Finite Group Databasebeta

← #15899123

Subgroups — #15899123

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×#11718752C211yesmaximal, characteristic, complemented
3#13117518C211yesmaximal, characteristic
4#13116171C211yesmaximal, characteristic, complemented
5#13116161C211yesmaximal, characteristic, complemented
6#13115984C211yesmaximal, characteristic, complemented
7#13115974C211yesmaximal, characteristic, complemented
8#13115794C211yesmaximal, characteristic, complemented
9#13115789C211yesmaximal, characteristic, complemented
10#13115148C211yesmaximal, characteristic
11#13115143C211yesmaximal, characteristic
12#13115035C211yesmaximal, characteristic
13#13115024C211yesmaximal, characteristic
14#13114820C211yesmaximal, characteristic
15C2×C13×#544C211yesmaximal, characteristic
16C13×#544—24no—
17C13×#544—24no—
18C2×C13×C4⋊Q8—21no—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#125—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#125C2211yescharacteristic
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C13×#117C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C2×C4×Dic26C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34#11718752—24no—
35#11718724—24no—
36#11718639—21no—
37#11718633—21no—
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718606—21no—
47#11718605—21no—
48C4×C4⋊Dic13C2211yescharacteristic
49#11718590C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13—21no—
64C22×Q8×C13—21no—
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C22×Dic26C2311yescharacteristic
68C13×C4⋊Q8—28no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×C4⋊Q8—22no—
72C13×C4⋊Q8D414yes—
73C13×#125—28no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125D414yes—
78C13×C22⋊Q8—28no—
79C13×C22⋊Q8—28no—
80C13×#117—22no—
81C13×#117—22no—
82C13×#117—22no—
83C13×#117—22no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C4⋊Dic13C2311yescharacteristic
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110#88178—22no—
111#88178Q814yescomplemented
112C2×#6101—21no—
113C2×#6101—21no—
114C2×#6101—21no—
115C2×C4×Dic13—21no—
116C2×C4×Dic13—21no—
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C4×Dic26—22no—
122C4×Dic26—22no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128C22⋊#1055—22no—
129C22⋊#1055—22no—
130#88050—22no—
131#88050—22no—
132#88050—22no—
133#88050—22no—
134#88048—22no—
135#88047—22no—
136#88047—22no—
137#88047—22no—
138C4⋊#1055—22no—
139C4⋊#1055—22no—
140#24311—131nomaximal, Sylow
141C24×C13C2×D411yescharacteristic
142C2×Q8×C13—24no—
143C2×Q8×C13—24no—
144C2×Q8×C13—81no—
145C2×Q8×C13—81no—
146C2×Q8×C13—81no—
147C2×Q8×C13—81no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—24no—
157C22×C4×C13—81no—
158C22×C4×C13—81no—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×Q812yes—
165C22×C4×C13#4112yes—
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26C2×Q812yes—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—24no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4C2×D412yes—
191C13×C4⋊C4C2×D412yes—
192C13×C4⋊C4C2×D412yes—
193C13×C4⋊C4C2×D412yes—
194C13×C22⋊C4—24no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C42×C13—24no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13C2×D412yes—
201C42×C13C2×D412yes—
202C22⋊Dic13—24no—
203C22⋊Dic13—81no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13C2×Q812yes—
210#6101—24no—
211#6101—42no—
212#6101—81no—
213C4×Dic13—42no—
214C4×Dic13—81no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#544D1311yescharacteristic
228C2×#479—131no—
229C2×#477—131no—
230#2323—131no—
231#2059—131no—
232#2057—131no—
233#2026—131no—
234#2024—131no—
235#1989—131no—
236#1988—131no—
237#1873—131no—
238#1872—131no—
239#1854—131no—
240#1852—131no—
241#1798—131no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13C22⋊Q812yes—
249C23×C13C22×D411yescharacteristic
250Q8×C13—84no—
251Q8×C13—84no—
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—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—84no—
281C2×C4×C13#12012yes—
282C2×C4×C13#12012yes—
283C2×C4×C13C22⋊Q812yes—
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×Q811yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C132−1+411yescharacteristic
289C2×C4×C132−1+411yescharacteristic
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302Dic26—22no—
303Dic26—22no—
304Dic26—41no—
305Dic26—41no—
306#1055—41no—
307#1055—41no—
308#1055—41no—
309#1055—41no—
310#544—24no—
311#544—24no—
312C2×C4⋊Q8—21no—
313C2×C4⋊Q8C2×D1311yescharacteristic
314C2×C4⋊Q8C2×D1311yescharacteristic
315C2×#125—21no—
316C2×#125C2×D1311yescharacteristic
317C2×#125C2×D1311yescharacteristic
318C2×C22⋊Q8—21no—
319C2×C22⋊Q8—21no—
320C2×C22⋊Q8—131no—
321C2×C4×Q8—131no—
322C2×#117C2×D1311yescharacteristic
323C2×#117C2×D1311yescharacteristic
324C22×C4⋊C4C2×D1311yescharacteristic
325#479—264no—
326#477—264no—
327C2×#107—131no—
328C2×#107—131no—
329C2×#107—131no—
330C2×#106—131no—
331C2×C4⋊C8—131no—
332C2×C4⋊C8—131no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×C22⋊C8—131no—
338C2×C22⋊C8—131no—
339#391—131no—
340#389—131no—
341#389—261no—
342#388—261no—
343#388—261no—
344#387—261no—
345#380—131no—
346C4×C4⋊C4—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#336—131no—
356#336—131no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13C2×#12011yescharacteristic
365C22×C13C2×C22⋊Q811yescharacteristic
366C22×C13#53611yescharacteristic
367C22×C13#57611yescharacteristic
368C22×C13#57711yescharacteristic
369C22×C13#57811yescharacteristic
370C22×C13#57811yescharacteristic
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—41no—
375C4×C13—42no—
376C4×C13—41no—
377C4×C13—42no—
378C4×C13—42no—
379C4×C13—42no—
380C4×C13#54811yescharacteristic
381C4×C13#54811yescharacteristic
382C4×C13D4×Q811yescharacteristic
383C4×C13D4×Q811yescharacteristic
384Dic13—42no—
385Dic13—42no—
386Dic13—81no—
387Dic13—81no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—131no—
391C23×C4—21no—
392C23×C4C22×D1311yescharacteristic
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C4⋊Q8—28no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—22no—
401C4⋊Q8C22⋊D1314yes—
402#125—28no—
403#125—22no—
404#125—22no—
405#125—22no—
406#125C22⋊D1314yes—
407C22⋊Q8—28no—
408C22⋊Q8—28no—
409C22⋊Q8—134no—
410C22⋊Q8—262no—
411C4×Q8—262no—
412C4×Q8—262no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—131no—
427C2×C4⋊C4—131no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4C22⋊D1311yescharacteristic
433C2×C4⋊C4C22⋊D1311yescharacteristic
434C2×C4⋊C4C22×D1311yescharacteristic
435C2×C4⋊C4C22×D1311yescharacteristic
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4C22⋊D1311yescharacteristic
442C2×C22⋊C4C22⋊D1311yescharacteristic
443C2×C42—21no—
444C2×C42—261no—
445C2×C42—261no—
446C2×C42C22×D1311yescharacteristic
447C2×C42C22×D1311yescharacteristic
448#107—262no—
449#107—262no—
450#107—262no—
451#106—262no—
452C4⋊C8—262no—
453C4⋊C8—262no—
454#103—262no—
455#103—262no—
456#103—262no—
457#103—262no—
458C22⋊C8—262no—
459C22⋊C8—262no—
460#95—261no—
461#95—261no—
462#95—261no—
463#95—261no—
464#95—261no—
465C2×C13—42no—
466C2×C13#240911yescharacteristic
467C2×C13#301111yescharacteristic
468C2×C13#301211yescharacteristic
469C2×C13#308211yescharacteristic
470C2×C13#308311yescharacteristic
471C2×C13#324211yescharacteristic
472C2×C13#324311yescharacteristic
473C24C2×C22⋊D1311yescharacteristic
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—81no—
477C2×Q8—81no—
478C2×Q8—81no—
479C2×Q8—81no—
480C2×Q8—132no—
481C2×Q8—261no—
482C2×Q8—261no—
483C2×Q8—261no—
484C2×Q8—261no—
485C2×Q8—261no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4Q8×D1312yes—
502C22×C4#613112yes—
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C23×D1311yescharacteristic
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—132no—
535C4⋊C4—264no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—522no—
542C4⋊C4—1041no—
543C4⋊C4C2×C22⋊D1312yes—
544C4⋊C4C2×C22⋊D1312yes—
545C4⋊C4C2×C22⋊D1312yes—
546C4⋊C4C2×C22⋊D1312yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—264no—
551C22⋊C4—1041no—
552C42—24no—
553C42—21no—
554C42—21no—
555C42—522no—
556C42—1041no—
557C42C2×C22⋊D1312yes—
558C42C2×C22⋊D1312yes—
559C13#2431111yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#8820012yes—
567C23C22×C22⋊D1311yescharacteristic
568Q8—84no—
569Q8—84no—
570Q8—262no—
571Q8—262no—
572Q8—521no—
573Q8—521no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4#8820012yes—
616C2×C4#8820712yes—
617C2×C4#8820712yes—
618C2×C4C2×Q8×D1311yescharacteristic
619C2×C4C2×#613111yescharacteristic
620C2×C4#8825411yescharacteristic
621C2×C4#8825411yescharacteristic
622C2×C4C22×C22⋊D1311yescharacteristic
623C2×C4C22×C22⋊D1311yescharacteristic
624C8—521no—
625C8—521no—
626C8—521no—
627C8—521no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#8820011yescharacteristic
636C22#1171952111yescharacteristic
637C22#1171954011yescharacteristic
638C22#1171954111yescharacteristic
639C22#1171954311yescharacteristic
640C22#1171954311yescharacteristic
641C22C2×#8820711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—522no—
652C4—522no—
653C4—1041no—
654C4—1041no—
655C4Q8×C22⋊D1311yescharacteristic
656C4Q8×C22⋊D1311yescharacteristic
657C4#1171952211yescharacteristic
658C4#1171952211yescharacteristic
659C2—42no—
660C2#1311819511yescharacteristic
661C2#1312413111yescharacteristic
662C2#1312414011yescharacteristic
663C2#1312467211yescharacteristic
664C2#1312468311yescharacteristic
665C2#1312610411yescharacteristic
666C2#1312611911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#24311
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
2. C2×#11718752C2semidirect
4. #13116171C2semidirect
5. #13116161C2semidirect
6. #13115984C2semidirect
7. #13115974C2semidirect
8. #13115794C2semidirect
9. #13115789C2semidirect
111. #88178Q8semidirect
559. C13#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×#117187522
#131175182
#131161712
#131161612
#131159842
#131159742
#131157942
#131157892
#131151482
#131151432
#131150352
#131150242
#131148202
C2×C13×#5442
#2431113