Finite Group Databasebeta

← #15673874

Subgroups — #15673874

Order 2944.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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×#10625103C211yesmaximal, characteristic
2#13093183C211yesmaximal, characteristic, complemented
3#13092435C211yesmaximal, characteristic, complemented
4C2×#10625015C211yesmaximal, characteristic, complemented
5#13092187C211yesmaximal, characteristic, complemented
6C23⋊#338C211yesmaximal, characteristic, complemented
7C23×#418C211yesmaximal, characteristic, complemented
8C22×D4×C23C2211yescharacteristic
9C2×#67288C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×#67273C412yescomplemented
13#10625103—22no—
14#10625103—22no—
15C2×#67272C412yescomplemented
16C2×#67267C2211yescharacteristic
17C2×#67267C2211yescharacteristic
18C2×#67267C2211yescharacteristic
19#10625078—22no—
20M16×D23—22no—
21#10625072—22no—
22C23×#102—22no—
23#10625015—22no—
24#10624987—22no—
25C24×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23—21no—
29C2×D4×C23—21no—
30C2×D4×C23—21no—
31C2×D4×C23C2×C412yes—
32C22×C4×C23C2311yescharacteristic
33C2×C22⋊D23—21no—
34#67288—21no—
35#67288—21no—
36#67288D412yes—
37#67288D412yes—
38C2×D92C2×C411yescharacteristic
39C2×C4×D23—21no—
40C2×Dic46C2×C411yescharacteristic
41M16×C23—21no—
42M16×C23—21no—
43C2×C8×C23D412yes—
44C4⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C42×C23—21no—
47#67273—24no—
48#67272—24no—
49#67267—21no—
50#67267—21no—
51#67267—21no—
52#67267—21no—
53#67267—21no—
54#67267D412yes—
55C2×C23⋊C8—21no—
56C2×C23⋊C8—21no—
57C2×C23⋊C8C2×C412yes—
58#67262—24no—
59C8×D23—24no—
60C23×C23—22no—
61C23×C23—41no—
62C23×C23—41no—
63C23×C23—82no—
64C23×C23#4111yescharacteristic
65C22×D23—21no—
66D4×C23—22no—
67D4×C23—22no—
68D4×C23—41no—
69D4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23C22×C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C2×C4×C23#4111yescharacteristic
77C22⋊D23—22no—
78C22⋊D23—22no—
79C2×Dic23—21no—
80D92—21no—
81D92C22⋊C412yes—
82C4×D23—22no—
83C4×D23—22no—
84Dic46—21no—
85Dic46C22⋊C412yes—
86C8×C23—22no—
87C23⋊C8—22no—
88C23⋊C8—22no—
89C23⋊C8—41no—
90#1903—231nomaximal, Sylow
91C22×C23—41no—
92C22×C23—42no—
93C22×C23—82no—
94C22×C23—82no—
95C22×C23—82no—
96C22×C23C4×D411yescharacteristic
97C22×C23#12111yescharacteristic
98C22×C23#12311yescharacteristic
99C2×D23—22no—
100C2×D23—81no—
101C4×C23—81no—
102C4×C23C2×C22⋊C411yescharacteristic
103C4×C23C4×D411yescharacteristic
104C4×C23#12011yescharacteristic
105C4×C23#12111yescharacteristic
106Dic23—22no—
107C2×AGL(1,ℤ/8)—231no—
108#568—231no—
109#421—231no—
110#418D2311yescharacteristic, complemented
111C2×#100—231no—
112#344—231no—
113#338—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23—82no—
118C2×C23#38611yescharacteristic
119D23—42no—
120C2×#41—231no—
121C22×D4C2×D2311yescharacteristic
122AGL(1,ℤ/8)—462no—
123AGL(1,ℤ/8)—462no—
124C2×SD16—232no—
125C2×D8—232no—
126#131—462no—
127#131—462no—
128C2×M16—231no—
129C2×M16—231no—
130C2×M16—231no—
131C2×M16—462no—
132C2×M16C2×D2311yescharacteristic
133#117C2×D2311yescharacteristic
134#104—462no—
135#102—22no—
136#100—462no—
137C23#190311yescharacteristic, complemented, Sylow
138C24—21no—
139#41—232no—
140#41—232no—
141#41—461no—
142#41—461no—
143C2×Q8—231no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—231no—
150C2×D4—461no—
151C2×D4C4×D2312yes—
152C22×C4—461no—
153C22×C4C22×D2311yescharacteristic
154SD16—464no—
155D8—464no—
156M16—21no—
157M16—21no—
158M16—232no—
159M16—464no—
160M16—461no—
161M16—461no—
162M16—461no—
163M16—461no—
164M16—461no—
165C2×C8—232no—
166C2×C8—464no—
167C2×C8—461no—
168C2×C8—461no—
169C2×C8C22⋊D2312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—461no—
178C23#6729011yescharacteristic
179Q8—232no—
180Q8—461no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—232no—
186D4—462no—
187D4—462no—
188D4—461no—
189C2×C4—41no—
190C2×C4—461no—
191C2×C4—462no—
192C2×C4—462no—
193C2×C4C2×C4×D2311yescharacteristic
194C2×C4#6728811yescharacteristic
195C2×C4D4×D2311yescharacteristic
196C2×C4D4×D2311yescharacteristic
197C2×C4D4×D2311yescharacteristic
198C2×C4C2×C22⋊D2311yescharacteristic
199C8—22no—
200C8—462no—
201C8—462no—
202C8—921no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—462no—
209C22—1841no—
210C22(C22⋊D23)⋊C411yescharacteristic
211C22#1062505411yescharacteristic
212C22#1062510911yescharacteristic
213C4—81no—
214C4—462no—
215C4C22⋊C4×D2311yescharacteristic
216C4#1062505511yescharacteristic
217C4C4×C22⋊D2311yescharacteristic
218C4#1062510811yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—922no—
224C2#1309229311yescharacteristic
subgroupG/H
centerC2#13092293
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#418C2
socleC2×C23#386
prime radicalC2×#10625103C2
cosocleC22×C4×C23C23
hypercenter#418D23
hypocenterC23#1903
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #13093183C2semidirect
3. #13092435C2semidirect
4. C2×#10625015C2semidirect
5. #13092187C2semidirect
6. C23⋊#338C2semidirect
7. C23×#418C2semidirect
12. C2×#67273C4semidirect
15. C2×#67272C4semidirect
110. #418D23semidirect
137. C23#1903semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
#130931832
#130924352
C2×#106250152
#130921872
C23⋊#3382
C23×#4182
#190323