Finite Group Databasebeta

← #10594082

Subgroups — #10594082

Order 576.

698 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C2×#3805C211yesmaximal, characteristic, complemented
2C22×D3×Dic3C211yesmaximal, characteristic, complemented
3#64086C211yesmaximal, characteristic, complemented
4C3×#886C211yesmaximal, characteristic, complemented
5C3×#882C211yesmaximal, characteristic, complemented
6#63976C211yesmaximal, characteristic, complemented
7#63961C211yesmaximal, characteristic, complemented
8#63902C212yesmaximal, complemented
9#63899C212yesmaximal, complemented
10#63898C212yesmaximal, complemented
11#63885C212yesmaximal, complemented
12#5656—31nomaximal
13#5586—31nomaximal
14C23×C3×D3C2211yescharacteristic
15C22×C3⋊Dic3C2211yescharacteristic
16C2×C3×#67C2211yescharacteristic
17C2×C3×#67C2211yescharacteristic
18C22×C3×Dic3C2211yescharacteristic
19C2×C3×D12C2212yes—
20C2×#627C2211yescharacteristic, complemented
21C2×#625C2212yes—
22C2×#625C2211yescharacteristic, complemented
23#3805—24no—
24C2×D3×Dic3—24no—
25C2×D3×Dic3C2212yes—
26C2×D3×Dic3C2212yes—
27C2×D3×Dic3C2211yescharacteristic, complemented
28C2×D3×Dic3C2211yescharacteristic, complemented
29C32×C22⋊C4C2211yescharacteristic
30#3757C2211yescharacteristic
31#3750C2212yescomplemented
32C4×C3⋊Dic3C2212yescomplemented
33C3×(C2×D3)⋊C4C2212yes—
34C3×(C2×D3)⋊C4C2212yescomplemented
35C3×C4⋊Dic3C2212yescomplemented
36#3724C2212yescomplemented
37(C2×D3)⋊Dic3C2212yes—
38(C2×D3)⋊Dic3C2212yescomplemented
39C23×Dic3—31no—
40C2×#237—31no—
41C2×#237—31no—
42C22×C4×D3—31no—
43C3×#123—31no—
44C3×#120—31no—
45#953—31no—
46#939—32no—
47#937—31no—
48#935—31no—
49D4×Dic3—32no—
50#929—31no—
51#896—32no—
52#893—32no—
53#886D311yescharacteristic, complemented
54#884—32no—
55#882D311yescharacteristic, complemented
56#67⋊C4—32no—
57#67⋊C4—32no—
58#878—32no—
59#877—31no—
60#877—31no—
61#877—61no—
62C23×C32C2311yescharacteristic
63C22×C3×D3—22no—
64C22×C3×D3—24no—
65C22×C3×D3C2311yescharacteristic
66C22×C3×D3C2311yescharacteristic
67C22×C3×D3C2312yes—
68C2×C32×C4C2312yes—
69C2×C3⋊Dic3D414yescomplemented
70C2×C3⋊Dic3C2312yes—
71C2×C3⋊Dic3C2311yescharacteristic
72C2×C3⋊Dic3C2311yescharacteristic
73C3×#67—22no—
74C3×#67—22no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3C2311yescharacteristic
77C2×C3×Dic3C2312yes—
78C2×C3×Dic3C2311yescharacteristic
79C3×D12—24no—
80#627—22no—
81#625—24no—
82#625—22no—
83D3×Dic3—24no—
84D3×Dic3—24no—
85D3×Dic3—22no—
86D3×Dic3—22no—
87#525—91noSylow
88C24×C3—31no—
89C23×D3C2×D311yescharacteristic
90C2×C3×D4—31no—
91C2×C3×D4—31no—
92C2×C3×D4—32no—
93C22×C3×C4—31no—
94C2×#67—32no—
95C2×#67—32no—
96C2×#67—31no—
97C2×#67—31no—
98C2×#67C2×D311yescharacteristic
99C2×#67C2×D311yescharacteristic
100C22×Dic3—31no—
101C22×Dic3—31no—
102C22×Dic3—32no—
103C22×Dic3—31no—
104C22×Dic3—32no—
105C22×Dic3—31no—
106C22×Dic3—61no—
107C22×Dic3—64no—
108C22×Dic3C2×D311yescharacteristic
109#237—64no—
110#237—64no—
111C2×D12C2×D312yes—
112C2×C4×D3—31no—
113C2×C4×D3—32no—
114C2×C4×D3—32no—
115C2×C4×D3—31no—
116C2×C4×D3—64no—
117C2×Dic6—31no—
118C2×Dic6—31no—
119C3×C4⋊C4—32no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4—32no—
122C3×C22⋊C4—32no—
123C3×C22⋊C4C2×D311yescharacteristic
124C3×C22⋊C4C2×D311yescharacteristic
125#217—31no—
126#217—31no—
127#217—32no—
128#217—32no—
129#217—61no—
130(C2×D3)⋊C4—32no—
131(C2×D3)⋊C4—32no—
132(C2×D3)⋊C4C2×D312yes—
133(C2×D3)⋊C4C2×D312yescomplemented
134C4⋊Dic3C2×D312yescomplemented
135Dic3⋊C4—32no—
136Dic3⋊C4—32no—
137Dic3⋊C4—32no—
138Dic3⋊C4—32no—
139Dic3⋊C4—62no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—62no—
143C22×C32—22no—
144C22×C32C2×D412yes—
145C22×C32C2411yescharacteristic
146C2×C3×D3—28no—
147C2×C3×D3—22no—
148C2×C3×D3—22no—
149C2×C3×D3—21no—
150C2×C3×D3—21no—
151C2×C3×D3—22no—
152C2×C3×D3—22no—
153C2×C3×D3#4114yescomplemented
154C32×C4—22no—
155C3⋊Dic3—22no—
156C3⋊Dic3C2×D412yes—
157C3⋊Dic3C2×D412yes—
158C3×Dic3—22no—
159C3×Dic3—21no—
160C3×Dic3—21no—
161C2×#41—91no—
162C23×C4—91no—
163#123—31no—
164#123—91no—
165C22⋊Q8—92no—
166#121—92no—
167#120—31no—
168#120—91no—
169C4×D4—92no—
170C4×D4—92no—
171#117—91no—
172C23×C3—21no—
173C23×C3—32no—
174C23×C3—31no—
175C23×C3—31no—
176C23×C3—64no—
177C23×C3—62no—
178C23×C3C22×D311yescharacteristic
179C23×C3C22×D311yescharacteristic
180C22×D3—22no—
181C22×D3—24no—
182C22×D3C22×D311yescharacteristic
183C22×D3C22×D311yescharacteristic
184C22×D3C22×D312yes—
185C3×D4—64no—
186C3×D4—62no—
187C3×D4—62no—
188C2×C3×C4—22no—
189C2×C3×C4—31no—
190C2×C3×C4—32no—
191C2×C3×C4—31no—
192C2×C3×C4—62no—
193C2×C3×C4C22×D312yes—
194C2×C3×C4C22×D312yes—
195#67—22no—
196#67—22no—
197#67—62no—
198#67—62no—
199#67—64no—
200#67—64no—
201C2×Dic3—22no—
202C2×Dic3—34no—
203C2×Dic3—34no—
204C2×Dic3—31no—
205C2×Dic3—31no—
206C2×Dic3—31no—
207C2×Dic3—31no—
208C2×Dic3—32no—
209C2×Dic3—32no—
210C2×Dic3—64no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3C22×D311yescharacteristic
219C2×Dic3C22×D312yes—
220C2×Dic3C22×D311yescharacteristic
221D12—24no—
222C4×D3—64no—
223C4×D3—64no—
224C4×D3—62no—
225C4×D3—62no—
226Dic6—62no—
227Dic6—62no—
228C2×C32—22no—
229C2×C32C22×D411yescharacteristic
230C2×C32C2×#4112yes—
231C3×D3—24no—
232C3×D3—41no—
233C3×D3—41no—
234C24—31no—
235#41—184no—
236C2×Q8—91no—
237C2×D4—31no—
238C2×D4—31no—
239C2×D4—32no—
240C2×D4—92no—
241C2×D4—91no—
242C22×C4—31no—
243C22×C4—92no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—91no—
248C22×C4—184no—
249C4⋊C4—32no—
250C4⋊C4—92no—
251C4⋊C4—92no—
252C22⋊C4—32no—
253C22⋊C4—32no—
254C22⋊C4—92no—
255C22⋊C4—92no—
256C22⋊C4—91no—
257C22⋊C4D3211yescharacteristic
258C42—92no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—34no—
264C22×C3—42no—
265C22×C3—68no—
266C22×C3—62no—
267C22×C3—62no—
268C22×C3—61no—
269C22×C3—61no—
270C22×C3—62no—
271C22×C3—62no—
272C22×C3D3×D412yes—
273C22×C3D3×D412yes—
274C22×C3C23×D311yescharacteristic
275C22×C3C23×D311yescharacteristic
276C2×D3—28no—
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—21no—
280C2×D3—21no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3#23714yescomplemented
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—42no—
287C3×C4—61no—
288C3×C4—61no—
289C3×C4—62no—
290Dic3—21no—
291Dic3—21no—
292Dic3—22no—
293Dic3—32no—
294Dic3—32no—
295Dic3—32no—
296Dic3—32no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301Dic3—122no—
302C32#52511yescharacteristic, complemented, Sylow
303C23—32no—
304C23—31no—
305C23—31no—
306C23—64no—
307C23—62no—
308C23C2×D3211yescharacteristic
309Q8—182no—
310D4—64no—
311D4—62no—
312D4—62no—
313D4—182no—
314D4—184no—
315C2×C4—31no—
316C2×C4—32no—
317C2×C4—31no—
318C2×C4—62no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—94no—
322C2×C4—92no—
323C2×C4—184no—
324C2×C4—184no—
325C2×C4—182no—
326C2×C4—182no—
327C2×C4C2×D3212yes—
328C2×C3—22no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—22no—
332C2×C3—42no—
333C2×C3—64no—
334C2×C3—121no—
335C2×C3—121no—
336C2×C3C2×D3×D411yescharacteristic
337C2×C3C2×D3×D411yescharacteristic
338C2×C3C2×#23712yes—
339C2×C3D3×#4112yes—
340D3—24no—
341D3—41no—
342D3—41no—
343C22—22no—
344C22—34no—
345C22—68no—
346C22—62no—
347C22—62no—
348C22—61no—
349C22—61no—
350C22—62no—
351C22—62no—
352C22#380212yes—
353C22C22×D3211yescharacteristic
354C4—22no—
355C4—62no—
356C4—61no—
357C4—61no—
358C4—92no—
359C4—92no—
360C4—182no—
361C3—21no—
362C3#558611yescharacteristic, complemented
363C3#565611yescharacteristic, complemented
364C2—22no—
365C2—64no—
366C2—121no—
367C2—121no—
368C2C2×#380211yescharacteristic
369C2D3×#23712yes—
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C22⋊C4C22
hypercenterC22⋊C4D32
hypocenterC32#525
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. C22×D3×Dic3C2semidirect
3. #64086C2semidirect
4. C3×#886C2semidirect
5. C3×#882C2semidirect
6. #63976C2semidirect
7. #63961C2semidirect
8. #63902C2semidirect
9. #63899C2semidirect
10. #63898C2semidirect
11. #63885C2semidirect
20. C2×#627C22semidirect
22. C2×#625C22semidirect
27. C2×D3×Dic3C22semidirect
28. C2×D3×Dic3C22semidirect
31. #3750C22semidirect
32. C4×C3⋊Dic3C22semidirect
34. C3×(C2×D3)⋊C4C22semidirect
35. C3×C4⋊Dic3C22semidirect
36. #3724C22semidirect
38. (C2×D3)⋊Dic3C22semidirect
53. #886D3semidirect
55. #882D3semidirect
69. C2×C3⋊Dic3D4semidirect
133. (C2×D3)⋊C4C2×D3semidirect
134. C4⋊Dic3C2×D3semidirect
153. C2×C3×D3#41semidirect
283. C2×D3#237semidirect
302. C32#525semidirect
362. C3#5586semidirect
363. C3#5656semidirect

Maximal subgroups

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

subgroupindex
C2×#38052
C22×D3×Dic32
#640862
C3×#8862
C3×#8822
#639762
#639612
#639022
#638992
#638982
#638852
#56563
#55863