Finite Group Databasebeta

← #16800256

Subgroups — #16800256

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719074C211yesmaximal, characteristic, complemented
2C2×#11719063C211yesmaximal, characteristic
3#13131007C211yesmaximal, characteristic, complemented
4#13130959C211yesmaximal, characteristic
5#13130908C211yesmaximal, characteristic, complemented
6#13130907C211yesmaximal, characteristic, complemented
7#13130906C211yesmaximal, characteristic, complemented
8#13130905C211yesmaximal, characteristic, complemented
9#13130752C211yesmaximal, characteristic, complemented
10#13130570C211yesmaximal, characteristic, complemented
11#13130570C211yesmaximal, characteristic, complemented
12C22⋊C4×#1057C211yesmaximal, characteristic, complemented
13C22⋊C4×#1057C211yesmaximal, characteristic, complemented
14C42×#1057C211yesmaximal, characteristic, complemented
15#13117377C211yesmaximal, characteristic
16C23×#1057C2211yescharacteristic
17C22×D13⋊C8C2211yescharacteristic
18C2×#88141C2211yescharacteristic
19C2×#88139C411yescharacteristic
20C2×#88135C2211yescharacteristic
21C2×C22⋊#1057C2211yescharacteristic
22C2×C22⋊#1057C2211yescharacteristic
23C2×C22⋊#1057C2211yescharacteristic
24C2×#88112C2211yescharacteristic
25C2×#88112C2211yescharacteristic
26C2×#88112C2211yescharacteristic
27C2×#88111C2211yescharacteristic
28C2×#88111C2211yescharacteristic
29C2×#88111C2211yescharacteristic
30C2×C4⋊#1057C2211yescharacteristic
31C2×C4×#1057C2211yescharacteristic
32C2×C4×#1057C2211yescharacteristic
33C2×C4×#1057C2211yescharacteristic
34C2×C4×#1057C2211yescharacteristic
35C2×C4×#1057C2211yescharacteristic
36C2×C4×#1057C2211yescharacteristic
37C2×C4×#1057C2211yescharacteristic
38C2×C4×#1057C2211yescharacteristic
39#11719074—24no—
40#11719063—24no—
41C13×#388C411yescharacteristic
42#11718651C411yescharacteristic
43#11718618C411yescharacteristic
44#11718606C411yescharacteristic
45C22⋊C4×Dic13C2211yescharacteristic
46C22⋊C4×Dic13C2211yescharacteristic
47#11718601C411yescharacteristic
48C42×Dic13C2211yescharacteristic
49#11718327C2211yescharacteristic
50#11718327C2211yescharacteristic
51#11718311C411yescharacteristic
52#11718307C411yescharacteristic
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
64C22×Dic26C2×C411yescharacteristic
65C22×#1057—22no—
66C22×#1057—22no—
67C22×#1057—22no—
68C22×#1057C2311yescharacteristic
69C22×#1057C2311yescharacteristic
70C22×#1057C2311yescharacteristic
71C22×#1057C2311yescharacteristic
72C22×#1057C2311yescharacteristic
73C22×#1057C2311yescharacteristic
74C22×#1057C2311yescharacteristic
75C22×#1057C2311yescharacteristic
76C2×D13⋊C8—22no—
77C2×D13⋊C8—22no—
78C2×D13⋊C8—22no—
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4C2×C411yescharacteristic
81C2×C13×C22⋊C4C2×C411yescharacteristic
82C2×C13×C22⋊C4C2×C411yescharacteristic
83C2×C42×C13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×#6103C2×C411yescharacteristic
87C2×#6103C2×C411yescharacteristic
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6101C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102#88141—22no—
103#88141—22no—
104#88139C818yescomplemented
105#88135—22no—
106#88135—22no—
107C22⋊#1057—22no—
108C22⋊#1057—22no—
109C22⋊#1057—22no—
110#88112—22no—
111#88112—22no—
112#88112—22no—
113#88111—22no—
114#88111—22no—
115#88111—22no—
116C4⋊#1057—22no—
117C4×#1057—22no—
118C4×#1057—22no—
119C4×#1057—22no—
120C4×#1057—22no—
121C4×#1057—22no—
122C4×#1057—22no—
123C4×#1057—22no—
124C4×#1057D414yes—
125C13×#95C2×C411yescharacteristic
126C13×#95C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131#88071C2×C411yescharacteristic
132#88071C2×C411yescharacteristic
133C8×#124—131nomaximal, Sylow
134C24×C13C22×C411yescharacteristic
135C23×D13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C2×C22⋊D13—22no—
143C2×C22⋊D13—22no—
144C2×C22⋊D13C2×C814yes—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C2411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×Dic26—22no—
165C2×Dic26—22no—
166C2×Dic26C2×C814yescomplemented
167C2×#1057—21no—
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—21no—
185C2×#1057—44no—
186C2×#1057C2×D412yes—
187C2×#1057C2×D412yes—
188C2×#1057#4112yes—
189C2×#1057#4112yes—
190C2×#1057#4112yes—
191C2×#1057#4112yes—
192D13⋊C8—44no—
193C13×C4⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4C2×C814yescomplemented
197C42×C13—22no—
198C22⋊Dic13—22no—
199C22⋊Dic13C2×C814yescomplemented
200#6103—22no—
201#6103—22no—
202#6103—22no—
203#6103C2×C814yescomplemented
204#6103C2×C814yescomplemented
205#6101—22no—
206#6101—22no—
207#6101—22no—
208C4×Dic13—22no—
209C4×Dic13—22no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215C4×Dic13—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13C2×C814yescomplemented
219C4×Dic13C2×D412yes—
220C4×Dic13#4112yes—
221C2×C8×Q8—131no—
222C2×C8×D4—131no—
223C4×#124—131no—
224#1984—131no—
225#1954—131no—
226#1923—131no—
227#1923—131no—
228#1923—131no—
229#1923—131no—
230#1831—131no—
231C8×C22⋊C4—131no—
232C8×C22⋊C4—131no—
233C8×C22⋊C4—131no—
234C8×C22⋊C4—131no—
235C42×C8—131no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13C22×C812yes—
243C23×C13C23×C411yescharacteristic
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—21no—
248C22×D13—21no—
249C22×D13—21no—
250C22×D13C22×C812yes—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
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×C13C4×D412yes—
266C2×C4×C13C22×C812yes—
267C2×C4×C13C22×C812yes—
268C2×C4×C13#13112yes—
269C22⋊D13—28no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13C4×D412yes—
287C2×Dic13C22×C812yes—
288C2×Dic13C22×C812yes—
289C2×Dic13C22×C812yes—
290C2×Dic13#13112yes—
291C2×Dic13#13112yes—
292C2×Dic13C22×D411yescharacteristic
293C2×Dic13C2×#4111yescharacteristic
294C2×Dic13C2×#4111yescharacteristic
295C2×Dic13C2×#4111yescharacteristic
296C2×Dic13C2×#4111yescharacteristic
297C2×Dic13C2×#4111yescharacteristic
298C4×D13—41no—
299C4×D13—41no—
300C4×D13—41no—
301C4×D13—41no—
302Dic26—28no—
303#1057—22no—
304#1057—22no—
305#1057—22no—
306#1057—41no—
307#1057—41no—
308#1057—41no—
309#1057—41no—
310#1057#12414yescomplemented
311C23×C8—131no—
312C23×C8—131no—
313C2×#124—131no—
314C2×C4×Q8—131no—
315C2×C4×D4—131no—
316C8×Q8—264no—
317C8×D4—264no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8—131no—
325C2×C22⋊C8—131no—
326C2×C22⋊C8—131no—
327C2×C22⋊C8—131no—
328C2×C4×C8—131no—
329C2×C4×C8—131no—
330C2×C4×C8—131no—
331C2×C4×C8—131no—
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334C2×C4×C8—131no—
335C2×C4×C8—131no—
336#391—131no—
337#390—131no—
338#388—131no—
339#388—131no—
340#388—131no—
341#388#26111yescharacteristic
342#382—131no—
343C4×C22⋊C4—131no—
344C4×C22⋊C4—131no—
345C4×C22⋊C4—131no—
346C4×C22⋊C4—131no—
347C43—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336—131no—
355#336—131no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13C2×C4×D411yescharacteristic
364C22×C13C4×#4111yescharacteristic
365C22×C13C4×#4111yescharacteristic
366C22×C13C23×C811yescharacteristic
367C22×C13C2×#13111yescharacteristic
368C22×C13C2×#13111yescharacteristic
369C22×C13C2×#13111yescharacteristic
370C2×D13—22no—
371C2×D13—22no—
372C2×D13—22no—
373C2×D13—41no—
374C2×D13—41no—
375C2×D13—41no—
376C2×D13—41no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—22no—
381C4×C13—41no—
382C4×C13—41no—
383Dic13—22no—
384Dic13—22no—
385Dic13—22no—
386Dic13—41no—
387Dic13—41no—
388Dic13C8×D414yes—
389Dic13C2×#12411yescharacteristic
390Dic13#52911yescharacteristic
391Dic13#52911yescharacteristic
392Dic13#53211yescharacteristic
393C22×Q8—131no—
394C22×D4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405C22×C8—262no—
406C22×C8—262no—
407C22×C8—262no—
408C22×C8—262no—
409C22×C8—262no—
410C22×C8—262no—
411#124—138no—
412C4×Q8—262no—
413C4×Q8—262no—
414C4×D4—262no—
415C4×D4—262no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4C2×#26111yescharacteristic
420C2×C22⋊C4—131no—
421C2×C22⋊C4—131no—
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4C2×#26111yescharacteristic
428C2×C22⋊C4C2×#26111yescharacteristic
429C2×C22⋊C4C2×#26111yescharacteristic
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—131no—
438C2×C42C2×#26111yescharacteristic
439C4⋊C8—262no—
440C4⋊C8—262no—
441C4⋊C8—262no—
442C4⋊C8—262no—
443C22⋊C8—262no—
444C22⋊C8—262no—
445C22⋊C8—262no—
446C22⋊C8—262no—
447C22⋊C8—262no—
448C22⋊C8—262no—
449C4×C8—134no—
450C4×C8—262no—
451C4×C8—262no—
452C4×C8—262no—
453C4×C8—262no—
454C4×C8—262no—
455C4×C8—262no—
456C4×C8—262no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462#95—131no—
463#95C2×#26111yescharacteristic
464#95C2×#26111yescharacteristic
465C2×C13—42no—
466C2×C13C4×#12411yescharacteristic
467C2×C13C2×C8×D411yescharacteristic
468C2×C13#293111yescharacteristic
469C2×C13C8×#4111yescharacteristic
470C2×C13C8×#4111yescharacteristic
471C2×C13#296611yescharacteristic
472C2×C13#296611yescharacteristic
473D13—42no—
474C24—131no—
475C24C22×#26111yescharacteristic
476C2×Q8—134no—
477C2×Q8—262no—
478C2×Q8—262no—
479C2×D4—134no—
480C2×D4—262no—
481C2×D4—262no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4C22×#26111yescharacteristic
502C22×C4C22×#26111yescharacteristic
503C22×C4C22×#26111yescharacteristic
504C22×C4C22×#26111yescharacteristic
505C22×C4C22×#26111yescharacteristic
506C22×C4C22×#26111yescharacteristic
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—132no—
511C2×C8—132no—
512C2×C8—132no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
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—524no—
532C2×C8—524no—
533C4⋊C4—22no—
534C4⋊C4—262no—
535C4⋊C4—262no—
536C4⋊C4—262no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—134no—
540C22⋊C4—134no—
541C22⋊C4—134no—
542C22⋊C4—262no—
543C22⋊C4—262no—
544C22⋊C4—262no—
545C22⋊C4—262no—
546C22⋊C4D13⋊C814yescomplemented
547C42—22no—
548C42—134no—
549C42—132no—
550C42—132no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42—261no—
555C42—261no—
556C42—261no—
557C42—261no—
558C42—261no—
559C42—262no—
560C42—262no—
561C13C8×#12411yescharacteristic, complemented, Sylow
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—132no—
569C23—261no—
570C23—261no—
571C23—261no—
572C23—261no—
573C23—261no—
574C23—261no—
575C23C2×D13⋊C812yes—
576C23C23×#26111yescharacteristic
577Q8—268no—
578D4—268no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—132no—
594C2×C4—131no—
595C2×C4—131no—
596C2×C4—132no—
597C2×C4—132no—
598C2×C4—131no—
599C2×C4—131no—
600C2×C4—131no—
601C2×C4—131no—
602C2×C4—132no—
603C2×C4—132no—
604C2×C4—132no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—261no—
614C2×C4—261no—
615C2×C4—261no—
616C2×C4—261no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4C2×D13⋊C812yes—
626C2×C4C2×D13⋊C812yes—
627C2×C4#8823812yes—
628C2×C4D4×#26112yes—
629C8—134no—
630C8—262no—
631C8—262no—
632C8—262no—
633C8—521no—
634C8—521no—
635C8—521no—
636C8—521no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—262no—
645C22—262no—
646C22—262no—
647C22—521no—
648C22—521no—
649C22—521no—
650C22—521no—
651C22C22×D13⋊C811yescharacteristic
652C22C2×#8823811yescharacteristic
653C22C2×D4×#26111yescharacteristic
654C22D13⋊#13111yescharacteristic
655C22D13⋊#13111yescharacteristic
656C22#41×#26111yescharacteristic
657C22#41×#26111yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—134no—
665C4—131no—
666C4—131no—
667C4—131no—
668C4—131no—
669C4—262no—
670C4—262no—
671C4—262no—
672C4—521no—
673C4—521no—
674C2—42no—
675C2—522no—
676C2#124×#26111yescharacteristic
677C2D4×D13⋊C811yescharacteristic
678C2#1313155911yescharacteristic
679C2#1313164011yescharacteristic
680C2#1313164111yescharacteristic
681C2#1313165111yescharacteristic
682C2#1313165411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C23×C8
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×Dic13C24
hypercenter#388#261
hypocenterC13C8×#124
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#11719074C2semidirect
3. #13131007C2semidirect
5. #13130908C2semidirect
6. #13130907C2semidirect
7. #13130906C2semidirect
8. #13130905C2semidirect
9. #13130752C2semidirect
10. #13130570C2semidirect
11. #13130570C2semidirect
12. C22⋊C4×#1057C2semidirect
13. C22⋊C4×#1057C2semidirect
14. C42×#1057C2semidirect
104. #88139C8semidirect
166. C2×Dic26C2×C8semidirect
196. C13×C22⋊C4C2×C8semidirect
199. C22⋊Dic13C2×C8semidirect
203. #6103C2×C8semidirect
204. #6103C2×C8semidirect
218. C4×Dic13C2×C8semidirect
310. #1057#124semidirect
546. C22⋊C4D13⋊C8semidirect
561. C13C8×#124semidirect

Maximal subgroups

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

subgroupindex
C2×#117190742
C2×#117190632
#131310072
#131309592
#131309082
#131309072
#131309062
#131309052
#131307522
#131305702
C22⋊C4×#10572
C42×#10572
#131173772
C8×#12413