Finite Group Databasebeta

← #15674301

Subgroups — #15674301

Order 2944.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#67274C211yesmaximal, characteristic
2C2×#10625004C211yesmaximal, characteristic, complemented
3#13092426C211yesmaximal, characteristic, complemented
4#13092423C211yesmaximal, characteristic
5C2×#10625005C211yesmaximal, characteristic
6#13092375C211yesmaximal, characteristic, complemented
7C2×C23×#101C211yesmaximal, characteristic, complemented
8C22×Q8×C23C2211yescharacteristic
9C22×D92C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C2×#67274—21no—
13C2×#67274—21no—
14C2×#67274—22no—
15C2×#67274C414yescomplemented
16#10625097C2211yescharacteristic
17C2×#67267C2211yescharacteristic
18C22×C23⋊C8C2211yescharacteristic
19C23×#101—22no—
20#10625017—22no—
21#10625005—22no—
22#10625004—22no—
23#10625003—22no—
24#10624997—21no—
25C8×Dic23—21no—
26C23×D23—21no—
27C2×Q8×C23—21no—
28C2×Q8×C23—21no—
29C2×Q8×C23—21no—
30C2×Q8×C23—21no—
31C2×Q8×C23—21no—
32C2×Q8×C23C2×C412yes—
33C22×C4×C23—21no—
34C22×C4×C23C2311yescharacteristic
35C2×D92—21no—
36C2×D92—21no—
37C2×D92—21no—
38C2×D92—21no—
39C2×D92—21no—
40C2×D92C2×C412yes—
41M16×C23—21no—
42M16×C23—21no—
43M16×C23—21no—
44M16×C23D412yes—
45C2×C8×C23—21no—
46C2×C8×C23—21no—
47C22⋊Dic23—21no—
48#67274—24no—
49#67274—24no—
50C4⋊Dic23D412yes—
51C4×Dic23—21no—
52#67267—21no—
53#67267—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8C2×C412yes—
56C2×C23⋊C8D411yescharacteristic
57C2×C23⋊C8D411yescharacteristic
58C2×C23⋊C8D412yes—
59C23×C23#4111yescharacteristic
60C22×D23—22no—
61C22×D23—41no—
62C22×D23—41no—
63C22×D23—82no—
64Q8×C23—22no—
65Q8×C23—22no—
66Q8×C23—41no—
67Q8×C23—41no—
68C2×C4×C23—22no—
69C2×C4×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
77C2×Dic23—22no—
78D92—22no—
79D92—22no—
80D92—41no—
81D92—41no—
82C8×C23—22no—
83C8×C23—41no—
84C23⋊C8—41no—
85C23⋊C8C22⋊C412yes—
86C23⋊C8C22⋊C412yes—
87#1977—231nomaximal, Sylow
88C22×C23—22no—
89C22×C23C4×D411yescharacteristic
90C22×C23#12111yescharacteristic
91C22×C23#12411yescharacteristic
92C2×D23—42no—
93C2×D23—82no—
94C2×D23—82no—
95C2×D23—82no—
96C4×C23—42no—
97C4×C23C2×C22⋊C411yescharacteristic
98C4×C23C4×D411yescharacteristic
99C4×C23#12111yescharacteristic
100C4×C23#12711yescharacteristic
101Dic23—42no—
102C22×SD16—231no—
103C2×#108—231no—
104#419—231no—
105#418—231no—
106C2×#101D2311yescharacteristic, complemented
107C2×#100—231no—
108#405—231no—
109C2×C23—21no—
110C2×C23—21no—
111C2×C23#39011yescharacteristic
112C2×C23#47112yes—
113D23—82no—
114C22×Q8C2×D2311yescharacteristic
115C22×D4—231no—
116C2×SD16—234no—
117C2×SD16—461no—
118C2×SD16—461no—
119C2×SD16—462no—
120C2×M16—231no—
121C2×M16C2×D2311yescharacteristic
122C2×M16C2×D2311yescharacteristic
123C22×C8—231no—
124#117—231no—
125#108—462no—
126#103—462no—
127#102—462no—
128#101—22no—
129#100—462no—
130#97—461no—
131C4×C8—461no—
132C23#197711yescharacteristic, complemented, Sylow
133C24—461no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C4×D2312yes—
140C2×D4—232no—
141C2×D4—461no—
142C2×D4—461no—
143C2×D4—461no—
144C2×D4—461no—
145C2×D4—461no—
146C22×C4—21no—
147C22×C4C22×D2311yescharacteristic
148SD16—464no—
149SD16—464no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—461no—
154M16—461no—
155M16C22⋊D2312yes—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—232no—
159C2×C8—231no—
160C2×C8—231no—
161C2×C8—232no—
162C2×C8—461no—
163C4⋊C4—232no—
164C22⋊C4—461no—
165C42—461no—
166C23—462no—
167C23—921no—
168C23—921no—
169C23—1842no—
170C23#6728811yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—462no—
176D4—462no—
177D4—921no—
178D4—921no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—462no—
183C2×C4C2×C4×D2311yescharacteristic
184C2×C4D4×D2311yescharacteristic
185C2×C4D4×D2311yescharacteristic
186C2×C4D4×D2311yescharacteristic
187C2×C4#6729011yescharacteristic
188C2×C4C2×C22⋊D2311yescharacteristic
189C8—22no—
190C8—41no—
191C8—232no—
192C8—232no—
193C8—921no—
194C22—22no—
195C22—922no—
196C22—1842no—
197C22—1842no—
198C22—1842no—
199C22#1062505511yescharacteristic
200C22#1062505611yescharacteristic
201C22C4×C22⋊D2311yescharacteristic
202C4—42no—
203C4—922no—
204C4C22⋊C4×D2311yescharacteristic
205C4(C22⋊D23)⋊C411yescharacteristic
206C4#1062511011yescharacteristic
207C4#1062511111yescharacteristic
208C2—21no—
209C2—21no—
210C2—1842no—
211C2#1309231711yescharacteristic
212C2#1309268312yes—
subgroupG/H
centerC22#10625055
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#101C2
socleC22×C23#121
prime radicalC22×D92C22
cosocleC22×C4×C23C23
hypercenterC2×#101D23
hypocenterC23#1977
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#10625004C2semidirect
3. #13092426C2semidirect
6. #13092375C2semidirect
7. C2×C23×#101C2semidirect
15. C2×#67274C4semidirect
106. C2×#101D23semidirect
132. C23#1977semidirect

Maximal subgroups

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

subgroupindex
C22×#672742
C2×#106250042
#130924262
#130924232
C2×#106250052
#130923752
C2×C23×#1012
#197723