Finite Group Databasebeta

← #15833071

Subgroups — #15833071

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124873C211yesmaximal, characteristic
2#13123932C211yesmaximal, characteristic
3#13123915C211yesmaximal, characteristic
4#13113707C211yesmaximal, characteristic, complemented
5#13113705C211yesmaximal, characteristic, complemented
6#13113688C211yesmaximal, characteristic, complemented
7#13113652C211yesmaximal, characteristic, complemented
8#13113652C211yesmaximal, characteristic, complemented
9Q16×#1055C211yesmaximal, characteristic, complemented
10#13113642C211yesmaximal, characteristic, complemented
11#13113615C211yesmaximal, characteristic
12#13113281C211yesmaximal, characteristic
13#13113255C211yesmaximal, characteristic
14#13113132C211yesmaximal, characteristic
15C13×#1584C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718847C411yescharacteristic
22#11718843C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718545C411yescharacteristic
28#11718536C411yescharacteristic
29#11718501—21no—
30#11718496C2211yescharacteristic
31#11718494—21no—
32#11718494C2211yescharacteristic
33#11718492—21no—
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718470C411yescharacteristic
38#11718469C411yescharacteristic
39#11718455C411yescharacteristic
40#11718454C411yescharacteristic
41#11718370—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44C4×#6094C2211yescharacteristic
45#11718346—21no—
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094—21no—
78#88151C2×C411yescharacteristic
79#88150—21no—
80C4⋊C4×D13—21no—
81C4⋊C4×D13C2×C411yescharacteristic
82#88143—21no—
83#88142C2×C411yescharacteristic
84#88141—21no—
85#88141C2×C411yescharacteristic
86#88126—21no—
87C42×D13—21no—
88C42×D13C2311yescharacteristic
89C4×Dic26—21no—
90C4×Dic26—21no—
91C4×Dic26C2311yescharacteristic
92C4×Dic26C2311yescharacteristic
93C13×#107C2×C411yescharacteristic
94C13×C4⋊C8—21no—
95C13×C4⋊C8—21no—
96C13×C4⋊C8C2311yescharacteristic
97C13×C4⋊C8C2311yescharacteristic
98C13×#103C2×C411yescharacteristic
99C13×#103C2×C411yescharacteristic
100C13×#97—21no—
101C4×C8×C13—21no—
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88060—21no—
108#88060—21no—
109#88060C2×C411yescharacteristic
110#88060C2×C411yescharacteristic
111#88060D411yescharacteristic
112#88060D411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88055—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054C2×C411yescharacteristic
124#88054C2×C411yescharacteristic
125#88054D411yescharacteristic
126#88054D411yescharacteristic
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17925—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147Q8×D13—22no—
148Q8×D13—22no—
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C2×D411yescharacteristic
153C2×C4×D13#4111yescharacteristic
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C13×Q16—22no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C42×C13—21no—
171C42×C13—21no—
172C42×C13C2411yescharacteristic
173#6107—22no—
174#6107—22no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13C22×C411yescharacteristic
180C4⋊Dic13C22×C411yescharacteristic
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203Dic52—22no—
204#6094—42no—
205#3104—131no—
206#2985—131no—
207#2982—131no—
208#1587—131no—
209#1587—131no—
210#1584—131no—
211#1584D1311yescharacteristic, complemented
212#1579—131no—
213#1579—131no—
214C8×Q16—131no—
215C8×Q16—131no—
216#1572—131no—
217#1491—131no—
218#1485—131no—
219#1453—131no—
220C22×D13C4×D411yescharacteristic
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13#13112yes—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13C23×C411yescharacteristic
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13C4×D411yescharacteristic
237C2×Dic13C4×D411yescharacteristic
238C2×Dic13C4×D411yescharacteristic
239C4×D13—24no—
240C4×D13—21no—
241C4×D13—21no—
242C4×D13—21no—
243C4×D13—21no—
244C4×D13—41no—
245C4×D13—81no—
246Dic26—24no—
247Dic26—21no—
248Dic26—21no—
249Dic26—21no—
250Dic26—81no—
251Dic26#13112yes—
252C8×C13—21no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—41no—
257C8×C13—41no—
258C8×C13—41no—
259#1055—22no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—41no—
265#1055—41no—
266#533—131no—
267C2×C4×Q8—131no—
268#484—131no—
269#484—131no—
270#477—131no—
271#477—131no—
272#462—131no—
273#462—131no—
274#451—131no—
275#451—131no—
276#446—131no—
277#446—261no—
278#446—261no—
279#446C2×D1311yescharacteristic
280C8×Q8—131no—
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—261no—
286C8×Q8—261no—
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×Q16C2×D1311yescharacteristic
292#433—261no—
293#433—261no—
294#432—131no—
295#431—131no—
296#431—131no—
297#431—131no—
298#431—261no—
299#431—261no—
300C4×M16—131no—
301#335—131no—
302#335C2×D1311yescharacteristic
303#334—131no—
304#334—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8C2×D1311yescharacteristic
312Q8⋊C8C2×D1311yescharacteristic
313#322—131no—
314#322—131no—
315#322C2×D1311yescharacteristic
316C82—131no—
317C22×C13C2×C4×D411yescharacteristic
318C2×D13—21no—
319C2×D13—21no—
320C2×D13—21no—
321C4×C13—22no—
322C4×C13—21no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13C2×#13111yescharacteristic
327C4×C13C2×#13111yescharacteristic
328C4×C13#57811yescharacteristic
329C4×C13#57811yescharacteristic
330Dic13—21no—
331Dic13—22no—
332Dic13—21no—
333Dic13—21no—
334Dic13—41no—
335Dic13—41no—
336Dic13—41no—
337C22×Q8—131no—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16—131no—
341C2×Q16C4×D1311yescharacteristic
342C2×M16—261no—
343C4⋊Q8—131no—
344C4⋊Q8—131no—
345#125—261no—
346C22⋊Q8—131no—
347C22⋊Q8—131no—
348C22⋊Q8—261no—
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—131no—
353C4×Q8—261no—
354C4×Q8—261no—
355C4×Q8—261no—
356C4×Q8C22×D1311yescharacteristic
357C4×Q8C22×D1311yescharacteristic
358#117—261no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—261no—
361C2×C42—131no—
362C2×C42—261no—
363#107—131no—
364#107—131no—
365#107—131no—
366#107C4×D1311yescharacteristic
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—131no—
374C4⋊C8—131no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8C22×D1311yescharacteristic
382C4⋊C8C22×D1311yescharacteristic
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103—131no—
389#103C4×D1311yescharacteristic
390#103C4×D1311yescharacteristic
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394C22⋊C8—131no—
395C22⋊C8—261no—
396C22⋊C8—261no—
397#97—21no—
398#97—261no—
399#97—261no—
400#97—261no—
401C4×C8—21no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—261no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8—261no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C4×C8C22×D1311yescharacteristic
414C2×C13#292911yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295611yescharacteristic
417D13—41no—
418C2×Q8—131no—
419C2×Q8—131no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×Q8—262no—
423C2×Q8—262no—
424C2×Q8C2×C4×D1311yescharacteristic
425C2×Q8C2×C4×D1311yescharacteristic
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—261no—
430C22×C4—261no—
431Q16—22no—
432Q16—262no—
433Q16—262no—
434Q16—262no—
435M16—522no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—131no—
440C2×C8—131no—
441C2×C8—131no—
442C2×C8—131no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8C2×C4×D1311yescharacteristic
447C2×C8C2×C4×D1311yescharacteristic
448C2×C8D4×D1311yescharacteristic
449C2×C8D4×D1311yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—131no—
453C4⋊C4—131no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4C2×C4×D1311yescharacteristic
465C4⋊C4C2×C4×D1311yescharacteristic
466C22⋊C4—261no—
467C22⋊C4—261no—
468C42—21no—
469C42—21no—
470C42—131no—
471C42—131no—
472C42—131no—
473C42—261no—
474C42—261no—
475C42—261no—
476C42—261no—
477C42C23×D1311yescharacteristic
478C13#1792511yescharacteristic, complemented, Sylow
479C23—131no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—132no—
484Q8—264no—
485Q8—261no—
486Q8—261no—
487Q8—261no—
488Q8—1041no—
489Q8#8816112yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—131no—
495C2×C4—131no—
496C2×C4—131no—
497C2×C4—264no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—261no—
502C2×C4—261no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—261no—
506C2×C4—521no—
507C2×C4—1041no—
508C2×C4C22×C4×D1311yescharacteristic
509C2×C4C2×D4×D1311yescharacteristic
510C2×C4#41×D1311yescharacteristic
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—262no—
519C8—261no—
520C8—261no—
521C8—261no—
522C8—261no—
523C8—521no—
524C8—521no—
525C22—261no—
526C22—261no—
527C22—261no—
528C22C4×D4×D1311yescharacteristic
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—261no—
535C4—261no—
536C4—261no—
537C4—262no—
538C4—521no—
539C4—521no—
540C4—521no—
541C4C2×#8816111yescharacteristic
542C4D13×#13111yescharacteristic
543C4#1171947111yescharacteristic
544C4#1171947611yescharacteristic
545C2—521no—
546C2#1312352711yescharacteristic
547C2#1312369911yescharacteristic
548C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#17925
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13113707C2semidirect
5. #13113705C2semidirect
6. #13113688C2semidirect
7. #13113652C2semidirect
8. #13113652C2semidirect
9. Q16×#1055C2semidirect
10. #13113642C2semidirect
15. C13×#1584C2semidirect
211. #1584D13semidirect
478. C13#17925semidirect

Maximal subgroups

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

subgroupindex
#131248732
#131239322
#131239152
#131137072
#131137052
#131136882
#131136522
Q16×#10552
#131136422
#131136152
#131132812
#131132552
#131131322
C13×#15842
#1792513