Finite Group Databasebeta

← #15672453

Subgroups — #15672453

Order 2944.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D92C211yesmaximal, characteristic, complemented
2#13092794C211yesmaximal, characteristic, complemented
3#13092613C211yesmaximal, characteristic, complemented
4#13092612C211yesmaximal, characteristic, complemented
5#13092160C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D23—21no—
9C22×D92—21no—
10C4×D4×C23C2211yescharacteristic
11C2×#67272—21no—
12#10625101—21no—
13C2×D184—21no—
14C2×D184—22no—
15#10625066—21no—
16#10625053—22no—
17#10625045C2211yescharacteristic
18#10625045C2211yescharacteristic, complemented
19C4×D92C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic, complemented
21C4×C8×C23C2211yescharacteristic, complemented
22#10625003—21no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic, complemented
25C23×D23—22no—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23—21no—
28C2×C22⋊D23—22no—
29D4×D23—42no—
30D4×D23—42no—
31C2×D92—22no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—21no—
35C2×D92—21no—
36C2×D92—21no—
37C2×D92—42no—
38C2×D92—42no—
39C2×D92D411yescharacteristic
40C2×D92D412yes—
41C2×C4×D23—21no—
42C2×C8×C23—21no—
43C2×C8×C23—21no—
44C4⋊C4×C23D411yescharacteristic
45C22⋊C4×C23—21no—
46C42×C23C2311yescharacteristic
47#67272—42no—
48(C2×D23)⋊C4—22no—
49(C2×D23)⋊C4—21no—
50C4⋊Dic23D411yescharacteristic
51C2×C23⋊C8—21no—
52D184—44no—
53D184—42no—
54C23×C23—21no—
55C22×D23—21no—
56C22×D23—22no—
57C22×D23—44no—
58C22×D23—44no—
59C22×D23—41no—
60C22×D23—82no—
61D4×C23—21no—
62D4×C23D812yescomplemented
63C2×C4×C23—21no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—44no—
70C2×Dic23—21no—
71D92—21no—
72D92—42no—
73D92—42no—
74D92—44no—
75D92—41no—
76D92—41no—
77D92—41no—
78D92—41no—
79D92—41no—
80D92—41no—
81D92—41no—
82D92—41no—
83D92D812yescomplemented
84C4×D23—41no—
85C4×D23—41no—
86C8×C23—22no—
87C8×C23—41no—
88C23⋊C8—41no—
89#1619—231nomaximal, Sylow
90C22×C23—22no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23#12011yescharacteristic
94C2×D23—22no—
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—42no—
98C2×D23—42no—
99C2×D23—42no—
100C2×D23—88no—
101C2×D23—81no—
102C2×D23—81no—
103C2×D23—81no—
104C4×C23—21no—
105C4×C23—41no—
106C4×C23C2×D811yescharacteristic
107C4×C23C2×D811yescharacteristic
108C4×C23AGL(1,ℤ/8)11yescharacteristic
109C4×C23AGL(1,ℤ/8)11yescharacteristic
110Dic23—41no—
111D42—231no—
112#493—231no—
113#459—231no—
114#459—231no—
115#331—231no—
116D4⋊C8—231no—
117D4⋊C8D2311yescharacteristic, complemented
118C2×C23—42no—
119C2×C23#44711yescharacteristic
120C2×C23#44711yescharacteristic
121C2×C23#45311yescharacteristic
122D23—42no—
123D23—82no—
124D23—161no—
125C22×D4—461no—
126C22×D4—461no—
127C2×D8—461no—
128C2×D8—462no—
129C2×D8—461no—
130#127—231no—
131#127—231no—
132#121—461no—
133#121—461no—
134#120—462no—
135C4×D4—231no—
136C4×D4C2×D2311yescharacteristic
137C4⋊C8—231no—
138C4⋊C8C2×D2311yescharacteristic, complemented
139#102—461no—
140#102—461no—
141C4×C8C2×D2311yescharacteristic, complemented
142C23#161911yescharacteristic, complemented, Sylow
143C24—462no—
144C2×D4—231no—
145C2×D4—232no—
146C2×D4—462no—
147C2×D4—462no—
148C2×D4—461no—
149C2×D4—461no—
150C2×D4—461no—
151C2×D4—461no—
152C2×D4—461no—
153C2×D4—922no—
154C2×D4—922no—
155C2×D4—922no—
156C2×D4—922no—
157C2×D4D9211yescharacteristic
158C22×C4—21no—
159C22×C4—461no—
160D8—924no—
161D8—922no—
162D8—922no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—461no—
166C4⋊C4—231no—
167C4⋊C4D9211yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—462no—
170C22⋊C4—461no—
171C42C22×D2311yescharacteristic
172C23—21no—
173C23—461no—
174C23—462no—
175C23—924no—
176C23—924no—
177C23—921no—
178C23—1842no—
179D4—21no—
180D4—232no—
181D4—461no—
182D4—922no—
183D4—922no—
184D4—924no—
185D4—924no—
186D4—921no—
187D4—921no—
188D4—921no—
189D4—921no—
190D4—921no—
191D4—921no—
192D4—921no—
193D4—921no—
194D4D18412yescomplemented
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—461no—
199C2×C4—921no—
200C2×C4—921no—
201C2×C4C2×D9211yescharacteristic
202C2×C4D4×D2311yescharacteristic
203C2×C4D4×D2311yescharacteristic
204C8—22no—
205C8—41no—
206C8—921no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—462no—
211C22—921no—
212C22—921no—
213C22—922no—
214C22—922no—
215C22—922no—
216C22—1848no—
217C22—1841no—
218C22—1841no—
219C22—1841no—
220C22#1062505311yescharacteristic
221C4—21no—
222C4—41no—
223C4—921no—
224C4C2×D18411yescharacteristic
225C4#1062507911yescharacteristic
226C4D8×D2311yescharacteristic
227C4#1062508511yescharacteristic
228C2—42no—
229C2—922no—
230C2—3681no—
231C2—1842no—
232C2#1309255211yescharacteristic
233C2#1309255311yescharacteristic
234C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
hypercenterD4⋊C8D23
hypocenterC23#1619
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. D4×D92C2semidirect
2. #13092794C2semidirect
3. #13092613C2semidirect
4. #13092612C2semidirect
5. #13092160C2semidirect
6. #13092146C2semidirect
7. C23×D4⋊C8C2semidirect
18. #10625045C22semidirect
20. C23×C4⋊C8C22semidirect
21. C4×C8×C23C22semidirect
24. C4⋊(C23⋊C8)C22semidirect
62. D4×C23D8semidirect
83. D92D8semidirect
117. D4⋊C8D23semidirect
138. C4⋊C8C2×D23semidirect
141. C4×C8C2×D23semidirect
142. C23#1619semidirect
194. D4D184semidirect

Maximal subgroups

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

subgroupindex
D4×D922
#130927942
#130926132
#130926122
#130921602
#130921462
C23×D4⋊C82
#161923