Finite Group Databasebeta

← C113×#13681 #43281701

Subgroups — C113×#13681 #43281701

Order 28928.

398 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3291C211yesmaximal, characteristic, complemented
2C113×#2204C212yesmaximal, complemented
3C113×#1624C211yesmaximal, characteristic, complemented
4C113×#1410C211yesmaximal, characteristic, complemented
5C113×#1405C212yesmaximal, complemented
6#577×C113—22no—
7#555×C113C2211yescharacteristic, complemented
8#492×C113C2211yescharacteristic
9#471×C113—22no—
10#459×C113—21no—
11#456×C113C2212yes—
12#454×C113—22no—
13#453×C113—21no—
14#443×C113—21no—
15#356×C113C2212yescomplemented
16#355×C113—22no—
17#333×C113C2211yescharacteristic, complemented
18D4⋊C8×C113—21no—
192−1+4×C113D412yes—
20H(5,𝔽2)×C113—21no—
21#137×C113—22no—
22#137×C113—42no—
23AGL(1,ℤ/8)×C113—22no—
24AGL(1,ℤ/8)×C113—42no—
25AGL(1,ℤ/8)×C113—42no—
26#135×C113—21no—
27#135×C113—42no—
28C2×SD16×C113—22no—
29C2×SD16×C113—42no—
30C2×D8×C113—41no—
31#131×C113—22no—
32C4⋊Q8×C113C2311yescharacteristic
33#127×C113D411yescharacteristic
34#124×C113—22no—
35#121×C113—41no—
36C4×D4×C113—21no—
37#117×C113—41no—
38#108×C113—21no—
39C4⋊C8×C113—21no—
40#104×C113—22no—
41#104×C113—42no—
42#102×C113—41no—
43#101×C113—22no—
44#101×C113D412yes—
45#100×C113—21no—
46C4×C8×C113D411yescharacteristic
47#41×C113—22no—
48#41×C113—42no—
49#41×C113—42no—
50#41×C113—42no—
51C2×Q8×C113—42no—
52C2×Q8×C113C2×D412yes—
53C2×D4×C113—21no—
54C2×D4×C113—22no—
55C2×D4×C113—21no—
56C2×D4×C113—41no—
57C2×D4×C113—42no—
58C2×D4×C113—81no—
59C22×C4×C113—41no—
60Q16×C113—21no—
61Q16×C113—42no—
62SD16×C113—22no—
63SD16×C113—42no—
64SD16×C113—42no—
65SD16×C113—42no—
66SD16×C113—42no—
67SD16×C113—82no—
68D8×C113—21no—
69D8×C113—42no—
70D8×C113—82no—
71D8×C113—82no—
72M16×C113—22no—
73M16×C113—42no—
74M16×C113—42no—
75C2×C8×C113—21no—
76C2×C8×C113—42no—
77C2×C8×C113—41no—
78C4⋊C4×C113—21no—
79C4⋊C4×C113—41no—
80C22⋊C4×C113—42no—
81C22⋊C4×C113—41no—
82C42×C113—22no—
83C42×C113C2×D411yescharacteristic
84C23×C113—41no—
85C23×C113—41no—
86C23×C113—81no—
87Q8×C113—22no—
88Q8×C113—42no—
89Q8×C113—42no—
90D4×C113—22no—
91D4×C113—42no—
92D4×C113—41no—
93D4×C113—41no—
94D4×C113—42no—
95D4×C113—42no—
96D4×C113—81no—
97D4×C113—81no—
98D4×C113—82no—
99D4×C113—82no—
100C2×C4×C113—21no—
101C2×C4×C113—22no—
102C2×C4×C113—42no—
103C2×C4×C113—41no—
104C2×C4×C113—81no—
105C2×C4×C113—81no—
106C2×C4×C113—82no—
107C2×C4×C113—81no—
108C2×C4×C113#12011yescharacteristic
109C8×C113—21no—
110C8×C113—21no—
111C8×C113—42no—
112C8×C113—81no—
113C8×C113—82no—
114C22×C113—42no—
115C22×C113—81no—
116C22×C113—81no—
117C22×C113—81no—
118C22×C113—81no—
119C22×C113—161no—
120C22×C113—321no—
121C22×C113B(4,𝔽2)11yescharacteristic
122C4×C113—21no—
123C4×C113—21no—
124C4×C113—21no—
125C4×C113—42no—
126C4×C113—42no—
127C4×C113—81no—
128#13681C11311yesmaximal, characteristic, direct product factor, Sylow
129C2×C113—21no—
130C2×C113—82no—
131C2×C113—161no—
132C2×C113—161no—
133C2×C113#219611yescharacteristic
134#3291C2×C11311yescharacteristic, complemented
135#2204C2×C11312yescomplemented
136#1624C2×C11311yescharacteristic, complemented
137#1410C2×C11311yescharacteristic, complemented
138#1405C2×C11312yescomplemented
139C113#1368111yescharacteristic, direct product factor, Sylow
140#577—22no—
141#555C22×C11311yescharacteristic, complemented
142#492C22×C11311yescharacteristic
143#471—22no—
144#459—21no—
145#456C22×C11312yes—
146#454—22no—
147#453—21no—
148#443—21no—
149#356C22×C11312yescomplemented
150#355—22no—
151#333C22×C11311yescharacteristic, complemented
152D4⋊C8—21no—
1532−1+4D4×C11312yes—
154H(5,𝔽2)—21no—
155#137—22no—
156#137—42no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—42no—
159AGL(1,ℤ/8)—42no—
160#135—21no—
161#135—42no—
162C2×SD16—22no—
163C2×SD16—42no—
164C2×D8—41no—
165#131—22no—
166C4⋊Q8C23×C11311yescharacteristic
167#127D4×C11311yescharacteristic
168#124—22no—
169#121—41no—
170C4×D4—21no—
171#117—41no—
172#108—21no—
173C4⋊C8—21no—
174#104—22no—
175#104—42no—
176#102—41no—
177#101—22no—
178#101D4×C11312yes—
179#100—21no—
180C4×C8D4×C11311yescharacteristic
181#41—22no—
182#41—42no—
183#41—42no—
184#41—42no—
185C2×Q8—42no—
186C2×Q8C2×D4×C11312yes—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—41no—
191C2×D4—42no—
192C2×D4—81no—
193C22×C4—41no—
194Q16—21no—
195Q16—42no—
196SD16—22no—
197SD16—42no—
198SD16—42no—
199SD16—42no—
200SD16—42no—
201SD16—82no—
202D8—21no—
203D8—42no—
204D8—82no—
205D8—82no—
206M16—22no—
207M16—42no—
208M16—42no—
209C2×C8—21no—
210C2×C8—42no—
211C2×C8—41no—
212C4⋊C4—21no—
213C4⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—41no—
216C42—22no—
217C42C2×D4×C11311yescharacteristic
218C23—41no—
219C23—41no—
220C23—81no—
221Q8—22no—
222Q8—42no—
223Q8—42no—
224D4—22no—
225D4—42no—
226D4—41no—
227D4—41no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—82no—
233D4—82no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4#120×C11311yescharacteristic
243C8—21no—
244C8—21no—
245C8—42no—
246C8—81no—
247C8—82no—
248C22—42no—
249C22—81no—
250C22—81no—
251C22—81no—
252C22—81no—
253C22—161no—
254C22—321no—
255C22B(4,𝔽2)×C11311yescharacteristic
256C4—21no—
257C4—21no—
258C4—21no—
259C4—42no—
260C4—42no—
261C4—81no—
262C2—21no—
263C2—82no—
264C2—161no—
265C2—161no—
266C2C113×#219611yescharacteristic
subgroupG/H
center, socleC2×C113#2196
commutator, Frattini, cosocleC4⋊Q8C23×C113
LCSG ▷ C4⋊Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C113 ◁ C2×C4×C113 ◁ C4⋊Q8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3291C2semidirect
2. C113×#2204C2semidirect
3. C113×#1624C2semidirect
4. C113×#1410C2semidirect
5. C113×#1405C2semidirect
7. #555×C113C22semidirect
15. #356×C113C22semidirect
17. #333×C113C22semidirect
128. #13681C113direct (N × H)
134. #3291C2×C113semidirect
135. #2204C2×C113semidirect
136. #1624C2×C113semidirect
137. #1410C2×C113semidirect
138. #1405C2×C113semidirect
139. C113#13681direct (N × H)
141. #555C22×C113semidirect
149. #356C22×C113semidirect
151. #333C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#32912
C113×#22042
C113×#16242
C113×#14102
C113×#14052
#13681113