Finite Group Databasebeta

← C151×#18211 #50323136

Subgroups — C151×#18211 #50323136

Order 38656.

1254 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3496×C151C211yesmaximal, characteristic
2#3103×C151C212yesmaximal, complemented
3#2580×C151C211yesmaximal, characteristic, complemented
4#1613×C151C214yesmaximal, complemented
5#1601×C151C214yesmaximal, complemented
6#1517×C151C212yesmaximal, complemented
7#1460×C151C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C151—21no—
9#547×C151—22no—
10#546×C151—24no—
11D42×C151—22no—
12#537×C151—21no—
13#534×C151C2214yes—
14#532×C151C2212yes—
15C2×#121×C151—22no—
16C2×C4×Q8×C151C2211yescharacteristic, complemented
17C2×C4×D4×C151C2211yescharacteristic
18#481×C151C2214yescomplemented
19#475×C151—22no—
20#460×C151—22no—
21#448×C151C2214yescomplemented
22C4×SD16×C151—24no—
23#431×C151C2212yescomplemented
24#399×C151C2212yescomplemented
25#393×C151C2212yescomplemented
26#390×C151—21no—
27#389×C151—21no—
28#385×C151—22no—
29#382×C151C2211yescharacteristic, complemented
30#327×C151C2218yescomplemented
31#323×C151C2214yescomplemented
32H(5,𝔽2)×C151—44no—
33H(5,𝔽2)×C151—44no—
34C2×#41×C151—24no—
35C2×#41×C151—22no—
36C22×Q8×C151C2311yescharacteristic
37C22×D4×C151—24no—
38C22×D4×C151—22no—
39C22×D4×C151—24no—
40C22×D4×C151D411yescharacteristic
41C23×C4×C151D412yes—
42C2×SD16×C151—24no—
43C4⋊Q8×C151D412yes—
44#127×C151D412yes—
45#124×C151—22no—
46#123×C151—28no—
47C22⋊Q8×C151—24no—
48#121×C151—24no—
49#121×C151—24no—
50#121×C151—24no—
51#121×C151—22no—
52#121×C151—24no—
53#121×C151C2314yes—
54#120×C151—28no—
55C4×Q8×C151—22no—
56C4×Q8×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151—22no—
59C4×D4×C151—22no—
60C4×D4×C151D414yes—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151D411yescharacteristic
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—22no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151C2312yes—
71C2×C42×C151—21no—
72C2×C42×C151C2311yescharacteristic
73#106×C151—24no—
74C4⋊C8×C151—22no—
75#103×C151—24no—
76#102×C151—24no—
77C22⋊C8×C151C2314yes—
78C4×C8×C151—22no—
79#95×C151—21no—
80#95×C151—22no—
81#95×C151C2312yes—
82C24×C151—24no—
83C24×C151C2×D412yes—
84#41×C151—416no—
85#41×C151—44no—
86#41×C151—44no—
87C2×Q8×C151—22no—
88C2×Q8×C151—22no—
89C2×Q8×C151—42no—
90C2×D4×C151—28no—
91C2×D4×C151—24no—
92C2×D4×C151—24no—
93C2×D4×C151—22no—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151—416no—
98C2×D4×C151—48no—
99C2×D4×C151—48no—
100C2×D4×C151—84no—
101C2×D4×C151SD1614yescomplemented
102C2×D4×C151C2×D414yes—
103C22×C4×C151—24no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—24no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—82no—
111C22×C4×C151C2×D412yes—
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2411yescharacteristic
115SD16×C151—48no—
116C2×C8×C151—24no—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—41no—
122C4⋊C4×C151—41no—
123C4⋊C4×C151—42no—
124C4⋊C4×C151—82no—
125C4⋊C4×C151C2×D414yes—
126C22⋊C4×C151—28no—
127C22⋊C4×C151—24no—
128C22⋊C4×C151—24no—
129C22⋊C4×C151—24no—
130C22⋊C4×C151—44no—
131C22⋊C4×C151—82no—
132C42×C151—42no—
133C42×C151C2×D412yes—
134C42×C151C2×D412yes—
135C23×C151—22no—
136C23×C151—22no—
137C23×C151—24no—
138C23×C151—42no—
139C23×C151—42no—
140C23×C151—48no—
141C23×C151—84no—
142C23×C151—84no—
143C23×C151C2×SD1614yes—
144C23×C151C22×D411yescharacteristic
145Q8×C151—24no—
146Q8×C151—42no—
147Q8×C151—44no—
148D4×C151—28no—
149D4×C151—44no—
150D4×C151—44no—
151D4×C151—416no—
152D4×C151—44no—
153D4×C151—44no—
154D4×C151—44no—
155D4×C151—84no—
156C2×C4×C151—22no—
157C2×C4×C151—24no—
158C2×C4×C151—22no—
159C2×C4×C151—41no—
160C2×C4×C151—41no—
161C2×C4×C151—44no—
162C2×C4×C151—41no—
163C2×C4×C151—48no—
164C2×C4×C151—41no—
165C2×C4×C151—48no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—42no—
173C2×C4×C151—82no—
174C2×C4×C151#12011yescharacteristic
175C2×C4×C151#12011yescharacteristic
176C2×C4×C151#12012yes—
177C2×C4×C151C2×SD1612yes—
178C2×C4×C151AGL(1,ℤ/8)12yes—
179C2×C4×C151C22×D412yes—
180C8×C151—44no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—24no—
184C22×C151—44no—
185C22×C151—42no—
186C22×C151—42no—
187C22×C151—44no—
188C22×C151—44no—
189C22×C151—44no—
190C22×C151—82no—
191C22×C151—168no—
192C22×C151C2×#12011yescharacteristic
193C22×C151C22×SD1611yescharacteristic
194C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—22no—
198C4×C151—44no—
199C4×C151—42no—
200C4×C151—42no—
201C4×C151—82no—
202C4×C151—81no—
203C4×C151#45014yes—
204C2×C151—21no—
205C2×C151—21no—
206C2×C151—44no—
207C2×C151—84no—
208C2×C151C2×#45011yescharacteristic
209C2×C151#301911yescharacteristic
210C2×C151#302511yescharacteristic
211#18211C15111yesmaximal, characteristic, direct product factor, Sylow
212C151#1821111yescharacteristic, direct product factor, Sylow
213#3496C2×C15111yescharacteristic
214#3103C2×C15112yescomplemented
215#2580C2×C15111yescharacteristic, complemented
216#1613C2×C15114yescomplemented
217#1601C2×C15114yescomplemented
218#1517C2×C15112yescomplemented
219#1460C2×C15111yescharacteristic, complemented
220C2×H(5,𝔽2)—21no—
221#547—22no—
222#546—24no—
223D42—22no—
224#537—21no—
225#534C22×C15114yes—
226#532C22×C15112yes—
227C2×#121—22no—
228C2×C4×Q8C22×C15111yescharacteristic, complemented
229C2×C4×D4C22×C15111yescharacteristic
230#481C22×C15114yescomplemented
231#475—22no—
232#460—22no—
233#448C22×C15114yescomplemented
234C4×SD16—24no—
235#431C22×C15112yescomplemented
236#399C22×C15112yescomplemented
237#393C22×C15112yescomplemented
238#390—21no—
239#389—21no—
240#385—22no—
241#382C22×C15111yescharacteristic, complemented
242#327C22×C15118yescomplemented
243#323C22×C15114yescomplemented
244H(5,𝔽2)—44no—
245H(5,𝔽2)—44no—
246C2×#41—24no—
247C2×#41—22no—
248C22×Q8C23×C15111yescharacteristic
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—22no—
252C22×D4D4×C15111yescharacteristic
253C23×C4D4×C15112yes—
254C2×SD16—24no—
255C4⋊Q8D4×C15112yes—
256#127D4×C15112yes—
257#124—22no—
258#123—28no—
259C22⋊Q8—24no—
260#121—24no—
261#121—24no—
262#121—24no—
263#121—22no—
264#121—24no—
265#121C23×C15114yes—
266#120—28no—
267C4×Q8—22no—
268C4×Q8—22no—
269C4×D4—22no—
270C4×D4—22no—
271C4×D4—22no—
272C4×D4D4×C15114yes—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4D4×C15111yescharacteristic
278C2×C4⋊C4C23×C15111yescharacteristic
279C2×C22⋊C4—24no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4C23×C15112yes—
283C2×C42—21no—
284C2×C42C23×C15111yescharacteristic
285#106—24no—
286C4⋊C8—22no—
287#103—24no—
288#102—24no—
289C22⋊C8C23×C15114yes—
290C4×C8—22no—
291#95—21no—
292#95—22no—
293#95C23×C15112yes—
294C24—24no—
295C24C2×D4×C15112yes—
296#41—416no—
297#41—44no—
298#41—44no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—42no—
302C2×D4—28no—
303C2×D4—24no—
304C2×D4—24no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—416no—
310C2×D4—48no—
311C2×D4—48no—
312C2×D4—84no—
313C2×D4SD16×C15114yescomplemented
314C2×D4C2×D4×C15114yes—
315C22×C4—24no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—82no—
323C22×C4C2×D4×C15112yes—
324C22×C4C2×D4×C15111yescharacteristic
325C22×C4C2×D4×C15111yescharacteristic
326C22×C4C24×C15111yescharacteristic
327SD16—48no—
328C2×C8—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—42no—
336C4⋊C4—82no—
337C4⋊C4C2×D4×C15114yes—
338C22⋊C4—28no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—44no—
343C22⋊C4—82no—
344C42—42no—
345C42C2×D4×C15112yes—
346C42C2×D4×C15112yes—
347C23—22no—
348C23—22no—
349C23—24no—
350C23—42no—
351C23—42no—
352C23—48no—
353C23—84no—
354C23—84no—
355C23C2×SD16×C15114yes—
356C23C22×D4×C15111yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—44no—
360D4—28no—
361D4—44no—
362D4—44no—
363D4—416no—
364D4—44no—
365D4—44no—
366D4—44no—
367D4—84no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—44no—
374C2×C4—48no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—48no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4#120×C15111yescharacteristic
387C2×C4#120×C15111yescharacteristic
388C2×C4#120×C15112yes—
389C2×C4C2×SD16×C15112yes—
390C2×C4AGL(1,ℤ/8)×C15112yes—
391C2×C4C22×D4×C15112yes—
392C8—44no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—44no—
397C22—42no—
398C22—42no—
399C22—44no—
400C22—44no—
401C22—44no—
402C22—82no—
403C22—168no—
404C22C2×#120×C15111yescharacteristic
405C22C22×SD16×C15111yescharacteristic
406C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
407C4—21no—
408C4—21no—
409C4—22no—
410C4—44no—
411C4—42no—
412C4—42no—
413C4—82no—
414C4—81no—
415C4#450×C15114yes—
416C2—21no—
417C2—21no—
418C2—44no—
419C2—84no—
420C2C2×#450×C15111yescharacteristic
421C2#3019×C15111yescharacteristic
422C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3496×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3103×C151C2semidirect
3. #2580×C151C2semidirect
4. #1613×C151C2semidirect
5. #1601×C151C2semidirect
6. #1517×C151C2semidirect
7. #1460×C151C2semidirect
16. C2×C4×Q8×C151C22semidirect
18. #481×C151C22semidirect
21. #448×C151C22semidirect
23. #431×C151C22semidirect
24. #399×C151C22semidirect
25. #393×C151C22semidirect
29. #382×C151C22semidirect
30. #327×C151C22semidirect
31. #323×C151C22semidirect
101. C2×D4×C151SD16semidirect
211. #18211C151direct (N × H)
212. C151#18211direct (N × H)
214. #3103C2×C151semidirect
215. #2580C2×C151semidirect
216. #1613C2×C151semidirect
217. #1601C2×C151semidirect
218. #1517C2×C151semidirect
219. #1460C2×C151semidirect
228. C2×C4×Q8C22×C151semidirect
230. #481C22×C151semidirect
233. #448C22×C151semidirect
235. #431C22×C151semidirect
236. #399C22×C151semidirect
237. #393C22×C151semidirect
241. #382C22×C151semidirect
242. #327C22×C151semidirect
243. #323C22×C151semidirect
313. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3496×C1512
#3103×C1512
#2580×C1512
#1613×C1512
#1601×C1512
#1517×C1512
#1460×C1512
#18211151