Finite Group Databasebeta

← #10695230

Subgroups — #10695230

Order 768.

616 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4928C211yesmaximal, characteristic
2C3×C4×C22⋊C8C211yesmaximal, characteristic
3#71530C211yesmaximal, characteristic
4#67674C214yesmaximal
5#9879—31nomaximal, Sylow
6C22×C3×C42C2211yescharacteristic
7C22×C4⋊Dic3C411yescharacteristic
8C22×C4⋊Dic3C411yescharacteristic
9C22×Dic3⋊C4C412yes—
10C2×C3×C22⋊C8C2212yes—
11C2×C3×C4×C8—21no—
12C2×C3⋊#95C2212yes—
13C2×#830C2212yes—
14#4928—21no—
15#4928—21no—
16#4928—21no—
17#4928—21no—
18C2×C4⋊(C3⋊C8)—21no—
19C3×#336—21no—
20#4524—21no—
21C2×#389—31no—
22#1797—31no—
23C4×C22⋊C8D311yescharacteristic
24#1280—34no—
25C23×C3×C4C2×C411yescharacteristic
26C23×C3×C4C2×C411yescharacteristic
27C23×C3×C4C2311yescharacteristic
28C23×Dic3C2×C412yes—
29C23×Dic3C2×C412yes—
30C22×C3×C8—22no—
31C2×C3×C42—42no—
32C2×C3×C42D411yescharacteristic
33C2×C3×C42D411yescharacteristic
34C2×C3×C42D411yescharacteristic
35C2×C3×C42D411yescharacteristic
36C2×C4⋊Dic3—21no—
37C2×C4⋊Dic3—21no—
38C2×C4⋊Dic3—22no—
39C2×C4⋊Dic3—21no—
40C2×C4⋊Dic3—21no—
41C2×C4⋊Dic3—42no—
42C2×C4⋊Dic3C814yescomplemented
43C2×Dic3⋊C4—22no—
44C2×Dic3⋊C4—22no—
45C2×Dic3⋊C4—44no—
46C22×C3⋊C8—22no—
47C3×C22⋊C8—22no—
48C3×C22⋊C8Q814yes—
49C3×C4×C8—42no—
50C3⋊#95—22no—
51C3⋊#95—22no—
52#830—24no—
53C4⋊(C3⋊C8)—42no—
54C22×C4⋊C4—31no—
55C22×C4⋊C4—32no—
56C22×C4⋊C4—31no—
57C22×C42C2×D311yescharacteristic
58C2×C4⋊C8—61no—
59C2×C22⋊C8—32no—
60C2×C22⋊C8C2×D312yes—
61C2×C4×C8—21no—
62#389—61no—
63#389—61no—
64#389—61no—
65#389—61no—
66C2×#95—32no—
67#336—21no—
68#336—61no—
69C24×C3C22×C411yescharacteristic
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4C22⋊C411yescharacteristic
78C22×C3×C4C22⋊C411yescharacteristic
79C22×C3×C4C22⋊C411yescharacteristic
80C22×C3×C4C22⋊C411yescharacteristic
81C22×C3×C4C2×C812yes—
82C22×C3×C4M1612yes—
83C22×C3×C4C2×D411yescharacteristic
84C22×C3×C4C2×D411yescharacteristic
85C22×C3×C4C2×Q812yes—
86C22×C3×C4#4112yes—
87C22×Dic3—22no—
88C22×Dic3—22no—
89C22×Dic3—22no—
90C22×Dic3—24no—
91C22×Dic3—42no—
92C22×Dic3—42no—
93C22×Dic3—42no—
94C22×Dic3—42no—
95C22×Dic3C2×C814yes—
96C2×C3×C8—24no—
97C2×C3×C8—42no—
98C2×C3×C8—42no—
99C3×C42—22no—
100C3×C42—22no—
101C3×C42—41no—
102C3×C42—41no—
103C4⋊Dic3—24no—
104C4⋊Dic3—24no—
105C4⋊Dic3—42no—
106C4⋊Dic3—42no—
107Dic3⋊C4—44no—
108Dic3⋊C4—44no—
109C2×C3⋊C8—42no—
110C2×C3⋊C8—42no—
111C2×C3⋊C8—42no—
112C23×C4—32no—
113C23×C4—32no—
114C23×C4C4×D311yescharacteristic
115C23×C4C4×D311yescharacteristic
116C23×C4C22×D311yescharacteristic
117C22×C8—22no—
118C22×C8—62no—
119C2×C4⋊C4—34no—
120C2×C4⋊C4—62no—
121C2×C4⋊C4—61no—
122C2×C4⋊C4—61no—
123C2×C4⋊C4—62no—
124C2×C4⋊C4—62no—
125C2×C4⋊C4—61no—
126C2×C4⋊C4—61no—
127C2×C4⋊C4—124no—
128C2×C4⋊C4—122no—
129C2×C42—42no—
130C2×C42D1211yescharacteristic
131C2×C42D1211yescharacteristic
132C2×C42#6711yescharacteristic
133C2×C42#6711yescharacteristic
134C4⋊C8—122no—
135C22⋊C8—22no—
136C22⋊C8—64no—
137C22⋊C8Dic614yes—
138C4×C8—42no—
139#95—62no—
140#95—62no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—21no—
145C23×C3C2×C22⋊C411yescharacteristic
146C23×C3C4×Q812yes—
147C23×C3C22×C811yescharacteristic
148C23×C3C2×M1611yescharacteristic
149C23×C3#13112yes—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—24no—
159C2×C3×C4—24no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4—44no—
166C2×C3×C4C22⋊C812yes—
167C2×C3×C4C22⋊C812yes—
168C2×C3×C4#9912yes—
169C2×C3×C4#10012yes—
170C2×C3×C4#10112yes—
171C2×C3×C4C22⋊Q812yes—
172C2×C3×C4#12411yescharacteristic
173C2×C3×C4C4⋊Q811yescharacteristic
174C2×Dic3—24no—
175C2×Dic3—44no—
176C2×Dic3—42no—
177C2×Dic3—42no—
178C2×Dic3—44no—
179C2×Dic3—42no—
180C2×Dic3—42no—
181C2×Dic3—42no—
182C2×Dic3—84no—
183C3×C8—44no—
184C3⋊C8—82no—
185C24C2×C4×D311yescharacteristic
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—34no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—62no—
195C22×C4—62no—
196C22×C4—62no—
197C22×C4—64no—
198C22×C4—122no—
199C22×C4—122no—
200C22×C4—122no—
201C22×C4—122no—
202C22×C4D3×C812yes—
203C22×C4ΓL(1,𝔽25)12yes—
204C22×C4(C2×D3)⋊C411yescharacteristic
205C22×C4(C2×D3)⋊C411yescharacteristic
206C22×C4(C2×D3)⋊C411yescharacteristic
207C22×C4(C2×D3)⋊C411yescharacteristic
208C22×C4C2×Dic612yes—
209C22×C4C2×D1211yescharacteristic
210C22×C4#23512yes—
211C22×C4C2×#6711yescharacteristic
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—122no—
216C2×C8—122no—
217C2×C8—122no—
218C4⋊C4—64no—
219C4⋊C4—64no—
220C4⋊C4—124no—
221C4⋊C4—122no—
222C4⋊C4—122no—
223C4⋊C4—124no—
224C42—22no—
225C42—22no—
226C42—41no—
227C42—41no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3#39111yescharacteristic
237C22×C3C2×C22⋊C811yescharacteristic
238C22×C3#40811yescharacteristic
239C22×C3C2×#9911yescharacteristic
240C22×C3#41011yescharacteristic
241C22×C3C2×#10011yescharacteristic
242C22×C3C2×#10111yescharacteristic
243C22×C3C8×Q812yes—
244C22×C3#44612yes—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—21no—
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4#32414yes—
252Dic3—44no—
253Dic3—82no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23C4×Dic612yes—
259C23C2×D3×C811yescharacteristic
260C23C2×ΓL(1,𝔽25)11yescharacteristic
261C23#90112yes—
262C23C2×(C2×D3)⋊C411yescharacteristic
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—64no—
280C2×C4—124no—
281C2×C4—122no—
282C2×C4—122no—
283C2×C4—124no—
284C2×C4—122no—
285C2×C4—122no—
286C2×C4—122no—
287C2×C4—244no—
288C2×C4#80612yes—
289C2×C4(C2×D3)⋊C812yes—
290C2×C4(C2×D3)⋊C812yes—
291C2×C4#82312yes—
292C2×C4#82412yes—
293C2×C4#86911yescharacteristic
294C2×C4#87511yescharacteristic
295C2×C4#92412yes—
296C8—44no—
297C8—242no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3C2×#32411yescharacteristic
301C2×C3#146011yescharacteristic
302C2×C3#147011yescharacteristic
303C2×C3#147111yescharacteristic
304C2×C3#198411yescharacteristic
305C2×C3#199611yescharacteristic
306C2×C3#199711yescharacteristic
307C22—22no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22C8×Dic612yes—
316C22#467912yes—
317C22#492911yescharacteristic
318C22C2×#80611yescharacteristic
319C22#500611yescharacteristic
320C22C2×(C2×D3)⋊C811yescharacteristic
321C22#511011yescharacteristic
322C22C2×#82311yescharacteristic
323C22C2×#82411yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—124no—
331C4—242no—
332C4#446914yes—
333C3#987911yescharacteristic, complemented, Sylow
334C2—22no—
335C2—22no—
336C2#6945711yescharacteristic
337C2#6978811yescharacteristic
338C2#6987911yescharacteristic
339C2#6992111yescharacteristic
340C2C2×#446911yescharacteristic
341C2#7078311yescharacteristic
342C2#7078711yescharacteristic
subgroupG/H
centerC23C2×(C2×D3)⋊C4
commutatorC23×C3C22×C8
FrattiniC23×C4C22×D3
FittingC3×C4×C22⋊C8C2
socleC23×C3C2×C22⋊C4
prime radicalC24×C3C22×C4
cosocleC23×C3×C4C23
hypercenterC4×C22⋊C8D3
hypocenterC3#9879
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
42. C2×C4⋊Dic3C8semidirect
333. C3#9879semidirect

Maximal subgroups

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

subgroupindex
C2×#49282
C3×C4×C22⋊C82
#715302
#676742
#98793