Finite Group Databasebeta

← #16796091

Subgroups — #16796091

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131637C211yesmaximal, characteristic
2#13131631C211yesmaximal, characteristic
3#13130482C211yesmaximal, characteristic, complemented
4#13130481C211yesmaximal, characteristic, complemented
5#13130462C211yesmaximal, characteristic, complemented
6#13130460C211yesmaximal, characteristic, complemented
7#13130460C211yesmaximal, characteristic, complemented
8#13130459C211yesmaximal, characteristic, complemented
9#13130431C211yesmaximal, characteristic, complemented
10#13130430C211yesmaximal, characteristic, complemented
11#13130403C211yesmaximal, characteristic
12#13130184C211yesmaximal, characteristic
13C2×#11718244C211yesmaximal, characteristic
14#13130047C211yesmaximal, characteristic
15#13124872C211yesmaximal, characteristic
16#11719327C2211yescharacteristic
17C2×#88141C2211yescharacteristic
18#11719158C2211yescharacteristic
19Q8×#1057C2211yescharacteristic
20#11719129—21no—
21#11719129C2211yescharacteristic
22C4×#6122—21no—
23C4×#6122C2211yescharacteristic
24C2×C4⋊#1057C2211yescharacteristic
25C2×C4×#1057C2211yescharacteristic
26#11719080—21no—
27#11719080C2211yescharacteristic
28#11719080C2211yescharacteristic
29#11719080C2211yescharacteristic
30#11719078—21no—
31#11719078—21no—
32#11719078—21no—
33#11719074C2211yescharacteristic
34#11719074C2211yescharacteristic
35#11719074C2211yescharacteristic
36#11719067—21no—
37#11719062—21no—
38C13×#484C411yescharacteristic
39#11718711C411yescharacteristic
40#11718631C411yescharacteristic
41#11718536C411yescharacteristic
42#11718536C411yescharacteristic
43#11718534C2211yescharacteristic
44#11718534C2211yescharacteristic
45#11718454C411yescharacteristic
46#11718454C411yescharacteristic
47#11718451C2211yescharacteristic
48#11718451C2211yescharacteristic
49#11718400C411yescharacteristic
50#11718379C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53#11718255C2211yescharacteristic
54#11718255C2211yescharacteristic
55#11718253C2211yescharacteristic
56#11718253C2211yescharacteristic
57#1057⋊C8C2211yescharacteristic
58#1057⋊C8C2211yescharacteristic
59#11718251C2211yescharacteristic
60#11718251C2211yescharacteristic
61#11718244C2211yescharacteristic
62#11718244C2211yescharacteristic
63#11718244C2211yescharacteristic
64#11718244C2211yescharacteristic
65#11718244C2211yescharacteristic
66#11718244C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C2×#6122—21no—
69C2×#6122D411yescharacteristic
70C2×#6122D411yescharacteristic
71C22×#1057—21no—
72C22×#1057—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C2×C13×C4⋊C4C2×C411yescharacteristic
75Q8×Dic13C2311yescharacteristic
76#88198C2×C411yescharacteristic
77C2×#6107C2×C411yescharacteristic
78C2×#6107C2×C411yescharacteristic
79#88178C2×C411yescharacteristic
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13C2311yescharacteristic
83C2×Dic52C2×C411yescharacteristic
84C2×Dic52C2×C411yescharacteristic
85#88143—21no—
86#88142C2×C411yescharacteristic
87#88141—21no—
88#88141—21no—
89#88141—21no—
90#88141C2×C411yescharacteristic
91#88141C2×C411yescharacteristic
92#88141C2311yescharacteristic
93#88141C2311yescharacteristic
94#88141C2311yescharacteristic
95#88132—21no—
96#88131—21no—
97#88112—21no—
98#88112—21no—
99#88112—21no—
100#88112—21no—
101#88112—21no—
102#88110—21no—
103#88110—21no—
104#88110—21no—
105#88110—21no—
106#88110D411yescharacteristic
107#88110D411yescharacteristic
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×#107C2×C411yescharacteristic
127C13×#107C2×C411yescharacteristic
128C13×#103C2×C411yescharacteristic
129C13×#103C2×C411yescharacteristic
130C13×C22⋊C8C2×C411yescharacteristic
131C22⋊#1055C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136C8×Dic13C2311yescharacteristic
137C8×Dic13C2311yescharacteristic
138#88050C2×C411yescharacteristic
139#88050C2×C411yescharacteristic
140#88050C2×C411yescharacteristic
141#88050C2×C411yescharacteristic
142#88047C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#18003—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13C22×C411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13#4111yescharacteristic
151C2×Dic26—22no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—41no—
155C2×Dic26C22×C411yescharacteristic
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158#6122—22no—
159#6122—22no—
160#6122—42no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—42no—
168C2×#1057—42no—
169C2×#1057C2×D411yescharacteristic
170C2×#1057C2×D411yescharacteristic
171C2×#1057C2×D411yescharacteristic
172C2×#1057C2×D411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C22⋊Dic13—21no—
182#6107—22no—
183#6107—41no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C411yescharacteristic
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13C22×C411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13#4111yescharacteristic
204C4×Dic13C2411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207Dic52—22no—
208Dic52—41no—
209#3104—131no—
210Q8×M16—131no—
211#2962—131no—
212#1593—131no—
213#1593—131no—
214#1587—131no—
215#1587—131no—
216#1587—131no—
217#1587—131no—
218#1579—131no—
219#1579—131no—
220#1570—131no—
221#1493—131no—
222C2×Q8⋊C8—131no—
223#1451—131no—
224C23×C13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×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—81no—
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C23×C411yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—41no—
241C2×Dic13—42no—
242C2×Dic13C4×D411yescharacteristic
243C2×Dic13C4×D411yescharacteristic
244C2×Dic13#13712yes—
245C2×Dic13#13712yes—
246C2×Dic13C22×D411yescharacteristic
247C2×Dic13C2×#4111yescharacteristic
248Dic26—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—42no—
254Dic26—81no—
255Dic26#13112yes—
256#1057—22no—
257#1057—21no—
258#1057—21no—
259#1057—21no—
260#1057—21no—
261#1057—41no—
262#1057—41no—
263#1057—41no—
264#1057—41no—
265#1057—41no—
266C8×C13—21no—
267C8×C13—21no—
268#1055—21no—
269#1055—21no—
270#533—131no—
271C2×C4×Q8—131no—
272#484—131no—
273#484#26111yescharacteristic
274#477—131no—
275#477—131no—
276#462—131no—
277#462—131no—
278#451—131no—
279#451—131no—
280#446—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286#446—261no—
287#446—261no—
288C8×Q8—131no—
289C8×Q8—131no—
290C8×Q8—131no—
291C8×Q8—131no—
292C4×Q16—131no—
293C4×Q16—131no—
294C4×Q16—131no—
295C4×Q16—131no—
296#431—131no—
297#424—261no—
298#423—131no—
299#423—261no—
300C2×C4⋊C8—131no—
301#405—261no—
302C4×M16—131no—
303C4×M16—261no—
304C2×C4×C8—131no—
305#334—131no—
306#334—131no—
307#334—131no—
308#334—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317#322—131no—
318#322—131no—
319#322—131no—
320#322—131no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13#44112yes—
324C22×C13C2×C4×D411yescharacteristic
325C4×C13—21no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13C2×#13111yescharacteristic
331C4×C13#56811yescharacteristic
332Dic13—22no—
333Dic13—21no—
334Dic13—21no—
335Dic13—41no—
336Dic13—41no—
337Dic13—41no—
338Dic13#44112yes—
339Dic13C2×#13711yescharacteristic
340Dic13C2×#13711yescharacteristic
341C22×Q8—131no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—261no—
349C22×C8—261no—
350C22×C8—261no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—261no—
356C22⋊Q8C2×#26111yescharacteristic
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—261no—
364C4×Q8—261no—
365C4×Q8—261no—
366#117—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4C2×#26111yescharacteristic
369C2×C42—131no—
370C2×C42—261no—
371#107—131no—
372#107—131no—
373#107C2×#26111yescharacteristic
374#107C2×#26111yescharacteristic
375C4⋊C8—131no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103C2×#26111yescharacteristic
398#103C2×#26111yescharacteristic
399C22⋊C8—131no—
400C22⋊C8C2×#26111yescharacteristic
401#97—131no—
402#97—131no—
403#97—261no—
404#97—261no—
405#97—261no—
406#97—261no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C2×C13—22no—
419C2×C13#293311yescharacteristic
420C2×C13C2×#44111yescharacteristic
421C2×C13#295611yescharacteristic
422C2×Q8—131no—
423C2×Q8—131no—
424C2×Q8—131no—
425C2×Q8—261no—
426C2×Q8—262no—
427C2×Q8—261no—
428C2×Q8—521no—
429C2×Q8C22×#26111yescharacteristic
430C22×C4—21no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—261no—
434C22×C4C22×#26111yescharacteristic
435Q16—262no—
436Q16—262no—
437Q16—521no—
438Q16—521no—
439M16—262no—
440M16—262no—
441M16—522no—
442C2×C8—131no—
443C2×C8—131no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—522no—
455C2×C8—522no—
456C2×C8C22×#26111yescharacteristic
457C2×C8C22×#26111yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—131no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C22×#26111yescharacteristic
472C4⋊C4C22×#26111yescharacteristic
473C4⋊C4C22×#26111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—261no—
476C42—131no—
477C42—131no—
478C42—131no—
479C42—131no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C13#1800311yescharacteristic, complemented, Sylow
487C23D4×#26111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—132no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—522no—
497Q8—1041no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—81no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—521no—
516C2×C4—522no—
517C2×C4D4×#26111yescharacteristic
518C2×C4C23×#26111yescharacteristic
519C8—21no—
520C8—21no—
521C8—261no—
522C8—261no—
523C8—261no—
524C8—261no—
525C8—262no—
526C8—261no—
527C8—261no—
528C8—521no—
529C8—521no—
530C8—521no—
531C8—521no—
532C8—521no—
533C22—21no—
534C22—21no—
535C22#1171911012yes—
536C22C2×D4×#26111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—131no—
543C4—131no—
544C4—132no—
545C4—262no—
546C4—261no—
547C4—261no—
548C4—521no—
549C4—521no—
550C4—521no—
551C4D13⋊#13111yescharacteristic
552C4#1171962911yescharacteristic
553C2—22no—
554C2#1313157011yescharacteristic
555C2C2×#1171911011yescharacteristic
556C2#1313161011yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#484C4
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenter#484#261
hypocenterC13#18003
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #13130482C2semidirect
4. #13130481C2semidirect
5. #13130462C2semidirect
6. #13130460C2semidirect
7. #13130460C2semidirect
8. #13130459C2semidirect
9. #13130431C2semidirect
10. #13130430C2semidirect
486. C13#18003semidirect

Maximal subgroups

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

subgroupindex
#131316372
#131316312
#131304822
#131304812
#131304622
#131304602
#131304592
#131304312
#131304302
#131304032
#131301842
C2×#117182442
#131300472
#131248722
#1800313