Finite Group Databasebeta

← #15777915

Subgroups — #15777915

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718901C211yesmaximal, characteristic
2#13123281C211yesmaximal, characteristic
3#13112966C214yesmaximal, complemented
4C2×C13×#413C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C22×C13×M16—21no—
7C2×#88180—21no—
8C22×#6099C411yescharacteristic, complemented
9C22×#6099C411yescharacteristic, complemented
10C13×#413—21no—
11C13×#413—21no—
12C13×#413C412yescomplemented
13C13×#413C2212yes—
14C2×C13×#101C412yescomplemented
15C2×C13×#100—21no—
16#11718901—21no—
17#11718901—21no—
18#11718901C412yes—
19#11718901C2212yes—
20#11718895—21no—
21#11718895—21no—
22#11718895C412yescomplemented
23#11718895C2212yes—
24C2×#88074—21no—
25C2×#88074C412yes—
26#11718868—21no—
27#11718868—21no—
28C2×C13×#41—41no—
29C2×C13×#41—41no—
30C2×C13×#41—41no—
31C2×C13×#41—41no—
32C2×C13×#41C2×C411yescharacteristic
33C2×C13×#41C2×C411yescharacteristic
34C2×C13×#41C2×C411yescharacteristic
35C2×C13×#41D411yescharacteristic
36C2×C13×#41D411yescharacteristic
37C2×C13×#41D411yescharacteristic
38C2×C13×#41Q811yescharacteristic
39C2×C13×#41C2311yescharacteristic
40C22×Q8×C13C2×C411yescharacteristic
41C22×D4×C13C2×C411yescharacteristic
42C22×D4×C13D411yescharacteristic
43C22×D4×C13Q811yescharacteristic
44C23×C4×C13C2×C411yescharacteristic
45C23×C4×C13D411yescharacteristic
46C23×C4×C13D411yescharacteristic
47C2×C13×M16—22no—
48C2×C13×M16—22no—
49C2×C13×M16—22no—
50C2×C13×M16—41no—
51C2×C13×M16—41no—
52C2×C13×M16—41no—
53C22×C8×C13—41no—
54C2×C22⋊Dic13—22no—
55#88180—22no—
56#88180—22no—
57#88180—41no—
58#88180—41no—
59C2×C4⋊Dic13—41no—
60C2×C4×Dic13—41no—
61C2×#6099—21no—
62C2×#6099—21no—
63C2×#6099—21no—
64C2×#6099—41no—
65C2×#6099—41no—
66C2×#6099—41no—
67C2×#6099—41no—
68C2×#6099C2×C412yescomplemented
69C22×#1055—21no—
70C22×#1055C2×C412yescomplemented
71C13×#101—22no—
72C13×#101C2×C414yescomplemented
73C13×#100—22no—
74C13×#100—22no—
75#88074—22no—
76#88074—22no—
77#88074—22no—
78#88074C2×C414yes—
79C22⋊#1055—22no—
80C22⋊#1055—22no—
81C22⋊#1055—22no—
82C22⋊#1055—22no—
83#12589—131nomaximal, Sylow
84C24×C13C22⋊C411yescharacteristic
85C24×C13C4⋊C411yescharacteristic
86C24×C13C4⋊C411yescharacteristic
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—41no—
94C13×#41—41no—
95C13×#41—41no—
96C13×#41—41no—
97C13×#41—41no—
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41—41no—
102C13×#41—41no—
103C2×Q8×C13—41no—
104C2×Q8×C13—41no—
105C2×Q8×C13C4211yescharacteristic
106C2×Q8×C13C22⋊C411yescharacteristic
107C2×Q8×C13C4⋊C411yescharacteristic
108C2×Q8×C13C22×C411yescharacteristic
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13C4211yescharacteristic
116C2×D4×C13C22⋊C411yescharacteristic
117C2×D4×C13C22⋊C411yescharacteristic
118C2×D4×C13C22⋊C411yescharacteristic
119C2×D4×C13C4⋊C411yescharacteristic
120C2×D4×C13C4⋊C411yescharacteristic
121C2×D4×C13C4⋊C411yescharacteristic
122C2×D4×C13C4⋊C411yescharacteristic
123C2×D4×C13C4⋊C411yescharacteristic
124C2×D4×C13C22×C411yescharacteristic
125C2×D4×C13C2×D411yescharacteristic
126C2×D4×C13C2×Q811yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C4211yescharacteristic
140C22×C4×C13C4211yescharacteristic
141C22×C4×C13C22⋊C411yescharacteristic
142C22×C4×C13C22⋊C411yescharacteristic
143C22×C4×C13C22⋊C411yescharacteristic
144C22×C4×C13C22⋊C411yescharacteristic
145C22×C4×C13C22⋊C411yescharacteristic
146C22×C4×C13C22⋊C411yescharacteristic
147C22×C4×C13C22⋊C411yescharacteristic
148C22×C4×C13C4⋊C411yescharacteristic
149C22×C4×C13C4⋊C411yescharacteristic
150C22×C4×C13C4⋊C411yescharacteristic
151C22×C4×C13C4⋊C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×Dic13—42no—
156C13×M16—24no—
157C13×M16—42no—
158C13×M16—42no—
159C13×M16—42no—
160C2×C8×C13—42no—
161C2×C8×C13—42no—
162C2×C8×C13—42no—
163C22⋊Dic13—24no—
164C22⋊Dic13—42no—
165C4⋊Dic13—42no—
166C4⋊Dic13—42no—
167C4×Dic13—42no—
168C4×Dic13—42no—
169#6099—42no—
170#6099—41no—
171#6099—41no—
172#6099—41no—
173#6099—41no—
174#6099—42no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—42no—
178C2×#1055—42no—
179C2×#413D1311yescharacteristic
180C2×#410—131no—
181#2879—131no—
182#1395—134no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—21no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—81no—
190C23×C13—81no—
191C23×C13—81no—
192C23×C13#9511yescharacteristic
193C23×C13#9511yescharacteristic
194C23×C13#9511yescharacteristic
195C23×C13#9511yescharacteristic
196C23×C13C2×C22⋊C411yescharacteristic
197C23×C13C2×C4⋊C411yescharacteristic
198C23×C13C2×C4⋊C411yescharacteristic
199Q8×C13—41no—
200Q8×C13—41no—
201Q8×C13—41no—
202Q8×C13—41no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—41no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—41no—
211D4×C13—41no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—41no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13#9511yescharacteristic
246C2×C4×C13#9511yescharacteristic
247C2×C4×C13#9511yescharacteristic
248C2×C4×C13#9511yescharacteristic
249C2×C4×C13#9911yescharacteristic
250C2×C4×C13#9911yescharacteristic
251C2×C4×C13#9911yescharacteristic
252C2×C4×C13#9911yescharacteristic
253C2×C4×C13C2×C4211yescharacteristic
254C2×C4×C13C2×C22⋊C411yescharacteristic
255C2×C4×C13C2×C22⋊C411yescharacteristic
256C2×C4×C13C2×C4⋊C411yescharacteristic
257C2×Dic13—44no—
258C2×Dic13—84no—
259C8×C13—44no—
260#1055—42no—
261#1055—42no—
262C22×#41C2×D1311yescharacteristic
263C22×M16—21no—
264C22×M16—131no—
265C22×M16—131no—
266C2×#117—261no—
267#413—21no—
268#413—21no—
269#413Dic1312yescomplemented
270#413C2×D1312yes—
271C2×#101Dic1312yescomplemented
272C2×#100—21no—
273#410—132no—
274#410—132no—
275#410—261no—
276#410—261no—
277C2×#99—132no—
278C2×#99—261no—
279#408—132no—
280#408—132no—
281#408—261no—
282#408—261no—
283#407—261no—
284#407—261no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—81no—
304C22×C13#34211yescharacteristic
305C22×C13#34211yescharacteristic
306C22×C13C2×#9511yescharacteristic
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13#34211yescharacteristic
314C4×C13#34211yescharacteristic
315C4×C13C2×#9911yescharacteristic
316C4×C13C2×#9911yescharacteristic
317Dic13—84no—
318C2×#41—41no—
319C2×#41—41no—
320C2×#41—41no—
321C2×#41—41no—
322C2×#41Dic2611yescharacteristic
323C2×#41C4×D1311yescharacteristic
324C2×#41C4×D1311yescharacteristic
325C2×#41D5211yescharacteristic
326C2×#41C2×Dic1311yescharacteristic
327C2×#41C22⋊D1311yescharacteristic
328C2×#41C22⋊D1311yescharacteristic
329C2×#41C22×D1311yescharacteristic
330C22×Q8C2×Dic1311yescharacteristic
331C22×D4Dic2611yescharacteristic
332C22×D4C4×D1311yescharacteristic
333C22×D4C22⋊D1311yescharacteristic
334C23×C4C4×D1311yescharacteristic
335C23×C4D5211yescharacteristic
336C23×C4C22⋊D1311yescharacteristic
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—41no—
341C2×M16—41no—
342C2×M16—41no—
343C2×M16—132no—
344C2×M16—261no—
345C2×M16—261no—
346C2×M16—261no—
347C2×M16—521no—
348C2×M16—521no—
349C2×M16—521no—
350C2×M16—521no—
351C22×C8—41no—
352C22×C8—132no—
353C22×C8—261no—
354#117—262no—
355#117—262no—
356#117—521no—
357#117—521no—
358C2×C4⋊C4—521no—
359C2×C22⋊C4—262no—
360C2×C42—521no—
361#101—22no—
362#101C2×Dic1314yescomplemented
363#100—22no—
364#100—22no—
365#99—134no—
366#99—262no—
367#99—262no—
368#99—262no—
369C22⋊C8—262no—
370C22⋊C8—262no—
371C22⋊C8—262no—
372C22⋊C8—262no—
373C2×C13—21no—
374C2×C13—21no—
375C2×C13—21no—
376C2×C13—41no—
377C2×C13—41no—
378C2×C13—41no—
379C2×C13—41no—
380C2×C13—41no—
381C2×C13—41no—
382C2×C13C2×#34211yescharacteristic
383C24#610111yescharacteristic
384C24#610111yescharacteristic
385C24#610311yescharacteristic
386#41—41no—
387#41—41no—
388#41—41no—
389#41—41no—
390#41—41no—
391#41—41no—
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8C4×Dic1311yescharacteristic
405C2×Q8C4⋊Dic1311yescharacteristic
406C2×Q8C22⋊Dic1311yescharacteristic
407C2×Q8C22×Dic1311yescharacteristic
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4C4×Dic1311yescharacteristic
415C2×D4#610111yescharacteristic
416C2×D4#610111yescharacteristic
417C2×D4#610111yescharacteristic
418C2×D4#610111yescharacteristic
419C2×D4C4⋊Dic1311yescharacteristic
420C2×D4#610311yescharacteristic
421C2×D4#610311yescharacteristic
422C2×D4C22⋊Dic1311yescharacteristic
423C2×D4C2×Dic2611yescharacteristic
424C2×D4C2×C4×D1311yescharacteristic
425C2×D4C2×C22⋊D1311yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—522no—
439C22×C4C4×Dic1311yescharacteristic
440C22×C4C4×Dic1311yescharacteristic
441C22×C4#610111yescharacteristic
442C22×C4#610111yescharacteristic
443C22×C4C4⋊Dic1311yescharacteristic
444C22×C4C4⋊Dic1311yescharacteristic
445C22×C4#610311yescharacteristic
446C22×C4#610311yescharacteristic
447C22×C4#610311yescharacteristic
448C22×C4#610311yescharacteristic
449C22×C4#610311yescharacteristic
450C22×C4C22⋊Dic1311yescharacteristic
451C22×C4C22⋊Dic1311yescharacteristic
452C22×C4C2×C4×D1311yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455M16—24no—
456M16—42no—
457M16—42no—
458M16—42no—
459M16—522no—
460M16—521no—
461M16—521no—
462M16—521no—
463M16—521no—
464M16—522no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8—42no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—522no—
471C2×C8—522no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C22⋊C4—264no—
475C22⋊C4—522no—
476C42—522no—
477C42—522no—
478C13#1258911yescharacteristic, complemented, Sylow
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—81no—
486C23—81no—
487C23—81no—
488C23#8807111yescharacteristic
489C23#8807111yescharacteristic
490C23#8807111yescharacteristic
491C23#8807111yescharacteristic
492C23C2×#610111yescharacteristic
493C23C2×#610111yescharacteristic
494C23C2×#610311yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—524no—
542C2×C4—1044no—
543C2×C4#8804611yescharacteristic
544C2×C4#8804611yescharacteristic
545C2×C4#8804611yescharacteristic
546C2×C4#8804611yescharacteristic
547C2×C4#8807111yescharacteristic
548C2×C4#8807111yescharacteristic
549C2×C4#8807111yescharacteristic
550C2×C4#8807111yescharacteristic
551C2×C4C2×C4×Dic1311yescharacteristic
552C2×C4C2×C4⋊Dic1311yescharacteristic
553C2×C4C2×#610311yescharacteristic
554C2×C4C2×C22⋊Dic1311yescharacteristic
555C8—44no—
556C8—522no—
557C8—522no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22#1171811911yescharacteristic
578C22#1171811911yescharacteristic
579C22C2×#8807111yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—1044no—
587C4#1171811911yescharacteristic
588C4#1171811911yescharacteristic
589C4C2×#8804611yescharacteristic
590C4C2×#8804611yescharacteristic
591C2—21no—
592C2—21no—
593C2—21no—
594C2—41no—
595C2—41no—
596C2—41no—
597C2—41no—
598C2—41no—
599C2—41no—
600C2C2×#1171811911yescharacteristic
subgroupG/H
centerC4C2×#88046
commutatorC2×C4×C13C2×C42
FrattiniC2×#41C22×D13
FittingC2×C13×#413C2
socleC2×C13C2×#342
prime radicalC22×C13×#41C22
cosocleC2×C13×#41C23
hypercenterC2×#413D13
hypocenterC13#12589
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
3. #13112966C2semidirect
8. C22×#6099C4semidirect
9. C22×#6099C4semidirect
12. C13×#413C4semidirect
14. C2×C13×#101C4semidirect
22. #11718895C4semidirect
68. C2×#6099C2×C4semidirect
70. C22×#1055C2×C4semidirect
72. C13×#101C2×C4semidirect
269. #413Dic13semidirect
271. C2×#101Dic13semidirect
362. #101C2×Dic13semidirect
478. C13#12589semidirect

Maximal subgroups

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

subgroupindex
C2×#117189012
#131232812
#131129662
C2×C13×#4132
#1258913