Finite Group Databasebeta

← #11790993

Subgroups — #11790993

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic
5C2×#63634C211yesmaximal, characteristic
6#10592628C211yesmaximal, characteristic
7C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
8#69677—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3756—22no—
14C2×#3756—22no—
15C2×#3756C414yescomplemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C32×#95—22no—
20#63662—22no—
21#63658—22no—
22#63637—22no—
23#63634—22no—
24C4×C3⋊(C3⋊C8)—22no—
25C22×#216—34no—
26C3×#391D314yes—
27C2×#835—34no—
28C2×#810—34no—
29C2×#807—34no—
30#4929—34no—
31C2×C4×C3⋊C8—34no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8C2×C412yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42—21no—
53C32×C42—21no—
54#3756—28no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)C2×C412yes—
60C2×C3⋊(C3⋊C8)D412yes—
61C2×C3⋊(C3⋊C8)D412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63#1969—91noSylow
64C22×C3×Q8C2×D314yes—
65C22×Dic6—34no—
66C2×C3×C4⋊C4C2×D314yes—
67C2×C3×C42C2×D314yes—
68C2×#216—316no—
69C2×#216—68no—
70C2×#216—68no—
71C2×C4⋊Dic3—34no—
72C22×C3⋊C8—34no—
73C22×C3⋊C8—34no—
74C3×#95—28no—
75#835—68no—
76C3⋊#95—68no—
77#810—68no—
78#807—68no—
79C4×C3⋊C8—68no—
80C23×C32C2×D411yescharacteristic
81C32×Q8—22no—
82C32×Q8—22no—
83C32×Q8—41no—
84C32×Q8—41no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—42no—
92C2×C32×C4Q1614yescomplemented
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—42no—
104#634—22no—
105#634—22no—
106#634—41no—
107#634—41no—
108C3⋊(C3⋊C8)—22no—
109C3⋊(C3⋊C8)C22⋊C414yes—
110C22×Q16—91no—
111C2×#107—91no—
112C2×#103—91no—
113C2×#103—91no—
114C2×C4×C8—91no—
115#391—91no—
116#391C3⋊D311yescharacteristic
117C2×C3×Q8—24no—
118C2×C3×Q8—24no—
119C2×C3×Q8—24no—
120C2×C3×Q8—24no—
121C2×C3×Q8—24no—
122C2×C3×Q8C4×D318yes—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4#6718yes—
126C22×C3×C4C22×D314yes—
127C22×Dic3—64no—
128C22×Dic3—64no—
129C2×Dic6—38no—
130C2×Dic6—64no—
131C2×Dic6—64no—
132C2×Dic6—64no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4—24no—
137C3×C42—24no—
138C3×C42—24no—
139#216—632no—
140C4⋊Dic3—64no—
141C4⋊Dic3—64no—
142C2×C3⋊C8—38no—
143C2×C3⋊C8—38no—
144C2×C3⋊C8—38no—
145C2×C3⋊C8—38no—
146C2×C3⋊C8—64no—
147C2×C3⋊C8—64no—
148C22×C32C4×D411yescharacteristic
149C22×C32#12111yescharacteristic
150C22×C32#12711yescharacteristic
151C22×C32C2×Q1612yes—
152C22×C32#13512yes—
153C32×C4—24no—
154C32×C4—42no—
155C32×C4—81no—
156C32×C4C2×C22⋊C411yescharacteristic
157C32×C4C4×D411yescharacteristic
158C32×C4#12111yescharacteristic
159C32×C4#12411yescharacteristic
160C3⋊Dic3—42no—
161C3⋊Dic3—81no—
162C22×Q8—91no—
163C22×Q8C2×C3⋊D311yescharacteristic
164C2×Q16—94no—
165C2×Q16—182no—
166C2×Q16—182no—
167C22×C8—91no—
168C22×C8—91no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4C2×C3⋊D311yescharacteristic
171C2×C42C2×C3⋊D311yescharacteristic
172#107—182no—
173#103—182no—
174#103—182no—
175C4×C8—182no—
176#95—22no—
177#95—182no—
178C23×C3C2×#6714yes—
179C3×Q8—28no—
180C3×Q8—28no—
181C3×Q8—44no—
182C3×Q8—44no—
183C2×C3×C4—28no—
184C2×C3×C4—28no—
185C2×C3×C4—28no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4—48no—
190C2×C3×C4#216116yescomplemented
191C2×C3×C4C2×C4×D314yes—
192C2×C3×C4#23514yes—
193C2×C3×C4D3×D414yes—
194C2×C3×C4D3×D414yes—
195C2×C3×C4D3×D414yes—
196C2×C3×C4#23714yes—
197C2×Dic3—68no—
198C2×Dic3—124no—
199C2×Dic3—124no—
200C2×Dic3—124no—
201C2×Dic3—128no—
202Dic6—68no—
203Dic6—68no—
204Dic6—124no—
205Dic6—124no—
206C3⋊C8—316no—
207C3⋊C8—68no—
208C2×C32#39011yescharacteristic
209C2×C32C4×Q1612yes—
210C2×C32#46712yes—
211C2×C32#49411yescharacteristic
212C2×C32#49511yescharacteristic
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—181no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C2×Q8C4×C3⋊D312yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—181no—
228C22×C4—181no—
229C22×C4#63812yes—
230C22×C4C22×C3⋊D311yescharacteristic
231Q16—188no—
232C2×C8—92no—
233C2×C8—92no—
234C2×C8—92no—
235C2×C8—92no—
236C2×C8—181no—
237C2×C8—181no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C42—21no—
243C42—21no—
244C22×C3C4×#6714yes—
245C22×C3#93914yes—
246C22×C3#94014yes—
247C22×C3C2×#21618yes—
248C22×C3#95018yes—
249C3×C4—216no—
250C3×C4—48no—
251C3×C4—84no—
252C3×C4D3×C22⋊C414yes—
253C3×C4#67⋊C414yes—
254C3×C4#88414yes—
255C3×C4#88514yes—
256Dic3—128no—
257Dic3—244no—
258C32#196911yescharacteristic, complemented, Sylow
259C23C2×#63811yescharacteristic
260Q8—22no—
261Q8—22no—
262Q8—41no—
263Q8—41no—
264Q8—182no—
265Q8—182no—
266Q8—361no—
267Q8—361no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—182no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—362no—
280C2×C4#375614yescomplemented
281C2×C4C2×C4×C3⋊D311yescharacteristic
282C2×C4#382811yescharacteristic
283C2×C4D4×C3⋊D311yescharacteristic
284C2×C4D4×C3⋊D311yescharacteristic
285C2×C4D4×C3⋊D311yescharacteristic
286C2×C4#383011yescharacteristic
287C8—94no—
288C8—182no—
289C2×C3#495714yes—
290C2×C3C4×#21618yes—
291C2×C3#505118yes—
292C2×C3#505914yes—
293C2×C3#509214yes—
294C22C4×#63811yescharacteristic
295C22#6414811yescharacteristic
296C22#6414911yescharacteristic
297C22C2×#375612yes—
298C22#6415912yes—
299C4—24no—
300C4—42no—
301C4—81no—
302C4—362no—
303C4—721no—
304C4C22⋊C4×C3⋊D311yescharacteristic
305C4#6409011yescharacteristic
306C4#6409311yescharacteristic
307C4#6409411yescharacteristic
308C3#6967714yescomplemented
309C2#1059265611yescharacteristic
310C2C4×#375612yes—
311C2#1059275012yes—
312C2#1059275811yescharacteristic
313C2#1059279111yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#391C3⋊D3
hypocenterC32#1969
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
15. C2×#3756C4semidirect
92. C2×C32×C4Q16semidirect
190. C2×C3×C4#216semidirect
258. C32#1969semidirect
280. C2×C4#3756semidirect
308. C3#69677semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C32×#3912
C2×#636622
C2×#636372
C2×#636342
#105926282
C2×C4×C3⋊(C3⋊C8)2
#696773