Finite Group Databasebeta

← C151×#7614 #50312539

Subgroups — C151×#7614 #50312539

Order 38656.

504 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2293×C151C211yesmaximal, characteristic
2#1831×C151C211yesmaximal, characteristic, complemented
3#1767×C151C211yesmaximal, characteristic, complemented
4#1271×C151C212yesmaximal, complemented
5#1270×C151C212yesmaximal
6C2×C4×D4×C151C411yescharacteristic
7C2×#117×C151—21no—
8C2×C4⋊C8×C151—21no—
9C2×C4⋊C8×C151—21no—
10C2×#97×C151—21no—
11#390×C151C411yescharacteristic
12#390×C151C2211yescharacteristic
13#389×C151C411yescharacteristic
14#389×C151C2211yescharacteristic
15#388×C151—21no—
16#388×C151—21no—
17C4×C4⋊C4×C151C411yescharacteristic
18C4×C22⋊C4×C151—21no—
19C43×C151C2211yescharacteristic
20#336×C151—21no—
21#336×C151C2212yes—
22#336×C151C2212yes—
23C22×D4×C151C2×C411yescharacteristic
24C23×C4×C151—21no—
25C22×C8×C151—22no—
26C22×C8×C151—22no—
27C4×D4×C151—22no—
28C4×D4×C151—22no—
29#117×C151—42no—
30#117×C151—42no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151C2×C411yescharacteristic
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C22⋊C4×C151—21no—
37C2×C22⋊C4×C151—21no—
38C2×C22⋊C4×C151—21no—
39C2×C22⋊C4×C151—21no—
40C2×C22⋊C4×C151—21no—
41C2×C42×C151—21no—
42C2×C42×C151C2×C411yescharacteristic
43C2×C42×C151C2×C411yescharacteristic
44C2×C42×C151D411yescharacteristic
45C2×C42×C151D411yescharacteristic
46C2×C42×C151D411yescharacteristic
47C2×C42×C151D411yescharacteristic
48C2×C42×C151C2311yescharacteristic
49C4⋊C8×C151—24no—
50C4⋊C8×C151—42no—
51#97×C151—42no—
52#95×C151—21no—
53#95×C151—21no—
54#95×C151—21no—
55C24×C151—21no—
56C2×D4×C151—21no—
57C2×D4×C151—41no—
58C2×D4×C151—41no—
59C2×D4×C151M1612yes—
60C22×C4×C151—24no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—42no—
65C22×C4×C151—42no—
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22×C411yescharacteristic
71C22×C4×C151C2×D411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C2×C8×C151—24no—
74C2×C8×C151—42no—
75C2×C8×C151—42no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C4⋊C4×C151—21no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—42no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151M1612yes—
86C22⋊C4×C151—24no—
87C22⋊C4×C151—42no—
88C22⋊C4×C151—42no—
89C22⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C42×C151—22no—
94C42×C151—21no—
95C42×C151—21no—
96C42×C151—21no—
97C42×C151—21no—
98C42×C151—41no—
99C42×C151—41no—
100C42×C151—41no—
101C42×C151—42no—
102C42×C151D812yes—
103C42×C151SD1612yes—
104C23×C151—22no—
105C23×C151—41no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—41no—
111C23×C151C2×C22⋊C411yescharacteristic
112D4×C151—42no—
113D4×C151—42no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—22no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—48no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151#10212yes—
140C2×C4×C151#10212yes—
141C2×C4×C151#10412yes—
142C2×C4×C151C2×M1611yescharacteristic
143C2×C4×C151C2×M1611yescharacteristic
144C2×C4×C151C2×D811yescharacteristic
145C2×C4×C151C2×SD1611yescharacteristic
146C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C151#13711yescharacteristic
148C8×C151—44no—
149C8×C151—82no—
150C22×C151—42no—
151C22×C151—42no—
152C22×C151—42no—
153C22×C151—81no—
154C22×C151—81no—
155C22×C151—81no—
156C22×C151—81no—
157C22×C151#40711yescharacteristic
158C22×C151#41011yescharacteristic
159C22×C151#41311yescharacteristic
160C22×C151C2×#10211yescharacteristic
161C22×C151#41711yescharacteristic
162C22×C151C2×#10411yescharacteristic
163C22×C151#42111yescharacteristic
164C4×C151—22no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—22no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—22no—
173C4×C151—42no—
174C4×C151—41no—
175C4×C151—81no—
176C4×C151—81no—
177C2×C151—82no—
178C2×C151#146411yescharacteristic
179C2×C151#148611yescharacteristic
180C2×C151#148911yescharacteristic
181C2×C151#150211yescharacteristic
182C2×C151#151211yescharacteristic
183C2×C151#153211yescharacteristic
184C2×C151#154711yescharacteristic
185#7614C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#761411yescharacteristic, direct product factor, Sylow
187#2293C2×C15111yescharacteristic
188#1831C2×C15111yescharacteristic, complemented
189#1767C2×C15111yescharacteristic, complemented
190#1271C2×C15112yescomplemented
191#1270C2×C15112yes—
192C2×C4×D4C4×C15111yescharacteristic
193C2×#117—21no—
194C2×C4⋊C8—21no—
195C2×C4⋊C8—21no—
196C2×#97—21no—
197#390C4×C15111yescharacteristic
198#390C22×C15111yescharacteristic
199#389C4×C15111yescharacteristic
200#389C22×C15111yescharacteristic
201#388—21no—
202#388—21no—
203C4×C4⋊C4C4×C15111yescharacteristic
204C4×C22⋊C4—21no—
205C43C22×C15111yescharacteristic
206#336—21no—
207#336C22×C15112yes—
208#336C22×C15112yes—
209C22×D4C2×C4×C15111yescharacteristic
210C23×C4—21no—
211C22×C8—22no—
212C22×C8—22no—
213C4×D4—22no—
214C4×D4—22no—
215#117—42no—
216#117—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×C4×C15111yescharacteristic
220C2×C4⋊C4C2×C4×C15111yescharacteristic
221C2×C4⋊C4C2×C4×C15111yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C42—21no—
228C2×C42C2×C4×C15111yescharacteristic
229C2×C42C2×C4×C15111yescharacteristic
230C2×C42D4×C15111yescharacteristic
231C2×C42D4×C15111yescharacteristic
232C2×C42D4×C15111yescharacteristic
233C2×C42D4×C15111yescharacteristic
234C2×C42C23×C15111yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—42no—
237#97—42no—
238#95—21no—
239#95—21no—
240#95—21no—
241C24—21no—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4M16×C15112yes—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C22⋊C4×C15111yescharacteristic
253C22×C4C22⋊C4×C15111yescharacteristic
254C22×C4C22⋊C4×C15111yescharacteristic
255C22×C4C22⋊C4×C15111yescharacteristic
256C22×C4C22×C4×C15111yescharacteristic
257C22×C4C2×D4×C15111yescharacteristic
258C22×C4C2×D4×C15111yescharacteristic
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4M16×C15112yes—
272C22⋊C4—24no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42—22no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—42no—
288C42D8×C15112yes—
289C42SD16×C15112yes—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C15111yescharacteristic
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—48no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4#102×C15112yes—
326C2×C4#102×C15112yes—
327C2×C4#104×C15112yes—
328C2×C4C2×M16×C15111yescharacteristic
329C2×C4C2×M16×C15111yescharacteristic
330C2×C4C2×D8×C15111yescharacteristic
331C2×C4C2×SD16×C15111yescharacteristic
332C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
333C2×C4#137×C15111yescharacteristic
334C8—44no—
335C8—82no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22#407×C15111yescharacteristic
344C22#410×C15111yescharacteristic
345C22#413×C15111yescharacteristic
346C22C2×#102×C15111yescharacteristic
347C22#417×C15111yescharacteristic
348C22C2×#104×C15111yescharacteristic
349C22#421×C15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—81no—
363C2—82no—
364C2#1464×C15111yescharacteristic
365C2#1486×C15111yescharacteristic
366C2#1489×C15111yescharacteristic
367C2#1502×C15111yescharacteristic
368C2#1512×C15111yescharacteristic
369C2#1532×C15111yescharacteristic
370C2#1547×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1831×C151C2semidirect
3. #1767×C151C2semidirect
4. #1271×C151C2semidirect
185. #7614C151direct (N × H)
186. C151#7614direct (N × H)
188. #1831C2×C151semidirect
189. #1767C2×C151semidirect
190. #1271C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2293×C1512
#1831×C1512
#1767×C1512
#1271×C1512
#1270×C1512
#7614151