Finite Group Databasebeta

← #11791137

Subgroups — #11791137

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic, complemented
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic
5C2×#63634C211yesmaximal, characteristic, complemented
6#10592638C211yesmaximal, characteristic
7C2×#63630C211yesmaximal, characteristic, complemented
8#69679—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3755—22no—
14C2×#3755—22no—
15C2×#3755C414yescomplemented
16C2×#3752—22no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C32×#95—22no—
21#63662—22no—
22#63636—22no—
23#63634—22no—
24#63630—22no—
25C22×#215—34no—
26C3×#391D314yescomplemented
27C2×#835—34no—
28C2×#809—34no—
29C2×#807—34no—
30#4939—34no—
31C2×#803—34no—
32C23×C3⋊D3—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8C2×C412yes—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4D412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42—21no—
53C32×C42—21no—
54#3755—28no—
55#3752—44no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C2×C3⋊(C3⋊C8)D412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63C2×C3⋊(C3⋊C8)D412yes—
64#1973—91noSylow
65C22×C3×Q8C2×D314yes—
66C22×D12—34no—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C3×C42C2×D314yes—
69C2×#215—316no—
70C2×#215—68no—
71C2×#215—68no—
72C2×(C2×D3)⋊C4—68no—
73C2×C4⋊Dic3—34no—
74C22×C3⋊C8—34no—
75C22×C3⋊C8—34no—
76C3×#95—28no—
77#835—68no—
78#809—68no—
79#807—68no—
80#803—68no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3—42no—
86C22×C3⋊D3—42no—
87C32×Q8—22no—
88C32×Q8—22no—
89C32×Q8—41no—
90C32×Q8—41no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4—42no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—42no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—22no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)C22⋊C414yescomplemented
113C22×SD16—91no—
114C2×#107—91no—
115C2×#103—91no—
116C2×#102—91no—
117C2×#97—91no—
118#391C3⋊D311yescharacteristic, complemented
119#390—91no—
120C23×D3—64no—
121C2×C3×Q8—24no—
122C2×C3×Q8—24no—
123C2×C3×Q8—24no—
124C2×C3×Q8—24no—
125C2×C3×Q8—24no—
126C2×C3×Q8C4×D318yes—
127C22×C3×C4—24no—
128C22×C3×C4—24no—
129C22×C3×C4#6718yes—
130C22×C3×C4C22×D314yes—
131C22×Dic3—64no—
132C2×D12—38no—
133C2×D12—64no—
134C2×D12—64no—
135C2×D12—64no—
136C2×D12—64no—
137C2×D12—64no—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—24no—
140C3×C42—24no—
141C3×C42—24no—
142#215—632no—
143(C2×D3)⋊C4—1216no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146C2×C3⋊C8—38no—
147C2×C3⋊C8—38no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—38no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C22×C32C4×D411yescharacteristic
153C22×C32#12111yescharacteristic
154C22×C32#12711yescharacteristic
155C22×C32AGL(1,ℤ/8)12yes—
156C22×C32#13712yes—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3—82no—
160C2×C3⋊D3—81no—
161C2×C3⋊D3—81no—
162C32×C4—42no—
163C32×C4—42no—
164C32×C4—81no—
165C32×C4C2×C22⋊C411yescharacteristic
166C32×C4C4×D411yescharacteristic
167C32×C4#12111yescharacteristic
168C32×C4#12411yescharacteristic
169C3⋊Dic3—81no—
170C22×Q8C2×C3⋊D311yescharacteristic
171C22×D4—91no—
172C2×SD16—94no—
173C2×SD16—182no—
174C2×SD16—182no—
175C22×C8—91no—
176C22×C8—91no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4—182no—
180C2×C42C2×C3⋊D311yescharacteristic
181#107—182no—
182#103—182no—
183#102—182no—
184#97—182no—
185#95—22no—
186C23×C3C2×#6714yes—
187C22×D3—68no—
188C22×D3—124no—
189C22×D3—124no—
190C22×D3—128no—
191C22×D3—128no—
192C3×Q8—28no—
193C3×Q8—28no—
194C3×Q8—44no—
195C3×Q8—44no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—28no—
199C2×C3×C4—28no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4—48no—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4#23514yes—
206C2×C3×C4D3×D414yes—
207C2×C3×C4D3×D414yes—
208C2×C3×C4D3×D414yes—
209C2×C3×C4#23714yes—
210C2×Dic3—124no—
211C2×Dic3—128no—
212D12—68no—
213D12—68no—
214D12—124no—
215D12—124no—
216C3⋊C8—316no—
217C3⋊C8—68no—
218C2×C32#39011yescharacteristic
219C2×C32#44012yes—
220C2×C32#46812yes—
221C2×C32#49611yescharacteristic
222C2×C32#49711yescharacteristic
223C3⋊D3—82no—
224C24—181no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8C4×C3⋊D312yes—
231C2×D4—92no—
232C2×D4—181no—
233C2×D4—181no—
234C2×D4—181no—
235C2×D4—181no—
236C2×D4—181no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—181no—
240C22×C4#63812yes—
241C22×C4C22×C3⋊D311yescharacteristic
242SD16—188no—
243C2×C8—92no—
244C2×C8—92no—
245C2×C8—92no—
246C2×C8—92no—
247C2×C8—181no—
248C2×C8—181no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—364no—
254C42—21no—
255C42—21no—
256C22×C3C4×#6714yes—
257C22×C3#93914yes—
258C22×C3#94014yes—
259C22×C3#94218yes—
260C22×C3#94918yes—
261C2×D3—128no—
262C2×D3—1216no—
263C2×D3—248no—
264C2×D3—244no—
265C2×D3—244no—
266C3×C4—48no—
267C3×C4—48no—
268C3×C4—84no—
269C3×C4D3×C22⋊C414yes—
270C3×C4#67⋊C414yes—
271C3×C4#88414yes—
272C3×C4#88514yes—
273Dic3—244no—
274C32#197311yescharacteristic, complemented, Sylow
275C23—182no—
276C23—361no—
277C23—361no—
278C23—362no—
279C23—362no—
280C23C2×#63811yescharacteristic
281Q8—22no—
282Q8—22no—
283Q8—41no—
284Q8—41no—
285D4—182no—
286D4—182no—
287D4—361no—
288D4—361no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—361no—
298C2×C4—362no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4#382811yescharacteristic
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4D4×C3⋊D311yescharacteristic
304C2×C4#383011yescharacteristic
305C8—94no—
306C8—182no—
307C2×C3#495714yes—
308C2×C3#502618yes—
309C2×C3#504918yes—
310C2×C3#505814yes—
311C2×C3#508614yes—
312D3—248no—
313C22—362no—
314C22—364no—
315C22—721no—
316C22—722no—
317C22—721no—
318C22C4×#63811yescharacteristic
319C22#6414811yescharacteristic
320C22#6414911yescharacteristic
321C22#6415112yes—
322C22#6415812yes—
323C4—42no—
324C4—42no—
325C4—81no—
326C4—721no—
327C4C22⋊C4×C3⋊D311yescharacteristic
328C4#6409011yescharacteristic
329C4#6409311yescharacteristic
330C4#6409411yescharacteristic
331C3#6967914yescomplemented
332C2—722no—
333C2#1059265611yescharacteristic
334C2#1059272512yes—
335C2#1059274812yes—
336C2#1059275711yescharacteristic
337C2#1059278511yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#391C3⋊D3
hypocenterC32#1973
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
2. C32×#391C2semidirect
3. C2×#63662C2semidirect
5. C2×#63634C2semidirect
7. C2×#63630C2semidirect
15. C2×#3755C4semidirect
26. C3×#391D3semidirect
112. C3⋊(C3⋊C8)C22⋊C4semidirect
118. #391C3⋊D3semidirect
274. C32#1973semidirect
331. C3#69679semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C32×#3912
C2×#636622
C2×#636362
C2×#636342
#105926382
C2×#636302
#696793