Finite Group Databasebeta

← #25016958

Subgroups — #25016958

Order 11008.

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

normal subgroups only

This group has 312 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
1#19144974C211yesmaximal, characteristic
2#356×D43C212yesmaximal
3#19132768C211yesmaximal, characteristic, complemented
4#19132767C212yesmaximal, complemented
5C43×#1413C211yesmaximal, characteristic, complemented
6#14583455C411yescharacteristic
7C4⋊Q8×D43C2211yescharacteristic
8#14583269C411yescharacteristic
9#14583268C411yescharacteristic
10#14583267C2211yescharacteristic
11#14583248—22no—
12#14582906—22no—
13#101×D43—22no—
14#14582851C411yescharacteristic
15#14582698C2212yes—
16#14582697—22no—
17C43×#491C2211yescharacteristic
18C43×#356C2212yes—
19C2×Q8×D43D412yes—
20C2×#10621872—21no—
21M16×D43—42no—
22#13063325C2×C411yescharacteristic
23#13063324—21no—
24#13063324—41no—
25#13063323D412yes—
26#13063317C2×C411yescharacteristic
27#13063303—41no—
28#13063290—41no—
29#13063283—21no—
30C4⋊C4×D43—41no—
31C42×D43C2×C411yescharacteristic
32#13063250—22no—
33#13063249—22no—
34#13063248—22no—
35#13063244—22no—
36#13063243—42no—
37#13063236C2×C411yescharacteristic
38C8×Dic43—21no—
39C4⋊Q8×C43C2311yescharacteristic
40#125×C43C2×C411yescharacteristic
41#103×C43—22no—
42#101×C43—22no—
43#97×C43C2×C411yescharacteristic
44C2×Q8×C43C2×D412yes—
45Q8×D43—42no—
46Q8×D43—42no—
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×C4×D43C22⋊C411yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—41no—
52C2×Dic86C22⋊C412yes—
53M16×C43—42no—
54C2×C8×C43—21no—
55C4⋊C4×C43—21no—
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C42×C43C22×C411yescharacteristic
59(C2×D43)⋊C4—41no—
60C4⋊Dic43—21no—
61C4⋊Dic43—41no—
62Dic43⋊C4—42no—
63Dic43⋊C4—41no—
64Dic43⋊C4—41no—
65C4×Dic43—21no—
66C4×Dic43—41no—
67C4×Dic43C22⋊C411yescharacteristic
68#10621877—42no—
69C2×C43⋊C8—21no—
70#10621872—42no—
71#10621872—82no—
72C8×D43—82no—
73C22×D43#9911yescharacteristic
74Q8×C43—42no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43C2×C22⋊C411yescharacteristic
79C2×Dic43—21no—
80C2×Dic43—22no—
81C2×Dic43—41no—
82C2×Dic43#9911yescharacteristic
83C4×D43—22no—
84C4×D43—42no—
85C4×D43—42no—
86C4×D43—42no—
87Dic86—42no—
88Dic86—82no—
89Dic86—82no—
90C8×C43—41no—
91C8×C43—82no—
92C43⋊C8—41no—
93C43⋊C8—82no—
94#13599—431nomaximal, Sylow
95C22×C43C2×#9911yescharacteristic
96C2×D43—41no—
97C2×D43#35412yes—
98C4×C43—21no—
99C4×C43—41no—
100C4×C43—42no—
101C4×C43—81no—
102Dic43—22no—
103Dic43—21no—
104Dic43—42no—
105Dic43—81no—
106#3139—431no—
107C2×#356—432no—
108#1413—431no—
109#1413—432no—
110#1413D4311yescharacteristic, complemented
111C2×C43—21no—
112C2×C43C2×#35411yescharacteristic
113D43—22no—
114#533—431no—
115C2×C4⋊Q8—431no—
116#491—431no—
117#491—431no—
118#491—431no—
119#491C2×D4311yescharacteristic
120#487—862no—
121#419—862no—
122C2×#101—862no—
123C4×M16—431no—
124#356—432no—
125#356—862no—
126#356C2×D4312yes—
127C43#1359911yescharacteristic, complemented, Sylow
128C22×Q8—432no—
129C2×M16—861no—
130C2×M16—1722no—
131C4⋊Q8—432no—
132C4⋊Q8—431no—
133C4⋊Q8—861no—
134C4⋊Q8—1721no—
135C4⋊Q8C22×D4311yescharacteristic
136#125—431no—
137#125C4×D4311yescharacteristic
138C22⋊Q8—1721no—
139C4×Q8—1721no—
140#117—861no—
141C2×C4⋊C4—1721no—
142C2×C42—431no—
143#103—22no—
144#103—862no—
145#103—862no—
146#103—862no—
147#101—22no—
148#101—862no—
149#101—1722no—
150#97—431no—
151#97C4×D4311yescharacteristic
152C4×C8—861no—
153C2×Q8—432no—
154C2×Q8—862no—
155C2×Q8—1721no—
156C2×Q8—1722no—
157C2×Q8—1722no—
158C2×Q8D4×D4312yes—
159C22×C4—431no—
160C22×C4—861no—
161C22×C4—862no—
162M16—42no—
163M16—3442no—
164M16—1722no—
165M16—1722no—
166C2×C8—21no—
167C2×C8—861no—
168C2×C8—3442no—
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—861no—
173C4⋊C4—1722no—
174C4⋊C4—1721no—
175C4⋊C4—1721no—
176C4⋊C4—1721no—
177C22⋊C4—1721no—
178C42—431no—
179C42—861no—
180C42—1721no—
181C42C2×C4×D4311yescharacteristic
182C23—431no—
183Q8—42no—
184Q8—3442no—
185Q8—3442no—
186Q8—1722no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—431no—
191C2×C4—862no—
192C2×C4—861no—
193C2×C4—862no—
194C2×C4—1722no—
195C2×C4—1722no—
196C2×C4—1722no—
197C2×C4—1721no—
198C2×C4C22⋊C4×D4311yescharacteristic
199C8—41no—
200C8—82no—
201C8—3442no—
202C8—1721no—
203C22—432no—
204C22—1721no—
205C22#99×D4311yescharacteristic
206C4—21no—
207C4—41no—
208C4—42no—
209C4—81no—
210C4—862no—
211C4—861no—
212C4—3441no—
213C4—1722no—
214C2—21no—
215C2—862no—
216C2#354×D4311yescharacteristic
subgroupG/H
centerC2#354×D43
commutatorC42×C43C22×C4
FrattiniC4⋊Q8C22×D43
FittingC43×#1413C2
socleC2×C43C2×#354
prime radicalC22×D43#99
cosocleC4⋊Q8×C43C23
hypercenter#1413D43
hypocenterC43#13599
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
3. #19132768C2semidirect
4. #19132767C2semidirect
5. C43×#1413C2semidirect
110. #1413D43semidirect
127. C43#13599semidirect

Maximal subgroups

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

subgroupindex
#191449742
#356×D432
#191327682
#191327672
C43×#14132
#1359943