Finite Group Databasebeta

← C131×#17654 #45703538

Subgroups — C131×#17654 #45703538

Order 33536.

960 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3518×C131C211yesmaximal, characteristic
2#2971×C131C211yesmaximal, characteristic, complemented
3#2875×C131C211yesmaximal, characteristic, complemented
4#1531×C131C213yesmaximal, complemented
5#1529×C131C213yesmaximal, complemented
6#1526×C131C213yesmaximal, complemented
7#1524×C131C213yesmaximal, complemented
8C2×#131×C131—21no—
9Q82×C131C411yescharacteristic
10#556×C131—23no—
11#556×C131C413yes—
12#555×C131C413yes—
13D4×Q8×C131C411yescharacteristic
14#548×C131—21no—
15#542×C131—23no—
16#533×C131C2213yes—
17#529×C131C2213yes—
18#519×C131—21no—
19C4×#41×C131C2211yescharacteristic
20C8×Q8×C131—21no—
21#436×C131—23no—
22#432×C131C2213yes—
23#405×C131—23no—
24C4×M16×C131C2213yes—
25C4×M16×C131C2213yes—
26C2×#97×C131C2213yes—
27#330×C131C2213yes—
28#330×C131C2213yes—
29#330×C131C2216yes—
30#329×C131C2211yescharacteristic
31#329×C131C2213yes—
32C2×#41×C131D411yescharacteristic
33C22×Q8×C131—21no—
34#131×C131—28no—
35C2×M16×C131—23no—
36C2×M16×C131—23no—
37C22×C8×C131—23no—
38C4⋊Q8×C131—23no—
39C4⋊Q8×C131C2×C413yes—
40C4⋊Q8×C131C2×C413yes—
41#126×C131—26no—
42#126×C131—23no—
43#125×C131C2313yes—
44#124×C131—23no—
45#124×C131—26no—
46#124×C131C2311yescharacteristic
47#123×C131—23no—
48C22⋊Q8×C131—23no—
49C22⋊Q8×C131—23no—
50C22⋊Q8×C131—23no—
51C22⋊Q8×C131C2×C413yes—
52#121×C131—23no—
53#121×C131C2×C413yes—
54C4×Q8×C131—21no—
55C4×Q8×C131—23no—
56C4×Q8×C131—23no—
57C4×Q8×C131—23no—
58C4×Q8×C131C2×C413yes—
59C4×Q8×C131C2×C411yescharacteristic
60C4×Q8×C131D411yescharacteristic
61C4×D4×C131—23no—
62C4×D4×C131C2×C413yes—
63C4×D4×C131C2×C413yes—
64C4×D4×C131D413yes—
65#117×C131—23no—
66#117×C131—23no—
67#117×C131C2×C416yes—
68#117×C131D413yes—
69C2×C42×C131C2313yes—
70C4⋊C8×C131—23no—
71C22⋊C8×C131—23no—
72#97×C131—23no—
73#97×C131C2311yescharacteristic
74#97×C131C2313yes—
75#97×C131C2311yescharacteristic
76#97×C131C2313yes—
77C4×C8×C131—23no—
78C4×C8×C131—23no—
79#41×C131—24no—
80C2×Q8×C131—23no—
81C2×Q8×C131—23no—
82C2×Q8×C131—44no—
83C2×Q8×C131C22⋊C411yescharacteristic
84C2×Q8×C131C22×C411yescharacteristic
85C2×D4×C131—23no—
86C2×D4×C131C22⋊C413yes—
87C2×D4×C131C22×C411yescharacteristic
88C22×C4×C131—23no—
89C22×C4×C131C22×C413yes—
90C22×C4×C131C2×D413yes—
91C22×C4×C131C2×D413yes—
92M16×C131—212no—
93M16×C131—46no—
94C2×C8×C131—212no—
95C2×C8×C131—21no—
96C2×C8×C131—23no—
97C2×C8×C131—21no—
98C2×C8×C131—23no—
99C4⋊C4×C131—23no—
100C4⋊C4×C131—23no—
101C4⋊C4×C131—23no—
102C4⋊C4×C131—23no—
103C4⋊C4×C131—23no—
104C4⋊C4×C131—23no—
105C4⋊C4×C131C22⋊C413yes—
106C4⋊C4×C131C22⋊C413yes—
107C4⋊C4×C131C22×C413yes—
108C4⋊C4×C131C22×C413yes—
109C22⋊C4×C131—26no—
110C22⋊C4×C131—23no—
111C22⋊C4×C131—23no—
112C22⋊C4×C131—23no—
113C22⋊C4×C131—21no—
114C22⋊C4×C131—21no—
115C22⋊C4×C131C22⋊C416yes—
116C42×C131—26no—
117C42×C131—23no—
118C42×C131C22×C413yes—
119C42×C131C2×D413yes—
120C42×C131C2×D413yes—
121C42×C131C2411yescharacteristic
122C23×C131—21no—
123C23×C131C2×C22⋊C413yes—
124Q8×C131—41no—
125Q8×C131—46no—
126Q8×C131—83no—
127Q8×C131#10414yes—
128D4×C131—26no—
129D4×C131—41no—
130D4×C131—83no—
131C2×C4×C131—26no—
132C2×C4×C131—21no—
133C2×C4×C131—23no—
134C2×C4×C131—23no—
135C2×C4×C131—43no—
136C2×C4×C131—43no—
137C2×C4×C131—46no—
138C2×C4×C131C2×C22⋊C413yes—
139C2×C4×C131C2×C22⋊C413yes—
140C2×C4×C131C2×C22⋊C413yes—
141C2×C4×C131C23×C411yescharacteristic
142C2×C4×C131C22×D411yescharacteristic
143C2×C4×C131C22×D411yescharacteristic
144C8×C131—22no—
145C8×C131—26no—
146C8×C131—22no—
147C8×C131—43no—
148C22×C131—23no—
149C22×C131—23no—
150C22×C131—23no—
151C22×C131—41no—
152C22×C131—41no—
153C22×C131—41no—
154C22×C131C22×C22⋊C411yescharacteristic
155C4×C131—21no—
156C4×C131—23no—
157C4×C131—21no—
158C4×C131—21no—
159C4×C131—23no—
160C4×C131—41no—
161C4×C131—43no—
162C4×C131—43no—
163C4×C131C2×#10416yes—
164C2×C131—43no—
165C2×C131—81no—
166C2×C131#288911yescharacteristic
167C2×C131C22×#10411yescharacteristic
168C2×C131#290111yescharacteristic
169#17654C13111yesmaximal, characteristic, direct product factor, Sylow
170C131#1765411yescharacteristic, direct product factor, Sylow
171#3518C2×C13111yescharacteristic
172#2971C2×C13111yescharacteristic, complemented
173#2875C2×C13111yescharacteristic, complemented
174#1531C2×C13113yescomplemented
175#1529C2×C13113yescomplemented
176#1526C2×C13113yescomplemented
177#1524C2×C13113yescomplemented
178C2×#131—21no—
179Q82C4×C13111yescharacteristic
180#556—23no—
181#556C4×C13113yes—
182#555C4×C13113yes—
183D4×Q8C4×C13111yescharacteristic
184#548—21no—
185#542—23no—
186#533C22×C13113yes—
187#529C22×C13113yes—
188#519—21no—
189C4×#41C22×C13111yescharacteristic
190C8×Q8—21no—
191#436—23no—
192#432C22×C13113yes—
193#405—23no—
194C4×M16C22×C13113yes—
195C4×M16C22×C13113yes—
196C2×#97C22×C13113yes—
197#330C22×C13113yes—
198#330C22×C13113yes—
199#330C22×C13116yes—
200#329C22×C13111yescharacteristic
201#329C22×C13113yes—
202C2×#41D4×C13111yescharacteristic
203C22×Q8—21no—
204#131—28no—
205C2×M16—23no—
206C2×M16—23no—
207C22×C8—23no—
208C4⋊Q8—23no—
209C4⋊Q8C2×C4×C13113yes—
210C4⋊Q8C2×C4×C13113yes—
211#126—26no—
212#126—23no—
213#125C23×C13113yes—
214#124—23no—
215#124—26no—
216#124C23×C13111yescharacteristic
217#123—23no—
218C22⋊Q8—23no—
219C22⋊Q8—23no—
220C22⋊Q8—23no—
221C22⋊Q8C2×C4×C13113yes—
222#121—23no—
223#121C2×C4×C13113yes—
224C4×Q8—21no—
225C4×Q8—23no—
226C4×Q8—23no—
227C4×Q8—23no—
228C4×Q8C2×C4×C13113yes—
229C4×Q8C2×C4×C13111yescharacteristic
230C4×Q8D4×C13111yescharacteristic
231C4×D4—23no—
232C4×D4C2×C4×C13113yes—
233C4×D4C2×C4×C13113yes—
234C4×D4D4×C13113yes—
235#117—23no—
236#117—23no—
237#117C2×C4×C13116yes—
238#117D4×C13113yes—
239C2×C42C23×C13113yes—
240C4⋊C8—23no—
241C22⋊C8—23no—
242#97—23no—
243#97C23×C13111yescharacteristic
244#97C23×C13113yes—
245#97C23×C13111yescharacteristic
246#97C23×C13113yes—
247C4×C8—23no—
248C4×C8—23no—
249#41—24no—
250C2×Q8—23no—
251C2×Q8—23no—
252C2×Q8—44no—
253C2×Q8C22⋊C4×C13111yescharacteristic
254C2×Q8C22×C4×C13111yescharacteristic
255C2×D4—23no—
256C2×D4C22⋊C4×C13113yes—
257C2×D4C22×C4×C13111yescharacteristic
258C22×C4—23no—
259C22×C4C22×C4×C13113yes—
260C22×C4C2×D4×C13113yes—
261C22×C4C2×D4×C13113yes—
262M16—212no—
263M16—46no—
264C2×C8—212no—
265C2×C8—21no—
266C2×C8—23no—
267C2×C8—21no—
268C2×C8—23no—
269C4⋊C4—23no—
270C4⋊C4—23no—
271C4⋊C4—23no—
272C4⋊C4—23no—
273C4⋊C4—23no—
274C4⋊C4—23no—
275C4⋊C4C22⋊C4×C13113yes—
276C4⋊C4C22⋊C4×C13113yes—
277C4⋊C4C22×C4×C13113yes—
278C4⋊C4C22×C4×C13113yes—
279C22⋊C4—26no—
280C22⋊C4—23no—
281C22⋊C4—23no—
282C22⋊C4—23no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4C22⋊C4×C13116yes—
286C42—26no—
287C42—23no—
288C42C22×C4×C13113yes—
289C42C2×D4×C13113yes—
290C42C2×D4×C13113yes—
291C42C24×C13111yescharacteristic
292C23—21no—
293C23C2×C22⋊C4×C13113yes—
294Q8—41no—
295Q8—46no—
296Q8—83no—
297Q8#104×C13114yes—
298D4—26no—
299D4—41no—
300D4—83no—
301C2×C4—26no—
302C2×C4—21no—
303C2×C4—23no—
304C2×C4—23no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—46no—
308C2×C4C2×C22⋊C4×C13113yes—
309C2×C4C2×C22⋊C4×C13113yes—
310C2×C4C2×C22⋊C4×C13113yes—
311C2×C4C23×C4×C13111yescharacteristic
312C2×C4C22×D4×C13111yescharacteristic
313C2×C4C22×D4×C13111yescharacteristic
314C8—22no—
315C8—26no—
316C8—22no—
317C8—43no—
318C22—23no—
319C22—23no—
320C22—23no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22C22×C22⋊C4×C13111yescharacteristic
325C4—21no—
326C4—23no—
327C4—21no—
328C4—21no—
329C4—23no—
330C4—41no—
331C4—43no—
332C4—43no—
333C4C2×#104×C13116yes—
334C2—43no—
335C2—81no—
336C2#2889×C13111yescharacteristic
337C2C22×#104×C13111yescharacteristic
338C2#2901×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C22×C22⋊C4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC42C24×C131
prime radical#3518×C131C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C4×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2971×C131C2semidirect
3. #2875×C131C2semidirect
4. #1531×C131C2semidirect
5. #1529×C131C2semidirect
6. #1526×C131C2semidirect
7. #1524×C131C2semidirect
169. #17654C131direct (N × H)
170. C131#17654direct (N × H)
172. #2971C2×C131semidirect
173. #2875C2×C131semidirect
174. #1531C2×C131semidirect
175. #1529C2×C131semidirect
176. #1526C2×C131semidirect
177. #1524C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3518×C1312
#2971×C1312
#2875×C1312
#1531×C1312
#1529×C1312
#1526×C1312
#1524×C1312
#17654131