Finite Group Databasebeta

← C2×#13130525 #16796788

Subgroups — C2×#13130525 #16796788

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D13⋊M16C211yesmaximal, characteristic
2C23×C4⋊#261C211yesmaximal, characteristic
3#13130525C218yesmaximal, direct product factor
4C2×#11718246C214yesmaximal, complemented
5C2×D13×#117C211yesmaximal, characteristic
6C24×#261—21no—
7C23×C4×D13C2211yescharacteristic
8C22×#6122—21no—
9C22×C4⋊#261—21no—
10C22×C4⋊#261—22no—
11C22×C4⋊#261—24no—
12C22×C4⋊#261C418yescomplemented
13C22×C4⋊#261C2212yes—
14C22×C4⋊#261C2214yes—
15C2×D13⋊M16—24no—
16C2×D13⋊M16—22no—
17C2×D13⋊M16C418yescomplemented
18C2×D13⋊M16C2214yes—
19C22×#6118—21no—
20C22×D13⋊C8C2212yes—
21C2×C13×#117C411yescharacteristic, complemented
22C2×#88180C411yescharacteristic, complemented
23D13×#117—22no—
24D13×#117—22no—
25D13×#117C414yescomplemented
26D13×#117C2214yes—
27C2×#88146C412yescomplemented
28C2×C4⋊C4×D13C2212yes—
29C2×C22⋊C4×D13—21no—
30C2×#88131—21no—
31C2×#88126—21no—
32C2×C42×D13—21no—
33#11718246C22116yescomplemented
34C24×D13D411yescharacteristic
35C23×#261—28no—
36C23×#261—22no—
37C23×#261—24no—
38C23×#261—48no—
39C23×C4×C13C2×C411yescharacteristic
40C23×Dic13D411yescharacteristic
41C22×C4×D13—22no—
42C22×C4×D13C2×C411yescharacteristic
43C22×C4×D13C2×C412yes—
44C22×C4×D13C2×C414yes—
45C22×C4×D13C2×C414yes—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D412yes—
48C22×C4×D13D411yescharacteristic
49C22×C4×D13D412yes—
50C22×C4×D13D414yes—
51C22×C4×D13Q814yes—
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2312yes—
54C2×#6122—28no—
55C2×#6122—24no—
56C22×#1057—22no—
57C2×C4⋊#261—216no—
58C2×C4⋊#261—28no—
59C2×C4⋊#261—22no—
60C2×C4⋊#261—24no—
61C2×C4⋊#261—24no—
62C2×C4⋊#261—28no—
63C2×C4⋊#261C2×C418yes—
64C2×C4⋊#261C2×C4116yescomplemented
65C2×C4⋊#261C2314yes—
66D13⋊M16—216no—
67D13⋊M16—28no—
68D13⋊M16C2×C4116yescomplemented
69C2×#6118—28no—
70C2×#6118—24no—
71C2×D13⋊C8—22no—
72C2×D13⋊C8—24no—
73C2×D13⋊C8C2×C418yescomplemented
74C2×D13⋊C8C2314yes—
75C13×#117—22no—
76C13×#117C2×C414yescomplemented
77C2×C13×C4⋊C4C2×C412yescomplemented
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C22⋊Dic13—21no—
81C2×#6103—22no—
82#88180—22no—
83#88180C2×C414yescomplemented
84C2×C4⋊Dic13C2×C412yescomplemented
85C2×#6101—22no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—22no—
88#88146—24no—
89#88146C2×C418yescomplemented
90C4⋊C4×D13—22no—
91C4⋊C4×D13—22no—
92C4⋊C4×D13C2×C414yescomplemented
93C4⋊C4×D13C2314yes—
94C22⋊C4×D13—24no—
95C22⋊C4×D13—24no—
96#88131—24no—
97#88131—24no—
98#88126—24no—
99#88126—24no—
100C42×D13—24no—
101C42×D13—24no—
102C2×#1736—131nomaximal, Sylow
103C24×C13C22⋊C411yescharacteristic
104C23×D13—24no—
105C23×D13—24no—
106C23×D13C22⋊C412yes—
107C23×D13C22⋊C411yescharacteristic
108C23×D13C22⋊C414yes—
109C23×D13C4⋊C414yes—
110C23×D13C2×D412yes—
111C23×D13C2×D411yescharacteristic
112C22×#261—28no—
113C22×#261—216no—
114C22×#261—24no—
115C22×#261—416no—
116C22×#261—432no—
117C22×#261—48no—
118C22×C4×C13—22no—
119C22×C4×C13C4214yes—
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22⋊C412yes—
122C22×C4×C13C4⋊C414yes—
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C412yes—
125C22×Dic13—22no—
126C22×Dic13C22⋊C412yes—
127C22×Dic13C22⋊C411yescharacteristic
128C22×Dic13C22⋊C414yes—
129C22×Dic13C4⋊C414yes—
130C22×Dic13C2×D412yes—
131C22×Dic13C2×D411yescharacteristic
132C2×C4×D13—24no—
133C2×C4×D13—24no—
134C2×C4×D13—44no—
135C2×C4×D13—44no—
136C2×C4×D13C4214yes—
137C2×C4×D13C4218yes—
138C2×C4×D13C22⋊C412yes—
139C2×C4×D13C22⋊C412yes—
140C2×C4×D13C22⋊C412yes—
141C2×C4×D13C22⋊C418yes—
142C2×C4×D13C22⋊C414yes—
143C2×C4×D13C22⋊C414yes—
144C2×C4×D13C22⋊C418yes—
145C2×C4×D13C4⋊C418yes—
146C2×C4×D13C4⋊C414yes—
147C2×C4×D13C4⋊C414yes—
148C2×C4×D13C4⋊C418yes—
149C2×C4×D13C4⋊C414yes—
150C2×C4×D13C4⋊C418yes—
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C22×C412yes—
153C2×C4×D13C22×C412yes—
154C2×C4×D13C22×C414yes—
155C2×C4×D13C22×C412yes—
156C2×C4×D13C22×C414yes—
157C2×C4×D13C2×D412yes—
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D412yes—
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D412yes—
162C2×C4×D13C2×D414yes—
163C2×C4×D13C2×Q814yes—
164C2×C4×D13C2×Q812yes—
165C2×C4×D13C2411yescharacteristic
166#6122—216no—
167C2×#1057—28no—
168C2×#1057—24no—
169C4⋊#261—28no—
170C4⋊#261—216no—
171C4⋊#261—24no—
172C4⋊#261C22×C418yes—
173#6118—216no—
174D13⋊C8—28no—
175D13⋊C8—24no—
176D13⋊C8C22×C418yescomplemented
177C13×C4⋊C4—22no—
178C13×C4⋊C4C22×C414yescomplemented
179C13×C22⋊C4—24no—
180C42×C13—24no—
181C22⋊Dic13—24no—
182#6103—28no—
183C4⋊Dic13—22no—
184C4⋊Dic13C22×C414yescomplemented
185#6101—24no—
186#6101—24no—
187C4×Dic13—24no—
188C4×Dic13—28no—
189C23×M16—131no—
190C22×#117—131no—
191C23×C4⋊C4—131no—
192#1736—138no—
193C2×#340—134no—
194C23×C13—24no—
195C23×C13#9514yes—
196C23×C13C2×C22⋊C412yes—
197C23×C13C2×C22⋊C411yescharacteristic
198C22×D13—24no—
199C22×D13—24no—
200C22×D13—24no—
201C22×D13—28no—
202C22×D13—28no—
203C22×D13—28no—
204C22×D13—216no—
205C22×D13#9514yes—
206C22×D13#9518yes—
207C22×D13C2×C22⋊C414yes—
208C22×D13C2×C22⋊C412yes—
209C22×D13C2×C22⋊C412yes—
210C22×D13C2×C22⋊C411yescharacteristic
211C22×D13C2×C4⋊C414yes—
212C22×D13C2×C4⋊C412yes—
213C22×D13AGL(1,ℤ/8)14yes—
214C22×D13#13714yes—
215C22×D13C22×D411yescharacteristic
216C2×#261—28no—
217C2×#261—432no—
218C2×#261—48no—
219C2×#261—416no—
220C2×C4×C13—24no—
221C2×C4×C13—44no—
222C2×C4×C13#9518yes—
223C2×C4×C13#9514yes—
224C2×C4×C13C2×C4214yes—
225C2×C4×C13C2×C4212yes—
226C2×C4×C13C2×C22⋊C412yes—
227C2×C4×C13C2×C22⋊C411yescharacteristic
228C2×C4×C13C2×C4⋊C414yes—
229C2×C4×C13C2×C4⋊C412yes—
230C2×C4×C13C23×C411yescharacteristic
231C2×Dic13—24no—
232C2×Dic13—44no—
233C2×Dic13#9518yes—
234C2×Dic13#9514yes—
235C2×Dic13C2×C22⋊C412yes—
236C2×Dic13C2×C22⋊C414yes—
237C2×Dic13C2×C22⋊C412yes—
238C2×Dic13C2×C22⋊C411yescharacteristic
239C2×Dic13C2×C4⋊C414yes—
240C2×Dic13C2×C4⋊C412yes—
241C2×Dic13C22×D411yescharacteristic
242C4×D13—44no—
243C4×D13—44no—
244C4×D13—48no—
245C4×D13#9518yes—
246C4×D13#9518yes—
247C4×D13#9518yes—
248C4×D13C2×C4214yes—
249C4×D13C2×C4212yes—
250C4×D13C2×C22⋊C412yes—
251C4×D13C2×C22⋊C414yes—
252C4×D13C2×C22⋊C412yes—
253C4×D13C2×C22⋊C414yes—
254C4×D13C2×C4⋊C414yes—
255C4×D13C2×C4⋊C412yes—
256C4×D13C2×C4⋊C414yes—
257C4×D13C2×C4⋊C412yes—
258C4×D13C2×C4⋊C412yes—
259C4×D13C2×C4⋊C414yes—
260C4×D13C23×C411yescharacteristic
261C4×D13C23×C411yescharacteristic
262C4×D13C22×D411yescharacteristic
263C4×D13C22×Q811yescharacteristic
264#1057—28no—
265C24×C4—131no—
266C24×C4—261no—
267C22×M16—138no—
268C22×M16—134no—
269C22×M16—261no—
270C22×M16—264no—
271C22×M16—262no—
272C22×M16—261no—
273C23×C8—132no—
274C2×#117—131no—
275C2×#117—134no—
276C2×#117—134no—
277C2×#117—132no—
278C2×#117—261no—
279C2×#117—261no—
280C2×#117—262no—
281C2×#117—262no—
282C2×#117#26111yescharacteristic, complemented
283C22×C4⋊C4—138no—
284C22×C4⋊C4—132no—
285C22×C4⋊C4—134no—
286C22×C4⋊C4—132no—
287C22×C4⋊C4—264no—
288C22×C4⋊C4—262no—
289C22×C4⋊C4—261no—
290C22×C22⋊C4—261no—
291C22×C42—261no—
292#340—1316no—
293C22×C13—24no—
294C22×C13—28no—
295C22×C13C2×#9514yes—
296C22×C13C2×#9512yes—
297C22×C13#41714yes—
298C22×C13C22×C22⋊C411yescharacteristic
299C2×D13—24no—
300C2×D13—28no—
301C2×D13—24no—
302C2×D13—24no—
303C2×D13—28no—
304C2×D13—216no—
305C2×D13C2×#9514yes—
306C2×D13C2×#9512yes—
307C2×D13#41714yes—
308C2×D13#41814yes—
309C2×D13#41914yes—
310C2×D13#42818yes—
311C2×D13C22×C22⋊C411yescharacteristic
312C2×D13C22×C4⋊C411yescharacteristic
313C2×D13C2×AGL(1,ℤ/8)12yes—
314C2×D13C2×#13712yes—
315#261—48no—
316C4×C13—44no—
317C4×C13C2×#9512yes—
318C4×C13C2×#9514yes—
319C4×C13C22×C4211yescharacteristic
320C4×C13C22×C4⋊C411yescharacteristic
321Dic13—44no—
322Dic13C2×#9512yes—
323Dic13C2×#9514yes—
324Dic13C22×C22⋊C411yescharacteristic
325Dic13C22×C4⋊C411yescharacteristic
326C25—131no—
327C23×C4—131no—
328C23×C4—134no—
329C23×C4—134no—
330C23×C4—134no—
331C23×C4—134no—
332C23×C4—132no—
333C23×C4—131no—
334C23×C4—132no—
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—132no—
338C23×C4—132no—
339C23×C4—131no—
340C23×C4—262no—
341C23×C4—262no—
342C23×C4—268no—
343C23×C4—264no—
344C23×C4—528no—
345C23×C4C2×#26111yescharacteristic
346C2×M16—1316no—
347C2×M16—268no—
348C2×M16—264no—
349C2×M16—2616no—
350C2×M16—268no—
351C2×M16—268no—
352C2×M16—264no—
353C22×C8—134no—
354C22×C8—138no—
355C22×C8—264no—
356C22×C8—262no—
357C22×C8—262no—
358#117—22no—
359#117—134no—
360#117—138no—
361#117—264no—
362#117—264no—
363#117—264no—
364#117—264no—
365#117—264no—
366#117—262no—
367#117C2×#26114yescomplemented
368C2×C4⋊C4—134no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—1316no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—134no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—2616no—
378C2×C4⋊C4—268no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—268no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4C2×#26112yescomplemented
384C2×C22⋊C4—21no—
385C2×C22⋊C4—264no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—262no—
388C2×C22⋊C4—261no—
389C2×C42—21no—
390C2×C42—264no—
391C2×C42—264no—
392C2×C42—262no—
393C2×C42—261no—
394C2×C13—24no—
395C2×C13#173614yescomplemented
396C2×C13C22×#9511yescharacteristic
397C2×C13C2×#41712yes—
398D13—24no—
399D13#173614yescomplemented
400D13C2×#41811yescharacteristic
401D13C2×#41911yescharacteristic
402D13C2×#42812yes—
403C24—131no—
404C24—134no—
405C24—134no—
406C24—132no—
407C24—132no—
408C24—131no—
409C24—264no—
410C24—264no—
411C24C22⋊#26111yescharacteristic
412C22×C4—22no—
413C22×C4—134no—
414C22×C4—134no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—131no—
418C22×C4—131no—
419C22×C4—134no—
420C22×C4—138no—
421C22×C4—134no—
422C22×C4—138no—
423C22×C4—134no—
424C22×C4—138no—
425C22×C4—138no—
426C22×C4—134no—
427C22×C4—132no—
428C22×C4—134no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—138no—
432C22×C4—134no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—138no—
436C22×C4—134no—
437C22×C4—132no—
438C22×C4—134no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—132no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—264no—
452C22×C4—268no—
453C22×C4—2616no—
454C22×C4—262no—
455C22×C4—524no—
456C22×C4—524no—
457C22×C4—528no—
458C22×C4—5232no—
459C22×C4—5216no—
460C22×C4C4×#26114yes—
461C22×C4C4⋊#26114yes—
462C22×C4C22⋊#26112yes—
463C22×C4C22⋊#26111yescharacteristic
464C22×C4C22×#26112yes—
465C22×C4C22×#26111yescharacteristic
466M16—2616no—
467M16—2616no—
468C2×C8—138no—
469C2×C8—264no—
470C2×C8—268no—
471C2×C8—264no—
472C2×C8—268no—
473C4⋊C4—22no—
474C4⋊C4—138no—
475C4⋊C4—134no—
476C4⋊C4—264no—
477C4⋊C4—264no—
478C4⋊C4—264no—
479C4⋊C4—268no—
480C4⋊C4—2616no—
481C4⋊C4—262no—
482C4⋊C4C22×#26114yescomplemented
483C22⋊C4—24no—
484C22⋊C4—268no—
485C22⋊C4—264no—
486C42—24no—
487C42—268no—
488C42—264no—
489C13C2×#173611yescharacteristic, complemented, Sylow
490C23—24no—
491C23—131no—
492C23—131no—
493C23—132no—
494C23—132no—
495C23—134no—
496C23—134no—
497C23—132no—
498C23—134no—
499C23—138no—
500C23—134no—
501C23—134no—
502C23—268no—
503C23—264no—
504C23—268no—
505C23—2616no—
506C23—264no—
507C23—268no—
508C23—264no—
509C23(C2×#261)⋊C414yes—
510C23C2×C22⋊#26112yes—
511C23C2×C22⋊#26111yescharacteristic
512C2×C4—24no—
513C2×C4—44no—
514C2×C4—132no—
515C2×C4—131no—
516C2×C4—131no—
517C2×C4—132no—
518C2×C4—134no—
519C2×C4—138no—
520C2×C4—134no—
521C2×C4—134no—
522C2×C4—132no—
523C2×C4—131no—
524C2×C4—131no—
525C2×C4—132no—
526C2×C4—134no—
527C2×C4—131no—
528C2×C4—132no—
529C2×C4—134no—
530C2×C4—131no—
531C2×C4—132no—
532C2×C4—134no—
533C2×C4—132no—
534C2×C4—134no—
535C2×C4—138no—
536C2×C4—138no—
537C2×C4—138no—
538C2×C4—132no—
539C2×C4—134no—
540C2×C4—132no—
541C2×C4—134no—
542C2×C4—268no—
543C2×C4—264no—
544C2×C4—524no—
545C2×C4—524no—
546C2×C4—528no—
547C2×C4—5216no—
548C2×C4—528no—
549C2×C4—5232no—
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⋊#26112yes—
558C2×C4C2×C22⋊#26111yescharacteristic
559C2×C4C23×#26111yescharacteristic
560C8—268no—
561C22—28no—
562C22—24no—
563C22—134no—
564C22—134no—
565C22—138no—
566C22—132no—
567C22—132no—
568C22—134no—
569C22—131no—
570C22—131no—
571C22—132no—
572C22—134no—
573C22—264no—
574C22—264no—
575C22—268no—
576C22—2616no—
577C22—268no—
578C22—264no—
579C22C2×(C2×#261)⋊C414yes—
580C22C2×(C2×#261)⋊C412yes—
581C22#1171916414yes—
582C22C22×C22⋊#26111yescharacteristic
583C4—44no—
584C4—131no—
585C4—131no—
586C4—134no—
587C4—132no—
588C4—528no—
589C4—524no—
590C4C2×(C2×#261)⋊C412yes—
591C4C2×(C2×#261)⋊C414yes—
592C4C22×C4×#26111yescharacteristic
593C4C22×C4⋊#26111yescharacteristic
594C2—24no—
595C2—131no—
596C2—131no—
597C2—132no—
598C2—134no—
599C2—264no—
600C2#1313052514yesdirect product factor
601C2C22×(C2×#261)⋊C411yescharacteristic
602C2C2×#1171916412yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13D4
cosocleC2×C4×D13C24
hypercenterC2×#117#261
hypocenterC13C2×#1736
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13130525C2direct (N × H)
4. C2×#11718246C2semidirect
12. C22×C4⋊#261C4semidirect
17. C2×D13⋊M16C4semidirect
21. C2×C13×#117C4semidirect
22. C2×#88180C4semidirect
25. D13×#117C4semidirect
27. C2×#88146C4semidirect
33. #11718246C22semidirect
64. C2×C4⋊#261C2×C4semidirect
68. D13⋊M16C2×C4semidirect
73. C2×D13⋊C8C2×C4semidirect
76. C13×#117C2×C4semidirect
77. C2×C13×C4⋊C4C2×C4semidirect
83. #88180C2×C4semidirect
84. C2×C4⋊Dic13C2×C4semidirect
89. #88146C2×C4semidirect
92. C4⋊C4×D13C2×C4semidirect
176. D13⋊C8C22×C4semidirect
178. C13×C4⋊C4C22×C4semidirect
184. C4⋊Dic13C22×C4semidirect
282. C2×#117#261semidirect
367. #117C2×#261semidirect
383. C2×C4⋊C4C2×#261semidirect
395. C2×C13#1736semidirect
399. D13#1736semidirect
482. C4⋊C4C22×#261semidirect
489. C13C2×#1736semidirect
600. C2#13130525direct (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
C23×C4⋊#2612
#131305252
C2×#117182462
C2×D13×#1172
C2×#173613