Finite Group Databasebeta

← C151×#17227 #50322152

Subgroups — C151×#17227 #50322152

Order 38656.

1010 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C151C211yesmaximal, characteristic
2C2×#398×C151C211yesmaximal, characteristic
3#1445×C151C212yesmaximal
4#1445×C151C211yesmaximal, characteristic
5#1442×C151C212yesmaximal
6#1442×C151C212yesmaximal
7#1442×C151C212yesmaximal
8#1442×C151C212yesmaximal
9#1441×C151C212yesmaximal
10C22×C4⋊C4×C151C2212yes—
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15#400×C151—24no—
16#398×C151—24no—
17C2×#95×C151C2211yescharacteristic
18C2×#95×C151C2212yes—
19C2×#95×C151C2212yes—
20C2×#95×C151C2212yes—
21C2×#95×C151C2211yescharacteristic
22C2×#95×C151C2212yes—
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C23×C4×C151C2312yes—
34C23×C4×C151C2312yes—
35C23×C4×C151C2312yes—
36C23×C4×C151C2312yes—
37C23×C4×C151C2311yescharacteristic
38C23×C4×C151C2311yescharacteristic
39C23×C4×C151C2311yescharacteristic
40C23×C4×C151C2312yes—
41C23×C4×C151C2312yes—
42C2×C4⋊C4×C151—24no—
43C2×C4⋊C4×C151—22no—
44C2×C4⋊C4×C151—22no—
45C2×C4⋊C4×C151—24no—
46C2×C4⋊C4×C151—24no—
47C2×C4⋊C4×C151—41no—
48C2×C4⋊C4×C151—41no—
49C2×C4⋊C4×C151—42no—
50C2×C4⋊C4×C151—42no—
51C2×C4⋊C4×C151—42no—
52C2×C4⋊C4×C151—41no—
53C2×C4⋊C4×C151—41no—
54C2×C4⋊C4×C151—41no—
55C2×C4⋊C4×C151—41no—
56C2×C4⋊C4×C151D414yes—
57#95×C151—22no—
58#95×C151—24no—
59#95×C151—22no—
60#95×C151—24no—
61#95×C151—24no—
62#95×C151—24no—
63#95×C151—24no—
64#95×C151—24no—
65#95×C151—24no—
66#95×C151—41no—
67#95×C151—42no—
68#95×C151—41no—
69#95×C151—42no—
70#95×C151—42no—
71#95×C151—42no—
72#95×C151—42no—
73C24×C151C2411yescharacteristic
74C22×C4×C151—22no—
75C22×C4×C151—22no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—22no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D412yes—
129C22×C4×C151#4114yes—
130C22×C4×C151#4114yes—
131C4⋊C4×C151—44no—
132C4⋊C4×C151—48no—
133C4⋊C4×C151—44no—
134C4⋊C4×C151—44no—
135C4⋊C4×C151—48no—
136C23×C151C22×D411yescharacteristic
137C23×C151C2×#4112yes—
138C23×C151C2×#4112yes—
139C23×C151H(5,𝔽2)11yescharacteristic
140C23×C151H(5,𝔽2)11yescharacteristic
141C23×C151H(5,𝔽2)12yes—
142C23×C1512−1+412yes—
143C23×C1512−1+412yes—
144C23×C1512−1+412yes—
145C2×C4×C151—22no—
146C2×C4×C151—22no—
147C2×C4×C151—22no—
148C2×C4×C151—22no—
149C2×C4×C151—22no—
150C2×C4×C151—24no—
151C2×C4×C151—24no—
152C2×C4×C151—24no—
153C2×C4×C151—24no—
154C2×C4×C151—24no—
155C2×C4×C151—24no—
156C2×C4×C151—24no—
157C2×C4×C151—24no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—42no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—42no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—42no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C22×C151#53411yescharacteristic
203C22×C151#53511yescharacteristic
204C22×C151#53611yescharacteristic
205C22×C151#53912yes—
206C22×C151#53912yes—
207C22×C151#54112yes—
208C22×C151#54112yes—
209C22×C151#54212yes—
210C22×C151#54212yes—
211C22×C151#54712yes—
212C22×C151#54812yes—
213C22×C151#55112yes—
214C22×C151#55212yes—
215C22×C151#55511yescharacteristic
216C22×C151#55911yescharacteristic
217C22×C151#56212yes—
218C22×C151#56212yes—
219C22×C151#56312yes—
220C22×C151#56311yescharacteristic
221C22×C151#56311yescharacteristic
222C22×C151#56412yes—
223C4×C151—42no—
224C4×C151—44no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—44no—
228C4×C151—82no—
229C4×C151—82no—
230C4×C151—82no—
231C4×C151—82no—
232C2×C151#271912yes—
233C2×C151#272312yes—
234C2×C151#272411yescharacteristic
235C2×C151#273111yescharacteristic
236C2×C151#274412yes—
237C2×C151#275412yes—
238C2×C151#281611yescharacteristic
239C2×C151#283912yes—
240C2×C151#283912yes—
241#17227C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#1722711yescharacteristic, direct product factor, Sylow
243C2×#400C2×C15111yescharacteristic
244C2×#398C2×C15111yescharacteristic
245#1445C2×C15112yes—
246#1445C2×C15111yescharacteristic
247#1442C2×C15112yes—
248#1442C2×C15112yes—
249#1442C2×C15112yes—
250#1442C2×C15112yes—
251#1441C2×C15112yes—
252C22×C4⋊C4C22×C15112yes—
253C22×C4⋊C4C22×C15112yes—
254C22×C4⋊C4C22×C15111yescharacteristic
255C22×C4⋊C4C22×C15111yescharacteristic
256C22×C4⋊C4C22×C15111yescharacteristic
257#400—24no—
258#398—24no—
259C2×#95C22×C15111yescharacteristic
260C2×#95C22×C15112yes—
261C2×#95C22×C15112yes—
262C2×#95C22×C15112yes—
263C2×#95C22×C15111yescharacteristic
264C2×#95C22×C15112yes—
265C2×#95C22×C15112yes—
266C2×#95C22×C15112yes—
267C2×#95C22×C15112yes—
268C2×#95C22×C15111yescharacteristic
269C2×#95C22×C15112yes—
270C2×#95C22×C15112yes—
271C2×#95C22×C15112yes—
272C2×#95C22×C15112yes—
273C2×#95C22×C15112yes—
274C2×#95C22×C15111yescharacteristic
275C23×C4C23×C15112yes—
276C23×C4C23×C15112yes—
277C23×C4C23×C15112yes—
278C23×C4C23×C15112yes—
279C23×C4C23×C15112yes—
280C23×C4C23×C15112yes—
281C23×C4C23×C15111yescharacteristic
282C23×C4C23×C15111yescharacteristic
283C23×C4C23×C15111yescharacteristic
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4D4×C15114yes—
299#95—24no—
300#95—24no—
301#95—24no—
302#95—24no—
303#95—22no—
304#95—24no—
305#95—22no—
306#95—24no—
307#95—24no—
308#95—41no—
309#95—42no—
310#95—41no—
311#95—42no—
312#95—42no—
313#95—42no—
314#95—42no—
315C24C24×C15111yescharacteristic
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4C2×D4×C15112yes—
369C22×C4C2×D4×C15112yes—
370C22×C4C2×D4×C15112yes—
371C22×C4#41×C15114yes—
372C22×C4#41×C15114yes—
373C4⋊C4—44no—
374C4⋊C4—48no—
375C4⋊C4—44no—
376C4⋊C4—44no—
377C4⋊C4—48no—
378C23C22×D4×C15111yescharacteristic
379C23C2×#41×C15112yes—
380C23C2×#41×C15112yes—
381C23H(5,𝔽2)×C15111yescharacteristic
382C23H(5,𝔽2)×C15111yescharacteristic
383C23H(5,𝔽2)×C15112yes—
384C232−1+4×C15112yes—
385C232−1+4×C15112yes—
386C232−1+4×C15112yes—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C22#534×C15111yescharacteristic
445C22#535×C15111yescharacteristic
446C22#536×C15111yescharacteristic
447C22#539×C15112yes—
448C22#539×C15112yes—
449C22#541×C15112yes—
450C22#541×C15112yes—
451C22#542×C15112yes—
452C22#542×C15112yes—
453C22#547×C15112yes—
454C22#548×C15112yes—
455C22#551×C15112yes—
456C22#552×C15112yes—
457C22#555×C15111yescharacteristic
458C22#559×C15111yescharacteristic
459C22#562×C15112yes—
460C22#562×C15112yes—
461C22#563×C15112yes—
462C22#563×C15111yescharacteristic
463C22#563×C15111yescharacteristic
464C22#564×C15112yes—
465C4—44no—
466C4—42no—
467C4—42no—
468C4—44no—
469C4—42no—
470C4—82no—
471C4—82no—
472C4—82no—
473C4—82no—
474C2#2719×C15112yes—
475C2#2723×C15112yes—
476C2#2724×C15111yescharacteristic
477C2#2731×C15111yescharacteristic
478C2#2744×C15112yes—
479C2#2754×C15112yes—
480C2#2816×C15111yescharacteristic
481C2#2839×C15112yes—
482C2#2839×C15112yes—
subgroupG/H
center, socle, prime radicalC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
241. #17227C151direct (N × H)
242. C151#17227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1512
C2×#398×C1512
#1445×C1512
#1442×C1512
#1441×C1512
#17227151