Finite Group Databasebeta

← #11791119

Subgroups — #11791119

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
2C2×C32×#103C211yesmaximal, characteristic, complemented
3#10592928C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic
5C2×#63642C211yesmaximal, characteristic, complemented
6#10592687C211yesmaximal, characteristic
7C2×#63634C211yesmaximal, characteristic, complemented
8#70260—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3755—22no—
14C2×#3755—22no—
15C2×#3755C414yescomplemented
16C2×#3752—22no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C32×#103—22no—
21#63658—22no—
22#63648—22no—
23#63642—22no—
24#63634—22no—
25C22×#215—34no—
26C2×C3×#103D314yescomplemented
27#5229—34no—
28C2×#821—34no—
29C2×#815—34no—
30#4988—34no—
31C2×#807—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×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3D412yes—
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—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3755—28no—
56#3752—44no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C2×C3⋊(C3⋊C8)C2×C412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63C2×C3⋊(C3⋊C8)D412yes—
64#1973—91noSylow
65C22×C3×Q8C2×D314yes—
66C22×D12—34no—
67C22×C3×C8C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69C2×#215—316no—
70C2×#215—68no—
71C2×#215—68no—
72C2×(C2×D3)⋊C4—68no—
73C2×C4⋊Dic3—34no—
74C2×C4×Dic3—34no—
75C22×C3⋊C8—34no—
76C3×#103—28no—
77C3⋊#95—68no—
78#821—68no—
79#815—68no—
80#807—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—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4—42no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—42no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—22no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—41no—
111C32×C8—22no—
112C3⋊(C3⋊C8)C22⋊C414yescomplemented
113C22×SD16—91no—
114C2×#107—91no—
115C2×#103C3⋊D311yescharacteristic, complemented
116C2×#102—91no—
117C2×#97—91no—
118#391—91no—
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×C4C22×D314yes—
130C22×Dic3—38no—
131C22×Dic3—64no—
132C2×D12—38no—
133C2×D12—64no—
134C2×D12—64no—
135C2×D12—64no—
136C2×D12—64no—
137C2×D12—64no—
138C2×C3×C8—24no—
139C2×C3×C8—24no—
140C2×C3×C8#6718yes—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143#215—632no—
144(C2×D3)⋊C4—1216no—
145C4⋊Dic3—64no—
146C4⋊Dic3—64no—
147C4×Dic3—64no—
148C4×Dic3—64no—
149C2×C3⋊C8—38no—
150C2×C3⋊C8—38no—
151C2×C3⋊C8—38no—
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—81no—
164C32×C4C2×C22⋊C411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12111yescharacteristic
167C32×C4#12411yescharacteristic
168C3⋊Dic3—42no—
169C3⋊Dic3—81no—
170C22×Q8C2×C3⋊D311yescharacteristic
171C22×D4—91no—
172C2×SD16—94no—
173C2×SD16—182no—
174C2×SD16—182no—
175C22×C8—91no—
176C22×C8C2×C3⋊D311yescharacteristic
177C2×C4⋊C4—91no—
178C2×C4⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4—182no—
180C2×C42—91no—
181#107—182no—
182#103—22no—
183#102—182no—
184#97—182no—
185#95—182no—
186C23×C3D3×D414yes—
187C22×D3—68no—
188C22×D3—124no—
189C22×D3—128no—
190C22×D3—128no—
191C22×D3—124no—
192C3×Q8—28no—
193C3×Q8—28no—
194C3×Q8—44no—
195C3×Q8—44no—
196C2×C3×C4—28no—
197C2×C3×C4—44no—
198C2×C3×C4—44no—
199C2×C3×C4—48no—
200C2×C3×C4—44no—
201C2×C3×C4C2×C4×D314yes—
202C2×C3×C4#23514yes—
203C2×C3×C4D3×D414yes—
204C2×C3×C4D3×D414yes—
205C2×C3×C4#23714yes—
206C2×C3×C4C2×#6714yes—
207C2×Dic3—68no—
208C2×Dic3—68no—
209C2×Dic3—68no—
210C2×Dic3—128no—
211C2×Dic3—124no—
212D12—68no—
213D12—68no—
214D12—124no—
215D12—124no—
216C3×C8—28no—
217C3⋊C8—316no—
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—92no—
240C22×C4—181no—
241C22×C4C22×C3⋊D311yescharacteristic
242SD16—188no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—92no—
246C2×C8—92no—
247C2×C8—92no—
248C2×C8#63812yes—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—364no—
254C42—181no—
255C42—181no—
256C22×C3#67⋊C414yes—
257C22×C3#88414yes—
258C22×C3#91418yes—
259C22×C3#91818yes—
260C22×C3#94014yes—
261C2×D3—128no—
262C2×D3—1216no—
263C2×D3—244no—
264C2×D3—244no—
265C2×D3—248no—
266C3×C4—48no—
267C3×C4—84no—
268C3×C4D3×C22⋊C414yes—
269C3×C4#88514yes—
270C3×C4C4×#6714yes—
271C3×C4#93914yes—
272Dic3—128no—
273Dic3—244no—
274C32#197311yescharacteristic, complemented, Sylow
275C23—182no—
276C23—361no—
277C23—362no—
278C23—362no—
279C23—361no—
280C23D4×C3⋊D311yescharacteristic
281Q8—22no—
282Q8—22no—
283Q8—41no—
284Q8—41no—
285D4—182no—
286D4—182no—
287D4—361no—
288D4—361no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—362no—
298C2×C4—361no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4#382811yescharacteristic
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4#383011yescharacteristic
304C2×C4C2×#63811yescharacteristic
305C8—22no—
306C8—94no—
307C2×C3#481218yes—
308C2×C3#481718yes—
309C2×C3#495714yes—
310C2×C3#517614yes—
311C2×C3#519014yes—
312D3—248no—
313C22—364no—
314C22—362no—
315C22—721no—
316C22—721no—
317C22—722no—
318C22#6409011yescharacteristic
319C22#6409311yescharacteristic
320C22#6412312yes—
321C22#6412712yes—
322C22#6414911yescharacteristic
323C4—42no—
324C4—81no—
325C4—362no—
326C4—721no—
327C4C22⋊C4×C3⋊D311yescharacteristic
328C4#6409411yescharacteristic
329C4C4×#63811yescharacteristic
330C4#6414811yescharacteristic
331C3#7026014yescomplemented
332C2—722no—
333C2#1059251112yes—
334C2#1059251612yes—
335C2#1059265611yescharacteristic
336C2#1059287511yescharacteristic
337C2#1059288911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. #10592928C2semidirect
5. C2×#63642C2semidirect
7. C2×#63634C2semidirect
15. C2×#3755C4semidirect
26. C2×C3×#103D3semidirect
112. C3⋊(C3⋊C8)C22⋊C4semidirect
115. C2×#103C3⋊D3semidirect
274. C32#1973semidirect
331. C3#70260semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C32×#1032
#105929282
C2×#636482
C2×#636422
#105926872
C2×#636342
#702603