Finite Group Databasebeta

← C2×C4×#88046 #15860566

Subgroups — C2×C4×#88046 #15860566

Order 3328.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C22×#88046C212yesmaximal
3C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
4C4×#88046C218yesmaximal, direct product factor
5C2×#11718119C212yesmaximal, complemented
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
7C24×C4×C13C2211yescharacteristic
8C23×C22⋊D13C2211yescharacteristic
9C23×C4×D13C411yescharacteristic, complemented
10C22×C13×C22⋊C4C2212yes—
11C22×C42×C13—21no—
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2212yes—
14C2×C4×C22⋊D13—21no—
15C2×C4×C22⋊D13—21no—
16C2×C4×C22⋊D13—22no—
17C2×C4×C22⋊D13—21no—
18C2×C4×C22⋊D13—22no—
19C2×C4×C22⋊D13—21no—
20C2×C4×C22⋊D13C414yescomplemented
21C2×C4×C22⋊D13C2214yes—
22C22×#6103C411yescharacteristic, complemented
23C22×#6101C411yescharacteristic, complemented
24C22×C4×Dic13—21no—
25C22×C4×Dic13C411yescharacteristic, complemented
26C4×C13×C22⋊C4—22no—
27C4×C13×C22⋊C4C2214yescomplemented
28C2×C13×#95—21no—
29C4×C22⋊Dic13—22no—
30C4×C22⋊Dic13C2214yescomplemented
31C2×#88071—21no—
32C2×#88046C4116yesdirect product factor
33C2×#88046C2218yes—
34#11718119C2218yescomplemented
35C25×C13C2311yescharacteristic
36C24×D13C2×C411yescharacteristic
37C23×C4×C13—22no—
38C23×C4×C13—44no—
39C23×C4×C13C2×C411yescharacteristic
40C23×C4×C13C2×C411yescharacteristic
41C23×C4×C13C2×C412yes—
42C23×C4×C13D411yescharacteristic
43C23×C4×C13D411yescharacteristic
44C23×C4×C13D412yes—
45C23×C4×C13D411yescharacteristic
46C23×C4×C13D412yes—
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2312yes—
49C22×C22⋊D13—21no—
50C22×C22⋊D13—21no—
51C22×C22⋊D13—21no—
52C22×C22⋊D13—21no—
53C22×C22⋊D13—24no—
54C22×C22⋊D13C2×C418yes—
55C22×C22⋊D13C2×C412yes—
56C22×C22⋊D13C2312yes—
57C23×Dic13—22no—
58C23×Dic13C2×C411yescharacteristic
59C23×Dic13C2×C411yescharacteristic
60C23×Dic13C2×C411yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—22no—
63C22×C4×D13—21no—
64C22×C4×D13—44no—
65C22×C4×D13C2×C414yescomplemented
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4C2×C418yescomplemented
69C2×C13×C22⋊C4C2314yes—
70C2×C42×C13—24no—
71C2×C42×C13—44no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—22no—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13C2×C412yes—
79C2×C22⋊Dic13C2×C418yescomplemented
80C2×C22⋊Dic13C2312yes—
81C2×C22⋊Dic13C2314yes—
82C4×C22⋊D13—24no—
83C4×C22⋊D13—24no—
84C4×C22⋊D13—24no—
85C4×C22⋊D13—24no—
86C4×C22⋊D13—24no—
87C4×C22⋊D13—24no—
88C4×C22⋊D13—24no—
89C4×C22⋊D13—24no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—22no—
93C2×#6103C2×C414yescomplemented
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×#6101C2×C414yescomplemented
98C2×C4×Dic13—21no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—44no—
103C2×C4×Dic13C2×C414yescomplemented
104C13×#95—24no—
105#88071—24no—
106#88046C2×C4132yesdirect product factor
107C2×C4×#99—131nomaximal, Sylow
108C24×C13—42no—
109C24×C13—42no—
110C24×C13C22×C411yescharacteristic
111C24×C13C22×C411yescharacteristic
112C24×C13C22×C414yes—
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C24×C13C2×D411yescharacteristic
116C24×C13C2×D411yescharacteristic
117C24×C13#4114yes—
118C24×C13C2411yescharacteristic
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—22no—
122C23×D13—42no—
123C23×D13—42no—
124C23×D13C4214yescomplemented
125C23×D13C22×C412yes—
126C22×C4×C13—24no—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—28no—
130C22×C4×C13—24no—
131C22×C4×C13—44no—
132C22×C4×C13—44no—
133C22×C4×C13—44no—
134C22×C4×C13—44no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—44no—
139C22×C4×C13—44no—
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C22⋊C412yes—
142C22×C4×C13C22⋊C411yescharacteristic
143C22×C4×C13C22⋊C411yescharacteristic
144C22×C4×C13C22⋊C412yes—
145C22×C4×C13C22⋊C412yes—
146C22×C4×C13C22⋊C412yes—
147C22×C4×C13C22⋊C412yes—
148C22×C4×C13C22⋊C412yes—
149C22×C4×C13C22⋊C411yescharacteristic
150C22×C4×C13C22×C412yes—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—22no—
158C2×C22⋊D13—24no—
159C2×C22⋊D13—28no—
160C2×C22⋊D13—28no—
161C2×C22⋊D13—28no—
162C2×C22⋊D13—28no—
163C2×C22⋊D13—22no—
164C2×C22⋊D13—22no—
165C2×C22⋊D13—24no—
166C2×C22⋊D13C4218yescomplemented
167C2×C22⋊D13C22×C418yes—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—28no—
176C22×Dic13—24no—
177C22×Dic13—44no—
178C22×Dic13—44no—
179C22×Dic13—42no—
180C22×Dic13—42no—
181C22×Dic13C4214yescomplemented
182C22×Dic13C22×C412yes—
183C22×Dic13C22×C412yes—
184C22×Dic13C22×C412yes—
185C2×C4×D13—24no—
186C2×C4×D13—24no—
187C2×C4×D13—44no—
188C2×C4×D13—48no—
189C2×C4×D13—44no—
190C2×C4×D13—48no—
191C13×C22⋊C4—28no—
192C13×C22⋊C4—24no—
193C13×C22⋊C4C22×C418yescomplemented
194C42×C13—48no—
195C22⋊Dic13—22no—
196C22⋊Dic13—22no—
197C22⋊Dic13—28no—
198C22⋊Dic13—22no—
199C22⋊Dic13—22no—
200C22⋊Dic13—24no—
201C22⋊Dic13C22×C418yescomplemented
202#6103—24no—
203#6103—24no—
204#6101—24no—
205#6101—24no—
206C4×Dic13—24no—
207C4×Dic13—24no—
208C4×Dic13—48no—
209C22×C4×D4—131no—
210C22×#99—132no—
211C2×C4×C22⋊C4—131no—
212C2×C4×C22⋊C4D1311yescharacteristic, complemented
213C4×#99—138no—
214C2×#342—132no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—48no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—48no—
230C23×C13—41no—
231C23×C13C2×C4212yes—
232C23×C13C2×C4212yes—
233C23×C13C2×C22⋊C411yescharacteristic
234C23×C13C2×C22⋊C411yescharacteristic
235C23×C13C2×C22⋊C411yescharacteristic
236C23×C13C2×C22⋊C411yescharacteristic
237C23×C13#11712yes—
238C23×C13#11712yes—
239C23×C13C4×D414yes—
240C23×C13C4×D414yes—
241C23×C13C4×D414yes—
242C23×C13C4×D414yes—
243C23×C13C23×C411yescharacteristic
244C23×C13C23×C412yes—
245C23×C13C22×D411yescharacteristic
246C23×C13C22×D411yescharacteristic
247C23×C13C2×#4112yes—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—24no—
251C22×D13—24no—
252C22×D13—42no—
253C22×D13—42no—
254C22×D13—48no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—48no—
259C22×D13—42no—
260C22×D13C2×C4214yescomplemented
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—24no—
265C2×C4×C13—24no—
266C2×C4×C13—24no—
267C2×C4×C13—24no—
268C2×C4×C13—24no—
269C2×C4×C13—24no—
270C2×C4×C13—28no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—44no—
278C2×C4×C13—44no—
279C2×C4×C13—416no—
280C2×C4×C13#9914yescomplemented
281C2×C4×C13C2×C22⋊C412yes—
282C2×C4×C13C2×C22⋊C412yes—
283C2×C4×C13C2×C22⋊C412yes—
284C2×C4×C13C2×C22⋊C412yes—
285C22⋊D13—28no—
286C22⋊D13—28no—
287C22⋊D13—28no—
288C22⋊D13—28no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—24no—
292C2×Dic13—24no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—28no—
296C2×Dic13—44no—
297C2×Dic13—42no—
298C2×Dic13—44no—
299C2×Dic13—416no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13C2×C4214yescomplemented
306C4×D13—48no—
307C4×D13—48no—
308C23×D4—131no—
309C24×C4—131no—
310C24×C4C2×D1311yescharacteristic
311C2×C4×D4—134no—
312C2×C4×D4—134no—
313C2×C4×D4—261no—
314C2×C4×D4—262no—
315C2×C4×D4—261no—
316C2×C4×D4—261no—
317C2×C4×D4—262no—
318C2×C4×D4—261no—
319C22×C4⋊C4—131no—
320C22×C22⋊C4—132no—
321C22×C22⋊C4—131no—
322C22×C22⋊C4—131no—
323C22×C22⋊C4C2×D1312yes—
324C22×C42—21no—
325C22×C42—131no—
326C22×C42—261no—
327C2×#99—1316no—
328C2×#99—138no—
329C4×C22⋊C4—22no—
330C4×C22⋊C4—134no—
331C4×C22⋊C4—262no—
332C4×C22⋊C4C2×D1314yescomplemented
333C2×#95—21no—
334C2×#95—261no—
335#342—138no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—28no—
349C22×C13—28no—
350C22×C13—24no—
351C22×C13—24no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—44no—
355C22×C13—44no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13C4×C22⋊C412yes—
359C22×C13C4×C22⋊C412yes—
360C22×C13C4×C22⋊C412yes—
361C22×C13C4×C22⋊C412yes—
362C22×C13C2×#9912yes—
363C22×C13#41012yes—
364C22×C13C22×C4211yescharacteristic
365C22×C13C22×C22⋊C411yescharacteristic
366C22×C13C2×#11711yescharacteristic
367C22×C13C2×C4×D412yes—
368C22×C13C2×C4×D412yes—
369C2×D13—24no—
370C2×D13—44no—
371C2×D13—48no—
372C2×D13—42no—
373C2×D13—42no—
374C2×D13—48no—
375C2×D13—44no—
376C4×C13—22no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—48no—
380C4×C13C2×#9914yescomplemented
381Dic13—24no—
382Dic13—48no—
383Dic13—42no—
384Dic13—42no—
385C25—131no—
386C25C22×D1311yescharacteristic
387C22×D4—132no—
388C22×D4—138no—
389C22×D4—132no—
390C22×D4—261no—
391C22×D4—261no—
392C22×D4—264no—
393C22×D4—261no—
394C22×D4—261no—
395C23×C4—22no—
396C23×C4—44no—
397C23×C4—131no—
398C23×C4—131no—
399C23×C4—131no—
400C23×C4—134no—
401C23×C4—262no—
402C23×C4—262no—
403C23×C4—261no—
404C23×C4—261no—
405C23×C4—524no—
406C23×C4C4×D1311yescharacteristic
407C23×C4C4×D1311yescharacteristic
408C23×C4C4×D1312yes—
409C23×C4D5211yescharacteristic
410C23×C4D5211yescharacteristic
411C23×C4D5212yes—
412C23×C4C22⋊D1311yescharacteristic
413C23×C4C22⋊D1311yescharacteristic
414C23×C4C22⋊D1312yes—
415C23×C4C22×D1312yes—
416C4×D4—264no—
417C4×D4—264no—
418C4×D4—264no—
419C4×D4—264no—
420C4×D4—264no—
421C4×D4—264no—
422C4×D4—264no—
423C4×D4—264no—
424C2×C4⋊C4—134no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—262no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—138no—
431C2×C22⋊C4—134no—
432C2×C22⋊C4—132no—
433C2×C22⋊C4—132no—
434C2×C22⋊C4—134no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—262no—
438C2×C22⋊C4—264no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4—261no—
442C2×C22⋊C4—261no—
443C2×C22⋊C4—262no—
444C2×C22⋊C4C4×D1318yescomplemented
445C2×C22⋊C4C22×D1314yes—
446C2×C42—24no—
447C2×C42—44no—
448C2×C42—134no—
449C2×C42—261no—
450C2×C42—262no—
451C2×C42—261no—
452C2×C42—264no—
453C2×C42—524no—
454#99—1332no—
455#95—24no—
456#95—264no—
457C2×C13—22no—
458C2×C13—22no—
459C2×C13—21no—
460C2×C13—22no—
461C2×C13—21no—
462C2×C13—22no—
463C2×C13—22no—
464C2×C13C4×#9914yescomplemented
465C2×C13C2×C4×C22⋊C411yescharacteristic
466C2×C13C22×#9911yescharacteristic
467C2×C13C2×#41011yescharacteristic
468D13—44no—
469C24—42no—
470C24—42no—
471C24—134no—
472C24—132no—
473C24—262no—
474C24—261no—
475C24—261no—
476C24—522no—
477C24—522no—
478C24C2×C4×D1311yescharacteristic
479C24C2×C4×D1311yescharacteristic
480C24C2×C4×D1314yes—
481C24C2×D5211yescharacteristic
482C24C2×D5211yescharacteristic
483C24#612714yes—
484C24C2×C22⋊D1311yescharacteristic
485C24C2×C22⋊D1311yescharacteristic
486C24C23×D1311yescharacteristic
487C2×D4—138no—
488C2×D4—138no—
489C2×D4—264no—
490C2×D4—268no—
491C2×D4—268no—
492C2×D4—262no—
493C2×D4—262no—
494C2×D4—268no—
495C2×D4—268no—
496C2×D4—262no—
497C2×D4—264no—
498C2×D4—262no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—28no—
503C22×C4—24no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—134no—
514C22×C4—132no—
515C22×C4—132no—
516C22×C4—132no—
517C22×C4—262no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—268no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—264no—
526C22×C4—264no—
527C22×C4—264no—
528C22×C4—524no—
529C22×C4—528no—
530C22×C4—528no—
531C22×C4—524no—
532C22×C4—524no—
533C22×C4—524no—
534C22×C4—522no—
535C22×C4—522no—
536C22×C4#610311yescharacteristic
537C22×C4#610312yes—
538C22×C4#610311yescharacteristic
539C22×C4#610311yescharacteristic
540C22×C4#610312yes—
541C22×C4#610312yes—
542C22×C4#610312yes—
543C22×C4#610312yes—
544C22×C4#610312yes—
545C22×C4#610311yescharacteristic
546C22×C4C2×C4×D1312yes—
547C22×C4C2×C4×D1312yes—
548C22×C4C2×D5212yes—
549C22×C4C2×D5212yes—
550C22×C4C2×C22⋊D1312yes—
551C22×C4C2×C22⋊D1312yes—
552C4⋊C4—264no—
553C4⋊C4—264no—
554C22⋊C4—28no—
555C22⋊C4—24no—
556C22⋊C4—138no—
557C22⋊C4—268no—
558C22⋊C4—262no—
559C22⋊C4—262no—
560C22⋊C4—262no—
561C22⋊C4—264no—
562C22⋊C4—262no—
563C22⋊C4—264no—
564C22⋊C4—264no—
565C22⋊C4C2×C4×D1318yescomplemented
566C42—48no—
567C42—264no—
568C42—264no—
569C42—528no—
570C13C2×C4×#9911yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—48no—
582C23—41no—
583C23—41no—
584C23—48no—
585C23—41no—
586C23—41no—
587C23—134no—
588C23—262no—
589C23—262no—
590C23—264no—
591C23—264no—
592C23—522no—
593C23—528no—
594C23—522no—
595C23—522no—
596C23—528no—
597C23—522no—
598C23—522no—
599C23—522no—
600C23C42×D1312yes—
601C23C42×D1312yes—
602C23#8812612yes—
603C23#8812612yes—
604C23C4×D5214yes—
605C23C4×D5214yes—
606C23C2×#610311yescharacteristic
607C23C2×#610311yescharacteristic
608C23C2×#610311yescharacteristic
609C23C2×#610311yescharacteristic
610C23C4×C22⋊D1314yes—
611C23C4×C22⋊D1314yes—
612C23C22×C4×D1311yescharacteristic
613C23C22×C4×D1312yes—
614C23C22×D5211yescharacteristic
615C23C2×#612712yes—
616C23C22×C22⋊D1311yescharacteristic
617D4—268no—
618D4—268no—
619D4—268no—
620D4—268no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—416no—
639C2×C4—44no—
640C2×C4—134no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—264no—
644C2×C4—264no—
645C2×C4—268no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—528no—
649C2×C4—524no—
650C2×C4—5216no—
651C2×C4—524no—
652C2×C4—522no—
653C2×C4—522no—
654C2×C4—522no—
655C2×C4—522no—
656C2×C4—528no—
657C2×C4—522no—
658C2×C4—522no—
659C2×C4#8804614yesdirect product factor
660C2×C4C2×#610312yes—
661C2×C4C2×#610312yes—
662C2×C4C2×#610312yes—
663C2×C4C2×#610312yes—
664C22—28no—
665C22—28no—
666C22—24no—
667C22—24no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—42no—
685C22—42no—
686C22—264no—
687C22—524no—
688C22—524no—
689C22—528no—
690C22—528no—
691C22—522no—
692C22—522no—
693C22C4×#610312yes—
694C22C4×#610312yes—
695C22C4×#610312yes—
696C22C4×#610312yes—
697C22C2×#8804612yes—
698C22#1171866712yes—
699C22C2×C42×D1311yescharacteristic
700C22C2×#8812611yescharacteristic
701C22C2×C4×D5212yes—
702C22C22×#610311yescharacteristic
703C22C2×C4×C22⋊D1312yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—264no—
709C4—528no—
710C4—522no—
711C4—522no—
712C4C2×#8804614yesdirect product factor
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—524no—
721C2C4×#8804614yesdirect product factor
722C2C2×C4×#610311yescharacteristic
723C2C22×#8804611yescharacteristic
724C2C2×#1171866711yescharacteristic
subgroupG/H
centerC22×C4#6103
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radicalC23×C22⋊D13C22
cosocleC24×C13C24
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×C4×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic13C2semidirect
4. C4×#88046C2direct (N × H)
5. C2×#11718119C2semidirect
6. C2×C4×C13×C22⋊C4C2semidirect
9. C23×C4×D13C4semidirect
20. C2×C4×C22⋊D13C4semidirect
22. C22×#6103C4semidirect
23. C22×#6101C4semidirect
25. C22×C4×Dic13C4semidirect
27. C4×C13×C22⋊C4C22semidirect
30. C4×C22⋊Dic13C22semidirect
32. C2×#88046C4direct (N × H)
34. #11718119C22semidirect
65. C22×C4×D13C2×C4semidirect
68. C2×C13×C22⋊C4C2×C4semidirect
79. C2×C22⋊Dic13C2×C4semidirect
93. C2×#6103C2×C4semidirect
97. C2×#6101C2×C4semidirect
103. C2×C4×Dic13C2×C4semidirect
106. #88046C2×C4direct (N × H)
124. C23×D13C42semidirect
166. C2×C22⋊D13C42semidirect
181. C22×Dic13C42semidirect
193. C13×C22⋊C4C22×C4semidirect
201. C22⋊Dic13C22×C4semidirect
212. C2×C4×C22⋊C4D13semidirect
260. C22×D13C2×C42semidirect
280. C2×C4×C13#99semidirect
305. C2×Dic13C2×C42semidirect
332. C4×C22⋊C4C2×D13semidirect
380. C4×C13C2×#99semidirect
444. C2×C22⋊C4C4×D13semidirect
464. C2×C13C4×#99semidirect
565. C22⋊C4C2×C4×D13semidirect
570. C13C2×C4×#99semidirect
659. C2×C4#88046direct (N × H)
712. C4C2×#88046direct (N × H)
721. C2C4×#88046direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C22×#880462
C2×C4×C22⋊Dic132
C4×#880462
C2×#117181192
C2×C4×C13×C22⋊C42
C2×C4×#9913