Finite Group Databasebeta

← #10594967

Subgroups — #10594967

Order 576.

523 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 523 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#638C211yesmaximal, characteristic, complemented
2C3×#930C211yesmaximal, characteristic, complemented
3C3×#926C211yesmaximal, characteristic, complemented
4#63969C212yesmaximal, complemented
5#63958C212yesmaximal, complemented
6#63916C211yesmaximal, characteristic, complemented
7#63900C211yesmaximal, characteristic, complemented
8#63898C211yesmaximal, characteristic, complemented
9#63880C212yesmaximal, complemented
10#63872C211yesmaximal, characteristic, complemented
11#63859C212yesmaximal, complemented
12#5614—31nomaximal
13#5530—31nomaximal
14C22×C32×C4C2211yescharacteristic
15C2×#638C2211yescharacteristic
16C2×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#67C2212yes—
18C2×C3×D12C2211yescharacteristic
19C2×#626C2212yes—
20C2×#624C2212yes—
21C2×D3×Dic3C2212yes—
22#3757C2211yescharacteristic
23#3752C2211yescharacteristic
24#3750C2211yescharacteristic
25C4×C3⋊Dic3C2211yescharacteristic
26C3×#217C2212yes—
27C3×(C2×D3)⋊C4C2212yes—
28C3×C4⋊Dic3C2211yescharacteristic
29C3×C4⋊Dic3C2211yescharacteristic
30C3×C4⋊Dic3C2211yescharacteristic
31C3×C4×Dic3C2212yes—
32#3724C2212yes—
33Dic3⋊Dic3C2212yes—
34Dic3⋊Dic3C2212yes—
35(C2×D3)⋊Dic3C2212yes—
36(C2×D3)⋊Dic3C2212yes—
37C3×#121—31no—
38C3×#117—31no—
39#938—32no—
40#938—31no—
41#935—32no—
42D4×Dic3—31no—
43#930D311yescharacteristic, complemented
44C4×#67—31no—
45C4×#67—31no—
46C4×#67—61no—
47#926D311yescharacteristic, complemented
48#895—31no—
49#893—31no—
50D3×C4⋊C4—31no—
51D3×C4⋊C4—31no—
52#890—31no—
53#890—31no—
54#884—32no—
55#883—32no—
56#67⋊C4—32no—
57#879—32no—
58#876—32no—
59C4×D12—32no—
60C23×C32C2311yescharacteristic
61C22×C3⋊D3C2311yescharacteristic
62C22×C3×D3C2312yes—
63C2×C32×C4—22no—
64C2×C32×C4C2311yescharacteristic
65C2×C32×C4C2311yescharacteristic
66#638—22no—
67C2×C3⋊Dic3C2311yescharacteristic
68C2×C3⋊Dic3C2311yescharacteristic
69C2×C3⋊Dic3C2311yescharacteristic
70C4×C3⋊D3—22no—
71C3×#67—42no—
72C2×C3×Dic3C2312yes—
73C2×C3×Dic3C2312yes—
74C2×C3×Dic3C2312yes—
75C3×D12—22no—
76#626—24no—
77#624—42no—
78D3×Dic3—42no—
79#553—91noSylow
80C2×C3×D4—32no—
81C2×C3×D4—31no—
82C22×C3×C4—21no—
83C22×C3×C4C2×D311yescharacteristic
84C22×C3×C4C2×D311yescharacteristic
85C2×#67—31no—
86C2×#67—31no—
87C2×#67—32no—
88C2×#67—61no—
89C2×#67C2×D312yes—
90C22×Dic3—32no—
91C2×D12—32no—
92C2×D12C2×D311yescharacteristic
93C2×C4×D3—31no—
94C2×C4×D3—31no—
95C2×C4×D3—32no—
96C2×C4×D3—32no—
97C2×C4×D3—32no—
98C2×C4×D3—61no—
99C3×C4⋊C4—31no—
100C3×C4⋊C4—31no—
101C3×C4⋊C4—31no—
102C3×C22⋊C4—32no—
103C3×C22⋊C4—32no—
104C3×C42—32no—
105#217—31no—
106#217—31no—
107#217—32no—
108#217—32no—
109#217—61no—
110#217C2×D312yes—
111(C2×D3)⋊C4—32no—
112(C2×D3)⋊C4—32no—
113(C2×D3)⋊C4—31no—
114(C2×D3)⋊C4—31no—
115(C2×D3)⋊C4—61no—
116(C2×D3)⋊C4C2×D312yes—
117C4⋊Dic3—32no—
118C4⋊Dic3—32no—
119C4⋊Dic3C2×D311yescharacteristic
120C4⋊Dic3C2×D311yescharacteristic
121C4⋊Dic3C2×D311yescharacteristic
122Dic3⋊C4—31no—
123Dic3⋊C4—31no—
124Dic3⋊C4—32no—
125Dic3⋊C4—32no—
126Dic3⋊C4—32no—
127Dic3⋊C4—32no—
128Dic3⋊C4—61no—
129C4×Dic3—31no—
130C4×Dic3—31no—
131C4×Dic3—61no—
132C4×Dic3C2×D312yes—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32C2411yescharacteristic
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C2×C3⋊D3#4112yes—
140C2×C3×D3—22no—
141C2×C3×D3—22no—
142C2×C3×D3—22no—
143C32×C4—21no—
144C32×C4#4112yes—
145C3⋊Dic3—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3—21no—
148C3×Dic3—22no—
149C3×Dic3—22no—
150C3×Dic3—22no—
151#126—92no—
152#125—91no—
153#123—92no—
154#121—31no—
155#121—92no—
156#121—91no—
157C4×D4—92no—
158C4×D4—91no—
159C4×D4—91no—
160#117—31no—
161C2×C4⋊C4—91no—
162C23×C3—21no—
163C23×C3—32no—
164C23×C3C22×D311yescharacteristic
165C23×C3C22×D311yescharacteristic
166C22×D3—31no—
167C22×D3—31no—
168C22×D3—61no—
169C22×D3C22×D312yes—
170C3×D4—62no—
171C3×D4—122no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—32no—
177C2×C3×C4—32no—
178C2×C3×C4—32no—
179C2×C3×C4—42no—
180C2×C3×C4C22×D311yescharacteristic
181C2×C3×C4C22×D311yescharacteristic
182C2×C3×C4C22×D311yescharacteristic
183C2×C3×C4C22×D311yescharacteristic
184#67—42no—
185#67—64no—
186#67—62no—
187#67—62no—
188#67—64no—
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—31no—
192C2×Dic3—31no—
193C2×Dic3—31no—
194C2×Dic3—31no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—122no—
199C2×Dic3C22×D312yes—
200C2×Dic3C22×D312yes—
201C2×Dic3C22×D312yes—
202D12—22no—
203D12—64no—
204C4×D3—62no—
205C4×D3—62no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—122no—
209C4×D3—122no—
210C2×C32—41no—
211C2×C32C2×#4111yescharacteristic
212C2×C32C2×#4111yescharacteristic
213C2×C32H(5,𝔽2)11yescharacteristic
214C3⋊D3—22no—
215C3×D3—42no—
216C2×D4—32no—
217C2×D4—31no—
218C2×D4—92no—
219C2×D4—91no—
220C22×C4—92no—
221C22×C4—92no—
222C22×C4—91no—
223C22×C4D3211yescharacteristic
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—31no—
227C4⋊C4—92no—
228C4⋊C4—92no—
229C4⋊C4—92no—
230C4⋊C4—91no—
231C22⋊C4—32no—
232C22⋊C4—32no—
233C22⋊C4—92no—
234C22⋊C4—92no—
235C22⋊C4—91no—
236C22⋊C4—91no—
237C42—32no—
238C42—91no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3—62no—
250C22×C3—62no—
251C22×C3—62no—
252C22×C3C23×D311yescharacteristic
253C22×C3C23×D311yescharacteristic
254C2×D3—22no—
255C2×D3—22no—
256C2×D3—22no—
257C2×D3—32no—
258C2×D3—32no—
259C2×D3—62no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—121no—
265C2×D3—121no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—22no—
269C3×C4—41no—
270C3×C4—62no—
271C3×C4—62no—
272C3×C4—62no—
273C3×C4#23512yes—
274C3×C4#23712yes—
275Dic3—22no—
276Dic3—22no—
277Dic3—22no—
278Dic3—62no—
279Dic3—61no—
280Dic3—61no—
281Dic3—61no—
282Dic3—61no—
283Dic3—61no—
284Dic3—61no—
285Dic3—121no—
286Dic3—121no—
287C32#55311yescharacteristic, complemented, Sylow
288C23—32no—
289C23—91no—
290C23C2×D3211yescharacteristic
291D4—62no—
292D4—122no—
293D4—184no—
294D4—182no—
295C2×C4—22no—
296C2×C4—32no—
297C2×C4—32no—
298C2×C4—32no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—182no—
303C2×C4—362no—
304C2×C4—362no—
305C2×C4C2×D3211yescharacteristic
306C2×C4C2×D3211yescharacteristic
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—42no—
311C2×C3—41no—
312C2×C3—41no—
313C2×C3—122no—
314C2×C3C2×#23511yescharacteristic
315C2×C3C2×#23711yescharacteristic
316C2×C3#100411yescharacteristic
317C2×C3D3×#4111yescharacteristic
318C2×C3D3×#4111yescharacteristic
319C2×C3#100911yescharacteristic
320D3—42no—
321D3—62no—
322D3—62no—
323D3—122no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—62no—
328C22—62no—
329C22—62no—
330C22—92no—
331C22—181no—
332C22—181no—
333C22C22×D3211yescharacteristic
334C4—21no—
335C4—62no—
336C4—62no—
337C4—62no—
338C4—181no—
339C4—181no—
340C4—181no—
341C4#380412yes—
342C3—21no—
343C3#553011yescharacteristic, complemented
344C3#561411yescharacteristic, complemented
345C2—41no—
346C2—122no—
347C2—182no—
348C2#6430611yescharacteristic
349C2#6430711yescharacteristic
350C2C2×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×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. C4×#638C2semidirect
2. C3×#930C2semidirect
3. C3×#926C2semidirect
4. #63969C2semidirect
5. #63958C2semidirect
6. #63916C2semidirect
7. #63900C2semidirect
8. #63898C2semidirect
9. #63880C2semidirect
10. #63872C2semidirect
11. #63859C2semidirect
43. #930D3semidirect
47. #926D3semidirect
287. C32#553semidirect
343. C3#5530semidirect
344. C3#5614semidirect

Maximal subgroups

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

subgroupindex
C4×#6382
C3×#9302
C3×#9262
#639692
#639582
#639162
#639002
#638982
#638802
#638722
#638592
#56143
#55303