Finite Group Databasebeta

← #16795796

Subgroups — #16795796

Order 3328.

558 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#13131740C211yesmaximal, characteristic
2#13131732C211yesmaximal, characteristic
3#13130483C211yesmaximal, characteristic, complemented
4#13130481C211yesmaximal, characteristic, complemented
5#13130476C211yesmaximal, characteristic, complemented
6#13130474C211yesmaximal, characteristic, complemented
7#13130462C211yesmaximal, characteristic, complemented
8#13130461C211yesmaximal, characteristic, complemented
9#13130450C211yesmaximal, characteristic, complemented
10#13130449C211yesmaximal, characteristic, complemented
11#13130407C211yesmaximal, characteristic
12#13130178C211yesmaximal, characteristic
13#13130158C211yesmaximal, characteristic
14#13130053C211yesmaximal, characteristic
15#13124870C211yesmaximal, characteristic
16C2×Q8×Dic13C2211yescharacteristic
17#11719327C2211yescharacteristic
18#11719158—21no—
19#11719158—21no—
20#11719158C2211yescharacteristic
21#11719158C2211yescharacteristic
22#11719158C2211yescharacteristic
23#11719158C2211yescharacteristic
24#11719158C2211yescharacteristic
25Q8×#1057C2211yescharacteristic
26#11719130C2211yescharacteristic
27#11719128—21no—
28#11719128—21no—
29C4×#6122C2211yescharacteristic
30#11719119C2211yescharacteristic
31#11719119C2211yescharacteristic
32#11719080—21no—
33#11719080C2211yescharacteristic
34#11719078—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×#6122—21no—
69C2×C13×Q16C2×C411yescharacteristic
70C2×C13×Q16C2×C411yescharacteristic
71C13×C22⋊Q8C2×C411yescharacteristic
72Q8×Dic13—21no—
73Q8×Dic13—21no—
74Q8×Dic13C2×C411yescharacteristic
75Q8×Dic13C2×C411yescharacteristic
76Q8×Dic13C2311yescharacteristic
77Q8×Dic13C2311yescharacteristic
78Q8×Dic13C2311yescharacteristic
79#88198C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2×C411yescharacteristic
84#88178C2×C411yescharacteristic
85C2×C4×Dic13—21no—
86C2×C4×Dic13C2311yescharacteristic
87#88143—21no—
88#88142C2×C411yescharacteristic
89#88141—21no—
90#88141C2311yescharacteristic
91#88132—21no—
92#88131—21no—
93C22⋊#1057—21no—
94C22⋊#1057—21no—
95C22⋊#1057D411yescharacteristic
96C22⋊#1057D411yescharacteristic
97#88112—21no—
98#88112—21no—
99#88112—21no—
100#88112—21no—
101#88112—21no—
102#88112—21no—
103#88110—21no—
104#88110—21no—
105#88110—21no—
106#88110—21no—
107#88110—21no—
108#88110—21no—
109#88110—21no—
110#88110—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057D411yescharacteristic
114C4⋊#1057D411yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
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#17953—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—41no—
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
158#6122—42no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057C2×D411yescharacteristic
166C2×#1057C2×D411yescharacteristic
167C2×#1057C2×D411yescharacteristic
168C2×#1057C2×D411yescharacteristic
169C13×Q16—41no—
170C13×Q16—41no—
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C22⋊Dic13—21no—
177#6107—41no—
178#6107—41no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13C22×C411yescharacteristic
200C4×Dic13C2×D411yescharacteristic
201C4×Dic13#4111yescharacteristic
202C4×Dic13C2411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205#3104—131no—
206#2985—131no—
207#2983—131no—
208#1593—131no—
209#1593—131no—
210#1591—131no—
211#1591—131no—
212#1587—131no—
213#1587—131no—
214#1584—131no—
215#1584—131no—
216#1572—131no—
217#1491—131no—
218#1485—131no—
219#1453—131no—
220C23×C13C4×D411yescharacteristic
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—42no—
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—42no—
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C23×C411yescharacteristic
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—41no—
244C2×Dic13—81no—
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C22×D411yescharacteristic
248C2×Dic13C2×#4111yescharacteristic
249Dic26—21no—
250Dic26—21no—
251Dic26—81no—
252#1057—22no—
253#1057—21no—
254#1057—21no—
255#1057—21no—
256#1057—21no—
257#1057—41no—
258#1057—41no—
259#1057—41no—
260#1057—41no—
261#1057—41no—
262C8×C13—21no—
263C8×C13—21no—
264#1055—21no—
265#1055—21no—
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#26111yescharacteristic
276#446—131no—
277#446—131no—
278#446—131no—
279#446—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292#433—261no—
293#433—261no—
294#432—131no—
295#432—261no—
296#432—261no—
297#431—131no—
298#431—131no—
299#431—131no—
300C4×M16—131no—
301#335—131no—
302#335—131no—
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⋊C8—131no—
312Q8⋊C8—131no—
313#322—131no—
314#322—131no—
315#322—131no—
316C82—131no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13C2×C4×D411yescharacteristic
321C4×C13—21no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13#56811yescharacteristic
327C4×C13#56811yescharacteristic
328Dic13—21no—
329Dic13—21no—
330Dic13—21no—
331Dic13—41no—
332Dic13—41no—
333Dic13—41no—
334Dic13—41no—
335Dic13#57811yescharacteristic
336Dic13#57811yescharacteristic
337C22×Q8C2×#26111yescharacteristic
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16C2×#26111yescharacteristic
341C2×Q16C2×#26111yescharacteristic
342C2×M16—261no—
343C4⋊Q8—131no—
344C4⋊Q8—131no—
345#125—261no—
346C22⋊Q8—131no—
347C22⋊Q8—261no—
348C22⋊Q8C2×#26111yescharacteristic
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—131no—
353C4×Q8—131no—
354C4×Q8—131no—
355C4×Q8—261no—
356C4×Q8—261no—
357C4×Q8—261no—
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#107—131no—
367C4⋊C8—131no—
368C4⋊C8—131no—
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⋊C8—261no—
382C4⋊C8—261no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103—131no—
389#103C2×#26111yescharacteristic
390#103C2×#26111yescharacteristic
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394C22⋊C8—261no—
395C22⋊C8—261no—
396C22⋊C8C2×#26111yescharacteristic
397#97—261no—
398#97—261no—
399#97—261no—
400#97—261no—
401#97—261no—
402#97—261no—
403#97—261no—
404#97—261no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—261no—
412C4×C8—261no—
413C4×C8—261no—
414C2×C13—41no—
415C2×C13#293011yescharacteristic
416C2×C13#295011yescharacteristic
417C2×C13#295611yescharacteristic
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—131no—
422C2×Q8—261no—
423C2×Q8C22×#26111yescharacteristic
424C2×Q8C22×#26111yescharacteristic
425C2×Q8C22×#26111yescharacteristic
426C22×C4—21no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—261no—
430C22×C4C22×#26111yescharacteristic
431Q16—41no—
432Q16—41no—
433Q16—521no—
434Q16—521no—
435M16—522no—
436C2×C8—131no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—131no—
441C2×C8—131no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8C22×#26111yescharacteristic
449C2×C8C22×#26111yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—131no—
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⋊C4—261no—
465C4⋊C4C22×#26111yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—261no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—131no—
472C42—261no—
473C42—261no—
474C42—261no—
475C42—261no—
476C42—261no—
477C42—261no—
478C13#1795311yescharacteristic, complemented, Sylow
479C23D4×#26111yescharacteristic
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—42no—
487Q8—261no—
488Q8—261no—
489Q8—1041no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—42no—
497C2×C4—131no—
498C2×C4—131no—
499C2×C4—131no—
500C2×C4—131no—
501C2×C4—261no—
502C2×C4—261no—
503C2×C4—261no—
504C2×C4—261no—
505C2×C4—261no—
506C2×C4—261no—
507C2×C4—521no—
508C2×C4—1041no—
509C2×C4D4×#26111yescharacteristic
510C2×C4C23×#26111yescharacteristic
511C8—21no—
512C8—21no—
513C8—261no—
514C8—261no—
515C8—261no—
516C8—261no—
517C8—262no—
518C8—261no—
519C8—261no—
520C8—521no—
521C8—521no—
522C8—521no—
523C8—521no—
524C8—521no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22C2×D4×#26111yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—131no—
535C4—131no—
536C4—261no—
537C4—261no—
538C4—261no—
539C4—521no—
540C4—521no—
541C4—521no—
542C4—521no—
543C4#1171962111yescharacteristic
544C4#1171962111yescharacteristic
545C2—41no—
546C2#1313155511yescharacteristic
547C2#1313159711yescharacteristic
548C2#1313161111yescharacteristic
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#17953
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. #13130483C2semidirect
4. #13130481C2semidirect
5. #13130476C2semidirect
6. #13130474C2semidirect
7. #13130462C2semidirect
8. #13130461C2semidirect
9. #13130450C2semidirect
10. #13130449C2semidirect
478. C13#17953semidirect

Maximal subgroups

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

subgroupindex
#131317402
#131317322
#131304832
#131304812
#131304762
#131304742
#131304622
#131304612
#131304502
#131304492
#131304072
#131301782
#131301582
#131300532
#131248702
#1795313