Finite Group Databasebeta

← #11786972

Subgroups — #11786972

Order 1152.

894 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63644C211yesmaximal, characteristic
5#10592683C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#70238—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12Q8×C3⋊Dic3—22no—
13Q8×C3⋊Dic3—22no—
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#103C414yescomplemented
22#63662—22no—
23#63658—21no—
24#63644—22no—
25C2×Q8×Dic3—34no—
26C2×C3×#103D314yes—
27C2×#835—34no—
28C2×#817—34no—
29#4984—34no—
30#4550—34no—
31#4529—34no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8D412yes—
37C2×C32×Q8Q812yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8C2×C412yes—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2×C412yes—
50C4⋊(C3⋊Dic3)—24no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—42no—
55C4⋊(C3⋊Dic3)D412yes—
56C4×C3⋊Dic3—24no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1865—91noSylow
63C22×C3×Q8C2×D314yes—
64C22×C3×C8C2×D314yes—
65C2×C3×C4⋊C4C2×D314yes—
66Q8×Dic3—68no—
67Q8×Dic3—68no—
68C2×C4⋊Dic3—34no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—64no—
71C2×C4⋊Dic3—64no—
72C2×C4×Dic3—34no—
73C2×C4×Dic3—64no—
74C22×C3⋊C8—34no—
75C3×#103Dic3116yescomplemented
76#835—68no—
77C3⋊#95—64no—
78#817—68no—
79C23×C32C2×D411yescharacteristic
80C32×Q8—22no—
81C32×Q8—22no—
82C32×Q8—22no—
83C32×Q8C4⋊C414yescomplemented
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×Q811yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3SD1612yes—
108C32×C8—22no—
109C3⋊(C3⋊C8)—41no—
110C2×C4×Q8—91no—
111C2×#106—91no—
112C2×#103—91no—
113C2×#103C3⋊D311yescharacteristic
114#389—91no—
115#340—91no—
116#336—91no—
117C2×C3×Q8—24no—
118C2×C3×Q8—24no—
119C2×C3×Q8—24no—
120C2×C3×Q8Dic618yes—
121C2×C3×Q8D1218yes—
122C2×C3×Q8C2×Dic318yes—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4C22×D314yes—
126C22×Dic3—34no—
127C22×Dic3—34no—
128C22×Dic3—64no—
129C22×Dic3—64no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C2×C3×C8C2×Dic318yes—
133C3×C4⋊C4—24no—
134C3×C4⋊C4C2×Dic318yes—
135C4⋊Dic3—38no—
136C4⋊Dic3—616no—
137C4⋊Dic3—64no—
138C4⋊Dic3—64no—
139C4⋊Dic3—64no—
140C4⋊Dic3—128no—
141C4×Dic3—616no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C2×C3⋊C8—64no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12011yescharacteristic
149C22×C32C22⋊Q811yescharacteristic
150C22×C32C2×SD1611yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32#13711yescharacteristic
153C22×C32#13711yescharacteristic
154C32×C4—24no—
155C32×C4—42no—
156C32×C4C2×C4⋊C411yescharacteristic
157C32×C4C4×D411yescharacteristic
158C32×C4C22⋊Q811yescharacteristic
159C32×C4#12311yescharacteristic
160C3⋊Dic3—22no—
161C3⋊Dic3—41no—
162C3⋊Dic3—42no—
163C3⋊Dic3—81no—
164C22×Q8C2×C3⋊D311yescharacteristic
165C22×C8—91no—
166C22×C8C2×C3⋊D311yescharacteristic
167C4×Q8—182no—
168C4×Q8—182no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—181no—
172C2×C4⋊C4—181no—
173C2×C4⋊C4C2×C3⋊D311yescharacteristic
174C2×C42—91no—
175C2×C42—181no—
176#106—182no—
177#103—182no—
178#103C3⋊Dic314yescomplemented
179#95—181no—
180C23×C3D3×D414yes—
181C3×Q8—28no—
182C3×Q8—28no—
183C3×Q8—28no—
184C3×Q8C4⋊Dic3116yescomplemented
185C2×C3×C4—28no—
186C2×C3×C4—28no—
187C2×C3×C4—28no—
188C2×C3×C4—28no—
189C2×C3×C4—44no—
190C2×C3×C4—44no—
191C2×C3×C4C2×Dic614yes—
192C2×C3×C4C2×D1214yes—
193C2×C3×C4D3×D414yes—
194C2×C3×C4#23714yes—
195C2×C3×C4#23714yes—
196C2×C3×C4C22×Dic314yes—
197C2×Dic3—38no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—68no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208C2×Dic3—124no—
209C3×C8—28no—
210C3⋊C8—124no—
211C2×C32#38511yescharacteristic
212C2×C32C4×SD1611yescharacteristic
213C2×C32#44111yescharacteristic
214C2×C32#44811yescharacteristic
215C2×C32#45211yescharacteristic
216C2×C32#47511yescharacteristic
217C2×C32#47911yescharacteristic
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8#63412yes—
222C2×Q8C4⋊(C3⋊D3)12yes—
223C2×Q8C2×C3⋊Dic312yes—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4C22×C3⋊D311yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—181no—
234C2×C8—181no—
235C2×C8—181no—
236C2×C8C2×C3⋊Dic312yes—
237C4⋊C4—21no—
238C4⋊C4—92no—
239C4⋊C4—184no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4—362no—
244C4⋊C4C2×C3⋊Dic312yes—
245C42—184no—
246C42—181no—
247C42—181no—
248C22×C3#87814yes—
249C22×C3#88214yes—
250C22×C3D3×SD1614yes—
251C22×C3#91614yes—
252C22×C3#91814yes—
253C22×C3#91814yes—
254C22×C3D4×Dic314yes—
255C3×C4—216no—
256C3×C4—48no—
257C3×C4#87814yes—
258C3×C4#88614yes—
259C3×C4C2×C4⋊Dic314yes—
260C3×C4D4×Dic314yes—
261Dic3—68no—
262Dic3—124no—
263Dic3—128no—
264Dic3—244no—
265C32#186511yescharacteristic, complemented, Sylow
266C23D4×C3⋊D311yescharacteristic
267Q8—22no—
268Q8—22no—
269Q8—22no—
270Q8C4⋊(C3⋊Dic3)14yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—92no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—182no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—361no—
285C2×C4—361no—
286C2×C4—361no—
287C2×C4—361no—
288C2×C4—361no—
289C2×C4C2×#63411yescharacteristic
290C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C2×C4#383011yescharacteristic
293C2×C4#383011yescharacteristic
294C2×C4C22×C3⋊Dic311yescharacteristic
295C8—22no—
296C8—361no—
297C2×C3#479114yes—
298C2×C3#479914yes—
299C2×C3#480614yes—
300C2×C3#480814yes—
301C2×C3#495014yes—
302C2×C3Dic3×SD1614yes—
303C2×C3#518414yes—
304C22#6408711yescharacteristic
305C22#6409111yescharacteristic
306C22SD16×C3⋊D311yescharacteristic
307C22#6412511yescharacteristic
308C22#6412711yescharacteristic
309C22#6412711yescharacteristic
310C22D4×C3⋊Dic311yescharacteristic
311C4—24no—
312C4—42no—
313C4—182no—
314C4—361no—
315C4—362no—
316C4—721no—
317C4#6408711yescharacteristic
318C4#6409511yescharacteristic
319C4C2×C4⋊(C3⋊Dic3)11yescharacteristic
320C4D4×C3⋊Dic311yescharacteristic
321C3#7023814yescomplemented
322C2#1059249011yescharacteristic
323C2#1059249811yescharacteristic
324C2#1059250511yescharacteristic
325C2#1059250711yescharacteristic
326C2#1059264911yescharacteristic
327C2SD16×C3⋊Dic311yescharacteristic
328C2#1059288311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1865
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
21. C32×#103C4semidirect
75. C3×#103Dic3semidirect
83. C32×Q8C4⋊C4semidirect
178. #103C3⋊Dic3semidirect
184. C3×Q8C4⋊Dic3semidirect
265. C32#1865semidirect
270. Q8C4⋊(C3⋊Dic3)semidirect
321. C3#70238semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C32×#1032
C2×#636622
C2×#636442
#105926832
#105894162
#105893952
#702383