Finite Group Databasebeta

← #11779657

Subgroups — #11779657

Order 1152.

582 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 129 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#10596013C211yesmaximal, characteristic
2C32×#476C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic, complemented
4#10592778C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic, complemented
7#10589348C211yesmaximal, characteristic, complemented
8#71147—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4×D4C2211yescharacteristic
11#64145—21no—
12#64135—21no—
13#64133—21no—
14#64096—21no—
15#64088—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C32×#106—21no—
19C32×C4⋊C8C2211yescharacteristic
20C32×#102—21no—
21#63662—22no—
22#63637—21no—
23#63634—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5542—34no—
27C3×#476D314yes—
28#5091—34no—
29#5079—34no—
30D4⋊(C3⋊C8)—34no—
31#4484—34no—
32#4482—34no—
33C2×C32×Q8—21no—
34C2×C32×D4D411yescharacteristic
35C22×C32×C4—21no—
36C2×#634—21no—
37C2×#634D411yescharacteristic
38C2×C32×C8—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4D411yescharacteristic
42C32×C22⋊C4—21no—
43C32×C42C2311yescharacteristic
44#3757—22no—
45#3757—22no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48C4⋊(C3⋊Dic3)D412yes—
49#3750—22no—
50#3750—21no—
51C4×C3⋊Dic3—22no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55#1638—91noSylow
56C3×C4⋊Q8C2×D314yes—
57C3×C4×D4C2×D314yes—
58#936—64no—
59#926—64no—
60#924—64no—
61#887—64no—
62#879—68no—
63#869—34no—
64C4×Dic6—34no—
65C3×#106—24no—
66C3×C4⋊C8C2×D314yes—
67C3×#102—24no—
68#835—68no—
69#810—64no—
70#807—64no—
71C4⋊(C3⋊C8)—34no—
72C4×C3⋊C8—34no—
73C23×C32—21no—
74C32×Q8—42no—
75C32×D4—21no—
76C32×D4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—22no—
87#634—21no—
88#634—21no—
89#634—41no—
90#634—41no—
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3⋊(C3⋊C8)—41no—
94#556—91no—
95#487—91no—
96#477—91no—
97#476C3⋊D311yescharacteristic
98#332—91no—
99Q8⋊C8—91no—
100D4⋊C8—91no—
101C2×C3×Q8—24no—
102C2×C3×D4#6714yes—
103C22×C3×C4—24no—
104C2×Dic6—34no—
105C2×Dic6—64no—
106C2×C3×C8—24no—
107C3×C4⋊C4—24no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4#6714yes—
110C3×C22⋊C4—24no—
111C3×C42C22×D314yes—
112#217—68no—
113#217—68no—
114C4⋊Dic3—34no—
115C4⋊Dic3—38no—
116C4⋊Dic3—64no—
117Dic3⋊C4—68no—
118Dic3⋊C4—64no—
119C4×Dic3—68no—
120C4×Dic3—64no—
121C2×C3⋊C8—64no—
122C2×C3⋊C8—64no—
123C22×C32—41no—
124C22×C32—41no—
125C22×C32—41no—
126C22×C32#12011yescharacteristic
127C32×C4—21no—
128C32×C4—41no—
129C32×C4—81no—
130C32×C4#13511yescharacteristic
131C32×C4#13511yescharacteristic
132C32×C4#13711yescharacteristic
133C32×C4#13711yescharacteristic
134C3⋊Dic3—41no—
135C3⋊Dic3—42no—
136C3⋊Dic3—41no—
137C4⋊Q8—91no—
138C4⋊Q8C2×C3⋊D311yescharacteristic
139#126—182no—
140#124—181no—
141C22⋊Q8—181no—
142C4×Q8—91no—
143C4×Q8—181no—
144C4×D4C2×C3⋊D311yescharacteristic
145#117—181no—
146#107—181no—
147#106—21no—
148C4⋊C8—91no—
149C4⋊C8C2×C3⋊D311yescharacteristic
150#103—181no—
151#103—182no—
152#102—21no—
153C4×C8—91no—
154C23×C3—24no—
155C3×Q8—48no—
156C3×D4—24no—
157C3×D4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4D3×D414yes—
163C2×C3×C4D3×D414yes—
164C2×C3×C4C2×#6714yes—
165C2×Dic3—64no—
166C2×Dic3—64no—
167C2×Dic3—68no—
168Dic6—64no—
169Dic6—64no—
170Dic6—124no—
171Dic6—124no—
172C3×C8—44no—
173C3⋊C8—124no—
174C3⋊C8—124no—
175C2×C32—81no—
176C2×C32#45211yescharacteristic
177C2×C32#45211yescharacteristic
178C2×C32#45411yescharacteristic
179C2×Q8—21no—
180C2×Q8—91no—
181C2×Q8—181no—
182C2×D4#63811yescharacteristic
183C22×C4—21no—
184C2×C8—21no—
185C2×C8—181no—
186C2×C8—181no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—92no—
190C4⋊C4—91no—
191C4⋊C4—182no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4#63811yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C42—182no—
199C42—181no—
200C42C22×C3⋊D311yescharacteristic
201C22×C3—44no—
202C22×C3—44no—
203C22×C3—44no—
204C22×C3#93714yes—
205C3×C4—24no—
206C3×C4—44no—
207C3×C4—84no—
208C3×C4#91514yes—
209C3×C4#91614yes—
210C3×C4#94214yes—
211C3×C4#95014yes—
212Dic3—124no—
213Dic3—124no—
214Dic3—128no—
215C32#163811yescharacteristic, complemented, Sylow
216C23—21no—
217Q8—42no—
218Q8—181no—
219Q8—181no—
220Q8—361no—
221Q8—361no—
222D4—21no—
223D4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—181no—
229C2×C4—182no—
230C2×C4—181no—
231C2×C4D4×C3⋊D311yescharacteristic
232C2×C4D4×C3⋊D311yescharacteristic
233C2×C4C2×#63811yescharacteristic
234C8—41no—
235C8—361no—
236C8—361no—
237C2×C3—84no—
238C2×C3#504714yes—
239C2×C3#517314yes—
240C2×C3#520114yes—
241C22—41no—
242C22—41no—
243C22—41no—
244C22#6414611yescharacteristic
245C4—21no—
246C4—41no—
247C4—81no—
248C4—361no—
249C4—361no—
250C4—362no—
251C4#6412411yescharacteristic
252C4#6412511yescharacteristic
253C4#6415111yescharacteristic
254C4#6415911yescharacteristic
255C3#7114714yescomplemented
256C2—81no—
257C2#1059274611yescharacteristic
258C2#1059287211yescharacteristic
259C2#1059290011yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#476C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#476C3⋊D3
hypocenterC32#1638
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
3. #10592790C2semidirect
4. #10592778C2semidirect
6. #10589350C2semidirect
7. #10589348C2semidirect
215. C32#1638semidirect
255. C3#71147semidirect

Maximal subgroups

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

subgroupindex
#105960132
C32×#4762
#105927902
#105927782
D4⋊(C3⋊(C3⋊C8))2
#105893502
#105893482
#711473