Finite Group Databasebeta

← C151×#24697 #50329622

Subgroups — C151×#24697 #50329622

Order 38656.

780 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
1C2×#476×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic
3#2568×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic
5#2073×C151C212yesmaximal
6#2055×C151C212yesmaximal
7#1993×C151C211yesmaximal, characteristic, complemented
8#1949×C151C212yesmaximal, complemented
9#1940×C151C211yesmaximal, characteristic, complemented
10#1927×C151C212yesmaximal, complemented
11#1805×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16#476×C151—24no—
17#440×C151—24no—
18C2×#107×C151C2211yescharacteristic
19C2×#106×C151C2212yes—
20C2×C4⋊C8×C151C2212yes—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×#103×C151C2211yescharacteristic
23C2×#103×C151C2212yes—
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2212yes—
26C2×#97×C151C2211yescharacteristic
27#400×C151—21no—
28#400×C151—21no—
29#391×C151—22no—
30#391×C151C2212yes—
31#390×C151C2212yes—
32#388×C151—22no—
33#382×C151C2211yescharacteristic
34#382×C151C2212yes—
35#381×C151—21no—
36C4×C4⋊C4×C151C2212yes—
37C4×C4⋊C4×C151C2211yescharacteristic
38C4×C22⋊C4×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2311yescharacteristic
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×Q8×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151D414yes—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151D412yes—
62C2×C4⋊C4×C151C2312yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151—22no—
69C2×C42×C151—21no—
70C2×C42×C151—22no—
71C2×C42×C151C2312yes—
72C2×C42×C151C2311yescharacteristic
73#107×C151—22no—
74#106×C151—24no—
75C4⋊C8×C151—24no—
76C4⋊C8×C151—22no—
77#103×C151—22no—
78#103×C151—24no—
79#102×C151—22no—
80#102×C151—24no—
81#97×C151—22no—
82#95×C151—21no—
83#95×C151—22no—
84#95×C151—21no—
85#95×C151—22no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151D411yescharacteristic
90#95×C151D411yescharacteristic
91C24×C151—21no—
92C2×Q8×C151—21no—
93C2×Q8×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—44no—
98C2×Q8×C151—42no—
99C2×Q8×C151#4112yes—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2×D412yes—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
108C22×C4×C151—24no—
109C22×C4×C151—21no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—82no—
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D412yes—
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2411yescharacteristic
118SD16×C151—28no—
119C2×C8×C151—21no—
120C2×C8×C151—21no—
121C2×C8×C151—21no—
122C2×C8×C151—22no—
123C2×C8×C151—22no—
124C2×C8×C151—22no—
125C2×C8×C151—21no—
126C2×C8×C151—21no—
127C2×C8×C151#4112yes—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—42no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151—42no—
138C4⋊C4×C151C2×D412yes—
139C22⋊C4×C151—24no—
140C22⋊C4×C151—44no—
141C22⋊C4×C151—82no—
142C42×C151—22no—
143C42×C151—22no—
144C42×C151—42no—
145C42×C151—82no—
146C42×C151C2×D412yes—
147C42×C151#4112yes—
148C23×C151—22no—
149C23×C151—41no—
150C23×C151—41no—
151C23×C151—42no—
152C23×C151—42no—
153C23×C151C22×D411yescharacteristic
154Q8×C151—22no—
155Q8×C151—22no—
156Q8×C151—41no—
157Q8×C151—41no—
158Q8×C151—84no—
159D4×C151—22no—
160D4×C151—22no—
161D4×C151—41no—
162D4×C151—41no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—41no—
178C2×C4×C151—42no—
179C2×C4×C151—44no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—84no—
184C2×C4×C151#12112yes—
185C2×C4×C151#12112yes—
186C2×C4×C151C22×D411yescharacteristic
187C2×C4×C151C2×#4111yescharacteristic
188C2×C4×C151C2×#4111yescharacteristic
189C2×C4×C151C2×#4111yescharacteristic
190C2×C4×C1512−1+411yescharacteristic
191C2×C4×C1512−1+411yescharacteristic
192C8×C151—22no—
193C8×C151—42no—
194C8×C151—41no—
195C22×C151—42no—
196C22×C151—42no—
197C22×C151—42no—
198C22×C151—82no—
199C22×C151—82no—
200C22×C151C2×#12111yescharacteristic
201C22×C151#54711yescharacteristic
202C22×C151#54811yescharacteristic
203C22×C151#57512yes—
204C22×C151#57712yes—
205C4×C151—22no—
206C4×C151—22no—
207C4×C151—42no—
208C4×C151—42no—
209C4×C151—42no—
210C4×C151—42no—
211C4×C151—82no—
212C4×C151—82no—
213C4×C151—81no—
214C4×C151#52511yescharacteristic
215C4×C151#53611yescharacteristic
216C4×C151#55211yescharacteristic
217C4×C151#55611yescharacteristic
218C2×C151—82no—
219C2×C151#241511yescharacteristic
220C2×C151#304011yescharacteristic
221C2×C151#304211yescharacteristic
222C2×C151#335012yes—
223C2×C151#337112yes—
224#24697C15111yesmaximal, characteristic, direct product factor, Sylow
225C151#2469711yescharacteristic, direct product factor, Sylow
226C2×#476C2×C15111yescharacteristic
227C2×#440C2×C15111yescharacteristic
228#2568C2×C15111yescharacteristic, complemented
229#2357C2×C15111yescharacteristic
230#2073C2×C15112yes—
231#2055C2×C15112yes—
232#1993C2×C15111yescharacteristic, complemented
233#1949C2×C15112yescomplemented
234#1940C2×C15111yescharacteristic, complemented
235#1927C2×C15112yescomplemented
236#1805C2×C15111yescharacteristic, complemented
237C22×SD16C22×C15111yescharacteristic
238C2×C4⋊Q8C22×C15111yescharacteristic
239C2×C4×Q8C22×C15111yescharacteristic
240C2×C4×D4C22×C15111yescharacteristic
241#476—24no—
242#440—24no—
243C2×#107C22×C15111yescharacteristic
244C2×#106C22×C15112yes—
245C2×C4⋊C8C22×C15112yes—
246C2×C4⋊C8C22×C15111yescharacteristic
247C2×#103C22×C15112yes—
248C2×#103C22×C15111yescharacteristic
249C2×#102C22×C15112yes—
250C2×#102C22×C15111yescharacteristic
251C2×#97C22×C15111yescharacteristic
252#400—21no—
253#400—21no—
254#391—22no—
255#391C22×C15112yes—
256#390C22×C15112yes—
257#388—22no—
258#382C22×C15112yes—
259#382C22×C15111yescharacteristic
260#381—21no—
261C4×C4⋊C4C22×C15112yes—
262C4×C4⋊C4C22×C15111yescharacteristic
263C4×C22⋊C4—21no—
264#340C22×C15112yes—
265#340C22×C15112yes—
266#340C22×C15112yes—
267#336C22×C15112yes—
268C22×Q8—21no—
269C22×Q8C23×C15111yescharacteristic
270C22×D4C23×C15111yescharacteristic
271C23×C4—21no—
272C2×SD16—22no—
273C2×SD16—22no—
274C2×SD16—22no—
275C22×C8C23×C15111yescharacteristic
276C22×C8C23×C15112yes—
277C22×C8C23×C15111yescharacteristic
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C4×Q8—22no—
281C4×Q8—22no—
282C4×D4—22no—
283C4×D4D4×C15114yes—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4D4×C15112yes—
287C2×C4⋊C4C23×C15111yescharacteristic
288C2×C4⋊C4C23×C15112yes—
289C2×C4⋊C4C23×C15112yes—
290C2×C4⋊C4C23×C15111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C42—21no—
295C2×C42—22no—
296C2×C42C23×C15112yes—
297C2×C42C23×C15111yescharacteristic
298#107—22no—
299#106—24no—
300C4⋊C8—24no—
301C4⋊C8—22no—
302#103—24no—
303#103—22no—
304#102—22no—
305#102—24no—
306#97—22no—
307#95—21no—
308#95—22no—
309#95—21no—
310#95—22no—
311#95—22no—
312#95—22no—
313#95—22no—
314#95D4×C15111yescharacteristic
315#95D4×C15111yescharacteristic
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—44no—
323C2×Q8—42no—
324C2×Q8#41×C15112yes—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4C2×D4×C15112yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—82no—
338C22×C4C2×D4×C15112yes—
339C22×C4C2×D4×C15112yes—
340C22×C4C2×D4×C15111yescharacteristic
341C22×C4C2×D4×C15111yescharacteristic
342C22×C4C24×C15111yescharacteristic
343SD16—28no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8#41×C15112yes—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4C2×D4×C15112yes—
364C22⋊C4—24no—
365C22⋊C4—44no—
366C22⋊C4—82no—
367C42—22no—
368C42—22no—
369C42—42no—
370C42—82no—
371C42C2×D4×C15112yes—
372C42#41×C15112yes—
373C23—22no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—42no—
378C23C22×D4×C15111yescharacteristic
379Q8—22no—
380Q8—22no—
381Q8—41no—
382Q8—41no—
383Q8—84no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4#121×C15112yes—
410C2×C4#121×C15112yes—
411C2×C4C22×D4×C15111yescharacteristic
412C2×C4C2×#41×C15111yescharacteristic
413C2×C4C2×#41×C15111yescharacteristic
414C2×C4C2×#41×C15111yescharacteristic
415C2×C42−1+4×C15111yescharacteristic
416C2×C42−1+4×C15111yescharacteristic
417C8—22no—
418C8—42no—
419C8—41no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—82no—
424C22—82no—
425C22C2×#121×C15111yescharacteristic
426C22#547×C15111yescharacteristic
427C22#548×C15111yescharacteristic
428C22#575×C15112yes—
429C22#577×C15112yes—
430C4—22no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4—82no—
438C4—81no—
439C4#525×C15111yescharacteristic
440C4#536×C15111yescharacteristic
441C4#552×C15111yescharacteristic
442C4#556×C15111yescharacteristic
443C2—82no—
444C2#2415×C15111yescharacteristic
445C2#3040×C15111yescharacteristic
446C2#3042×C15111yescharacteristic
447C2#3350×C15112yes—
448C2#3371×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2568×C151C2semidirect
7. #1993×C151C2semidirect
8. #1949×C151C2semidirect
9. #1940×C151C2semidirect
10. #1927×C151C2semidirect
11. #1805×C151C2semidirect
224. #24697C151direct (N × H)
225. C151#24697direct (N × H)
228. #2568C2×C151semidirect
232. #1993C2×C151semidirect
233. #1949C2×C151semidirect
234. #1940C2×C151semidirect
235. #1927C2×C151semidirect
236. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
C2×#440×C1512
#2568×C1512
#2357×C1512
#2073×C1512
#2055×C1512
#1993×C1512
#1949×C1512
#1940×C1512
#1927×C1512
#1805×C1512
#24697151