Finite Group Databasebeta

← C151×#19177 #50324102

Subgroups — C151×#19177 #50324102

Order 38656.

650 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3141×C151C211yesmaximal, characteristic
2#3103×C151C211yesmaximal, characteristic
3C2×#462×C151C211yesmaximal, characteristic, complemented
4Q8×M16×C151C211yesmaximal, characteristic, complemented
5#1702×C151C212yesmaximal, complemented
6#1700×C151C212yesmaximal, complemented
7#1682×C151C212yesmaximal, complemented
8#1680×C151C212yesmaximal, complemented
9#1565×C151C211yesmaximal, characteristic, complemented
10#1549×C151C211yesmaximal, characteristic, complemented
11#1547×C151C211yesmaximal, characteristic
12C22×Q16×C151—21no—
13#532×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×C4×Q8×C151C2211yescharacteristic
16#489×C151—22no—
17#487×C151C2212yes—
18#486×C151C2212yes—
19#481×C151—21no—
20#475×C151C2211yescharacteristic
21#475×C151C2211yescharacteristic
22#462×C151—21no—
23#462×C151—21no—
24#462×C151C2212yes—
25#462×C151C2212yes—
26#460×C151C2211yescharacteristic
27#460×C151C2211yescharacteristic
28#448×C151—21no—
29#446×C151—22no—
30#446×C151C2212yes—
31C8×Q8×C151C2212yes—
32C4×SD16×C151—21no—
33C4×SD16×C151—21no—
34#431×C151C2211yescharacteristic
35#423×C151—21no—
36#423×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38#417×C151—21no—
39#417×C151—21no—
40C2×#103×C151—21no—
41C4×M16×C151—21no—
42C4×M16×C151C2211yescharacteristic
43#335×C151C2212yes—
44#334×C151C2212yes—
45#332×C151C2212yes—
46#332×C151C2212yes—
47#332×C151C2212yes—
48#331×C151C2212yes—
49C2×#41×C151—21no—
50C22×Q8×C151—21no—
51C22×Q8×C151D411yescharacteristic
52C2×Q16×C151—22no—
53C2×Q16×C151—22no—
54C2×Q16×C151—44no—
55C2×SD16×C151—21no—
56C2×SD16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151D411yescharacteristic
59C2×M16×C151D411yescharacteristic
60C22×C8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151C2312yes—
65C4⋊Q8×C151C2311yescharacteristic
66#127×C151C2311yescharacteristic
67#124×C151—21no—
68#121×C151—21no—
69#121×C151—21no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×Q8×C151D411yescharacteristic
73C4×Q8×C151D411yescharacteristic
74C4×Q8×C151C2311yescharacteristic
75C4×Q8×C151C2311yescharacteristic
76C4×D4×C151—21no—
77C4×D4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151D411yescharacteristic
82C2×C42×C151—21no—
83C2×C42×C151C2311yescharacteristic
84#106×C151—21no—
85#106×C151—21no—
86C4⋊C8×C151—22no—
87C4⋊C8×C151—22no—
88C4⋊C8×C151—21no—
89C4⋊C8×C151—21no—
90C4⋊C8×C151C2312yes—
91C4⋊C8×C151C2312yes—
92C4⋊C8×C151C2311yescharacteristic
93C4⋊C8×C151C2311yescharacteristic
94#103×C151—22no—
95#103×C151—22no—
96#103×C151—22no—
97#103×C151—22no—
98#103×C151—21no—
99#103×C151—21no—
100#102×C151—22no—
101#102×C151—22no—
102#102×C151—21no—
103#102×C151—21no—
104C22⋊C8×C151—21no—
105#97×C151—22no—
106#97×C151D412yes—
107C4×C8×C151—22no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—42no—
111#41×C151—42no—
112C2×Q8×C151—21no—
113C2×Q8×C151—22no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—41no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151—41no—
120C2×Q8×C151C2×D411yescharacteristic
121C2×Q8×C151C2×D411yescharacteristic
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—41no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—41no—
129C22×C4×C151—41no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151#4111yescharacteristic
133Q16×C151—44no—
134Q16×C151—44no—
135SD16×C151—42no—
136SD16×C151—42no—
137M16×C151—22no—
138M16×C151—22no—
139M16×C151—42no—
140C2×C8×C151—22no—
141C2×C8×C151—21no—
142C2×C8×C151—21no—
143C2×C8×C151—22no—
144C2×C8×C151—42no—
145C2×C8×C151C2×D412yes—
146C2×C8×C151C2×D412yes—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—41no—
157C4⋊C4×C151—41no—
158C4⋊C4×C151C2×D411yescharacteristic
159C4⋊C4×C151C2×D411yescharacteristic
160C22⋊C4×C151—41no—
161C22⋊C4×C151—41no—
162C42×C151—21no—
163C42×C151—21no—
164C42×C151—21no—
165C42×C151—21no—
166C42×C151C2×D411yescharacteristic
167C42×C151C2×D411yescharacteristic
168C42×C151#4111yescharacteristic
169C42×C151C2411yescharacteristic
170C23×C151—41no—
171C23×C151#12111yescharacteristic
172Q8×C151—21no—
173Q8×C151—21no—
174Q8×C151—21no—
175Q8×C151—42no—
176Q8×C151—41no—
177Q8×C151—42no—
178Q8×C151—41no—
179Q8×C151—42no—
180Q8×C151—82no—
181Q8×C151AGL(1,ℤ/8)12yes—
182D4×C151—41no—
183D4×C151—41no—
184D4×C151—41no—
185D4×C151—41no—
186D4×C151—81no—
187D4×C151—82no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—41no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—41no—
198C2×C4×C151—81no—
199C2×C4×C151—82no—
200C2×C4×C151—82no—
201C2×C4×C151#12111yescharacteristic
202C2×C4×C151#12111yescharacteristic
203C2×C4×C151#12111yescharacteristic
204C2×C4×C151#13512yes—
205C2×C4×C151#13712yes—
206C2×C4×C151C22×D411yescharacteristic
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C2×#4111yescharacteristic
209C8×C151—22no—
210C8×C151—22no—
211C8×C151—42no—
212C8×C151—42no—
213C8×C151—41no—
214C8×C151—41no—
215C22×C151—21no—
216C22×C151—21no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151#46412yes—
221C22×C151C2×#12111yescharacteristic
222C4×C151—21no—
223C4×C151—22no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—41no—
227C4×C151—41no—
228C4×C151—41no—
229C4×C151—81no—
230C4×C151—82no—
231C4×C151#46412yes—
232C4×C151C2×#13511yescharacteristic
233C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C151C2×#13711yescharacteristic
235C4×C151#57511yescharacteristic
236C2×C151—22no—
237C2×C151—161no—
238C2×C151C2×#46411yescharacteristic
239C2×C151#305511yescharacteristic
240C2×C151#306911yescharacteristic
241#19177C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#1917711yescharacteristic, direct product factor, Sylow
243#3141C2×C15111yescharacteristic
244#3103C2×C15111yescharacteristic
245C2×#462C2×C15111yescharacteristic, complemented
246Q8×M16C2×C15111yescharacteristic, complemented
247#1702C2×C15112yescomplemented
248#1700C2×C15112yescomplemented
249#1682C2×C15112yescomplemented
250#1680C2×C15112yescomplemented
251#1565C2×C15111yescharacteristic, complemented
252#1549C2×C15111yescharacteristic, complemented
253#1547C2×C15111yescharacteristic
254C22×Q16—21no—
255#532C22×C15111yescharacteristic
256C2×C4⋊Q8C22×C15111yescharacteristic
257C2×C4×Q8C22×C15111yescharacteristic
258#489—22no—
259#487C22×C15112yes—
260#486C22×C15112yes—
261#481—21no—
262#475C22×C15111yescharacteristic
263#475C22×C15111yescharacteristic
264#462—21no—
265#462—21no—
266#462C22×C15112yes—
267#462C22×C15112yes—
268#460C22×C15111yescharacteristic
269#460C22×C15111yescharacteristic
270#448—21no—
271#446—22no—
272#446C22×C15112yes—
273C8×Q8C22×C15112yes—
274C4×SD16—21no—
275C4×SD16—21no—
276#431C22×C15111yescharacteristic
277#423—21no—
278#423C22×C15111yescharacteristic
279C2×C4⋊C8C22×C15111yescharacteristic
280#417—21no—
281#417—21no—
282C2×#103—21no—
283C4×M16—21no—
284C4×M16C22×C15111yescharacteristic
285#335C22×C15112yes—
286#334C22×C15112yes—
287#332C22×C15112yes—
288#332C22×C15112yes—
289#332C22×C15112yes—
290#331C22×C15112yes—
291C2×#41—21no—
292C22×Q8—21no—
293C22×Q8D4×C15111yescharacteristic
294C2×Q16—22no—
295C2×Q16—22no—
296C2×Q16—44no—
297C2×SD16—21no—
298C2×SD16—21no—
299C2×M16—21no—
300C2×M16D4×C15111yescharacteristic
301C2×M16D4×C15111yescharacteristic
302C22×C8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C15112yes—
307C4⋊Q8C23×C15111yescharacteristic
308#127C23×C15111yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C15111yescharacteristic
315C4×Q8D4×C15111yescharacteristic
316C4×Q8C23×C15111yescharacteristic
317C4×Q8C23×C15111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C15111yescharacteristic
324C2×C42—21no—
325C2×C42C23×C15111yescharacteristic
326#106—21no—
327#106—21no—
328C4⋊C8—22no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8C23×C15112yes—
333C4⋊C8C23×C15112yes—
334C4⋊C8C23×C15111yescharacteristic
335C4⋊C8C23×C15111yescharacteristic
336#103—21no—
337#103—21no—
338#103—22no—
339#103—22no—
340#103—22no—
341#103—22no—
342#102—22no—
343#102—22no—
344#102—21no—
345#102—21no—
346C22⋊C8—21no—
347#97—22no—
348#97D4×C15112yes—
349C4×C8—22no—
350C4×C8—21no—
351C4×C8C23×C15112yes—
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8C2×D4×C15111yescharacteristic
363C2×Q8C2×D4×C15111yescharacteristic
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4C2×D4×C15111yescharacteristic
373C22×C4C2×D4×C15111yescharacteristic
374C22×C4#41×C15111yescharacteristic
375Q16—44no—
376Q16—44no—
377SD16—42no—
378SD16—42no—
379M16—22no—
380M16—22no—
381M16—42no—
382C2×C8—22no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8C2×D4×C15112yes—
388C2×C8C2×D4×C15112yes—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4C2×D4×C15111yescharacteristic
401C4⋊C4C2×D4×C15111yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42C2×D4×C15111yescharacteristic
409C42C2×D4×C15111yescharacteristic
410C42#41×C15111yescharacteristic
411C42C24×C15111yescharacteristic
412C23—41no—
413C23#121×C15111yescharacteristic
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—41no—
419Q8—42no—
420Q8—41no—
421Q8—42no—
422Q8—82no—
423Q8AGL(1,ℤ/8)×C15112yes—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—81no—
429D4—82no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4#121×C15111yescharacteristic
444C2×C4#121×C15111yescharacteristic
445C2×C4#121×C15111yescharacteristic
446C2×C4#135×C15112yes—
447C2×C4#137×C15112yes—
448C2×C4C22×D4×C15111yescharacteristic
449C2×C4C22×D4×C15111yescharacteristic
450C2×C4C2×#41×C15111yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22#464×C15112yes—
463C22C2×#121×C15111yescharacteristic
464C4—21no—
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—82no—
473C4#464×C15112yes—
474C4C2×#135×C15111yescharacteristic
475C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
476C4C2×#137×C15111yescharacteristic
477C4#575×C15111yescharacteristic
478C2—22no—
479C2—161no—
480C2C2×#464×C15111yescharacteristic
481C2#3055×C15111yescharacteristic
482C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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
3. C2×#462×C151C2semidirect
4. Q8×M16×C151C2semidirect
5. #1702×C151C2semidirect
6. #1700×C151C2semidirect
7. #1682×C151C2semidirect
8. #1680×C151C2semidirect
9. #1565×C151C2semidirect
10. #1549×C151C2semidirect
241. #19177C151direct (N × H)
242. C151#19177direct (N × H)
245. C2×#462C2×C151semidirect
246. Q8×M16C2×C151semidirect
247. #1702C2×C151semidirect
248. #1700C2×C151semidirect
249. #1682C2×C151semidirect
250. #1680C2×C151semidirect
251. #1565C2×C151semidirect
252. #1549C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3141×C1512
#3103×C1512
C2×#462×C1512
Q8×M16×C1512
#1702×C1512
#1700×C1512
#1682×C1512
#1680×C1512
#1565×C1512
#1549×C1512
#1547×C1512
#19177151