Finite Group Databasebeta

← C151×#24064 #50328989

Subgroups — C151×#24064 #50328989

Order 38656.

1144 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C151C211yesmaximal, characteristic
2C2×#484×C151C212yesmaximal
3C2×#389×C151C211yesmaximal, characteristic
4#2057×C151C212yesmaximal, complemented
5#2043×C151C212yesmaximal, complemented
6#1872×C151C212yesmaximal
7#1863×C151C214yesmaximal, complemented
8#1817×C151C211yesmaximal, characteristic
9#533×C151—28no—
10C2×C4⋊Q8×C151C2211yescharacteristic
11C2×C4⋊Q8×C151C2211yescharacteristic
12C2×#125×C151—21no—
13C2×C22⋊Q8×C151—21no—
14C2×C22⋊Q8×C151C2212yes—
15C2×C4×Q8×C151—21no—
16C2×C4×Q8×C151C2212yes—
17C2×#117×C151—21no—
18C22×C4⋊C4×C151—21no—
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#484×C151—28no—
23C2×#107×C151C2214yes—
24C2×#103×C151C2214yes—
25C2×#103×C151C2214yes—
26C2×C22⋊C8×C151C2212yes—
27#389×C151—21no—
28#389×C151—21no—
29#389×C151C2212yes—
30#389×C151C2212yes—
31C2×#95×C151—21no—
32#340×C151C2214yes—
33#336×C151C2212yes—
34#336×C151C2212yes—
35C22×Q8×C151—21no—
36C22×Q8×C151C2312yes—
37C23×C4×C151—21no—
38C23×C4×C151—21no—
39C23×C4×C151D411yescharacteristic
40C23×C4×C151D411yescharacteristic
41C23×C4×C151C2311yescharacteristic
42C22×C8×C151C2314yes—
43C4⋊Q8×C151—24no—
44C4⋊Q8×C151—24no—
45#125×C151—28no—
46C22⋊Q8×C151—28no—
47C22⋊Q8×C151—24no—
48C22⋊Q8×C151D418yes—
49C4×Q8×C151—28no—
50C4×Q8×C151—24no—
51C4×Q8×C151—24no—
52#117×C151—28no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—44no—
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2312yes—
68C2×C22⋊C4×C151—22no—
69C2×C42×C151—24no—
70C2×C42×C151—22no—
71C2×C42×C151D411yescharacteristic
72C2×C42×C151D411yescharacteristic
73C2×C42×C151C2311yescharacteristic
74C2×C42×C151C2311yescharacteristic
75#107×C151—28no—
76#103×C151—28no—
77#103×C151—28no—
78C22⋊C8×C151—24no—
79#95×C151—22no—
80#95×C151—22no—
81C24×C151C2×D411yescharacteristic
82C2×Q8×C151—24no—
83C2×Q8×C151—22no—
84C2×Q8×C151—24no—
85C2×Q8×C151—24no—
86C2×Q8×C151—42no—
87C2×Q8×C151—42no—
88C2×Q8×C151C2×D414yes—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—24no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—41no—
101C22×C4×C151—42no—
102C22×C4×C151—42no—
103C22×C4×C151—42no—
104C22×C4×C151—42no—
105C22×C4×C151—42no—
106C22×C4×C151Q1614yes—
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D414yes—
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2411yescharacteristic
114C2×C8×C151—24no—
115C2×C8×C151—24no—
116C2×C8×C151—24no—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—24no—
120C4⋊C4×C151—28no—
121C4⋊C4×C151—24no—
122C4⋊C4×C151—28no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—24no—
126C4⋊C4×C151—44no—
127C4⋊C4×C151—42no—
128C4⋊C4×C151—44no—
129C4⋊C4×C151C2×D414yes—
130C4⋊C4×C151#4114yes—
131C22⋊C4×C151—28no—
132C42×C151—28no—
133C42×C151—22no—
134C42×C151—22no—
135C42×C151—22no—
136C42×C151—22no—
137C23×C151—21no—
138C23×C151—21no—
139C23×C151—21no—
140C23×C151—21no—
141C23×C151#12012yes—
142C23×C151C2×Q1612yes—
143C23×C151#13712yes—
144C23×C151C22×D411yescharacteristic
145Q8×C151—28no—
146Q8×C151—48no—
147Q8×C151—44no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—28no—
157C2×C4×C151—28no—
158C2×C4×C151—24no—
159C2×C4×C151—24no—
160C2×C4×C151—21no—
161C2×C4×C151—24no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—44no—
165C2×C4×C151—48no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151—84no—
176C2×C4×C151#12012yes—
177C2×C4×C151C2×Q1612yes—
178C2×C4×C151C2×Q1612yes—
179C2×C4×C151AGL(1,ℤ/8)12yes—
180C2×C4×C151C22×D412yes—
181C2×C4×C151C2×#4112yes—
182C2×C4×C1512−1+412yes—
183C8×C151—44no—
184C22×C151—22no—
185C22×C151—22no—
186C22×C151—22no—
187C22×C151—22no—
188C22×C151—22no—
189C22×C151—22no—
190C22×C151#45114yes—
191C22×C151C2×#12011yescharacteristic
192C22×C151#52511yescharacteristic
193C22×C151#53611yescharacteristic
194C22×C151C22×Q1611yescharacteristic
195C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
196C22×C151C2×#13711yescharacteristic
197C22×C151#57511yescharacteristic
198C4×C151—22no—
199C4×C151—22no—
200C4×C151—22no—
201C4×C151—22no—
202C4×C151—44no—
203C4×C151—44no—
204C4×C151—41no—
205C4×C151—44no—
206C4×C151—82no—
207C4×C151#54714yes—
208C2×C151—24no—
209C2×C151#240611yescharacteristic
210C2×C151C2×#45111yescharacteristic
211C2×C151#300611yescharacteristic
212C2×C151#310411yescharacteristic
213C2×C151#311011yescharacteristic
214C2×C151#323011yescharacteristic
215C2×C151#323611yescharacteristic
216#24064C15111yesmaximal, characteristic, direct product factor, Sylow
217C151#2406411yescharacteristic, direct product factor, Sylow
218C2×#533C2×C15111yescharacteristic
219C2×#484C2×C15112yes—
220C2×#389C2×C15111yescharacteristic
221#2057C2×C15112yescomplemented
222#2043C2×C15112yescomplemented
223#1872C2×C15112yes—
224#1863C2×C15114yescomplemented
225#1817C2×C15111yescharacteristic
226#533—28no—
227C2×C4⋊Q8C22×C15111yescharacteristic
228C2×C4⋊Q8C22×C15111yescharacteristic
229C2×#125—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C22×C15112yes—
232C2×C4×Q8—21no—
233C2×C4×Q8C22×C15112yes—
234C2×#117—21no—
235C22×C4⋊C4—21no—
236C22×C4⋊C4C22×C15111yescharacteristic
237C22×C4⋊C4C22×C15111yescharacteristic
238C22×C42C22×C15111yescharacteristic
239#484—28no—
240C2×#107C22×C15114yes—
241C2×#103C22×C15114yes—
242C2×#103C22×C15114yes—
243C2×C22⋊C8C22×C15112yes—
244#389—21no—
245#389—21no—
246#389C22×C15112yes—
247#389C22×C15112yes—
248C2×#95—21no—
249#340C22×C15114yes—
250#336C22×C15112yes—
251#336C22×C15112yes—
252C22×Q8—21no—
253C22×Q8C23×C15112yes—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4D4×C15111yescharacteristic
257C23×C4D4×C15111yescharacteristic
258C23×C4C23×C15111yescharacteristic
259C22×C8C23×C15114yes—
260C4⋊Q8—24no—
261C4⋊Q8—24no—
262#125—28no—
263C22⋊Q8—28no—
264C22⋊Q8—24no—
265C22⋊Q8D4×C15118yes—
266C4×Q8—28no—
267C4×Q8—24no—
268C4×Q8—24no—
269#117—28no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4C23×C15112yes—
283C2×C4⋊C4C23×C15112yes—
284C2×C4⋊C4C23×C15112yes—
285C2×C22⋊C4—22no—
286C2×C42—22no—
287C2×C42—24no—
288C2×C42D4×C15111yescharacteristic
289C2×C42D4×C15111yescharacteristic
290C2×C42C23×C15111yescharacteristic
291C2×C42C23×C15111yescharacteristic
292#107—28no—
293#103—28no—
294#103—28no—
295C22⋊C8—24no—
296#95—22no—
297#95—22no—
298C24C2×D4×C15111yescharacteristic
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8C2×D4×C15114yes—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4Q16×C15114yes—
324C22×C4C2×D4×C15111yescharacteristic
325C22×C4C2×D4×C15111yescharacteristic
326C22×C4C2×D4×C15114yes—
327C22×C4C2×D4×C15111yescharacteristic
328C22×C4C2×D4×C15111yescharacteristic
329C22×C4C2×D4×C15111yescharacteristic
330C22×C4C24×C15111yescharacteristic
331C2×C8—24no—
332C2×C8—24no—
333C2×C8—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—28no—
338C4⋊C4—24no—
339C4⋊C4—28no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—44no—
344C4⋊C4—42no—
345C4⋊C4—44no—
346C4⋊C4C2×D4×C15114yes—
347C4⋊C4#41×C15114yes—
348C22⋊C4—28no—
349C42—28no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42—22no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23#120×C15112yes—
359C23C2×Q16×C15112yes—
360C23#137×C15112yes—
361C23C22×D4×C15111yescharacteristic
362Q8—28no—
363Q8—48no—
364Q8—44no—
365C2×C4—28no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—44no—
382C2×C4—48no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—84no—
393C2×C4#120×C15112yes—
394C2×C4C2×Q16×C15112yes—
395C2×C4C2×Q16×C15112yes—
396C2×C4AGL(1,ℤ/8)×C15112yes—
397C2×C4C22×D4×C15112yes—
398C2×C4C2×#41×C15112yes—
399C2×C42−1+4×C15112yes—
400C8—44no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22#451×C15114yes—
408C22C2×#120×C15111yescharacteristic
409C22#525×C15111yescharacteristic
410C22#536×C15111yescharacteristic
411C22C22×Q16×C15111yescharacteristic
412C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
413C22C2×#137×C15111yescharacteristic
414C22#575×C15111yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—44no—
420C4—44no—
421C4—41no—
422C4—44no—
423C4—82no—
424C4#547×C15114yes—
425C2—24no—
426C2#2406×C15111yescharacteristic
427C2C2×#451×C15111yescharacteristic
428C2#3006×C15111yescharacteristic
429C2#3104×C15111yescharacteristic
430C2#3110×C15111yescharacteristic
431C2#3230×C15111yescharacteristic
432C2#3236×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #2057×C151C2semidirect
5. #2043×C151C2semidirect
7. #1863×C151C2semidirect
216. #24064C151direct (N × H)
217. C151#24064direct (N × H)
221. #2057C2×C151semidirect
222. #2043C2×C151semidirect
224. #1863C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
C2×#484×C1512
C2×#389×C1512
#2057×C1512
#2043×C1512
#1872×C1512
#1863×C1512
#1817×C1512
#24064151