Finite Group Databasebeta

← C2×#13131344 #16807567

Subgroups — C2×#13131344 #16807567

Order 3328.

3526 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×#88237C212yesmaximal
2#13131344C2116yesmaximal, direct product factor
3C2×#11719083C212yesmaximal, complemented
4C2×#11719082C214yesmaximal, complemented
5C2×#11719135C212yesmaximal
6C2×#11719136C211yesmaximal, characteristic
7C2×C4⋊C4×#261C212yesmaximal, complemented
8C2×C4×C22⋊#261C211yesmaximal, characteristic
9C22×C4⋊C4×D13C211yesmaximal, characteristic
10C23×C4×D13C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C22⋊#261C2211yescharacteristic
13C22×C22⋊#261C2212yes—
14C22×C22⋊#261C2211yescharacteristic
15C2×#88237—216no—
16C2×#88237C22116yes—
17C22×C4⋊#261C2212yes—
18C22×C4⋊#261C2214yes—
19C22×C4×#261C2212yes—
20C22×C4×#261C2214yes—
21C22×C13×C4⋊C4C411yescharacteristic, complemented
22C22×C4⋊Dic13C411yescharacteristic, complemented
23C22×#6101C412yescomplemented
24C2×C4⋊C4×D13C418yescomplemented
25C2×C4⋊C4×D13C411yescharacteristic, complemented
26C2×C4⋊C4×D13C411yescharacteristic, complemented
27C2×C4⋊C4×D13C412yescomplemented
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×C4⋊C4×D13C2212yes—
30C2×C4⋊C4×D13C2211yescharacteristic
31C2×C4⋊C4×D13C2218yes—
32#11719136C2218yes—
33#11719135C22116yes—
34C4×C22⋊#261C2218yes—
35C2×(C2×#261)⋊C4C2212yes—
36C2×(C2×#261)⋊C4C2214yes—
37C2×(C2×#261)⋊C4C2212yes—
38C2×(C2×#261)⋊C4C2214yes—
39#11719083C22116yescomplemented
40#11719082C22132yescomplemented
41C4⋊C4×#261C22116yescomplemented
42C24×D13C2311yescharacteristic
43C23×#261C2314yes—
44C23×#261C2312yes—
45C23×#261C2312yes—
46C23×C4×C13C2×C412yes—
47C23×C4×C13C2×C411yescharacteristic
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2×C412yes—
50C22×C4×D13—28no—
51C22×C4×D13—28no—
52C22×C4×D13—28no—
53C22×C4×D13C2×C418yes—
54C22×C4×D13C2×C412yes—
55C22×C4×D13C2×C412yes—
56C22×C4×D13C2×C411yescharacteristic
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13C2×C414yes—
59C22×C4×D13C2312yes—
60C22×C4×D13C2312yes—
61C22×C4×D13C2318yes—
62C22×C4×D13C2311yescharacteristic
63C22×C4×D13C2314yes—
64C22×C4×D13C2311yescharacteristic
65C2×C22⋊#261—28no—
66C2×C22⋊#261—24no—
67C2×C22⋊#261D418yes—
68C2×C22⋊#261C2318yes—
69C2×C22⋊#261C2314yes—
70C2×C22⋊#261C2314yes—
71#88237—264no—
72C2×C4⋊#261—216no—
73C2×C4⋊#261—28no—
74C2×C4⋊#261C2318yes—
75C2×C4⋊#261C23116yes—
76C2×C4×#261—216no—
77C2×C4×#261—28no—
78C2×C4×#261C23116yes—
79C2×C4×#261C2318yes—
80C2×C13×C4⋊C4C2×C412yes—
81C2×C13×C4⋊C4C2×C411yescharacteristic
82C2×C13×C4⋊C4C2×C411yescharacteristic
83C2×C13×C4⋊C4C2×C418yescomplemented
84C2×C4⋊Dic13C2×C412yes—
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×C4⋊Dic13C2×C411yescharacteristic
87C2×C4⋊Dic13C2×C418yescomplemented
88C2×#6101C2×C412yes—
89C2×#6101C2×C412yes—
90C2×#6101C2×C412yes—
91C2×#6101C2×C412yes—
92C2×#6101C2×C4116yescomplemented
93C4⋊C4×D13C2×C418yes—
94C4⋊C4×D13C2×C414yes—
95C4⋊C4×D13C2×C414yes—
96C4⋊C4×D13C2×C418yescomplemented
97C4⋊C4×D13C2×C418yescomplemented
98C4⋊C4×D13C2×C4116yescomplemented
99C4⋊C4×D13C2314yes—
100C4⋊C4×D13C2318yes—
101C4⋊C4×D13C2314yes—
102(C2×#261)⋊C4C23116yes—
103(C2×#261)⋊C4C2318yes—
104(C2×#261)⋊C4C2318yes—
105(C2×#261)⋊C4C23116yes—
106C2×#2344—131nomaximal, Sylow
107C24×C13C22×C411yescharacteristic
108C23×D13—24no—
109C23×D13—24no—
110C23×D13C22×C412yes—
111C23×D13C22×C411yescharacteristic
112C23×D13C2×D414yes—
113C23×D13#4114yes—
114C23×D13C2412yes—
115C23×D13C2411yescharacteristic
116C22×#261—24no—
117C22×#261—24no—
118C22×#261—28no—
119C22×#261—24no—
120C22×#261—28no—
121C22×#261—24no—
122C22×#261—28no—
123C22×#261—24no—
124C22×#261C2×D418yes—
125C22×#261C2414yes—
126C22×#261C2418yes—
127C22×#261C2414yes—
128C22×C4×C13—28no—
129C22×C4×C13—24no—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C418yes—
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C411yescharacteristic
136C22×Dic13—28no—
137C22×Dic13—24no—
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C412yes—
140C22×Dic13C22×C412yes—
141C22×Dic13C22×C414yes—
142C22×Dic13C22×C418yes—
143C22×Dic13C22×C411yescharacteristic
144C2×C4×D13—28no—
145C2×C4×D13—28no—
146C2×C4×D13—232no—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—216no—
150C2×C4×D13—24no—
151C2×C4×D13—216no—
152C2×C4×D13—24no—
153C2×C4×D13—24no—
154C2×C4×D13—24no—
155C2×C4×D13—24no—
156C2×C4×D13—216no—
157C2×C4×D13—216no—
158C2×C4×D13C22×C412yes—
159C2×C4×D13C22×C414yes—
160C2×C4×D13C22×C414yes—
161C2×C4×D13C22×C418yes—
162C2×C4×D13C22×C418yes—
163C2×C4×D13C22×C414yes—
164C2×C4×D13C22×C414yes—
165C2×C4×D13C22×C412yes—
166C2×C4×D13#4118yes—
167C2×C4×D13C2412yes—
168C2×C4×D13C2414yes—
169C2×C4×D13C2414yes—
170C2×C4×D13C2412yes—
171C22⋊#261—216no—
172C22⋊#261—28no—
173C22⋊#261C2×D4116yes—
174C4⋊#261—232no—
175C4⋊#261—216no—
176C4×#261—232no—
177C4×#261—216no—
178C13×C4⋊C4C22×C418yes—
179C13×C4⋊C4C22×C414yes—
180C13×C4⋊C4C22×C414yes—
181C4⋊Dic13C22×C418yes—
182C4⋊Dic13C22×C414yes—
183C4⋊Dic13C22×C414yes—
184#6101C22×C418yes—
185#6101C22×C418yes—
186#6101C22×C418yes—
187#6101C22×C418yes—
188C22×#117—132no—
189C23×C4⋊C4—131no—
190#2344—1316no—
191C2×#389—132no—
192C2×#387—134no—
193C2×#381—132no—
194C2×#380—131no—
195C2×C4×C4⋊C4—132no—
196C2×C4×C22⋊C4—131no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13C4×D414yes—
200C23×C13C23×C412yes—
201C23×C13C23×C411yescharacteristic
202C22×D13—22no—
203C22×D13—22no—
204C22×D13—24no—
205C22×D13—24no—
206C22×D13—216no—
207C22×D13—216no—
208C22×D13—24no—
209C22×D13—24no—
210C22×D13C4×D414yes—
211C22×D13C4×D418yes—
212C22×D13C23×C412yes—
213C22×D13C23×C411yescharacteristic
214C22×D13C22×D414yes—
215C22×D13C22×D412yes—
216C22×D13C2×#4114yes—
217C22×D13C2×#4114yes—
218C22×D13C2×#4112yes—
219C22×D132−1+414yes—
220C22×D13C2511yescharacteristic
221C2×#261—216no—
222C2×#261—24no—
223C2×#261—24no—
224C2×#261—28no—
225C2×#261—24no—
226C2×#261—28no—
227C2×#261—24no—
228C2×#261—28no—
229C2×#261—24no—
230C2×#261—416no—
231C2×#261—48no—
232C2×#261C22×D418yes—
233C2×C4×C13—22no—
234C2×C4×C13—216no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—28no—
238C2×C4×C13#11714yescomplemented
239C2×C4×C13C23×C414yes—
240C2×C4×C13C23×C414yes—
241C2×C4×C13C23×C412yes—
242C2×C4×C13C23×C412yes—
243C2×Dic13—22no—
244C2×Dic13—216no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—28no—
248C2×Dic13#11714yescomplemented
249C2×Dic13C23×C412yes—
250C2×Dic13C23×C414yes—
251C2×Dic13C23×C414yes—
252C2×Dic13C23×C412yes—
253C4×D13—24no—
254C4×D13—216no—
255C4×D13—216no—
256C4×D13—28no—
257C4×D13—28no—
258C4×D13—24no—
259C4×D13—24no—
260C4×D13—24no—
261C4×D13—24no—
262C4×D13—24no—
263C4×D13—28no—
264C4×D13—28no—
265C4×D13#11718yescomplemented
266C4×D13C2×#4118yes—
267C24×C4—132no—
268C24×C4—131no—
269C2×#117—1316no—
270C2×#117—2616no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—132no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4—138no—
280C22×C4⋊C4—138no—
281C22×C4⋊C4—134no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4#26111yescharacteristic, complemented
284C22×C22⋊C4—131no—
285C22×C22⋊C4—132no—
286C22×C22⋊C4—131no—
287C22×C42—134no—
288C22×C42—132no—
289#389—1316no—
290#387—1332no—
291#381—1316no—
292#380—138no—
293C4×C4⋊C4—1316no—
294C4×C22⋊C4—138no—
295C2×#95—132no—
296C2×#95—134no—
297C2×#95—132no—
298C2×#95—134no—
299C22×C13—28no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13C2×#11712yes—
303C22×C13C2×C4×D414yes—
304C22×C13C2×C4×D412yes—
305C22×C13#51912yes—
306C22×C13C24×C411yescharacteristic
307C2×D13—28no—
308C2×D13—22no—
309C2×D13—22no—
310C2×D13—216no—
311C2×D13—28no—
312C2×D13—28no—
313C2×D13C2×#11712yes—
314C2×D13C2×C4×D414yes—
315C2×D13C2×C4×D412yes—
316C2×D13#51912yes—
317C2×D13#54718yes—
318C2×D13#55218yes—
319C2×D13C23×D411yescharacteristic
320C2×D13C22×#4112yes—
321C2×D13C22×#4111yescharacteristic
322C2×D13C2×2−1+412yes—
323#261—28no—
324#261—48no—
325#261—44no—
326C4×C13—22no—
327C4×C13—24no—
328C4×C13—24no—
329C4×C13C2×#11714yescomplemented
330Dic13—22no—
331Dic13—24no—
332Dic13—24no—
333Dic13C2×#11714yescomplemented
334C25—131no—
335C23×C4—131no—
336C23×C4—132no—
337C23×C4—131no—
338C23×C4—132no—
339C23×C4—132no—
340C23×C4—138no—
341C23×C4—131no—
342C23×C4—132no—
343C23×C4—134no—
344C23×C4—131no—
345C23×C4—134no—
346C23×C4—138no—
347C23×C4—132no—
348C23×C4—132no—
349C23×C4—131no—
350C23×C4—134no—
351C23×C4—132no—
352C23×C4—268no—
353C23×C4—268no—
354C23×C4—268no—
355C23×C4C2×#26112yes—
356C23×C4C2×#26111yescharacteristic
357#117—2664no—
358C2×C4⋊C4—132no—
359C2×C4⋊C4—132no—
360C2×C4⋊C4—132no—
361C2×C4⋊C4—132no—
362C2×C4⋊C4—1316no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—138no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—1316no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—138no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—1316no—
377C2×C4⋊C4—138no—
378C2×C4⋊C4—2616no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4C2×#26112yes—
381C2×C4⋊C4C2×#26111yescharacteristic
382C2×C4⋊C4C2×#26111yescharacteristic
383C2×C4⋊C4C2×#26118yescomplemented
384C2×C22⋊C4—134no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—138no—
387C2×C22⋊C4—134no—
388C2×C22⋊C4—268no—
389C2×C22⋊C4—264no—
390C2×C42—1316no—
391C2×C42—138no—
392C2×C42—2616no—
393C2×C42—268no—
394#95—138no—
395#95—1316no—
396#95—138no—
397#95—1316no—
398C2×C13—24no—
399C2×C13#234414yescomplemented
400C2×C13C22×#11711yescharacteristic
401C2×C13C22×C4×D411yescharacteristic
402C2×C13C2×#51911yescharacteristic
403D13—24no—
404D13#234414yescomplemented
405D13C2×#54712yes—
406D13C2×#55212yes—
407C24—131no—
408C24—134no—
409C24—134no—
410C24—132no—
411C24—132no—
412C24—131no—
413C24—264no—
414C24—264no—
415C24C22×#26111yescharacteristic
416C22×C4—28no—
417C22×C4—24no—
418C22×C4—131no—
419C22×C4—138no—
420C22×C4—132no—
421C22×C4—132no—
422C22×C4—134no—
423C22×C4—138no—
424C22×C4—134no—
425C22×C4—138no—
426C22×C4—131no—
427C22×C4—132no—
428C22×C4—132no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—134no—
434C22×C4—132no—
435C22×C4—134no—
436C22×C4—138no—
437C22×C4—138no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—138no—
441C22×C4—264no—
442C22×C4—2616no—
443C22×C4—2616no—
444C22×C4—264no—
445C22×C4—264no—
446C22×C4—2616no—
447C22×C4—264no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—2616no—
451C22×C4—2632no—
452C22×C4—268no—
453C22×C4—268no—
454C22×C4—264no—
455C22×C4—264no—
456C22×C4—264no—
457C22×C4—268no—
458C22×C4—264no—
459C22×C4—268no—
460C22×C4—264no—
461C22×C4—264no—
462C22×C4—268no—
463C22×C4—268no—
464C22×C4—264no—
465C22×C4C22×#26118yes—
466C22×C4C22×#26114yes—
467C22×C4C22×#26111yescharacteristic
468C22×C4C22×#26112yes—
469C22×C4C22×#26112yes—
470C22×C4C22×#26111yescharacteristic
471C4⋊C4—138no—
472C4⋊C4—138no—
473C4⋊C4—138no—
474C4⋊C4—138no—
475C4⋊C4—138no—
476C4⋊C4—134no—
477C4⋊C4—134no—
478C4⋊C4—2632no—
479C4⋊C4—2616no—
480C4⋊C4C22×#26118yes—
481C4⋊C4C22×#26114yes—
482C4⋊C4C22×#26114yes—
483C22⋊C4—1316no—
484C22⋊C4—2616no—
485C22⋊C4—268no—
486C42—2632no—
487C42—2616no—
488C13C2×#234411yescharacteristic, complemented, Sylow
489C23—22no—
490C23—22no—
491C23—134no—
492C23—132no—
493C23—132no—
494C23—134no—
495C23—131no—
496C23—131no—
497C23—134no—
498C23—134no—
499C23—138no—
500C23—134no—
501C23—132no—
502C23—264no—
503C23—264no—
504C23—264no—
505C23—264no—
506C23—2616no—
507C23—2616no—
508C23—262no—
509C23—262no—
510C23D4×#26114yes—
511C23C23×#26112yes—
512C23C23×#26111yescharacteristic
513C2×C4—22no—
514C2×C4—216no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—134no—
519C2×C4—132no—
520C2×C4—138no—
521C2×C4—138no—
522C2×C4—138no—
523C2×C4—132no—
524C2×C4—134no—
525C2×C4—134no—
526C2×C4—268no—
527C2×C4—264no—
528C2×C4—264no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—268no—
532C2×C4—268no—
533C2×C4—264no—
534C2×C4—264no—
535C2×C4—2616no—
536C2×C4—2616no—
537C2×C4—268no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—2616no—
541C2×C4—262no—
542C2×C4—2616no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—268no—
546C2×C4—268no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—268no—
550C2×C4—264no—
551C2×C4—268no—
552C2×C4—5216no—
553C2×C4—528no—
554C2×C4#8823714yescomplemented
555C2×C4C23×#26112yes—
556C2×C4C23×#26114yes—
557C2×C4C23×#26114yes—
558C2×C4C23×#26112yes—
559C22—22no—
560C22—22no—
561C22—28no—
562C22—132no—
563C22—132no—
564C22—132no—
565C22—131no—
566C22—131no—
567C22—132no—
568C22—132no—
569C22—138no—
570C22—138no—
571C22—134no—
572C22—268no—
573C22—268no—
574C22—2616no—
575C22—262no—
576C22—262no—
577C22—268no—
578C22C2×#8823712yes—
579C22C2×D4×#26114yes—
580C22C2×D4×#26112yes—
581C22#1171962712yes—
582C22C24×#26111yescharacteristic
583C4—22no—
584C4—24no—
585C4—24no—
586C4—134no—
587C4—268no—
588C4—262no—
589C4—264no—
590C4—264no—
591C4—528no—
592C4—524no—
593C4C2×#8823714yescomplemented
594C2—24no—
595C2—132no—
596C2—132no—
597C2—134no—
598C2—264no—
599C2#1313134414yesdirect product factor
600C2C22×#8823711yescharacteristic
601C2C22×D4×#26111yescharacteristic
602C2C2×#1171962711yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#2344
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13131344C2direct (N × H)
3. C2×#11719083C2semidirect
4. C2×#11719082C2semidirect
7. C2×C4⋊C4×#261C2semidirect
21. C22×C13×C4⋊C4C4semidirect
22. C22×C4⋊Dic13C4semidirect
23. C22×#6101C4semidirect
24. C2×C4⋊C4×D13C4semidirect
25. C2×C4⋊C4×D13C4semidirect
26. C2×C4⋊C4×D13C4semidirect
27. C2×C4⋊C4×D13C4semidirect
39. #11719083C22semidirect
40. #11719082C22semidirect
41. C4⋊C4×#261C22semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
87. C2×C4⋊Dic13C2×C4semidirect
92. C2×#6101C2×C4semidirect
96. C4⋊C4×D13C2×C4semidirect
97. C4⋊C4×D13C2×C4semidirect
98. C4⋊C4×D13C2×C4semidirect
238. C2×C4×C13#117semidirect
248. C2×Dic13#117semidirect
265. C4×D13#117semidirect
283. C22×C4⋊C4#261semidirect
329. C4×C13C2×#117semidirect
333. Dic13C2×#117semidirect
383. C2×C4⋊C4C2×#261semidirect
399. C2×C13#2344semidirect
404. D13#2344semidirect
488. C13C2×#2344semidirect
554. C2×C4#88237semidirect
593. C4C2×#88237semidirect
599. C2#13131344direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882372
#131313442
C2×#117190832
C2×#117190822
C2×#117191352
C2×#117191362
C2×C4⋊C4×#2612
C2×C4×C22⋊#2612
C22×C4⋊C4×D132
C2×#234413