C13C23×C414yes—
266C23×C13C23×C412yes—
267C23×C13C2×#4112yes—
268C23×C13C2×#4112yes—
269C23×C13C2×#4112yes—
270C23×C13C2×#4112yes—
271C23×C13H(5,𝔽2)12yes—
272C23×C132−1+412yes—
273C23×C13C2511yescharacteristic
274C2×C4×C13—28no—
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—416no—
293C2×C4×C13—44no—
294C2×C4×C13C23×C414yes—
295C2×C4×C13C23×C414yes—
296C2×C4×C13C2×#4114yes—
297C2×C4×C13C2×#4114yes—
298C2×C4×C13C2×#4114yes—
299C2×Dic13—28no—
300C2×Dic13—28no—
301C2×Dic13—28no—
302C2×Dic13—28no—
303C2×Dic13—28no—
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—44no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13C23×C414yes—
327C2×Dic13C23×C414yes—
328C2×Dic13C23×C414yes—
329C2×Dic13C23×C414yes—
330C2×Dic13C2×#4114yes—
331C24×C4C2×D1311yescharacteristic
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⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C22⋊C4—131no—
343C22×C22⋊C4—131no—
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4C2×D1311yescharacteristic
347C22×C22⋊C4C2×D1311yescharacteristic
348C22×C42—131no—
349C22×C42—131no—
350C22×C42—131no—
351C22×C42—131no—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42C2×D1311yescharacteristic
355C22×C42C2×D1311yescharacteristic
356#389—138no—
357#388—138no—
358#388—138no—
359#388—138no—
360#387—138no—
361#387—138no—
362#387—138no—
363#385—138no—
364C4×C4⋊C4—138no—
365C4×C4⋊C4—138no—
366C4×C4⋊C4—138no—
367C4×C22⋊C4—138no—
368C4×C22⋊C4C2×D1318yes—
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×#95—131no—
379C2×#95—131no—
380C2×#95C2×D1311yescharacteristic
381C2×#95C2×D1311yescharacteristic
382C22×C13—24no—
383C22×C13—24no—
384C22×C13—24no—
385C22×C13—416no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13C4×#4114yes—
391C22×C13C4×#4114yes—
392C22×C13#52014yes—
393C22×C13#55114yes—
394C22×C13#55214yes—
395C22×C13#55314yes—
396C22×C13#55614yes—
397C22×C13C24×C411yescharacteristic
398C22×C13C22×#4111yescharacteristic
399C22×C13C22×#4111yescharacteristic
400C22×C13C22×#4111yescharacteristic
401C22×C13C22×#4111yescharacteristic
402C22×C13C2×H(5,𝔽2)11yescharacteristic
403C22×C13C2×2−1+411yescharacteristic
404C4×C13—24no—
405C4×C13—24no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—24no—
409C4×C13—42no—
410Dic13—24no—
411Dic13—24no—
412Dic13—24no—
413Dic13—24no—
414Dic13—24no—
415Dic13—42no—
416Dic13—42no—
417Dic13—42no—
418C25C22×D1311yescharacteristic
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—42no—
422C23×C4—131no—
423C23×C4—131no—
424C23×C4—131no—
425C23×C4—131no—
426C23×C4—131no—
427C23×C4—131no—
428C23×C4—131no—
429C23×C4—131no—
430C23×C4C22×D1311yescharacteristic
431C23×C4C22×D1314yes—
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437#126—1364no—
438C2×C4⋊C4—138no—
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—134no—
448C2×C4⋊C4—134no—
449C2×C4⋊C4—264no—
450C2×C4⋊C4—264no—
451C2×C4⋊C4—264no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—522no—
454C2×C22⋊C4—24no—
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—264no—
462C2×C22⋊C4—522no—
463C2×C22⋊C4C4×D1318yes—
464C2×C22⋊C4C22×D1314yes—
465C2×C22⋊C4C22×D1314yes—
466C2×C42—24no—
467C2×C42—42no—
468C2×C42—138no—
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×C42C22×D1314yes—
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—
494C2×C13—44no—
495C2×C13#237318yescomplemented
496C2×C13C2×C4×#4111yescharacteristic
497C2×C13C2×C4×#4111yescharacteristic
498C2×C13C2×#52011yescharacteristic
499C2×C13C2×#55111yescharacteristic
500C2×C13C2×#55211yescharacteristic
501C2×C13C2×#55311yescharacteristic
502C2×C13C2×#55611yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24C2×C4×D1314yes—
510C24C23×D1312yes—
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—28no—
526C22×C4—28no—
527C22×C4—44no—
528C22×C4—416no—
529C22×C4—134no—
530C22×C4—134no—
531C22×C4—134no—
532C22×C4—134no—
533C22×C4—134no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—262no—
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—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4C2×C4×D1314yes—
562C22×C4C2×C4×D1314yes—
563C22×C4#612714yes—
564C22×C4#612714yes—
565C22×C4#612914yes—
566C22×C4C23×D1312yes—
567C22×C4C23×D1312yes—
568C22×C4C23×D1312yes—
569C22×C4C23×D1312yes—
570C22×C4C23×D1312yes—
571C22×C4C23×D1312yes—
572C4⋊C4—1316no—
573C4⋊C4—1316no—
574C4⋊C4—1316no—
575C4⋊C4—268no—
576C4⋊C4—268no—
577C4⋊C4—268no—
578C4⋊C4—268no—
579C4⋊C4—524no—
580C22⋊C4—28no—
581C22⋊C4—1316no—
582C22⋊C4—1316no—
583C22⋊C4—268no—
584C22⋊C4—524no—
585C22⋊C4C2×C4×D13116yes—
586C42—28no—
587C42—44no—
588C42—1316no—
589C42—268no—
590C42—268no—
591C42—268no—
592C42—524no—
593C42—524no—
594C13C2×#237311yescharacteristic, complemented, Sylow
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D1314yes—
609C23C22×C4×D1312yes—
610C23C2×#612712yes—
611C23C2×#612712yes—
612C23C2×#612912yes—
613C23#8825112yes—
614C23#41×D1312yes—
615C23#8825712yes—
616C23C24×D1311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
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—416no—
636C2×C4—44no—
637C2×C4—134no—
638C2×C4—134no—
639C2×C4—134no—
640C2×C4—134no—
641C2×C4—134no—
642C2×C4—268no—
643C2×C4—268no—
644C2×C4—268no—
645C2×C4—268no—
646C2×C4—268no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
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—524no—
667C2×C4—524no—
668C2×C4—524no—
669C2×C4C22×C4×D1314yes—
670C2×C4C22×C4×D1314yes—
671C2×C4C2×#612714yes—
672C2×C4C2×#612714yes—
673C2×C4C2×#612914yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22C4×#612714yes—
683C22#1171920014yes—
684C22#1171923414yes—
685C22C4×#612914yes—
686C22#1171924514yes—
687C22#1171924714yes—
688C22#1171925114yes—
689C22C23×C4×D1311yescharacteristic
690C22C22×#612711yescharacteristic
691C22C22×#612711yescharacteristic
692C22C22×#612911yescharacteristic
693C22C2×#8825111yescharacteristic
694C22C2×#41×D1311yescharacteristic
695C22C2×#8825711yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—42no—
702C4—264no—
703C4—264no—
704C4—264no—
705C4—264no—
706C4—264no—
707C4—522no—
708C4—522no—
709C4—522no—
710C2—44no—
711C2#1311795718yesdirect product factor
712C2C2×C4×#612911yescharacteristic
713C2C2×C4×#612711yescharacteristic
714C2C2×#1171925111yescharacteristic
715C2C2×#1171920011yescharacteristic
716C2C2×#1171923411yescharacteristic
717C2C2×#1171924511yescharacteristic
718C2C2×#1171924711yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2373
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13117957C2direct (N × H)
3. C2×#11718589C2semidirect
7. C2×#11718316C2semidirect
8. C2×#11718314C2semidirect
9. C2×#11718594C2semidirect
11. C2×C4×#6101C2semidirect
12. C2×#11718310C2semidirect
13. C2×#11718310C2semidirect
15. C2×#11718593C2semidirect
40. C2×#88133C4semidirect
60. #11718594C22semidirect
61. #11718593C22semidirect
62. C4×#6101C22semidirect
63. #11718589C22semidirect
64. #11718316C22semidirect
65. #11718314C22semidirect
66. #11718310C22semidirect
67. #11718310C22semidirect
104. C2×C4⋊Dic13C2×C4semidirect
111. C2×#6101C2×C4semidirect
112. C2×#6101C2×C4semidirect
124. C2×C4×Dic13C2×C4semidirect
131. #88133C2×C4semidirect
223. C4⋊Dic13C22×C4semidirect
228. #6101C22×C4semidirect
229. #6101C22×C4semidirect
235. C4×Dic13C22×C4semidirect
495. C2×C13#2373semidirect
594. C13C2×#2373semidirect
711. C2#13117957direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881332
#131179572
C2×#117185892
C2×#117186062
C2×#117186122
C2×#117183162
C2×#117183142
C2×#117185942
C2×#117188712
C2×C4×#61012
C2×#117183102
C2×C4×C22⋊Dic132
C2×#117185932
C2×C4×C13×C22⋊C42
C2×#237313