Finite Group Databasebeta

← C113×#8734 #43276754

Subgroups — C113×#8734 #43276754

Order 28928.

622 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2273C211yesmaximal, characteristic
2C2×#323×C113C212yesmaximal
3C113×#1282C214yesmaximal, complemented
4C22×C22⋊C4×C113C411yescharacteristic
5C22×C22⋊C4×C113C411yescharacteristic
6C22×C22⋊C4×C113C2211yescharacteristic
7C2×C22⋊C8×C113C2214yes—
8C4×C22⋊C4×C113—22no—
9C4×C22⋊C4×C113—22no—
10C4×C22⋊C4×C113C412yes—
11C4×C22⋊C4×C113C2212yes—
12#323×C113—22no—
13#323×C113—22no—
14C25×C113C2×C411yescharacteristic
15C23×C4×C113—21no—
16C23×C4×C113—21no—
17C23×C4×C113C2×C411yescharacteristic
18C23×C4×C113C2311yescharacteristic
19C22×C8×C113—24no—
20C2×C22⋊C4×C113—21no—
21C2×C22⋊C4×C113—21no—
22C2×C22⋊C4×C113—22no—
23C2×C22⋊C4×C113—24no—
24C2×C22⋊C4×C113—24no—
25C2×C22⋊C4×C113C814yescomplemented
26C2×C22⋊C4×C113C2×C412yes—
27C2×C22⋊C4×C113C2×C412yes—
28C2×C22⋊C4×C113D412yes—
29C2×C22⋊C4×C113D412yes—
30C2×C42×C113—22no—
31C2×C42×C113—22no—
32C22⋊C8×C113—24no—
33C22⋊C8×C113—24no—
34#95×C113—22no—
35#95×C113—22no—
36C24×C113—22no—
37C24×C113—22no—
38C24×C113—81no—
39C24×C113—81no—
40C24×C113C22⋊C411yescharacteristic
41C24×C113C22⋊C411yescharacteristic
42C24×C113C2×C812yes—
43C24×C113M1612yes—
44C24×C113C22×C411yescharacteristic
45C22×C4×C113—22no—
46C22×C4×C113—22no—
47C22×C4×C113—24no—
48C22×C4×C113—24no—
49C22×C4×C113—22no—
50C22×C4×C113—81no—
51C22×C4×C113—81no—
52C22×C4×C113—81no—
53C22×C4×C113—81no—
54C22×C4×C113—81no—
55C22×C4×C113—81no—
56C22×C4×C113C22⋊C412yes—
57C22×C4×C113C2×D412yes—
58C22×C4×C113#4114yes—
59C2×C8×C113—44no—
60C2×C8×C113—84no—
61C22⋊C4×C113—24no—
62C22⋊C4×C113—24no—
63C22⋊C4×C113—22no—
64C22⋊C4×C113—22no—
65C22⋊C4×C113—24no—
66C22⋊C4×C113—24no—
67C22⋊C4×C113C2×C814yes—
68C22⋊C4×C113M1614yes—
69C42×C113—82no—
70C42×C113—82no—
71C23×C113—21no—
72C23×C113—21no—
73C23×C113—21no—
74C23×C113—21no—
75C23×C113—24no—
76C23×C113—24no—
77C23×C113—41no—
78C23×C113—41no—
79C23×C113—41no—
80C23×C113—41no—
81C23×C113—41no—
82C23×C113—41no—
83C23×C113—82no—
84C23×C113—82no—
85C23×C113—82no—
86C23×C113—82no—
87C23×C113—84no—
88C23×C113C22⋊C812yes—
89C23×C113C22⋊C812yes—
90C23×C113C2×C22⋊C411yescharacteristic
91C23×C113#11712yes—
92C23×C113C22×C811yescharacteristic
93C23×C113C2×M1611yescharacteristic
94C23×C113C2×M1612yes—
95C2×C4×C113—22no—
96C2×C4×C113—24no—
97C2×C4×C113—24no—
98C2×C4×C113—42no—
99C2×C4×C113—44no—
100C2×C4×C113—42no—
101C2×C4×C113—42no—
102C2×C4×C113—42no—
103C2×C4×C113—42no—
104C2×C4×C113—42no—
105C2×C4×C113—82no—
106C2×C4×C113—84no—
107C2×C4×C113—84no—
108C2×C4×C113#12314yes—
109C8×C113—84no—
110C22×C113—21no—
111C22×C113—22no—
112C22×C113—21no—
113C22×C113—22no—
114C22×C113—22no—
115C22×C113—22no—
116C22×C113—41no—
117C22×C113—41no—
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—42no—
121C22×C113—42no—
122C22×C113—42no—
123C22×C113—41no—
124C22×C113—41no—
125C22×C113—41no—
126C22×C113—41no—
127C22×C113—84no—
128C22×C113—84no—
129C22×C113#38111yescharacteristic
130C22×C113C2×C22⋊C811yescharacteristic
131C22×C113#40711yescharacteristic
132C22×C113#43112yes—
133C22×C113#43212yes—
134C4×C113—24no—
135C4×C113—44no—
136C4×C113—44no—
137C4×C113—42no—
138#8734C11311yesmaximal, characteristic, direct product factor, Sylow
139C2×C113—21no—
140C2×C113—21no—
141C2×C113—22no—
142C2×C113—22no—
143C2×C113—42no—
144C2×C113—42no—
145C2×C113#181711yescharacteristic
146C2×C113#182811yescharacteristic
147C2×C113#182911yescharacteristic
148#2273C2×C11311yescharacteristic
149C2×#323C2×C11312yes—
150#1282C2×C11314yescomplemented
151C113#873411yescharacteristic, direct product factor, Sylow
152C22×C22⋊C4C4×C11311yescharacteristic
153C22×C22⋊C4C4×C11311yescharacteristic
154C22×C22⋊C4C22×C11311yescharacteristic
155C2×C22⋊C8C22×C11314yes—
156C4×C22⋊C4—22no—
157C4×C22⋊C4—22no—
158C4×C22⋊C4C4×C11312yes—
159C4×C22⋊C4C22×C11312yes—
160#323—22no—
161#323—22no—
162C25C2×C4×C11311yescharacteristic
163C23×C4—21no—
164C23×C4—21no—
165C23×C4C2×C4×C11311yescharacteristic
166C23×C4C23×C11311yescharacteristic
167C22×C8—24no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—24no—
172C2×C22⋊C4—24no—
173C2×C22⋊C4C8×C11314yescomplemented
174C2×C22⋊C4C2×C4×C11312yes—
175C2×C22⋊C4C2×C4×C11312yes—
176C2×C22⋊C4D4×C11312yes—
177C2×C22⋊C4D4×C11312yes—
178C2×C42—22no—
179C2×C42—22no—
180C22⋊C8—24no—
181C22⋊C8—24no—
182#95—22no—
183#95—22no—
184C24—22no—
185C24—22no—
186C24—81no—
187C24—81no—
188C24C22⋊C4×C11311yescharacteristic
189C24C22⋊C4×C11311yescharacteristic
190C24C2×C8×C11312yes—
191C24M16×C11312yes—
192C24C22×C4×C11311yescharacteristic
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—24no—
197C22×C4—22no—
198C22×C4—81no—
199C22×C4—81no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4C22⋊C4×C11312yes—
205C22×C4C2×D4×C11312yes—
206C22×C4#41×C11314yes—
207C2×C8—44no—
208C2×C8—84no—
209C22⋊C4—24no—
210C22⋊C4—24no—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4C2×C8×C11314yes—
216C22⋊C4M16×C11314yes—
217C42—82no—
218C42—82no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—24no—
224C23—24no—
225C23—41no—
226C23—41no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—82no—
232C23—82no—
233C23—82no—
234C23—82no—
235C23—84no—
236C23C22⋊C8×C11312yes—
237C23C22⋊C8×C11312yes—
238C23C2×C22⋊C4×C11311yescharacteristic
239C23#117×C11312yes—
240C23C22×C8×C11311yescharacteristic
241C23C2×M16×C11311yescharacteristic
242C23C2×M16×C11312yes—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—84no—
255C2×C4—84no—
256C2×C4#123×C11314yes—
257C8—84no—
258C22—21no—
259C22—22no—
260C22—21no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—84no—
276C22—84no—
277C22#381×C11311yescharacteristic
278C22C2×C22⋊C8×C11311yescharacteristic
279C22#407×C11311yescharacteristic
280C22#431×C11312yes—
281C22#432×C11312yes—
282C4—24no—
283C4—44no—
284C4—44no—
285C4—42no—
286C2—21no—
287C2—21no—
288C2—22no—
289C2—22no—
290C2—42no—
291C2—42no—
292C2C113×#181711yescharacteristic
293C2C113×#182811yescharacteristic
294C2C113×#182911yescharacteristic
subgroupG/H
center, socleC22×C113#381
commutatorC23C22×C8×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC25×C113C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1282C2semidirect
25. C2×C22⋊C4×C113C8semidirect
138. #8734C113direct (N × H)
150. #1282C2×C113semidirect
151. C113#8734direct (N × H)
173. C2×C22⋊C4C8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#22732
C2×#323×C1132
C113×#12822
#8734113