Finite Group Databasebeta

← #10594396

Subgroups — #10594396

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#64106C211yesmaximal, characteristic, complemented
2C3×#896C211yesmaximal, characteristic, complemented
3C3×#889C211yesmaximal, characteristic, complemented
4#63904C211yesmaximal, characteristic
5#63896C211yesmaximal, characteristic, complemented
6#63895C211yesmaximal, characteristic, complemented
7#63893C211yesmaximal, characteristic, complemented
8D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#63888C211yesmaximal, characteristic, complemented
10#63883C211yesmaximal, characteristic, complemented
11#63881C211yesmaximal, characteristic
12#63880C211yesmaximal, characteristic
13#63845C211yesmaximal, characteristic, complemented
14Dic3×Dic6C211yesmaximal, characteristic, complemented
15#63840C211yesmaximal, characteristic, complemented
16#5690—31nomaximal
17#5635—31nomaximal
18C2×C4×C3⋊D3C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×C4×D3C2211yescharacteristic
21C2×C3×Dic6C2211yescharacteristic
22C2×#627C2211yescharacteristic
23C2×#626C2211yescharacteristic
24C2×#624C2211yescharacteristic
25C2×#624C2211yescharacteristic
26C2×D3×Dic3C2211yescharacteristic
27C2×D3×Dic3C2211yescharacteristic
28C32×C4⋊C4C2211yescharacteristic
29#3752C2211yescharacteristic
30#3752C2211yescharacteristic
31C4⋊(C3⋊Dic3)C2211yescharacteristic
32C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×(C2×D3)⋊C4C2211yescharacteristic
35C3×C4⋊Dic3C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×Dic3⋊C4C2211yescharacteristic
41C3×Dic3⋊C4C2211yescharacteristic
42C3×C4×Dic3C2211yescharacteristic
43#3724C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49#3722C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#125—31no—
54C3×C22⋊Q8—31no—
55#946—31no—
56Q8×Dic3—31no—
57C4×#67—31no—
58C2×C4⋊Dic3—31no—
59#897—31no—
60#897—31no—
61#897—31no—
62#897—31no—
63#897—61no—
64#896—31no—
65#896—31no—
66#896—31no—
67#896D311yescharacteristic, complemented
68#893—31no—
69#893—31no—
70D3×C4⋊C4—31no—
71D3×C4⋊C4—31no—
72D3×C4⋊C4—31no—
73#890—31no—
74#889—31no—
75#889D311yescharacteristic, complemented
76#888—31no—
77#888—31no—
78#67⋊C4—31no—
79#67⋊C4—31no—
80#878—31no—
81#878—31no—
82C4×D12—31no—
83C4×Dic6—31no—
84C22×C3⋊D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C2×C32×C4C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊D3—41no—
93#634—41no—
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C3×C4×D3—22no—
102C3×Dic6—22no—
103#627—41no—
104#626Q814yescomplemented
105#624—22no—
106#624—41no—
107D3×Dic3—41no—
108D3×Dic3—41no—
109#554—91noSylow
110C2×C3×Q8—31no—
111C22×C3×C4—31no—
112C2×#67—31no—
113C22×Dic3—31no—
114C22×Dic3—31no—
115C2×D12—31no—
116C2×C4×D3—31no—
117C2×C4×D3—31no—
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—61no—
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—21no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—31no—
140C3×C4⋊C4C2×D311yescharacteristic
141C3×C4⋊C4C2×D311yescharacteristic
142C3×C22⋊C4—31no—
143C3×C22⋊C4—31no—
144C3×C42—31no—
145#217—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—61no—
154(C2×D3)⋊C4—61no—
155(C2×D3)⋊C4C2×D311yescharacteristic
156(C2×D3)⋊C4C2×D311yescharacteristic
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—31no—
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—31no—
166C4⋊Dic3—61no—
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⋊C4—31no—
176Dic3⋊C4C2×D311yescharacteristic
177Dic3⋊C4C2×D311yescharacteristic
178Dic3⋊C4C2×D311yescharacteristic
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×C32C2411yescharacteristic
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3C2×Q812yes—
191C2×C3×D3—21no—
192C2×C3×D3—21no—
193C2×C3×D3C2×Q812yes—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—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—31no—
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—91no—
218C4×D4—91no—
219C4×D4—91no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—91no—
222C23×C3—31no—
223C22×D3—31no—
224C22×D3—31no—
225C22×D3—61no—
226C22×D3C22×D311yescharacteristic
227C3×Q8—62no—
228C2×C3×C4—21no—
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×C4C22×D311yescharacteristic
240C2×C3×C4C22×D311yescharacteristic
241C2×C3×C4C22×D311yescharacteristic
242C2×C3×C4C22×D311yescharacteristic
243C2×C3×C4C22×D311yescharacteristic
244C2×C3×C4C22×D311yescharacteristic
245#67—34no—
246C2×Dic3—31no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—31no—
250C2×Dic3—31no—
251C2×Dic3—31no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—121no—
256C2×Dic3—121no—
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C2×Dic3C22×D311yescharacteristic
263C2×Dic3C22×D311yescharacteristic
264D12—34no—
265C4×D3—22no—
266C4×D3—62no—
267C4×D3—62no—
268C4×D3—121no—
269C4×D3—121no—
270C4×D3—121no—
271C4×D3—121no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—122no—
275Dic6—22no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—121no—
280Dic6—122no—
281C2×C32C22×Q811yescharacteristic
282C2×C32C2×#4111yescharacteristic
283C2×C32H(5,𝔽2)11yescharacteristic
284C3⋊D3—22no—
285C3×D3—22no—
286C2×Q8—31no—
287C2×Q8—91no—
288C2×Q8—91no—
289C2×D4—91no—
290C22×C4—31no—
291C22×C4—91no—
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—31no—
302C4⋊C4—31no—
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⋊C4D3211yescharacteristic
312C22⋊C4—31no—
313C22⋊C4—31no—
314C22⋊C4—91no—
315C22⋊C4—91no—
316C22⋊C4—91no—
317C22⋊C4—91no—
318C42—31no—
319C42—91no—
320C42—91no—
321C22×C3—21no—
322C22×C3—32no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3C23×D311yescharacteristic
326C22×C3C23×D311yescharacteristic
327C2×D3—21no—
328C2×D3—21no—
329C2×D3—32no—
330C2×D3—32no—
331C2×D3—62no—
332C2×D3—61no—
333C2×D3—61no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3D3×Q812yes—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—32no—
347C3×C4—32no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—61no—
351C3×C4—61no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—61no—
355Dic3—21no—
356Dic3—21no—
357Dic3—21no—
358Dic3—21no—
359Dic3—21no—
360Dic3—61no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3—61no—
366Dic3—121no—
367Dic3—121no—
368Dic3—121no—
369Dic3#23712yes—
370Dic3D3×Q812yes—
371C32#55411yescharacteristic, complemented, Sylow
372C23—31no—
373C23—91no—
374Q8—62no—
375Q8—361no—
376Q8—361no—
377D4—94no—
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—182no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4—361no—
393C2×C4—361no—
394C2×C4C2×D3211yescharacteristic
395C2×C4C2×D3211yescharacteristic
396C2×C4C2×D3211yescharacteristic
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—62no—
401C2×C3C2×#23711yescharacteristic
402C2×C3C2×D3×Q811yescharacteristic
403C2×C3C2×D3×Q811yescharacteristic
404C2×C3D3×#4111yescharacteristic
405C2×C3#100911yescharacteristic
406C2×C3#100911yescharacteristic
407D3—22no—
408D3—62no—
409D3—62no—
410D3—122no—
411C22—32no—
412C22—61no—
413C22—61no—
414C22—92no—
415C22—181no—
416C22—181no—
417C22C22×D3211yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—32no—
422C4—32no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—61no—
427C4—61no—
428C4—181no—
429C4—181no—
430C4—181no—
431C3—21no—
432C3#563511yescharacteristic, complemented
433C3#569011yescharacteristic, complemented
434C2—62no—
435C2—182no—
436C2#6430811yescharacteristic
437C2D3×#23711yescharacteristic
438C2D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radicalC2×#626C22
hypercenterC4⋊C4D32
hypocenterC32#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64106C2semidirect
2. C3×#896C2semidirect
3. C3×#889C2semidirect
5. #63896C2semidirect
6. #63895C2semidirect
7. #63893C2semidirect
8. D3×C4⋊Dic3C2semidirect
9. #63888C2semidirect
10. #63883C2semidirect
13. #63845C2semidirect
14. Dic3×Dic6C2semidirect
15. #63840C2semidirect
67. #896D3semidirect
75. #889D3semidirect
104. #626Q8semidirect
371. C32#554semidirect
432. C3#5635semidirect
433. C3#5690semidirect

Maximal subgroups

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

subgroupindex
#641062
C3×#8962
C3×#8892
#639042
#638962
#638952
#638932
D3×C4⋊Dic32
#638882
#638832
#638812
#638802
#638452
Dic3×Dic62
#638402
#56903
#56353