Finite Group Databasebeta

← #11774243

Subgroups — #11774243

Order 1152.

587 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3795C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic, complemented
3C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70754—31nomaximal
9#68165—31nomaximal
10C2×#3795C411yescharacteristic
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14C4×#625—21no—
15Dic3×D12C411yescharacteristic
16#63879—21no—
17#63877—21no—
18C4×D3×Dic3—21no—
19#63844C411yescharacteristic
20#63841C411yescharacteristic
21C2×D3×C3⋊C8—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×C8×Dic3—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28Dic3×C3⋊C8—21no—
29C4×#237—31no—
30C4×#235—31no—
31C3×#431—31no—
32C2×C4×C3⋊C8—31no—
33#4833D311yescharacteristic, complemented
34C4×D3×C8—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42#4483D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3795—22no—
54#3795C814yescomplemented
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72Dic32—21no—
73D3×C3⋊C8—24no—
74#1476—91noSylow
75C2×#237—31no—
76C2×#235—31no—
77C3×C4×D4—31no—
78C2×C3×C42—31no—
79D4×Dic3—31no—
80C4×#67—61no—
81C4×#67—61no—
82C4×#67—61no—
83#926—31no—
84C2×C4×Dic3—61no—
85C22×C3⋊C8—61no—
86C2×D3×C8—61no—
87#892—31no—
88#887—31no—
89#67⋊C4—61no—
90#877—61no—
91C4×D12—31no—
92C4×D12C2×D311yescharacteristic
93#872—61no—
94C42×D3—61no—
95C42×D3C2×D311yescharacteristic
96C4×Dic6—31no—
97C4×Dic6—31no—
98C4×Dic6—31no—
99C4×Dic6—61no—
100C3×C4⋊C8—21no—
101C3×C4⋊C8—31no—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4⋊C8C2×D311yescharacteristic
104C3×C22⋊C8—61no—
105C3×C4×C8—31no—
106C3×C4×C8—61no—
107(C2×D3)⋊C8—21no—
108C8×Dic3—21no—
109C8×Dic3—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3C22⋊C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123#634—21no—
124#634C2×C812yescomplemented
125C2×C3×Dic3—21no—
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C3×D12—21no—
130C3×D12C2×C812yescomplemented
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—22no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×C4×D3C2×C812yes—
137C3×C4×D3M1612yes—
138#625—24no—
139D3×Dic3—24no—
140D3×Dic3—42no—
141C32×C8—41no—
142C3⋊(C3⋊C8)—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C4×#41—91no—
146#431—31no—
147C2×C4×C8—91no—
148Q8⋊C8—91no—
149Q8⋊C8—91no—
150D4⋊C8—31no—
151D4⋊C8—91no—
152C2×C3×D4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C2×#67—61no—
158C2×#67—61no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161#237—34no—
162#237—62no—
163#235—34no—
164#235—62no—
165C2×D12C4×D311yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3C4×D311yescharacteristic
170C2×C4×D3D1211yescharacteristic
171C2×C4×D3#6711yescharacteristic
172C2×Dic6—31no—
173C2×Dic6—31no—
174C2×Dic6—61no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—41no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—31no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42—31no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42C22×D311yescharacteristic
187C3×C42C22×D311yescharacteristic
188#217—61no—
189#217—61no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193C4⋊Dic3—31no—
194C4⋊Dic3—31no—
195C4⋊Dic3—61no—
196C4⋊Dic3C4×D311yescharacteristic
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—121no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—121no—
209C4×Dic3C4×D311yescharacteristic
210C4×Dic3D1211yescharacteristic
211C4×Dic3#6711yescharacteristic
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—64no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—121no—
218D3×C8—64no—
219C22×C32C2×C22⋊C411yescharacteristic
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—22no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3C22⋊C812yes—
226C32×C4—21no—
227C32×C4C22×C811yescharacteristic
228C32×C4C2×M1611yescharacteristic
229C32×C4#13511yescharacteristic
230C32×C4#13511yescharacteristic
231C3⋊Dic3—22no—
232C3⋊Dic3—41no—
233C3×Dic3—21no—
234C3×Dic3—41no—
235C3×Dic3C22⋊C812yes—
236C3×Dic3#10412yes—
237C2×#41—91no—
238C22×C8—181no—
239C4×Q8—91no—
240C4×Q8—91no—
241C4×D4—31no—
242C4×D4—91no—
243C4×D4—181no—
244C4×D4—181no—
245#117—91no—
246#117—181no—
247C2×C42—31no—
248C2×C42—181no—
249C4⋊C8—31no—
250C4⋊C8D3211yescharacteristic
251C22⋊C8—61no—
252C4×C8—31no—
253C4×C8—61no—
254C4×C8—91no—
255C4×C8—181no—
256C23×C3—31no—
257C23×C3—61no—
258C22×D3—21no—
259C22×D3(C2×D3)⋊C411yescharacteristic
260C3×D4—32no—
261C3×D4—61no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—31no—
266C2×C3×C4—31no—
267C2×C3×C4—32no—
268C2×C3×C4—32no—
269C2×C3×C4—31no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282#67—64no—
283#67—64no—
284C2×Dic3—21no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—64no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—121no—
291C2×Dic3—121no—
292C2×Dic3—122no—
293C2×Dic3(C2×D3)⋊C411yescharacteristic
294C2×Dic3(C2×D3)⋊C411yescharacteristic
295C2×Dic3(C2×D3)⋊C411yescharacteristic
296D12—21no—
297D12D3×C812yescomplemented
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—22no—
301C4×D3—41no—
302C4×D3—41no—
303C4×D3—64no—
304C4×D3—122no—
305C4×D3D3×C812yes—
306C4×D3ΓL(1,𝔽25)12yes—
307Dic6—32no—
308Dic6—32no—
309Dic6—62no—
310Dic6—61no—
311Dic6—61no—
312Dic6—121no—
313C3×C8—41no—
314C3×C8—41no—
315C3×C8—62no—
316C3×C8—81no—
317C3×C8—121no—
318C3⋊C8—22no—
319C3⋊C8—41no—
320C3⋊C8—62no—
321C3⋊C8—62no—
322C3⋊C8—122no—
323C2×C32C2×C22⋊C811yescharacteristic
324C2×C32#41611yescharacteristic
325C2×C32C2×#10411yescharacteristic
326C3×D3—22no—
327C3×D3—42no—
328#41—94no—
329#41—182no—
330C2×Q8—91no—
331C2×D4—31no—
332C2×D4—181no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—61no—
337C22×C4—181no—
338C22×C4—181no—
339C2×C8—21no—
340C2×C8—61no—
341C2×C8—61no—
342C2×C8—184no—
343C2×C8—181no—
344C4⋊C4—31no—
345C4⋊C4—91no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C22⋊C4—61no—
349C22⋊C4—181no—
350C22⋊C4—181no—
351C42—31no—
352C42—31no—
353C42—31no—
354C42—181no—
355C42—181no—
356C42—181no—
357C42C2×D3211yescharacteristic
358C22×C3—21no—
359C22×C3—32no—
360C22×C3—61no—
361C22×C3—61no—
362C22×C3—62no—
363C22×C3—121no—
364C22×C3—121no—
365C22×C3D3×C22⋊C411yescharacteristic
366C22×C3C2×(C2×D3)⋊C411yescharacteristic
367C2×D3—21no—
368C2×D3—21no—
369C2×D3—22no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3(C2×D3)⋊C812yes—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—32no—
380C3×C4—32no—
381C3×C4—41no—
382C3×C4—61no—
383C3×C4—121no—
384C3×C4C2×D3×C811yescharacteristic
385C3×C4C2×D3×C811yescharacteristic
386C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
387C3×C4D3×M1611yescharacteristic
388C3×C4#91211yescharacteristic
389C3×C4#91611yescharacteristic
390C3×C4#95011yescharacteristic
391C3×C4#95011yescharacteristic
392Dic3—21no—
393Dic3—41no—
394Dic3—62no—
395Dic3—62no—
396Dic3—122no—
397Dic3—121no—
398Dic3—121no—
399Dic3—241no—
400Dic3(C2×D3)⋊C812yes—
401Dic3#82512yes—
402C32#147611yescharacteristic, complemented, Sylow
403C23—31no—
404C23—61no—
405Q8—92no—
406Q8—181no—
407D4—32no—
408D4—61no—
409D4—184no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—31no—
415C2×C4—62no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—184no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—362no—
425C2×C4C4×D3211yescharacteristic
426C2×C4D3×D1211yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C8—41no—
429C8—62no—
430C8—121no—
431C8—182no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—62no—
436C2×C3—122no—
437C2×C3D3×C22⋊C811yescharacteristic
438C2×C3#477211yescharacteristic
439C2×C3D3×#10411yescharacteristic
440C2×C3#500211yescharacteristic
441C2×C3C2×(C2×D3)⋊C811yescharacteristic
442C2×C3C2×#82511yescharacteristic
443D3—22no—
444D3—42no—
445C22—32no—
446C22—61no—
447C22—61no—
448C22—62no—
449C22—121no—
450C22—121no—
451C22D3×(C2×D3)⋊C411yescharacteristic
452C4—21no—
453C4—32no—
454C4—32no—
455C4—61no—
456C4—121no—
457C4—182no—
458C4—361no—
459C4D32×C811yescharacteristic
460C4D3×ΓL(1,𝔽25)11yescharacteristic
461C4#6393311yescharacteristic
462C4#6394711yescharacteristic
463C3—21no—
464C3#6816511yescharacteristic, complemented
465C3#7075411yescharacteristic, complemented
466C2—62no—
467C2—122no—
468C2#1059060811yescharacteristic
469C2D3×(C2×D3)⋊C811yescharacteristic
470C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3795C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1476
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4833C2semidirect
3. C4×D3×C3⋊C8C2semidirect
4. #10589350C2semidirect
5. C3×#4483C2semidirect
6. #10589085C2semidirect
7. #10589080C2semidirect
33. #4833D3semidirect
42. #4483D3semidirect
54. #3795C8semidirect
124. #634C2×C8semidirect
130. C3×D12C2×C8semidirect
297. D12D3×C8semidirect
402. C32#1476semidirect
464. C3#68165semidirect
465. C3#70754semidirect

Maximal subgroups

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

subgroupindex
C4×#37952
C3×#48332
C4×D3×C3⋊C82
#105893502
C3×#44832
#105890852
#105890802
#707543
#681653