Finite Group Databasebeta

← C151×#18212 #50323137

Subgroups — C151×#18212 #50323137

Order 38656.

1058 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic, complemented
2#3101×C151C212yesmaximal, complemented
3#2535×C151C211yesmaximal, characteristic
4#1608×C151C214yesmaximal, complemented
5#1596×C151C214yesmaximal, complemented
6#1518×C151C212yesmaximal, complemented
7#1460×C151C211yesmaximal, characteristic, complemented
8#554×C151—22no—
9#554×C151—24no—
10D4×Q8×C151—22no—
11#544×C151—21no—
12#543×C151C2214yes—
13#533×C151C2212yes—
14C2×C22⋊Q8×C151—22no—
15C2×#121×C151—21no—
16#518×C151—21no—
17C2×C4×D4×C151C2211yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19#483×C151C2214yes—
20#476×C151—22no—
21#461×C151—22no—
22#450×C151C2214yes—
23C4×SD16×C151—24no—
24#431×C151C2212yes—
25#397×C151C2212yes—
26#392×C151C2212yes—
27#386×C151—22no—
28#382×C151C2211yescharacteristic
29#380×C151—21no—
30#328×C151C2218yes—
31#323×C151C2214yes—
32C22×Q8×C151—22no—
33C22×D4×C151—22no—
34C22×D4×C151D411yescharacteristic
35C22×D4×C151C2311yescharacteristic
36C23×C4×C151—21no—
37C23×C4×C151D412yes—
38C2×SD16×C151—24no—
39C4⋊Q8×C151—24no—
40C4⋊Q8×C151D412yescomplemented
41C4⋊Q8×C151D412yescomplemented
42#125×C151—24no—
43#125×C151—22no—
44C22⋊Q8×C151—24no—
45C22⋊Q8×C151—24no—
46C22⋊Q8×C151—22no—
47C22⋊Q8×C151—24no—
48C22⋊Q8×C151—28no—
49C22⋊Q8×C151—28no—
50C22⋊Q8×C151C2314yes—
51#121×C151—44no—
52C4×Q8×C151—22no—
53C4×Q8×C151D414yescomplemented
54C4×D4×C151—24no—
55C4×D4×C151—24no—
56C4×D4×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151—22no—
59C4×D4×C151—22no—
60#117×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—24no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151D411yescharacteristic
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151C2312yes—
71C2×C42×C151C2311yescharacteristic
72#106×C151—24no—
73C4⋊C8×C151—22no—
74#103×C151—24no—
75#102×C151—24no—
76C22⋊C8×C151C2314yes—
77C4×C8×C151—22no—
78#95×C151—22no—
79#95×C151—21no—
80#95×C151C2312yes—
81C24×C151—21no—
82C24×C151C2×D412yes—
83C2×Q8×C151—24no—
84C2×Q8×C151—22no—
85C2×Q8×C151—84no—
86C2×Q8×C151C2×D414yes—
87C2×D4×C151—22no—
88C2×D4×C151—22no—
89C2×D4×C151—22no—
90C2×D4×C151—42no—
91C2×D4×C151—44no—
92C2×D4×C151—44no—
93C2×D4×C151—82no—
94C2×D4×C151SD1614yescomplemented
95C22×C4×C151—24no—
96C22×C4×C151—24no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—21no—
101C22×C4×C151—42no—
102C22×C4×C151—42no—
103C22×C4×C151—42no—
104C22×C4×C151—82no—
105C22×C4×C151C2×D412yes—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2411yescharacteristic
109SD16×C151—48no—
110C2×C8×C151—24no—
111C4⋊C4×C151—24no—
112C4⋊C4×C151—28no—
113C4⋊C4×C151—22no—
114C4⋊C4×C151—24no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—42no—
121C4⋊C4×C151C2×D414yes—
122C22⋊C4×C151—28no—
123C22⋊C4×C151—24no—
124C22⋊C4×C151—24no—
125C22⋊C4×C151—44no—
126C22⋊C4×C151—41no—
127C22⋊C4×C151—41no—
128C22⋊C4×C151—82no—
129C42×C151—24no—
130C42×C151C2×D412yes—
131C42×C151C2×D412yes—
132C23×C151—22no—
133C23×C151—22no—
134C23×C151—22no—
135C23×C151—42no—
136C23×C151—42no—
137C23×C151—41no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151—41no—
141C23×C151—41no—
142C23×C151—41no—
143C23×C151C2×SD1614yes—
144C23×C151C22×D411yescharacteristic
145Q8×C151—44no—
146Q8×C151—44no—
147Q8×C151—84no—
148D4×C151—24no—
149D4×C151—28no—
150D4×C151—42no—
151D4×C151—88no—
152C2×C4×C151—24no—
153C2×C4×C151—22no—
154C2×C4×C151—24no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—44no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—42no—
164C2×C4×C151—41no—
165C2×C4×C151—82no—
166C2×C4×C151—84no—
167C2×C4×C151—84no—
168C2×C4×C151—84no—
169C2×C4×C151#12011yescharacteristic
170C2×C4×C151#12011yescharacteristic
171C2×C4×C151#12012yes—
172C2×C4×C151C2×SD1612yes—
173C2×C4×C151#13712yes—
174C2×C4×C151C22×D412yes—
175C8×C151—44no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—24no—
179C22×C151—44no—
180C22×C151—42no—
181C22×C151—42no—
182C22×C151—42no—
183C22×C151—42no—
184C22×C151—42no—
185C22×C151—82no—
186C22×C151—81no—
187C22×C151—81no—
188C22×C151—81no—
189C22×C151—81no—
190C22×C151C2×#12011yescharacteristic
191C22×C151C22×SD1611yescharacteristic
192C22×C151C2×#13711yescharacteristic
193C4×C151—21no—
194C4×C151—21no—
195C4×C151—22no—
196C4×C151—42no—
197C4×C151—44no—
198C4×C151—44no—
199C4×C151—82no—
200C4×C151—81no—
201C4×C151#44814yes—
202C2×C151—21no—
203C2×C151—21no—
204C2×C151—44no—
205C2×C151—82no—
206C2×C151C2×#44811yescharacteristic
207C2×C151#301911yescharacteristic
208C2×C151#302511yescharacteristic
209#18212C15111yesmaximal, characteristic, direct product factor, Sylow
210C151#1821211yescharacteristic, direct product factor, Sylow
211#3501C2×C15111yescharacteristic, complemented
212#3101C2×C15112yescomplemented
213#2535C2×C15111yescharacteristic
214#1608C2×C15114yescomplemented
215#1596C2×C15114yescomplemented
216#1518C2×C15112yescomplemented
217#1460C2×C15111yescharacteristic, complemented
218#554—22no—
219#554—24no—
220D4×Q8—22no—
221#544—21no—
222#543C22×C15114yes—
223#533C22×C15112yes—
224C2×C22⋊Q8—22no—
225C2×#121—21no—
226#518—21no—
227C2×C4×D4C22×C15111yescharacteristic
228C2×C4×D4C22×C15111yescharacteristic
229#483C22×C15114yes—
230#476—22no—
231#461—22no—
232#450C22×C15114yes—
233C4×SD16—24no—
234#431C22×C15112yes—
235#397C22×C15112yes—
236#392C22×C15112yes—
237#386—22no—
238#382C22×C15111yescharacteristic
239#380—21no—
240#328C22×C15118yes—
241#323C22×C15114yes—
242C22×Q8—22no—
243C22×D4—22no—
244C22×D4D4×C15111yescharacteristic
245C22×D4C23×C15111yescharacteristic
246C23×C4—21no—
247C23×C4D4×C15112yes—
248C2×SD16—24no—
249C4⋊Q8—24no—
250C4⋊Q8D4×C15112yescomplemented
251C4⋊Q8D4×C15112yescomplemented
252#125—24no—
253#125—22no—
254C22⋊Q8—24no—
255C22⋊Q8—24no—
256C22⋊Q8—28no—
257C22⋊Q8—22no—
258C22⋊Q8—24no—
259C22⋊Q8—28no—
260C22⋊Q8C23×C15114yes—
261#121—44no—
262C4×Q8—22no—
263C4×Q8D4×C15114yescomplemented
264C4×D4—24no—
265C4×D4—24no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—22no—
270#117—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C15111yescharacteristic
275C2×C4⋊C4C23×C15111yescharacteristic
276C2×C22⋊C4—24no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4C23×C15112yes—
281C2×C42C23×C15111yescharacteristic
282#106—24no—
283C4⋊C8—22no—
284#103—24no—
285#102—24no—
286C22⋊C8C23×C15114yes—
287C4×C8—22no—
288#95—22no—
289#95—21no—
290#95C23×C15112yes—
291C24—21no—
292C24C2×D4×C15112yes—
293C2×Q8—24no—
294C2×Q8—22no—
295C2×Q8—84no—
296C2×Q8C2×D4×C15114yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—42no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—82no—
304C2×D4SD16×C15114yescomplemented
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—82no—
315C22×C4C2×D4×C15112yes—
316C22×C4C2×D4×C15111yescharacteristic
317C22×C4C2×D4×C15111yescharacteristic
318C22×C4C24×C15111yescharacteristic
319SD16—48no—
320C2×C8—24no—
321C4⋊C4—24no—
322C4⋊C4—28no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—42no—
331C4⋊C4C2×D4×C15114yes—
332C22⋊C4—28no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—44no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—82no—
339C42—24no—
340C42C2×D4×C15112yes—
341C42C2×D4×C15112yes—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—42no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23C2×SD16×C15114yes—
354C23C22×D4×C15111yescharacteristic
355Q8—44no—
356Q8—44no—
357Q8—84no—
358D4—24no—
359D4—28no—
360D4—42no—
361D4—88no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—84no—
377C2×C4—84no—
378C2×C4—84no—
379C2×C4#120×C15111yescharacteristic
380C2×C4#120×C15111yescharacteristic
381C2×C4#120×C15112yes—
382C2×C4C2×SD16×C15112yes—
383C2×C4#137×C15112yes—
384C2×C4C22×D4×C15112yes—
385C8—44no—
386C22—21no—
387C22—21no—
388C22—24no—
389C22—44no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22C2×#120×C15111yescharacteristic
401C22C22×SD16×C15111yescharacteristic
402C22C2×#137×C15111yescharacteristic
403C4—21no—
404C4—21no—
405C4—22no—
406C4—42no—
407C4—44no—
408C4—44no—
409C4—82no—
410C4—81no—
411C4#448×C15114yes—
412C2—21no—
413C2—21no—
414C2—44no—
415C2—82no—
416C2C2×#448×C15111yescharacteristic
417C2#3019×C15111yescharacteristic
418C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2535×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
1. #3501×C151C2semidirect
2. #3101×C151C2semidirect
4. #1608×C151C2semidirect
5. #1596×C151C2semidirect
6. #1518×C151C2semidirect
7. #1460×C151C2semidirect
40. C4⋊Q8×C151D4semidirect
41. C4⋊Q8×C151D4semidirect
53. C4×Q8×C151D4semidirect
94. C2×D4×C151SD16semidirect
209. #18212C151direct (N × H)
210. C151#18212direct (N × H)
211. #3501C2×C151semidirect
212. #3101C2×C151semidirect
214. #1608C2×C151semidirect
215. #1596C2×C151semidirect
216. #1518C2×C151semidirect
217. #1460C2×C151semidirect
250. C4⋊Q8D4×C151semidirect
251. C4⋊Q8D4×C151semidirect
263. C4×Q8D4×C151semidirect
304. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3101×C1512
#2535×C1512
#1608×C1512
#1596×C1512
#1518×C1512
#1460×C1512
#18212151