Finite Group Databasebeta

← C151×#13222 #50318147

Subgroups — C151×#13222 #50318147

Order 38656.

628 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2534×C151C211yesmaximal, characteristic
2C2×#352×C151C212yesmaximal, complemented
3C2×AΣL(1,𝔽16)×C151C212yesmaximal
4#1800×C151C211yesmaximal, characteristic, complemented
5C4×#99×C151C211yesmaximal, characteristic, complemented
6C2×#123×C151C2211yescharacteristic
7C2×#120×C151C2211yescharacteristic
8C2×C4×D4×C151C2211yescharacteristic
9C22×C22⋊C4×C151C411yescharacteristic, complemented
10#423×C151—21no—
11C2×#100×C151C2212yes—
12C2×#99×C151C2212yes—
13#396×C151—21no—
14#394×C151—21no—
15#388×C151—21no—
16#386×C151—21no—
17#381×C151C411yescharacteristic, complemented
18#380×C151C411yescharacteristic, complemented
19#379×C151C411yescharacteristic, complemented
20C4×C22⋊C4×C151—21no—
21#352×C151—24no—
22AΣL(1,𝔽16)×C151—24no—
23#343×C151—21no—
24#342×C151—21no—
25C25×C151C2×C411yescharacteristic
26C22×D4×C151—21no—
27C22×D4×C151C2311yescharacteristic
28C23×C4×C151C2×C411yescharacteristic
29C23×C4×C151C2×C411yescharacteristic
30C23×C4×C151D411yescharacteristic
31C2×M16×C151—22no—
32#123×C151—22no—
33#123×C151—22no—
34#120×C151—22no—
35#120×C151—22no—
36C4×D4×C151—41no—
37C4×D4×C151—41no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C22⋊C4×C151—21no—
42C2×C22⋊C4×C151—21no—
43C2×C22⋊C4×C151—21no—
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—22no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—41no—
49C2×C22⋊C4×C151—41no—
50C2×C22⋊C4×C151C2×C411yescharacteristic
51C2×C22⋊C4×C151C2×C411yescharacteristic
52C2×C22⋊C4×C151C2×C411yescharacteristic
53C2×C22⋊C4×C151D411yescharacteristic
54C2×C42×C151—41no—
55C2×C42×C151D411yescharacteristic
56C4⋊C8×C151—41no—
57C4⋊C8×C151—41no—
58#100×C151—22no—
59#100×C151—22no—
60#99×C151—22no—
61#99×C151D414yes—
62#95×C151—21no—
63#95×C151—21no—
64#95×C151—21no—
65#95×C151—41no—
66C24×C151—21no—
67C24×C151—22no—
68C24×C151—41no—
69C24×C151—42no—
70C24×C151—41no—
71C24×C151—81no—
72C24×C151C22×C411yescharacteristic
73C24×C151C2×D411yescharacteristic
74C2×D4×C151—41no—
75C2×D4×C151—41no—
76C2×D4×C151—42no—
77C2×D4×C151—42no—
78C2×D4×C151—81no—
79C2×D4×C151C2×D412yes—
80C2×D4×C151#4112yes—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—21no—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—22no—
89C22×C4×C151—42no—
90C22×C4×C151—41no—
91C22×C4×C151—41no—
92C22×C4×C151—81no—
93C22×C4×C151—81no—
94C22×C4×C151C22⋊C411yescharacteristic
95C22×C4×C151C22⋊C411yescharacteristic
96C22×C4×C151C22⋊C411yescharacteristic
97C22×C4×C151C22⋊C411yescharacteristic
98C22×C4×C151C2×D411yescharacteristic
99M16×C151—42no—
100M16×C151—42no—
101C2×C8×C151—42no—
102C4⋊C4×C151—41no—
103C4⋊C4×C151—41no—
104C4⋊C4×C151—41no—
105C4⋊C4×C151—81no—
106C22⋊C4×C151—22no—
107C22⋊C4×C151—22no—
108C22⋊C4×C151—24no—
109C22⋊C4×C151—41no—
110C22⋊C4×C151—41no—
111C22⋊C4×C151—42no—
112C22⋊C4×C151—42no—
113C22⋊C4×C151—42no—
114C22⋊C4×C151—42no—
115C22⋊C4×C151—41no—
116C22⋊C4×C151—41no—
117C22⋊C4×C151—41no—
118C22⋊C4×C151—41no—
119C22⋊C4×C151—81no—
120C42×C151—21no—
121C42×C151—21no—
122C42×C151—82no—
123C23×C151—21no—
124C23×C151—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—22no—
128C23×C151—41no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151—41no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151—41no—
135C23×C151—42no—
136C23×C151—42no—
137C23×C151—41no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151—82no—
141C23×C151—84no—
142C23×C151—84no—
143C23×C151—82no—
144C23×C151C2×C22⋊C411yescharacteristic
145C23×C151C4×D412yes—
146C23×C151#12112yes—
147D4×C151—42no—
148D4×C151—42no—
149D4×C151—84no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—41no—
156C2×C4×C151—42no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151—44no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—41no—
170C2×C4×C151—81no—
171C2×C4×C151—81no—
172C2×C4×C151—81no—
173C2×C4×C151—82no—
174C2×C4×C151—82no—
175C2×C4×C151—82no—
176C2×C4×C151#9911yescharacteristic
177C2×C4×C151#9911yescharacteristic
178C2×C4×C151#12411yescharacteristic
179C2×C4×C151#12711yescharacteristic
180C8×C151—82no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—42no—
186C22×C151—42no—
187C22×C151—42no—
188C22×C151—42no—
189C22×C151—42no—
190C22×C151—41no—
191C22×C151—41no—
192C22×C151—41no—
193C22×C151—41no—
194C22×C151—42no—
195C22×C151—81no—
196C22×C151—81no—
197C22×C151—81no—
198C22×C151—84no—
199C22×C151—84no—
200C22×C151—81no—
201C22×C151—81no—
202C22×C151#39011yescharacteristic
203C22×C151C2×#9911yescharacteristic
204C22×C151#41011yescharacteristic
205C4×C151—21no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—41no—
210C4×C151—41no—
211C4×C151—41no—
212C4×C151—81no—
213C4×C151—81no—
214C4×C151—84no—
215C4×C151—81no—
216C2×C151—21no—
217C2×C151—21no—
218C2×C151—42no—
219C2×C151—42no—
220C2×C151—82no—
221C2×C151#196411yescharacteristic
222C2×C151#212011yescharacteristic
223C2×C151#212111yescharacteristic
224#13222C15111yesmaximal, characteristic, direct product factor, Sylow
225C151#1322211yescharacteristic, direct product factor, Sylow
226#2534C2×C15111yescharacteristic
227C2×#352C2×C15112yescomplemented
228C2×AΣL(1,𝔽16)C2×C15112yes—
229#1800C2×C15111yescharacteristic, complemented
230C4×#99C2×C15111yescharacteristic, complemented
231C2×#123C22×C15111yescharacteristic
232C2×#120C22×C15111yescharacteristic
233C2×C4×D4C22×C15111yescharacteristic
234C22×C22⋊C4C4×C15111yescharacteristic, complemented
235#423—21no—
236C2×#100C22×C15112yes—
237C2×#99C22×C15112yes—
238#396—21no—
239#394—21no—
240#388—21no—
241#386—21no—
242#381C4×C15111yescharacteristic, complemented
243#380C4×C15111yescharacteristic, complemented
244#379C4×C15111yescharacteristic, complemented
245C4×C22⋊C4—21no—
246#352—24no—
247AΣL(1,𝔽16)—24no—
248#343—21no—
249#342—21no—
250C25C2×C4×C15111yescharacteristic
251C22×D4—21no—
252C22×D4C23×C15111yescharacteristic
253C23×C4C2×C4×C15111yescharacteristic
254C23×C4C2×C4×C15111yescharacteristic
255C23×C4D4×C15111yescharacteristic
256C2×M16—22no—
257#123—22no—
258#123—22no—
259#120—22no—
260#120—22no—
261C4×D4—41no—
262C4×D4—41no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C15111yescharacteristic
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4C2×C4×C15111yescharacteristic
276C2×C22⋊C4C2×C4×C15111yescharacteristic
277C2×C22⋊C4C2×C4×C15111yescharacteristic
278C2×C22⋊C4D4×C15111yescharacteristic
279C2×C42—41no—
280C2×C42D4×C15111yescharacteristic
281C4⋊C8—41no—
282C4⋊C8—41no—
283#100—22no—
284#100—22no—
285#99—22no—
286#99D4×C15114yes—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—41no—
291C24—21no—
292C24—22no—
293C24—41no—
294C24—42no—
295C24—41no—
296C24—81no—
297C24C22×C4×C15111yescharacteristic
298C24C2×D4×C15111yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—81no—
304C2×D4C2×D4×C15112yes—
305C2×D4#41×C15112yes—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—81no—
318C22×C4—81no—
319C22×C4C22⋊C4×C15111yescharacteristic
320C22×C4C22⋊C4×C15111yescharacteristic
321C22×C4C22⋊C4×C15111yescharacteristic
322C22×C4C22⋊C4×C15111yescharacteristic
323C22×C4C2×D4×C15111yescharacteristic
324M16—42no—
325M16—42no—
326C2×C8—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—81no—
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—24no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—81no—
345C42—21no—
346C42—21no—
347C42—82no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—82no—
366C23—84no—
367C23—84no—
368C23—82no—
369C23C2×C22⋊C4×C15111yescharacteristic
370C23C4×D4×C15112yes—
371C23#121×C15112yes—
372D4—42no—
373D4—42no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4#99×C15111yescharacteristic
402C2×C4#99×C15111yescharacteristic
403C2×C4#124×C15111yescharacteristic
404C2×C4#127×C15111yescharacteristic
405C8—82no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—81no—
427C22#390×C15111yescharacteristic
428C22C2×#99×C15111yescharacteristic
429C22#410×C15111yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4—81no—
439C4—84no—
440C4—81no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—82no—
446C2#1964×C15111yescharacteristic
447C2#2120×C15111yescharacteristic
448C2#2121×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radicalC2×#120×C151C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#352×C151C2semidirect
4. #1800×C151C2semidirect
5. C4×#99×C151C2semidirect
9. C22×C22⋊C4×C151C4semidirect
17. #381×C151C4semidirect
18. #380×C151C4semidirect
19. #379×C151C4semidirect
224. #13222C151direct (N × H)
225. C151#13222direct (N × H)
227. C2×#352C2×C151semidirect
229. #1800C2×C151semidirect
230. C4×#99C2×C151semidirect
234. C22×C22⋊C4C4×C151semidirect
242. #381C4×C151semidirect
243. #380C4×C151semidirect
244. #379C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2534×C1512
C2×#352×C1512
C2×AΣL(1,𝔽16)×C1512
#1800×C1512
C4×#99×C1512
#13222151