Finite Group Databasebeta

← #10595151

Subgroups — #10595151

Order 576.

623 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#237C211yesmaximal, characteristic, complemented
2C2×#3805C211yesmaximal, characteristic, complemented
3#64144C211yesmaximal, characteristic, complemented
4C3×#939C211yesmaximal, characteristic, complemented
5Dic3×#67C211yesmaximal, characteristic, complemented
6Dic3×#67C211yesmaximal, characteristic, complemented
7#63970C211yesmaximal, characteristic, complemented
8#63969C211yesmaximal, characteristic, complemented
9C2×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#63964C211yesmaximal, characteristic, complemented
11#63961C211yesmaximal, characteristic, complemented
12#63905C211yesmaximal, characteristic, complemented
13#63887C211yesmaximal, characteristic, complemented
14D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5824—31nomaximal
17#5611—31nomaximal
18C2×C32×D4C2211yescharacteristic
19C22×C3⋊Dic3C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C2×C3×#67C2211yescharacteristic
22C2×C3×#67C2211yescharacteristic
23C2×C3×#67C2211yescharacteristic
24C22×C3×Dic3C2211yescharacteristic
25C22×C3×Dic3C2211yescharacteristic
26C22×C3×Dic3C2211yescharacteristic
27C3×#237—24no—
28C2×C3×C4×D3C2211yescharacteristic
29C2×C3×Dic6C2211yescharacteristic
30C2×#627C2211yescharacteristic
31C2×#625C2211yescharacteristic
32#3805—24no—
33C2×D3×Dic3C2211yescharacteristic
34C2×D3×Dic3C2211yescharacteristic
35C2×D3×Dic3C2211yescharacteristic
36#3757C2211yescharacteristic
37#3757C2211yescharacteristic
38#3757C2211yescharacteristic
39#3750C2211yescharacteristic
40#3750C2211yescharacteristic
41C3×#217C2211yescharacteristic
42C3×(C2×D3)⋊C4C2211yescharacteristic
43C3×Dic3⋊C4C2211yescharacteristic
44#3724C2211yescharacteristic
45#3724C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49Dic3⋊Dic3C2211yescharacteristic
50Dic3⋊Dic3C2211yescharacteristic
51(C2×D3)⋊Dic3C2211yescharacteristic
52(C2×D3)⋊Dic3C2211yescharacteristic
53(C2×D3)⋊Dic3C2211yescharacteristic
54Dic32C2211yescharacteristic
55C2×C3×#41—31no—
56C2×#237—31no—
57C2×#237—31no—
58C2×#237D311yescharacteristic, complemented
59C3×#121—31no—
60#946—31no—
61#944—31no—
62#939—31no—
63#939D311yescharacteristic, complemented
64#938—31no—
65#935—31no—
66#935—31no—
67#935—31no—
68#935—31no—
69#935—61no—
70D4×Dic3—31no—
71D4×Dic3—31no—
72#929—31no—
73#929—31no—
74C4×#67—31no—
75C4×#67—31no—
76C2×C4⋊Dic3—31no—
77#924—31no—
78C2×Dic3⋊C4—31no—
79C2×Dic3⋊C4—31no—
80D3×C4⋊C4—31no—
81#888—31no—
82#883—31no—
83#883—31no—
84#878—31no—
85#878—31no—
86C23×C32C2311yescharacteristic
87C23×C32C2311yescharacteristic
88C22×C3×D3C2311yescharacteristic
89C22×C3×D3C2311yescharacteristic
90C32×D4—22no—
91C2×C32×C4C2311yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊Dic3C2311yescharacteristic
97C3×#67—22no—
98C3×#67—22no—
99C3×#67—22no—
100C3×#67D414yescomplemented
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3C2311yescharacteristic
105C2×C3×Dic3C2311yescharacteristic
106C2×C3×Dic3C2311yescharacteristic
107C2×C3×Dic3C2311yescharacteristic
108C2×C3×Dic3C2311yescharacteristic
109C2×C3×Dic3C2311yescharacteristic
110C3×C4×D3—22no—
111C3×Dic6—22no—
112#627—22no—
113#625—22no—
114D3×Dic3—22no—
115D3×Dic3—22no—
116D3×Dic3—22no—
117#547—91noSylow
118C3×#41—64no—
119C2×C3×Q8—31no—
120C2×C3×D4—21no—
121C2×C3×D4—31no—
122C2×C3×D4—31no—
123C2×C3×D4—31no—
124C2×C3×D4—31no—
125C2×C3×D4C2×D311yescharacteristic
126C2×C3×D4C2×D311yescharacteristic
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C22×C3×C4—31no—
131C2×#67—31no—
132C2×#67—31no—
133C2×#67C2×D311yescharacteristic
134C2×#67C2×D311yescharacteristic
135C2×#67C2×D311yescharacteristic
136C2×#67C2×D311yescharacteristic
137C22×Dic3—31no—
138C22×Dic3—31no—
139C22×Dic3—31no—
140C22×Dic3—31no—
141C22×Dic3—31no—
142C22×Dic3—61no—
143C22×Dic3C2×D311yescharacteristic
144C22×Dic3C2×D311yescharacteristic
145C22×Dic3C2×D311yescharacteristic
146#237—24no—
147#237—64no—
148#237—64no—
149C2×C4×D3—31no—
150C2×C4×D3—31no—
151C2×C4×D3—31no—
152C2×C4×D3C2×D311yescharacteristic
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6C2×D311yescharacteristic
156C3×C4⋊C4—31no—
157C3×C22⋊C4—31no—
158C3×C22⋊C4—31no—
159#217—31no—
160#217—31no—
161#217—31no—
162#217—31no—
163#217—31no—
164#217—31no—
165#217—31no—
166#217—31no—
167#217—31no—
168#217—61no—
169#217—61no—
170#217—61no—
171#217C2×D311yescharacteristic
172(C2×D3)⋊C4—31no—
173(C2×D3)⋊C4—31no—
174(C2×D3)⋊C4—31no—
175(C2×D3)⋊C4C2×D311yescharacteristic
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181Dic3⋊C4—31no—
182Dic3⋊C4—31no—
183Dic3⋊C4—31no—
184Dic3⋊C4—31no—
185Dic3⋊C4—31no—
186Dic3⋊C4—31no—
187Dic3⋊C4—31no—
188Dic3⋊C4—31no—
189Dic3⋊C4—31no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—31no—
193Dic3⋊C4—31no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4C2×D311yescharacteristic
197C4×Dic3—31no—
198C4×Dic3—31no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32C2×D412yes—
205C22×C32C2411yescharacteristic
206C2×C3×D3—21no—
207C2×C3×D3—21no—
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3C2×D412yes—
212C32×C4—21no—
213C3⋊Dic3—21no—
214C3⋊Dic3—21no—
215C3⋊Dic3—21no—
216C3⋊Dic3—21no—
217C3×Dic3—21no—
218C3×Dic3—21no—
219C3×Dic3—21no—
220C3×Dic3—21no—
221C3×Dic3C2×D412yes—
222C3×Dic3#4112yescomplemented
223C2×#41—31no—
224C2×#41—91no—
225C4⋊Q8—91no—
226#123—91no—
227#123—91no—
228#123—91no—
229#123—91no—
230C22⋊Q8—91no—
231C22⋊Q8—91no—
232#121—31no—
233#121—91no—
234C4×D4—91no—
235C4×D4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—91no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—31no—
241C23×C3—31no—
242C23×C3C22×D311yescharacteristic
243C23×C3C22×D311yescharacteristic
244C23×C3C22×D311yescharacteristic
245C23×C3C22×D311yescharacteristic
246C22×D3C22×D311yescharacteristic
247C22×D3C22×D311yescharacteristic
248C3×Q8—62no—
249C3×D4—22no—
250C3×D4—22no—
251C3×D4—34no—
252C3×D4—42no—
253C3×D4—62no—
254C3×D4—62no—
255C3×D4—62no—
256C2×C3×C4—21no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4C22×D311yescharacteristic
268C2×C3×C4C22×D311yescharacteristic
269#67—22no—
270#67—22no—
271#67—22no—
272#67—62no—
273#67—62no—
274#67#6714yescomplemented
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—22no—
278C2×Dic3—31no—
279C2×Dic3—31no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—31no—
285C2×Dic3—31no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—122no—
296C2×Dic3C22×D311yescharacteristic
297C2×Dic3C22×D311yescharacteristic
298C2×Dic3C22×D311yescharacteristic
299C2×Dic3C22×D311yescharacteristic
300C2×Dic3C22×D311yescharacteristic
301C2×Dic3C22×D311yescharacteristic
302C4×D3—22no—
303C4×D3—62no—
304C4×D3—62no—
305C4×D3—62no—
306Dic6—22no—
307Dic6—62no—
308Dic6—62no—
309C2×C32—22no—
310C2×C32—41no—
311C2×C32C22×D411yescharacteristic
312C2×C32C2×#4111yescharacteristic
313C2×C322−1+411yescharacteristic
314C3×D3—22no—
315C3×D3—41no—
316#41—64no—
317#41—184no—
318C2×Q8—31no—
319C2×Q8—91no—
320C2×D4—31no—
321C2×D4—31no—
322C2×D4—31no—
323C2×D4—31no—
324C2×D4—91no—
325C2×D4D3211yescharacteristic
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—31no—
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—
340C4⋊C4—91no—
341C4⋊C4—91no—
342C4⋊C4—91no—
343C4⋊C4—91no—
344C22⋊C4—31no—
345C22⋊C4—31no—
346C22⋊C4—91no—
347C22⋊C4—91no—
348C22⋊C4—91no—
349C22⋊C4—91no—
350C22⋊C4—91no—
351C22⋊C4—91no—
352C42—91no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—32no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—61no—
372C22×C3—61no—
373C22×C3—61no—
374C22×C3—61no—
375C22×C3—61no—
376C22×C3D3×D412yes—
377C22×C3C2×#6712yes—
378C22×C3C23×D311yescharacteristic
379C22×C3C23×D311yescharacteristic
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—21no—
385C2×D3C2×#6712yes—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—32no—
389C3×C4—32no—
390C3×C4—41no—
391C3×C4—61no—
392C3×C4—61no—
393C3×C4—61no—
394C3×C4—61no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—21no—
399Dic3—61no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—61no—
407Dic3—121no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411Dic3#23712yescomplemented
412Dic3C2×#6712yes—
413C32#54711yescharacteristic, complemented, Sylow
414C23—31no—
415C23—31no—
416C23C2×D3211yescharacteristic
417C23C2×D3211yescharacteristic
418Q8—62no—
419Q8—182no—
420D4—22no—
421D4—34no—
422D4—62no—
423D4—62no—
424D4—62no—
425D4—182no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—91no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4C2×D3211yescharacteristic
445C2×C3—22no—
446C2×C3—22no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—42no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—62no—
454C2×C3—81no—
455C2×C3—121no—
456C2×C3C2×D3×D411yescharacteristic
457C2×C3C2×#23711yescharacteristic
458C2×C3D3×#4111yescharacteristic
459C2×C3#101011yescharacteristic
460C2×C3#101011yescharacteristic
461C2×C3C22×#6711yescharacteristic
462D3—22no—
463D3—41no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—32no—
470C22—61no—
471C22—61no—
472C22—61no—
473C22—61no—
474C22—61no—
475C22D3×#6712yes—
476C22C22×D3211yescharacteristic
477C4—21no—
478C4—32no—
479C4—32no—
480C4—61no—
481C4—61no—
482C4—61no—
483C4—61no—
484C4—181no—
485C4—181no—
486C4—181no—
487C4—181no—
488C3—21no—
489C3#561111yescharacteristic, complemented
490C3#582411yescharacteristic, complemented
491C2—22no—
492C2—41no—
493C2—62no—
494C2—121no—
495C2#6430911yescharacteristic
496C2D3×#23711yescharacteristic
497C2C2×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×D4C22
hypercenterC2×D4D32
hypocenterC32#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#237C2semidirect
2. C2×#3805C2semidirect
3. #64144C2semidirect
4. C3×#939C2semidirect
5. Dic3×#67C2semidirect
6. Dic3×#67C2semidirect
7. #63970C2semidirect
8. #63969C2semidirect
9. C2×Dic3⋊Dic3C2semidirect
10. #63964C2semidirect
11. #63961C2semidirect
12. #63905C2semidirect
13. #63887C2semidirect
14. D3×Dic3⋊C4C2semidirect
15. #63839C2semidirect
58. C2×#237D3semidirect
63. #939D3semidirect
100. C3×#67D4semidirect
222. C3×Dic3#41semidirect
274. #67#67semidirect
411. Dic3#237semidirect
413. C32#547semidirect
489. C3#5611semidirect
490. C3#5824semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#2372
C2×#38052
#641442
C3×#9392
Dic3×#672
#639702
#639692
C2×Dic3⋊Dic32
#639642
#639612
#639052
#638872
D3×Dic3⋊C42
#638392
#58243
#56113