Finite Group Databasebeta

← C113×#13612 #43281632

Subgroups — C113×#13612 #43281632

Order 28928.

304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3223C211yesmaximal, characteristic
2C113×#2135C211yesmaximal, characteristic
3C113×#2133C211yesmaximal, characteristic
4C113×#1413C212yesmaximal, complemented
5C113×#1411C212yesmaximal, complemented
6#541×C113C411yescharacteristic
7#536×C113C2211yescharacteristic
8#497×C113C411yescharacteristic
9#494×C113C2211yescharacteristic
10#491×C113C2211yescharacteristic
11#488×C113C411yescharacteristic
12#464×C113—21no—
13#462×C113—21no—
14#452×C113—21no—
15#451×C113—21no—
16#433×C113C411yescharacteristic
17#413×C113—21no—
18C2×#101×C113—21no—
19#356×C113—21no—
20#356×C113C2212yes—
21#356×C113C2212yes—
22#355×C113—21no—
23C2×#41×C113D411yescharacteristic
24C22×Q8×C113D411yescharacteristic
25C2×Q16×C113—21no—
26C2×Q16×C113—21no—
27C2×Q16×C113—21no—
28C2×SD16×C113—21no—
29C2×M16×C113—41no—
30C2×M16×C113—41no—
31C4⋊Q8×C113C2×C411yescharacteristic
32C4⋊Q8×C113D411yescharacteristic
33C4⋊Q8×C113C2311yescharacteristic
34#126×C113—41no—
35#125×C113—41no—
36#125×C113C2×C411yescharacteristic
37#124×C113C2×C411yescharacteristic
38#124×C113D411yescharacteristic
39#123×C113—41no—
40C22⋊Q8×C113—21no—
41C22⋊Q8×C113—41no—
42C4×Q8×C113—21no—
43#117×C113C2×C411yescharacteristic
44C4⋊C8×C113—21no—
45#103×C113—21no—
46#103×C113—21no—
47#103×C113—21no—
48#102×C113—21no—
49#101×C113—22no—
50#101×C113—22no—
51#101×C113—41no—
52#100×C113—41no—
53C22⋊C8×C113—21no—
54#97×C113C2×C411yescharacteristic
55C4×C8×C113C2×C411yescharacteristic
56#41×C113—81no—
57C2×Q8×C113—21no—
58C2×Q8×C113—21no—
59C2×Q8×C113—81no—
60C2×Q8×C113C22⋊C411yescharacteristic
61C2×Q8×C113C2×D411yescharacteristic
62C2×Q8×C113C2×D411yescharacteristic
63C2×D4×C113—21no—
64C2×D4×C113C22⋊C411yescharacteristic
65C22×C4×C113—21no—
66C22×C4×C113—21no—
67C22×C4×C113C22⋊C411yescharacteristic
68Q16×C113—81no—
69Q16×C113—81no—
70Q16×C113—81no—
71SD16×C113—81no—
72M16×C113—42no—
73M16×C113—42no—
74M16×C113—81no—
75M16×C113—81no—
76C2×C8×C113—21no—
77C2×C8×C113—21no—
78C2×C8×C113—81no—
79C2×C8×C113—81no—
80C4⋊C4×C113—21no—
81C4⋊C4×C113—21no—
82C4⋊C4×C113—41no—
83C4⋊C4×C113—41no—
84C4⋊C4×C113—41no—
85C4⋊C4×C113—41no—
86C4⋊C4×C113—41no—
87C4⋊C4×C113—41no—
88C22⋊C4×C113—21no—
89C22⋊C4×C113—41no—
90C22⋊C4×C113—41no—
91C22⋊C4×C113—41no—
92C42×C113—41no—
93C42×C113C22⋊C411yescharacteristic
94C42×C113C22×C411yescharacteristic
95C23×C113—21no—
96C23×C113#9911yescharacteristic
97Q8×C113—41no—
98Q8×C113—41no—
99Q8×C113—41no—
100Q8×C113—41no—
101Q8×C113—41no—
102Q8×C113—81no—
103D4×C113—41no—
104D4×C113—81no—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—41no—
111C2×C4×C113—41no—
112C2×C4×C113—41no—
113C2×C4×C113—41no—
114C2×C4×C113—41no—
115C2×C4×C113—41no—
116C2×C4×C113—41no—
117C2×C4×C113#9911yescharacteristic
118C2×C4×C113C2×C22⋊C411yescharacteristic
119C8×C113—41no—
120C8×C113—41no—
121C8×C113—82no—
122C8×C113—82no—
123C22×C113—21no—
124C22×C113—41no—
125C22×C113—41no—
126C22×C113—81no—
127C22×C113C2×#9911yescharacteristic
128C4×C113—21no—
129C4×C113—21no—
130C4×C113—41no—
131C4×C113—41no—
132C4×C113—41no—
133C4×C113—41no—
134C4×C113—41no—
135C4×C113—81no—
136C4×C113—81no—
137#13612C11311yesmaximal, characteristic, direct product factor, Sylow
138C2×C113—21no—
139C2×C113—41no—
140C2×C113—81no—
141C2×C113#212711yescharacteristic
142#3223C2×C11311yescharacteristic
143#2135C2×C11311yescharacteristic
144#2133C2×C11311yescharacteristic
145#1413C2×C11312yescomplemented
146#1411C2×C11312yescomplemented
147C113#1361211yescharacteristic, direct product factor, Sylow
148#541C4×C11311yescharacteristic
149#536C22×C11311yescharacteristic
150#497C4×C11311yescharacteristic
151#494C22×C11311yescharacteristic
152#491C22×C11311yescharacteristic
153#488C4×C11311yescharacteristic
154#464—21no—
155#462—21no—
156#452—21no—
157#451—21no—
158#433C4×C11311yescharacteristic
159#413—21no—
160C2×#101—21no—
161#356—21no—
162#356C22×C11312yes—
163#356C22×C11312yes—
164#355—21no—
165C2×#41D4×C11311yescharacteristic
166C22×Q8D4×C11311yescharacteristic
167C2×Q16—21no—
168C2×Q16—21no—
169C2×Q16—21no—
170C2×SD16—21no—
171C2×M16—41no—
172C2×M16—41no—
173C4⋊Q8C2×C4×C11311yescharacteristic
174C4⋊Q8D4×C11311yescharacteristic
175C4⋊Q8C23×C11311yescharacteristic
176#126—41no—
177#125—41no—
178#125C2×C4×C11311yescharacteristic
179#124C2×C4×C11311yescharacteristic
180#124D4×C11311yescharacteristic
181#123—41no—
182C22⋊Q8—21no—
183C22⋊Q8—41no—
184C4×Q8—21no—
185#117C2×C4×C11311yescharacteristic
186C4⋊C8—21no—
187#103—21no—
188#103—21no—
189#103—21no—
190#102—21no—
191#101—22no—
192#101—22no—
193#101—41no—
194#100—41no—
195C22⋊C8—21no—
196#97C2×C4×C11311yescharacteristic
197C4×C8C2×C4×C11311yescharacteristic
198#41—81no—
199C2×Q8—21no—
200C2×Q8—21no—
201C2×Q8—81no—
202C2×Q8C22⋊C4×C11311yescharacteristic
203C2×Q8C2×D4×C11311yescharacteristic
204C2×Q8C2×D4×C11311yescharacteristic
205C2×D4—21no—
206C2×D4C22⋊C4×C11311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C22⋊C4×C11311yescharacteristic
210Q16—81no—
211Q16—81no—
212Q16—81no—
213SD16—81no—
214M16—42no—
215M16—42no—
216M16—81no—
217M16—81no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—81no—
221C2×C8—81no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—41no—
235C42C22⋊C4×C11311yescharacteristic
236C42C22×C4×C11311yescharacteristic
237C23—21no—
238C23#99×C11311yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—81no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4#99×C11311yescharacteristic
260C2×C4C2×C22⋊C4×C11311yescharacteristic
261C8—41no—
262C8—41no—
263C8—82no—
264C8—82no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#99×C11311yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2C113×#212711yescharacteristic
subgroupG/H
center, socleC2×C113#2127
commutatorC42C22×C4×C113
Frattini, cosocleC4⋊Q8C23×C113
prime radicalC2×#41×C113D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C113 ◁ C22×C4×C113 ◁ #536×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. C113×#1413C2semidirect
5. C113×#1411C2semidirect
137. #13612C113direct (N × H)
145. #1413C2×C113semidirect
146. #1411C2×C113semidirect
147. C113#13612direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#32232
C113×#21352
C113×#21332
C113×#14132
C113×#14112
#13612113