Finite Group Databasebeta

← #11790351

Subgroups — #11790351

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
2#10591359C211yesmaximal, characteristic
3C2×#63573C212yesmaximal
4C2×#63572C211yesmaximal, characteristic
5C3×#4529C212yesmaximal
6#68796—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×C4×C3⋊Dic3—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13C2×#3724—21no—
14C2×#3724—21no—
15#63658—21no—
16#63573—24no—
17#63572C414yescomplemented
18C2×#817—32no—
19C2×Dic3⋊C8—32no—
20#4975—32no—
21Dic3×C4⋊C4—32no—
22Dic3×C4⋊C4—61no—
23C2×#808—32no—
24C3×#340—32no—
25#4529D312yes—
26C22×C32×C4—21no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3×Dic3—22no—
32C32×C4⋊C4—21no—
33C32×C4⋊C4Q812yes—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)D412yes—
36C4×C3⋊Dic3—42no—
37C4×C3⋊Dic3C2×C412yes—
38C4×C3⋊Dic3Q812yes—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8C2×C414yes—
44#3724—42no—
45#3724—42no—
46#1948—91noSylow
47C22×C3×C8—32no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4—32no—
50C2×C3×C4⋊C4C2×D312yes—
51C2×C4⋊Dic3—32no—
52C2×C4⋊Dic3—61no—
53C2×C4⋊Dic3C2×D312yes—
54C2×Dic3⋊C4—62no—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—62no—
59C2×C4×Dic3—62no—
60C22×C3⋊C8C2×D312yes—
61C3⋊#95—62no—
62C3⋊#95—62no—
63#817—64no—
64Dic3⋊C8—38no—
65#808—64no—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4—22no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4C22×C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4C2×Q811yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C32×C4#4111yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3C4⋊C412yes—
82C2×C3⋊Dic3C4⋊C412yes—
83C2×C3⋊Dic3SD1612yes—
84C2×C3⋊Dic3SD1612yes—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C3×C3⋊C8—24no—
89C2×#106—92no—
90C2×C4⋊C8—91no—
91#384—91no—
92C4×C4⋊C4—91no—
93#340—32no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C22×C3×C4C22×D312yes—
99C22×Dic3—22no—
100C22×Dic3—32no—
101C22×Dic3—32no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—62no—
105C22×Dic3—62no—
106C2×C3×C8—34no—
107C2×C3×C8—62no—
108C2×C3×C8—62no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4—62no—
114C3×C4⋊C4Dic614yes—
115C4⋊Dic3—22no—
116C4⋊Dic3—22no—
117C4⋊Dic3—34no—
118C4⋊Dic3—62no—
119C4⋊Dic3—62no—
120C4⋊Dic3—62no—
121Dic3⋊C4—124no—
122Dic3⋊C4—124no—
123C4×Dic3—34no—
124C4×Dic3—34no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—124no—
128C4×Dic3—124no—
129C2×C3⋊C8—22no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8C4×D314yes—
132C22×C32C2×C4⋊C411yescharacteristic
133C22×C32#12111yescharacteristic
134C22×C32C22⋊Q811yescharacteristic
135C22×C32C2×SD1611yescharacteristic
136C22×C32C2×SD1611yescharacteristic
137C22×C32AGL(1,ℤ/8)11yescharacteristic
138C22×C32#13711yescharacteristic
139C32×C4—42no—
140C32×C4C4×D411yescharacteristic
141C32×C4C4×Q811yescharacteristic
142C32×C4#12511yescharacteristic
143C32×C4C4⋊Q811yescharacteristic
144C3⋊Dic3—22no—
145C3⋊Dic3—42no—
146C3⋊Dic3#10614yescomplemented
147C3×Dic3—82no—
148C22×C8—32no—
149C2×C4⋊C4—32no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—181no—
152C2×C4⋊C4—181no—
153C2×C4⋊C4D3211yescharacteristic
154C2×C42—91no—
155C2×C42—181no—
156#106—184no—
157C4⋊C8—94no—
158#95—181no—
159C23×C3—21no—
160C23×C3D3×D412yes—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—42no—
170C2×C3×C4—42no—
171C2×C3×C4—42no—
172C2×C3×C4—42no—
173C2×C3×C4—122no—
174C2×C3×C4—122no—
175C2×C3×C4—122no—
176C2×C3×C4C2×Dic612yes—
177C2×C3×C4C2×C4×D312yes—
178C2×C3×C4#23512yes—
179C2×C3×C4D3×D412yes—
180C2×C3×C4#23712yes—
181C2×C3×C4D3×Q812yes—
182C2×Dic3—34no—
183C2×Dic3—34no—
184C2×Dic3—34no—
185C2×Dic3—34no—
186C2×Dic3—42no—
187C2×Dic3—42no—
188C2×Dic3—42no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—122no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C3×C8—64no—
204C3⋊C8—24no—
205C2×C32#38911yescharacteristic
206C2×C32C2×#10611yescharacteristic
207C2×C32#42811yescharacteristic
208C2×C32#46011yescharacteristic
209C2×C32#46111yescharacteristic
210C2×C32#47511yescharacteristic
211C2×C32#47611yescharacteristic
212C22×C4—21no—
213C22×C4—62no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—181no—
217C22×C4C2×D3211yescharacteristic
218C2×C8—34no—
219C2×C8—62no—
220C2×C8—62no—
221C4⋊C4—21no—
222C4⋊C4—62no—
223C4⋊C4—62no—
224C4⋊C4—92no—
225C4⋊C4—181no—
226C4⋊C4—362no—
227C4⋊C4—362no—
228C4⋊C4#62712yes—
229C42—92no—
230C42—92no—
231C42—362no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3#87812yes—
240C22×C3#88412yes—
241C22×C3D3×C4⋊C412yes—
242C22×C3#91112yes—
243C22×C3D3×SD1612yes—
244C22×C3D3×SD1612yes—
245C22×C3#91812yes—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—44no—
251C3×C4—44no—
252C3×C4—242no—
253C3×C4C4×Dic612yes—
254C3×C4#67⋊C412yes—
255C3×C4#88812yes—
256C3×C4#88912yes—
257Dic3—38no—
258Dic3—64no—
259Dic3—64no—
260Dic3—82no—
261Dic3—122no—
262Dic3—124no—
263Dic3—124no—
264C32#194811yescharacteristic, complemented, Sylow
265C23#381111yescharacteristic
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—92no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—92no—
273C2×C4—122no—
274C2×C4—122no—
275C2×C4—122no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—182no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4#379711yescharacteristic
282C2×C4#379811yescharacteristic
283C2×C4C4×D3211yescharacteristic
284C2×C4#380211yescharacteristic
285C2×C4#380511yescharacteristic
286C2×C4C2×#62711yescharacteristic
287C8—64no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3#464712yes—
296C2×C3#476112yes—
297C2×C3#476212yes—
298C2×C3#479112yes—
299C2×C3#481812yes—
300C2×C3D3×#10612yes—
301C2×C3#488112yes—
302C22#6388311yescharacteristic
303C22#6391211yescharacteristic
304C22#6392711yescharacteristic
305C22#6393011yescharacteristic
306C22#6394011yescharacteristic
307C22#6394511yescharacteristic
308C22#6398211yescharacteristic
309C4—42no—
310C4—94no—
311C4—182no—
312C4—242no—
313C4—362no—
314C4#6387011yescharacteristic
315C4#6390211yescharacteristic
316C4C4×#62711yescharacteristic
317C4#6391911yescharacteristic
318C3—21no—
319C3#6879612yescomplemented
320C2#1059055311yescharacteristic
321C2#1059056511yescharacteristic
322C2#1059057511yescharacteristic
323C2#1059058211yescharacteristic
324C2#1059132811yescharacteristic
325C2#1059149511yescharacteristic
326C2#1059163011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1948
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
17. #63572C4semidirect
146. C3⋊Dic3#106semidirect
264. C32#1948semidirect
319. C3#68796semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C3⋊Dic32
#105913592
C2×#635732
C2×#635722
C3×#45292
#687963