Finite Group Databasebeta

← #11786075

Subgroups — #11786075

Order 1152.

525 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592676C211yesmaximal, characteristic
2#10591359C211yesmaximal, characteristic
3C2×#63555C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68849—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12C2×#3724—21no—
13C2×#3724—21no—
14#63658—21no—
15#63658—21no—
16#63555C414yescomplemented
17C2×#815—32no—
18#4977—32no—
19#4977—61no—
20#4975—32no—
21C3×#340—32no—
22#4551—32no—
23#4529—32no—
24#4529D312yes—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3×Dic3—22no—
31C32×C4⋊C4—22no—
32C4⋊(C3⋊Dic3)—22no—
33C4×C3⋊Dic3C2×C412yes—
34C4×C3⋊Dic3Q812yes—
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38C2×C3×C3⋊C8—22no—
39C2×C3×C3⋊C8C2×C414yes—
40#3724—42no—
41#3724—42no—
42#1836—91noSylow
43C22×C3×C8—32no—
44C2×C3×C4⋊C4—21no—
45C2×C3×C4⋊C4—32no—
46C2×C3×C4⋊C4C2×D312yes—
47C2×C4⋊Dic3—32no—
48C2×C4⋊Dic3—61no—
49C2×C4⋊Dic3C2×D312yes—
50C2×Dic3⋊C4—62no—
51C2×Dic3⋊C4—62no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—61no—
54C22×C3⋊C8C2×D312yes—
55C3⋊#95—62no—
56C3⋊#95—62no—
57C3⋊#95—62no—
58C3⋊#95—62no—
59#815—38no—
60C23×C32C2×D411yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4C22×C411yescharacteristic
65C2×C32×C4C2×Q811yescharacteristic
66C2×C32×C4#4112yes—
67C2×C32×C4#4112yes—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C4⋊C412yes—
76C2×C3⋊Dic3C4⋊C412yes—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C3×C3⋊C8—24no—
81C2×#97—91no—
82#384—91no—
83#382—91no—
84#340—32no—
85#340—92no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—21no—
89C22×C3×C4—62no—
90C22×C3×C4C22×D312yes—
91C22×Dic3—22no—
92C22×Dic3—32no—
93C22×Dic3—32no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C2×C3×C8—34no—
99C2×C3×C8—62no—
100C2×C3×C8—62no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—42no—
104C3×C4⋊C4—62no—
105C3×C4⋊C4—62no—
106C4⋊Dic3—22no—
107C4⋊Dic3—22no—
108C4⋊Dic3—62no—
109C4⋊Dic3—62no—
110C4⋊Dic3—122no—
111Dic3⋊C4—124no—
112Dic3⋊C4—124no—
113C4×Dic3—34no—
114C4×Dic3—34no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C2×C3⋊C8—22no—
118C2×C3⋊C8—22no—
119C2×C3⋊C8C4×D314yes—
120C22×C32C2×C4⋊C411yescharacteristic
121C22×C32#12411yescharacteristic
122C22×C32#12411yescharacteristic
123C22×C32AGL(1,ℤ/8)11yescharacteristic
124C22×C32AGL(1,ℤ/8)11yescharacteristic
125C22×C32#13711yescharacteristic
126C22×C32#13711yescharacteristic
127C32×C4—81no—
128C32×C4#11712yes—
129C32×C4#12512yes—
130C3⋊Dic3—22no—
131C3⋊Dic3—22no—
132C3⋊Dic3—81no—
133C3×Dic3—82no—
134C22×C8—32no—
135C2×C4⋊C4—32no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—181no—
138C2×C4⋊C4—181no—
139C2×C4⋊C4D3211yescharacteristic
140C2×C42—91no—
141#97—94no—
142#95—181no—
143#95—181no—
144C23×C3—21no—
145C23×C3D3×D412yes—
146C2×C3×C4—22no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—42no—
151C2×C3×C4—42no—
152C2×C3×C4—42no—
153C2×C3×C4—42no—
154C2×C3×C4—42no—
155C2×C3×C4—42no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×C3×C4—122no—
159C2×C3×C4C2×C4×D312yes—
160C2×C3×C4#23512yes—
161C2×C3×C4#23512yes—
162C2×C3×C4#23712yes—
163C2×C3×C4#23712yes—
164C2×C3×C4D3×Q812yes—
165C2×Dic3—34no—
166C2×Dic3—34no—
167C2×Dic3—42no—
168C2×Dic3—42no—
169C2×Dic3—42no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—121no—
177C2×Dic3—121no—
178C2×Dic3—121no—
179C2×Dic3—121no—
180C2×Dic3—122no—
181C2×Dic3—122no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184C2×Dic3—122no—
185C2×Dic3—122no—
186C3×C8—64no—
187C3⋊C8—24no—
188C2×C32#38211yescharacteristic
189C2×C32#42811yescharacteristic
190C2×C32#42811yescharacteristic
191C2×C32#48911yescharacteristic
192C2×C32#48911yescharacteristic
193C2×C32#49011yescharacteristic
194C2×C32#49111yescharacteristic
195C22×C4—21no—
196C22×C4—62no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—181no—
200C22×C4C2×D3211yescharacteristic
201C2×C8—34no—
202C2×C8—62no—
203C2×C8—62no—
204C4⋊C4—22no—
205C4⋊C4—62no—
206C4⋊C4—62no—
207C4⋊C4—182no—
208C4⋊C4—362no—
209C4⋊C4—362no—
210C42—92no—
211C42—92no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3#88512yes—
220C22×C3#88512yes—
221C22×C3D3×C4⋊C412yes—
222C22×C3#91112yes—
223C22×C3#91412yes—
224C22×C3#91512yes—
225C22×C3#91812yes—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—82no—
229C3×C4—82no—
230C3×C4—242no—
231C3×C4#87212yes—
232C3×C4#87712yes—
233C3×C4#88912yes—
234C3×C4#88912yes—
235Dic3—64no—
236Dic3—64no—
237Dic3—82no—
238Dic3—122no—
239Dic3—122no—
240Dic3—242no—
241Dic3—242no—
242C32#183611yescharacteristic, complemented, Sylow
243C23#381111yescharacteristic
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—92no—
248C2×C4—92no—
249C2×C4—122no—
250C2×C4—122no—
251C2×C4—122no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4#379512yes—
260C2×C4#379711yescharacteristic
261C2×C4C4×D3211yescharacteristic
262C2×C4#380412yes—
263C8—64no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3#465012yes—
272C2×C3#476412yes—
273C2×C3#476512yes—
274C2×C3#479412yes—
275C2×C3#479712yes—
276C2×C3#486112yes—
277C2×C3#488112yes—
278C22#6388311yescharacteristic
279C22#6391311yescharacteristic
280C22#6392711yescharacteristic
281C22#6393111yescharacteristic
282C22#6394111yescharacteristic
283C22#6394511yescharacteristic
284C22#6395311yescharacteristic
285C4—81no—
286C4—182no—
287C4—182no—
288C4—242no—
289C4—721no—
290C4#6384712yes—
291C4#6387712yes—
292C3—21no—
293C3#6884912yescomplemented
294C2#1059055411yescharacteristic
295C2#1059056811yescharacteristic
296C2#1059058211yescharacteristic
297C2#1059058411yescharacteristic
298C2#1059124711yescharacteristic
299C2#1059149611yescharacteristic
300C2#1059163211yescharacteristic
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#1836
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
16. #63555C4semidirect
242. C32#1836semidirect
293. C3#68849semidirect

Maximal subgroups

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

subgroupindex
#105926762
#105913592
C2×#635552
C3×#45292
#105891642
#688493