Finite Group Databasebeta

← #11858679

Subgroups — #11858679

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2#10594776C212yesmaximal
3#10592824C211yesmaximal, characteristic, complemented
4C3×#5125C211yesmaximal, characteristic, complemented
5C2×#63577C212yesmaximal, complemented
6#10590912C214yesmaximal, complemented
7D3×#819C214yesmaximal, complemented
8#83789—31nomaximal
9#79260—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2212yes—
13C2×C3×#208C2212yes—
14C22×C3×C3⋊C8C2211yescharacteristic
15C3×#907C418yes—
16C2×C3×ΓL(1,𝔽25)C2212yes—
17C2×C3×D3×C8C2212yes—
18#63815—24no—
19#63814—24no—
20D3×#208C2218yes—
21#63646C2214yes—
22C3×#819C2214yes—
23#63577C2214yes—
24#63577C2214yes—
25C2×C3×#131—31no—
26#5819—32no—
27#5745—32no—
28C2×#907D311yescharacteristic
29C3×#430—31no—
30#5125—31no—
31#5125—31no—
32#5125—34no—
33#5125—61no—
34#5125D311yescharacteristic, complemented
35C2×#822—32no—
36C2×#819—32no—
37C2×#819—34no—
38#4893—34no—
39D3×#108—34no—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67Q812yes—
42C3×#235C2×C414yes—
43C3×#235D414yes—
44C2×C3×D12Q811yescharacteristic
45C2×C3×C4×D3C2312yes—
46C2×C3×Dic6Q811yescharacteristic
47C32×M16C2×C414yes—
48C2×C32×C8C2312yes—
49#3748—22no—
50#3748C2314yes—
51C2×C3⋊(C3⋊C8)—22no—
52C3×#208—22no—
53C3×#208C2314yes—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8C2×C414yes—
56C2×C3×C3⋊C8C2311yescharacteristic
57C2×C3×C3⋊C8C2311yescharacteristic
58C3×ΓL(1,𝔽25)C2×C418yes—
59C3×D3×C8C2×C418yes—
60#3711—28no—
61D3×C3⋊C8—28no—
62#2916—91noSylow
63C2×C3×#41—31no—
64C2×#235C2×D311yescharacteristic
65C3×#131—38no—
66C2×C3×M16—21no—
67C2×C3×M16—32no—
68C2×C3×M16—32no—
69C2×C3×M16C2×D311yescharacteristic
70C2×C3×M16C2×D311yescharacteristic
71C22×C3×C8—31no—
72C22×C3×C8—32no—
73#948—64no—
74#948—64no—
75C2×#208—32no—
76C2×#208—32no—
77C2×#208—38no—
78C2×#208—62no—
79C2×#208C2×D312yes—
80C22×C3⋊C8C2×D311yescharacteristic
81#907—64no—
82#907Dic318yes—
83D3×M16—38no—
84#901—64no—
85C2×ΓL(1,𝔽25)C2×D312yes—
86C2×D3×C8C2×D312yes—
87C3×#108—34no—
88#822—34no—
89#822—34no—
90#819—34no—
91#819—34no—
92#819—34no—
93#819—34no—
94#819—64no—
95#819C2×D314yes—
96C23×C32C2×Q811yescharacteristic
97C22×C3×D3C2×Q812yes—
98C2×C32×C4C22×C412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×Q811yescharacteristic
101C2×C32×C4C2411yescharacteristic
102C3×#67C4⋊C418yes—
103C2×C3×Dic3C2×Q812yes—
104C3×D12C4⋊C414yes—
105C3×C4×D3C22×C414yes—
106C3×C4×D3C2×D414yes—
107C3×Dic6C4⋊C414yes—
108C32×C8C22×C414yes—
109C3⋊(C3⋊C8)—24no—
110C3×C3⋊C8—24no—
111C3×C3⋊C8C22×C412yes—
112C3×C3⋊C8C22×C412yes—
113#568—92no—
114C2×#131—31no—
115#430—31no—
116#430—94no—
117#430—91no—
118C2×#108—94no—
119C2×#108—92no—
120C3×#41—34no—
121C3×#41—34no—
122C2×C3×Q8—31no—
123C2×C3×D4—32no—
124C2×C3×D4—31no—
125C22×C3×C4—21no—
126C22×C3×C4—32no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C2×#67Dic612yes—
130#235D1214yes—
131#235C2×Dic314yes—
132C2×D12Dic611yescharacteristic
133C2×C4×D3C22×D312yes—
134C2×Dic6Dic611yescharacteristic
135C3×M16—24no—
136C3×M16—38no—
137C3×M16—34no—
138C3×M16—62no—
139C3×M16C4×D314yes—
140C3×M16C2×Dic314yes—
141C2×C3×C8—22no—
142C2×C3×C8—34no—
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C2×C3×C8—38no—
146C2×C3×C8—62no—
147C2×C3×C8C22×D312yes—
148C2×C3×C8C22×D312yes—
149#208—22no—
150#208—34no—
151#208—34no—
152#208—64no—
153#208—68no—
154#208—62no—
155#208—62no—
156#208—122no—
157#208C22×D314yes—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—68no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—122no—
163C2×C3⋊C8C2×Dic314yes—
164C2×C3⋊C8C22×D311yescharacteristic
165C2×C3⋊C8C22×D311yescharacteristic
166ΓL(1,𝔽25)—68no—
167ΓL(1,𝔽25)C2×Dic318yes—
168D3×C8—68no—
169D3×C8C2×Dic318yes—
170C22×C32—41no—
171C22×C32C2×C4⋊C412yes—
172C22×C32C22×Q811yescharacteristic
173C2×C3×D3—42no—
174C2×C3×D3C2×C4⋊C414yes—
175C32×C4C2×C4⋊C412yes—
176C32×C4C23×C411yescharacteristic
177C32×C4C22×D411yescharacteristic
178C3×Dic3C2×C4⋊C414yes—
179C2×#41—31no—
180#131—38no—
181#131—184no—
182#131—184no—
183C2×M16—32no—
184C2×M16—32no—
185C2×M16—98no—
186C2×M16—92no—
187C2×M16D3211yescharacteristic
188C22×C8—31no—
189C22×C8—32no—
190#108—34no—
191#108—94no—
192#108—94no—
193#108—94no—
194C23×C3—21no—
195C23×C3—32no—
196C23×C3C2×Dic611yescharacteristic
197C23×C3D3×Q811yescharacteristic
198C22×D3C2×Dic612yes—
199C3×Q8—34no—
200C3×D4—38no—
201C3×D4—34no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—32no—
207C2×C3×C4—34no—
208C2×C3×C4—34no—
209C2×C3×C4C2×Dic611yescharacteristic
210C2×C3×C4C2×C4×D312yes—
211C2×C3×C4C2×D1212yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4D3×Q811yescharacteristic
214C2×C3×C4C22×Dic312yes—
215C2×C3×C4C23×D311yescharacteristic
216C2×C3×C4C23×D311yescharacteristic
217#67C4⋊Dic318yes—
218C2×Dic3C2×Dic612yes—
219D12C4⋊Dic314yes—
220C4×D3C2×D1214yes—
221C4×D3C22×Dic314yes—
222Dic6C4⋊Dic314yes—
223C3×C8—24no—
224C3×C8—32no—
225C3×C8—32no—
226C3×C8—64no—
227C3×C8C2×C4×D314yes—
228C3×C8C22×Dic314yes—
229C3⋊C8—24no—
230C3⋊C8—64no—
231C3⋊C8—64no—
232C3⋊C8—124no—
233C3⋊C8C22×Dic312yes—
234C3⋊C8C22×Dic312yes—
235C2×C32—21no—
236C2×C32—22no—
237C2×C32C22×C4⋊C411yescharacteristic
238C3×D3—24no—
239#41—34no—
240#41—34no—
241C2×Q8—31no—
242C2×D4—32no—
243C2×D4—31no—
244C22×C4—32no—
245C22×C4C2×D3211yescharacteristic
246M16—38no—
247M16—34no—
248M16—62no—
249M16—94no—
250M16—188no—
251M16—182no—
252M16D3×Dic314yes—
253C2×C8—31no—
254C2×C8—31no—
255C2×C8—34no—
256C2×C8—38no—
257C2×C8—62no—
258C2×C8—188no—
259C2×C8—182no—
260C2×C8C2×D3212yes—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—34no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—81no—
267C22×C3—122no—
268C22×C3D3×C4⋊C412yes—
269C22×C3C2×C4⋊Dic312yes—
270C22×C3C22×Dic611yescharacteristic
271C22×C3C2×D3×Q811yescharacteristic
272C2×D3—42no—
273C2×D3C2×C4⋊Dic314yes—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—22no—
277C3×C4—34no—
278C3×C4D3×C4⋊C412yes—
279C3×C4C2×C4⋊Dic312yes—
280C3×C4C22×C4×D311yescharacteristic
281C3×C4C22×D1211yescharacteristic
282C3×C4C2×D3×D411yescharacteristic
283C3×C4C23×Dic311yescharacteristic
284Dic3C2×C4⋊Dic314yes—
285C32#291611yescharacteristic, complemented, Sylow
286C23—32no—
287C23D3×Dic611yescharacteristic
288Q8—34no—
289D4—38no—
290D4—34no—
291C2×C4—32no—
292C2×C4—34no—
293C2×C4—34no—
294C2×C4D3×Dic611yescharacteristic
295C2×C4D3×D1212yes—
296C2×C4C2×D3×Dic312yes—
297C2×C4C22×D3211yescharacteristic
298C8—32no—
299C8—32no—
300C8—64no—
301C8—184no—
302C8C2×D3×Dic314yes—
303C2×C3—21no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—21no—
308C2×C3—41no—
309C2×C3—42no—
310C2×C3—64no—
311C2×C3C2×D3×C4⋊C411yescharacteristic
312C2×C3C22×C4⋊Dic311yescharacteristic
313D3—24no—
314C22—34no—
315C22—41no—
316C22—122no—
317C22D3×C4⋊Dic312yes—
318C22C2×D3×Dic611yescharacteristic
319C4—34no—
320C4D3×C4⋊Dic312yes—
321C4C2×D3×D1211yescharacteristic
322C4C22×D3×Dic311yescharacteristic
323C3—21no—
324C3#7926011yescharacteristic, complemented
325C3#8378911yescharacteristic, complemented
326C2—21no—
327C2—22no—
328C2—64no—
329C2C2×D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C22×C4⋊C4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2916
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10592824C2semidirect
4. C3×#5125C2semidirect
5. C2×#63577C2semidirect
6. #10590912C2semidirect
7. D3×#819C2semidirect
34. #5125D3semidirect
285. C32#2916semidirect
324. C3#79260semidirect
325. C3#83789semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105947762
#105928242
C3×#51252
C2×#635772
#105909122
D3×#8192
#837893
#792603