Finite Group Databasebeta

← C151×#10354 #50315279

Subgroups — C151×#10354 #50315279

Order 38656.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2552×C151C211yesmaximal, characteristic, complemented
2#1982×C151C211yesmaximal, characteristic
3#1982×C151C211yesmaximal, characteristic
4#1957×C151C211yesmaximal, characteristic
5#1296×C151C211yesmaximal, characteristic, complemented
6#1279×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C2×#127×C151C2211yescharacteristic
9C2×#125×C151—21no—
10C2×C4⋊C8×C151C2211yescharacteristic
11C2×C4⋊C8×C151C2211yescharacteristic
12C2×#102×C151—22no—
13C2×#102×C151—21no—
14C2×#102×C151—21no—
15C2×#102×C151—21no—
16C2×#102×C151—21no—
17C2×C4×C8×C151C2211yescharacteristic
18#398×C151—22no—
19#389×C151—21no—
20#389×C151—21no—
21#384×C151—21no—
22#384×C151C2211yescharacteristic
23C4×C4⋊C4×C151C2211yescharacteristic
24C4×C4⋊C4×C151C2211yescharacteristic
25C22×D4×C151—21no—
26C22×D4×C151—21no—
27C22×D4×C151—21no—
28C22×C8×C151—21no—
29C22×C8×C151—21no—
30C22×C8×C151—21no—
31#127×C151—21no—
32#127×C151—21no—
33#127×C151—21no—
34#127×C151Q812yes—
35#125×C151—42no—
36#125×C151—42no—
37C2×C4⋊C4×C151—22no—
38C2×C4⋊C4×C151—22no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151—21no—
41C2×C4⋊C4×C151—22no—
42C2×C4⋊C4×C151D411yescharacteristic
43C2×C4⋊C4×C151D411yescharacteristic
44C2×C4⋊C4×C151D411yescharacteristic
45C2×C4⋊C4×C151D411yescharacteristic
46C2×C4⋊C4×C151D412yes—
47C2×C42×C151—21no—
48C2×C42×C151—21no—
49C2×C42×C151C2311yescharacteristic
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54#102×C151—42no—
55#102×C151—42no—
56#102×C151—44no—
57#102×C151—42no—
58#102×C151—42no—
59C4×C8×C151—21no—
60C4×C8×C151—21no—
61#95×C151—22no—
62#95×C151—21no—
63#95×C151—21no—
64C24×C151—41no—
65C2×D4×C151—22no—
66C2×D4×C151—22no—
67C2×D4×C151—22no—
68C2×D4×C151—42no—
69C2×D4×C151—42no—
70C2×D4×C151—41no—
71C2×D4×C151—41no—
72C2×D4×C151—41no—
73C2×D4×C151—41no—
74C2×D4×C151—41no—
75C2×D4×C151—41no—
76C2×D4×C151—41no—
77C2×D4×C151—41no—
78C2×D4×C151—41no—
79C2×D4×C151—41no—
80C2×D4×C151—41no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—21no—
84C22×C4×C151—21no—
85C22×C4×C151—22no—
86C22×C4×C151C2×D411yescharacteristic
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151C2×D411yescharacteristic
89C2×C8×C151—22no—
90C2×C8×C151—41no—
91C2×C8×C151—41no—
92C2×C8×C151—41no—
93C2×C8×C151—41no—
94C2×C8×C151—41no—
95C2×C8×C151—41no—
96C2×C8×C151—41no—
97C2×C8×C151—41no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151—42no—
105C4⋊C4×C151—44no—
106C4⋊C4×C151—44no—
107C4⋊C4×C151—41no—
108C4⋊C4×C151—41no—
109C4⋊C4×C151—41no—
110C4⋊C4×C151—41no—
111C4⋊C4×C151—82no—
112C4⋊C4×C151D812yes—
113C4⋊C4×C151SD1612yes—
114C42×C151—41no—
115C42×C151—41no—
116C42×C151—41no—
117C42×C151—41no—
118C42×C151C2×Q811yescharacteristic
119C42×C151#4111yescharacteristic
120C42×C151#4111yescharacteristic
121C42×C151#4111yescharacteristic
122C23×C151—42no—
123C23×C151—81no—
124C23×C151—81no—
125C23×C151—81no—
126C23×C151—81no—
127C23×C151—81no—
128C23×C151—81no—
129C23×C151#12011yescharacteristic
130D4×C151—44no—
131D4×C151—42no—
132D4×C151—42no—
133D4×C151—42no—
134D4×C151—42no—
135D4×C151—82no—
136D4×C151—81no—
137D4×C151—81no—
138D4×C151—81no—
139D4×C151—81no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—22no—
143C2×C4×C151—22no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—42no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—42no—
154C2×C4×C151—42no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151C22⋊Q811yescharacteristic
158C2×C4×C151C22⋊Q811yescharacteristic
159C2×C4×C151C22⋊Q811yescharacteristic
160C2×C4×C151#12411yescharacteristic
161C2×C4×C151#12411yescharacteristic
162C2×C4×C151#12411yescharacteristic
163C2×C4×C151C2×D811yescharacteristic
164C2×C4×C151C2×SD1611yescharacteristic
165C2×C4×C151#13511yescharacteristic
166C2×C4×C151#13511yescharacteristic
167C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C151#13711yescharacteristic
171C8×C151—42no—
172C8×C151—81no—
173C8×C151—81no—
174C22×C151—82no—
175C22×C151—82no—
176C22×C151—82no—
177C22×C151—161no—
178C22×C151—161no—
179C22×C151—161no—
180C22×C151—161no—
181C22×C151#39311yescharacteristic
182C22×C151#44711yescharacteristic
183C22×C151#44811yescharacteristic
184C22×C151#44911yescharacteristic
185C22×C151#44911yescharacteristic
186C22×C151#45311yescharacteristic
187C22×C151#45411yescharacteristic
188C4×C151—21no—
189C4×C151—21no—
190C4×C151—42no—
191C4×C151—42no—
192C4×C151—81no—
193C4×C151—82no—
194C4×C151—81no—
195C4×C151#47411yescharacteristic
196C4×C151#47611yescharacteristic
197C4×C151#47811yescharacteristic
198C4×C151#47811yescharacteristic
199C4×C151#48611yescharacteristic
200C4×C151#48811yescharacteristic
201C4×C151#48911yescharacteristic
202C4×C151#49011yescharacteristic
203C2×C151—162no—
204C2×C151#162111yescharacteristic
205C2×C151#162211yescharacteristic
206C2×C151#162511yescharacteristic
207C2×C151#162611yescharacteristic
208C2×C151#202311yescharacteristic
209C2×C151#202511yescharacteristic
210C2×C151#202711yescharacteristic
211#10354C15111yesmaximal, characteristic, direct product factor, Sylow
212C151#1035411yescharacteristic, direct product factor, Sylow
213#2552C2×C15111yescharacteristic, complemented
214#1982C2×C15111yescharacteristic
215#1982C2×C15111yescharacteristic
216#1957C2×C15111yescharacteristic
217#1296C2×C15111yescharacteristic, complemented
218#1279C2×C15111yescharacteristic, complemented
219#1279C2×C15111yescharacteristic, complemented
220C2×#127C22×C15111yescharacteristic
221C2×#125—21no—
222C2×C4⋊C8C22×C15111yescharacteristic
223C2×C4⋊C8C22×C15111yescharacteristic
224C2×#102—22no—
225C2×#102—21no—
226C2×#102—21no—
227C2×#102—21no—
228C2×#102—21no—
229C2×C4×C8C22×C15111yescharacteristic
230#398—22no—
231#389—21no—
232#389—21no—
233#384—21no—
234#384C22×C15111yescharacteristic
235C4×C4⋊C4C22×C15111yescharacteristic
236C4×C4⋊C4C22×C15111yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243#127—21no—
244#127—21no—
245#127—21no—
246#127Q8×C15112yes—
247#125—42no—
248#125—42no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4D4×C15111yescharacteristic
255C2×C4⋊C4D4×C15111yescharacteristic
256C2×C4⋊C4D4×C15111yescharacteristic
257C2×C4⋊C4D4×C15111yescharacteristic
258C2×C4⋊C4D4×C15112yes—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42C23×C15111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#102—42no—
267#102—42no—
268#102—44no—
269#102—42no—
270#102—42no—
271C4×C8—21no—
272C4×C8—21no—
273#95—22no—
274#95—21no—
275#95—21no—
276C24—41no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4C2×D4×C15111yescharacteristic
299C22×C4C2×D4×C15111yescharacteristic
300C22×C4C2×D4×C15111yescharacteristic
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C4⋊C4D8×C15112yes—
325C4⋊C4SD16×C15112yes—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42C2×Q8×C15111yescharacteristic
331C42#41×C15111yescharacteristic
332C42#41×C15111yescharacteristic
333C42#41×C15111yescharacteristic
334C23—42no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23#120×C15111yescharacteristic
342D4—44no—
343D4—42no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—81no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4C22⋊Q8×C15111yescharacteristic
370C2×C4C22⋊Q8×C15111yescharacteristic
371C2×C4C22⋊Q8×C15111yescharacteristic
372C2×C4#124×C15111yescharacteristic
373C2×C4#124×C15111yescharacteristic
374C2×C4#124×C15111yescharacteristic
375C2×C4C2×D8×C15111yescharacteristic
376C2×C4C2×SD16×C15111yescharacteristic
377C2×C4#135×C15111yescharacteristic
378C2×C4#135×C15111yescharacteristic
379C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
380C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
381C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
382C2×C4#137×C15111yescharacteristic
383C8—42no—
384C8—81no—
385C8—81no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—161no—
390C22—161no—
391C22—161no—
392C22—161no—
393C22#393×C15111yescharacteristic
394C22#447×C15111yescharacteristic
395C22#448×C15111yescharacteristic
396C22#449×C15111yescharacteristic
397C22#449×C15111yescharacteristic
398C22#453×C15111yescharacteristic
399C22#454×C15111yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4#474×C15111yescharacteristic
408C4#476×C15111yescharacteristic
409C4#478×C15111yescharacteristic
410C4#478×C15111yescharacteristic
411C4#486×C15111yescharacteristic
412C4#488×C15111yescharacteristic
413C4#489×C15111yescharacteristic
414C4#490×C15111yescharacteristic
415C2—162no—
416C2#1621×C15111yescharacteristic
417C2#1622×C15111yescharacteristic
418C2#1625×C15111yescharacteristic
419C2#1626×C15111yescharacteristic
420C2#2023×C15111yescharacteristic
421C2#2025×C15111yescharacteristic
422C2#2027×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2552×C151C2semidirect
5. #1296×C151C2semidirect
6. #1279×C151C2semidirect
7. #1279×C151C2semidirect
211. #10354C151direct (N × H)
212. C151#10354direct (N × H)
213. #2552C2×C151semidirect
217. #1296C2×C151semidirect
218. #1279C2×C151semidirect
219. #1279C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2552×C1512
#1982×C1512
#1957×C1512
#1296×C1512
#1279×C1512
#10354151