Finite Group Databasebeta

← #11802691

Subgroups — #11802691

Order 1152.

1677 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic
2C2×#63955C212yesmaximal
3#10592910C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic
5#10591696C212yesmaximal
6#10591261C218yesmaximal, complemented
7#84062—31nomaximal
8#74053—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C22×C3×Dic6—28no—
13C22×C3×Dic6C418yescomplemented
14C22×C3×Dic6C2214yes—
15C2×#3757C2212yes—
16C2×C3×#217C2212yes—
17C2×Dic3⋊Dic3C2214yes—
18#63955—28no—
19C2×Dic32C2214yes—
20#63658C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2218yes—
23C23×C3×Q8—31no—
24C23×Dic6D311yescharacteristic
25C2×#926—32no—
26C2×#877—32no—
27C3×#381—31no—
28#5229—38no—
29#5211—31no—
30#5211—31no—
31#5211—32no—
32#5211—61no—
33#5211D311yescharacteristic
34#4943—32no—
35#4646—38no—
36C24×C32C2311yescharacteristic
37C22×C32×C4—24no—
38C22×C32×C4C2×C414yes—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3C2314yes—
41C22×C3×Dic3—24no—
42C22×C3×Dic3C2×C414yes—
43C22×C3×Dic3C2×C414yes—
44C22×C3×Dic3D418yes—
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2312yes—
47C22×C3×Dic3C2312yes—
48C2×C3×Dic6—232no—
49C2×C3×Dic6—28no—
50C2×C3×Dic6—28no—
51C2×C3×Dic6C2×C4116yes—
52#3757—24no—
53C3×#217—24no—
54Dic3⋊Dic3—28no—
55Dic32—28no—
56#2310—91noSylow
57C22×C3×Q8—38no—
58C22×C3×Q8—34no—
59C22×C3×Q8—68no—
60C23×C3×C4—21no—
61C23×C3×C4—31no—
62C23×C3×C4—31no—
63C23×C3×C4C2×D311yescharacteristic
64C23×C3×C4C2×D311yescharacteristic
65C23×Dic3C2×D311yescharacteristic
66C23×Dic3C2×D311yescharacteristic
67C22×Dic6—28no—
68C22×Dic6Dic318yescomplemented
69C22×Dic6C2×D314yes—
70C2×C3×C22⋊C4—32no—
71C2×#217—32no—
72C2×#217—32no—
73C2×#217—62no—
74C2×#217C2×D312yes—
75#926—68no—
76C2×C4⋊Dic3—34no—
77C2×Dic3⋊C4—34no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—34no—
80#877—68no—
81C3×#95—34no—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95—38no—
85C3⋊#95—38no—
86C3⋊#95—64no—
87C3⋊#95C2×D314yes—
88C23×C32—24no—
89C23×C32C22×C412yes—
90C23×C32C2×D414yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—28no—
93C2×C32×C4—24no—
94C2×C32×C4C22×C414yes—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—28no—
97C2×C3×Dic3—28no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—28no—
101C2×C3×Dic3C22⋊C4116yes—
102C2×C3×Dic3C22×C414yes—
103C2×C3×Dic3C22×C414yes—
104C2×C3×Dic3C2×D414yes—
105C2×C3×Dic3C2×D414yes—
106C3×Dic6—232no—
107C23×Q8—31no—
108C2×#117—92no—
109#391—98no—
110#381—31no—
111#381—92no—
112#381—91no—
113C24×C3—21no—
114C24×C3C22×D311yescharacteristic
115C24×C3C22×D311yescharacteristic
116C2×C3×Q8—316no—
117C2×C3×Q8—632no—
118C2×C3×Q8—68no—
119C2×C3×Q8—68no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—22no—
124C22×C3×C4—34no—
125C22×C3×C4—38no—
126C22×C3×C4—32no—
127C22×C3×C4—34no—
128C22×C3×C4—32no—
129C22×C3×C4—34no—
130C22×C3×C4—44no—
131C22×C3×C4—64no—
132C22×C3×C4C4×D314yes—
133C22×C3×C4C2×Dic314yes—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×Dic3—24no—
137C22×Dic3—34no—
138C22×Dic3—34no—
139C22×Dic3—64no—
140C22×Dic3C2×Dic314yes—
141C22×Dic3C2×Dic314yes—
142C22×Dic3#6718yes—
143C22×Dic3C22×D314yes—
144C22×Dic3C22×D312yes—
145C22×Dic3C22×D312yes—
146C2×Dic6—232no—
147C2×Dic6—28no—
148C2×Dic6—28no—
149C2×Dic6C2×Dic3116yes—
150C3×C22⋊C4—64no—
151#217—24no—
152#217—64no—
153#217—64no—
154#217—124no—
155C4⋊Dic3—68no—
156Dic3⋊C4—68no—
157C4×Dic3—68no—
158C4×Dic3—68no—
159C22×C32—24no—
160C22×C32—28no—
161C22×C32C2×C22⋊C414yes—
162C22×C32C23×C411yescharacteristic
163C22×C32C22×D412yes—
164C22×C322−1+414yes—
165C32×C4—24no—
166C3⋊Dic3—44no—
167C3×Dic3—24no—
168C3×Dic3—44no—
169C3×Dic3C2×C22⋊C418yes—
170C22×Q8—38no—
171C22×Q8—34no—
172C22×Q8—68no—
173C23×C4—31no—
174C23×C4—31no—
175C23×C4D3211yescharacteristic
176#117—188no—
177C2×C4⋊C4—94no—
178C2×C22⋊C4—32no—
179C2×C22⋊C4—92no—
180C2×C42—94no—
181#95—34no—
182#95—98no—
183#95—94no—
184C23×C3—24no—
185C23×C3—24no—
186C23×C3—21no—
187C23×C3—22no—
188C23×C3—24no—
189C23×C3—44no—
190C23×C3C2×C4×D312yes—
191C23×C3D3×D414yes—
192C23×C3C22×Dic312yes—
193C23×C3C2×#6714yes—
194C23×C3C23×D311yescharacteristic
195C23×C3C23×D311yescharacteristic
196C3×Q8—632no—
197C2×C3×C4—28no—
198C2×C3×C4—28no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—316no—
203C2×C3×C4—34no—
204C2×C3×C4—34no—
205C2×C3×C4—34no—
206C2×C3×C4—34no—
207C2×C3×C4—44no—
208C2×C3×C4—48no—
209C2×C3×C4—68no—
210C2×C3×C4—64no—
211C2×C3×C4—68no—
212C2×C3×C4—64no—
213C2×C3×C4C2×C4×D314yes—
214C2×C3×C4C22×Dic314yes—
215C2×Dic3—28no—
216C2×Dic3—24no—
217C2×Dic3—24no—
218C2×Dic3—28no—
219C2×Dic3—64no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—64no—
223C2×Dic3—124no—
224C2×Dic3—128no—
225C2×Dic3#217116yes—
226C2×Dic3C22×Dic314yes—
227C2×Dic3C22×Dic314yes—
228C2×Dic3C2×#6714yes—
229C2×Dic3C2×#6714yes—
230Dic6—232no—
231C2×C32—24no—
232C2×C32C22×C22⋊C411yescharacteristic
233C2×C32#51912yes—
234C2×C32#53614yes—
235C24C2×D3211yescharacteristic
236C2×Q8—316no—
237C2×Q8—68no—
238C2×Q8—68no—
239C2×Q8—632no—
240C22×C4—24no—
241C22×C4—32no—
242C22×C4—34no—
243C22×C4—38no—
244C22×C4—32no—
245C22×C4—34no—
246C22×C4—34no—
247C22×C4—64no—
248C22×C4—94no—
249C22×C4D3×Dic314yes—
250C22×C4C2×D3212yes—
251C4⋊C4—188no—
252C22⋊C4—64no—
253C22⋊C4—184no—
254C42—188no—
255C22×C3—28no—
256C22×C3—24no—
257C22×C3—24no—
258C22×C3—28no—
259C22×C3—24no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—24no—
263C22×C3—44no—
264C22×C3—48no—
265C22×C3D3×C22⋊C414yes—
266C22×C3C2×#21714yes—
267C22×C3C22×C4×D311yescharacteristic
268C22×C3C2×D3×D412yes—
269C22×C3#100714yes—
270C22×C3#101014yes—
271C22×C3C23×Dic311yescharacteristic
272C22×C3C22×#6712yes—
273C3×C4—24no—
274C3×C4—24no—
275C3×C4—38no—
276C3×C4—44no—
277C3×C4—64no—
278C3×C4—124no—
279Dic3—24no—
280Dic3—44no—
281Dic3—124no—
282Dic3—124no—
283Dic3—244no—
284Dic3C2×#21718yes—
285C32#231011yescharacteristic, complemented, Sylow
286C23—24no—
287C23C2×D3×Dic312yes—
288C23D3×#6714yes—
289C23C22×D3211yescharacteristic
290Q8—632no—
291C2×C4—24no—
292C2×C4—28no—
293C2×C4—34no—
294C2×C4—34no—
295C2×C4—34no—
296C2×C4—316no—
297C2×C4—34no—
298C2×C4—64no—
299C2×C4—68no—
300C2×C4—68no—
301C2×C4—64no—
302C2×C4—188no—
303C2×C4—184no—
304C2×C4C2×D3×Dic314yes—
305C2×C3—24no—
306C2×C3—24no—
307C2×C3—22no—
308C2×C3—24no—
309C2×C3—21no—
310C2×C3—44no—
311C2×C3C2×D3×C22⋊C411yescharacteristic
312C2×C3#551612yes—
313C2×C3#564814yes—
314C2×C3#581212yes—
315C2×C3#581614yes—
316C2×C3C22×#21711yescharacteristic
317C22—24no—
318C22—28no—
319C22D3×#21714yes—
320C22#6429714yes—
321C22C22×D3×Dic311yescharacteristic
322C22C2×D3×#6712yes—
323C4—24no—
324C4—38no—
325C4—64no—
326C4—124no—
327C4—364no—
328C3—21no—
329C3#7405311yescharacteristic, complemented
330C3#8406211yescharacteristic, complemented
331C2—24no—
332C2#1059481812yes—
333C2#1059489714yes—
334C2C2×D3×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591261C2semidirect
13. C22×C3×Dic6C4semidirect
68. C22×Dic6Dic3semidirect
285. C32#2310semidirect
329. C3#74053semidirect
330. C3#84062semidirect

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C2×#639552
#105929102
C3×#52112
#105916962
#105912612
#840623
#740533