Finite Group Databasebeta

← #16796303

Subgroups — #16796303

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131745C211yesmaximal, characteristic
2#13131739C211yesmaximal, characteristic
3#13130481C211yesmaximal, characteristic, complemented
4#13130476C211yesmaximal, characteristic, complemented
5#13130462C211yesmaximal, characteristic, complemented
6#13130461C211yesmaximal, characteristic, complemented
7#13130449C211yesmaximal, characteristic, complemented
8#13130447C211yesmaximal, characteristic, complemented
9#13130429C211yesmaximal, characteristic, complemented
10#13130423C211yesmaximal, characteristic, complemented
11#13130407C211yesmaximal, characteristic
12#13130198C211yesmaximal, characteristic
13#13130138C211yesmaximal, characteristic
14#13130057C211yesmaximal, characteristic
15#13124870C211yesmaximal, characteristic
16C2×Q8×Dic13C2211yescharacteristic
17#11719327C2211yescharacteristic
18#11719158—21no—
19#11719158—21no—
20#11719158C2211yescharacteristic
21#11719158C2211yescharacteristic
22#11719158C2211yescharacteristic
23Q8×#1057C2211yescharacteristic
24Q8×#1057C2211yescharacteristic
25Q8×#1057C2211yescharacteristic
26#11719130—21no—
27#11719130C2211yescharacteristic
28#11719125—21no—
29#11719125C2211yescharacteristic
30#11719119C2211yescharacteristic
31#11719119C2211yescharacteristic
32#11719080C2211yescharacteristic
33#11719078—21no—
34#11719074—21no—
35#11719074C2211yescharacteristic
36#11719068—21no—
37#11719068—21no—
38C13×#451C411yescharacteristic
39#11718889C411yescharacteristic
40Q16×Dic13C2211yescharacteristic
41Q16×Dic13C2211yescharacteristic
42#11718843C411yescharacteristic
43#11718843C411yescharacteristic
44#11718705C411yescharacteristic
45#11718455C411yescharacteristic
46#11718455C411yescharacteristic
47#11718451C2211yescharacteristic
48#11718451C2211yescharacteristic
49#11718383C411yescharacteristic
50#11718379C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53Q8⋊#1057C2211yescharacteristic
54Q8⋊#1057C2211yescharacteristic
55Q8⋊#1057C2211yescharacteristic
56Q8⋊#1057C2211yescharacteristic
57#11718256C2211yescharacteristic
58#11718255C2211yescharacteristic
59#11718254C2211yescharacteristic
60#11718253C2211yescharacteristic
61#1057⋊C8C2211yescharacteristic
62#1057⋊C8C2211yescharacteristic
63#11718251C2211yescharacteristic
64C8×#1057C2211yescharacteristic
65#11718244C2211yescharacteristic
66#11718244C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C13×C22⋊Q8C2×C411yescharacteristic
71Q8×Dic13—21no—
72Q8×Dic13—21no—
73Q8×Dic13C2×C411yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75Q8×Dic13C2311yescharacteristic
76Q8×Dic13C2311yescharacteristic
77Q8×Dic13C2311yescharacteristic
78#88198C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2×C411yescharacteristic
83#88178C2×C411yescharacteristic
84C2×C4×Dic13—21no—
85C2×C4×Dic13C2311yescharacteristic
86#88143—21no—
87#88142C2×C411yescharacteristic
88#88141—21no—
89#88141C2311yescharacteristic
90#88132—21no—
91#88131—21no—
92C22⋊#1057—21no—
93C22⋊#1057—21no—
94C22⋊#1057—21no—
95C22⋊#1057D411yescharacteristic
96C22⋊#1057D411yescharacteristic
97#88112—21no—
98#88112—21no—
99#88112—21no—
100#88112—21no—
101#88112D411yescharacteristic
102#88112D411yescharacteristic
103#88110—21no—
104#88110—21no—
105#88110—21no—
106#88110—21no—
107#88110—21no—
108C4⋊#1057—21no—
109C4⋊#1057—21no—
110C4⋊#1057—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057C2311yescharacteristic
114C4⋊#1057C2311yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4×#1057—21no—
118C4×#1057—21no—
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057C2311yescharacteristic
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C13×#103C2×C411yescharacteristic
127C13×#103C2×C411yescharacteristic
128C13×C22⋊C8C2×C411yescharacteristic
129#88075C2×C411yescharacteristic
130#88075C2×C411yescharacteristic
131#88075C2×C411yescharacteristic
132#88075C2×C411yescharacteristic
133C22⋊#1055C2×C411yescharacteristic
134#88058C2×C411yescharacteristic
135#88058C2×C411yescharacteristic
136#88056C2×C411yescharacteristic
137#88056C2×C411yescharacteristic
138#88054C2×C411yescharacteristic
139#88054C2×C411yescharacteristic
140C8×Dic13C2311yescharacteristic
141C8×Dic13C2311yescharacteristic
142#88047C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#18032—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C2×Q8×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057C2×D411yescharacteristic
165C2×#1057C2×D411yescharacteristic
166C2×#1057C2×D411yescharacteristic
167C2×#1057C2×D411yescharacteristic
168C13×Q16—22no—
169C13×Q16—41no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C22⋊C4—21no—
175C22⋊Dic13—21no—
176#6107—22no—
177#6107—41no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13C22×C411yescharacteristic
199C4×Dic13C2×D411yescharacteristic
200C4×Dic13#4111yescharacteristic
201C4×Dic13C2411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204#3104—131no—
205#2986—131no—
206#2984—131no—
207#1593—131no—
208#1591—131no—
209#1587—131no—
210#1587—131no—
211#1584—131no—
212#1584—131no—
213#1579—131no—
214C8×Q16—131no—
215#1572—131no—
216#1497—131no—
217#1479—131no—
218#1454—131no—
219C23×C13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—42no—
226Q8×C13#13112yes—
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—42no—
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C23×C411yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C22×D411yescharacteristic
247C2×Dic13C2×#4111yescharacteristic
248Dic26—21no—
249Dic26—21no—
250Dic26—42no—
251#1057—21no—
252#1057—21no—
253#1057—21no—
254#1057—21no—
255#1057—41no—
256#1057—41no—
257#1057—41no—
258#1057—41no—
259#1057—41no—
260#1057—41no—
261C8×C13—21no—
262C8×C13—21no—
263#1055—21no—
264#1055—21no—
265#533—131no—
266C2×C4×Q8—131no—
267#484—131no—
268#484—131no—
269#477—131no—
270#477—131no—
271#462—131no—
272#462—131no—
273#451—131no—
274#451#26111yescharacteristic
275#446—131no—
276#446—131no—
277#446—131no—
278#446—131no—
279#446—261no—
280#446—261no—
281#446—261no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—261no—
287C4×Q16—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291#433—261no—
292#433—261no—
293#432—131no—
294#432—261no—
295#431—131no—
296#431—131no—
297#431—131no—
298#431—131no—
299#431—261no—
300#335—131no—
301#335—131no—
302#334—131no—
303#334—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312#322—131no—
313#322—131no—
314#322—131no—
315C82—131no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13C2×C4×D411yescharacteristic
320C4×C13—21no—
321C4×C13—22no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13C2×#13111yescharacteristic
326C4×C13#56811yescharacteristic
327Dic13—21no—
328Dic13—21no—
329Dic13—21no—
330Dic13—41no—
331Dic13—41no—
332Dic13—41no—
333Dic13—41no—
334Dic13#57811yescharacteristic
335Dic13#57811yescharacteristic
336C22×Q8C2×#26111yescharacteristic
337C2×Q16—131no—
338C2×Q16—131no—
339C2×Q16C2×#26111yescharacteristic
340C2×Q16C2×#26111yescharacteristic
341C4⋊Q8—131no—
342C4⋊Q8—131no—
343#125—261no—
344C22⋊Q8—131no—
345C22⋊Q8—261no—
346C22⋊Q8C2×#26111yescharacteristic
347C4×Q8—131no—
348C4×Q8—131no—
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—131no—
353C4×Q8—261no—
354C4×Q8—261no—
355C4×Q8—261no—
356#117—261no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
359C2×C42—131no—
360C2×C42—261no—
361#107—131no—
362#107—131no—
363#107—131no—
364#107—131no—
365C4⋊C8—131no—
366C4⋊C8—131no—
367C4⋊C8—131no—
368C4⋊C8—131no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103C2×#26111yescharacteristic
389#103C2×#26111yescharacteristic
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—261no—
394C22⋊C8—261no—
395C22⋊C8—261no—
396C22⋊C8C2×#26111yescharacteristic
397#97—261no—
398#97—261no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—261no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8—261no—
413C2×C13—41no—
414C2×C13#293311yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—41no—
420C2×Q8—131no—
421C2×Q8—261no—
422C2×Q8C22×#26111yescharacteristic
423C2×Q8C22×#26111yescharacteristic
424C2×Q8C22×#26111yescharacteristic
425C22×C4—21no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4C22×#26111yescharacteristic
430Q16—22no—
431Q16—41no—
432Q16—262no—
433Q16—521no—
434C2×C8—131no—
435C2×C8—131no—
436C2×C8—131no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8C22×#26111yescharacteristic
447C2×C8C22×#26111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—131no—
450C4⋊C4—131no—
451C4⋊C4—131no—
452C4⋊C4—261no—
453C4⋊C4—261no—
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⋊C4C22×#26111yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—261no—
466C42—131no—
467C42—131no—
468C42—131no—
469C42—131no—
470C42—261no—
471C42—261no—
472C42—261no—
473C42—261no—
474C42—261no—
475C42—261no—
476C13#1803211yescharacteristic, complemented, Sylow
477C23D4×#26111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—42no—
484Q8—261no—
485Q8—261no—
486Q8—522no—
487Q8#8823812yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—42no—
495C2×C4—131no—
496C2×C4—131no—
497C2×C4—131no—
498C2×C4—131no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—261no—
502C2×C4—261no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—521no—
506C2×C4—522no—
507C2×C4D4×#26111yescharacteristic
508C2×C4C23×#26111yescharacteristic
509C8—21no—
510C8—21no—
511C8—261no—
512C8—261no—
513C8—261no—
514C8—261no—
515C8—261no—
516C8—261no—
517C8—521no—
518C8—521no—
519C8—521no—
520C8—521no—
521C8—521no—
522C8—521no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×#26111yescharacteristic
527C4—21no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—131no—
533C4—131no—
534C4—261no—
535C4—261no—
536C4—261no—
537C4—521no—
538C4—521no—
539C4—521no—
540C4—521no—
541C4C2×#8823811yescharacteristic
542C4#1171962111yescharacteristic
543C2—41no—
544C2#1313156811yescharacteristic
545C2#1313159711yescharacteristic
546C2#1313160911yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#451C4
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenter#451#261
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #13130481C2semidirect
4. #13130476C2semidirect
5. #13130462C2semidirect
6. #13130461C2semidirect
7. #13130449C2semidirect
8. #13130447C2semidirect
9. #13130429C2semidirect
10. #13130423C2semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131317452
#131317392
#131304812
#131304762
#131304622
#131304612
#131304492
#131304472
#131304292
#131304232
#131304072
#131301982
#131301382
#131300572
#131248702
#1803213