Finite Group Databasebeta

← C113×#10361 #43278381

Subgroups — C113×#10361 #43278381

Order 28928.

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2845C211yesmaximal, characteristic
2C113×#1993C212yesmaximal
3C113×#1960C211yesmaximal, characteristic
4C113×#1295C211yesmaximal, characteristic
5C113×#1295C212yesmaximal
6C2×C4⋊Q8×C113C2211yescharacteristic
7C2×#103×C113—22no—
8C2×#97×C113C2211yescharacteristic
9C2×#97×C113C2212yes—
10#398×C113—22no—
11#398×C113—22no—
12#398×C113—22no—
13#382×C113C2211yescharacteristic
14#382×C113C2212yes—
15#340×C113—22no—
16#340×C113—22no—
17C22×Q8×C113—21no—
18C22×C8×C113—22no—
19C22×C8×C113—21no—
20C4⋊Q8×C113—22no—
21C4⋊Q8×C113—21no—
22C4⋊Q8×C113Q812yes—
23C2×C4⋊C4×C113—22no—
24C2×C4⋊C4×C113—22no—
25C2×C4⋊C4×C113—22no—
26C2×C4⋊C4×C113—22no—
27C2×C4⋊C4×C113D412yes—
28C2×C4⋊C4×C113D412yes—
29C2×C4⋊C4×C113D412yes—
30C2×C42×C113C2311yescharacteristic
31#103×C113—44no—
32#97×C113—22no—
33#97×C113—22no—
34#97×C113—22no—
35#95×C113—22no—
36#95×C113—22no—
37#95×C113—22no—
38#95×C113—22no—
39C2×Q8×C113—22no—
40C2×Q8×C113—42no—
41C2×Q8×C113—42no—
42C2×Q8×C113—41no—
43C22×C4×C113—22no—
44C22×C4×C113—22no—
45C22×C4×C113—22no—
46C22×C4×C113—41no—
47C22×C4×C113C2×D412yes—
48C22×C4×C113C2×D411yescharacteristic
49C2×C8×C113—22no—
50C2×C8×C113—24no—
51C2×C8×C113—41no—
52C2×C8×C113—42no—
53C2×C8×C113—42no—
54C2×C8×C113—41no—
55C4⋊C4×C113—24no—
56C4⋊C4×C113—42no—
57C4⋊C4×C113—42no—
58C4⋊C4×C113—42no—
59C4⋊C4×C113—42no—
60C4⋊C4×C113—82no—
61C4⋊C4×C113—82no—
62C4⋊C4×C113—82no—
63C42×C113C2×Q811yescharacteristic
64C42×C113#4112yes—
65C42×C113#4111yescharacteristic
66C23×C113#12011yescharacteristic
67Q8×C113—44no—
68Q8×C113—82no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—42no—
74C2×C4×C113—42no—
75C2×C4×C113—42no—
76C2×C4×C113—42no—
77C2×C4×C113—42no—
78C2×C4×C113—42no—
79C2×C4×C113—42no—
80C2×C4×C113—42no—
81C2×C4×C113—42no—
82C2×C4×C113—42no—
83C2×C4×C113—81no—
84C2×C4×C113—81no—
85C2×C4×C113C22⋊Q812yes—
86C2×C4×C113C22⋊Q811yescharacteristic
87C2×C4×C113#12412yes—
88C2×C4×C113#12411yescharacteristic
89C8×C113—42no—
90C8×C113—44no—
91C22×C113#39311yescharacteristic
92C22×C113#45311yescharacteristic
93C22×C113#45411yescharacteristic
94C22×C113#45512yes—
95C22×C113#45612yes—
96C4×C113—21no—
97C4×C113—21no—
98C4×C113—22no—
99C4×C113—22no—
100C4×C113—82no—
101C4×C113—82no—
102C4×C113—82no—
103C4×C113—82no—
104#10361C11311yesmaximal, characteristic, direct product factor, Sylow
105C2×C113#166112yes—
106C2×C113#166211yescharacteristic
107C2×C113#166311yescharacteristic
108C2×C113#202711yescharacteristic
109C2×C113#202812yes—
110#2845C2×C11311yescharacteristic
111#1993C2×C11312yes—
112#1960C2×C11311yescharacteristic
113#1295C2×C11311yescharacteristic
114#1295C2×C11312yes—
115C113#1036111yescharacteristic, direct product factor, Sylow
116C2×C4⋊Q8C22×C11311yescharacteristic
117C2×#103—22no—
118C2×#97C22×C11311yescharacteristic
119C2×#97C22×C11312yes—
120#398—22no—
121#398—22no—
122#398—22no—
123#382C22×C11311yescharacteristic
124#382C22×C11312yes—
125#340—22no—
126#340—22no—
127C22×Q8—21no—
128C22×C8—22no—
129C22×C8—21no—
130C4⋊Q8—22no—
131C4⋊Q8—21no—
132C4⋊Q8Q8×C11312yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4D4×C11312yes—
138C2×C4⋊C4D4×C11312yes—
139C2×C4⋊C4D4×C11312yes—
140C2×C42C23×C11311yescharacteristic
141#103—44no—
142#97—22no—
143#97—22no—
144#97—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—41no—
157C22×C4C2×D4×C11312yes—
158C22×C4C2×D4×C11311yescharacteristic
159C2×C8—22no—
160C2×C8—24no—
161C2×C8—41no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—82no—
171C4⋊C4—82no—
172C4⋊C4—82no—
173C42C2×Q8×C11311yescharacteristic
174C42#41×C11312yes—
175C42#41×C11311yescharacteristic
176C23#120×C11311yescharacteristic
177Q8—44no—
178Q8—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4C22⋊Q8×C11312yes—
196C2×C4C22⋊Q8×C11311yescharacteristic
197C2×C4#124×C11312yes—
198C2×C4#124×C11311yescharacteristic
199C8—42no—
200C8—44no—
201C22#393×C11311yescharacteristic
202C22#453×C11311yescharacteristic
203C22#454×C11311yescharacteristic
204C22#455×C11312yes—
205C22#456×C11312yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—82no—
214C2C113×#166112yes—
215C2C113×#166211yescharacteristic
216C2C113×#166311yescharacteristic
217C2C113×#202711yescharacteristic
218C2C113×#202812yes—
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
104. #10361C113direct (N × H)
115. C113#10361direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#28452
C113×#19932
C113×#19602
C113×#12952
#10361113