Finite Group Databasebeta

← C151×#18724 #50323649

Subgroups — C151×#18724 #50323649

Order 38656.

932 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic
2#3226×C151C211yesmaximal, characteristic, complemented
3#3209×C151C211yesmaximal, characteristic, complemented
4#3141×C151C211yesmaximal, characteristic, complemented
5#1644×C151C214yesmaximal, complemented
6#1641×C151C214yesmaximal, complemented
7#1543×C151C211yesmaximal, characteristic, complemented
8#1485×C151C211yesmaximal, characteristic, complemented
9#1484×C151C211yesmaximal, characteristic, complemented
10#562×C151—22no—
11#554×C151—21no—
12#554×C151C2212yes—
13#550×C151—21no—
14#550×C151C2212yes—
15#547×C151—21no—
16#547×C151—21no—
17#540×C151—22no—
18#537×C151—22no—
19#537×C151—22no—
20#533×C151C2211yescharacteristic
21#532×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#500×C151—21no—
25#494×C151—21no—
26#489×C151—22no—
27#487×C151—21no—
28#487×C151C2212yes—
29#486×C151—21no—
30#486×C151C2212yes—
31#480×C151—22no—
32#474×C151C2214yes—
33#462×C151C2214yes—
34#451×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#417×C151—22no—
38C4×M16×C151C2211yescharacteristic
39#333×C151C2212yes—
40#331×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42D4⋊C8×C151C2214yes—
43C2×#41×C151—22no—
44C2×#41×C151—21no—
45C2×#41×C151—22no—
46C2×#41×C151D412yes—
47C22×Q8×C151—21no—
48C2×Q16×C151—24no—
49C2×M16×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151C2312yes—
57C4⋊Q8×C151C2311yescharacteristic
58#127×C151—22no—
59#127×C151D411yescharacteristic
60#127×C151C2311yescharacteristic
61#125×C151—22no—
62#125×C151—21no—
63#124×C151—21no—
64#124×C151D412yes—
65#123×C151—24no—
66#123×C151—24no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—24no—
69C22⋊Q8×C151—21no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—24no—
72C22⋊Q8×C151D412yes—
73#121×C151—24no—
74#121×C151—24no—
75#121×C151—22no—
76#121×C151—24no—
77#121×C151—24no—
78#121×C151—21no—
79#121×C151—21no—
80#121×C151—21no—
81#121×C151—22no—
82#121×C151D412yes—
83C4×Q8×C151—21no—
84C4×Q8×C151C2312yes—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151—21no—
88C4×D4×C151—21no—
89C4×D4×C151—21no—
90C4×D4×C151C2312yes—
91#117×C151—21no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151—24no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—24no—
101#103×C151—24no—
102#102×C151—24no—
103#102×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—44no—
111#41×C151—82no—
112#41×C151—84no—
113#41×C151—84no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—41no—
118C2×Q8×C151—82no—
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—21no—
129C2×D4×C151C2×D412yes—
130C2×D4×C151C2×D412yes—
131C22×C4×C151—24no—
132C22×C4×C151—24no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—41no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139Q16×C151—84no—
140M16×C151—42no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—41no—
157C4⋊C4×C151—41no—
158C4⋊C4×C151C2×D412yes—
159C4⋊C4×C151C2×D412yes—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—24no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—22no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C42×C151—22no—
168C42×C151C2×D411yescharacteristic
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2411yescharacteristic
172C23×C151—22no—
173C23×C151—22no—
174C23×C151#12011yescharacteristic
175Q8×C151—24no—
176Q8×C151—42no—
177Q8×C151—42no—
178Q8×C151—44no—
179Q8×C151—81no—
180Q8×C151—82no—
181D4×C151—24no—
182D4×C151—42no—
183D4×C151—42no—
184D4×C151—42no—
185D4×C151—42no—
186D4×C151—81no—
187D4×C151—82no—
188D4×C151—82no—
189D4×C151—84no—
190D4×C151—84no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—44no—
199C2×C4×C151—44no—
200C2×C4×C151—42no—
201C2×C4×C151—84no—
202C2×C4×C151—84no—
203C2×C4×C151—82no—
204C2×C4×C151#12011yescharacteristic
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151#12011yescharacteristic
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C22×D411yescharacteristic
209C2×C4×C151C22×D411yescharacteristic
210C8×C151—42no—
211C8×C151—42no—
212C8×C151—42no—
213C22×C151—21no—
214C22×C151—21no—
215C22×C151—21no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151C2×#12011yescharacteristic
223C4×C151—21no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—42no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—82no—
231C4×C151#45512yes—
232C4×C151#57612yes—
233C4×C151#57812yes—
234C2×C151—41no—
235C2×C151—82no—
236C2×C151—82no—
237C2×C151#300811yescharacteristic
238C2×C151#301111yescharacteristic
239C2×C151C2×#45511yescharacteristic
240#18724C15111yesmaximal, characteristic, direct product factor, Sylow
241C151#1872411yescharacteristic, direct product factor, Sylow
242#3548C2×C15111yescharacteristic
243#3226C2×C15111yescharacteristic, complemented
244#3209C2×C15111yescharacteristic, complemented
245#3141C2×C15111yescharacteristic, complemented
246#1644C2×C15114yescomplemented
247#1641C2×C15114yescomplemented
248#1543C2×C15111yescharacteristic, complemented
249#1485C2×C15111yescharacteristic, complemented
250#1484C2×C15111yescharacteristic, complemented
251#562—22no—
252#554—21no—
253#554C22×C15112yes—
254#550—21no—
255#550C22×C15112yes—
256#547—21no—
257#547—21no—
258#540—22no—
259#537—22no—
260#537—22no—
261#533C22×C15111yescharacteristic
262#532C22×C15111yescharacteristic
263#532C22×C15111yescharacteristic
264C2×C4⋊Q8C22×C15111yescharacteristic
265#500—21no—
266#494—21no—
267#489—22no—
268#487—21no—
269#487C22×C15112yes—
270#486—21no—
271#486C22×C15112yes—
272#480—22no—
273#474C22×C15114yes—
274#462C22×C15114yes—
275#451—22no—
276#431C22×C15111yescharacteristic
277#431C22×C15111yescharacteristic
278#417—22no—
279C4×M16C22×C15111yescharacteristic
280#333C22×C15112yes—
281#331C22×C15112yes—
282Q8⋊C8C22×C15114yes—
283D4⋊C8C22×C15114yes—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—21no—
287C2×#41D4×C15112yes—
288C22×Q8—21no—
289C2×Q16—24no—
290C2×M16—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8D4×C15111yescharacteristic
295C4⋊Q8D4×C15111yescharacteristic
296C4⋊Q8D4×C15111yescharacteristic
297C4⋊Q8C23×C15112yes—
298C4⋊Q8C23×C15111yescharacteristic
299#127—22no—
300#127D4×C15111yescharacteristic
301#127C23×C15111yescharacteristic
302#125—22no—
303#125—21no—
304#124—21no—
305#124D4×C15112yes—
306#123—24no—
307#123—24no—
308C22⋊Q8—22no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—21no—
313C22⋊Q8D4×C15112yes—
314#121—24no—
315#121—24no—
316#121—22no—
317#121—24no—
318#121—24no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—22no—
323#121D4×C15112yes—
324C4×Q8—21no—
325C4×Q8C23×C15112yes—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4C23×C15112yes—
332#117—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C42C23×C15111yescharacteristic
338#107—24no—
339C4⋊C8C23×C15112yes—
340C4⋊C8C23×C15112yes—
341#103—24no—
342#103—24no—
343#102—24no—
344#102—24no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347#97—21no—
348C4×C8—21no—
349C4×C8—21no—
350C4×C8C23×C15112yes—
351#41—44no—
352#41—82no—
353#41—84no—
354#41—84no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—82no—
360C2×Q8C2×D4×C15112yes—
361C2×Q8C2×D4×C15112yes—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×D4×C15112yes—
371C2×D4C2×D4×C15112yes—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4C2×D4×C15111yescharacteristic
378C22×C4C2×D4×C15111yescharacteristic
379C22×C4C2×D4×C15111yescharacteristic
380Q16—84no—
381M16—42no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C15112yes—
400C4⋊C4C2×D4×C15112yes—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C42—22no—
409C42C2×D4×C15111yescharacteristic
410C42C2×D4×C15111yescharacteristic
411C42C2×D4×C15111yescharacteristic
412C42C24×C15111yescharacteristic
413C23—22no—
414C23—22no—
415C23#120×C15111yescharacteristic
416Q8—24no—
417Q8—42no—
418Q8—42no—
419Q8—44no—
420Q8—81no—
421Q8—82no—
422D4—24no—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—81no—
428D4—82no—
429D4—82no—
430D4—84no—
431D4—84no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—84no—
443C2×C4—84no—
444C2×C4—82no—
445C2×C4#120×C15111yescharacteristic
446C2×C4#120×C15111yescharacteristic
447C2×C4#120×C15111yescharacteristic
448C2×C4C22×D4×C15111yescharacteristic
449C2×C4C22×D4×C15111yescharacteristic
450C2×C4C22×D4×C15111yescharacteristic
451C8—42no—
452C8—42no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22C2×#120×C15111yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4#455×C15112yes—
473C4#576×C15112yes—
474C4#578×C15112yes—
475C2—41no—
476C2—82no—
477C2—82no—
478C2#3008×C15111yescharacteristic
479C2#3011×C15111yescharacteristic
480C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3548×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3226×C151C2semidirect
3. #3209×C151C2semidirect
4. #3141×C151C2semidirect
5. #1644×C151C2semidirect
6. #1641×C151C2semidirect
7. #1543×C151C2semidirect
8. #1485×C151C2semidirect
9. #1484×C151C2semidirect
240. #18724C151direct (N × H)
241. C151#18724direct (N × H)
243. #3226C2×C151semidirect
244. #3209C2×C151semidirect
245. #3141C2×C151semidirect
246. #1644C2×C151semidirect
247. #1641C2×C151semidirect
248. #1543C2×C151semidirect
249. #1485C2×C151semidirect
250. #1484C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3226×C1512
#3209×C1512
#3141×C1512
#1644×C1512
#1641×C1512
#1543×C1512
#1485×C1512
#1484×C1512
#18724151