Finite Group Databasebeta

← C151×#8904 #50313829

Subgroups — C151×#8904 #50313829

Order 38656.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2906×C151C211yesmaximal, characteristic
2#1806×C151C211yesmaximal, characteristic
3#1570×C151C211yesmaximal, characteristic, complemented
4#1566×C151C211yesmaximal, characteristic, complemented
5#1476×C151C211yesmaximal, characteristic
6#1303×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C2×#131×C151—21no—
9C4×#41×C151C2211yescharacteristic
10#431×C151C2211yescharacteristic
11#424×C151—21no—
12#424×C151—22no—
13#423×C151—21no—
14#423×C151C2211yescharacteristic
15#423×C151C2211yescharacteristic
16C2×C4⋊C8×C151—21no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×#104×C151—21no—
19C2×C4×C8×C151C2211yescharacteristic
20C4×C4⋊C4×C151C2211yescharacteristic
21#339×C151—21no—
22#334×C151—22no—
23#334×C151—21no—
24#334×C151—21no—
25Q8⋊C8×C151C411yescharacteristic, complemented
26Q8⋊C8×C151C411yescharacteristic, complemented
27D4⋊C8×C151C411yescharacteristic, complemented
28D4⋊C8×C151C411yescharacteristic, complemented
29C2×#41×C151D411yescharacteristic
30#131×C151—42no—
31#131×C151—42no—
32C2×M16×C151—22no—
33C2×M16×C151—21no—
34C2×M16×C151—21no—
35C22×C8×C151—22no—
36C22×C8×C151—21no—
37C22×C8×C151—21no—
38C4×Q8×C151C2×C411yescharacteristic
39C4×Q8×C151Q811yescharacteristic
40C4×D4×C151—21no—
41C4×D4×C151—21no—
42C4×D4×C151C2×C411yescharacteristic
43C4×D4×C151Q811yescharacteristic
44#117×C151—21no—
45#117×C151D411yescharacteristic
46C2×C4⋊C4×C151—21no—
47C2×C42×C151—21no—
48C2×C42×C151—21no—
49C2×C42×C151C2311yescharacteristic
50C4⋊C8×C151—22no—
51C4⋊C8×C151—22no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55C4⋊C8×C151—21no—
56C4⋊C8×C151C2×C411yescharacteristic
57C4⋊C8×C151C2×C411yescharacteristic
58C4⋊C8×C151D411yescharacteristic
59C4⋊C8×C151D411yescharacteristic
60C4⋊C8×C151D412yes—
61#104×C151—42no—
62C22⋊C8×C151—21no—
63C4×C8×C151—21no—
64C4×C8×C151—21no—
65C4×C8×C151C2×C411yescharacteristic
66C4×C8×C151C2×C411yescharacteristic
67#95×C151—21no—
68#41×C151—21no—
69#41×C151—21no—
70#41×C151SD1612yes—
71#41×C151SD1612yes—
72C2×Q8×C151C4⋊C411yescharacteristic
73C2×D4×C151—21no—
74C2×D4×C151C4⋊C411yescharacteristic
75C22×C4×C151—21no—
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151—41no—
79C22×C4×C151C2×D411yescharacteristic
80C22×C4×C151#4111yescharacteristic
81C22×C4×C151#4111yescharacteristic
82M16×C151—44no—
83M16×C151—41no—
84M16×C151—41no—
85M16×C151—41no—
86M16×C151—41no—
87C2×C8×C151—21no—
88C2×C8×C151—21no—
89C2×C8×C151—21no—
90C2×C8×C151—21no—
91C2×C8×C151—21no—
92C2×C8×C151—22no—
93C2×C8×C151—21no—
94C2×C8×C151—42no—
95C2×C8×C151—44no—
96C2×C8×C151—41no—
97C2×C8×C151—41no—
98C2×C8×C151—41no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—22no—
102C4⋊C4×C151—41no—
103C4⋊C4×C151C4⋊C411yescharacteristic
104C4⋊C4×C151C4⋊C411yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C42×C151—21no—
109C42×C151—21no—
110C42×C151—21no—
111C42×C151—41no—
112C42×C151—41no—
113C42×C151C22×C411yescharacteristic
114C42×C151C2×D411yescharacteristic
115C42×C151C2×D411yescharacteristic
116C42×C151C2×Q811yescharacteristic
117C23×C151—21no—
118C23×C151#12311yescharacteristic
119Q8×C151—21no—
120Q8×C151#10612yes—
121D4×C151—22no—
122D4×C151—22no—
123D4×C151—21no—
124D4×C151#10612yes—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—42no—
136C2×C4×C151—81no—
137C2×C4×C151—81no—
138C2×C4×C151—81no—
139C2×C4×C151C2×C4⋊C411yescharacteristic
140C2×C4×C151C4×D411yescharacteristic
141C2×C4×C151C4×D411yescharacteristic
142C2×C4×C151#12011yescharacteristic
143C2×C4×C151C22⋊Q811yescharacteristic
144C2×C4×C151C22⋊Q811yescharacteristic
145C2×C4×C151C2×SD1611yescharacteristic
146C2×C4×C151C2×SD1611yescharacteristic
147C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C151#13711yescharacteristic
149C8×C151—22no—
150C8×C151—41no—
151C8×C151—41no—
152C8×C151—41no—
153C8×C151—41no—
154C8×C151—42no—
155C8×C151—41no—
156C8×C151—81no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—22no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151#38511yescharacteristic
163C22×C151#48111yescharacteristic
164C22×C151#48311yescharacteristic
165C4×C151—22no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—82no—
172C4×C151C2×#10611yescharacteristic
173C4×C151#42811yescharacteristic
174C4×C151#44311yescharacteristic
175C4×C151#44411yescharacteristic
176C4×C151#44811yescharacteristic
177C4×C151#45011yescharacteristic
178C2×C151—21no—
179C2×C151—21no—
180C2×C151—42no—
181C2×C151#185311yescharacteristic
182C2×C151#186111yescharacteristic
183C2×C151#186611yescharacteristic
184#8904C15111yesmaximal, characteristic, direct product factor, Sylow
185C151#890411yescharacteristic, direct product factor, Sylow
186#2906C2×C15111yescharacteristic
187#1806C2×C15111yescharacteristic
188#1570C2×C15111yescharacteristic, complemented
189#1566C2×C15111yescharacteristic, complemented
190#1476C2×C15111yescharacteristic
191#1303C2×C15111yescharacteristic, complemented
192#1279C2×C15111yescharacteristic, complemented
193C2×#131—21no—
194C4×#41C22×C15111yescharacteristic
195#431C22×C15111yescharacteristic
196#424—21no—
197#424—22no—
198#423—21no—
199#423C22×C15111yescharacteristic
200#423C22×C15111yescharacteristic
201C2×C4⋊C8—21no—
202C2×C4⋊C8C22×C15111yescharacteristic
203C2×#104—21no—
204C2×C4×C8C22×C15111yescharacteristic
205C4×C4⋊C4C22×C15111yescharacteristic
206#339—21no—
207#334—22no—
208#334—21no—
209#334—21no—
210Q8⋊C8C4×C15111yescharacteristic, complemented
211Q8⋊C8C4×C15111yescharacteristic, complemented
212D4⋊C8C4×C15111yescharacteristic, complemented
213D4⋊C8C4×C15111yescharacteristic, complemented
214C2×#41D4×C15111yescharacteristic
215#131—42no—
216#131—42no—
217C2×M16—22no—
218C2×M16—21no—
219C2×M16—21no—
220C22×C8—22no—
221C22×C8—21no—
222C22×C8—21no—
223C4×Q8C2×C4×C15111yescharacteristic
224C4×Q8Q8×C15111yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4C2×C4×C15111yescharacteristic
228C4×D4Q8×C15111yescharacteristic
229#117—21no—
230#117D4×C15111yescharacteristic
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C23×C15111yescharacteristic
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C15111yescharacteristic
242C4⋊C8C2×C4×C15111yescharacteristic
243C4⋊C8D4×C15111yescharacteristic
244C4⋊C8D4×C15111yescharacteristic
245C4⋊C8D4×C15112yes—
246#104—42no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C15111yescharacteristic
251C4×C8C2×C4×C15111yescharacteristic
252#95—21no—
253#41—21no—
254#41—21no—
255#41SD16×C15112yes—
256#41SD16×C15112yes—
257C2×Q8C4⋊C4×C15111yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊C4×C15111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4C2×D4×C15111yescharacteristic
265C22×C4#41×C15111yescharacteristic
266C22×C4#41×C15111yescharacteristic
267M16—44no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4C4⋊C4×C15111yescharacteristic
289C4⋊C4C4⋊C4×C15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42C22×C4×C15111yescharacteristic
299C42C2×D4×C15111yescharacteristic
300C42C2×D4×C15111yescharacteristic
301C42C2×Q8×C15111yescharacteristic
302C23—21no—
303C23#123×C15111yescharacteristic
304Q8—21no—
305Q8#106×C15112yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#106×C15112yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C4⋊C4×C15111yescharacteristic
325C2×C4C4×D4×C15111yescharacteristic
326C2×C4C4×D4×C15111yescharacteristic
327C2×C4#120×C15111yescharacteristic
328C2×C4C22⋊Q8×C15111yescharacteristic
329C2×C4C22⋊Q8×C15111yescharacteristic
330C2×C4C2×SD16×C15111yescharacteristic
331C2×C4C2×SD16×C15111yescharacteristic
332C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
333C2×C4#137×C15111yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—42no—
340C8—41no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#385×C15111yescharacteristic
348C22#481×C15111yescharacteristic
349C22#483×C15111yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4C2×#106×C15111yescharacteristic
358C4#428×C15111yescharacteristic
359C4#443×C15111yescharacteristic
360C4#444×C15111yescharacteristic
361C4#448×C15111yescharacteristic
362C4#450×C15111yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#1853×C15111yescharacteristic
367C2#1861×C15111yescharacteristic
368C2#1866×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#120
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#385
prime radicalC2×#41×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1570×C151C2semidirect
4. #1566×C151C2semidirect
6. #1303×C151C2semidirect
7. #1279×C151C2semidirect
25. Q8⋊C8×C151C4semidirect
26. Q8⋊C8×C151C4semidirect
27. D4⋊C8×C151C4semidirect
28. D4⋊C8×C151C4semidirect
184. #8904C151direct (N × H)
185. C151#8904direct (N × H)
188. #1570C2×C151semidirect
189. #1566C2×C151semidirect
191. #1303C2×C151semidirect
192. #1279C2×C151semidirect
210. Q8⋊C8C4×C151semidirect
211. Q8⋊C8C4×C151semidirect
212. D4⋊C8C4×C151semidirect
213. D4⋊C8C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2906×C1512
#1806×C1512
#1570×C1512
#1566×C1512
#1476×C1512
#1303×C1512
#1279×C1512
#8904151