Finite Group Databasebeta

← #15920974

Subgroups — #15920974

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118550C211yesmaximal, characteristic
2#13117713C211yesmaximal, characteristic
3#13116402C211yesmaximal, characteristic, complemented
4#13116339C211yesmaximal, characteristic, complemented
5#13116326C211yesmaximal, characteristic, complemented
6#13116173C211yesmaximal, characteristic, complemented
7#13115792C211yesmaximal, characteristic, complemented
8#13115593C211yesmaximal, characteristic, complemented
9#13115424C211yesmaximal, characteristic, complemented
10#13115413C211yesmaximal, characteristic, complemented
11#13115037C211yesmaximal, characteristic
12#13115018C211yesmaximal, characteristic
13#13114867C211yesmaximal, characteristic
14#13114555C211yesmaximal, characteristic
15C13×#1823C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×#88144C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#380C2211yescharacteristic
22#11718873—21no—
23#11718873C2211yescharacteristic
24C4×C22⋊Dic13—21no—
25C4×C22⋊Dic13C2211yescharacteristic
26C2×#88058C2211yescharacteristic
27C2×#88057C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30#11718646C2211yescharacteristic
31#11718646C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718642—21no—
34#11718642—21no—
35#11718637C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718610—21no—
42#11718609—21no—
43#11718316—21no—
44#11718308—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4Q814yes—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13D411yescharacteristic
74C2×C22⋊Dic13D411yescharacteristic
75#88180—22no—
76#88180—41no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×#6099—22no—
95C2×#6099—22no—
96C2×#6099—41no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88144—22no—
100#88144—41no—
101C13×C22⋊C8—22no—
102C13×#95—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88058—41no—
113#88057—22no—
114#88054—22no—
115#88054—41no—
116#88048—22no—
117#88047—41no—
118#26018—131nomaximal, Sylow
119C24×C13C2×D411yescharacteristic
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—24no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—81no—
130C22×C4×C13—81no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×Q812yes—
133C22×C4×C13#4112yes—
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C13×C4⋊C4—24no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4C2×Q812yes—
157C13×C4⋊C4C2×Q812yes—
158C13×C22⋊C4—81no—
159C22⋊Dic13—22no—
160C22⋊Dic13—41no—
161C22⋊Dic13—42no—
162C22⋊Dic13—42no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—42no—
171C4⋊Dic13—81no—
172C4⋊Dic13—81no—
173C4⋊Dic13—81no—
174C4⋊Dic13#4112yes—
175#6101—42no—
176#6101—42no—
177#6101—42no—
178#6101—81no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—21no—
183C4×Dic13—42no—
184C4×Dic13—81no—
185C4×Dic13—81no—
186#6099—44no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055#4112yes—
193#2441—131no—
194#2345—131no—
195#2100—131no—
196#2088—131no—
197#2086—131no—
198#2059—131no—
199#1989—131no—
200#1947—131no—
201#1920—131no—
202#1919—131no—
203#1854—131no—
204#1851—131no—
205#1823D1311yescharacteristic
206#1809—131no—
207#1736—131no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13C22⋊Q812yes—
215C23×C13C22×D411yescharacteristic
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—84no—
235C2×C4×C13C22⋊Q812yes—
236C2×C4×C13C22×Q811yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—22no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13#13712yes—
266C8×C13—41no—
267C8×C13—41no—
268#1055—22no—
269#1055—41no—
270C22×M16—131no—
271C2×#125—131no—
272C2×#117—131no—
273C22×C4⋊C4C2×D1311yescharacteristic
274C2×#107—131no—
275C2×#107—131no—
276C2×#106—131no—
277C2×#106—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C22⋊C8C2×D1311yescharacteristic
281#399—261no—
282#396—261no—
283#389—131no—
284#389—131no—
285#389—131no—
286#389—131no—
287#389—261no—
288#387—261no—
289#387—261no—
290#387—261no—
291#384—131no—
292#380—131no—
293#380—261no—
294#380C2×D1311yescharacteristic
295C4×C4⋊C4—131no—
296C4×C4⋊C4—131no—
297C4×C22⋊C4—131no—
298C4×C22⋊C4—261no—
299#340—131no—
300#340—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340C2×D1311yescharacteristic
308#340C2×D1311yescharacteristic
309#340C2×D1311yescharacteristic
310#340C2×D1311yescharacteristic
311#336—131no—
312#336—131no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—41no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13C2×C22⋊Q811yescharacteristic
321C22×C13#54611yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13C2×#13711yescharacteristic
324C22×C13#57511yescharacteristic
325C22×C13#57611yescharacteristic
326C22×C13#57711yescharacteristic
327C4×C13—22no—
328C4×C13—42no—
329C4×C13—42no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13#53311yescharacteristic
333C4×C13#54411yescharacteristic
334C4×C13#55111yescharacteristic
335C4×C13#55211yescharacteristic
336Dic13—22no—
337Dic13—41no—
338Dic13—42no—
339Dic13—41no—
340Dic13—41no—
341Dic13—81no—
342Dic13—81no—
343Dic13—81no—
344C23×C4—21no—
345C23×C4C22×D1311yescharacteristic
346C2×M16—262no—
347C2×M16—262no—
348C2×M16—521no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8C22×D1311yescharacteristic
352C22×C8C22×D1311yescharacteristic
353#125—262no—
354#125—521no—
355#117—262no—
356#117—521no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4Dic2614yes—
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—131no—
378C2×C22⋊C4—131no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C42—131no—
382C2×C42—131no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386#107—521no—
387#107—521no—
388#106—262no—
389#106—262no—
390C4⋊C8—262no—
391C4⋊C8—521no—
392C22⋊C8—22no—
393#95—21no—
394#95—131no—
395#95—131no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403C2×C13—42no—
404C2×C13#243811yescharacteristic
405C2×C13#307811yescharacteristic
406C2×C13#308111yescharacteristic
407C2×C13#330911yescharacteristic
408C2×C13#333111yescharacteristic
409C2×C13#334611yescharacteristic
410C2×C13#335111yescharacteristic
411C24D4×D1311yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4C2×Dic2612yes—
432C22×C4D4×D1311yescharacteristic
433C22×C4#612912yes—
434C22×C4C23×D1311yescharacteristic
435M16—524no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—132no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—132no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—522no—
464C4⋊C4—522no—
465C4⋊C4—522no—
466C4⋊C4—522no—
467C4⋊C4—1041no—
468C4⋊C4—1041no—
469C4⋊C4—1041no—
470C4⋊C4—1041no—
471C4⋊C4C2×Dic2612yes—
472C4⋊C4C2×Dic2612yes—
473C22⋊C4—81no—
474C22⋊C4—262no—
475C22⋊C4—521no—
476C22⋊C4—522no—
477C22⋊C4—522no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—522no—
483C42—1041no—
484C42—1041no—
485C13#2601811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#8813212yes—
493C23C2×D4×D1311yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—84no—
513C2×C4—132no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—262no—
525C2×C4—261no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4#8813212yes—
538C2×C4C22×Dic2611yescharacteristic
539C2×C4C2×#612911yescharacteristic
540C2×C4#41×D1311yescharacteristic
541C2×C4#41×D1311yescharacteristic
542C2×C4#8825611yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—41no—
545C8—41no—
546C8—262no—
547C8—521no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#8813211yescharacteristic
556C22#1171935911yescharacteristic
557C22#1171936011yescharacteristic
558C22#1171946211yescharacteristic
559C22#1171946711yescharacteristic
560C22D13×#13711yescharacteristic
561C22#1171948211yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—262no—
568C4—521no—
569C4—521no—
570C4—521no—
571C4—522no—
572C4—1041no—
573C4—1041no—
574C4—1041no—
575C4#1171922211yescharacteristic
576C4#1171922411yescharacteristic
577C4#1171935511yescharacteristic
578C4#1171936311yescharacteristic
579C2—42no—
580C2#1311851411yescharacteristic
581C2#1312463811yescharacteristic
582C2#1312466311yescharacteristic
583C2#1312684511yescharacteristic
584C2#1312715011yescharacteristic
585C2#1312732411yescharacteristic
586C2#1312739911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1823C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1823D13
hypocenterC13#26018
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #13116402C2semidirect
4. #13116339C2semidirect
5. #13116326C2semidirect
6. #13116173C2semidirect
7. #13115792C2semidirect
8. #13115593C2semidirect
9. #13115424C2semidirect
10. #13115413C2semidirect
485. C13#26018semidirect

Maximal subgroups

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

subgroupindex
#131185502
#131177132
#131164022
#131163392
#131163262
#131161732
#131157922
#131155932
#131154242
#131154132
#131150372
#131150182
#131148672
#131145552
C13×#18232
#2601813