Finite Group Databasebeta

← C151×#23094 #50328019

Subgroups — C151×#23094 #50328019

Order 38656.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic
2#2365×C151C211yesmaximal, characteristic, complemented
3#2354×C151C211yesmaximal, characteristic
4#1968×C151C212yesmaximal
5#1956×C151C211yesmaximal, characteristic, complemented
6#1948×C151C211yesmaximal, characteristic, complemented
7#1927×C151C212yesmaximal, complemented
8#1880×C151C212yesmaximal
9C8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
10C4×#103×C151C212yesmaximal, complemented
11C4×#102×C151C211yesmaximal, characteristic
12C22×SD16×C151C2212yes—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×Q8×C151C2212yes—
15C2×C4×D4×C151C2211yescharacteristic
16C2×#117×C151—21no—
17#461×C151C418yescomplemented
18C2×#106×C151C2212yes—
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×#103×C151C2212yes—
21C2×#103×C151C2212yes—
22C2×#103×C151C2212yes—
23C2×#102×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×C4×C8×C151C2211yescharacteristic
26C2×C4×C8×C151C2212yes—
27#391×C151C2212yes—
28#390×C151C2212yes—
29#389×C151—21no—
30#388×C151—22no—
31#387×C151—22no—
32#384×C151C2211yescharacteristic
33#380×C151—21no—
34C4×C4⋊C4×C151—21no—
35C4×C4⋊C4×C151C2212yes—
36C4×C4⋊C4×C151C2211yescharacteristic
37C4×C4⋊C4×C151C2211yescharacteristic
38#340×C151C2212yes—
39#340×C151C2211yescharacteristic
40#340×C151C2211yescharacteristic
41#336×C151C2212yes—
42C22×Q8×C151C2312yes—
43C22×D4×C151C2311yescharacteristic
44C23×C4×C151—21no—
45C2×SD16×C151—42no—
46C2×SD16×C151—42no—
47C2×SD16×C151C2×C418yes—
48C22×C8×C151C2311yescharacteristic
49C22×C8×C151C2312yes—
50C22×C8×C151C2311yescharacteristic
51C4⋊Q8×C151—22no—
52C4⋊Q8×C151C2×C414yes—
53C4×Q8×C151—24no—
54C4×Q8×C151—42no—
55C4×D4×C151—22no—
56C4×D4×C151C2×C414yes—
57#117×C151—44no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151D411yescharacteristic
64C2×C4⋊C4×C151D411yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—21no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C42×C151—21no—
73C2×C42×C151—22no—
74C2×C42×C151—22no—
75C2×C42×C151C2312yes—
76C2×C42×C151C2311yescharacteristic
77#106×C151—42no—
78C4⋊C8×C151C2×C414yes—
79#103×C151—24no—
80#103×C151—42no—
81#103×C151C2×C418yes—
82#102×C151—22no—
83#102×C151—22no—
84C4×C8×C151—22no—
85C4×C8×C151—42no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—21no—
89#95×C151—22no—
90#95×C151D412yes—
91C24×C151—21no—
92C2×Q8×C151—22no—
93C2×Q8×C151—22no—
94C2×Q8×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151—22no—
97C2×Q8×C151C22×C414yes—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151C22×C412yes—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—24no—
108C22×C4×C151—21no—
109C22×C4×C151—22no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151C2×D412yes—
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D412yes—
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2411yescharacteristic
117SD16×C151—48no—
118C2×C8×C151—21no—
119C2×C8×C151—21no—
120C2×C8×C151—22no—
121C2×C8×C151—22no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151—21no—
125C2×C8×C151C22×C414yes—
126C2×C8×C151#4112yes—
127C4⋊C4×C151—24no—
128C4⋊C4×C151—24no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—44no—
137C4⋊C4×C151—42no—
138C4⋊C4×C151—81no—
139C4⋊C4×C151SD1614yescomplemented
140C4⋊C4×C151C22×C412yes—
141C4⋊C4×C151#4112yes—
142C22⋊C4×C151—24no—
143C22⋊C4×C151—44no—
144C22⋊C4×C151—82no—
145C42×C151—22no—
146C42×C151—22no—
147C42×C151—44no—
148C42×C151—44no—
149C42×C151—42no—
150C42×C151C22×C412yes—
151C42×C151#4112yes—
152C23×C151—22no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151C22×D411yescharacteristic
160Q8×C151—24no—
161Q8×C151—24no—
162Q8×C151—42no—
163Q8×C151—42no—
164D4×C151—22no—
165D4×C151—22no—
166D4×C151—41no—
167D4×C151—41no—
168C2×C4×C151—22no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—22no—
172C2×C4×C151—24no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—41no—
184C2×C4×C151—48no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151C4×D412yes—
192C2×C4×C151C4×D412yes—
193C2×C4×C151C2×SD1614yes—
194C2×C4×C151C2×SD1612yes—
195C2×C4×C151#13512yes—
196C2×C4×C151C23×C411yescharacteristic
197C2×C4×C151C2×#4111yescharacteristic
198C2×C4×C151C2×#4111yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C2×C4×C151H(5,𝔽2)11yescharacteristic
201C2×C4×C151H(5,𝔽2)11yescharacteristic
202C8×C151—24no—
203C8×C151—22no—
204C8×C151—41no—
205C22×C151—42no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—81no—
209C22×C151—81no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151C2×C4×D411yescharacteristic
213C22×C151#54611yescharacteristic
214C22×C151#55011yescharacteristic
215C22×C151C22×SD1611yescharacteristic
216C22×C151C2×#13511yescharacteristic
217C22×C151#57711yescharacteristic
218C22×C151#57811yescharacteristic
219C4×C151—22no—
220C4×C151—24no—
221C4×C151—44no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—82no—
226C4×C151—81no—
227C4×C151C4×SD1614yes—
228C4×C151C4×#4111yescharacteristic
229C4×C151#51811yescharacteristic
230C4×C151#55311yescharacteristic
231C4×C151#55511yescharacteristic
232C2×C151—82no—
233C2×C151#236311yescharacteristic
234C2×C151C2×C4×SD1611yescharacteristic
235C2×C151#294711yescharacteristic
236C2×C151#329811yescharacteristic
237C2×C151#330311yescharacteristic
238C2×C151#339211yescharacteristic
239C2×C151#339311yescharacteristic
240#23094C15111yesmaximal, characteristic, direct product factor, Sylow
241C151#2309411yescharacteristic, direct product factor, Sylow
242C2×#461C2×C15111yescharacteristic
243#2365C2×C15111yescharacteristic, complemented
244#2354C2×C15111yescharacteristic
245#1968C2×C15112yes—
246#1956C2×C15111yescharacteristic, complemented
247#1948C2×C15111yescharacteristic, complemented
248#1927C2×C15112yescomplemented
249#1880C2×C15112yes—
250C8×C4⋊C4C2×C15111yescharacteristic, complemented
251C4×#103C2×C15112yescomplemented
252C4×#102C2×C15111yescharacteristic
253C22×SD16C22×C15112yes—
254C2×C4⋊Q8C22×C15111yescharacteristic
255C2×C4×Q8C22×C15112yes—
256C2×C4×D4C22×C15111yescharacteristic
257C2×#117—21no—
258#461C4×C15118yescomplemented
259C2×#106C22×C15112yes—
260C2×C4⋊C8C22×C15111yescharacteristic
261C2×#103C22×C15112yes—
262C2×#103C22×C15112yes—
263C2×#103C22×C15112yes—
264C2×#102C22×C15111yescharacteristic
265C2×#102C22×C15111yescharacteristic
266C2×C4×C8C22×C15111yescharacteristic
267C2×C4×C8C22×C15112yes—
268#391C22×C15112yes—
269#390C22×C15112yes—
270#389—21no—
271#388—22no—
272#387—22no—
273#384C22×C15111yescharacteristic
274#380—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4C22×C15112yes—
277C4×C4⋊C4C22×C15111yescharacteristic
278C4×C4⋊C4C22×C15111yescharacteristic
279#340C22×C15112yes—
280#340C22×C15111yescharacteristic
281#340C22×C15111yescharacteristic
282#336C22×C15112yes—
283C22×Q8C23×C15112yes—
284C22×D4C23×C15111yescharacteristic
285C23×C4—21no—
286C2×SD16—42no—
287C2×SD16—42no—
288C2×SD16C2×C4×C15118yes—
289C22×C8C23×C15111yescharacteristic
290C22×C8C23×C15111yescharacteristic
291C22×C8C23×C15112yes—
292C4⋊Q8—22no—
293C4⋊Q8C2×C4×C15114yes—
294C4×Q8—24no—
295C4×Q8—42no—
296C4×D4—22no—
297C4×D4C2×C4×C15114yes—
298#117—44no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C15111yescharacteristic
305C2×C4⋊C4D4×C15111yescharacteristic
306C2×C4⋊C4C23×C15112yes—
307C2×C4⋊C4C23×C15111yescharacteristic
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C4⋊C4C23×C15111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—21no—
316C2×C42C23×C15112yes—
317C2×C42C23×C15111yescharacteristic
318#106—42no—
319C4⋊C8C2×C4×C15114yes—
320#103—24no—
321#103—42no—
322#103C2×C4×C15118yes—
323#102—22no—
324#102—22no—
325C4×C8—22no—
326C4×C8—42no—
327#95—22no—
328#95—22no—
329#95—21no—
330#95—22no—
331#95D4×C15112yes—
332C24—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8C22×C4×C15114yes—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4C22×C4×C15112yes—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4C2×D4×C15112yes—
354C22×C4C2×D4×C15111yescharacteristic
355C22×C4C2×D4×C15112yes—
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C24×C15111yescharacteristic
358SD16—48no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C22×C4×C15114yes—
367C2×C8#41×C15112yes—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—44no—
378C4⋊C4—42no—
379C4⋊C4—81no—
380C4⋊C4SD16×C15114yescomplemented
381C4⋊C4C22×C4×C15112yes—
382C4⋊C4#41×C15112yes—
383C22⋊C4—24no—
384C22⋊C4—44no—
385C22⋊C4—82no—
386C42—22no—
387C42—22no—
388C42—44no—
389C42—44no—
390C42—42no—
391C42C22×C4×C15112yes—
392C42#41×C15112yes—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23C22×D4×C15111yescharacteristic
401Q8—24no—
402Q8—24no—
403Q8—42no—
404Q8—42no—
405D4—22no—
406D4—22no—
407D4—41no—
408D4—41no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—48no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4C4×D4×C15112yes—
433C2×C4C4×D4×C15112yes—
434C2×C4C2×SD16×C15114yes—
435C2×C4C2×SD16×C15112yes—
436C2×C4#135×C15112yes—
437C2×C4C23×C4×C15111yescharacteristic
438C2×C4C2×#41×C15111yescharacteristic
439C2×C4C2×#41×C15111yescharacteristic
440C2×C4C2×#41×C15111yescharacteristic
441C2×C4H(5,𝔽2)×C15111yescharacteristic
442C2×C4H(5,𝔽2)×C15111yescharacteristic
443C8—24no—
444C8—22no—
445C8—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22C2×C4×D4×C15111yescharacteristic
454C22#546×C15111yescharacteristic
455C22#550×C15111yescharacteristic
456C22C22×SD16×C15111yescharacteristic
457C22C2×#135×C15111yescharacteristic
458C22#577×C15111yescharacteristic
459C22#578×C15111yescharacteristic
460C4—22no—
461C4—24no—
462C4—44no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—81no—
468C4C4×SD16×C15114yes—
469C4C4×#41×C15111yescharacteristic
470C4#518×C15111yescharacteristic
471C4#553×C15111yescharacteristic
472C4#555×C15111yescharacteristic
473C2—82no—
474C2#2363×C15111yescharacteristic
475C2C2×C4×SD16×C15111yescharacteristic
476C2#2947×C15111yescharacteristic
477C2#3298×C15111yescharacteristic
478C2#3303×C15111yescharacteristic
479C2#3392×C15111yescharacteristic
480C2#3393×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×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
2. #2365×C151C2semidirect
5. #1956×C151C2semidirect
6. #1948×C151C2semidirect
7. #1927×C151C2semidirect
9. C8×C4⋊C4×C151C2semidirect
10. C4×#103×C151C2semidirect
17. #461×C151C4semidirect
139. C4⋊C4×C151SD16semidirect
240. #23094C151direct (N × H)
241. C151#23094direct (N × H)
243. #2365C2×C151semidirect
246. #1956C2×C151semidirect
247. #1948C2×C151semidirect
248. #1927C2×C151semidirect
250. C8×C4⋊C4C2×C151semidirect
251. C4×#103C2×C151semidirect
258. #461C4×C151semidirect
380. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
#2365×C1512
#2354×C1512
#1968×C1512
#1956×C1512
#1948×C1512
#1927×C1512
#1880×C1512
C8×C4⋊C4×C1512
C4×#103×C1512
C4×#102×C1512
#23094151