Finite Group Databasebeta

← C151×#13029 #50317954

Subgroups — C151×#13029 #50317954

Order 38656.

512 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
1C2×#509×C151C211yesmaximal, characteristic
2C2×#443×C151C211yesmaximal, characteristic, complemented
3C2×#361×C151C211yesmaximal, characteristic, complemented
4#2139×C151C211yesmaximal, characteristic, complemented
5#1970×C151C211yesmaximal, characteristic, complemented
6#1387×C151C211yesmaximal, characteristic, complemented
7#1376×C151C211yesmaximal, characteristic, complemented
8C2×#135×C151C2211yescharacteristic
9C22×D8×C151C2211yescharacteristic
10C2×#131×C151—21no—
11#509×C151—22no—
12#509×C151C414yescomplemented
13C2×SD32×C151—21no—
14C2×D16×C151—21no—
15C2×M32×C151C2211yescharacteristic
16C2×M32×C151C2211yescharacteristic
17#443×C151—22no—
18#443×C151—22no—
19C2×#108×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#104×C151—21no—
22C2×#102×C151—21no—
23C2×C4×C8×C151C2211yescharacteristic
24#390×C151—21no—
25#361×C151—22no—
26#358×C151—21no—
27#357×C151—21no—
28C2×#41×C151—21no—
29C22×D4×C151—21no—
30#135×C151—21no—
31#135×C151—21no—
32#135×C151C2×C412yes—
33#135×C151D412yes—
34C2×Q16×C151D411yescharacteristic
35C2×SD16×C151—21no—
36C2×D8×C151—21no—
37C2×D8×C151—21no—
38C2×D8×C151—21no—
39C2×D8×C151—21no—
40C2×D8×C151—21no—
41C2×D8×C151C2×C412yes—
42C2×D8×C151D411yescharacteristic
43#131×C151—24no—
44#131×C151—42no—
45C2×M16×C151—21no—
46C2×M16×C151—41no—
47C22×C8×C151—41no—
48C22×C8×C151D411yescharacteristic
49C22×C8×C151C2311yescharacteristic
50C2×C4⋊C4×C151—21no—
51C2×C22⋊C4×C151—42no—
52C2×C42×C151D411yescharacteristic
53SD32×C151—24no—
54D16×C151—24no—
55M32×C151—21no—
56M32×C151—21no—
57M32×C151—21no—
58M32×C151C2×C412yes—
59C2×C16×C151—21no—
60C2×C16×C151—21no—
61#108×C151—21no—
62#108×C151D412yes—
63#107×C151—21no—
64#107×C151—21no—
65#104×C151—24no—
66#102×C151—41no—
67#102×C151—41no—
68C4×C8×C151—21no—
69C4×C8×C151—21no—
70C24×C151—41no—
71#41×C151—22no—
72#41×C151—22no—
73#41×C151—41no—
74#41×C151—41no—
75C2×Q8×C151—21no—
76C2×D4×C151—22no—
77C2×D4×C151—21no—
78C2×D4×C151—41no—
79C2×D4×C151—41no—
80C2×D4×C151—41no—
81C2×D4×C151—41no—
82C2×D4×C151—41no—
83C2×D4×C151—41no—
84C22×C4×C151—21no—
85C22×C4×C151—41no—
86C22×C4×C151—41no—
87C22×C4×C151C2×D411yescharacteristic
88Q16×C151—21no—
89Q16×C151C22⋊C412yescomplemented
90SD16×C151—22no—
91SD16×C151—22no—
92D8×C151—22no—
93D8×C151—22no—
94D8×C151—21no—
95D8×C151—41no—
96D8×C151—41no—
97D8×C151C22⋊C412yescomplemented
98M16×C151—22no—
99M16×C151—44no—
100M16×C151—41no—
101C2×C8×C151—21no—
102C2×C8×C151—21no—
103C2×C8×C151—44no—
104C2×C8×C151—41no—
105C2×C8×C151D811yescharacteristic
106C2×C8×C151D811yescharacteristic
107C2×C8×C151C22×C411yescharacteristic
108C2×C8×C151C2×D411yescharacteristic
109C2×C8×C151C2×D411yescharacteristic
110C2×C8×C151C2×D411yescharacteristic
111C2×C8×C151#4111yescharacteristic
112C2×C8×C151#4111yescharacteristic
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C22⋊C4×C151—84no—
116C42×C151—21no—
117C42×C151—21no—
118C16×C151—22no—
119C16×C151—41no—
120C23×C151—41no—
121C23×C151—42no—
122C23×C151—82no—
123C23×C151—82no—
124C23×C151—81no—
125C23×C151—81no—
126C23×C151AGL(1,ℤ/8)11yescharacteristic
127Q8×C151—22no—
128Q8×C151—41no—
129D4×C151—22no—
130D4×C151—42no—
131D4×C151—42no—
132D4×C151—42no—
133D4×C151—42no—
134D4×C151—41no—
135D4×C151—81no—
136D4×C151—81no—
137C2×C4×C151—22no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—82no—
144C2×C4×C151—81no—
145C2×C4×C151C4×D411yescharacteristic
146C2×C4×C151#12011yescharacteristic
147C2×C4×C151#12111yescharacteristic
148C2×C4×C151C2×D811yescharacteristic
149C2×C4×C151#13511yescharacteristic
150C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
151C8×C151—21no—
152C8×C151—21no—
153C8×C151—42no—
154C8×C151C2×C22⋊C411yescharacteristic
155C8×C151C4×D411yescharacteristic
156C8×C151#12111yescharacteristic
157C8×C151#12311yescharacteristic
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—42no—
161C22×C151—84no—
162C22×C151—81no—
163C22×C151—81no—
164C22×C151—82no—
165C22×C151—162no—
166C22×C151—161no—
167C22×C151—161no—
168C22×C151#44211yescharacteristic
169C22×C151#44911yescharacteristic
170C22×C151#45911yescharacteristic
171C4×C151—42no—
172C4×C151—42no—
173C4×C151—161no—
174C4×C151#38611yescharacteristic
175C4×C151C4×D811yescharacteristic
176C4×C151#44711yescharacteristic
177C4×C151#46311yescharacteristic
178C2×C151—21no—
179C2×C151—21no—
180C2×C151—82no—
181C2×C151—162no—
182C2×C151#187911yescharacteristic
183C2×C151#221211yescharacteristic
184C2×C151#221311yescharacteristic
185#13029C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#1302911yescharacteristic, direct product factor, Sylow
187C2×#509C2×C15111yescharacteristic
188C2×#443C2×C15111yescharacteristic, complemented
189C2×#361C2×C15111yescharacteristic, complemented
190#2139C2×C15111yescharacteristic, complemented
191#1970C2×C15111yescharacteristic, complemented
192#1387C2×C15111yescharacteristic, complemented
193#1376C2×C15111yescharacteristic, complemented
194C2×#135C22×C15111yescharacteristic
195C22×D8C22×C15111yescharacteristic
196C2×#131—21no—
197#509—22no—
198#509C4×C15114yescomplemented
199C2×SD32—21no—
200C2×D16—21no—
201C2×M32C22×C15111yescharacteristic
202C2×M32C22×C15111yescharacteristic
203#443—22no—
204#443—22no—
205C2×#108C22×C15111yescharacteristic
206C2×#107C22×C15111yescharacteristic
207C2×#104—21no—
208C2×#102—21no—
209C2×C4×C8C22×C15111yescharacteristic
210#390—21no—
211#361—22no—
212#358—21no—
213#357—21no—
214C2×#41—21no—
215C22×D4—21no—
216#135—21no—
217#135—21no—
218#135C2×C4×C15112yes—
219#135D4×C15112yes—
220C2×Q16D4×C15111yescharacteristic
221C2×SD16—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8C2×C4×C15112yes—
228C2×D8D4×C15111yescharacteristic
229#131—24no—
230#131—42no—
231C2×M16—21no—
232C2×M16—41no—
233C22×C8—41no—
234C22×C8D4×C15111yescharacteristic
235C22×C8C23×C15111yescharacteristic
236C2×C4⋊C4—21no—
237C2×C22⋊C4—42no—
238C2×C42D4×C15111yescharacteristic
239SD32—24no—
240D16—24no—
241M32—21no—
242M32—21no—
243M32—21no—
244M32C2×C4×C15112yes—
245C2×C16—21no—
246C2×C16—21no—
247#108—21no—
248#108D4×C15112yes—
249#107—21no—
250#107—21no—
251#104—24no—
252#102—41no—
253#102—41no—
254C4×C8—21no—
255C4×C8—21no—
256C24—41no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C2×D4×C15111yescharacteristic
274Q16—21no—
275Q16C22⋊C4×C15112yescomplemented
276SD16—22no—
277SD16—22no—
278D8—22no—
279D8—22no—
280D8—21no—
281D8—41no—
282D8—41no—
283D8C22⋊C4×C15112yescomplemented
284M16—22no—
285M16—44no—
286M16—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—44no—
290C2×C8—41no—
291C2×C8D8×C15111yescharacteristic
292C2×C8D8×C15111yescharacteristic
293C2×C8C22×C4×C15111yescharacteristic
294C2×C8C2×D4×C15111yescharacteristic
295C2×C8C2×D4×C15111yescharacteristic
296C2×C8C2×D4×C15111yescharacteristic
297C2×C8#41×C15111yescharacteristic
298C2×C8#41×C15111yescharacteristic
299C4⋊C4—41no—
300C4⋊C4—41no—
301C22⋊C4—84no—
302C42—21no—
303C42—21no—
304C16—22no—
305C16—41no—
306C23—41no—
307C23—42no—
308C23—82no—
309C23—82no—
310C23—81no—
311C23—81no—
312C23AGL(1,ℤ/8)×C15111yescharacteristic
313Q8—22no—
314Q8—41no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—41no—
321D4—81no—
322D4—81no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4C4×D4×C15111yescharacteristic
332C2×C4#120×C15111yescharacteristic
333C2×C4#121×C15111yescharacteristic
334C2×C4C2×D8×C15111yescharacteristic
335C2×C4#135×C15111yescharacteristic
336C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
337C8—21no—
338C8—21no—
339C8—42no—
340C8C2×C22⋊C4×C15111yescharacteristic
341C8C4×D4×C15111yescharacteristic
342C8#121×C15111yescharacteristic
343C8#123×C15111yescharacteristic
344C22—21no—
345C22—21no—
346C22—42no—
347C22—84no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—162no—
352C22—161no—
353C22—161no—
354C22#442×C15111yescharacteristic
355C22#449×C15111yescharacteristic
356C22#459×C15111yescharacteristic
357C4—42no—
358C4—42no—
359C4—161no—
360C4#386×C15111yescharacteristic
361C4C4×D8×C15111yescharacteristic
362C4#447×C15111yescharacteristic
363C4#463×C15111yescharacteristic
364C2—21no—
365C2—21no—
366C2—82no—
367C2—162no—
368C2#1879×C15111yescharacteristic
369C2#2212×C15111yescharacteristic
370C2#2213×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#459
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radicalC2×#509×C151C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C151C2semidirect
3. C2×#361×C151C2semidirect
4. #2139×C151C2semidirect
5. #1970×C151C2semidirect
6. #1387×C151C2semidirect
7. #1376×C151C2semidirect
12. #509×C151C4semidirect
89. Q16×C151C22⋊C4semidirect
97. D8×C151C22⋊C4semidirect
185. #13029C151direct (N × H)
186. C151#13029direct (N × H)
188. C2×#443C2×C151semidirect
189. C2×#361C2×C151semidirect
190. #2139C2×C151semidirect
191. #1970C2×C151semidirect
192. #1387C2×C151semidirect
193. #1376C2×C151semidirect
198. #509C4×C151semidirect
275. Q16C22⋊C4×C151semidirect
283. D8C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1512
C2×#443×C1512
C2×#361×C1512
#2139×C1512
#1970×C1512
#1387×C1512
#1376×C1512
#13029151