Finite Group Databasebeta

← C113×#9421 #43277441

Subgroups — C113×#9421 #43277441

Order 28928.

488 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C113×#3152C211yesmaximal, characteristic
2C113×#2980C211yesmaximal, characteristic
3C113×#1556C212yesmaximal, complemented
4C113×#1536C211yesmaximal, characteristic
5C113×#1291C212yesmaximal, complemented
6C2×#137×C113—22no—
7#532×C113C2211yescharacteristic
8C2×C4⋊Q8×C113C2211yescharacteristic
9#497×C113—22no—
10#494×C113C412yes—
11#492×C113C412yes—
12#435×C113—24no—
13#432×C113C2212yes—
14#432×C113C2212yes—
15#408×C113—22no—
16C4×M16×C113C2211yescharacteristic
17#332×C113—24no—
18#329×C113—22no—
19C2×#41×C113D412yes—
20C22×Q8×C113—21no—
21#137×C113—44no—
22#137×C113—44no—
23C2×Q16×C113—24no—
24C2×SD16×C113—24no—
25C2×M16×C113—21no—
26C2×M16×C113—22no—
27C22×C8×C113—22no—
28C4⋊Q8×C113—22no—
29C4⋊Q8×C113—21no—
30C4⋊Q8×C113C2×C412yes—
31C4⋊Q8×C113C2×C411yescharacteristic
32#127×C113C2×C411yescharacteristic
33#124×C113D412yes—
34#121×C113—22no—
35C4×D4×C113—22no—
36C2×C4⋊C4×C113—22no—
37C2×C42×C113C2311yescharacteristic
38C4⋊C8×C113—22no—
39C4⋊C8×C113D414yes—
40C22⋊C8×C113—24no—
41C22⋊C8×C113—22no—
42C22⋊C8×C113—22no—
43#97×C113—21no—
44#97×C113—22no—
45#97×C113—22no—
46C4×C8×C113C2×C412yes—
47#41×C113—42no—
48#41×C113—42no—
49C2×Q8×C113—22no—
50C2×Q8×C113—42no—
51C2×Q8×C113—42no—
52C2×Q8×C113—41no—
53C2×Q8×C113C22⋊C412yes—
54C2×D4×C113—22no—
55C2×D4×C113—22no—
56C2×D4×C113C22⋊C412yes—
57C22×C4×C113—22no—
58C22×C4×C113—41no—
59C22×C4×C113C2×D411yescharacteristic
60C22×C4×C113#4112yes—
61Q16×C113—48no—
62SD16×C113—48no—
63M16×C113—24no—
64M16×C113—82no—
65C2×C8×C113—22no—
66C2×C8×C113—24no—
67C2×C8×C113—42no—
68C2×C8×C113—82no—
69C4⋊C4×C113—22no—
70C4⋊C4×C113—24no—
71C4⋊C4×C113—42no—
72C22⋊C4×C113—24no—
73C42×C113C22×C411yescharacteristic
74C42×C113C2×D411yescharacteristic
75C42×C113C2×D412yes—
76C23×C113—22no—
77C23×C113#12311yescharacteristic
78Q8×C113—42no—
79Q8×C113—44no—
80Q8×C113—82no—
81D4×C113—42no—
82D4×C113—82no—
83D4×C113—82no—
84C2×C4×C113—22no—
85C2×C4×C113—22no—
86C2×C4×C113—42no—
87C2×C4×C113—42no—
88C2×C4×C113—42no—
89C2×C4×C113—42no—
90C2×C4×C113—81no—
91C2×C4×C113—81no—
92C2×C4×C113C2×C22⋊C411yescharacteristic
93C2×C4×C113C4×D412yes—
94C2×C4×C113#12011yescharacteristic
95C2×C4×C113#12112yes—
96C8×C113—24no—
97C8×C113—44no—
98C8×C113—82no—
99C22×C113—21no—
100C22×C113—22no—
101C22×C113—42no—
102C22×C113—44no—
103C22×C113#38611yescharacteristic
104C4×C113—21no—
105C4×C113—22no—
106C4×C113—22no—
107C4×C113—42no—
108C4×C113—82no—
109C4×C113#45312yes—
110#9421C11311yesmaximal, characteristic, direct product factor, Sylow
111C2×C113—41no—
112C2×C113—82no—
113C2×C113#188711yescharacteristic
114C2×C113#190212yes—
115#3152C2×C11311yescharacteristic
116#2980C2×C11311yescharacteristic
117#1556C2×C11312yescomplemented
118#1536C2×C11311yescharacteristic
119#1291C2×C11312yescomplemented
120C113#942111yescharacteristic, direct product factor, Sylow
121C2×#137—22no—
122#532C22×C11311yescharacteristic
123C2×C4⋊Q8C22×C11311yescharacteristic
124#497—22no—
125#494C4×C11312yes—
126#492C4×C11312yes—
127#435—24no—
128#432C22×C11312yes—
129#432C22×C11312yes—
130#408—22no—
131C4×M16C22×C11311yescharacteristic
132#332—24no—
133#329—22no—
134C2×#41D4×C11312yes—
135C22×Q8—21no—
136#137—44no—
137#137—44no—
138C2×Q16—24no—
139C2×SD16—24no—
140C2×M16—21no—
141C2×M16—22no—
142C22×C8—22no—
143C4⋊Q8—22no—
144C4⋊Q8—21no—
145C4⋊Q8C2×C4×C11312yes—
146C4⋊Q8C2×C4×C11311yescharacteristic
147#127C2×C4×C11311yescharacteristic
148#124D4×C11312yes—
149#121—22no—
150C4×D4—22no—
151C2×C4⋊C4—22no—
152C2×C42C23×C11311yescharacteristic
153C4⋊C8—22no—
154C4⋊C8D4×C11314yes—
155C22⋊C8—24no—
156C22⋊C8—22no—
157C22⋊C8—22no—
158#97—21no—
159#97—22no—
160#97—22no—
161C4×C8C2×C4×C11312yes—
162#41—42no—
163#41—42no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8C22⋊C4×C11312yes—
169C2×D4—22no—
170C2×D4—22no—
171C2×D4C22⋊C4×C11312yes—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C11311yescharacteristic
175C22×C4#41×C11312yes—
176Q16—48no—
177SD16—48no—
178M16—24no—
179M16—82no—
180C2×C8—22no—
181C2×C8—24no—
182C2×C8—42no—
183C2×C8—82no—
184C4⋊C4—22no—
185C4⋊C4—24no—
186C4⋊C4—42no—
187C22⋊C4—24no—
188C42C22×C4×C11311yescharacteristic
189C42C2×D4×C11311yescharacteristic
190C42C2×D4×C11312yes—
191C23—22no—
192C23#123×C11311yescharacteristic
193Q8—42no—
194Q8—44no—
195Q8—82no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4C2×C22⋊C4×C11311yescharacteristic
208C2×C4C4×D4×C11312yes—
209C2×C4#120×C11311yescharacteristic
210C2×C4#121×C11312yes—
211C8—24no—
212C8—44no—
213C8—82no—
214C22—21no—
215C22—22no—
216C22—42no—
217C22—44no—
218C22#386×C11311yescharacteristic
219C4—21no—
220C4—22no—
221C4—22no—
222C4—42no—
223C4—82no—
224C4#453×C11312yes—
225C2—41no—
226C2—82no—
227C2C113×#188711yescharacteristic
228C2C113×#190212yes—
subgroupG/H
center, socleC22×C113#386
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radical#532×C113C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1556C2semidirect
5. C113×#1291C2semidirect
110. #9421C113direct (N × H)
117. #1556C2×C113semidirect
119. #1291C2×C113semidirect
120. C113#9421direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#31522
C113×#29802
C113×#15562
C113×#15362
C113×#12912
#9421113