Finite Group Databasebeta

← C151×#19155 #50324080

Subgroups — C151×#19155 #50324080

Order 38656.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3131×C151C211yesmaximal, characteristic
2#3104×C151C211yesmaximal, characteristic, complemented
3#3103×C151C211yesmaximal, characteristic
4C2×#446×C151C211yesmaximal, characteristic, complemented
5#1704×C151C212yesmaximal, complemented
6#1702×C151C212yesmaximal, complemented
7#1700×C151C212yesmaximal, complemented
8#1698×C151C212yesmaximal, complemented
9#1564×C151C211yesmaximal, characteristic, complemented
10#1542×C151C211yesmaximal, characteristic, complemented
11#1540×C151C211yesmaximal, characteristic
12#533×C151C2211yescharacteristic
13#532×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15#488×C151—21no—
16#488×C151—21no—
17#487×C151C2211yescharacteristic
18#487×C151C2211yescharacteristic
19#486×C151C2211yescharacteristic
20#486×C151C2211yescharacteristic
21#484×C151—21no—
22#481×C151—21no—
23#477×C151C2212yes—
24#475×C151C2212yes—
25#462×C151C2212yes—
26#460×C151C2212yes—
27#451×C151—21no—
28#448×C151—21no—
29#446×C151—21no—
30#446×C151—21no—
31#446×C151C2212yes—
32#446×C151C2212yes—
33C4×Q16×C151—22no—
34C4×SD16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37C2×C4⋊C8×C151—21no—
38C2×C4⋊C8×C151C2211yescharacteristic
39#416×C151—21no—
40#416×C151—21no—
41C2×#97×C151—21no—
42C2×C4×C8×C151C2211yescharacteristic
43#335×C151C2212yes—
44#334×C151C2212yes—
45#333×C151C2212yes—
46#332×C151C2212yes—
47#332×C151C2212yes—
48#331×C151C2212yes—
49C2×#41×C151—21no—
50C22×Q8×C151D411yescharacteristic
51C2×Q16×C151—22no—
52C2×SD16×C151—22no—
53C22×C8×C151—21no—
54C22×C8×C151D411yescharacteristic
55C22×C8×C151D411yescharacteristic
56C4⋊Q8×C151C2311yescharacteristic
57C4⋊Q8×C151C2311yescharacteristic
58C4⋊Q8×C151C2311yescharacteristic
59#127×C151C2311yescharacteristic
60#125×C151—21no—
61#124×C151—21no—
62C22⋊Q8×C151—21no—
63C22⋊Q8×C151—21no—
64#121×C151—21no—
65#121×C151—21no—
66C4×Q8×C151—21no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151D412yes—
71C4×Q8×C151C2312yes—
72C4×D4×C151—21no—
73C4×D4×C151—21no—
74#117×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151D411yescharacteristic
77C2×C42×C151—21no—
78C2×C42×C151C2311yescharacteristic
79#107×C151—22no—
80#106×C151—22no—
81C4⋊C8×C151—22no—
82C4⋊C8×C151—22no—
83C4⋊C8×C151—21no—
84C4⋊C8×C151C2312yes—
85C4⋊C8×C151C2312yes—
86C4⋊C8×C151C2312yes—
87#103×C151—21no—
88#103×C151—21no—
89#103×C151—21no—
90#103×C151—21no—
91#103×C151—22no—
92#103×C151—22no—
93#103×C151—22no—
94#102×C151—21no—
95#102×C151—21no—
96#102×C151—21no—
97#102×C151—21no—
98#102×C151—22no—
99C22⋊C8×C151—21no—
100C22⋊C8×C151—21no—
101#97×C151—22no—
102#97×C151—22no—
103C4×C8×C151—21no—
104C4×C8×C151—21no—
105C4×C8×C151D411yescharacteristic
106C4×C8×C151D411yescharacteristic
107C4×C8×C151C2311yescharacteristic
108C4×C8×C151C2311yescharacteristic
109#41×C151—42no—
110#41×C151—42no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—42no—
116C2×Q8×C151C2×D412yes—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—41no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—41no—
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151#4111yescharacteristic
127Q16×C151—44no—
128SD16×C151—44no—
129C2×C8×C151—22no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151—42no—
135C2×C8×C151C2×D411yescharacteristic
136C2×C8×C151C2×D411yescharacteristic
137C2×C8×C151C2×D411yescharacteristic
138C2×C8×C151C2×D411yescharacteristic
139C4⋊C4×C151—22no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—41no—
152C22⋊C4×C151—41no—
153C22⋊C4×C151—41no—
154C42×C151—22no—
155C42×C151—22no—
156C42×C151—41no—
157C42×C151C2×D411yescharacteristic
158C42×C151C2×D411yescharacteristic
159C42×C151#4111yescharacteristic
160C42×C151C2411yescharacteristic
161C23×C151—41no—
162C23×C151#12111yescharacteristic
163Q8×C151—22no—
164Q8×C151—22no—
165Q8×C151—42no—
166Q8×C151—41no—
167Q8×C151—41no—
168Q8×C151—42no—
169Q8×C151—81no—
170D4×C151—41no—
171D4×C151—41no—
172D4×C151—42no—
173D4×C151—81no—
174D4×C151—82no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—82no—
185C2×C4×C151#12111yescharacteristic
186C2×C4×C151#12111yescharacteristic
187C2×C4×C151#12111yescharacteristic
188C2×C4×C151#13512yes—
189C2×C4×C151#13712yes—
190C2×C4×C151C22×D411yescharacteristic
191C2×C4×C151C22×D411yescharacteristic
192C2×C4×C151C2×#4111yescharacteristic
193C8×C151—21no—
194C8×C151—21no—
195C8×C151—21no—
196C8×C151—21no—
197C8×C151—42no—
198C8×C151—42no—
199C8×C151—42no—
200C22×C151—21no—
201C22×C151—21no—
202C22×C151—81no—
203C22×C151—81no—
204C22×C151—81no—
205C22×C151#46412yes—
206C22×C151C2×#12111yescharacteristic
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—21no—
210C4×C151—42no—
211C4×C151—42no—
212C4×C151—81no—
213C4×C151—81no—
214C4×C151—81no—
215C4×C151#46412yes—
216C4×C151C2×#13511yescharacteristic
217C4×C151C2×#13711yescharacteristic
218C4×C151#57512yes—
219C2×C151—22no—
220C2×C151—161no—
221C2×C151C2×#46411yescharacteristic
222C2×C151#305411yescharacteristic
223C2×C151#306711yescharacteristic
224#19155C15111yesmaximal, characteristic, direct product factor, Sylow
225C151#1915511yescharacteristic, direct product factor, Sylow
226#3131C2×C15111yescharacteristic
227#3104C2×C15111yescharacteristic, complemented
228#3103C2×C15111yescharacteristic
229C2×#446C2×C15111yescharacteristic, complemented
230#1704C2×C15112yescomplemented
231#1702C2×C15112yescomplemented
232#1700C2×C15112yescomplemented
233#1698C2×C15112yescomplemented
234#1564C2×C15111yescharacteristic, complemented
235#1542C2×C15111yescharacteristic, complemented
236#1540C2×C15111yescharacteristic
237#533C22×C15111yescharacteristic
238#532C22×C15111yescharacteristic
239C2×C4×Q8C22×C15111yescharacteristic
240#488—21no—
241#488—21no—
242#487C22×C15111yescharacteristic
243#487C22×C15111yescharacteristic
244#486C22×C15111yescharacteristic
245#486C22×C15111yescharacteristic
246#484—21no—
247#481—21no—
248#477C22×C15112yes—
249#475C22×C15112yes—
250#462C22×C15112yes—
251#460C22×C15112yes—
252#451—21no—
253#448—21no—
254#446—21no—
255#446—21no—
256#446C22×C15112yes—
257#446C22×C15112yes—
258C4×Q16—22no—
259C4×SD16—22no—
260#431C22×C15111yescharacteristic
261#431C22×C15111yescharacteristic
262C2×C4⋊C8—21no—
263C2×C4⋊C8C22×C15111yescharacteristic
264#416—21no—
265#416—21no—
266C2×#97—21no—
267C2×C4×C8C22×C15111yescharacteristic
268#335C22×C15112yes—
269#334C22×C15112yes—
270#333C22×C15112yes—
271#332C22×C15112yes—
272#332C22×C15112yes—
273#331C22×C15112yes—
274C2×#41—21no—
275C22×Q8D4×C15111yescharacteristic
276C2×Q16—22no—
277C2×SD16—22no—
278C22×C8—21no—
279C22×C8D4×C15111yescharacteristic
280C22×C8D4×C15111yescharacteristic
281C4⋊Q8C23×C15111yescharacteristic
282C4⋊Q8C23×C15111yescharacteristic
283C4⋊Q8C23×C15111yescharacteristic
284#127C23×C15111yescharacteristic
285#125—21no—
286#124—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—21no—
290#121—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C15112yes—
296C4×Q8C23×C15112yes—
297C4×D4—21no—
298C4×D4—21no—
299#117—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C15111yescharacteristic
302C2×C42—21no—
303C2×C42C23×C15111yescharacteristic
304#107—22no—
305#106—22no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308C4⋊C8—21no—
309C4⋊C8C23×C15112yes—
310C4⋊C8C23×C15112yes—
311C4⋊C8C23×C15112yes—
312#103—22no—
313#103—22no—
314#103—21no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—22no—
319#102—21no—
320#102—21no—
321#102—21no—
322#102—21no—
323#102—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—22no—
327#97—22no—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8D4×C15111yescharacteristic
331C4×C8D4×C15111yescharacteristic
332C4×C8C23×C15111yescharacteristic
333C4×C8C23×C15111yescharacteristic
334#41—42no—
335#41—42no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C15112yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C15111yescharacteristic
350C22×C4C2×D4×C15111yescharacteristic
351C22×C4#41×C15111yescharacteristic
352Q16—44no—
353SD16—44no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—42no—
360C2×C8C2×D4×C15111yescharacteristic
361C2×C8C2×D4×C15111yescharacteristic
362C2×C8C2×D4×C15111yescharacteristic
363C2×C8C2×D4×C15111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4C2×D4×C15112yes—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42—22no—
380C42—22no—
381C42—41no—
382C42C2×D4×C15111yescharacteristic
383C42C2×D4×C15111yescharacteristic
384C42#41×C15111yescharacteristic
385C42C24×C15111yescharacteristic
386C23—41no—
387C23#121×C15111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—41no—
392Q8—41no—
393Q8—42no—
394Q8—81no—
395D4—41no—
396D4—41no—
397D4—42no—
398D4—81no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4#121×C15111yescharacteristic
411C2×C4#121×C15111yescharacteristic
412C2×C4#121×C15111yescharacteristic
413C2×C4#135×C15112yes—
414C2×C4#137×C15112yes—
415C2×C4C22×D4×C15111yescharacteristic
416C2×C4C22×D4×C15111yescharacteristic
417C2×C4C2×#41×C15111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—42no—
424C8—42no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22#464×C15112yes—
431C22C2×#121×C15111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4#464×C15112yes—
441C4C2×#135×C15111yescharacteristic
442C4C2×#137×C15111yescharacteristic
443C4#575×C15112yes—
444C2—22no—
445C2—161no—
446C2C2×#464×C15111yescharacteristic
447C2#3054×C15111yescharacteristic
448C2#3067×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutator, Frattini, cosocleC42C24×C151
socleC22×C151C2×#121
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3104×C151C2semidirect
4. C2×#446×C151C2semidirect
5. #1704×C151C2semidirect
6. #1702×C151C2semidirect
7. #1700×C151C2semidirect
8. #1698×C151C2semidirect
9. #1564×C151C2semidirect
10. #1542×C151C2semidirect
224. #19155C151direct (N × H)
225. C151#19155direct (N × H)
227. #3104C2×C151semidirect
229. C2×#446C2×C151semidirect
230. #1704C2×C151semidirect
231. #1702C2×C151semidirect
232. #1700C2×C151semidirect
233. #1698C2×C151semidirect
234. #1564C2×C151semidirect
235. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3131×C1512
#3104×C1512
#3103×C1512
C2×#446×C1512
#1704×C1512
#1702×C1512
#1700×C1512
#1698×C1512
#1564×C1512
#1542×C1512
#1540×C1512
#19155151