Finite Group Databasebeta

← #10594076

Subgroups — #10594076

Order 576.

617 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3805C211yesmaximal, characteristic, complemented
2C2×D3×Dic6C211yesmaximal, characteristic, complemented
3#64087C211yesmaximal, characteristic, complemented
4C3×#885C211yesmaximal, characteristic, complemented
5C3×#884C211yesmaximal, characteristic, complemented
6#67⋊Dic3C211yesmaximal, characteristic, complemented
7#63970C211yesmaximal, characteristic, complemented
8#63959C211yesmaximal, characteristic, complemented
9#63913C211yesmaximal, characteristic, complemented
10#63893C211yesmaximal, characteristic, complemented
11Dic3×D12C211yesmaximal, characteristic, complemented
12#63887C211yesmaximal, characteristic, complemented
13#63885C211yesmaximal, characteristic, complemented
14#63879C211yesmaximal, characteristic, complemented
15#63837C211yesmaximal, characteristic, complemented
16#5677—31nomaximal
17#5598—31nomaximal
18C22×C3⋊Dic3C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×D12C2211yescharacteristic
24C2×C3×C4×D3C2211yescharacteristic
25C2×C3×Dic6C2211yescharacteristic
26C2×#627C2211yescharacteristic
27C2×#627C2211yescharacteristic
28C2×#625C2211yescharacteristic
29C2×#625C2211yescharacteristic
30#3805—24no—
31C2×D3×Dic3C2211yescharacteristic
32C2×D3×Dic3C2211yescharacteristic
33C2×D3×Dic3C2211yescharacteristic
34C2×D3×Dic3C2211yescharacteristic
35D3×Dic6—24no—
36C32×C22⋊C4C2211yescharacteristic
37#3757C2211yescharacteristic
38C4⋊(C3⋊Dic3)C2211yescharacteristic
39#3750C2211yescharacteristic
40#3750C2211yescharacteristic
41C3×#217C2211yescharacteristic
42C3×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D3)⋊C4C2211yescharacteristic
44C3×(C2×D3)⋊C4C2211yescharacteristic
45C3×Dic3⋊C4C2211yescharacteristic
46C3×C4×Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53Dic32C2211yescharacteristic
54Dic32C2211yescharacteristic
55C2×D3×Q8—31no—
56C2×#237—31no—
57C2×#237—31no—
58C22×Dic6—31no—
59C3×#124—31no—
60C3×#121—31no—
61#946—31no—
62#939—31no—
63#939—31no—
64#938—31no—
65#936—31no—
66D4×Dic3—31no—
67D4×Dic3—31no—
68C4×#67—31no—
69#897—31no—
70#887—31no—
71#885—31no—
72#885—31no—
73#885—31no—
74#885D311yescharacteristic, complemented
75#884—31no—
76#884D311yescharacteristic, complemented
77#67⋊C4—31no—
78#67⋊C4—31no—
79#878—31no—
80#878—31no—
81#878—31no—
82#878—31no—
83#878—61no—
84C4×D12—31no—
85C4×Dic6—31no—
86C23×C32C2311yescharacteristic
87C22×C3×D3C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C2×C32×C4C2311yescharacteristic
91C2×C32×C4C2311yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97#634—22no—
98C3×#67—22no—
99C3×#67—22no—
100C3×#67—22no—
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C3×D12—22no—
107C3×C4×D3—22no—
108C3×Dic6—22no—
109#627—22no—
110#627D414yescomplemented
111#625—22no—
112#625—22no—
113D3×Dic3—22no—
114D3×Dic3—22no—
115D3×Dic3—22no—
116D3×Dic3—22no—
117#548—91noSylow
118C2×C3×Q8—31no—
119C2×C3×D4—31no—
120C2×C3×D4—31no—
121C2×C3×D4—31no—
122C2×C3×D4—31no—
123C22×C3×C4—31no—
124C2×#67—31no—
125C2×#67—31no—
126C2×#67—31no—
127C2×#67—31no—
128C2×#67C2×D311yescharacteristic
129C2×#67C2×D311yescharacteristic
130C2×#67C2×D311yescharacteristic
131C22×Dic3—31no—
132C22×Dic3—31no—
133C22×Dic3—31no—
134C22×Dic3—31no—
135C22×Dic3—31no—
136C22×Dic3—31no—
137C22×Dic3—61no—
138D3×Q8—64no—
139#237—64no—
140#237—64no—
141C2×D12C2×D311yescharacteristic
142C2×C4×D3—31no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—31no—
146C2×C4×D3C2×D311yescharacteristic
147C2×Dic6—31no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—31no—
151C2×Dic6—31no—
152C2×Dic6—31no—
153C2×Dic6—61no—
154C2×Dic6—64no—
155C2×Dic6C2×D311yescharacteristic
156C3×C4⋊C4—31no—
157C3×C22⋊C4—21no—
158C3×C22⋊C4—31no—
159C3×C22⋊C4—31no—
160C3×C22⋊C4—31no—
161C3×C22⋊C4—31no—
162C3×C22⋊C4C2×D311yescharacteristic
163C3×C22⋊C4C2×D311yescharacteristic
164C3×C42—31no—
165#217—31no—
166#217—31no—
167#217—31no—
168#217—31no—
169#217—31no—
170#217—31no—
171#217—61no—
172#217C2×D311yescharacteristic
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4—31no—
176(C2×D3)⋊C4—31no—
177(C2×D3)⋊C4C2×D311yescharacteristic
178(C2×D3)⋊C4C2×D311yescharacteristic
179(C2×D3)⋊C4C2×D311yescharacteristic
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185Dic3⋊C4—31no—
186Dic3⋊C4—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4C2×D311yescharacteristic
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—31no—
197C4×Dic3—31no—
198C4×Dic3C2×D311yescharacteristic
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32C2411yescharacteristic
203C2×C3×D3—21no—
204C2×C3×D3—21no—
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3—21no—
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3#4112yescomplemented
212C32×C4—21no—
213C32×C4—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3—21no—
216C3⋊Dic3—21no—
217C3⋊Dic3C2×D412yes—
218C3×Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3C2×D412yes—
222C3×Dic3C2×D412yes—
223C2×#41—91no—
224C22×Q8—91no—
225#124—31no—
226#124—91no—
227#124—91no—
228C22⋊Q8—91no—
229C22⋊Q8—91no—
230C22⋊Q8—91no—
231#121—31no—
232#121—91no—
233#121—91no—
234C4×Q8—91no—
235C4×D4—91no—
236C4×D4—91no—
237C4×D4—91no—
238C23×C3—21no—
239C23×C3—31no—
240C23×C3—31no—
241C23×C3—31no—
242C23×C3C22×D311yescharacteristic
243C23×C3C22×D311yescharacteristic
244C22×D3C22×D311yescharacteristic
245C22×D3C22×D311yescharacteristic
246C22×D3C22×D311yescharacteristic
247C3×Q8—62no—
248C3×D4—62no—
249C3×D4—62no—
250C3×D4—62no—
251C3×D4—62no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—62no—
260C2×C3×C4C22×D311yescharacteristic
261C2×C3×C4C22×D311yescharacteristic
262C2×C3×C4C22×D311yescharacteristic
263C2×C3×C4C22×D311yescharacteristic
264#67—22no—
265#67—22no—
266#67—22no—
267#67—62no—
268#67—62no—
269#67—62no—
270#67—62no—
271C2×Dic3—31no—
272C2×Dic3—31no—
273C2×Dic3—31no—
274C2×Dic3—31no—
275C2×Dic3—31no—
276C2×Dic3—31no—
277C2×Dic3—31no—
278C2×Dic3—31no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—122no—
290C2×Dic3C22×D311yescharacteristic
291C2×Dic3C22×D311yescharacteristic
292C2×Dic3C22×D311yescharacteristic
293C2×Dic3C22×D311yescharacteristic
294C2×Dic3C22×D311yescharacteristic
295D12—22no—
296C4×D3—22no—
297C4×D3—62no—
298C4×D3—62no—
299C4×D3—62no—
300C4×D3—62no—
301Dic6—22no—
302Dic6—34no—
303Dic6—34no—
304Dic6—62no—
305Dic6—62no—
306Dic6—62no—
307Dic6—62no—
308Dic6—122no—
309C2×C32—41no—
310C2×C32C22×D411yescharacteristic
311C2×C32C2×#4111yescharacteristic
312C2×C322−1+411yescharacteristic
313C3×D3—22no—
314C3×D3—41no—
315C3×D3—41no—
316#41—184no—
317C2×Q8—31no—
318C2×Q8—91no—
319C2×Q8—91no—
320C2×Q8—91no—
321C2×Q8—184no—
322C2×D4—31no—
323C2×D4—31no—
324C2×D4—31no—
325C2×D4—31no—
326C2×D4—91no—
327C2×D4—91no—
328C22×C4—31no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C4⋊C4—31no—
335C4⋊C4—91no—
336C4⋊C4—91no—
337C4⋊C4—91no—
338C4⋊C4—91no—
339C4⋊C4—91no—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—31no—
343C22⋊C4—31no—
344C22⋊C4—91no—
345C22⋊C4—91no—
346C22⋊C4—91no—
347C22⋊C4—91no—
348C22⋊C4—91no—
349C22⋊C4D3211yescharacteristic
350C42—31no—
351C42—91no—
352C42—91no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—32no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3—61no—
369C22×C3—61no—
370C22×C3—61no—
371C22×C3—61no—
372C22×C3C23×D311yescharacteristic
373C22×C3C23×D311yescharacteristic
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—21no—
378C2×D3—21no—
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—21no—
382C2×D3#23712yescomplemented
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—32no—
388C3×C4—32no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—61no—
392C3×C4—61no—
393C3×C4—61no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—32no—
398Dic3—32no—
399Dic3—62no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3D3×D412yes—
410Dic3D3×D412yes—
411C32#54811yescharacteristic, complemented, Sylow
412C23—31no—
413C23—31no—
414C23—31no—
415C23C2×D3211yescharacteristic
416Q8—62no—
417Q8—94no—
418Q8—182no—
419Q8—182no—
420D4—62no—
421D4—62no—
422D4—62no—
423D4—62no—
424D4—182no—
425D4—182no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—62no—
432C2×C4—91no—
433C2×C4—91no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4C2×D3211yescharacteristic
442C2×C4C2×D3211yescharacteristic
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3—62no—
450C2×C3—121no—
451C2×C3—121no—
452C2×C3C2×D3×D411yescharacteristic
453C2×C3C2×D3×D411yescharacteristic
454C2×C3C2×#23711yescharacteristic
455C2×C3D3×#4111yescharacteristic
456C2×C3#101011yescharacteristic
457C2×C3#101011yescharacteristic
458D3—22no—
459D3—41no—
460D3—41no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—32no—
465C22—61no—
466C22—61no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—61no—
473C22C22×D3211yescharacteristic
474C4—21no—
475C4—21no—
476C4—32no—
477C4—32no—
478C4—61no—
479C4—61no—
480C4—61no—
481C4—92no—
482C4—181no—
483C4—181no—
484C4—181no—
485C3—21no—
486C3#559811yescharacteristic, complemented
487C3#567711yescharacteristic, complemented
488C2—41no—
489C2—62no—
490C2—121no—
491C2—121no—
492C2#6429811yescharacteristic
493C2D32×D411yescharacteristic
494C2D3×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#3805C2semidirect
2. C2×D3×Dic6C2semidirect
3. #64087C2semidirect
4. C3×#885C2semidirect
5. C3×#884C2semidirect
6. #67⋊Dic3C2semidirect
7. #63970C2semidirect
8. #63959C2semidirect
9. #63913C2semidirect
10. #63893C2semidirect
11. Dic3×D12C2semidirect
12. #63887C2semidirect
13. #63885C2semidirect
14. #63879C2semidirect
15. #63837C2semidirect
74. #885D3semidirect
76. #884D3semidirect
110. #627D4semidirect
211. C2×C3×D3#41semidirect
382. C2×D3#237semidirect
411. C32#548semidirect
486. C3#5598semidirect
487. C3#5677semidirect

Maximal subgroups

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

subgroupindex
C2×#38052
C2×D3×Dic62
#640872
C3×#8852
C3×#8842
#67⋊Dic32
#639702
#639592
#639132
#638932
Dic3×D122
#638872
#638852
#638792
#638372
#56773
#55983