Finite Group Databasebeta

← #10594133

Subgroups — #10594133

Order 576.

493 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64087C211yesmaximal, characteristic, complemented
2C3×#67⋊C4C211yesmaximal, characteristic
3C3×#878C211yesmaximal, characteristic, complemented
4#67⋊Dic3C211yesmaximal, characteristic
5Dic3×#67C211yesmaximal, characteristic
6C2×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7#63964C211yesmaximal, characteristic, complemented
8#63893C211yesmaximal, characteristic, complemented
9#63887C211yesmaximal, characteristic, complemented
10D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
11#63867C211yesmaximal, characteristic, complemented
12#63857C211yesmaximal, characteristic, complemented
13#63846C211yesmaximal, characteristic, complemented
14Dic3×Dic6C211yesmaximal, characteristic, complemented
15#63840C211yesmaximal, characteristic, complemented
16#5635—31nomaximal
17#5539—31nomaximal
18C22×C3⋊Dic3C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C22×C3×Dic3C2211yescharacteristic
22C22×C3×Dic3C2211yescharacteristic
23C2×C3×C4×D3C2211yescharacteristic
24C2×C3×Dic6C2211yescharacteristic
25C2×#627C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27C2×D3×Dic3C2211yescharacteristic
28C32×C22⋊C4C2211yescharacteristic
29#3757C2211yescharacteristic
30C4⋊(C3⋊Dic3)C2211yescharacteristic
31#3750C2211yescharacteristic
32#3750C2211yescharacteristic
33C3×#217C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×C4⋊Dic3C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40#3724C2211yescharacteristic
41Dic3⋊Dic3C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×C22⋊Q8—31no—
54C3×C4×D4—31no—
55#946—31no—
56Q8×Dic3—31no—
57D4×Dic3—31no—
58D4×Dic3—31no—
59C4×#67—31no—
60C2×C4⋊Dic3—31no—
61#924—31no—
62#924—31no—
63C2×Dic3⋊C4—31no—
64C2×Dic3⋊C4—31no—
65#897—31no—
66#897—31no—
67D3×C4⋊C4—31no—
68#890—31no—
69#889—31no—
70#889—31no—
71#888—31no—
72#888—31no—
73#67⋊C4—31no—
74#67⋊C4D311yescharacteristic
75#878—31no—
76#878—31no—
77#878—31no—
78#878—31no—
79#878—31no—
80#878—61no—
81#878D311yescharacteristic, complemented
82#870—31no—
83C4×Dic6—31no—
84C23×C32C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C2×C32×C4C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93#634—41no—
94C3×#67Q814yescomplemented
95C2×C3×Dic3—22no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C2×C3×Dic3C2311yescharacteristic
103C2×C3×Dic3C2311yescharacteristic
104C3×C4×D3—41no—
105C3×Dic6—22no—
106#627—41no—
107D3×Dic3—22no—
108D3×Dic3—41no—
109#554—91noSylow
110C2×C3×Q8—31no—
111C2×C3×D4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C2×#67C2×D311yescharacteristic
116C22×Dic3—31no—
117C22×Dic3—31no—
118C22×Dic3—31no—
119C22×Dic3—31no—
120C22×Dic3—61no—
121C22×Dic3C2×D311yescharacteristic
122C22×Dic3C2×D311yescharacteristic
123C2×C4×D3—31no—
124C2×C4×D3—31no—
125C2×C4×D3C2×D311yescharacteristic
126C2×Dic6—31no—
127C2×Dic6—31no—
128C2×Dic6—31no—
129C2×Dic6—31no—
130C2×Dic6—61no—
131C2×Dic6C2×D311yescharacteristic
132C3×C4⋊C4—31no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C22⋊C4—21no—
137C3×C22⋊C4—31no—
138C3×C22⋊C4—31no—
139C3×C22⋊C4C2×D311yescharacteristic
140C3×C22⋊C4C2×D311yescharacteristic
141C3×C42—31no—
142#217—31no—
143#217—31no—
144#217—31no—
145#217—31no—
146#217—61no—
147#217C2×D311yescharacteristic
148(C2×D3)⋊C4—31no—
149(C2×D3)⋊C4—31no—
150(C2×D3)⋊C4C2×D311yescharacteristic
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—31no—
154C4⋊Dic3—31no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—61no—
162C4⋊Dic3C2×D311yescharacteristic
163Dic3⋊C4—31no—
164Dic3⋊C4—31no—
165Dic3⋊C4—31no—
166Dic3⋊C4—31no—
167Dic3⋊C4—31no—
168Dic3⋊C4—31no—
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—31no—
172Dic3⋊C4—31no—
173Dic3⋊C4—31no—
174Dic3⋊C4—31no—
175Dic3⋊C4—31no—
176Dic3⋊C4—31no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4C2×D311yescharacteristic
180Dic3⋊C4C2×D311yescharacteristic
181Dic3⋊C4C2×D311yescharacteristic
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—31no—
185C4×Dic3—31no—
186C4×Dic3C2×D311yescharacteristic
187C22×C32—21no—
188C22×C32—21no—
189C22×C32C2×Q812yes—
190C22×C32C2411yescharacteristic
191C2×C3×D3—21no—
192C2×C3×D3—21no—
193C2×C3×D3C2×Q812yes—
194C32×C4—21no—
195C32×C4—21no—
196C3⋊Dic3—21no—
197C3⋊Dic3—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C3×Dic3—21no—
204C3×Dic3—21no—
205C3×Dic3C2×Q812yes—
206C3×Dic3#4112yes—
207C4⋊Q8—91no—
208#125—91no—
209#125—91no—
210C22⋊Q8—31no—
211C22⋊Q8—91no—
212C22⋊Q8—91no—
213C22⋊Q8—91no—
214C22⋊Q8—91no—
215C22⋊Q8—91no—
216C4×Q8—91no—
217C4×D4—31no—
218C4×D4—91no—
219C4×D4—91no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—91no—
222C23×C3—21no—
223C23×C3—31no—
224C23×C3C22×D311yescharacteristic
225C23×C3C22×D311yescharacteristic
226C22×D3C22×D311yescharacteristic
227C3×Q8—62no—
228C3×D4—34no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—31no—
237C2×C3×C4—31no—
238C2×C3×C4—62no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4C22×D311yescharacteristic
242C2×C3×C4C22×D311yescharacteristic
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245#67Dic614yescomplemented
246C2×Dic3—22no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—31no—
250C2×Dic3—31no—
251C2×Dic3—31no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C2×Dic3—41no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—62no—
261C2×Dic3—121no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264C2×Dic3—122no—
265C2×Dic3C22×D311yescharacteristic
266C2×Dic3C22×D311yescharacteristic
267C2×Dic3C22×D311yescharacteristic
268C2×Dic3C22×D311yescharacteristic
269C2×Dic3C22×D311yescharacteristic
270C2×Dic3C22×D311yescharacteristic
271C2×Dic3C22×D311yescharacteristic
272C4×D3—41no—
273C4×D3—62no—
274C4×D3—121no—
275Dic6—22no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—121no—
280Dic6—122no—
281C2×C32—22no—
282C2×C32C22×Q811yescharacteristic
283C2×C32C2×#4111yescharacteristic
284C2×C32H(5,𝔽2)11yescharacteristic
285C3×D3—22no—
286C2×Q8—31no—
287C2×Q8—91no—
288C2×Q8—91no—
289C2×D4—31no—
290C22×C4—31no—
291C22×C4—31no—
292C22×C4—31no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—91no—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—91no—
310C4⋊C4—91no—
311C4⋊C4—91no—
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4—91no—
317C22⋊C4D3211yescharacteristic
318C42—31no—
319C42—91no—
320C42—91no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—32no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—61no—
331C22×C3—61no—
332C22×C3C2×Dic612yes—
333C22×C3D3×Q812yes—
334C22×C3C23×D311yescharacteristic
335C22×C3C23×D311yescharacteristic
336C2×D3—21no—
337C2×D3—21no—
338C2×D3C2×Dic612yes—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—32no—
344C3×C4—32no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—61no—
348C3×C4—61no—
349C3×C4—61no—
350C3×C4—61no—
351C3×C4—61no—
352Dic3—21no—
353Dic3—21no—
354Dic3—21no—
355Dic3—21no—
356Dic3—21no—
357Dic3—62no—
358Dic3—61no—
359Dic3—61no—
360Dic3—61no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3—61no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369Dic3C2×Dic612yes—
370Dic3#23712yes—
371C32#55411yescharacteristic, complemented, Sylow
372C23—31no—
373C23C2×D3211yescharacteristic
374Q8—62no—
375Q8—361no—
376Q8—361no—
377D4—34no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—62no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—182no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4C2×D3211yescharacteristic
396C2×C4C2×D3211yescharacteristic
397C2×C3—22no—
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—42no—
403C2×C3—62no—
404C2×C3C22×Dic611yescharacteristic
405C2×C3C2×#23711yescharacteristic
406C2×C3#100411yescharacteristic
407C2×C3C2×D3×Q811yescharacteristic
408C2×C3D3×#4111yescharacteristic
409C2×C3#100911yescharacteristic
410D3—22no—
411C22—21no—
412C22—21no—
413C22—32no—
414C22—61no—
415C22—61no—
416C22D3×Dic612yes—
417C22C22×D3211yescharacteristic
418C4—21no—
419C4—21no—
420C4—32no—
421C4—32no—
422C4—61no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—181no—
428C4—181no—
429C4—181no—
430C4—181no—
431C3—21no—
432C3#553911yescharacteristic, complemented
433C3#563511yescharacteristic, complemented
434C2—22no—
435C2—62no—
436C2C2×D3×Dic611yescharacteristic
437C2D3×#23711yescharacteristic
438C2#6431411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
prime radicalC2×C3×#67C22
hypercenterC22⋊C4D32
hypocenterC32#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #64087C2semidirect
3. C3×#878C2semidirect
6. C2×Dic3⋊Dic3C2semidirect
7. #63964C2semidirect
8. #63893C2semidirect
9. #63887C2semidirect
10. D3×Dic3⋊C4C2semidirect
11. #63867C2semidirect
12. #63857C2semidirect
13. #63846C2semidirect
14. Dic3×Dic6C2semidirect
15. #63840C2semidirect
81. #878D3semidirect
94. C3×#67Q8semidirect
245. #67Dic6semidirect
371. C32#554semidirect
432. C3#5539semidirect
433. C3#5635semidirect

Maximal subgroups

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

subgroupindex
#640872
C3×#67⋊C42
C3×#8782
#67⋊Dic32
Dic3×#672
C2×Dic3⋊Dic32
#639642
#638932
#638872
D3×Dic3⋊C42
#638672
#638572
#638462
Dic3×Dic62
#638402
#56353
#55393