Finite Group Databasebeta

← C151×#9919 #50314844

Subgroups — C151×#9919 #50314844

Order 38656.

716 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C211yesmaximal, characteristic
2#2618×C151C211yesmaximal, characteristic
3C2×#398×C151C211yesmaximal, characteristic, complemented
4#1823×C151C211yesmaximal, characteristic, complemented
5C2×#327×C151C211yesmaximal, characteristic
6C2×#324×C151C211yesmaximal, characteristic, complemented
7#1294×C151C211yesmaximal, characteristic, complemented
8C2×#123×C151—21no—
9C2×#121×C151C2211yescharacteristic
10C22×C4⋊C4×C151—21no—
11C22×C4⋊C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13#480×C151—22no—
14#480×C151—22no—
15C2×#107×C151—21no—
16C2×#102×C151—21no—
17C2×C22⋊C8×C151C2211yescharacteristic
18C2×C22⋊C8×C151C2211yescharacteristic
19#398×C151—21no—
20#398×C151—22no—
21#398×C151—22no—
22#396×C151—22no—
23#394×C151—21no—
24#386×C151—21no—
25#380×C151C2211yescharacteristic
26C2×#95×C151—21no—
27C2×#95×C151C2211yescharacteristic
28#340×C151—22no—
29#327×C151—22no—
30#324×C151—22no—
31C22×D4×C151—21no—
32C22×D4×C151D411yescharacteristic
33C23×C4×C151—21no—
34C23×C4×C151—21no—
35C23×C4×C151D411yescharacteristic
36C23×C4×C151D411yescharacteristic
37C23×C4×C151C2311yescharacteristic
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40#123×C151—42no—
41#123×C151—42no—
42#121×C151—21no—
43#121×C151—21no—
44#121×C151—21no—
45#121×C151—21no—
46C2×C4⋊C4×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—22no—
51C2×C4⋊C4×C151—24no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—42no—
60C2×C4⋊C4×C151—42no—
61C2×C4⋊C4×C151D411yescharacteristic
62C2×C4⋊C4×C151D412yes—
63C2×C4⋊C4×C151D412yes—
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—21no—
68#107×C151—24no—
69#102×C151—24no—
70C22⋊C8×C151—21no—
71C22⋊C8×C151—21no—
72C22⋊C8×C151—21no—
73C22⋊C8×C151D412yes—
74#95×C151—24no—
75#95×C151—22no—
76#95×C151—21no—
77#95×C151—21no—
78#95×C151D412yes—
79C24×C151—21no—
80C24×C151C2×D411yescharacteristic
81C2×D4×C151—21no—
82C2×D4×C151—21no—
83C2×D4×C151—42no—
84C2×D4×C151—41no—
85C2×D4×C151—41no—
86C2×D4×C151—41no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C22×C4×C151—24no—
91C22×C4×C151—22no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—42no—
105C22×C4×C151—42no—
106C22×C4×C151—41no—
107C22×C4×C151—41no—
108C22×C4×C151—42no—
109C22×C4×C151—41no—
110C22×C4×C151—41no—
111C22×C4×C151—41no—
112C22×C4×C151—41no—
113C22×C4×C151—41no—
114C22×C4×C151—41no—
115C22×C4×C151D812yes—
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151#4111yescharacteristic
122C2×C8×C151—22no—
123C2×C8×C151—42no—
124C2×C8×C151—42no—
125C2×C8×C151—41no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—42no—
131C4⋊C4×C151—48no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—41no—
134C4⋊C4×C151—41no—
135C4⋊C4×C151—41no—
136C4⋊C4×C151—41no—
137C4⋊C4×C151—41no—
138C4⋊C4×C151—41no—
139C22⋊C4×C151—44no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—41no—
142C22⋊C4×C151—41no—
143C22⋊C4×C151—41no—
144C22⋊C4×C151—82no—
145C23×C151—22no—
146C23×C151—22no—
147C23×C151—41no—
148C23×C151—41no—
149C23×C151—41no—
150C23×C151—42no—
151C23×C151—42no—
152C23×C151#12011yescharacteristic
153C23×C151#12011yescharacteristic
154C23×C151#12111yescharacteristic
155C23×C151C2×D811yescharacteristic
156C23×C151#13511yescharacteristic
157C23×C151AGL(1,ℤ/8)11yescharacteristic
158C23×C151AGL(1,ℤ/8)11yescharacteristic
159D4×C151—42no—
160D4×C151—81no—
161D4×C151—81no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—81no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—24no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—44no—
176C2×C4×C151—44no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151—42no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—41no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—81no—
196C2×C4×C151—81no—
197C2×C4×C151—81no—
198C2×C4×C151—81no—
199C2×C4×C151—81no—
200C2×C4×C151#12011yescharacteristic
201C2×C4×C151#12111yescharacteristic
202C2×C4×C151#12111yescharacteristic
203C2×C4×C151#12711yescharacteristic
204C8×C151—42no—
205C8×C151—81no—
206C22×C151—22no—
207C22×C151—22no—
208C22×C151—22no—
209C22×C151—22no—
210C22×C151—21no—
211C22×C151—21no—
212C22×C151—21no—
213C22×C151—21no—
214C22×C151—82no—
215C22×C151—82no—
216C22×C151—81no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151#39211yescharacteristic
220C22×C151#44711yescharacteristic
221C22×C151#44711yescharacteristic
222C22×C151#44911yescharacteristic
223C22×C151#44911yescharacteristic
224C22×C151#45612yes—
225C22×C151#45812yes—
226C22×C151#46611yescharacteristic
227C22×C151#46911yescharacteristic
228C4×C151—21no—
229C4×C151—21no—
230C4×C151—21no—
231C4×C151—21no—
232C4×C151—44no—
233C4×C151—42no—
234C4×C151—82no—
235C4×C151—82no—
236C4×C151—81no—
237C4×C151—81no—
238C2×C151—21no—
239C2×C151—21no—
240C2×C151—21no—
241C2×C151—21no—
242C2×C151—161no—
243C2×C151#160912yes—
244C2×C151#161012yes—
245C2×C151#199911yescharacteristic
246C2×C151#200511yescharacteristic
247C2×C151#202211yescharacteristic
248#9919C15111yesmaximal, characteristic, direct product factor, Sylow
249C151#991911yescharacteristic, direct product factor, Sylow
250C2×#480C2×C15111yescharacteristic
251#2618C2×C15111yescharacteristic
252C2×#398C2×C15111yescharacteristic, complemented
253#1823C2×C15111yescharacteristic, complemented
254C2×#327C2×C15111yescharacteristic
255C2×#324C2×C15111yescharacteristic, complemented
256#1294C2×C15111yescharacteristic, complemented
257C2×#123—21no—
258C2×#121C22×C15111yescharacteristic
259C22×C4⋊C4—21no—
260C22×C4⋊C4C22×C15111yescharacteristic
261C22×C4⋊C4C22×C15111yescharacteristic
262#480—22no—
263#480—22no—
264C2×#107—21no—
265C2×#102—21no—
266C2×C22⋊C8C22×C15111yescharacteristic
267C2×C22⋊C8C22×C15111yescharacteristic
268#398—21no—
269#398—22no—
270#398—22no—
271#396—22no—
272#394—21no—
273#386—21no—
274#380C22×C15111yescharacteristic
275C2×#95—21no—
276C2×#95C22×C15111yescharacteristic
277#340—22no—
278#327—22no—
279#324—22no—
280C22×D4—21no—
281C22×D4D4×C15111yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4D4×C15111yescharacteristic
285C23×C4D4×C15111yescharacteristic
286C23×C4C23×C15111yescharacteristic
287C22×C8—21no—
288C22×C8—21no—
289#123—42no—
290#123—42no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4D4×C15112yes—
311C2×C4⋊C4D4×C15111yescharacteristic
312C2×C4⋊C4D4×C15112yes—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317#107—24no—
318#102—24no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8D4×C15112yes—
323#95—24no—
324#95—22no—
325#95—21no—
326#95—21no—
327#95D4×C15112yes—
328C24—21no—
329C24C2×D4×C15111yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—42no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4D8×C15112yes—
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C2×D4×C15111yescharacteristic
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4#41×C15111yescharacteristic
371C2×C8—22no—
372C2×C8—42no—
373C2×C8—42no—
374C2×C8—41no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—42no—
380C4⋊C4—48no—
381C4⋊C4—44no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C22⋊C4—44no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—82no—
394C23—22no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23#120×C15111yescharacteristic
402C23#120×C15111yescharacteristic
403C23#121×C15111yescharacteristic
404C23C2×D8×C15111yescharacteristic
405C23#135×C15111yescharacteristic
406C23AGL(1,ℤ/8)×C15111yescharacteristic
407C23AGL(1,ℤ/8)×C15111yescharacteristic
408D4—42no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—81no—
413D4—81no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4#120×C15111yescharacteristic
450C2×C4#121×C15111yescharacteristic
451C2×C4#121×C15111yescharacteristic
452C2×C4#127×C15111yescharacteristic
453C8—42no—
454C8—81no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—82no—
464C22—82no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22#392×C15111yescharacteristic
469C22#447×C15111yescharacteristic
470C22#447×C15111yescharacteristic
471C22#449×C15111yescharacteristic
472C22#449×C15111yescharacteristic
473C22#456×C15112yes—
474C22#458×C15112yes—
475C22#466×C15111yescharacteristic
476C22#469×C15111yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—82no—
484C4—82no—
485C4—81no—
486C4—81no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—161no—
492C2#1609×C15112yes—
493C2#1610×C15112yes—
494C2#1999×C15111yescharacteristic
495C2#2005×C15111yescharacteristic
496C2#2022×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC23×C4C23×C151
prime radicalC2×#121×C151C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#398×C151C2semidirect
4. #1823×C151C2semidirect
6. C2×#324×C151C2semidirect
7. #1294×C151C2semidirect
248. #9919C151direct (N × H)
249. C151#9919direct (N × H)
252. C2×#398C2×C151semidirect
253. #1823C2×C151semidirect
255. C2×#324C2×C151semidirect
256. #1294C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1512
#2618×C1512
C2×#398×C1512
#1823×C1512
C2×#327×C1512
C2×#324×C1512
#1294×C1512
#9919151