Finite Group Databasebeta

← #11868645

Subgroups — #11868645

Order 1152.

1320 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596159C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4#10592765C211yesmaximal, characteristic, complemented
5#10592708C211yesmaximal, characteristic, complemented
6#10592589C211yesmaximal, characteristic, complemented
7#10592580C211yesmaximal, characteristic, complemented
8#10592569C211yesmaximal, characteristic, complemented
9#10592560C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592536C211yesmaximal, characteristic, complemented
12#10592469C211yesmaximal, characteristic
13#10592469C211yesmaximal, characteristic
14#10592460C211yesmaximal, characteristic, complemented
15#10592458C211yesmaximal, characteristic, complemented
16#81166—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C32×#125C2211yescharacteristic, complemented
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×#3743C2211yescharacteristic
24C2×#3743C2211yescharacteristic
25#64105—21no—
26#64105—21no—
27#64102C2211yescharacteristic
28#64101C2211yescharacteristic
29#64101C2211yescharacteristic
30C4⋊C4×C3⋊D3C2211yescharacteristic
31#64097C2211yescharacteristic, complemented
32#64097C2211yescharacteristic, complemented
33#64096—21no—
34#64096—21no—
35#64090—21no—
36C22⋊C4×C3⋊D3—21no—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C42×C3⋊D3C2211yescharacteristic
39#64079C2211yescharacteristic, complemented
40C32×#107C2211yescharacteristic, complemented
41C32×#106C2211yescharacteristic, complemented
42C32×C4⋊C8C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63645C2211yescharacteristic, complemented
50#63644C2211yescharacteristic, complemented
51#63641C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic, complemented
56#63635C2211yescharacteristic, complemented
57#63634C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5688—34no—
61C4×D3×D4—34no—
62C3×#478D314yescomplemented
63#5066—34no—
64#5009—34no—
65#4890—34no—
66#4881—34no—
67#4870—34no—
68#4861—34no—
69#4847—34no—
70#4837—34no—
71#4770—34no—
72#4770—34no—
73#4761—34no—
74#4759—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C2×#638—21no—
79C22×C3⋊Dic3—21no—
80D4×C3⋊D3—22no—
81D4×C3⋊D3Q814yescomplemented
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—44no—
87C2×C4×C3⋊D3D411yescharacteristic
88C2×C4×C3⋊D3D411yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C2×#634—21no—
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C42C2311yescharacteristic
101#3757—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3743—22no—
122#3743—22no—
123#3077—91noSylow
124C2×D3×D4—34no—
125C22×C4×D3—64no—
126C3×#125C2×D314yescomplemented
127C3×C4×D4C2×D314yes—
128D4×Dic3—34no—
129C4×#67—64no—
130C2×ΓL(1,𝔽25)—34no—
131C2×ΓL(1,𝔽25)—34no—
132#896—64no—
133#896—64no—
134#893—34no—
135#892—34no—
136#892—34no—
137D3×C4⋊C4—34no—
138#888—34no—
139#888—34no—
140#887—64no—
141#887—64no—
142#67⋊C4—64no—
143D3×C22⋊C4—64no—
144C4×D12—34no—
145C42×D3—34no—
146#870—34no—
147C3×#107C2×D314yescomplemented
148C3×#106C2×D314yescomplemented
149C3×C4⋊C8C2×D314yescomplemented
150C3×#102C2×D314yes—
151C3×#102C2×D314yes—
152#832—34no—
153#832—34no—
154#821—34no—
155#821—34no—
156#818—34no—
157#817—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160#809—34no—
161#809—34no—
162#808—34no—
163#808—34no—
164#807—34no—
165#807—34no—
166C4⋊(C3⋊C8)—34no—
167C23×C32—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—24no—
170C22×C3⋊D3—42no—
171C22×C3⋊D3—42no—
172C22×C3⋊D3C2×D411yescharacteristic
173C32×D4—21no—
174C32×D4C2×Q812yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—42no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—42no—
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)C2×Q812yes—
192C4×C3⋊D3—22no—
193C4×C3⋊D3—41no—
194C4×C3⋊D3—42no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3C2×Q812yes—
198C4×C3⋊D3#4112yes—
199#634—42no—
200#634—42no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#533—91no—
206C2×C4×D4—91no—
207#478—91no—
208#478—91no—
209#478—91no—
210#478C3⋊D311yescharacteristic, complemented
211#476—91no—
212#476—91no—
213#474—91no—
214#474—91no—
215#428—91no—
216#428—91no—
217#423—91no—
218#418—91no—
219#418—91no—
220C23×D3—64no—
221C2×C3×D4C22×D314yes—
222C22×C3×C4—24no—
223C2×#67—64no—
224C22×Dic3—64no—
225D3×D4—316no—
226D3×D4—68no—
227C2×D12—34no—
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—1216no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C2×C3×C8C22×D314yes—
238C2×C3×C8C22×D314yes—
239C3×C4⋊C4—24no—
240C3×C4⋊C4—24no—
241C3×C4⋊C4C22×D314yes—
242C3×C4⋊C4C22×D314yes—
243C3×C4⋊C4C22×D314yes—
244C3×C22⋊C4—24no—
245C3×C42C22×D314yes—
246#217—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3—34no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—34no—
266ΓL(1,𝔽25)—68no—
267ΓL(1,𝔽25)—68no—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—21no—
273C2×C3⋊D3—21no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—48no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3C22⋊Q812yes—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4C22×Q811yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—21no—
287C3⋊Dic3—41no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3⋊Dic3C22⋊Q812yes—
291C3⋊Dic3AGL(1,ℤ/8)12yes—
292C22×D4—91no—
293C23×C4—181no—
294C2×M16—91no—
295C2×M16—91no—
296C4⋊Q8—91no—
297C4⋊Q8—91no—
298#125—91no—
299#125C2×C3⋊D311yescharacteristic, complemented
300C22⋊Q8—181no—
301C22⋊Q8—181no—
302C4×Q8—181no—
303C4×Q8—181no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—91no—
307C4×D4—181no—
308C4×D4—181no—
309C4×D4C2×C3⋊D311yescharacteristic
310#117—91no—
311#117—91no—
312C2×C4⋊C4—91no—
313C2×C22⋊C4—181no—
314C2×C42—91no—
315#107—91no—
316#107—91no—
317#107—91no—
318#107C2×C3⋊D311yescharacteristic, complemented
319#106—91no—
320#106—91no—
321#106—91no—
322#106C2×C3⋊D311yescharacteristic, complemented
323C4⋊C8—91no—
324C4⋊C8—91no—
325C4⋊C8—91no—
326C4⋊C8C2×C3⋊D311yescharacteristic, complemented
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332#102—91no—
333#102C2×C3⋊D311yescharacteristic
334#102C2×C3⋊D311yescharacteristic
335C23×C3—24no—
336C22×D3—34no—
337C22×D3—616no—
338C22×D3—64no—
339C22×D3—128no—
340C22×D3—128no—
341C3×D4—24no—
342C3×D4D3×Q818yes—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—48no—
347C2×C3×C4D3×D414yes—
348C2×C3×C4D3×D414yes—
349C2×C3×C4C23×D314yes—
350#67—616no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—128no—
358D12—38no—
359D12—64no—
360C4×D3—38no—
361C4×D3—38no—
362C4×D3—68no—
363C4×D3—128no—
364C4×D3—124no—
365C4×D3—128no—
366C4×D3—128no—
367Dic6—128no—
368Dic6—128no—
369C3×C8—24no—
370C3×C8—24no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—42no—
374C2×C32C2×C22⋊Q811yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C32#57511yescharacteristic
377C3⋊D3—22no—
378C3⋊D3—42no—
379C24—181no—
380C2×Q8—181no—
381C2×Q8—181no—
382C2×D4—94no—
383C2×D4—91no—
384C2×D4—182no—
385C2×D4—181no—
386C2×D4C22×C3⋊D311yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—364no—
396M16—182no—
397M16—182no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8C22×C3⋊D311yescharacteristic
401C2×C8C22×C3⋊D311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4C22×C3⋊D311yescharacteristic
413C4⋊C4C22×C3⋊D311yescharacteristic
414C4⋊C4C22×C3⋊D311yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C42—91no—
422C42—91no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42C22×C3⋊D311yescharacteristic
427C22×C3—28no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3C2×D3×D414yes—
431C2×D3—38no—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—68no—
435C2×D3—1232no—
436C2×D3—124no—
437C2×D3—124no—
438C3×C4—24no—
439C3×C4—24no—
440C3×C4—44no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4C2×D3×Q814yes—
444C3×C4D3×#4114yes—
445Dic3—38no—
446Dic3—38no—
447Dic3—64no—
448Dic3—124no—
449Dic3—124no—
450Dic3—124no—
451C32#307711yescharacteristic, complemented, Sylow
452C23—21no—
453C23—91no—
454C23—184no—
455C23—181no—
456C23—362no—
457C23—362no—
458Q8—362no—
459Q8—362no—
460D4—21no—
461D4—92no—
462D4—184no—
463D4—181no—
464D4Q8×C3⋊D312yes—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—91no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—361no—
479C2×C4—362no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4D4×C3⋊D311yescharacteristic
484C2×C4D4×C3⋊D311yescharacteristic
485C2×C4C23×C3⋊D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—48no—
491C2×C3D3×C22⋊Q814yes—
492C2×C3#576814yes—
493C2×C3D3×AGL(1,ℤ/8)14yes—
494D3—68no—
495D3—128no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—92no—
500C22—181no—
501C22—181no—
502C22—182no—
503C22—368no—
504C22—361no—
505C22—361no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—92no—
513C4—92no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×Q8×C3⋊D311yescharacteristic
519C4#41×C3⋊D311yescharacteristic
520C3#8116614yescomplemented
521C2—42no—
522C2—182no—
523C2—362no—
524C2C3⋊D3×C22⋊Q811yescharacteristic
525C2#1059623911yescharacteristic
526C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#478C3⋊D3
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10596159C2semidirect
3. C32×#478C2semidirect
4. #10592765C2semidirect
5. #10592708C2semidirect
6. #10592589C2semidirect
7. #10592580C2semidirect
8. #10592569C2semidirect
9. #10592560C2semidirect
10. #10592546C2semidirect
11. #10592536C2semidirect
14. #10592460C2semidirect
15. #10592458C2semidirect
19. C32×#125C22semidirect
31. #64097C22semidirect
32. #64097C22semidirect
39. #64079C22semidirect
40. C32×#107C22semidirect
41. C32×#106C22semidirect
42. C32×C4⋊C8C22semidirect
49. #63645C22semidirect
50. #63644C22semidirect
51. #63641C22semidirect
52. #63641C22semidirect
55. #63635C22semidirect
56. #63635C22semidirect
57. #63634C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×#478D3semidirect
81. D4×C3⋊D3Q8semidirect
126. C3×#125C2×D3semidirect
147. C3×#107C2×D3semidirect
148. C3×#106C2×D3semidirect
149. C3×C4⋊C8C2×D3semidirect
210. #478C3⋊D3semidirect
299. #125C2×C3⋊D3semidirect
318. #107C2×C3⋊D3semidirect
322. #106C2×C3⋊D3semidirect
326. C4⋊C8C2×C3⋊D3semidirect
451. C32#3077semidirect
520. C3#81166semidirect

Maximal subgroups

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

subgroupindex
#105961592
C4×D4×C3⋊D32
C32×#4782
#105927652
#105927082
#105925892
#105925802
#105925692
#105925602
#105925462
#105925362
#105924692
#105924602
#105924582
#811663