Finite Group Databasebeta

← C4×#11718308 #15784113

Subgroups — C4×#11718308 #15784113

Order 3328.

1918 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C212yesmaximal
2C2×C4×#6101C211yesmaximal, characteristic
3C2×C4×#6101C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic
6C2×C42×Dic13C211yesmaximal, characteristic
7#13113070C212yesmaximal
8#13113067C212yesmaximal
9#13113064C212yesmaximal
10C4×#88071C211yesmaximal, characteristic
11C4×C13×#95C211yesmaximal, characteristic
12C22×C42×C13C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2212yes—
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C4×C4⋊Dic13—24no—
36C4×#6101—24no—
37C4×#6101—24no—
38C4×#6101C418yescomplemented
39C42×Dic13—24no—
40#11718308C4116yesdirect product factor
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C2×C42×C13—22no—
53C2×C42×C13—22no—
54C2×C42×C13—22no—
55C2×C42×C13—22no—
56C2×C42×C13—22no—
57C2×C42×C13—22no—
58C2×C42×C13—22no—
59C2×C42×C13C2×C414yes—
60C2×C42×C13Q814yes—
61C2×C4⋊Dic13—24no—
62C2×C4⋊Dic13—24no—
63C2×C4⋊Dic13C2×C418yes—
64C2×#6101—24no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101C2×C418yes—
70C2×#6101C2×C418yes—
71C2×#6101C2×C414yes—
72C2×#6101C2×C418yes—
73C2×#6101C2×C414yes—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13C2×C418yes—
87C2×C4×Dic13C2×C414yes—
88C2×C4×Dic13C2×C414yes—
89C2×C4×Dic13D414yes—
90C2×C4×Dic13D414yes—
91C2×C4×Dic13Q814yes—
92C13×#95—24no—
93C13×#95C2×C418yes—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071C2×C418yes—
99#88071C2×C414yes—
100#88071C2×C414yes—
101C4×#389—131nomaximal, Sylow
102C24×C13C2411yescharacteristic
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C414yes—
122C22×C4×C13C22×C412yes—
123C22×C4×C13C22×C414yes—
124C22×C4×C13C22×C414yes—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×Q814yes—
129C22×C4×C13C2×Q812yes—
130C22×C4×C13C2×Q812yes—
131C22×C4×C13#4114yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13C22×C412yes—
154C22×Dic13C22×C414yes—
155C22×Dic13C22×C412yes—
156C22×Dic13C22×C414yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C414yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C414yes—
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D414yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×Q812yes—
165C22×Dic13C2×Q812yes—
166C22×Dic13#4114yes—
167C22×Dic13#4114yes—
168C42×C13—28no—
169C42×C13—28no—
170C42×C13—44no—
171C4⋊Dic13—216no—
172#6101—28no—
173#6101—216no—
174#6101—216no—
175#6101C42116yescomplemented
176C4×Dic13—216no—
177C4×Dic13—28no—
178C4×Dic13—28no—
179C4×Dic13—216no—
180C4×Dic13—44no—
181C4×Dic13C4⋊C4116yescomplemented
182C2×#389—132no—
183C2×C4×C4⋊C4—131no—
184C2×C4×C4⋊C4—131no—
185C2×C4×C4⋊C4—131no—
186C2×C4×C4⋊C4—131no—
187C2×C43—131no—
188#1436—132no—
189#1436—132no—
190C4⋊#95—132no—
191C4×#95—131no—
192C4×#95D1311yescharacteristic
193C23×C13C23×C411yescharacteristic
194C23×C13C23×C412yes—
195C23×C13C22×D411yescharacteristic
196C23×C13C22×D411yescharacteristic
197C23×C13C22×Q811yescharacteristic
198C23×C13C22×Q811yescharacteristic
199C23×C13C2×#4112yes—
200C23×C13C2×#4111yescharacteristic
201C23×C13C2×#4112yes—
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4112yes—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13C2×C4214yes—
227C2×C4×C13C2×C4⋊C414yes—
228C2×C4×C13C4×D414yes—
229C2×C4×C13C4×Q818yes—
230C2×C4×C13C4×Q814yes—
231C2×C4×C13#12114yes—
232C2×C4×C13C22⋊Q814yes—
233C2×C4×C13#12514yes—
234C2×C4×C13C4⋊Q814yes—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—22no—
239C2×Dic13—24no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13C2×C4214yes—
262C2×Dic13C2×C4214yes—
263C2×Dic13C2×C4⋊C414yes—
264C2×Dic13C2×C4⋊C414yes—
265C2×Dic13#11714yes—
266C2×Dic13C4×D418yes—
267C2×Dic13C4×D418yes—
268C2×Dic13C4×Q818yes—
269C22×C4⋊C4—131no—
270C22×C4⋊C4—131no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—132no—
273C22×C4⋊C4—132no—
274C22×C42—131no—
275C22×C42—132no—
276C22×C42—131no—
277C22×C42—131no—
278C22×C42—132no—
279C22×C42—131no—
280C22×C42C2×D1311yescharacteristic
281C22×C42C2×D1311yescharacteristic
282C22×C42C2×D1311yescharacteristic
283#389—1316no—
284C4×C4⋊C4—138no—
285C4×C4⋊C4—264no—
286C4×C4⋊C4—264no—
287C4×C4⋊C4—264no—
288C2×#95—132no—
289C2×#95—131no—
290C2×#95—131no—
291C2×#95—132no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95C2×D1312yes—
296C2×#95C2×D1312yes—
297C43—264no—
298C22×C13C22×C4211yescharacteristic
299C22×C13C22×C4⋊C411yescharacteristic
300C22×C13C2×#11711yescharacteristic
301C22×C13C2×C4×D411yescharacteristic
302C22×C13C2×C4×D412yes—
303C22×C13C2×C4×D412yes—
304C22×C13C2×C4×Q812yes—
305C22×C13C2×C4×Q811yescharacteristic
306C22×C13C2×C4×Q812yes—
307C22×C13C4×#4112yes—
308C22×C13C4×#4111yescharacteristic
309C22×C13C4×#4111yescharacteristic
310C22×C13C4×#4112yes—
311C22×C13C2×#12111yescharacteristic
312C22×C13C2×C22⋊Q811yescharacteristic
313C22×C13#52512yes—
314C22×C13C2×#12511yescharacteristic
315C22×C13#52912yes—
316C22×C13#52912yes—
317C22×C13C2×C4⋊Q811yescharacteristic
318C22×C13#53212yes—
319C22×C13#53312yes—
320C22×C13#53312yes—
321C4×C13—24no—
322C4×C13—28no—
323C4×C13—42no—
324C4×C13—44no—
325C4×C13#38918yescomplemented
326Dic13—24no—
327Dic13—24no—
328Dic13—28no—
329Dic13—42no—
330Dic13—44no—
331Dic13C4×C4⋊C418yescomplemented
332C23×C4—131no—
333C23×C4—131no—
334C23×C4—132no—
335C23×C4—131no—
336C23×C4—132no—
337C23×C4—131no—
338C23×C4C22×D1312yes—
339C23×C4C22×D1311yescharacteristic
340C23×C4C22×D1312yes—
341C23×C4C22×D1311yescharacteristic
342C23×C4C22×D1311yescharacteristic
343C2×C4⋊C4—134no—
344C2×C4⋊C4—138no—
345C2×C4⋊C4—134no—
346C2×C4⋊C4—138no—
347C2×C4⋊C4—138no—
348C2×C4⋊C4—138no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—264no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—134no—
364C2×C42—134no—
365C2×C42—134no—
366C2×C42—134no—
367C2×C42—138no—
368C2×C42—134no—
369C2×C42—264no—
370C2×C42—264no—
371C2×C42—264no—
372C2×C42—264no—
373C2×C42—264no—
374C2×C42—262no—
375C2×C42—262no—
376C2×C42—262no—
377C2×C42—262no—
378C2×C42—262no—
379C2×C42—262no—
380C2×C42—262no—
381C2×C42Dic2614yes—
382C2×C42C4×D1314yes—
383#95—24no—
384#95—134no—
385#95—134no—
386#95—138no—
387#95—264no—
388#95—264no—
389#95—264no—
390#95—264no—
391#95C4×D1318yes—
392C2×C13C2×C4×C4⋊C411yescharacteristic
393C2×C13C42×D411yescharacteristic
394C2×C13C42×Q811yescharacteristic
395C2×C13C2×#38911yescharacteristic
396C2×C13#229311yescharacteristic
397C2×C13#229511yescharacteristic
398C2×C13#229611yescharacteristic
399C2×C13C4×#12112yes—
400C2×C13C4×C22⋊Q812yes—
401C2×C13C4×#12512yes—
402C2×C13C4×C4⋊Q812yes—
403C24C23×D1311yescharacteristic
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—132no—
422C22×C4—134no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—134no—
426C22×C4—132no—
427C22×C4—132no—
428C22×C4—134no—
429C22×C4—134no—
430C22×C4—132no—
431C22×C4—134no—
432C22×C4—132no—
433C22×C4—134no—
434C22×C4—132no—
435C22×C4—134no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4C2×Dic2614yes—
456C22×C4C2×Dic2612yes—
457C22×C4C2×C4×D1312yes—
458C22×C4C2×C4×D1314yes—
459C22×C4C2×C4×D1314yes—
460C22×C4C2×C4×D1312yes—
461C22×C4C2×C4×D1314yes—
462C22×C4C2×C4×D1312yes—
463C22×C4#612714yes—
464C22×C4#612712yes—
465C22×C4D4×D1312yes—
466C22×C4D4×D1312yes—
467C22×C4#612912yes—
468C22×C4Q8×D1312yes—
469C4⋊C4—1316no—
470C4⋊C4—268no—
471C4⋊C4—2616no—
472C4⋊C4—2616no—
473C4⋊C4—2616no—
474C42—28no—
475C42—28no—
476C42—44no—
477C42—1316no—
478C42—2616no—
479C42—2616no—
480C42—268no—
481C42—268no—
482C42—524no—
483C13C4×#38911yescharacteristic, complemented, Sylow
484C23C22×Dic2611yescharacteristic
485C23C22×C4×D1311yescharacteristic
486C23C22×C4×D1312yes—
487C23C2×#612711yescharacteristic
488C23C2×#612712yes—
489C23C2×D4×D1311yescharacteristic
490C23C2×D4×D1311yescharacteristic
491C23C2×#612911yescharacteristic
492C23C2×Q8×D1311yescharacteristic
493C23#41×D1312yes—
494C23#41×D1312yes—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—134no—
518C2×C4—134no—
519C2×C4—134no—
520C2×C4—138no—
521C2×C4—138no—
522C2×C4—134no—
523C2×C4—134no—
524C2×C4—138no—
525C2×C4—262no—
526C2×C4—264no—
527C2×C4—262no—
528C2×C4—264no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—264no—
535C2×C4—264no—
536C2×C4—264no—
537C2×C4—264no—
538C2×C4—264no—
539C2×C4—262no—
540C2×C4—264no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4C4×Dic2618yes—
552C2×C4C4×Dic2614yes—
553C2×C4C42×D1314yes—
554C2×C4#8813214yes—
555C2×C4#8813514yes—
556C2×C4#8813814yes—
557C2×C4#8814214yes—
558C2×C4#8814314yes—
559C2×C4C4⋊C4×D1314yes—
560C22C2×C4×Dic2611yescharacteristic
561C22C2×C4×Dic2612yes—
562C22C2×C42×D1311yescharacteristic
563C22C4×#612711yescharacteristic
564C22C4×#612712yes—
565C22C2×#8813211yescharacteristic
566C22C2×#8813511yescharacteristic
567C22C2×#8813811yescharacteristic
568C22C2×#8814211yescharacteristic
569C22C2×#8814311yescharacteristic
570C22C2×C4⋊C4×D1311yescharacteristic
571C22#1171922212yes—
572C22D13×#11711yescharacteristic
573C22#1171922711yescharacteristic
574C22#1171923312yes—
575C22C4×#612912yes—
576C22#1171924312yes—
577C22C4×D4×D1312yes—
578C22C4×D4×D1312yes—
579C22#1171925212yes—
580C22#1171925312yes—
581C22C4×Q8×D1312yes—
582C22#1171928312yes—
583C4—28no—
584C4—24no—
585C4—42no—
586C4—44no—
587C4—138no—
588C4—264no—
589C4—268no—
590C4—264no—
591C4—522no—
592C4—524no—
593C4#1171830818yesdirect product factor
594C2C4×C4⋊C4×D1311yescharacteristic
595C2C4×#8813511yescharacteristic
596C2C42×Dic2611yescharacteristic
597C2C2×#1171830811yescharacteristic
598C2#1311729911yescharacteristic
599C2#1311730811yescharacteristic
600C2#1311731611yescharacteristic
601C2C4×#8813812yes—
602C2C4×#8813212yes—
603C2C4×#8814312yes—
604C2C4×#8814212yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC4×C13×#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4×#95D13
hypocenterC13C4×#389
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
38. C4×#6101C4semidirect
40. #11718308C4direct (N × H)
175. #6101C42semidirect
181. C4×Dic13C4⋊C4semidirect
325. C4×C13#389semidirect
331. Dic13C4×C4⋊C4semidirect
483. C13C4×#389semidirect
593. C4#11718308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×C4×#61012
C2×C4×C4⋊Dic132
C2×C42×Dic132
#131130702
#131130672
#131130642
C4×#880712
C4×C13×#952
C4×#38913