Finite Group Databasebeta

← C151×#23821 #50328746

Subgroups — C151×#23821 #50328746

Order 38656.

798 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
2C4×#124×C151C211yesmaximal, characteristic
3#2101×C151C212yesmaximal, complemented
4#2072×C151C211yesmaximal, characteristic, complemented
5#2071×C151C211yesmaximal, characteristic
6#2042×C151C212yesmaximal
7#2024×C151C211yesmaximal, characteristic, complemented
8#2023×C151C211yesmaximal, characteristic
9#1763×C151C212yesmaximal, complemented
10#1762×C151C212yesmaximal
11#1745×C151C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×#124×C151C2211yescharacteristic
14C2×C4×Q8×C151—21no—
15C2×C4×Q8×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17C2×#103×C151C2212yes—
18C2×#103×C151C2212yes—
19C2×#102×C151C2212yes—
20C2×#102×C151C2212yes—
21C2×#97×C151C2212yes—
22#391×C151—21no—
23#391×C151C2211yescharacteristic
24#390×C151C2211yescharacteristic
25#389×C151—21no—
26#389×C151C2212yes—
27#388×C151—21no—
28#388×C151—21no—
29#384×C151C2211yescharacteristic
30#382×C151C2211yescharacteristic
31C4×C4⋊C4×C151—21no—
32C4×C4⋊C4×C151C2212yes—
33C4×C22⋊C4×C151—21no—
34C4×C22⋊C4×C151—21no—
35C43×C151C2211yescharacteristic
36#340×C151C2212yes—
37#340×C151C2212yes—
38#340×C151C2212yes—
39#340×C151C2212yes—
40#336×C151C2212yes—
41#336×C151C2211yescharacteristic
42#336×C151C2211yescharacteristic
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C22×C8×C151C2312yes—
48C22×C8×C151C2312yes—
49C4⋊Q8×C151—24no—
50#124×C151—22no—
51#124×C151—22no—
52C4×Q8×C151—24no—
53C4×Q8×C151—44no—
54C4×D4×C151—24no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151C2311yescharacteristic
61C2×C4⋊C4×C151C2311yescharacteristic
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2312yes—
64C2×C22⋊C4×C151—21no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—21no—
69C2×C42×C151—21no—
70C2×C42×C151—22no—
71C2×C42×C151D411yescharacteristic
72C2×C42×C151D411yescharacteristic
73C2×C42×C151D411yescharacteristic
74C2×C42×C151D411yescharacteristic
75C2×C42×C151C2311yescharacteristic
76C2×C42×C151C2311yescharacteristic
77C2×C42×C151C2311yescharacteristic
78#103×C151—24no—
79#103×C151—24no—
80#102×C151—24no—
81#102×C151—24no—
82#97×C151—24no—
83#95×C151—21no—
84#95×C151—21no—
85#95×C151—21no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89C24×C151—21no—
90C2×Q8×C151—24no—
91C2×Q8×C151—21no—
92C2×Q8×C151—22no—
93C2×Q8×C151—22no—
94C2×Q8×C151—42no—
95C2×Q8×C151—42no—
96C2×Q8×C151#4112yes—
97C2×D4×C151—22no—
98C2×D4×C151—22no—
99C2×D4×C151—21no—
100C2×D4×C151#4112yes—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—42no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2411yescharacteristic
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—22no—
122C4⋊C4×C151—24no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—42no—
129C4⋊C4×C151—44no—
130C4⋊C4×C151—42no—
131C4⋊C4×C151—42no—
132C4⋊C4×C151#4114yes—
133C22⋊C4×C151—24no—
134C22⋊C4×C151—24no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—42no—
137C22⋊C4×C151—42no—
138C42×C151—22no—
139C42×C151—22no—
140C42×C151—21no—
141C42×C151—21no—
142C42×C151—22no—
143C42×C151—41no—
144C42×C151—41no—
145C42×C151—44no—
146C42×C151—42no—
147C42×C151#4114yes—
148C23×C151—22no—
149C23×C151—41no—
150C23×C151—41no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151C22×D411yescharacteristic
156Q8×C151—24no—
157Q8×C151—48no—
158Q8×C151—42no—
159D4×C151—24no—
160D4×C151—42no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—24no—
170C2×C4×C151—22no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—41no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151—41no—
190C2×C4×C151—84no—
191C2×C4×C151#12412yes—
192C2×C4×C151#12412yes—
193C2×C4×C151AGL(1,ℤ/8)12yes—
194C2×C4×C151#13712yes—
195C2×C4×C151C2×#4111yescharacteristic
196C2×C4×C151C2×#4112yes—
197C2×C4×C151C2×#4111yescharacteristic
198C2×C4×C151C2×#4112yes—
199C8×C151—42no—
200C8×C151—42no—
201C22×C151—42no—
202C22×C151—42no—
203C22×C151—42no—
204C22×C151—81no—
205C22×C151—81no—
206C22×C151—81no—
207C22×C151—81no—
208C22×C151#52511yescharacteristic
209C22×C151#52511yescharacteristic
210C22×C151C2×#12411yescharacteristic
211C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
212C22×C151C2×#13711yescharacteristic
213C22×C151#57511yescharacteristic
214C22×C151#57511yescharacteristic
215C4×C151—22no—
216C4×C151—22no—
217C4×C151—22no—
218C4×C151—22no—
219C4×C151—44no—
220C4×C151—41no—
221C4×C151—41no—
222C4×C151—42no—
223C4×C151—82no—
224C4×C151—81no—
225C4×C151—81no—
226C4×C151#52912yes—
227C4×C151#52912yes—
228C2×C151—82no—
229C2×C151#239811yescharacteristic
230C2×C151#311411yescharacteristic
231C2×C151#311511yescharacteristic
232C2×C151#311611yescharacteristic
233C2×C151#311711yescharacteristic
234C2×C151#314011yescharacteristic
235C2×C151#314111yescharacteristic
236#23821C15111yesmaximal, characteristic, direct product factor, Sylow
237C151#2382111yescharacteristic, direct product factor, Sylow
238C4×C4⋊Q8C2×C15111yescharacteristic, complemented
239C4×#124C2×C15111yescharacteristic
240#2101C2×C15112yescomplemented
241#2072C2×C15111yescharacteristic, complemented
242#2071C2×C15111yescharacteristic
243#2042C2×C15112yes—
244#2024C2×C15111yescharacteristic, complemented
245#2023C2×C15111yescharacteristic
246#1763C2×C15112yescomplemented
247#1762C2×C15112yes—
248#1745C2×C15111yescharacteristic, complemented
249C2×C4⋊Q8C22×C15111yescharacteristic
250C2×#124C22×C15111yescharacteristic
251C2×C4×Q8—21no—
252C2×C4×Q8C22×C15111yescharacteristic
253C2×C4×D4C22×C15111yescharacteristic
254C2×#103C22×C15112yes—
255C2×#103C22×C15112yes—
256C2×#102C22×C15112yes—
257C2×#102C22×C15112yes—
258C2×#97C22×C15112yes—
259#391—21no—
260#391C22×C15111yescharacteristic
261#390C22×C15111yescharacteristic
262#389—21no—
263#389C22×C15112yes—
264#388—21no—
265#388—21no—
266#384C22×C15111yescharacteristic
267#382C22×C15111yescharacteristic
268C4×C4⋊C4—21no—
269C4×C4⋊C4C22×C15112yes—
270C4×C22⋊C4—21no—
271C4×C22⋊C4—21no—
272C43C22×C15111yescharacteristic
273#340C22×C15112yes—
274#340C22×C15112yes—
275#340C22×C15112yes—
276#340C22×C15112yes—
277#336C22×C15111yescharacteristic
278#336C22×C15111yescharacteristic
279#336C22×C15112yes—
280C22×Q8—21no—
281C22×Q8C23×C15111yescharacteristic
282C22×D4C23×C15111yescharacteristic
283C23×C4—21no—
284C22×C8C23×C15112yes—
285C22×C8C23×C15112yes—
286C4⋊Q8—24no—
287#124—22no—
288#124—22no—
289C4×Q8—24no—
290C4×Q8—44no—
291C4×D4—24no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4C23×C15111yescharacteristic
298C2×C4⋊C4C23×C15111yescharacteristic
299C2×C4⋊C4C23×C15112yes—
300C2×C4⋊C4C23×C15112yes—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C42—22no—
307C2×C42—21no—
308C2×C42D4×C15111yescharacteristic
309C2×C42D4×C15111yescharacteristic
310C2×C42D4×C15111yescharacteristic
311C2×C42D4×C15111yescharacteristic
312C2×C42C23×C15111yescharacteristic
313C2×C42C23×C15111yescharacteristic
314C2×C42C23×C15111yescharacteristic
315#103—24no—
316#103—24no—
317#102—24no—
318#102—24no—
319#97—24no—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—22no—
325#95—22no—
326C24—21no—
327C2×Q8—24no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8#41×C15112yes—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4#41×C15112yes—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4C2×D4×C15111yescharacteristic
347C22×C4C2×D4×C15111yescharacteristic
348C22×C4C2×D4×C15111yescharacteristic
349C22×C4C2×D4×C15111yescharacteristic
350C22×C4C2×D4×C15111yescharacteristic
351C22×C4C2×D4×C15111yescharacteristic
352C22×C4C24×C15111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—44no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4#41×C15114yes—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C42—22no—
376C42—22no—
377C42—21no—
378C42—21no—
379C42—22no—
380C42—41no—
381C42—41no—
382C42—44no—
383C42—42no—
384C42#41×C15114yes—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23C22×D4×C15111yescharacteristic
393Q8—24no—
394Q8—48no—
395Q8—42no—
396D4—24no—
397D4—42no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—84no—
428C2×C4#124×C15112yes—
429C2×C4#124×C15112yes—
430C2×C4AGL(1,ℤ/8)×C15112yes—
431C2×C4#137×C15112yes—
432C2×C4C2×#41×C15111yescharacteristic
433C2×C4C2×#41×C15111yescharacteristic
434C2×C4C2×#41×C15112yes—
435C2×C4C2×#41×C15112yes—
436C8—42no—
437C8—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22#525×C15111yescharacteristic
446C22#525×C15111yescharacteristic
447C22C2×#124×C15111yescharacteristic
448C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
449C22C2×#137×C15111yescharacteristic
450C22#575×C15111yescharacteristic
451C22#575×C15111yescharacteristic
452C4—22no—
453C4—22no—
454C4—22no—
455C4—22no—
456C4—44no—
457C4—41no—
458C4—41no—
459C4—42no—
460C4—82no—
461C4—81no—
462C4—81no—
463C4#529×C15112yes—
464C4#529×C15112yes—
465C2—82no—
466C2#2398×C15111yescharacteristic
467C2#3114×C15111yescharacteristic
468C2#3115×C15111yescharacteristic
469C2#3116×C15111yescharacteristic
470C2#3117×C15111yescharacteristic
471C2#3140×C15111yescharacteristic
472C2#3141×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊Q8×C151C2semidirect
3. #2101×C151C2semidirect
4. #2072×C151C2semidirect
7. #2024×C151C2semidirect
9. #1763×C151C2semidirect
11. #1745×C151C2semidirect
236. #23821C151direct (N × H)
237. C151#23821direct (N × H)
238. C4×C4⋊Q8C2×C151semidirect
240. #2101C2×C151semidirect
241. #2072C2×C151semidirect
244. #2024C2×C151semidirect
246. #1763C2×C151semidirect
248. #1745C2×C151semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C1512
C4×#124×C1512
#2101×C1512
#2072×C1512
#2071×C1512
#2042×C1512
#2024×C1512
#2023×C1512
#1763×C1512
#1762×C1512
#1745×C1512
#23821151