Finite Group Databasebeta

← #16803173

Subgroups — #16803173

Order 3328.

1500 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719063C212yesmaximal, complemented
2#13131007C212yesmaximal, complemented
3#13130810C212yesmaximal, complemented
4#13130809C212yesmaximal, complemented
5#13130728C211yesmaximal, characteristic, complemented
6#13130727C211yesmaximal, characteristic, complemented
7#13130692C211yesmaximal, characteristic, complemented
8C4×C22⋊#1057C211yesmaximal, characteristic, complemented
9#13130497C211yesmaximal, characteristic, complemented
10C2×#11718290C211yesmaximal, characteristic, complemented
11C2×C4×#6129C211yesmaximal, characteristic
12C22×#6129C411yescharacteristic
13C23×#1057C2212yes—
14C22×D13⋊C8C2212yes—
15C2×C4×D4×C13C411yescharacteristic
16C2×D4×Dic13C2211yescharacteristic
17C2×C4×C22⋊D13C411yescharacteristic
18C2×C4×C22⋊D13C411yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C4×#6129—28no—
22C2×#88146C411yescharacteristic
23C2×#88141C2211yescharacteristic
24C2×#88135C2211yescharacteristic
25C2×#88135C2211yescharacteristic
26C2×#88131C411yescharacteristic
27C2×#88131C411yescharacteristic
28C2×C42×D13C2211yescharacteristic
29C2×C4×Dic26C411yescharacteristic
30C2×C22⋊#1057C2212yes—
31C2×C22⋊#1057C2212yes—
32C2×C22⋊#1057C2212yes—
33C2×#88112C2212yes—
34C2×#88111C2212yes—
35C2×C4×#1057C2212yes—
36#11719063—28no—
37#11718290C2211yescharacteristic
38#11718290C2212yes—
39#11718290C2211yescharacteristic
40#11718290C2212yes—
41#11718290C2211yescharacteristic
42#11718290C2212yes—
43#11718290C2212yes—
44#11718290C2211yescharacteristic
45C22×D4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C22×C22⋊D13C2×C411yescharacteristic
49C22×C22⋊D13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C411yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C2×#6129—24no—
55C2×#6129—24no—
56C2×#6129C818yescomplemented
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13C2×C411yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×Dic26C2×C411yescharacteristic
61C22×#1057—24no—
62C22×#1057—24no—
63C22×#1057—42no—
64C22×#1057C2312yes—
65C22×#1057C2312yes—
66C22×#1057C2312yes—
67C22×#1057C2312yes—
68C2×D13⋊C8—24no—
69C2×D13⋊C8—24no—
70C2×D13⋊C8—42no—
71C4×D4×C13—24no—
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C22⋊C4C2×C411yescharacteristic
74C2×C13×C22⋊C4C2×C411yescharacteristic
75C2×C42×C13C2×C411yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78D4×Dic13—24no—
79C4×C22⋊D13—24no—
80C4×C22⋊D13—24no—
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×C4×Dic13—24no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99#88146—24no—
100#88141—24no—
101#88135—24no—
102#88135D418yes—
103#88131—24no—
104#88131—24no—
105C42×D13—24no—
106C4×Dic26—24no—
107C22⋊#1057—24no—
108C22⋊#1057—24no—
109C22⋊#1057—42no—
110#88112—24no—
111#88111—24no—
112C4×#1057—24no—
113#22469—131nomaximal, Sylow
114C24×C13C22×C411yescharacteristic
115C24×C13C22×C411yescharacteristic
116C23×D13C22×C411yescharacteristic
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13C2×C814yescomplemented
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C2×C22⋊D13—22no—
132C2×C22⋊D13—22no—
133C2×C22⋊D13C22⋊C414yes—
134C2×C22⋊D13C2×C814yes—
135C2×C22⋊D13C2×C814yescomplemented
136C2×C22⋊D13M1614yes—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13C2×C814yescomplemented
149C22×Dic13C2×C814yescomplemented
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C2×D414yes—
157C22×Dic13C2411yescharacteristic
158#6129—232no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—41no—
167C2×C4×D13C2×C814yescomplemented
168C2×C4×D13C2×D414yes—
169C2×Dic26—22no—
170C2×Dic26—22no—
171C2×Dic26C2×C814yescomplemented
172C2×#1057—22no—
173C2×#1057—22no—
174C2×#1057—22no—
175C2×#1057—22no—
176C2×#1057—22no—
177C2×#1057—22no—
178C2×#1057—22no—
179C2×#1057—22no—
180C2×#1057—22no—
181C2×#1057—22no—
182C2×#1057—22no—
183C2×#1057—48no—
184C2×#1057#4114yescomplemented
185D13⋊C8—48no—
186C13×C4⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4C22⋊C414yes—
189C42×C13—22no—
190C22⋊Dic13—22no—
191C22⋊Dic13—22no—
192#6103—22no—
193#6103C22⋊C414yes—
194C4⋊Dic13—22no—
195#6101—22no—
196#6101—22no—
197#6101—22no—
198#6101C22⋊C414yes—
199C4×Dic13—22no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—22no—
203C4×Dic13—22no—
204C4×Dic13—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13C2×D414yes—
208C2×C4×#41—131no—
209C2×C8×D4—132no—
210#1984—132no—
211#1869—132no—
212#1869—132no—
213#1817—131no—
214#1817—131no—
215#1797—131no—
216C4×C22⋊C8—131no—
217C2×#336—131no—
218C2×#336—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C2×C22⋊C412yes—
230C23×C13C22×C812yes—
231C23×C13C22×C812yes—
232C23×C13C2×M1612yes—
233C23×C13C23×C411yescharacteristic
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13C2×C22⋊C412yes—
239C22×D13C22×C812yes—
240C22×D13C2×M1612yes—
241D4×C13—28no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—44no—
254C2×C4×C13—44no—
255C2×C4×C13C2×C22⋊C412yes—
256C2×C4×C13C2×C22⋊C412yes—
257C2×C4×C13C22×C812yes—
258C2×C4×C13#13112yes—
259C22⋊D13—28no—
260C22⋊D13C22⋊C8116yescomplemented
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—28no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—28no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13C2×C22⋊C412yes—
280C2×Dic13C2×C22⋊C412yes—
281C2×Dic13C22×C812yes—
282C2×Dic13C22×C812yes—
283C2×Dic13C22×C812yes—
284C2×Dic13C2×M1612yes—
285C2×Dic13C22×D412yes—
286C2×Dic13C2×#4112yes—
287C2×Dic13H(5,𝔽2)11yescharacteristic
288C2×Dic132−1+411yescharacteristic
289C4×D13—28no—
290C4×D13—24no—
291C4×D13—24no—
292C4×D13—44no—
293Dic26—28no—
294#1057—24no—
295#1057—42no—
296#1057—42no—
297#1057—42no—
298C22×#41—131no—
299C23×C8—132no—
300C23×C8—132no—
301C4×#41—268no—
302C2×C4×Q8—131no—
303C2×C4×Q8—131no—
304C2×C4×D4—131no—
305C2×C4×D4—131no—
306C2×C4×D4—131no—
307C2×C4×D4—131no—
308C2×C4×D4—131no—
309C2×C4×D4#26111yescharacteristic
310C2×#117—131no—
311C2×#117—131no—
312C2×#117—131no—
313C22×C42—131no—
314C22×C42—131no—
315C22×C42—131no—
316C8×D4—268no—
317C2×C4⋊C8—132no—
318C2×C22⋊C8—132no—
319C2×C22⋊C8—132no—
320C2×C22⋊C8—132no—
321C2×C22⋊C8—132no—
322C2×C4×C8—132no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—132no—
327#336—132no—
328#336—132no—
329#336—132no—
330#336—131no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×C22⋊C814yes—
345C22×C13C22×C22⋊C411yescharacteristic
346C22×C13C4×#4111yescharacteristic
347C22×C13#52011yescharacteristic
348C22×C13C23×C811yescharacteristic
349C22×C13C22×M1611yescharacteristic
350C22×C13C2×#13111yescharacteristic
351C22×C13#56811yescharacteristic
352C2×D13—22no—
353C2×D13—22no—
354C2×D13—22no—
355C2×D13—22no—
356C2×D13—22no—
357C2×D13—22no—
358C2×D13C2×C22⋊C814yes—
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364Dic13—22no—
365Dic13—22no—
366Dic13—22no—
367Dic13—41no—
368Dic13—41no—
369Dic13C2×C22⋊C814yes—
370Dic13#54612yes—
371Dic13#54712yes—
372C2×#41—138no—
373C2×#41—264no—
374C2×#41—264no—
375C22×Q8—131no—
376C22×D4—131no—
377C22×D4—131no—
378C22×D4C2×#26111yescharacteristic
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4C2×#26111yescharacteristic
387C23×C4C2×#26111yescharacteristic
388C22×C8—132no—
389C22×C8—132no—
390C22×C8—132no—
391C22×C8—132no—
392C22×C8—264no—
393C22×C8—264no—
394C22×C8—264no—
395C22×C8—264no—
396C22×C8—522no—
397C22×C8—522no—
398C4×Q8—264no—
399C4×Q8—264no—
400C4×D4—24no—
401C4×D4—138no—
402C4×D4—264no—
403C4×D4—264no—
404C4×D4—264no—
405C4×D4—264no—
406#117—264no—
407#117—264no—
408#117—264no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4C2×#26111yescharacteristic
415C2×C22⋊C4—131no—
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C22⋊C4—131no—
419C2×C22⋊C4C2×#26111yescharacteristic
420C2×C22⋊C4C2×#26111yescharacteristic
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—131no—
430C2×C42—264no—
431C2×C42—264no—
432C2×C42—264no—
433C2×C42C2×#26111yescharacteristic
434C4⋊C8—264no—
435C22⋊C8—264no—
436C22⋊C8—264no—
437C22⋊C8—264no—
438C22⋊C8—522no—
439C4×C8—264no—
440C2×C13—24no—
441C2×C13—42no—
442C2×C13#233911yescharacteristic
443C2×C13C22×C22⋊C811yescharacteristic
444C2×C13#288011yescharacteristic
445C2×C13C8×#4111yescharacteristic
446C2×C13#297011yescharacteristic
447C2×C13#298811yescharacteristic
448C2×C13#299011yescharacteristic
449D13—24no—
450C24—131no—
451C24C22×#26111yescharacteristic
452C24C22×#26111yescharacteristic
453#41—2632no—
454C2×Q8—134no—
455C2×Q8—262no—
456C2×Q8—262no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—134no—
460C2×D4—134no—
461C2×D4—134no—
462C2×D4—134no—
463C2×D4—262no—
464C2×D4—262no—
465C2×D4D13⋊C814yescomplemented
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—134no—
475C22×C4—134no—
476C22×C4—134no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—134no—
481C22×C4—134no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—262no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4—261no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—261no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—521no—
503C22×C4C22×#26111yescharacteristic
504C22×C4C22×#26111yescharacteristic
505C22×C4C22×#26111yescharacteristic
506C22×C4C22×#26111yescharacteristic
507C22×C4C22×#26111yescharacteristic
508C2×C8—134no—
509C2×C8—262no—
510C2×C8—262no—
511C2×C8—262no—
512C2×C8—262no—
513C2×C8—262no—
514C2×C8—262no—
515C2×C8—262no—
516C2×C8—262no—
517C2×C8—262no—
518C2×C8—262no—
519C2×C8—262no—
520C2×C8—528no—
521C2×C8—528no—
522C4⋊C4—22no—
523C4⋊C4—134no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C4⋊C4—262no—
527C4⋊C4—262no—
528C22⋊C4—22no—
529C22⋊C4—134no—
530C22⋊C4—262no—
531C22⋊C4—262no—
532C22⋊C4—262no—
533C22⋊C4C22⋊#26114yes—
534C42—22no—
535C42—134no—
536C42—262no—
537C42—262no—
538C42—262no—
539C42—262no—
540C42—262no—
541C42—262no—
542C42—262no—
543C42—262no—
544C13#2246911yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—132no—
556C23—132no—
557C23—132no—
558C23—261no—
559C23—261no—
560C23—261no—
561C23—261no—
562C23C2×D13⋊C812yes—
563C23C2×D13⋊C812yes—
564C23D13⋊M1612yes—
565C23C2×C22⋊#26112yes—
566C23C23×#26111yescharacteristic
567Q8—268no—
568D4—28no—
569D4—1316no—
570D4—268no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—132no—
585C2×C4—132no—
586C2×C4—132no—
587C2×C4—131no—
588C2×C4—131no—
589C2×C4—132no—
590C2×C4—132no—
591C2×C4—132no—
592C2×C4—132no—
593C2×C4—132no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—268no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—268no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—268no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—524no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4C2×D13⋊C812yes—
617C2×C4#8823812yes—
618C2×C4C2×C22⋊#26112yes—
619C2×C4C2×C22⋊#26112yes—
620C8—264no—
621C8—522no—
622C8—522no—
623C8—522no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—134no—
638C22—262no—
639C22—262no—
640C22—262no—
641C22—262no—
642C22—262no—
643C22—262no—
644C22D13⋊(C22⋊C8)14yes—
645C22C22×D13⋊C811yescharacteristic
646C22C2×D13⋊M1611yescharacteristic
647C22C2×#8823811yescharacteristic
648C22#1171962111yescharacteristic
649C22#41×#26111yescharacteristic
650C22#1171963111yescharacteristic
651C22C22×C22⋊#26111yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—132no—
658C4—132no—
659C4—134no—
660C4—262no—
661C4—262no—
662C4—262no—
663C4—521no—
664C4—521no—
665C2—24no—
666C2—42no—
667C2—264no—
668C2#1313133911yescharacteristic
669C2C2×D13⋊(C22⋊C8)11yescharacteristic
670C2#1313142411yescharacteristic
671C2#1313164111yescharacteristic
672C2#1313167611yescharacteristic
673C2#1313175211yescharacteristic
674C2#1313176111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C23×C8
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×#6129C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13#22469
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11719063C2semidirect
2. #13131007C2semidirect
3. #13130810C2semidirect
4. #13130809C2semidirect
5. #13130728C2semidirect
6. #13130727C2semidirect
7. #13130692C2semidirect
8. C4×C22⋊#1057C2semidirect
9. #13130497C2semidirect
10. C2×#11718290C2semidirect
56. C2×#6129C8semidirect
119. C2×D4×C13C2×C8semidirect
135. C2×C22⋊D13C2×C8semidirect
148. C22×Dic13C2×C8semidirect
149. C22×Dic13C2×C8semidirect
167. C2×C4×D13C2×C8semidirect
171. C2×Dic26C2×C8semidirect
184. C2×#1057#41semidirect
260. C22⋊D13C22⋊C8semidirect
465. C2×D4D13⋊C8semidirect
544. C13#22469semidirect

Maximal subgroups

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

subgroupindex
C2×#117190632
#131310072
#131308102
#131308092
#131307282
#131307272
#131306922
C4×C22⋊#10572
#131304972
C2×#117182902
C2×C4×#61292
#2246913