Finite Group Databasebeta

← C2×#13130515 #16796774

Subgroups — C2×#13130515 #16796774

Order 3328.

2270 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
1C22×D13⋊M16C211yesmaximal, characteristic
2C22×#88237C211yesmaximal, characteristic
3#13130515C218yesmaximal, direct product factor
4C2×#11718247C214yesmaximal, complemented
5C22×#88146C211yesmaximal, characteristic
6C23×C4×D13C2211yescharacteristic
7C22×C22⋊#261—21no—
8C22×#6122—21no—
9C2×#88237—24no—
10C2×#88237—22no—
11C2×#88237C418yescomplemented
12C2×#88237C2214yes—
13C22×C4⋊#261—21no—
14C22×C4×#261C2212yes—
15C2×D13⋊M16—24no—
16C2×D13⋊M16—22no—
17C2×D13⋊M16C418yescomplemented
18C2×D13⋊M16C2214yes—
19C22×#6118C2212yes—
20C22×D13⋊C8—21no—
21C22×C13×C4⋊C4C411yescharacteristic, complemented
22C22×#6103—21no—
23C22×C4⋊Dic13C411yescharacteristic, complemented
24C22×C4×Dic13—21no—
25C2×#88146—21no—
26C2×#88146—22no—
27C2×#88146—21no—
28C2×#88146—22no—
29C2×#88146C414yescomplemented
30C2×#88146C412yescomplemented
31C2×#88146C2212yes—
32C2×#88146C2214yes—
33#11718247C22116yescomplemented
34C24×D13D411yescharacteristic
35C23×#261—22no—
36C23×C4×C13—21no—
37C23×C4×C13C2×C411yescharacteristic
38C23×Dic13—21no—
39C23×Dic13D411yescharacteristic
40C22×C4×D13C2×C412yes—
41C22×C4×D13C2×C411yescharacteristic
42C22×C4×D13C2×C414yes—
43C22×C4×D13C2×C414yes—
44C22×C4×D13D411yescharacteristic
45C22×C4×D13D412yes—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D412yes—
48C22×C4×D13D414yes—
49C22×C4×D13Q814yes—
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2312yes—
52C2×C22⋊#261—28no—
53C2×C22⋊#261—24no—
54C2×#6122—28no—
55C2×#6122—24no—
56C22×#1057—22no—
57#88237—216no—
58#88237—28no—
59#88237C2×C4116yescomplemented
60C2×C4⋊#261—28no—
61C2×C4⋊#261—24no—
62C2×C4×#261—22no—
63C2×C4×#261—24no—
64C2×C4×#261C2×C418yescomplemented
65C2×C4×#261C2314yes—
66D13⋊M16—216no—
67D13⋊M16—28no—
68D13⋊M16C2×C4116yescomplemented
69C2×#6118—22no—
70C2×#6118—24no—
71C2×#6118C2×C418yescomplemented
72C2×#6118C2314yes—
73C2×D13⋊C8—28no—
74C2×D13⋊C8—24no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2×C412yes—
78C2×C13×C4⋊C4C2×C414yescomplemented
79C2×#6103—24no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—24no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2×C412yes—
86C2×C4⋊Dic13C2×C414yescomplemented
87C2×C4×Dic13—24no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—24no—
91#88146—24no—
92#88146—24no—
93#88146—24no—
94#88146—22no—
95#88146—24no—
96#88146—22no—
97#88146—24no—
98#88146C2×C414yes—
99#88146C2×C418yescomplemented
100#88146C2314yes—
101C2×#1733—131nomaximal, Sylow
102C24×C13C22⋊C411yescharacteristic
103C23×D13—42no—
104C23×D13—42no—
105C23×D13C22⋊C411yescharacteristic
106C23×D13C22⋊C412yes—
107C23×D13C22⋊C414yes—
108C23×D13C4⋊C414yes—
109C23×D13C2×D411yescharacteristic
110C23×D13C2×D412yes—
111C22×#261—28no—
112C22×#261—24no—
113C22×#261—44no—
114C22×#261—44no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—44no—
118C22×C4×C13C4214yes—
119C22×C4×C13C22⋊C412yes—
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C4⋊C414yes—
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C412yes—
124C22×Dic13—22no—
125C22×Dic13—24no—
126C22×Dic13—44no—
127C22×Dic13C22⋊C412yes—
128C22×Dic13C22⋊C411yescharacteristic
129C22×Dic13C22⋊C414yes—
130C22×Dic13C4⋊C414yes—
131C22×Dic13C2×D411yescharacteristic
132C22×Dic13C2×D412yes—
133C2×C4×D13C4214yes—
134C2×C4×D13C4218yes—
135C2×C4×D13C22⋊C412yes—
136C2×C4×D13C22⋊C412yes—
137C2×C4×D13C22⋊C412yes—
138C2×C4×D13C22⋊C414yes—
139C2×C4×D13C22⋊C418yes—
140C2×C4×D13C22⋊C414yes—
141C2×C4×D13C22⋊C418yes—
142C2×C4×D13C4⋊C414yes—
143C2×C4×D13C4⋊C418yes—
144C2×C4×D13C4⋊C414yes—
145C2×C4×D13C4⋊C418yes—
146C2×C4×D13C4⋊C414yes—
147C2×C4×D13C4⋊C418yes—
148C2×C4×D13C22×C411yescharacteristic
149C2×C4×D13C22×C412yes—
150C2×C4×D13C22×C412yes—
151C2×C4×D13C22×C414yes—
152C2×C4×D13C22×C412yes—
153C2×C4×D13C22×C414yes—
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13C2×D412yes—
156C2×C4×D13C2×D412yes—
157C2×C4×D13C2×D411yescharacteristic
158C2×C4×D13C2×D412yes—
159C2×C4×D13C2×D414yes—
160C2×C4×D13C2×Q812yes—
161C2×C4×D13C2×Q814yes—
162C2×C4×D13C2411yescharacteristic
163C22⋊#261—216no—
164#6122—216no—
165C2×#1057—28no—
166C2×#1057—24no—
167C4⋊#261—216no—
168C4×#261—28no—
169C4×#261—24no—
170C4×#261C22×C418yescomplemented
171#6118—28no—
172#6118—24no—
173#6118C22×C418yescomplemented
174D13⋊C8—216no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—24no—
177C13×C4⋊C4C22×C414yes—
178#6103—24no—
179#6103—28no—
180#6103—24no—
181C4⋊Dic13—22no—
182C4⋊Dic13—24no—
183C4⋊Dic13C22×C414yes—
184C4×Dic13—24no—
185C4×Dic13—28no—
186C4×Dic13—24no—
187C23×M16—131no—
188C22×#117—131no—
189C22×#117—131no—
190#1733—138no—
191C2×#339—134no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13#9514yes—
195C23×C13C2×C22⋊C412yes—
196C23×C13C2×C22⋊C411yescharacteristic
197C22×D13—22no—
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—22no—
201C22×D13—42no—
202C22×D13—42no—
203C22×D13—48no—
204C22×D13—48no—
205C22×D13—42no—
206C22×D13—42no—
207C22×D13#9514yes—
208C22×D13#9518yes—
209C22×D13C2×C22⋊C412yes—
210C22×D13C2×C22⋊C411yescharacteristic
211C22×D13C2×C22⋊C412yes—
212C22×D13C2×C22⋊C414yes—
213C22×D13C2×C4⋊C412yes—
214C22×D13C2×C4⋊C414yes—
215C22×D13C22×D411yescharacteristic
216C2×#261—28no—
217C2×#261—44no—
218C2×#261—44no—
219C2×#261—416no—
220C2×C4×C13—24no—
221C2×C4×C13—48no—
222C2×C4×C13—44no—
223C2×C4×C13#9518yes—
224C2×C4×C13#9514yes—
225C2×C4×C13C2×C4214yes—
226C2×C4×C13C2×C4212yes—
227C2×C4×C13C2×C22⋊C411yescharacteristic
228C2×C4×C13C2×C22⋊C412yes—
229C2×C4×C13C2×C4⋊C414yes—
230C2×C4×C13C2×C4⋊C412yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×Dic13—24no—
233C2×Dic13—48no—
234C2×Dic13—44no—
235C2×Dic13#9518yes—
236C2×Dic13#9514yes—
237C2×Dic13C2×C22⋊C412yes—
238C2×Dic13C2×C22⋊C414yes—
239C2×Dic13C2×C22⋊C411yescharacteristic
240C2×Dic13C2×C22⋊C412yes—
241C2×Dic13C2×C4⋊C414yes—
242C2×Dic13C2×C4⋊C412yes—
243C2×Dic13C22×D411yescharacteristic
244C4×D13#9518yes—
245C4×D13#9518yes—
246C4×D13#9518yes—
247C4×D13C2×C4212yes—
248C4×D13C2×C4214yes—
249C4×D13C2×C22⋊C414yes—
250C4×D13C2×C22⋊C412yes—
251C4×D13C2×C22⋊C412yes—
252C4×D13C2×C22⋊C414yes—
253C4×D13C2×C4⋊C412yes—
254C4×D13C2×C4⋊C414yes—
255C4×D13C2×C4⋊C412yes—
256C4×D13C2×C4⋊C414yes—
257C4×D13C2×C4⋊C412yes—
258C4×D13C2×C4⋊C414yes—
259C4×D13C23×C411yescharacteristic
260C4×D13C23×C411yescharacteristic
261C4×D13C22×D411yescharacteristic
262C4×D13C22×Q811yescharacteristic
263#1057—28no—
264C24×C4—131no—
265C22×M16—132no—
266C22×M16—138no—
267C22×M16—134no—
268C22×M16—264no—
269C22×M16—262no—
270C22×M16—261no—
271C23×C8—261no—
272C2×#117—138no—
273C2×#117—134no—
274C2×#117—132no—
275C2×#117—132no—
276C2×#117—134no—
277C2×#117—134no—
278C2×#117—261no—
279C2×#117—262no—
280C2×#117—261no—
281C2×#117—262no—
282C2×#117—264no—
283C2×#117—262no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—261no—
286C22×C4⋊C4#26111yescharacteristic, complemented
287C22×C22⋊C4—261no—
288C22×C22⋊C4—261no—
289C22×C42—132no—
290C22×C42—261no—
291#339—1316no—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—28no—
295C22×C13C2×#9514yes—
296C22×C13C2×#9512yes—
297C22×C13#42112yes—
298C22×C13#42112yes—
299C22×C13C22×C22⋊C411yescharacteristic
300C2×D13—21no—
301C2×D13—21no—
302C2×D13—21no—
303C2×D13—22no—
304C2×D13—21no—
305C2×D13—22no—
306C2×D13—24no—
307C2×D13—28no—
308C2×D13—24no—
309C2×D13—48no—
310C2×D13—44no—
311C2×D13—44no—
312C2×D13C2×#9514yes—
313C2×D13C2×#9512yes—
314C2×D13C22×C22⋊C411yescharacteristic
315C2×D13C22×C4⋊C411yescharacteristic
316#261—48no—
317C4×C13—44no—
318C4×C13C2×#9514yes—
319C4×C13C2×#9512yes—
320C4×C13C22×C4211yescharacteristic
321C4×C13C22×C4⋊C411yescharacteristic
322Dic13—44no—
323Dic13C2×#9512yes—
324Dic13C2×#9514yes—
325Dic13C22×C22⋊C411yescharacteristic
326Dic13C22×C4⋊C411yescharacteristic
327C25—131no—
328C23×C4—21no—
329C23×C4—131no—
330C23×C4—134no—
331C23×C4—134no—
332C23×C4—134no—
333C23×C4—134no—
334C23×C4—131no—
335C23×C4—132no—
336C23×C4—131no—
337C23×C4—132no—
338C23×C4—132no—
339C23×C4—131no—
340C23×C4—132no—
341C23×C4—131no—
342C23×C4—262no—
343C23×C4—261no—
344C23×C4C2×#26111yescharacteristic
345C2×M16—134no—
346C2×M16—138no—
347C2×M16—1316no—
348C2×M16—264no—
349C2×M16—262no—
350C2×M16—2616no—
351C2×M16—268no—
352C2×M16—268no—
353C2×M16—264no—
354C22×C8—268no—
355C22×C8—264no—
356C22×C8—262no—
357#117—1316no—
358#117—134no—
359#117—138no—
360#117—134no—
361#117—262no—
362#117—262no—
363#117—264no—
364#117—264no—
365#117—264no—
366#117—264no—
367#117—264no—
368#117—2616no—
369#117—268no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—132no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—268no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C2×#26112yes—
379C2×C4⋊C4C2×#26114yescomplemented
380C2×C22⋊C4—264no—
381C2×C22⋊C4—264no—
382C2×C22⋊C4—262no—
383C2×C22⋊C4—262no—
384C2×C22⋊C4—268no—
385C2×C22⋊C4—264no—
386C2×C42—134no—
387C2×C42—138no—
388C2×C42—264no—
389C2×C42—264no—
390C2×C42—262no—
391C2×C42—262no—
392C2×C42—264no—
393C2×C42—262no—
394C2×C13—24no—
395C2×C13#173314yescomplemented
396C2×C13C22×#9511yescharacteristic
397C2×C13C2×#42111yescharacteristic
398C2×C13C2×#42111yescharacteristic
399D13—21no—
400D13—21no—
401D13—22no—
402D13—24no—
403C24—131no—
404C24—131no—
405C24—134no—
406C24—134no—
407C24—132no—
408C24—132no—
409C24—522no—
410C24—522no—
411C24C22⋊#26111yescharacteristic
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—44no—
415C22×C4—134no—
416C22×C4—134no—
417C22×C4—132no—
418C22×C4—132no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—134no—
422C22×C4—138no—
423C22×C4—134no—
424C22×C4—138no—
425C22×C4—134no—
426C22×C4—138no—
427C22×C4—134no—
428C22×C4—138no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—132no—
432C22×C4—134no—
433C22×C4—134no—
434C22×C4—138no—
435C22×C4—132no—
436C22×C4—134no—
437C22×C4—134no—
438C22×C4—138no—
439C22×C4—132no—
440C22×C4—134no—
441C22×C4—131no—
442C22×C4—132no—
443C22×C4—132no—
444C22×C4—131no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—132no—
451C22×C4—264no—
452C22×C4—268no—
453C22×C4—264no—
454C22×C4—262no—
455C22×C4—524no—
456C22×C4—524no—
457C22×C4—524no—
458C22×C4C4×#26114yes—
459C22×C4C4⋊#26114yes—
460C22×C4C22⋊#26112yes—
461C22×C4C22⋊#26111yescharacteristic
462C22×C4C22×#26112yes—
463C22×C4C22×#26111yescharacteristic
464M16—138no—
465M16—264no—
466M16—268no—
467M16—2616no—
468C2×C8—2616no—
469C2×C8—264no—
470C2×C8—268no—
471C4⋊C4—22no—
472C4⋊C4—24no—
473C4⋊C4—134no—
474C4⋊C4—2616no—
475C4⋊C4—262no—
476C4⋊C4—264no—
477C4⋊C4C22×#26114yes—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—268no—
481C22⋊C4—2616no—
482C42—138no—
483C42—264no—
484C42—264no—
485C42—268no—
486C42—264no—
487C42—268no—
488C13C2×#173311yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—131no—
492C23—132no—
493C23—131no—
494C23—132no—
495C23—134no—
496C23—132no—
497C23—134no—
498C23—138no—
499C23—134no—
500C23—262no—
501C23—262no—
502C23—262no—
503C23—262no—
504C23—528no—
505C23—528no—
506C23—522no—
507C23—522no—
508C23—522no—
509C23—522no—
510C23(C2×#261)⋊C414yes—
511C23C2×C22⋊#26112yes—
512C23C2×C22⋊#26111yescharacteristic
513C2×C4—24no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4—131no—
517C2×C4—132no—
518C2×C4—131no—
519C2×C4—132no—
520C2×C4—134no—
521C2×C4—138no—
522C2×C4—134no—
523C2×C4—134no—
524C2×C4—132no—
525C2×C4—131no—
526C2×C4—131no—
527C2×C4—132no—
528C2×C4—134no—
529C2×C4—131no—
530C2×C4—132no—
531C2×C4—134no—
532C2×C4—131no—
533C2×C4—132no—
534C2×C4—134no—
535C2×C4—134no—
536C2×C4—132no—
537C2×C4—138no—
538C2×C4—138no—
539C2×C4—138no—
540C2×C4—132no—
541C2×C4—134no—
542C2×C4—132no—
543C2×C4—134no—
544C2×C4—268no—
545C2×C4—264no—
546C2×C4—528no—
547C2×C4—5216no—
548C2×C4—524no—
549C2×C4—524no—
550C2×C4—524no—
551C2×C4(C2×#261)⋊C418yes—
552C2×C4(C2×#261)⋊C414yes—
553C2×C4C2×C4×#26114yes—
554C2×C4C2×C4×#26112yes—
555C2×C4C2×C4⋊#26114yes—
556C2×C4C2×C4⋊#26112yes—
557C2×C4C2×C22⋊#26111yescharacteristic
558C2×C4C2×C22⋊#26112yes—
559C2×C4C23×#26111yescharacteristic
560C8—268no—
561C22—28no—
562C22—22no—
563C22—22no—
564C22—131no—
565C22—131no—
566C22—134no—
567C22—132no—
568C22—264no—
569C22—268no—
570C22—264no—
571C22—261no—
572C22—261no—
573C22—262no—
574C22—261no—
575C22—261no—
576C22—262no—
577C22—524no—
578C22—528no—
579C22—524no—
580C22C2×(C2×#261)⋊C414yes—
581C22C2×(C2×#261)⋊C412yes—
582C22#1171914012yes—
583C22#1171915512yes—
584C22C22×C22⋊#26111yescharacteristic
585C4—44no—
586C4—131no—
587C4—131no—
588C4—132no—
589C4—134no—
590C4—528no—
591C4—524no—
592C4C2×(C2×#261)⋊C412yes—
593C4C2×(C2×#261)⋊C414yes—
594C4C22×C4×#26111yescharacteristic
595C4C22×C4⋊#26111yescharacteristic
596C2—24no—
597C2—261no—
598C2—261no—
599C2—262no—
600C2—264no—
601C2#1313051514yesdirect product factor
602C2C22×(C2×#261)⋊C411yescharacteristic
603C2C2×#1171914011yescharacteristic
604C2C2×#1171915511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13D4
cosocleC2×C4×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1733
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13130515C2direct (N × H)
4. C2×#11718247C2semidirect
11. C2×#88237C4semidirect
17. C2×D13⋊M16C4semidirect
21. C22×C13×C4⋊C4C4semidirect
23. C22×C4⋊Dic13C4semidirect
29. C2×#88146C4semidirect
30. C2×#88146C4semidirect
33. #11718247C22semidirect
59. #88237C2×C4semidirect
64. C2×C4×#261C2×C4semidirect
68. D13⋊M16C2×C4semidirect
71. C2×#6118C2×C4semidirect
78. C2×C13×C4⋊C4C2×C4semidirect
86. C2×C4⋊Dic13C2×C4semidirect
99. #88146C2×C4semidirect
170. C4×#261C22×C4semidirect
173. #6118C22×C4semidirect
286. C22×C4⋊C4#261semidirect
379. C2×C4⋊C4C2×#261semidirect
395. C2×C13#1733semidirect
488. C13C2×#1733semidirect
601. C2#13130515direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D13⋊M162
C22×#882372
#131305152
C2×#117182472
C22×#881462
C2×#173313