Finite Group Databasebeta

← #15673876

Subgroups — #15673876

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×#10625079C211yesmaximal, characteristic
2#13093183C211yesmaximal, characteristic, complemented
3#13092435C211yesmaximal, characteristic, complemented
4#13092421C211yesmaximal, characteristic, complemented
5C2×#10625005C211yesmaximal, characteristic, complemented
6C23⋊#338C211yesmaximal, characteristic, complemented
7C23×#344C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×D92C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C23×#117C2211yescharacteristic
13C2×#67267C2211yescharacteristic
14C2×#67267C2211yescharacteristic
15#10625079—22no—
16#10625079—22no—
17#10625078—22no—
18M16×D23—22no—
19C2×D184C412yescomplemented
20C2×#67263C412yescomplemented
21#10625072—22no—
22#10625005—22no—
23#10624991—22no—
24#10624987—22no—
25C23×D23—21no—
26C22×C4×C23C2311yescharacteristic
27C2×C22⋊D23—21no—
28#67288—21no—
29#67288—21no—
30#67288D412yes—
31#67288D412yes—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—21no—
35C2×D92—21no—
36C2×D92—21no—
37C2×D92C2×C412yes—
38C2×D92C2×C411yescharacteristic
39C2×C4×D23—21no—
40C2×Dic46C2×C411yescharacteristic
41M16×C23—21no—
42M16×C23—21no—
43M16×C23—21no—
44M16×C23D412yes—
45C2×C8×C23—21no—
46C2×C8×C23C2×C412yes—
47C4⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C42×C23—21no—
50#67267—21no—
51#67267—21no—
52#67267—21no—
53#67267—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8D412yes—
56D184—24no—
57#67263—24no—
58#67262—24no—
59C8×D23—24no—
60C23×C23#4111yescharacteristic
61C22×D23—21no—
62C22×D23—22no—
63C22×D23—41no—
64C22×D23—41no—
65C22×D23—82no—
66C2×C4×C23—41no—
67C2×C4×C23C22×C411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23#4111yescharacteristic
73C22⋊D23—22no—
74C22⋊D23—22no—
75C2×Dic23—21no—
76D92—22no—
77D92—21no—
78D92—22no—
79D92—41no—
80D92—41no—
81D92C22⋊C412yes—
82C4×D23—22no—
83C4×D23—22no—
84Dic46—21no—
85Dic46C22⋊C412yes—
86C8×C23—22no—
87C8×C23—22no—
88C23⋊C8—22no—
89C23⋊C8—41no—
90#1903—231nomaximal, Sylow
91C22×C23—41no—
92C22×C23C4×D411yescharacteristic
93C22×C23#12111yescharacteristic
94C22×C23#12311yescharacteristic
95C2×D23—22no—
96C2×D23—42no—
97C2×D23—81no—
98C2×D23—82no—
99C2×D23—82no—
100C2×D23—82no—
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#418—231no—
111C2×#100—231no—
112#344D2311yescharacteristic, complemented
113#338—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23#38611yescharacteristic
118D23—42no—
119D23—82no—
120C2×#41—231no—
121C22×D4—231no—
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—462no—
131C2×M16C2×D2311yescharacteristic
132C2×M16C2×D2311yescharacteristic
133#117C2×D2311yescharacteristic
134#104—462no—
135#102—462no—
136#100—462no—
137C23#190311yescharacteristic, complemented, Sylow
138C24—461no—
139#41—232no—
140#41—232no—
141#41—461no—
142#41—461no—
143C2×Q8—231no—
144C2×D4—231no—
145C2×D4—232no—
146C2×D4—461no—
147C2×D4—461no—
148C2×D4—461no—
149C2×D4—461no—
150C2×D4—461no—
151C2×D4—461no—
152C22×C4—461no—
153C22×C4C22×D2311yescharacteristic
154SD16—464no—
155D8—464no—
156M16—21no—
157M16—21no—
158M16—21no—
159M16—464no—
160M16—461no—
161M16—461no—
162M16—461no—
163M16—461no—
164M16D9212yes—
165C2×C8—21no—
166C2×C8—232no—
167C2×C8—464no—
168C2×C8—461no—
169C2×C8C4×D2312yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—461no—
174C23—462no—
175C23—921no—
176C23—921no—
177C23—1842no—
178C23#6728811yescharacteristic
179Q8—232no—
180Q8—461no—
181D4—232no—
182D4—462no—
183D4—462no—
184D4—462no—
185D4—461no—
186D4—462no—
187D4—921no—
188D4—921no—
189C2×C4—41no—
190C2×C4—461no—
191C2×C4—462no—
192C2×C4—462no—
193C2×C4C2×C4×D2311yescharacteristic
194C2×C4C2×D9211yescharacteristic
195C2×C4D4×D2311yescharacteristic
196C2×C4D4×D2311yescharacteristic
197C2×C4D4×D2311yescharacteristic
198C2×C4#6729211yescharacteristic
199C8—22no—
200C8—22no—
201C8—462no—
202C8—921no—
203C22—41no—
204C22—462no—
205C22—922no—
206C22—1841no—
207C22—1842no—
208C22—1842no—
209C22—1842no—
210C22C4×D9211yescharacteristic
211C22#1062505511yescharacteristic
212C22#1062506511yescharacteristic
213C4—81no—
214C4—462no—
215C4C22⋊C4×D2311yescharacteristic
216C4#1062505311yescharacteristic
217C4#1062506411yescharacteristic
218C4#1062506611yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—922no—
223C2—1842no—
224C2#1309229511yescharacteristic
subgroupG/H
centerC2#13092295
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#344C2
socleC2×C23#386
prime radicalC2×#10625079C2
cosocleC22×C4×C23C23
hypercenter#344D23
hypocenterC23#1903
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #13093183C2semidirect
3. #13092435C2semidirect
4. #13092421C2semidirect
5. C2×#10625005C2semidirect
6. C23⋊#338C2semidirect
7. C23×#344C2semidirect
19. C2×D184C4semidirect
20. C2×#67263C4semidirect
112. #344D23semidirect
137. C23#1903semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
#130931832
#130924352
#130924212
C2×#106250052
C23⋊#3382
C23×#3442
#190323