Finite Group Databasebeta

← #11792239

Subgroups — #11792239

Order 1152.

1218 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64117C212yesmaximal, complemented
2#10595981C211yesmaximal, characteristic, complemented
3C2×#63652C212yesmaximal, complemented
4#10592687C211yesmaximal, characteristic, complemented
5C32×#343C211yesmaximal, characteristic, complemented
6#69008—34nomaximal
7C2×#3828C2212yes—
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—22no—
12C2×#3752—22no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64117—24no—
15#64117—24no—
16C2×#3745—22no—
17C2×#3744—22no—
18#64106—22no—
19#64104—22no—
20#63652—24no—
21C2×#908—38no—
22#5510—34no—
23C2×#825—38no—
24#4988—34no—
25C3×#343D314yescomplemented
26C23×C3⋊D3—21no—
27C22×C32×C4D412yes—
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C22×C3⋊Dic3—21no—
31#3828—22no—
32#3828—22no—
33#3828—22no—
34#3828—22no—
35C2×C4⋊(C3⋊D3)—22no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)D412yes—
40C2×C4⋊(C3⋊D3)D412yescomplemented
41C2×C4×C3⋊D3—22no—
42C2×#634D412yes—
43C32×M16—22no—
44C32×M16D414yescomplemented
45C2×C32×C8—22no—
46C32×C4⋊C4—22no—
47#3752—24no—
48#3752—44no—
49C4⋊(C3⋊Dic3)—22no—
50C4×C3⋊Dic3—22no—
51#3745—28no—
52#3744—28no—
53#2006—91noSylow
54C2×#235—38no—
55C22×D12—34no—
56C2×C3×M16C2×D318yes—
57C2×C3×C4⋊C4C2×D314yes—
58#930—68no—
59C2×(C2×D3)⋊C4—68no—
60C2×C4×Dic3—34no—
61#908—616no—
62#908—616no—
63C2×D24—68no—
64C2×#204—68no—
65#897—68no—
66#895—68no—
67#825—616no—
68C23×C32C2×D411yescharacteristic
69C22×C3⋊D3—22no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3—42no—
72C22×C3⋊D3—42no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—41no—
75C2×C32×C4—22no—
76C2×C32×C4—42no—
77C2×C32×C4C2×D412yes—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D412yes—
80C2×C32×C4#4111yescharacteristic
81#638—42no—
82#638—42no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C4⋊(C3⋊D3)—24no—
88C4⋊(C3⋊D3)—22no—
89C4⋊(C3⋊D3)—22no—
90C4⋊(C3⋊D3)—42no—
91C4⋊(C3⋊D3)—82no—
92C4×C3⋊D3—42no—
93C4×C3⋊D3—42no—
94#634—22no—
95#634—22no—
96C32×C8—24no—
97C2×AGL(1,ℤ/8)—92no—
98#537—91no—
99C2×#104—92no—
100#390—91no—
101#343C3⋊D311yescharacteristic, complemented
102C23×D3—64no—
103C22×C3×C4D1218yes—
104C22×C3×C4C22×D314yes—
105C2×#67—68no—
106C22×Dic3—64no—
107#235—68no—
108#235—68no—
109#235—68no—
110#235—68no—
111C2×D12—38no—
112C2×D12—38no—
113C2×D12—68no—
114C2×D12—68no—
115C2×D12—64no—
116C2×D12—68no—
117C2×C4×D3—68no—
118C2×Dic6—38no—
119C3×M16—28no—
120C3×M16D12116yescomplemented
121C2×C3×C8—28no—
122C3×C4⋊C4—28no—
123(C2×D3)⋊C4—616no—
124(C2×D3)⋊C4—1216no—
125C4⋊Dic3—68no—
126C4×Dic3—68no—
127D24—632no—
128#204—632no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32#12011yescharacteristic
132C22×C32#12111yescharacteristic
133C22×C32#12711yescharacteristic
134C2×C3⋊D3—44no—
135C2×C3⋊D3—42no—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—82no—
140C2×C3⋊D3—81no—
141C2×C3⋊D3—81no—
142C32×C4—42no—
143C32×C4#12012yes—
144C32×C4#12112yes—
145C3⋊Dic3—42no—
146C3⋊Dic3—42no—
147C2×#41—92no—
148C22×D4—91no—
149AGL(1,ℤ/8)—184no—
150AGL(1,ℤ/8)—184no—
151C2×SD16—182no—
152C2×D8—182no—
153C2×M16C2×C3⋊D312yes—
154C22⋊Q8—182no—
155#121—182no—
156#121—182no—
157C2×C4⋊C4C2×C3⋊D311yescharacteristic
158C2×C22⋊C4—182no—
159C2×C42—91no—
160#104—184no—
161C23×C3C2×D1214yes—
162C22×D3—68no—
163C22×D3—68no—
164C22×D3—128no—
165C22×D3—128no—
166C22×D3—124no—
167C22×D3—124no—
168C2×C3×C4—28no—
169C2×C3×C4—48no—
170C2×C3×C4C2×D1218yes—
171C2×C3×C4D3×D414yes—
172C2×C3×C4D3×D418yes—
173C2×C3×C4#23914yes—
174#67—128no—
175#67—128no—
176C2×Dic3—68no—
177C2×Dic3—68no—
178C2×Dic3—124no—
179C2×Dic3—124no—
180D12—616no—
181D12—68no—
182D12—68no—
183D12—128no—
184D12—248no—
185C4×D3—128no—
186C4×D3—128no—
187Dic6—68no—
188Dic6—68no—
189C3×C8—216no—
190C2×C32—21no—
191C2×C32—21no—
192C2×C32#39211yescharacteristic
193C2×C32#45311yescharacteristic
194C2×C32#45411yescharacteristic
195C3⋊D3—82no—
196C3⋊D3—82no—
197C24—181no—
198#41—182no—
199#41—182no—
200#41—182no—
201#41—182no—
202C2×Q8—92no—
203C2×D4—92no—
204C2×D4—92no—
205C2×D4—182no—
206C2×D4—182no—
207C2×D4—182no—
208C2×D4—182no—
209C2×D4—181no—
210C22×C4—181no—
211C22×C4—182no—
212C22×C4C4⋊(C3⋊D3)12yes—
213C22×C4C22×C3⋊D311yescharacteristic
214SD16—188no—
215D8—188no—
216M16—22no—
217M16C4⋊(C3⋊D3)14yescomplemented
218C2×C8—22no—
219C4⋊C4—22no—
220C4⋊C4—182no—
221C22⋊C4—184no—
222C22⋊C4—364no—
223C42—182no—
224C22×C3—24no—
225C22×C3—24no—
226C22×C3#87414yes—
227C22×C3#88214yes—
228C22×C3#89514yes—
229C2×D3—1216no—
230C2×D3—128no—
231C2×D3—128no—
232C2×D3—128no—
233C2×D3—128no—
234C2×D3—248no—
235C2×D3—244no—
236C2×D3—244no—
237C3×C4—48no—
238C3×C4#88218yes—
239C3×C4#89518yes—
240Dic3—128no—
241Dic3—128no—
242C32#200611yescharacteristic, complemented, Sylow
243C23—182no—
244C23—182no—
245C23—362no—
246C23—362no—
247C23—361no—
248C23—361no—
249C23C2×C4⋊(C3⋊D3)11yescharacteristic
250Q8—182no—
251Q8—182no—
252D4—182no—
253D4—184no—
254D4—182no—
255D4—362no—
256D4—362no—
257D4—362no—
258D4—722no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—182no—
262C2×C4—182no—
263C2×C4—361no—
264C2×C4—361no—
265C2×C4—362no—
266C2×C4—362no—
267C2×C4C2×C4⋊(C3⋊D3)12yes—
268C2×C4D4×C3⋊D311yescharacteristic
269C2×C4D4×C3⋊D312yes—
270C2×C4#383211yescharacteristic
271C8—24no—
272C2×C3—24no—
273C2×C3—24no—
274C2×C3#467114yes—
275C2×C3#474714yes—
276C2×C3#475314yes—
277D3—248no—
278D3—248no—
279C22—21no—
280C22—21no—
281C22—364no—
282C22—362no—
283C22—362no—
284C22—362no—
285C22—362no—
286C22—722no—
287C22—721no—
288C22—721no—
289C22#6408311yescharacteristic
290C22#6409111yescharacteristic
291C22#6410411yescharacteristic
292C4—42no—
293C4—362no—
294C4—362no—
295C4#6409112yes—
296C4#6410412yes—
297C3#6900814yescomplemented
298C2—21no—
299C2—21no—
300C2—722no—
301C2—722no—
302C2#1059237011yescharacteristic
303C2#1059244611yescharacteristic
304C2#1059245211yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#120
hypercenter#343C3⋊D3
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. #10595981C2semidirect
3. C2×#63652C2semidirect
4. #10592687C2semidirect
5. C32×#343C2semidirect
25. C3×#343D3semidirect
40. C2×C4⋊(C3⋊D3)D4semidirect
44. C32×M16D4semidirect
101. #343C3⋊D3semidirect
120. C3×M16D12semidirect
217. M16C4⋊(C3⋊D3)semidirect
242. C32#2006semidirect
297. C3#69008semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105959812
C2×#636522
#105926872
C32×#3432
#690083