Finite Group Databasebeta

← #11779461

Subgroups — #11779461

Order 1152.

618 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 143 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
1Q8×#634C211yesmaximal, characteristic
2#10592720C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic
4#10592398C211yesmaximal, characteristic
5C32×Q8⋊C8C211yesmaximal, characteristic
6#10589347C211yesmaximal, characteristic
7#10589322C211yesmaximal, characteristic
8#68267—34nomaximal
9C32×C4×Q8C2211yescharacteristic
10Q8×C3⋊Dic3—21no—
11C2×#3746—22no—
12#64097—22no—
13#64097—21no—
14#64078—21no—
15#64078C2211yescharacteristic
16#64078C2211yescharacteristic
17C4×#634—21no—
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4×C8C2211yescharacteristic
21#63662—21no—
22#63645—21no—
23#63643—21no—
24#63634—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26Q8×Dic6—34no—
27#5021—34no—
28#4850—34no—
29#4699—34no—
30C3×Q8⋊C8D314yes—
31#4481—34no—
32#4456—34no—
33C2×C32×Q8D411yescharacteristic
34C2×#634—21no—
35C2×#634—22no—
36C2×#634D411yescharacteristic
37C2×#634D412yes—
38C2×C32×C8—21no—
39C2×C32×C8—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4D411yescharacteristic
42C32×C42—21no—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)—22no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—22no—
51#3750—21no—
52C4×C3⋊Dic3—22no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55#3746—44no—
56#1633—91noSylow
57C3×C4×Q8C2×D314yes—
58Q8×Dic3—64no—
59C2×Dic12—68no—
60#888—68no—
61#888—64no—
62#869—34no—
63#869—34no—
64#869—64no—
65C4×Dic6—34no—
66C4×Dic6—64no—
67C3×C4⋊C8C2×D314yes—
68C3×C4×C8C2×D314yes—
69#835—64no—
70#818—64no—
71#816—64no—
72#807—64no—
73C4⋊(C3⋊C8)—34no—
74C32×Q8—21no—
75C32×Q8Q1612yescomplemented
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—41no—
85#634—21no—
86#634—42no—
87#634—42no—
88#634—82no—
89#634Q1612yescomplemented
90C32×C8—22no—
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93Q82—91no—
94#494—91no—
95#477—91no—
96#477—91no—
97#333—91no—
98Q8⋊C8—91no—
99Q8⋊C8C3⋊D311yescharacteristic
100C2×C3×Q8D1214yes—
101C2×Dic6—34no—
102C2×Dic6—38no—
103C2×Dic6—64no—
104C2×Dic6—68no—
105C2×C3×C8—24no—
106C2×C3×C8—24no—
107C3×C4⋊C4—24no—
108C3×C4⋊C4D1214yes—
109C3×C42—24no—
110C3×C42C22×D314yes—
111C4⋊Dic3—34no—
112C4⋊Dic3—68no—
113C4⋊Dic3—64no—
114C4⋊Dic3—64no—
115C4⋊Dic3—64no—
116C4⋊Dic3—64no—
117Dic3⋊C4—68no—
118Dic3⋊C4—64no—
119C4×Dic3—68no—
120C4×Dic3—64no—
121C2×C3⋊C8—64no—
122Dic12—1216no—
123C22×C32#12011yescharacteristic
124C32×C4—22no—
125C32×C4—21no—
126C32×C4—41no—
127C32×C4C2×Q1611yescharacteristic
128C32×C4C2×Q1611yescharacteristic
129C32×C4#13711yescharacteristic
130C32×C4#13711yescharacteristic
131C3⋊Dic3—22no—
132C3⋊Dic3—42no—
133C3⋊Dic3—41no—
134C3⋊Dic3—81no—
135C2×Q16—182no—
136C4⋊Q8—91no—
137C4⋊Q8—91no—
138C4⋊Q8—181no—
139C4⋊Q8—182no—
140C4⋊Q8—181no—
141C4×Q8—91no—
142C4×Q8—181no—
143C4×Q8—181no—
144C4×Q8C2×C3⋊D311yescharacteristic
145#107—181no—
146#107—181no—
147C4⋊C8—91no—
148C4⋊C8C2×C3⋊D311yescharacteristic
149#103—181no—
150#103—181no—
151C4×C8C2×C3⋊D311yescharacteristic
152C3×Q8—24no—
153C3×Q8Dic1218yescomplemented
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4C2×D1214yes—
157C2×C3×C4D3×D414yes—
158C2×C3×C4D3×D414yes—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—68no—
162C2×Dic3—124no—
163Dic6—38no—
164Dic6—64no—
165Dic6—128no—
166Dic6—128no—
167Dic6—248no—
168C3×C8—28no—
169C3×C8—44no—
170C3⋊C8—124no—
171C2×C32#45111yescharacteristic
172C2×C32#45111yescharacteristic
173C2×C32#45311yescharacteristic
174C2×Q8—91no—
175C2×Q8—92no—
176C2×Q8—182no—
177C2×Q8—181no—
178C2×Q8C4⋊(C3⋊D3)11yescharacteristic
179Q16—364no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—181no—
183C4⋊C4—21no—
184C4⋊C4—91no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—181no—
190C4⋊C4—181no—
191C4⋊C4—181no—
192C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
193C42—21no—
194C42—182no—
195C42—181no—
196C42C22×C3⋊D311yescharacteristic
197C22×C3#88214yes—
198C3×C4—28no—
199C3×C4—24no—
200C3×C4—44no—
201C3×C4C2×Dic1214yes—
202C3×C4#90914yes—
203C3×C4#91514yes—
204C3×C4D3×Q1614yes—
205Dic3—68no—
206Dic3—128no—
207Dic3—124no—
208Dic3—244no—
209C32#163311yescharacteristic, complemented, Sylow
210Q8—21no—
211Q8—92no—
212Q8—181no—
213Q8—362no—
214Q8—362no—
215Q8—722no—
216Q8#374612yescomplemented
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—181no—
220C2×C4—181no—
221C2×C4—182no—
222C2×C4—361no—
223C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
224C2×C4D4×C3⋊D311yescharacteristic
225C2×C4D4×C3⋊D311yescharacteristic
226C8—22no—
227C8—41no—
228C8—361no—
229C2×C3#473914yes—
230C2×C3#480914yes—
231C2×C3#482214yes—
232C22#6409111yescharacteristic
233C4—21no—
234C4—22no—
235C4—41no—
236C4—182no—
237C4—362no—
238C4—361no—
239C4—721no—
240C4C2×#374611yescharacteristic
241C4#6411811yescharacteristic
242C4#6412411yescharacteristic
243C4Q16×C3⋊D311yescharacteristic
244C3#6826714yescomplemented
245C2#1059243811yescharacteristic
246C2#1059250811yescharacteristic
247C2#1059252111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×Q8⋊C8C2
socle, prime radicalC22×C32#120
hypercenterQ8⋊C8C3⋊D3
hypocenterC32#1633
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
75. C32×Q8Q16semidirect
89. #634Q16semidirect
153. C3×Q8Dic12semidirect
209. C32#1633semidirect
216. Q8#3746semidirect
244. C3#68267semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
#105927202
#105925492
#105923982
C32×Q8⋊C82
#105893472
#105893222
#682673