Finite Group Databasebeta

← #16797675

Subgroups — #16797675

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719065C211yesmaximal, characteristic
2C2×#11719064C211yesmaximal, characteristic
3#13130635C211yesmaximal, characteristic, complemented
4#13130635C211yesmaximal, characteristic, complemented
5#13130622C211yesmaximal, characteristic, complemented
6#13130578C211yesmaximal, characteristic, complemented
7#13130577C211yesmaximal, characteristic, complemented
8#13130574C211yesmaximal, characteristic, complemented
9#13130573C211yesmaximal, characteristic, complemented
10#13130566C211yesmaximal, characteristic, complemented
11#13130565C211yesmaximal, characteristic, complemented
12#13130553C211yesmaximal, characteristic, complemented
13#13130503C211yesmaximal, characteristic, complemented
14#13130502C211yesmaximal, characteristic, complemented
15#13117296C211yesmaximal, characteristic
16C22×#6122C2211yescharacteristic
17C23×#1057C2211yescharacteristic
18C22×#6118C2211yescharacteristic
19C22×D13⋊C8C2211yescharacteristic
20C2×#88146C2211yescharacteristic
21C2×#88135C2211yescharacteristic
22C2×#88131C2211yescharacteristic
23C2×C22⋊#1057C2211yescharacteristic
24C2×C22⋊#1057C2211yescharacteristic
25C2×#88111C2211yescharacteristic
26C2×#88111C2211yescharacteristic
27C2×#88110C2211yescharacteristic
28C2×#88110C2211yescharacteristic
29C2×#88110C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×#88110C2211yescharacteristic
32C2×#88110C2211yescharacteristic
33C2×C4⋊#1057C2211yescharacteristic
34C2×C4⋊#1057C2211yescharacteristic
35C2×C4×#1057C2211yescharacteristic
36C2×C4×#1057C2211yescharacteristic
37#11719065C418yescomplemented
38#11719064C418yescomplemented
39C13×#388C411yescharacteristic
40#11718633C411yescharacteristic
41#11718618C411yescharacteristic
42#11718618C411yescharacteristic
43#11718612C411yescharacteristic
44C22⋊C4×Dic13C2211yescharacteristic
45#11718601C411yescharacteristic
46C42×Dic13C2211yescharacteristic
47#11718330C411yescharacteristic
48#11718327C2211yescharacteristic
49#11718310C2211yescharacteristic
50#11718308C411yescharacteristic
51#11718290C2211yescharacteristic
52#11718290C2211yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61C22×C22⋊D13C2×C411yescharacteristic
62C23×Dic13C2311yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C2×#6122—41no—
65C2×#6122—41no—
66C2×#6122C2×C414yes—
67C22×#1057—41no—
68C22×#1057—41no—
69C22×#1057C2×C414yes—
70C22×#1057C2311yescharacteristic
71C22×#1057C2311yescharacteristic
72C22×#1057C2311yescharacteristic
73C22×#1057C2311yescharacteristic
74C22×#1057C2311yescharacteristic
75C22×#1057C2311yescharacteristic
76C22×#1057C2311yescharacteristic
77C22×#1057C2311yescharacteristic
78C2×#6118—41no—
79C2×#6118—41no—
80C2×#6118C2×C414yes—
81C2×D13⋊C8—41no—
82C2×D13⋊C8—41no—
83C2×D13⋊C8C2×C414yes—
84C2×C13×C4⋊C4C2×C411yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C13×C22⋊C4C2×C411yescharacteristic
87C2×C13×C22⋊C4C2×C411yescharacteristic
88C2×C42×C13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×#6101C2×C411yescharacteristic
102C2×C4×Dic13C2×C411yescharacteristic
103C2×C4×Dic13C2×C411yescharacteristic
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110#88146—41no—
111#88146—41no—
112#88135C2×C414yes—
113#88135C2×C414yes—
114#88131—41no—
115#88131—41no—
116C22⋊#1057C2×C414yes—
117C22⋊#1057C2×C414yes—
118#88111C2×C414yes—
119#88111C2×C414yes—
120#88110—41no—
121#88110—41no—
122#88110—41no—
123#88110—41no—
124#88110C2×C414yes—
125#88110C2×C414yes—
126C4⋊#1057C2×C414yes—
127C4⋊#1057C2×C414yes—
128C4×#1057—41no—
129C4×#1057—41no—
130C13×#95C2×C411yescharacteristic
131C13×#95C2×C411yescharacteristic
132#88071C2×C411yescharacteristic
133#88071C2×C411yescharacteristic
134#88071C2×C411yescharacteristic
135#88071C2×C411yescharacteristic
136#20563—131nomaximal, Sylow
137C24×C13C22×C411yescharacteristic
138C23×D13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C2×C22⋊D13—41no—
146C2×C22⋊D13—41no—
147C2×C22⋊D13C4214yes—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C22×C411yescharacteristic
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C2411yescharacteristic
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13C22×C412yes—
166C2×C4×D13C22×C412yes—
167#6122—44no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—21no—
178C2×#1057—21no—
179C2×#1057—21no—
180C2×#1057—21no—
181C2×#1057—21no—
182C2×#1057—21no—
183C2×#1057—21no—
184C2×#1057—44no—
185C2×#1057C22×C412yes—
186C2×#1057C22×C412yes—
187C2×#1057C22×C412yes—
188C2×#1057C22×C412yes—
189C2×#1057C22×C412yes—
190C2×#1057C22×C412yes—
191C2×#1057C22×C412yes—
192C2×#1057C22×C412yes—
193#6118—44no—
194D13⋊C8—44no—
195C13×C4⋊C4—41no—
196C13×C22⋊C4—41no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4C4214yes—
199C42×C13—41no—
200C22⋊Dic13—41no—
201C22⋊Dic13—41no—
202#6103—41no—
203#6103—41no—
204#6103—41no—
205#6103—41no—
206#6103C4214yes—
207C4⋊Dic13—41no—
208#6101—41no—
209#6101—41no—
210#6101—41no—
211#6101—41no—
212#6101C4214yes—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220C4×Dic13—21no—
221C4×Dic13—41no—
222C4×Dic13—41no—
223C4×Dic13—41no—
224C4×Dic13C22×C412yes—
225C4×Dic13C22×C412yes—
226C2×#435—131no—
227C2×#435—131no—
228#2293—131no—
229#1771—131no—
230#1771—131no—
231#1767—131no—
232#1753—131no—
233#1753—131no—
234#1752—131no—
235#1752—131no—
236#1750—131no—
237#1750—131no—
238#1745—131no—
239#1729—131no—
240#1729—131no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13C2×C4212yes—
248C23×C13C23×C411yescharacteristic
249C22×D13—21no—
250C22×D13—21no—
251C22×D13—21no—
252C22×D13—21no—
253C22×D13—21no—
254C22×D13—21no—
255C22×D13C2×C4212yes—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13C2×C4212yes—
273C2×C4×C13C2×C4212yes—
274C22⋊D13—44no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13C2×C4212yes—
296C2×Dic13C2×C4212yes—
297C2×Dic13C23×C411yescharacteristic
298C2×Dic13C23×C411yescharacteristic
299C2×Dic13H(5,𝔽2)11yescharacteristic
300C2×Dic13H(5,𝔽2)11yescharacteristic
301C2×Dic13H(5,𝔽2)11yescharacteristic
302C2×Dic132−1+411yescharacteristic
303C4×D13—22no—
304C4×D13—22no—
305C4×D13—22no—
306C4×D13—22no—
307#1057—22no—
308#1057—22no—
309#1057—22no—
310#1057—22no—
311#1057—22no—
312#1057—22no—
313#1057—22no—
314#1057—22no—
315C22×M16—131no—
316C22×M16—131no—
317C23×C8—131no—
318C23×C8—131no—
319C2×C4×D4—131no—
320C2×#117—131no—
321C2×#117—131no—
322#435—138no—
323#435—138no—
324C2×C4⋊C8—131no—
325C2×C4⋊C8—131no—
326C2×C22⋊C8—131no—
327C2×C22⋊C8—131no—
328C2×C22⋊C8—131no—
329C2×C22⋊C8—131no—
330C2×#97—131no—
331C2×#97—131no—
332C2×#97—131no—
333C2×#97—131no—
334C2×#97—131no—
335C2×#97—131no—
336C2×C4×C8—131no—
337C2×C4×C8—131no—
338#390—131no—
339#390—131no—
340#389—131no—
341#389—131no—
342#388—131no—
343#388—131no—
344#388—131no—
345#388#26111yescharacteristic
346C4×C4⋊C4—131no—
347C4×C22⋊C4—131no—
348C4×C22⋊C4—131no—
349C43—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336—131no—
355#336—131no—
356#336—131no—
357#336—131no—
358#336—131no—
359#336—131no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13C22×C4211yescharacteristic
368C22×C13#51811yescharacteristic
369C22×C13#52011yescharacteristic
370C22×C13#56811yescharacteristic
371C22×C13#56811yescharacteristic
372C22×C13#56811yescharacteristic
373C22×C13#56811yescharacteristic
374C2×D13—22no—
375C2×D13—22no—
376C2×D13—22no—
377C2×D13—41no—
378C2×D13—41no—
379C2×D13—41no—
380C2×D13—41no—
381C4×C13—22no—
382C4×C13—22no—
383C4×C13—41no—
384C4×C13—41no—
385C4×C13—41no—
386C4×C13—41no—
387Dic13—22no—
388Dic13—22no—
389Dic13—41no—
390Dic13—41no—
391Dic13—41no—
392Dic13—41no—
393Dic13#51811yescharacteristic
394Dic13#51811yescharacteristic
395Dic13#52011yescharacteristic
396Dic13#52011yescharacteristic
397C22×D4—131no—
398C23×C4—131no—
399C23×C4—131no—
400C2×M16—134no—
401C2×M16—134no—
402C2×M16—521no—
403C2×M16—521no—
404C2×M16—521no—
405C2×M16—521no—
406C22×C8—131no—
407C22×C8—131no—
408C22×C8—131no—
409C22×C8—131no—
410C22×C8—131no—
411C22×C8—131no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—134no—
415C22×C8—134no—
416C22×C8—521no—
417C22×C8—521no—
418C22×C8—521no—
419C22×C8—521no—
420C4×D4—134no—
421C4×D4—134no—
422#117—521no—
423#117—521no—
424#117—521no—
425#117—521no—
426C2×C4⋊C4—131no—
427C2×C4⋊C4—131no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4C2×#26111yescharacteristic
433C2×C22⋊C4—131no—
434C2×C22⋊C4—131no—
435C2×C22⋊C4—131no—
436C2×C22⋊C4—131no—
437C2×C22⋊C4—131no—
438C2×C22⋊C4—131no—
439C2×C22⋊C4—131no—
440C2×C22⋊C4C2×#26111yescharacteristic
441C2×C22⋊C4C2×#26111yescharacteristic
442C2×C22⋊C4C2×#26111yescharacteristic
443C2×C42—131no—
444C2×C42—131no—
445C2×C42—131no—
446C2×C42—131no—
447C2×C42—131no—
448C2×C42—131no—
449C2×C42—131no—
450C2×C42—131no—
451C2×C42C2×#26111yescharacteristic
452C4⋊C8—134no—
453C4⋊C8—134no—
454C22⋊C8—134no—
455C22⋊C8—134no—
456C22⋊C8—134no—
457C22⋊C8—134no—
458#97—134no—
459#97—134no—
460#97—521no—
461#97—521no—
462#97—521no—
463#97—521no—
464C4×C8—521no—
465C4×C8—521no—
466#95—131no—
467#95—131no—
468#95—131no—
469#95—131no—
470#95C2×#26111yescharacteristic
471#95C2×#26111yescharacteristic
472C2×C13—42no—
473C2×C13#227511yescharacteristic
474C2×C13#287311yescharacteristic
475C2×C13#287511yescharacteristic
476C2×C13#298011yescharacteristic
477C2×C13#298011yescharacteristic
478C2×C13#299511yescharacteristic
479C2×C13#299511yescharacteristic
480D13—42no—
481C24—131no—
482C24C22×#26111yescharacteristic
483C2×D4—134no—
484C2×D4—521no—
485C2×D4—521no—
486C22×C4—131no—
487C22×C4—132no—
488C22×C4—132no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4—131no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4C22×#26111yescharacteristic
506C22×C4C22×#26111yescharacteristic
507C22×C4C22×#26111yescharacteristic
508C22×C4C22×#26111yescharacteristic
509C22×C4C22×#26111yescharacteristic
510C22×C4C22×#26111yescharacteristic
511M16—524no—
512M16—524no—
513C2×C8—132no—
514C2×C8—132no—
515C2×C8—132no—
516C2×C8—132no—
517C2×C8—132no—
518C2×C8—132no—
519C2×C8—132no—
520C2×C8—132no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—524no—
538C2×C8—524no—
539C4⋊C4—41no—
540C4⋊C4—134no—
541C4⋊C4—521no—
542C4⋊C4—521no—
543C4⋊C4—521no—
544C4⋊C4—521no—
545C4⋊C4—521no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—134no—
549C22⋊C4—521no—
550C22⋊C4—521no—
551C22⋊C4—521no—
552C22⋊C4—521no—
553C22⋊C4—521no—
554C22⋊C4—521no—
555C22⋊C4C4×#26114yes—
556C42—41no—
557C42—132no—
558C42—132no—
559C42—261no—
560C42—261no—
561C42—261no—
562C42—261no—
563C42—261no—
564C42—261no—
565C42—261no—
566C42—261no—
567C42—521no—
568C42—521no—
569C42—521no—
570C13#2056311yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—132no—
578C23—261no—
579C23—261no—
580C23—261no—
581C23—261no—
582C23—261no—
583C23—261no—
584C23C2×C4×#26112yes—
585C23C23×#26111yescharacteristic
586D4—524no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—131no—
604C2×C4—131no—
605C2×C4—131no—
606C2×C4—131no—
607C2×C4—131no—
608C2×C4—131no—
609C2×C4—132no—
610C2×C4—132no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—262no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—261no—
620C2×C4—261no—
621C2×C4—261no—
622C2×C4—261no—
623C2×C4—261no—
624C2×C4—261no—
625C2×C4—261no—
626C2×C4—261no—
627C2×C4—261no—
628C2×C4—261no—
629C2×C4—261no—
630C2×C4—261no—
631C2×C4—261no—
632C2×C4—261no—
633C2×C4—261no—
634C2×C4—261no—
635C2×C4C2×C4×#26112yes—
636C2×C4C2×C4×#26112yes—
637C8—262no—
638C8—262no—
639C8—262no—
640C8—262no—
641C8—262no—
642C8—262no—
643C8—262no—
644C8—262no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—262no—
653C22—262no—
654C22—262no—
655C22—521no—
656C22—521no—
657C22—521no—
658C22—521no—
659C22C22×C4×#26111yescharacteristic
660C22#1171962111yescharacteristic
661C22#1171962311yescharacteristic
662C22#1171962911yescharacteristic
663C22#1171962911yescharacteristic
664C22#1171962911yescharacteristic
665C22#1171963111yescharacteristic
666C4—22no—
667C4—22no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—131no—
673C4—131no—
674C4—131no—
675C4—131no—
676C4—262no—
677C4—262no—
678C4—521no—
679C4—521no—
680C4—521no—
681C4—521no—
682C2—42no—
683C2—522no—
684C2#1313127511yescharacteristic
685C2#1313140111yescharacteristic
686C2#1313140711yescharacteristic
687C2#1313172011yescharacteristic
688C2#1313172211yescharacteristic
689C2#1313179011yescharacteristic
690C2#1313179111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×Dic13C24
hypercenter#388#261
hypocenterC13#20563
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #13130635C2semidirect
4. #13130635C2semidirect
5. #13130622C2semidirect
6. #13130578C2semidirect
7. #13130577C2semidirect
8. #13130574C2semidirect
9. #13130573C2semidirect
10. #13130566C2semidirect
11. #13130565C2semidirect
12. #13130553C2semidirect
13. #13130503C2semidirect
14. #13130502C2semidirect
37. #11719065C4semidirect
38. #11719064C4semidirect
570. C13#20563semidirect

Maximal subgroups

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

subgroupindex
C2×#117190652
C2×#117190642
#131306352
#131306222
#131305782
#131305772
#131305742
#131305732
#131305662
#131305652
#131305532
#131305032
#131305022
#131172962
#2056313