Finite Group Databasebeta

← #15913214

Subgroups — #15913214

Order 3328.

860 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718752C211yesmaximal, characteristic, complemented
2C2×#11718672C211yesmaximal, characteristic
3#13119745C211yesmaximal, characteristic
4#13116267C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13116039C211yesmaximal, characteristic, complemented
7#13116032C211yesmaximal, characteristic, complemented
8#13115810C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115267C211yesmaximal, characteristic, complemented
11#13115257C211yesmaximal, characteristic, complemented
12#13114867C211yesmaximal, characteristic, complemented
13#13114863C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2547C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#124—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#397—21no—
25C13×#397—21no—
26C13×#391—21no—
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32#11718883—21no—
33#11718873C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718752—24no—
38#11718672—24no—
39#11718641—21no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718605—21no—
49#11718605—21no—
50#11718597C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D4×C13D411yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C22×Dic26C2311yescharacteristic
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C13×#124—44no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C42×C13—21no—
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92#88178—22no—
93#88178—22no—
94#88178—41no—
95#88178—41no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099—41no—
103C22×#1055—22no—
104C22×#1055—22no—
105C22×#1055—41no—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C4×Dic26—22no—
111C4×Dic26—22no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122C22⋊#1055—22no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88048—41no—
128#88047—22no—
129#88047—22no—
130#88047—41no—
131C4⋊#1055D414yes—
132#88043—22no—
133#25352—131nomaximal, Sylow
134C24×C13C2×D411yescharacteristic
135C24×C13C2×D411yescharacteristic
136C2×Q8×C13—42no—
137C2×Q8×C13—42no—
138C2×Q8×C13—42no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—41no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
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—21no—
157C22×C4×C13—21no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2411yescharacteristic
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26#4112yes—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—42no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—42no—
186C13×C22⋊C4—42no—
187C13×C22⋊C4—42no—
188C13×C22⋊C4—42no—
189C42×C13—42no—
190C42×C13C2×D412yes—
191C42×C13#4112yes—
192C22⋊Dic13—42no—
193C22⋊Dic13—42no—
194C22⋊Dic13—42no—
195C22⋊Dic13—42no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202#6101—42no—
203#6101—42no—
204#6101—42no—
205C4×Dic13—42no—
206#6099—44no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—44no—
217C2×#1055C2×D412yes—
218C2×#1055C2×D412yes—
219C2×#1055#4112yes—
220C2×#477—131no—
221C2×#435—131no—
222#2547D1311yescharacteristic
223#2536—131no—
224#2076—131no—
225#2075—131no—
226#2036—131no—
227#2035—131no—
228#1993—131no—
229#1949—131no—
230#1894—131no—
231#1892—131no—
232#1809—131no—
233#1808—131no—
234#1763—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13AGL(1,ℤ/8)12yes—
249C23×C13C22×D411yescharacteristic
250Q8×C13—84no—
251D4×C13—44no—
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—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
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—41no—
281C2×C4×C13—41no—
282C2×C4×C13#12112yes—
283C2×C4×C13#12112yes—
284C2×C4×C13C22×D411yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C13H(5,𝔽2)11yescharacteristic
289C2×C4×C132−1+411yescharacteristic
290C2×Dic13—22no—
291C2×Dic13—41no—
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—22no—
307#1055—22no—
308#1055—22no—
309#1055—41no—
310C22×M16—131no—
311C23×C8—131no—
312C2×C4⋊Q8C2×D1311yescharacteristic
313C2×#124—21no—
314C2×C22⋊Q8—131no—
315C2×C22⋊Q8—131no—
316C2×C4×Q8—131no—
317C2×C4×D4C2×D1311yescharacteristic
318#477—264no—
319#435—264no—
320C2×#107—131no—
321C2×#107—131no—
322C2×#107—131no—
323C2×#106—131no—
324C2×C4⋊C8—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C2×C22⋊C8—131no—
330C2×C22⋊C8—131no—
331C2×#97—131no—
332#398—261no—
333#397—21no—
334#397—21no—
335#394—261no—
336#391—21no—
337#388—261no—
338#388—261no—
339#382—131no—
340#380—131no—
341#380—131no—
342#380C2×D1311yescharacteristic
343#380C2×D1311yescharacteristic
344#380C2×D1311yescharacteristic
345#380C2×D1311yescharacteristic
346C4×C4⋊C4C2×D1311yescharacteristic
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13C2×#12111yescharacteristic
370C22×C13#54611yescharacteristic
371C22×C13#54711yescharacteristic
372C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C13#57511yescharacteristic
374C22×C13#57811yescharacteristic
375C22×C13#57811yescharacteristic
376C4×C13—22no—
377C4×C13—22no—
378C4×C13—41no—
379C4×C13—41no—
380C4×C13—81no—
381C4×C13—81no—
382C4×C13—81no—
383C4×C13—81no—
384C4×C13#52911yescharacteristic
385C4×C13#54211yescharacteristic
386C4×C13#54611yescharacteristic
387C4×C13#54811yescharacteristic
388Dic13—42no—
389Dic13—81no—
390Dic13—81no—
391Dic13—81no—
392C22×Q8—21no—
393C22×Q8—131no—
394C22×D4C22⋊D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C23×C4C22×D1311yescharacteristic
397C2×M16—262no—
398C2×M16—262no—
399C2×M16—521no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—262no—
405C22×C8—262no—
406C22×C8—521no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409#124—44no—
410C22⋊Q8—262no—
411C22⋊Q8—262no—
412C22⋊Q8—521no—
413C22⋊Q8—521no—
414C4×Q8—262no—
415C4×Q8—262no—
416C4×D4—22no—
417C4×D4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4C22⋊D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C4⋊C4C22×D1311yescharacteristic
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4C22⋊D1311yescharacteristic
439C2×C22⋊C4C22⋊D1311yescharacteristic
440C2×C42—21no—
441C2×C42—261no—
442C2×C42C22×D1311yescharacteristic
443#107—262no—
444#107—262no—
445#107—521no—
446#106—521no—
447C4⋊C8—134no—
448#103—262no—
449#103—262no—
450#103—262no—
451#103—262no—
452C22⋊C8—262no—
453C22⋊C8—262no—
454#97—262no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—261no—
461#95—261no—
462#95—261no—
463#95—261no—
464C2×C13—42no—
465C2×C13—81no—
466C2×C13#242711yescharacteristic
467C2×C13#305511yescharacteristic
468C2×C13#305911yescharacteristic
469C2×C13#330811yescharacteristic
470C2×C13#331311yescharacteristic
471C2×C13#334311yescharacteristic
472C2×C13#334911yescharacteristic
473C24C2×C22⋊D1311yescharacteristic
474C24C2×C22⋊D1311yescharacteristic
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—132no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×Q8—261no—
483C2×Q8—261no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C23×D1311yescharacteristic
512M16—524no—
513C2×C8—132no—
514C2×C8—132no—
515C2×C8—132no—
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—524no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—522no—
543C4⋊C4—522no—
544C4⋊C4—522no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—522no—
552C22⋊C4—522no—
553C22⋊C4—522no—
554C22⋊C4—522no—
555C42—42no—
556C42—522no—
557C42D4×D1312yes—
558C42#612912yes—
559C13#2535211yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#8818612yes—
574C23C22×C22⋊D1311yescharacteristic
575Q8—84no—
576Q8—262no—
577Q8—262no—
578Q8—521no—
579Q8—521no—
580D4—44no—
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—41no—
592C2×C4—41no—
593C2×C4—41no—
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—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—262no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4#8819312yes—
624C2×C4#8819312yes—
625C2×C4C2×D4×D1311yescharacteristic
626C2×C4C2×#612911yescharacteristic
627C2×C4#41×D1311yescharacteristic
628C2×C4#41×D1311yescharacteristic
629C2×C4#8825611yescharacteristic
630C2×C4#8825711yescharacteristic
631C8—262no—
632C8—262no—
633C8—262no—
634C8—521no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#8818611yescharacteristic
650C22C2×#8819311yescharacteristic
651C22#1171952711yescharacteristic
652C22#1171952911yescharacteristic
653C22#1171953411yescharacteristic
654C22#1171954311yescharacteristic
655C22#1171954311yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—522no—
665C4—1041no—
666C4—1041no—
667C4—1041no—
668C4#1171938111yescharacteristic
669C4#1171938211yescharacteristic
670C4#1171938511yescharacteristic
671C4#1171938711yescharacteristic
672C2—42no—
673C2—81no—
674C2#1311841611yescharacteristic
675C2#1312445111yescharacteristic
676C2#1312448811yescharacteristic
677C2#1312682111yescharacteristic
678C2#1312689611yescharacteristic
679C2#1312727011yescharacteristic
680C2#1312736011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2547C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2547D13
hypocenterC13#25352
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#11718752C2semidirect
4. #13116267C2semidirect
5. #13116262C2semidirect
6. #13116039C2semidirect
7. #13116032C2semidirect
8. #13115810C2semidirect
9. #13115604C2semidirect
10. #13115267C2semidirect
11. #13115257C2semidirect
12. #13114867C2semidirect
13. #13114863C2semidirect
14. #13114669C2semidirect
559. C13#25352semidirect

Maximal subgroups

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

subgroupindex
C2×#117187522
C2×#117186722
#131197452
#131162672
#131162622
#131160392
#131160322
#131158102
#131156042
#131152672
#131152572
#131148672
#131148632
#131146692
C13×#25472
#2535213