Finite Group Databasebeta

← C151×#18353 #50323278

Subgroups — C151×#18353 #50323278

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#3195×C151C212yesmaximal, complemented
3#2638×C151C211yesmaximal, characteristic
4#1611×C151C212yesmaximal, complemented
5#1608×C151C212yesmaximal, complemented
6#1605×C151C212yesmaximal, complemented
7#1602×C151C212yesmaximal, complemented
8#1511×C151C212yesmaximal, complemented
9#1465×C151C211yesmaximal, characteristic
10#554×C151—24no—
11#554×C151—22no—
12D4×Q8×C151—22no—
13#544×C151C2212yes—
14#543×C151—21no—
15#543×C151C2212yes—
16#533×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151C2212yes—
19C2×C22⋊Q8×C151C2211yescharacteristic
20#518×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22#483×C151—22no—
23#483×C151C2214yes—
24#470×C151—24no—
25#451×C151—22no—
26#451×C151C2214yes—
27#407×C151C2212yes—
28#398×C151C2211yescharacteristic
29#397×C151—21no—
30#397×C151C2211yescharacteristic
31#395×C151C2211yescharacteristic
32#394×C151—21no—
33#393×C151C2211yescharacteristic
34#387×C151—21no—
35#385×C151—21no—
36#381×C151C2211yescharacteristic
37#328×C151C2214yes—
38#328×C151C2214yes—
39#324×C151C2212yes—
40#323×C151C2212yes—
41C22×Q8×C151—21no—
42C22×Q8×C151D412yes—
43C22×Q8×C151C2311yescharacteristic
44C22×D4×C151D411yescharacteristic
45C23×C4×C151D411yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C2×Q16×C151—24no—
48C2×M16×C151—22no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—24no—
52#125×C151—22no—
53#125×C151—24no—
54C22⋊Q8×C151—22no—
55C22⋊Q8×C151—22no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151—24no—
58C22⋊Q8×C151—22no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151D414yes—
67C22⋊Q8×C151C2314yes—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×D4×C151—24no—
71C4×D4×C151—24no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74#117×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151D412yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151D411yescharacteristic
91C2×C22⋊C4×C151C2311yescharacteristic
92C2×C42×C151D411yescharacteristic
93#106×C151—24no—
94#103×C151—24no—
95#103×C151—24no—
96C22⋊C8×C151—22no—
97C22⋊C8×C151C2314yes—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151C2311yescharacteristic
104#95×C151C2311yescharacteristic
105C24×C151C2×D411yescharacteristic
106C24×C151C2×D411yescharacteristic
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—81no—
112C2×Q8×C151—82no—
113C2×Q8×C151—82no—
114C2×Q8×C151C2×D414yes—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—81no—
129C22×C4×C151—81no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2411yescharacteristic
137Q16×C151—84no—
138M16×C151—82no—
139C2×C8×C151—24no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151—81no—
155C4⋊C4×C151C2×D414yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—42no—
162C22⋊C4×C151—42no—
163C22⋊C4×C151—81no—
164C22⋊C4×C151—81no—
165C42×C151—24no—
166C42×C151—21no—
167C42×C151—21no—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151#12012yes—
177C23×C151#13712yes—
178C23×C151C22×D411yescharacteristic
179Q8×C151—44no—
180Q8×C151—44no—
181Q8×C151—44no—
182Q8×C151—82no—
183Q8×C151—82no—
184D4×C151—28no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—24no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—24no—
191C2×C4×C151—42no—
192C2×C4×C151—41no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—81no—
211C2×C4×C151—82no—
212C2×C4×C151—82no—
213C2×C4×C151—82no—
214C2×C4×C151—82no—
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151#13712yes—
218C2×C4×C151C22×D412yes—
219C8×C151—44no—
220C22×C151—21no—
221C22×C151—21no—
222C22×C151—22no—
223C22×C151—22no—
224C22×C151—22no—
225C22×C151—22no—
226C22×C151—42no—
227C22×C151—41no—
228C22×C151—41no—
229C22×C151—81no—
230C22×C151—81no—
231C22×C151—81no—
232C22×C151C2×#12011yescharacteristic
233C22×C151C2×#13711yescharacteristic
234C22×C151C2×#13711yescharacteristic
235C4×C151—22no—
236C4×C151—22no—
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—41no—
240C4×C151—44no—
241C4×C151—41no—
242C4×C151—44no—
243C4×C151—81no—
244C4×C151—81no—
245C4×C151—81no—
246C4×C151—81no—
247C2×C151—21no—
248C2×C151—21no—
249C2×C151—42no—
250C2×C151—42no—
251C2×C151#300411yescharacteristic
252C2×C151#302211yescharacteristic
253C2×C151#302611yescharacteristic
254#18353C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#1835311yescharacteristic, direct product factor, Sylow
256#3501C2×C15111yescharacteristic
257#3195C2×C15112yescomplemented
258#2638C2×C15111yescharacteristic
259#1611C2×C15112yescomplemented
260#1608C2×C15112yescomplemented
261#1605C2×C15112yescomplemented
262#1602C2×C15112yescomplemented
263#1511C2×C15112yescomplemented
264#1465C2×C15111yescharacteristic
265#554—24no—
266#554—22no—
267D4×Q8—22no—
268#544C22×C15112yes—
269#543—21no—
270#543C22×C15112yes—
271#533—21no—
272C2×C22⋊Q8—21no—
273C2×C22⋊Q8C22×C15112yes—
274C2×C22⋊Q8C22×C15111yescharacteristic
275#518—21no—
276C2×C4×D4C22×C15111yescharacteristic
277#483—22no—
278#483C22×C15114yes—
279#470—24no—
280#451—22no—
281#451C22×C15114yes—
282#407C22×C15112yes—
283#398C22×C15111yescharacteristic
284#397—21no—
285#397C22×C15111yescharacteristic
286#395C22×C15111yescharacteristic
287#394—21no—
288#393C22×C15111yescharacteristic
289#387—21no—
290#385—21no—
291#381C22×C15111yescharacteristic
292#328C22×C15114yes—
293#328C22×C15114yes—
294#324C22×C15112yes—
295#323C22×C15112yes—
296C22×Q8—21no—
297C22×Q8D4×C15112yes—
298C22×Q8C23×C15111yescharacteristic
299C22×D4D4×C15111yescharacteristic
300C23×C4D4×C15111yescharacteristic
301C23×C4C23×C15111yescharacteristic
302C2×Q16—24no—
303C2×M16—22no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—24no—
307#125—22no—
308#125—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8D4×C15114yes—
322C22⋊Q8C23×C15114yes—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×D4—24no—
326C4×D4—24no—
327C4×D4—22no—
328C4×D4—22no—
329#117—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C15112yes—
337C2×C4⋊C4C23×C15111yescharacteristic
338C2×C4⋊C4C23×C15111yescharacteristic
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4D4×C15111yescharacteristic
346C2×C22⋊C4C23×C15111yescharacteristic
347C2×C42D4×C15111yescharacteristic
348#106—24no—
349#103—24no—
350#103—24no—
351C22⋊C8—22no—
352C22⋊C8C23×C15114yes—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95C23×C15111yescharacteristic
359#95C23×C15111yescharacteristic
360C24C2×D4×C15111yescharacteristic
361C24C2×D4×C15111yescharacteristic
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—81no—
367C2×Q8—82no—
368C2×Q8—82no—
369C2×Q8C2×D4×C15114yes—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15112yes—
390C22×C4C2×D4×C15112yes—
391C22×C4C24×C15111yescharacteristic
392Q16—84no—
393M16—82no—
394C2×C8—24no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4C2×D4×C15114yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—81no—
419C22⋊C4—81no—
420C42—24no—
421C42—21no—
422C42—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23#120×C15112yes—
432C23#137×C15112yes—
433C23C22×D4×C15111yescharacteristic
434Q8—44no—
435Q8—44no—
436Q8—44no—
437Q8—82no—
438Q8—82no—
439D4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—81no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4#120×C15111yescharacteristic
471C2×C4#120×C15111yescharacteristic
472C2×C4#137×C15112yes—
473C2×C4C22×D4×C15112yes—
474C8—44no—
475C22—21no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22C2×#120×C15111yescharacteristic
488C22C2×#137×C15111yescharacteristic
489C22C2×#137×C15111yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—44no—
496C4—41no—
497C4—44no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C2—21no—
503C2—21no—
504C2—42no—
505C2—42no—
506C2#3004×C15111yescharacteristic
507C2#3022×C15111yescharacteristic
508C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3195×C151C2semidirect
4. #1611×C151C2semidirect
5. #1608×C151C2semidirect
6. #1605×C151C2semidirect
7. #1602×C151C2semidirect
8. #1511×C151C2semidirect
254. #18353C151direct (N × H)
255. C151#18353direct (N × H)
257. #3195C2×C151semidirect
259. #1611C2×C151semidirect
260. #1608C2×C151semidirect
261. #1605C2×C151semidirect
262. #1602C2×C151semidirect
263. #1511C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3195×C1512
#2638×C1512
#1611×C1512
#1608×C1512
#1605×C1512
#1602×C1512
#1511×C1512
#1465×C1512
#18353151