Finite Group Databasebeta

← C113×#10576 #43278596

Subgroups — C113×#10576 #43278596

Order 28928.

406 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2571C211yesmaximal, characteristic
2C113×#1948C212yesmaximal
3C113×#1845C211yesmaximal, characteristic
4C113×#1296C211yesmaximal, characteristic
5C113×#1279C212yesmaximal
6C2×#107×C113—22no—
7C2×#106×C113—22no—
8C2×C4⋊C8×C113C2212yes—
9C2×C4×C8×C113C2211yescharacteristic
10#400×C113—22no—
11#389×C113—22no—
12#384×C113C2211yescharacteristic
13#384×C113C2211yescharacteristic
14#382×C113—22no—
15C4×C4⋊C4×C113C2212yes—
16#340×C113—22no—
17C22×C8×C113—21no—
18C22×C8×C113—22no—
19C2×C4⋊C4×C113—22no—
20C2×C4⋊C4×C113—22no—
21C2×C4⋊C4×C113—21no—
22C2×C4⋊C4×C113—22no—
23C2×C4⋊C4×C113D412yes—
24C2×C4⋊C4×C113D412yes—
25C2×C4⋊C4×C113D412yes—
26C2×C42×C113—22no—
27C2×C42×C113C2311yescharacteristic
28#107×C113—44no—
29#106×C113—44no—
30C4⋊C8×C113—22no—
31C4⋊C8×C113Q814yes—
32C4×C8×C113—21no—
33C4×C8×C113Q812yes—
34#95×C113—22no—
35#95×C113—24no—
36#95×C113—22no—
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—22no—
40C22×C4×C113—41no—
41C22×C4×C113C2×D411yescharacteristic
42C22×C4×C113C2×D412yes—
43C2×C8×C113—22no—
44C2×C8×C113—22no—
45C2×C8×C113—22no—
46C2×C8×C113—24no—
47C2×C8×C113—42no—
48C2×C8×C113—42no—
49C4⋊C4×C113—22no—
50C4⋊C4×C113—22no—
51C4⋊C4×C113—22no—
52C4⋊C4×C113—22no—
53C4⋊C4×C113—42no—
54C4⋊C4×C113—42no—
55C4⋊C4×C113—42no—
56C4⋊C4×C113—42no—
57C4⋊C4×C113—42no—
58C4⋊C4×C113—42no—
59C4⋊C4×C113—82no—
60C42×C113—42no—
61C42×C113—42no—
62C42×C113C2×Q811yescharacteristic
63C42×C113C2×Q812yes—
64C42×C113#4111yescharacteristic
65C23×C113#12011yescharacteristic
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—42no—
69C2×C4×C113—44no—
70C2×C4×C113—42no—
71C2×C4×C113—42no—
72C2×C4×C113—42no—
73C2×C4×C113—42no—
74C2×C4×C113—42no—
75C2×C4×C113—42no—
76C2×C4×C113—82no—
77C2×C4×C113—81no—
78C2×C4×C113C22⋊Q811yescharacteristic
79C2×C4×C113C22⋊Q812yes—
80C2×C4×C113C4⋊Q811yescharacteristic
81C2×C4×C113C4⋊Q812yes—
82C2×C4×C113#13512yes—
83C2×C4×C113#13512yes—
84C2×C4×C113AGL(1,ℤ/8)12yes—
85C2×C4×C113#13712yes—
86C8×C113—24no—
87C8×C113—44no—
88C22×C113#39511yescharacteristic
89C22×C113#44912yes—
90C22×C113#45212yes—
91C22×C113#45311yescharacteristic
92C22×C113#45611yescharacteristic
93C4×C113—21no—
94C4×C113—21no—
95C4×C113—82no—
96C4×C113—82no—
97C4×C113—82no—
98C4×C113—161no—
99C4×C113#47812yes—
100C4×C113#47912yes—
101C4×C113#49912yes—
102C4×C113#50112yes—
103#10576C11311yesmaximal, characteristic, direct product factor, Sylow
104C2×C113#162011yescharacteristic
105C2×C113#163411yescharacteristic
106C2×C113#165012yes—
107C2×C113#205912yes—
108C2×C113#206011yescharacteristic
109#2571C2×C11311yescharacteristic
110#1948C2×C11312yes—
111#1845C2×C11311yescharacteristic
112#1296C2×C11311yescharacteristic
113#1279C2×C11312yes—
114C113#1057611yescharacteristic, direct product factor, Sylow
115C2×#107—22no—
116C2×#106—22no—
117C2×C4⋊C8C22×C11312yes—
118C2×C4×C8C22×C11311yescharacteristic
119#400—22no—
120#389—22no—
121#384C22×C11311yescharacteristic
122#384C22×C11311yescharacteristic
123#382—22no—
124C4×C4⋊C4C22×C11312yes—
125#340—22no—
126C22×C8—21no—
127C22×C8—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4D4×C11312yes—
133C2×C4⋊C4D4×C11312yes—
134C2×C4⋊C4D4×C11312yes—
135C2×C42—22no—
136C2×C42C23×C11311yescharacteristic
137#107—44no—
138#106—44no—
139C4⋊C8—22no—
140C4⋊C8Q8×C11314yes—
141C4×C8—21no—
142C4×C8Q8×C11312yes—
143#95—22no—
144#95—24no—
145#95—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4C2×D4×C11311yescharacteristic
151C22×C4C2×D4×C11312yes—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—42no—
157C2×C8—42no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C42—42no—
170C42—42no—
171C42C2×Q8×C11311yescharacteristic
172C42C2×Q8×C11312yes—
173C42#41×C11311yescharacteristic
174C23#120×C11311yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4C22⋊Q8×C11311yescharacteristic
188C2×C4C22⋊Q8×C11312yes—
189C2×C4C4⋊Q8×C11311yescharacteristic
190C2×C4C4⋊Q8×C11312yes—
191C2×C4#135×C11312yes—
192C2×C4#135×C11312yes—
193C2×C4AGL(1,ℤ/8)×C11312yes—
194C2×C4#137×C11312yes—
195C8—24no—
196C8—44no—
197C22#395×C11311yescharacteristic
198C22#449×C11312yes—
199C22#452×C11312yes—
200C22#453×C11311yescharacteristic
201C22#456×C11311yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—161no—
208C4#478×C11312yes—
209C4#479×C11312yes—
210C4#499×C11312yes—
211C4#501×C11312yes—
212C2C113×#162011yescharacteristic
213C2C113×#163411yescharacteristic
214C2C113×#165012yes—
215C2C113×#205912yes—
216C2C113×#206011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C113#120
commutator, Frattini, cosocleC2×C42C23×C113
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
103. #10576C113direct (N × H)
114. C113#10576direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#25712
C113×#19482
C113×#18452
C113×#12962
C113×#12792
#10576113