Finite Group Databasebeta

← C151×#18338 #50323263

Subgroups — C151×#18338 #50323263

Order 38656.

928 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461×C151C211yesmaximal, characteristic
2#3218×C151C212yesmaximal, complemented
3#2567×C151C211yesmaximal, characteristic, complemented
4#1605×C151C212yesmaximal, complemented
5#1604×C151C212yesmaximal
6#1603×C151C214yesmaximal, complemented
7#1509×C151C212yesmaximal, complemented
8#1467×C151C211yesmaximal, characteristic, complemented
9#544×C151C2211yescharacteristic
10#542×C151—22no—
11#541×C151—22no—
12#539×C151—21no—
13#539×C151C2212yes—
14#537×C151C2211yescharacteristic
15#536×C151—21no—
16#533×C151—22no—
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151—22no—
19#529×C151—21no—
20#529×C151C2212yes—
21C4×#41×C151—21no—
22C2×C4×Q8×C151C2211yescharacteristic
23#497×C151—22no—
24#491×C151—22no—
25#462×C151—22no—
26#461×C151—22no—
27#451×C151C2214yes—
28#448×C151C2214yes—
29#432×C151C2212yes—
30#395×C151C2212yes—
31#395×C151C2212yes—
32#391×C151—21no—
33#389×C151—21no—
34#389×C151—21no—
35#384×C151—21no—
36C4×C4⋊C4×C151C2211yescharacteristic
37#328×C151C2214yes—
38#327×C151C2214yes—
39#324×C151C2212yes—
40#324×C151C2212yes—
41C2×#41×C151—21no—
42C22×Q8×C151D411yescharacteristic
43C22×Q8×C151C2312yes—
44C2×Q16×C151—24no—
45C2×SD16×C151—24no—
46C4⋊Q8×C151—22no—
47C4⋊Q8×C151—22no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151—22no—
50#126×C151—22no—
51#126×C151—22no—
52#126×C151—22no—
53#126×C151—22no—
54#125×C151—21no—
55#125×C151—22no—
56#125×C151—22no—
57#125×C151—22no—
58#125×C151D412yes—
59#124×C151—22no—
60#124×C151—21no—
61#124×C151D412yes—
62#123×C151—22no—
63#123×C151—22no—
64#123×C151—22no—
65#123×C151—22no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—21no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151C2312yes—
73#121×C151—22no—
74#121×C151—21no—
75#121×C151C2312yes—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151—21no—
79C4×Q8×C151—22no—
80C4×Q8×C151—22no—
81C4×Q8×C151D412yes—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151—21no—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151D412yes—
88#117×C151—22no—
89#117×C151—22no—
90#117×C151—21no—
91#117×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—22no—
96C2×C4⋊C4×C151—22no—
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C42×C151—22no—
101C2×C42×C151—21no—
102C2×C42×C151D411yescharacteristic
103C2×C42×C151D411yescharacteristic
104C2×C42×C151C2311yescharacteristic
105C4⋊C8×C151—22no—
106#103×C151—24no—
107#103×C151—24no—
108C22⋊C8×C151C2314yes—
109#97×C151—22no—
110#95×C151—22no—
111#95×C151—22no—
112#95×C151C2312yes—
113#41×C151—42no—
114#41×C151—42no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—24no—
120C2×Q8×C151—41no—
121C2×Q8×C151—82no—
122C2×Q8×C151C2×D412yes—
123C2×D4×C151—21no—
124C2×D4×C151—22no—
125C2×D4×C151—21no—
126C2×D4×C151C2×D412yes—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2411yescharacteristic
139Q16×C151—84no—
140SD16×C151—84no—
141C2×C8×C151—24no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—42no—
159C4⋊C4×C151—41no—
160C4⋊C4×C151—41no—
161C4⋊C4×C151—82no—
162C4⋊C4×C151—82no—
163C4⋊C4×C151C2×D412yes—
164C4⋊C4×C151C2×D412yes—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151—21no—
177C42×C151—22no—
178C42×C151—21no—
179C42×C151—21no—
180C42×C151—21no—
181C42×C151—42no—
182C42×C151C2×D412yes—
183C42×C151C2×D412yes—
184C23×C151—22no—
185C23×C151C22×D411yescharacteristic
186Q8×C151—44no—
187Q8×C151—42no—
188Q8×C151—42no—
189Q8×C151—44no—
190Q8×C151—44no—
191Q8×C151—81no—
192D4×C151—42no—
193D4×C151—42no—
194D4×C151—42no—
195D4×C151—42no—
196D4×C151—81no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—21no—
201C2×C4×C151—22no—
202C2×C4×C151—24no—
203C2×C4×C151—21no—
204C2×C4×C151—22no—
205C2×C4×C151—21no—
206C2×C4×C151—22no—
207C2×C4×C151—21no—
208C2×C4×C151—22no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—41no—
212C2×C4×C151—44no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—44no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—82no—
222C2×C4×C151#12012yes—
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151#12011yescharacteristic
225C2×C4×C151#13712yes—
226C2×C4×C151C22×D412yes—
227C8×C151—44no—
228C22×C151—21no—
229C22×C151—21no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—42no—
233C22×C151C2×#12011yescharacteristic
234C22×C151C2×#13711yescharacteristic
235C22×C151#57511yescharacteristic
236C4×C151—22no—
237C4×C151—22no—
238C4×C151—21no—
239C4×C151—22no—
240C4×C151—44no—
241C4×C151—41no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—41no—
245C4×C151—41no—
246C4×C151—42no—
247C4×C151—82no—
248C4×C151#45612yes—
249C2×C151—21no—
250C2×C151—21no—
251C2×C151—82no—
252C2×C151#300711yescharacteristic
253C2×C151C2×#45611yescharacteristic
254C2×C151#302711yescharacteristic
255#18338C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#1833811yescharacteristic, direct product factor, Sylow
257#3461C2×C15111yescharacteristic
258#3218C2×C15112yescomplemented
259#2567C2×C15111yescharacteristic, complemented
260#1605C2×C15112yescomplemented
261#1604C2×C15112yes—
262#1603C2×C15114yescomplemented
263#1509C2×C15112yescomplemented
264#1467C2×C15111yescharacteristic, complemented
265#544C22×C15111yescharacteristic
266#542—22no—
267#541—22no—
268#539—21no—
269#539C22×C15112yes—
270#537C22×C15111yescharacteristic
271#536—21no—
272#533—22no—
273C2×C4⋊Q8C22×C15111yescharacteristic
274#529—22no—
275#529—21no—
276#529C22×C15112yes—
277C4×#41—21no—
278C2×C4×Q8C22×C15111yescharacteristic
279#497—22no—
280#491—22no—
281#462—22no—
282#461—22no—
283#451C22×C15114yes—
284#448C22×C15114yes—
285#432C22×C15112yes—
286#395C22×C15112yes—
287#395C22×C15112yes—
288#391—21no—
289#389—21no—
290#389—21no—
291#384—21no—
292C4×C4⋊C4C22×C15111yescharacteristic
293#328C22×C15114yes—
294#327C22×C15114yes—
295#324C22×C15112yes—
296#324C22×C15112yes—
297C2×#41—21no—
298C22×Q8D4×C15111yescharacteristic
299C22×Q8C23×C15112yes—
300C2×Q16—24no—
301C2×SD16—24no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306#126—22no—
307#126—22no—
308#126—22no—
309#126—22no—
310#125—21no—
311#125—22no—
312#125—22no—
313#125—22no—
314#125D4×C15112yes—
315#124—22no—
316#124—21no—
317#124D4×C15112yes—
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—21no—
327C22⋊Q8—22no—
328C22⋊Q8C23×C15112yes—
329#121—22no—
330#121—21no—
331#121C23×C15112yes—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8D4×C15112yes—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4D4×C15112yes—
344#117—22no—
345#117—22no—
346#117—21no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4D4×C15111yescharacteristic
354C2×C4⋊C4C23×C15111yescharacteristic
355C2×C4⋊C4C23×C15111yescharacteristic
356C2×C42—22no—
357C2×C42—21no—
358C2×C42D4×C15111yescharacteristic
359C2×C42D4×C15111yescharacteristic
360C2×C42C23×C15111yescharacteristic
361C4⋊C8—22no—
362#103—24no—
363#103—24no—
364C22⋊C8C23×C15114yes—
365#97—22no—
366#95—22no—
367#95—22no—
368#95C23×C15112yes—
369#41—42no—
370#41—42no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—24no—
376C2×Q8—41no—
377C2×Q8—82no—
378C2×Q8C2×D4×C15112yes—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4C2×D4×C15112yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15111yescharacteristic
390C22×C4C2×D4×C15111yescharacteristic
391C22×C4C2×D4×C15111yescharacteristic
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C24×C15111yescharacteristic
395Q16—84no—
396SD16—84no—
397C2×C8—24no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—41no—
415C4⋊C4—42no—
416C4⋊C4—41no—
417C4⋊C4—82no—
418C4⋊C4—82no—
419C4⋊C4C2×D4×C15112yes—
420C4⋊C4C2×D4×C15112yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C42—22no—
431C42—22no—
432C42—21no—
433C42—22no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—42no—
438C42C2×D4×C15112yes—
439C42C2×D4×C15112yes—
440C23—22no—
441C23C22×D4×C15111yescharacteristic
442Q8—44no—
443Q8—42no—
444Q8—42no—
445Q8—44no—
446Q8—44no—
447Q8—81no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—82no—
478C2×C4#120×C15111yescharacteristic
479C2×C4#120×C15112yes—
480C2×C4#120×C15111yescharacteristic
481C2×C4#137×C15112yes—
482C2×C4C22×D4×C15112yes—
483C8—44no—
484C22—21no—
485C22—21no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22C2×#120×C15111yescharacteristic
490C22C2×#137×C15111yescharacteristic
491C22#575×C15111yescharacteristic
492C4—22no—
493C4—22no—
494C4—21no—
495C4—22no—
496C4—44no—
497C4—41no—
498C4—42no—
499C4—42no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—82no—
504C4#456×C15112yes—
505C2—21no—
506C2—21no—
507C2—82no—
508C2#3007×C15111yescharacteristic
509C2C2×#456×C15111yescharacteristic
510C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#537×C151C22
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. #3218×C151C2semidirect
3. #2567×C151C2semidirect
4. #1605×C151C2semidirect
6. #1603×C151C2semidirect
7. #1509×C151C2semidirect
8. #1467×C151C2semidirect
255. #18338C151direct (N × H)
256. C151#18338direct (N × H)
258. #3218C2×C151semidirect
259. #2567C2×C151semidirect
260. #1605C2×C151semidirect
262. #1603C2×C151semidirect
263. #1509C2×C151semidirect
264. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3461×C1512
#3218×C1512
#2567×C1512
#1605×C1512
#1604×C1512
#1603×C1512
#1509×C1512
#1467×C1512
#18338151