Finite Group Databasebeta

← #10593934

Subgroups — #10593934

Order 576.

515 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#872C211yesmaximal, characteristic, complemented
3C3×C4×Dic6C211yesmaximal, characteristic, complemented
4#63910C211yesmaximal, characteristic
5#63907C211yesmaximal, characteristic, complemented
6C4×#626C211yesmaximal, characteristic, complemented
7C4×#626C211yesmaximal, characteristic, complemented
8#63897C211yesmaximal, characteristic, complemented
9#63888C211yesmaximal, characteristic, complemented
10C4×#624C211yesmaximal, characteristic, complemented
11#63874C211yesmaximal, characteristic, complemented
12#63861C211yesmaximal, characteristic, complemented
13#63854C211yesmaximal, characteristic, complemented
14#63848C211yesmaximal, characteristic, complemented
15#63845C211yesmaximal, characteristic, complemented
16#5580—31nomaximal
17#5528—31nomaximal
18C2×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C4×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×D3C2211yescharacteristic
22C2×C3×Dic6C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#626C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×#624C2211yescharacteristic
27C32×C42C2211yescharacteristic
28#3752C2211yescharacteristic
29#3752C2211yescharacteristic
30C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×C4⋊Dic3C2211yescharacteristic
34C3×Dic3⋊C4C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×C4×Dic3C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41#3724C2211yescharacteristic
42#3724C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45#3722C2211yescharacteristic
46#3722C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×C4×Q8—31no—
54C3×#117—31no—
55#947—31no—
56#946—31no—
57C4×#67—31no—
58C4×#67—31no—
59#898—31no—
60#898—31no—
61#898—31no—
62#896—31no—
63#895—31no—
64#894—31no—
65#894—31no—
66#894—31no—
67#890—31no—
68#889—31no—
69#885—31no—
70#884—31no—
71#883—31no—
72#879—31no—
73C4×D12—31no—
74C4×D12—31no—
75C4×D12—31no—
76C4×D12—31no—
77C4×D12—61no—
78#872—31no—
79#872—31no—
80#872D311yescharacteristic, complemented
81C42×D3—31no—
82C42×D3—31no—
83C4×Dic6D311yescharacteristic, complemented
84C22×C3⋊D3C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C4⋊(C3⋊D3)—22no—
93C4×C3⋊D3—22no—
94C4×C3⋊D3—22no—
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C3×C4×D3—22no—
103C3×Dic6—22no—
104#626—22no—
105#626—22no—
106#624—22no—
107#624—22no—
108#529—91noSylow
109C2×C3×Q8—31no—
110C22×C3×C4—31no—
111C2×#67—31no—
112C2×#67—31no—
113C2×D12—31no—
114C2×D12—31no—
115C2×D12—31no—
116C2×D12—31no—
117C2×D12—61no—
118C2×C4×D3—31no—
119C2×C4×D3—31no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—31no—
125C2×C4×D3—31no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3C2×D311yescharacteristic
129C2×Dic6C2×D311yescharacteristic
130C3×C4⋊C4—31no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C22⋊C4—31no—
136C3×C22⋊C4—31no—
137C3×C42—21no—
138C3×C42—31no—
139C3×C42—31no—
140C3×C42—31no—
141C3×C42C2×D311yescharacteristic
142C3×C42C2×D311yescharacteristic
143#217—31no—
144#217—31no—
145(C2×D3)⋊C4—31no—
146(C2×D3)⋊C4—31no—
147(C2×D3)⋊C4—31no—
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4—31no—
150(C2×D3)⋊C4—31no—
151(C2×D3)⋊C4—31no—
152(C2×D3)⋊C4—31no—
153(C2×D3)⋊C4—31no—
154(C2×D3)⋊C4—31no—
155(C2×D3)⋊C4—31no—
156(C2×D3)⋊C4—31no—
157(C2×D3)⋊C4—31no—
158(C2×D3)⋊C4—31no—
159(C2×D3)⋊C4—61no—
160(C2×D3)⋊C4—61no—
161(C2×D3)⋊C4C2×D311yescharacteristic
162(C2×D3)⋊C4C2×D311yescharacteristic
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—61no—
168C4⋊Dic3C2×D311yescharacteristic
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—31no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4C2×D311yescharacteristic
176Dic3⋊C4C2×D311yescharacteristic
177Dic3⋊C4C2×D311yescharacteristic
178Dic3⋊C4C2×D311yescharacteristic
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3C2×D311yescharacteristic
184C4×Dic3C2×D311yescharacteristic
185C4×Dic3C2×D311yescharacteristic
186C22×C32C2411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3#4112yes—
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4#4112yes—
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3#4112yes—
208#126—91no—
209#126—91no—
210#125—91no—
211#124—91no—
212#123—91no—
213#123—91no—
214C22⋊Q8—91no—
215#121—91no—
216C4×Q8—31no—
217C4×D4—91no—
218C4×D4—91no—
219C4×D4—91no—
220#117—31no—
221#117—91no—
222C2×C42—91no—
223C23×C3—31no—
224C22×D3—31no—
225C22×D3—31no—
226C22×D3—31no—
227C22×D3—31no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3C22×D311yescharacteristic
231C3×Q8—62no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—31no—
239C2×C3×C4—31no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242C2×C3×C4—62no—
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245C2×C3×C4C22×D311yescharacteristic
246C2×C3×C4C22×D311yescharacteristic
247C2×C3×C4C22×D311yescharacteristic
248C2×C3×C4C22×D311yescharacteristic
249#67—62no—
250#67—62no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263C2×Dic3C22×D311yescharacteristic
264D12—62no—
265D12—62no—
266D12—64no—
267D12—62no—
268D12—62no—
269C4×D3—22no—
270C4×D3—62no—
271C4×D3—62no—
272C4×D3—62no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—122no—
279C4×D3—122no—
280Dic6—22no—
281C2×C32C2×#4111yescharacteristic
282C2×C32C2×#4111yescharacteristic
283C2×C32C2×#4111yescharacteristic
284C3⋊D3—22no—
285C3⋊D3—41no—
286C3×D3—41no—
287C2×Q8—31no—
288C2×D4—91no—
289C2×D4—91no—
290C2×D4—91no—
291C22×C4—31no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C22⋊C4—31no—
307C22⋊C4—31no—
308C22⋊C4—91no—
309C22⋊C4—91no—
310C22⋊C4—91no—
311C22⋊C4—91no—
312C22⋊C4—91no—
313C22⋊C4—91no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C42—31no—
317C42—31no—
318C42—31no—
319C42—91no—
320C42—91no—
321C42D3211yescharacteristic
322C22×C3—21no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—61no—
326C22×C3C23×D311yescharacteristic
327C22×C3C23×D311yescharacteristic
328C2×D3—21no—
329C2×D3—21no—
330C2×D3—21no—
331C2×D3—32no—
332C2×D3—32no—
333C2×D3—62no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—61no—
337C2×D3—61no—
338C2×D3—62no—
339C2×D3—61no—
340C2×D3—61no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—61no—
344C2×D3—61no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C3×C4—22no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—22no—
355C3×C4—32no—
356C3×C4—41no—
357C3×C4—61no—
358C3×C4—61no—
359C3×C4—61no—
360C3×C4—61no—
361C3×C4—61no—
362C3×C4—61no—
363C3×C4#23512yes—
364C3×C4#23912yes—
365Dic3—21no—
366Dic3—21no—
367Dic3—21no—
368Dic3—21no—
369Dic3—21no—
370Dic3—21no—
371Dic3—61no—
372Dic3—61no—
373Dic3—61no—
374Dic3—61no—
375Dic3—121no—
376Dic3—121no—
377Dic3#23512yes—
378C32#52911yescharacteristic, complemented, Sylow
379C23—31no—
380C23—91no—
381C23—91no—
382Q8—62no—
383D4—182no—
384D4—182no—
385D4—182no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—31no—
391C2×C4—31no—
392C2×C4—31no—
393C2×C4—62no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4C2×D3211yescharacteristic
401C2×C4C2×D3211yescharacteristic
402C2×C4C2×D3211yescharacteristic
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—121no—
407C2×C3C2×#23511yescharacteristic
408C2×C3C2×#23511yescharacteristic
409C2×C3C2×#23911yescharacteristic
410C2×C3D3×#4111yescharacteristic
411C2×C3D3×#4111yescharacteristic
412C2×C3D3×#4111yescharacteristic
413D3—41no—
414D3—62no—
415D3—62no—
416D3—122no—
417D3—122no—
418D3—121no—
419D3—121no—
420C22—61no—
421C22—61no—
422C22—61no—
423C22—92no—
424C22—181no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22—181no—
429C22C22×D3211yescharacteristic
430C4—21no—
431C4—21no—
432C4—32no—
433C4—61no—
434C4—61no—
435C4—61no—
436C4—61no—
437C4—61no—
438C4—61no—
439C4—181no—
440C4—181no—
441C4#379912yes—
442C3—21no—
443C3#552811yescharacteristic, complemented
444C3#558011yescharacteristic, complemented
445C2—121no—
446C2—182no—
447C2—361no—
448C2C2×#379911yescharacteristic
449C2D3×#23511yescharacteristic
450C2#6430611yescharacteristic
subgroupG/H
centerC2×C4C2×D32
commutator, socle, cosocleC22×C32C24
FrattiniC22C22×D32
FittingC32×C42C22
prime radical#63910C2
hypercenterC42D32
hypocenterC32#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C3⋊D3)C2semidirect
2. C3×#872C2semidirect
3. C3×C4×Dic6C2semidirect
5. #63907C2semidirect
6. C4×#626C2semidirect
7. C4×#626C2semidirect
8. #63897C2semidirect
9. #63888C2semidirect
10. C4×#624C2semidirect
11. #63874C2semidirect
12. #63861C2semidirect
13. #63854C2semidirect
14. #63848C2semidirect
15. #63845C2semidirect
80. #872D3semidirect
83. C4×Dic6D3semidirect
378. C32#529semidirect
443. C3#5528semidirect
444. C3#5580semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C3⋊D3)2
C3×#8722
C3×C4×Dic62
#639102
#639072
C4×#6262
#638972
#638882
C4×#6242
#638742
#638612
#638542
#638482
#638452
#55803
#55283