Finite Group Databasebeta

← #11792230

Subgroups — #11792230

Order 1152.

1218 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#64141C212yesmaximal, complemented
2#10595981C211yesmaximal, characteristic, complemented
3C32×#390C211yesmaximal, characteristic, complemented
4C2×#63632C212yesmaximal, complemented
5#10589396C211yesmaximal, characteristic, complemented
6#69664—34nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×#3828C2212yes—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C22⋊C4—22no—
11C2×C32×C42C2211yescharacteristic
12C2×#3754—22no—
13#64141—24no—
14#64141—24no—
15C2×#3753—22no—
16#64139—22no—
17C2×#3748C2212yes—
18#64106—22no—
19#64104—22no—
20#63632—24no—
21C2×#932—38no—
22#5510—34no—
23C3×#390D314yescomplemented
24C2×#805—38no—
25#4530—34no—
26C24×C32—21no—
27C2×C32×D4—22no—
28C2×C32×D4—22no—
29C2×C32×D4—21no—
30C2×C32×D4D412yescomplemented
31C22×C32×C4—21no—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35#3828—22no—
36#3828—22no—
37#3828—22no—
38#3828—22no—
39C2×C4⋊(C3⋊D3)—22no—
40C2×C4⋊(C3⋊D3)D412yes—
41C2×C4×C3⋊D3—22no—
42C2×#634D412yes—
43C32×C4⋊C4—22no—
44C32×C22⋊C4—44no—
45C32×C42—22no—
46#3754—28no—
47#3753—28no—
48#3752—24no—
49C4⋊(C3⋊Dic3)—22no—
50#3748—22no—
51#3748D414yescomplemented
52C2×C3⋊(C3⋊C8)—22no—
53#2006—91noSylow
54C22×C3×D4C2×D314yes—
55C2×#235—38no—
56C2×C3×C4⋊C4C2×D314yes—
57C2×C3×C22⋊C4—28no—
58C2×C3×C42C2×D314yes—
59C2×#214—68no—
60#932—616no—
61#932—616no—
62C2×#213—68no—
63#930—68no—
64C2×#208—38no—
65#897—68no—
66#895—68no—
67#805—616no—
68C23×C32—22no—
69C23×C32—42no—
70C23×C32—42no—
71C23×C32—41no—
72C23×C32—41no—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—22no—
75C32×D4—24no—
76C32×D4—42no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C32×C4C2×D412yes—
85C2×C32×C4#4111yescharacteristic
86#638—42no—
87#638—42no—
88C2×C3⋊Dic3—22no—
89C4⋊(C3⋊D3)—22no—
90C4⋊(C3⋊D3)—22no—
91C4⋊(C3⋊D3)—82no—
92C4×C3⋊D3—42no—
93C4×C3⋊D3—42no—
94#634—22no—
95#634—22no—
96C3⋊(C3⋊C8)—24no—
97C2×AGL(1,ℤ/8)—92no—
98#537—91no—
99C2×#104—92no—
100#390C3⋊D311yescharacteristic, complemented
101#343—91no—
102C24×C3—24no—
103C2×C3×D4—24no—
104C2×C3×D4—28no—
105C2×C3×D4—28no—
106C2×C3×D4D1218yescomplemented
107C22×C3×C4—24no—
108C22×C3×C4#6718yes—
109C22×C3×C4C22×D314yes—
110C2×#67—68no—
111#235—68no—
112#235—68no—
113#235—68no—
114#235—68no—
115C2×D12—38no—
116C2×D12—68no—
117C2×C4×D3—68no—
118C2×Dic6—38no—
119C3×C4⋊C4—28no—
120C3×C22⋊C4—416no—
121C3×C42—28no—
122#214—632no—
123#213—632no—
124(C2×D3)⋊C4—616no—
125C4⋊Dic3—68no—
126#208—316no—
127#208—68no—
128C2×C3⋊C8—68no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—44no—
132C22×C32—42no—
133C22×C32—82no—
134C22×C32—81no—
135C22×C32—81no—
136C22×C32#12011yescharacteristic
137C22×C32#12111yescharacteristic
138C22×C32#12711yescharacteristic
139C2×C3⋊D3—42no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3—42no—
142C32×C4—42no—
143C32×C4—42no—
144C32×C4#12012yes—
145C32×C4#12112yes—
146C3⋊Dic3—42no—
147C2×#41—92no—
148C22×D4C2×C3⋊D311yescharacteristic
149AGL(1,ℤ/8)—184no—
150AGL(1,ℤ/8)—184no—
151C2×SD16—182no—
152C2×D8—182no—
153C2×M16—92no—
154C22⋊Q8—182no—
155#121—182no—
156#121—182no—
157C2×C4⋊C4C2×C3⋊D311yescharacteristic
158C2×C22⋊C4—22no—
159C2×C42C2×C3⋊D311yescharacteristic
160#104—184no—
161C23×C3—28no—
162C23×C3—48no—
163C23×C3—48no—
164C23×C3—44no—
165C23×C3—44no—
166C23×C3C2×#6714yes—
167C22×D3—68no—
168C3×D4—216no—
169C3×D4—48no—
170C2×C3×C4—28no—
171C2×C3×C4—28no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174C2×C3×C4—48no—
175C2×C3×C4C2×D1214yes—
176C2×C3×C4#23514yes—
177C2×C3×C4D3×D418yes—
178C2×C3×C4D3×D418yes—
179#67—128no—
180#67—128no—
181C2×Dic3—68no—
182D12—68no—
183D12—68no—
184D12—248no—
185C4×D3—128no—
186C4×D3—128no—
187Dic6—68no—
188Dic6—68no—
189C3⋊C8—616no—
190C2×C32—21no—
191C2×C32—21no—
192C2×C32—82no—
193C2×C32#39211yescharacteristic
194C2×C32#45311yescharacteristic
195C2×C32#45411yescharacteristic
196C3⋊D3—82no—
197C24—21no—
198#41—182no—
199#41—182no—
200#41—182no—
201#41—182no—
202C2×Q8—92no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—92no—
207C2×D4—182no—
208C2×D4—182no—
209C2×D4C4⋊(C3⋊D3)12yescomplemented
210C22×C4—21no—
211C22×C4—182no—
212C22×C4#63812yes—
213C22×C4C22×C3⋊D311yescharacteristic
214SD16—188no—
215D8—188no—
216M16—94no—
217M16—182no—
218C2×C8—182no—
219C4⋊C4—22no—
220C4⋊C4—182no—
221C22⋊C4—44no—
222C22⋊C4—184no—
223C42—22no—
224C22×C3—24no—
225C22×C3—24no—
226C22×C3—416no—
227C22×C3—48no—
228C22×C3—88no—
229C22×C3—84no—
230C22×C3—84no—
231C22×C3#93014yes—
232C22×C3#93714yes—
233C22×C3#94014yes—
234C2×D3—128no—
235C2×D3—128no—
236C2×D3—128no—
237C3×C4—48no—
238C3×C4—48no—
239C3×C4#88218yes—
240C3×C4#88418yes—
241Dic3—128no—
242C32#200611yescharacteristic, complemented, Sylow
243C23—22no—
244C23—42no—
245C23—42no—
246C23—41no—
247C23—41no—
248C23—182no—
249C23C2×#63811yescharacteristic
250Q8—182no—
251Q8—182no—
252D4—24no—
253D4—42no—
254D4—182no—
255D4—182no—
256D4—362no—
257D4—362no—
258D4—722no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—182no—
265C2×C4—362no—
266C2×C4—362no—
267C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
268C2×C4#382811yescharacteristic
269C2×C4D4×C3⋊D312yes—
270C2×C4D4×C3⋊D312yes—
271C8—184no—
272C2×C3—24no—
273C2×C3—24no—
274C2×C3—88no—
275C2×C3#496014yes—
276C2×C3#506214yes—
277C2×C3#507714yes—
278D3—248no—
279C22—21no—
280C22—21no—
281C22—44no—
282C22—42no—
283C22—82no—
284C22—81no—
285C22—81no—
286C22—362no—
287C22—362no—
288C22—362no—
289C22#6413911yescharacteristic
290C22#6414611yescharacteristic
291C22#6414911yescharacteristic
292C4—42no—
293C4—42no—
294C4—362no—
295C4#6409112yes—
296C4#6409312yes—
297C3#6966414yescomplemented
298C2—21no—
299C2—21no—
300C2—82no—
301C2—722no—
302C2#1059265911yescharacteristic
303C2#1059276111yescharacteristic
304C2#1059277611yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC22×C32#120
hypercenter#390C3⋊D3
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. #10595981C2semidirect
3. C32×#390C2semidirect
4. C2×#63632C2semidirect
5. #10589396C2semidirect
23. C3×#390D3semidirect
30. C2×C32×D4D4semidirect
51. #3748D4semidirect
100. #390C3⋊D3semidirect
106. C2×C3×D4D12semidirect
209. C2×D4C4⋊(C3⋊D3)semidirect
242. C32#2006semidirect
297. C3#69664semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
#105959812
C32×#3902
C2×#636322
#105893962
#696643