Finite Group Databasebeta

← C113×#8495 #43276515

Subgroups — C113×#8495 #43276515

Order 28928.

620 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3556C211yesmaximal, characteristic
2C113×#1995C211yesmaximal, characteristic
3C113×#1559C212yesmaximal
4C113×#1537C211yesmaximal, characteristic
5C113×#1506C212yesmaximal
6#564×C113—22no—
7#557×C113—22no—
8#557×C113—22no—
9#557×C113C414yescomplemented
10#541×C113—24no—
11#541×C113—22no—
12#533×C113C2212yes—
13#533×C113C2211yescharacteristic
14#432×C113C2212yes—
15#423×C113C2211yescharacteristic
16#376×C113C2211yescharacteristic
17#339×C113—22no—
18#333×C113—22no—
19#332×C113—22no—
20#330×C113—22no—
21#328×C113—24no—
22C2×M16×C113—21no—
23C4⋊Q8×C113—22no—
24C4⋊Q8×C113—24no—
25C4⋊Q8×C113C2×C412yes—
26C4⋊Q8×C113D412yes—
27C4⋊Q8×C113D412yes—
28#126×C113—28no—
29#125×C113—22no—
30#125×C113—28no—
31#125×C113—28no—
32#125×C113—24no—
33#125×C113—28no—
34#125×C113—22no—
35#125×C113D412yes—
36C22⋊Q8×C113—22no—
37C22⋊Q8×C113—22no—
38C22⋊Q8×C113D414yes—
39C4×Q8×C113—24no—
40C4×Q8×C113—24no—
41C4×Q8×C113—24no—
42C4×Q8×C113—22no—
43C4×Q8×C113—22no—
44C4×Q8×C113C2×C414yes—
45#117×C113—22no—
46#117×C113D412yes—
47C2×C42×C113—21no—
48C2×C42×C113C2311yescharacteristic
49C4⋊C8×C113—22no—
50C4⋊C8×C113—22no—
51C22⋊C8×C113—22no—
52#97×C113—22no—
53#95×C113—22no—
54C2×Q8×C113—22no—
55C2×Q8×C113—22no—
56C2×Q8×C113C22⋊C414yes—
57C22×C4×C113—41no—
58C22×C4×C113C2×D411yescharacteristic
59C22×C4×C113C2×D412yes—
60M16×C113—42no—
61C2×C8×C113—42no—
62C2×C8×C113—41no—
63C4⋊C4×C113—28no—
64C4⋊C4×C113—28no—
65C4⋊C4×C113—28no—
66C4⋊C4×C113—22no—
67C4⋊C4×C113—24no—
68C4⋊C4×C113—22no—
69C4⋊C4×C113—22no—
70C4⋊C4×C113—22no—
71C4⋊C4×C113—24no—
72C4⋊C4×C113—24no—
73C4⋊C4×C113C22⋊C414yes—
74C4⋊C4×C113C22⋊C414yes—
75C22⋊C4×C113—24no—
76C22⋊C4×C113—22no—
77C42×C113—28no—
78C42×C113—24no—
79C42×C113—22no—
80C42×C113—22no—
81C42×C113—41no—
82C42×C113C22×C411yescharacteristic
83C42×C113C2×D411yescharacteristic
84C42×C113C2×D412yes—
85C23×C113#12011yescharacteristic
86Q8×C113—44no—
87Q8×C113—44no—
88Q8×C113—42no—
89Q8×C113—42no—
90C2×C4×C113—21no—
91C2×C4×C113—21no—
92C2×C4×C113—24no—
93C2×C4×C113—24no—
94C2×C4×C113—24no—
95C2×C4×C113—42no—
96C2×C4×C113—42no—
97C2×C4×C113—82no—
98C2×C4×C113C2×C22⋊C412yes—
99C2×C4×C113C2×C22⋊C411yescharacteristic
100C2×C4×C113#12012yes—
101C2×C4×C113#12011yescharacteristic
102C8×C113—82no—
103C8×C113—81no—
104C22×C113—21no—
105C22×C113—22no—
106C22×C113#37911yescharacteristic
107C4×C113—21no—
108C4×C113—22no—
109C4×C113—22no—
110C4×C113—44no—
111C4×C113—44no—
112C4×C113—44no—
113C4×C113—82no—
114C4×C113#45411yescharacteristic
115C4×C113#45611yescharacteristic
116#8495C11311yesmaximal, characteristic, direct product factor, Sylow
117C2×C113—41no—
118C2×C113#179311yescharacteristic
119C2×C113#179612yes—
120#3556C2×C11311yescharacteristic
121#1995C2×C11311yescharacteristic
122#1559C2×C11312yes—
123#1537C2×C11311yescharacteristic
124#1506C2×C11312yes—
125C113#849511yescharacteristic, direct product factor, Sylow
126#564—22no—
127#557—22no—
128#557—22no—
129#557C4×C11314yescomplemented
130#541—24no—
131#541—22no—
132#533C22×C11312yes—
133#533C22×C11311yescharacteristic
134#432C22×C11312yes—
135#423C22×C11311yescharacteristic
136#376C22×C11311yescharacteristic
137#339—22no—
138#333—22no—
139#332—22no—
140#330—22no—
141#328—24no—
142C2×M16—21no—
143C4⋊Q8—22no—
144C4⋊Q8—24no—
145C4⋊Q8C2×C4×C11312yes—
146C4⋊Q8D4×C11312yes—
147C4⋊Q8D4×C11312yes—
148#126—28no—
149#125—22no—
150#125—28no—
151#125—28no—
152#125—24no—
153#125—28no—
154#125—22no—
155#125D4×C11312yes—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158C22⋊Q8D4×C11314yes—
159C4×Q8—24no—
160C4×Q8—24no—
161C4×Q8—24no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8C2×C4×C11314yes—
165#117—22no—
166#117D4×C11312yes—
167C2×C42—21no—
168C2×C42C23×C11311yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C22⋊C8—22no—
172#97—22no—
173#95—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8C22⋊C4×C11314yes—
177C22×C4—41no—
178C22×C4C2×D4×C11311yescharacteristic
179C22×C4C2×D4×C11312yes—
180M16—42no—
181C2×C8—42no—
182C2×C8—41no—
183C4⋊C4—28no—
184C4⋊C4—28no—
185C4⋊C4—28no—
186C4⋊C4—22no—
187C4⋊C4—24no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4C22⋊C4×C11314yes—
194C4⋊C4C22⋊C4×C11314yes—
195C22⋊C4—24no—
196C22⋊C4—22no—
197C42—28no—
198C42—24no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42C22×C4×C11311yescharacteristic
203C42C2×D4×C11311yescharacteristic
204C42C2×D4×C11312yes—
205C23#120×C11311yescharacteristic
206Q8—44no—
207Q8—44no—
208Q8—42no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4C2×C22⋊C4×C11312yes—
219C2×C4C2×C22⋊C4×C11311yescharacteristic
220C2×C4#120×C11312yes—
221C2×C4#120×C11311yescharacteristic
222C8—82no—
223C8—81no—
224C22—21no—
225C22—22no—
226C22#379×C11311yescharacteristic
227C4—21no—
228C4—22no—
229C4—22no—
230C4—44no—
231C4—44no—
232C4—44no—
233C4—82no—
234C4#454×C11311yescharacteristic
235C4#456×C11311yescharacteristic
236C2—41no—
237C2C113×#179311yescharacteristic
238C2C113×#179612yes—
subgroupG/H
center, socleC22×C113#379
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC23×C113#120
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
9. #557×C113C4semidirect
116. #8495C113direct (N × H)
125. C113#8495direct (N × H)
129. #557C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35562
C113×#19952
C113×#15592
C113×#15372
C113×#15062
#8495113