Finite Group Databasebeta

← #10594218

Subgroups — #10594218

Order 576.

523 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64090C211yesmaximal, characteristic, complemented
2C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#67⋊C4C211yesmaximal, characteristic, complemented
4#63980C211yesmaximal, characteristic, complemented
5#63978C211yesmaximal, characteristic, complemented
6#63978C211yesmaximal, characteristic, complemented
7C2×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#63906C211yesmaximal, characteristic, complemented
9#63905C211yesmaximal, characteristic, complemented
10C4×#626C211yesmaximal, characteristic, complemented
11#63868C211yesmaximal, characteristic, complemented
12#63867C211yesmaximal, characteristic, complemented
13#63862C211yesmaximal, characteristic, complemented
14#63855C211yesmaximal, characteristic, complemented
15#63853C211yesmaximal, characteristic, complemented
16#5565—31nomaximal
17#5540—31nomaximal
18C2×#638C2211yescharacteristic
19C22×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C22×C3×Dic3C2211yescharacteristic
24C22×C3×Dic3C2211yescharacteristic
25C2×C3×C4×D3C2211yescharacteristic
26C2×C3×C4×D3C2211yescharacteristic
27C2×#626C2211yescharacteristic
28C2×#626C2211yescharacteristic
29C2×#625C2211yescharacteristic
30C32×C22⋊C4C2211yescharacteristic
31#3752C2211yescharacteristic
32#3750C2211yescharacteristic
33C4×C3⋊Dic3C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D3)⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×C4×Dic3C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40#3724C2211yescharacteristic
41Dic3⋊Dic3C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47#3722C2211yescharacteristic
48#3722C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53C3×C4×D4—31no—
54C3×C4×D4—31no—
55#939—31no—
56#939—31no—
57#939—31no—
58#939—31no—
59#930—31no—
60#930—31no—
61#930—31no—
62#929—31no—
63C4×#67—31no—
64#926—31no—
65C2×C4⋊Dic3—31no—
66C2×Dic3⋊C4—31no—
67#898—31no—
68#898—31no—
69#894—31no—
70#889—31no—
71#884—31no—
72#883—31no—
73#883—31no—
74#67⋊C4—31no—
75#67⋊C4—31no—
76#67⋊C4—61no—
77#67⋊C4D311yescharacteristic, complemented
78#67⋊C4D311yescharacteristic, complemented
79#879—31no—
80#876—31no—
81C4×D12—31no—
82#872—31no—
83#870—31no—
84C23×C32C2311yescharacteristic
85C22×C3⋊D3C2311yescharacteristic
86C22×C3×D3C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C32×C4C2311yescharacteristic
90#638—22no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊D3—41no—
96C3×#67—22no—
97C3×#67—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C3×C4×D3—22no—
107C3×C4×D3—41no—
108#626—22no—
109#626—41no—
110#625—41no—
111#553—91noSylow
112C2×C3×D4—31no—
113C2×C3×D4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—31no—
116C22×C3×C4—31no—
117C22×C3×C4—31no—
118C2×#67—31no—
119C2×#67—31no—
120C2×#67—31no—
121C2×#67—31no—
122C2×#67—31no—
123C2×#67—31no—
124C2×#67—61no—
125C2×#67C2×D311yescharacteristic
126C2×#67C2×D311yescharacteristic
127C22×Dic3—31no—
128C22×Dic3—31no—
129C22×Dic3—61no—
130C22×Dic3C2×D311yescharacteristic
131C22×Dic3C2×D311yescharacteristic
132C2×D12—31no—
133C2×D12—31no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—61no—
137C2×C4×D3C2×D311yescharacteristic
138C2×C4×D3C2×D311yescharacteristic
139C3×C4⋊C4—31no—
140C3×C4⋊C4—31no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—31no—
143C3×C22⋊C4—31no—
144C3×C22⋊C4C2×D311yescharacteristic
145C3×C22⋊C4C2×D311yescharacteristic
146C3×C42—31no—
147C3×C42—31no—
148#217—31no—
149#217—31no—
150#217—31no—
151#217—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—31no—
160(C2×D3)⋊C4—31no—
161(C2×D3)⋊C4—31no—
162(C2×D3)⋊C4—61no—
163(C2×D3)⋊C4C2×D311yescharacteristic
164(C2×D3)⋊C4C2×D311yescharacteristic
165C4⋊Dic3—31no—
166C4⋊Dic3—31no—
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—31no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—31no—
178Dic3⋊C4—31no—
179Dic3⋊C4—31no—
180Dic3⋊C4—31no—
181Dic3⋊C4—61no—
182Dic3⋊C4C2×D311yescharacteristic
183Dic3⋊C4C2×D311yescharacteristic
184C4×Dic3—31no—
185C4×Dic3—31no—
186C4×Dic3—61no—
187C4×Dic3C2×D311yescharacteristic
188C4×Dic3C2×D311yescharacteristic
189C22×C32—21no—
190C22×C32—21no—
191C22×C32#4112yes—
192C22×C32C2411yescharacteristic
193C2×C3⋊D3—21no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
196C2×C3×D3—21no—
197C2×C3×D3—21no—
198C2×C3×D3—21no—
199C2×C3×D3—21no—
200C2×C3×D3—21no—
201C2×C3×D3—21no—
202C32×C4—21no—
203C32×C4—21no—
204C3⋊Dic3—21no—
205C3⋊Dic3—21no—
206C3⋊Dic3—21no—
207C3×Dic3—21no—
208C3×Dic3—21no—
209C3×Dic3—21no—
210C3×Dic3—21no—
211C3×Dic3—21no—
212C3×Dic3#4112yes—
213#126—91no—
214#126—91no—
215#125—91no—
216#123—91no—
217#123—91no—
218#121—91no—
219#121—91no—
220#121—91no—
221#121—91no—
222C4×D4—31no—
223C4×D4—31no—
224C4×D4—91no—
225C4×D4—91no—
226#117—91no—
227C2×C4⋊C4—91no—
228C23×C3—21no—
229C23×C3—31no—
230C23×C3—31no—
231C23×C3C22×D311yescharacteristic
232C23×C3C22×D311yescharacteristic
233C22×D3—31no—
234C22×D3—31no—
235C22×D3—61no—
236C22×D3C22×D311yescharacteristic
237C22×D3C22×D311yescharacteristic
238C3×D4—62no—
239C3×D4—62no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4C22×D311yescharacteristic
253C2×C3×C4C22×D311yescharacteristic
254C2×C3×C4C22×D311yescharacteristic
255C2×C3×C4C22×D311yescharacteristic
256#67—22no—
257#67—22no—
258#67—64no—
259#67—62no—
260#67—62no—
261#67—62no—
262#67—121no—
263#67—121no—
264#67—121no—
265C2×Dic3—22no—
266C2×Dic3—31no—
267C2×Dic3—31no—
268C2×Dic3—31no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—31no—
272C2×Dic3—41no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3—122no—
279C2×Dic3C22×D311yescharacteristic
280C2×Dic3C22×D311yescharacteristic
281C2×Dic3C22×D311yescharacteristic
282C2×Dic3C22×D311yescharacteristic
283C2×Dic3C22×D311yescharacteristic
284C2×Dic3C22×D311yescharacteristic
285D12—62no—
286D12—121no—
287C4×D3—22no—
288C4×D3—41no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—122no—
292C2×C32—22no—
293C2×C32C2×#4111yescharacteristic
294C2×C32C2×#4111yescharacteristic
295C2×C32H(5,𝔽2)11yescharacteristic
296C3⋊D3—41no—
297C3×D3—41no—
298C3×D3—41no—
299C2×D4—31no—
300C2×D4—31no—
301C2×D4—91no—
302C2×D4—91no—
303C2×D4—91no—
304C2×D4—91no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—91no—
310C22×C4—91no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—91no—
321C22⋊C4—31no—
322C22⋊C4—31no—
323C22⋊C4—91no—
324C22⋊C4—91no—
325C22⋊C4—91no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—91no—
329C22⋊C4—91no—
330C22⋊C4D3211yescharacteristic
331C42—31no—
332C42—31no—
333C42—91no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—61no—
343C22×C3—61no—
344C22×C3—61no—
345C22×C3—61no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3#23512yes—
349C22×C3#23512yes—
350C22×C3C23×D311yescharacteristic
351C22×C3C23×D311yescharacteristic
352C2×D3—21no—
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—62no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—121no—
366C2×D3—121no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—32no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—61no—
377C3×C4—61no—
378C3×C4—61no—
379Dic3—21no—
380Dic3—21no—
381Dic3—21no—
382Dic3—21no—
383Dic3—21no—
384Dic3—62no—
385Dic3—62no—
386Dic3—61no—
387Dic3—61no—
388Dic3—61no—
389Dic3—61no—
390Dic3—61no—
391Dic3—61no—
392Dic3—121no—
393Dic3#23712yes—
394C32#55311yescharacteristic, complemented, Sylow
395C23—31no—
396C23—31no—
397C23—91no—
398C23C2×D3211yescharacteristic
399D4—62no—
400D4—62no—
401D4—182no—
402D4—182no—
403D4—361no—
404D4—361no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—361no—
419C2×C4—361no—
420C2×C4C2×D3211yescharacteristic
421C2×C4C2×D3211yescharacteristic
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—42no—
428C2×C3—121no—
429C2×C3—121no—
430C2×C3C2×#23511yescharacteristic
431C2×C3C2×#23511yescharacteristic
432C2×C3C2×#23711yescharacteristic
433C2×C3#100411yescharacteristic
434C2×C3D3×#4111yescharacteristic
435C2×C3#100911yescharacteristic
436D3—41no—
437D3—41no—
438D3—122no—
439D3—121no—
440D3—121no—
441C22—21no—
442C22—21no—
443C22—61no—
444C22—61no—
445C22—61no—
446C22—61no—
447C22—61no—
448C22—61no—
449C22—181no—
450C22—181no—
451C22—181no—
452C22#379812yes—
453C22C22×D3211yescharacteristic
454C4—21no—
455C4—21no—
456C4—32no—
457C4—61no—
458C4—61no—
459C4—61no—
460C4—61no—
461C4—61no—
462C4—181no—
463C4—181no—
464C4—181no—
465C3—21no—
466C3#554011yescharacteristic, complemented
467C3#556511yescharacteristic, complemented
468C2—22no—
469C2—121no—
470C2—121no—
471C2—361no—
472C2C2×#379811yescharacteristic
473C2D3×#23711yescharacteristic
474C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64090C2semidirect
2. C3×#67⋊C4C2semidirect
3. C3×#67⋊C4C2semidirect
4. #63980C2semidirect
5. #63978C2semidirect
6. #63978C2semidirect
7. C2×Dic3⋊Dic3C2semidirect
8. #63906C2semidirect
9. #63905C2semidirect
10. C4×#626C2semidirect
11. #63868C2semidirect
12. #63867C2semidirect
13. #63862C2semidirect
14. #63855C2semidirect
15. #63853C2semidirect
77. #67⋊C4D3semidirect
78. #67⋊C4D3semidirect
394. C32#553semidirect
466. C3#5540semidirect
467. C3#5565semidirect

Maximal subgroups

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

subgroupindex
#640902
C3×#67⋊C42
#639802
#639782
C2×Dic3⋊Dic32
#639062
#639052
C4×#6262
#638682
#638672
#638622
#638552
#638532
#55653
#55403