Finite Group Databasebeta

← #11870583

Subgroups — #11870583

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596162C211yesmaximal, characteristic, complemented
2C4×#3832C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4#10592765C211yesmaximal, characteristic, complemented
5#10592727C211yesmaximal, characteristic, complemented
6#10592587C211yesmaximal, characteristic, complemented
7#10592571C211yesmaximal, characteristic, complemented
8#10592565C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592543C211yesmaximal, characteristic, complemented
11#10592532C211yesmaximal, characteristic, complemented
12#10592509C211yesmaximal, characteristic
13#10592507C211yesmaximal, characteristic, complemented
14#10592489C211yesmaximal, characteristic, complemented
15#10592487C211yesmaximal, characteristic, complemented
16#81204—34nomaximal
17C2×#3832C2211yescharacteristic
18C32×#125C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25#64107—21no—
26#64106C2211yescharacteristic
27#64104C2211yescharacteristic
28#64103—21no—
29#64102—21no—
30#64102—21no—
31#64102C2211yescharacteristic
32#64102C2211yescharacteristic
33#64101—21no—
34#64101—21no—
35#64101C2211yescharacteristic
36#64096C2211yescharacteristic
37#64084C2211yescharacteristic
38C4×C4⋊(C3⋊D3)—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C42×C3⋊D3—21no—
41C42×C3⋊D3C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63648C2211yescharacteristic
48#63647C2211yescharacteristic
49#63647C2211yescharacteristic
50#63643C2211yescharacteristic
51C8×C3⋊Dic3C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53#63637C2211yescharacteristic
54#63636C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5691—34no—
61C4×#239—34no—
62C3×#479D314yescomplemented
63#5066—34no—
64#5028—34no—
65#4888—34no—
66#4872—34no—
67#4866—34no—
68#4852—34no—
69#4844—34no—
70#4833—34no—
71#4810—34no—
72#4808—34no—
73#4790—34no—
74#4788—34no—
75C2×C32×Q8C2311yescharacteristic
76#3832—22no—
77#3832—22no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4⋊(C3⋊D3)C2311yescharacteristic
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3D411yescharacteristic
87C2×C4×C3⋊D3D411yescharacteristic
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×#634C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C42—21no—
99C32×C42C2311yescharacteristic
100#3756—22no—
101#3755—22no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3D411yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3745—22no—
123#3744—22no—
124#3102—91noSylow
125C2×#239—34no—
126C3×#125C2×D314yes—
127C3×C4×Q8C2×D314yes—
128Q8×Dic3—34no—
129C2×#216—34no—
130C2×#215—34no—
131C2×D24—34no—
132C2×#204—34no—
133#898—64no—
134#897—34no—
135#895—34no—
136#894—64no—
137#893—34no—
138#893—34no—
139#893—64no—
140#893—64no—
141#892—34no—
142#892—64no—
143#892—64no—
144#887—34no—
145#875—34no—
146C4×D12—34no—
147C4×D12—64no—
148C42×D3—34no—
149C42×D3—64no—
150C3×#107C2×D314yes—
151C3×#106C2×D314yes—
152C3×C4⋊C8C2×D314yes—
153C3×#103C2×D314yes—
154C3×#103C2×D314yes—
155#821—34no—
156(C2×D3)⋊C8—34no—
157(C2×D3)⋊C8—34no—
158#816—34no—
159C8×Dic3—34no—
160C8×Dic3—34no—
161#810—34no—
162#809—34no—
163#809—34no—
164#809—34no—
165#808—34no—
166#807—34no—
167C4⋊(C3⋊C8)—34no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3C2×D411yescharacteristic
171C32×Q8—21no—
172C32×Q8#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C4⋊(C3⋊D3)—24no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)—42no—
190C4⋊(C3⋊D3)#4112yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—21no—
193C4×C3⋊D3—21no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—41no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—42no—
199#634—21no—
200#634—21no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#529—91no—
206C4×#41—91no—
207#485—91no—
208#482—91no—
209#479C3⋊D311yescharacteristic, complemented
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C2×C3×Q8C22×D314yes—
221#239—68no—
222#239—68no—
223C2×D12—34no—
224C2×D12—34no—
225C2×D12—64no—
226C2×D12—64no—
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×Dic6—34no—
235C2×C3×C8C22×D314yes—
236C2×C3×C8C22×D314yes—
237C3×C4⋊C4—24no—
238C3×C4⋊C4—24no—
239C3×C4⋊C4—24no—
240C3×C4⋊C4C22×D314yes—
241C3×C4⋊C4C22×D314yes—
242C3×C4⋊C4C22×D314yes—
243C3×C42—24no—
244C3×C42C22×D314yes—
245#216—68no—
246#215—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—34no—
256C4⋊Dic3—64no—
257C4⋊Dic3—64no—
258Dic3⋊C4—64no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267D24—68no—
268#204—68no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—21no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—21no—
273C2×C3⋊D3—21no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—22no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4C2×#4111yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3#13512yes—
292C2×#41—91no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—181no—
298#125C2×C3⋊D311yescharacteristic
299#124—91no—
300#123—181no—
301C22⋊Q8—91no—
302#121—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8C2×C3⋊D311yescharacteristic
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4—181no—
312#117—91no—
313#117—181no—
314#117—181no—
315C2×C42—91no—
316C2×C42—181no—
317#107—91no—
318#107C2×C3⋊D311yescharacteristic
319#106—91no—
320#106C2×C3⋊D311yescharacteristic
321C4⋊C8—91no—
322C4⋊C8C2×C3⋊D311yescharacteristic
323#103—91no—
324#103—91no—
325#103C2×C3⋊D311yescharacteristic
326#103C2×C3⋊D311yescharacteristic
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331C22⋊C8—91no—
332C22⋊C8—91no—
333C4×C8—91no—
334C4×C8—91no—
335C22×D3—34no—
336C22×D3—64no—
337C22×D3—64no—
338C3×Q8—24no—
339C3×Q8#23918yes—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4D3×D414yes—
345C2×C3×C4D3×D414yes—
346C2×C3×C4C23×D314yes—
347C2×Dic3—34no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352D12—38no—
353D12—616no—
354D12—64no—
355D12—64no—
356D12—64no—
357D12—128no—
358C4×D3—68no—
359C4×D3—616no—
360C4×D3—64no—
361C4×D3—64no—
362C4×D3—128no—
363C4×D3—128no—
364C4×D3—124no—
365C4×D3—128no—
366Dic6—64no—
367Dic6—64no—
368C3×C8—24no—
369C3×C8—24no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C2×C32#52511yescharacteristic
373C2×C32C2×#13511yescharacteristic
374C2×C32#57511yescharacteristic
375C3⋊D3—41no—
376C3⋊D3—42no—
377C3⋊D3—81no—
378#41—182no—
379#41—182no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—91no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4—181no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4—181no—
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8C22×C3⋊D311yescharacteristic
400C2×C8C22×C3⋊D311yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4C22×C3⋊D311yescharacteristic
409C4⋊C4C22×C3⋊D311yescharacteristic
410C4⋊C4C22×C3⋊D311yescharacteristic
411C22⋊C4—181no—
412C22⋊C4—181no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—91no—
421C42—91no—
422C42—91no—
423C42—181no—
424C42—181no—
425C42—181no—
426C42C22×C3⋊D311yescharacteristic
427C22×C3C2×D3×D414yes—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—68no—
431C2×D3—64no—
432C2×D3—124no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—28no—
440C3×C4—44no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4C2×#23914yes—
444C3×C4D3×#4114yes—
445Dic3—38no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—91no—
452C23—181no—
453C23—181no—
454Q8—21no—
455Q8—181no—
456Q8—181no—
457Q8#383212yes—
458D4—92no—
459D4—184no—
460D4—181no—
461D4—181no—
462D4—181no—
463D4—362no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—91no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—182no—
472C2×C4—184no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—361no—
478C2×C4—362no—
479C2×C4—362no—
480C2×C4—362no—
481C2×C4D4×C3⋊D311yescharacteristic
482C2×C4D4×C3⋊D311yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—21no—
485C8—21no—
486C8—181no—
487C8—181no—
488C2×C3#562714yes—
489C2×C3D3×#13514yes—
490C2×C3#577714yes—
491D3—124no—
492D3—128no—
493D3—244no—
494C22—182no—
495C22—181no—
496C22—181no—
497C22—181no—
498C22—361no—
499C22—361no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C2×D4×C3⋊D311yescharacteristic
504C4—22no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—41no—
510C4—92no—
511C4—181no—
512C4—181no—
513C4—361no—
514C4—361no—
515C4C2×#383211yescharacteristic
516C4#41×C3⋊D311yescharacteristic
517C3#8120414yescomplemented
518C2—361no—
519C2—362no—
520C2—721no—
521C2#1059609811yescharacteristic
522C2C3⋊D3×#13511yescharacteristic
523C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radical#10592509C2
hypercenter#479C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #10596162C2semidirect
2. C4×#3832C2semidirect
3. C32×#479C2semidirect
4. #10592765C2semidirect
5. #10592727C2semidirect
6. #10592587C2semidirect
7. #10592571C2semidirect
8. #10592565C2semidirect
9. #10592551C2semidirect
10. #10592543C2semidirect
11. #10592532C2semidirect
13. #10592507C2semidirect
14. #10592489C2semidirect
15. #10592487C2semidirect
62. C3×#479D3semidirect
209. #479C3⋊D3semidirect
450. C32#3102semidirect
517. C3#81204semidirect

Maximal subgroups

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

subgroupindex
#105961622
C4×#38322
C32×#4792
#105927652
#105927272
#105925872
#105925712
#105925652
#105925512
#105925432
#105925322
#105925092
#105925072
#105924892
#105924872
#812043