Finite Group Databasebeta

← C151×#23748 #50328673

Subgroups — C151×#23748 #50328673

Order 38656.

782 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2317×C151C211yesmaximal, characteristic
2#2317×C151C211yesmaximal, characteristic
3#2101×C151C212yesmaximal, complemented
4#2101×C151C212yesmaximal, complemented
5#2100×C151C212yesmaximal, complemented
6#2099×C151C212yesmaximal, complemented
7#1736×C151C211yesmaximal, characteristic
8#1736×C151C211yesmaximal, characteristic
9#1735×C151C211yesmaximal, characteristic
10C2×#340×C151C211yesmaximal, characteristic
11#1729×C151C211yesmaximal, characteristic
12C22×M16×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19#389×C151—21no—
20#389×C151—21no—
21#389×C151C2212yes—
22#389×C151C2212yes—
23#385×C151—22no—
24#385×C151—22no—
25#384×C151—21no—
26#384×C151C2212yes—
27#382×C151—21no—
28#382×C151C2212yes—
29#340×C151C2211yescharacteristic
30#340×C151C2212yes—
31#340×C151C2212yes—
32#340×C151C2212yes—
33#340×C151C2211yescharacteristic
34#340×C151C2212yes—
35#340×C151C2212yes—
36#340×C151C2211yescharacteristic
37#340×C151C2211yescharacteristic
38#340×C151C2212yes—
39#336×C151C2212yes—
40#336×C151C2212yes—
41C23×C4×C151—21no—
42C23×C4×C151—21no—
43C23×C4×C151C2311yescharacteristic
44C2×M16×C151—22no—
45C2×M16×C151—22no—
46C2×M16×C151—22no—
47C22×C8×C151—22no—
48C22×C8×C151—22no—
49C22×C8×C151—22no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2311yescharacteristic
52C22×C8×C151C2312yes—
53#117×C151—22no—
54#117×C151—22no—
55#117×C151—22no—
56#117×C151—22no—
57#117×C151—22no—
58#117×C151Q814yes—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151D411yescharacteristic
70C2×C4⋊C4×C151D411yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2312yes—
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151D412yes—
80C2×C42×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151C2312yes—
83#95×C151—22no—
84#95×C151—22no—
85#95×C151—22no—
86#95×C151—22no—
87C24×C151C2×D411yescharacteristic
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—42no—
95C22×C4×C151—42no—
96C22×C4×C151—81no—
97C22×C4×C151—81no—
98C22×C4×C151—81no—
99C22×C4×C151—81no—
100C22×C4×C151C2×D412yes—
101C22×C4×C151C2×D412yes—
102C22×C4×C151C2×D411yescharacteristic
103C22×C4×C151C2×Q812yes—
104C22×C4×C151#4112yes—
105C22×C4×C151#4112yes—
106C22×C4×C151#4112yes—
107C22×C4×C151#4112yes—
108C22×C4×C151#4112yes—
109C22×C4×C151C2411yescharacteristic
110M16×C151—44no—
111C2×C8×C151—21no—
112C2×C8×C151—21no—
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C2×C8×C151—21no—
116C2×C8×C151—21no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151—22no—
120C2×C8×C151—44no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—82no—
136C4⋊C4×C151—82no—
137C4⋊C4×C151—82no—
138C4⋊C4×C151—82no—
139C4⋊C4×C151C2×Q812yes—
140C4⋊C4×C151C2×Q812yes—
141C22⋊C4×C151—24no—
142C22⋊C4×C151—24no—
143C22⋊C4×C151—42no—
144C42×C151—24no—
145C42×C151—22no—
146C42×C151—22no—
147C42×C151—42no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151C22⋊Q812yes—
153C23×C151#12312yes—
154C23×C151#12412yes—
155C23×C151C22×D411yescharacteristic
156C2×C4×C151—22no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—22no—
160C2×C4×C151—22no—
161C2×C4×C151—22no—
162C2×C4×C151—22no—
163C2×C4×C151—22no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—42no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—42no—
172C2×C4×C151—41no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151—41no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—84no—
181C2×C4×C151—84no—
182C2×C4×C151C22⋊Q812yes—
183C2×C4×C151#12312yes—
184C2×C4×C151#12412yes—
185C2×C4×C151#12514yes—
186C2×C4×C151#12514yes—
187C2×C4×C151#12614yes—
188C2×C4×C151#12614yes—
189C2×C4×C151C22×Q811yescharacteristic
190C2×C4×C151C2×#4111yescharacteristic
191C2×C4×C151C2×#4111yescharacteristic
192C2×C4×C151C2×#4111yescharacteristic
193C2×C4×C151C2×#4111yescharacteristic
194C2×C4×C151C2×#4111yescharacteristic
195C8×C151—41no—
196C8×C151—41no—
197C8×C151—42no—
198C22×C151—22no—
199C22×C151—22no—
200C22×C151—22no—
201C22×C151—22no—
202C22×C151—22no—
203C22×C151—22no—
204C22×C151#40014yes—
205C22×C151C2×C22⋊Q811yescharacteristic
206C22×C151C2×#12311yescharacteristic
207C22×C151C2×#12411yescharacteristic
208C22×C151#57611yescharacteristic
209C22×C151#57711yescharacteristic
210C22×C151#57711yescharacteristic
211C22×C151#57811yescharacteristic
212C4×C151—42no—
213C4×C151—42no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—82no—
217C4×C151—81no—
218C4×C151—82no—
219C4×C151—81no—
220C4×C151#40014yes—
221C4×C151C2×#12511yescharacteristic
222C4×C151C2×#12511yescharacteristic
223C4×C151C2×#12611yescharacteristic
224C4×C151C2×#12611yescharacteristic
225C2×C151—24no—
226C2×C151C2×#40011yescharacteristic
227C2×C151#308311yescharacteristic
228C2×C151#308411yescharacteristic
229C2×C151#309611yescharacteristic
230C2×C151#309711yescharacteristic
231C2×C151#313611yescharacteristic
232C2×C151#313711yescharacteristic
233#23748C15111yesmaximal, characteristic, direct product factor, Sylow
234C151#2374811yescharacteristic, direct product factor, Sylow
235#2317C2×C15111yescharacteristic
236#2317C2×C15111yescharacteristic
237#2101C2×C15112yescomplemented
238#2101C2×C15112yescomplemented
239#2100C2×C15112yescomplemented
240#2099C2×C15112yescomplemented
241#1736C2×C15111yescharacteristic
242#1736C2×C15111yescharacteristic
243#1735C2×C15111yescharacteristic
244C2×#340C2×C15111yescharacteristic
245#1729C2×C15111yescharacteristic
246C22×M16C22×C15111yescharacteristic
247C23×C8C22×C15111yescharacteristic
248C2×#117C22×C15111yescharacteristic
249C2×#117C22×C15111yescharacteristic
250C2×#117C22×C15111yescharacteristic
251C22×C4⋊C4C22×C15111yescharacteristic
252C22×C4⋊C4C22×C15111yescharacteristic
253#389—21no—
254#389—21no—
255#389C22×C15112yes—
256#389C22×C15112yes—
257#385—22no—
258#385—22no—
259#384—21no—
260#384C22×C15112yes—
261#382—21no—
262#382C22×C15112yes—
263#340C22×C15111yescharacteristic
264#340C22×C15112yes—
265#340C22×C15112yes—
266#340C22×C15112yes—
267#340C22×C15111yescharacteristic
268#340C22×C15112yes—
269#340C22×C15112yes—
270#340C22×C15111yescharacteristic
271#340C22×C15111yescharacteristic
272#340C22×C15112yes—
273#336C22×C15112yes—
274#336C22×C15112yes—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4C23×C15111yescharacteristic
278C2×M16—22no—
279C2×M16—22no—
280C2×M16—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8C23×C15111yescharacteristic
285C22×C8C23×C15111yescharacteristic
286C22×C8C23×C15112yes—
287#117—22no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—22no—
292#117Q8×C15114yes—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4D4×C15111yescharacteristic
304C2×C4⋊C4D4×C15111yescharacteristic
305C2×C4⋊C4C23×C15112yes—
306C2×C4⋊C4C23×C15112yes—
307C2×C4⋊C4C23×C15111yescharacteristic
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C4⋊C4C23×C15111yescharacteristic
310C2×C4⋊C4C23×C15111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4D4×C15112yes—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42C23×C15112yes—
317#95—22no—
318#95—22no—
319#95—22no—
320#95—22no—
321C24C2×D4×C15111yescharacteristic
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—81no—
334C22×C4C2×D4×C15112yes—
335C22×C4C2×D4×C15112yes—
336C22×C4C2×D4×C15111yescharacteristic
337C22×C4C2×Q8×C15112yes—
338C22×C4#41×C15112yes—
339C22×C4#41×C15112yes—
340C22×C4#41×C15112yes—
341C22×C4#41×C15112yes—
342C22×C4#41×C15112yes—
343C22×C4C24×C15111yescharacteristic
344M16—44no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—44no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—82no—
370C4⋊C4—82no—
371C4⋊C4—82no—
372C4⋊C4—82no—
373C4⋊C4C2×Q8×C15112yes—
374C4⋊C4C2×Q8×C15112yes—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—42no—
378C42—24no—
379C42—22no—
380C42—22no—
381C42—42no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23C22⋊Q8×C15112yes—
387C23#123×C15112yes—
388C23#124×C15112yes—
389C23C22×D4×C15111yescharacteristic
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—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—84no—
415C2×C4—84no—
416C2×C4C22⋊Q8×C15112yes—
417C2×C4#123×C15112yes—
418C2×C4#124×C15112yes—
419C2×C4#125×C15114yes—
420C2×C4#125×C15114yes—
421C2×C4#126×C15114yes—
422C2×C4#126×C15114yes—
423C2×C4C22×Q8×C15111yescharacteristic
424C2×C4C2×#41×C15111yescharacteristic
425C2×C4C2×#41×C15111yescharacteristic
426C2×C4C2×#41×C15111yescharacteristic
427C2×C4C2×#41×C15111yescharacteristic
428C2×C4C2×#41×C15111yescharacteristic
429C8—41no—
430C8—41no—
431C8—42no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22#400×C15114yes—
439C22C2×C22⋊Q8×C15111yescharacteristic
440C22C2×#123×C15111yescharacteristic
441C22C2×#124×C15111yescharacteristic
442C22#576×C15111yescharacteristic
443C22#577×C15111yescharacteristic
444C22#577×C15111yescharacteristic
445C22#578×C15111yescharacteristic
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—82no—
454C4#400×C15114yes—
455C4C2×#125×C15111yescharacteristic
456C4C2×#125×C15111yescharacteristic
457C4C2×#126×C15111yescharacteristic
458C4C2×#126×C15111yescharacteristic
459C2—24no—
460C2C2×#400×C15111yescharacteristic
461C2#3083×C15111yescharacteristic
462C2#3084×C15111yescharacteristic
463C2#3096×C15111yescharacteristic
464C2#3097×C15111yescharacteristic
465C2#3136×C15111yescharacteristic
466C2#3137×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2101×C151C2semidirect
4. #2101×C151C2semidirect
5. #2100×C151C2semidirect
6. #2099×C151C2semidirect
233. #23748C151direct (N × H)
234. C151#23748direct (N × H)
237. #2101C2×C151semidirect
238. #2101C2×C151semidirect
239. #2100C2×C151semidirect
240. #2099C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2317×C1512
#2101×C1512
#2100×C1512
#2099×C1512
#1736×C1512
#1735×C1512
C2×#340×C1512
#1729×C1512
#23748151