Finite Group Databasebeta

← C151×#9120 #50314045

Subgroups — C151×#9120 #50314045

Order 38656.

684 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×M16×C151C211yesmaximal, characteristic, complemented
2#2850×C151C211yesmaximal, characteristic
3#1749×C151C211yesmaximal, characteristic, complemented
4C2×#329×C151C212yesmaximal, complemented
5#1295×C151C212yesmaximal, complemented
6C22×M16×C151—21no—
7C2×#124×C151C2211yescharacteristic
8C2×C22⋊Q8×C151C411yescharacteristic
9C2×#121×C151C411yescharacteristic
10C22×C42×C151C2211yescharacteristic
11C2×C22⋊C8×C151—21no—
12C4×M16×C151—24no—
13C2×#97×C151C2212yes—
14C2×#97×C151C2212yes—
15C2×C4×C8×C151—21no—
16#391×C151C411yescharacteristic
17#390×C151C411yescharacteristic
18#388×C151—21no—
19#388×C151—21no—
20#386×C151—21no—
21#386×C151—21no—
22#382×C151C2211yescharacteristic
23#336×C151—21no—
24#329×C151—24no—
25C22×Q8×C151C2×C411yescharacteristic
26C22×D4×C151—21no—
27C22×D4×C151C2×C411yescharacteristic
28C23×C4×C151C2×C411yescharacteristic
29C23×C4×C151D411yescharacteristic
30C23×C4×C151D411yescharacteristic
31C2×M16×C151—24no—
32C2×M16×C151—24no—
33C2×M16×C151—24no—
34C22×C8×C151—22no—
35C22×C8×C151—22no—
36#124×C151—22no—
37#124×C151—22no—
38C22⋊Q8×C151—42no—
39#121×C151—42no—
40C2×C4⋊C4×C151—21no—
41C2×C4⋊C4×C151C2×C411yescharacteristic
42C2×C4⋊C4×C151C2×C411yescharacteristic
43C2×C22⋊C4×C151—21no—
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—21no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—21no—
49C2×C42×C151—22no—
50C2×C42×C151—22no—
51C2×C42×C151C2×C411yescharacteristic
52C2×C42×C151D411yescharacteristic
53C2×C42×C151D411yescharacteristic
54C2×C42×C151C2311yescharacteristic
55C22⋊C8×C151—24no—
56#97×C151—22no—
57#97×C151—22no—
58#97×C151—22no—
59#97×C151D414yescomplemented
60C4×C8×C151—24no—
61#95×C151—21no—
62#95×C151—21no—
63#95×C151—21no—
64#95×C151—21no—
65C24×C151—21no—
66C24×C151C22⋊C411yescharacteristic
67C2×Q8×C151—22no—
68C2×Q8×C151—41no—
69C2×Q8×C151—41no—
70C2×D4×C151—22no—
71C2×D4×C151—41no—
72C2×D4×C151—41no—
73C2×D4×C151—42no—
74C2×D4×C151—42no—
75C2×D4×C151—42no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151—22no—
81C22×C4×C151—22no—
82C22×C4×C151—22no—
83C22×C4×C151—22no—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—41no—
88C22×C4×C151—41no—
89C22×C4×C151C22⋊C411yescharacteristic
90C22×C4×C151C22⋊C411yescharacteristic
91C22×C4×C151C22⋊C411yescharacteristic
92C22×C4×C151C22×C411yescharacteristic
93C22×C4×C151C2×D411yescharacteristic
94C22×C4×C151C2×D411yescharacteristic
95M16×C151—216no—
96C2×C8×C151—24no—
97C2×C8×C151—24no—
98C2×C8×C151—24no—
99C2×C8×C151—24no—
100C2×C8×C151—42no—
101C2×C8×C151—42no—
102C4⋊C4×C151—41no—
103C4⋊C4×C151—41no—
104C4⋊C4×C151—42no—
105C22⋊C4×C151—42no—
106C22⋊C4×C151—42no—
107C22⋊C4×C151—42no—
108C22⋊C4×C151—42no—
109C22⋊C4×C151—41no—
110C22⋊C4×C151—42no—
111C22⋊C4×C151—41no—
112C42×C151—22no—
113C42×C151—21no—
114C42×C151—22no—
115C42×C151—21no—
116C42×C151C2×D412yes—
117C42×C151#4112yes—
118C23×C151—21no—
119C23×C151—21no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151—21no—
123C23×C151—21no—
124C23×C151—41no—
125C23×C151—41no—
126C23×C151—41no—
127C23×C151—41no—
128C23×C151—41no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151#10412yes—
132C23×C151C2×C22⋊C411yescharacteristic
133Q8×C151—82no—
134D4×C151—82no—
135D4×C151—84no—
136C2×C4×C151—24no—
137C2×C4×C151—24no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—44no—
151C2×C4×C151—44no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151—41no—
161C2×C4×C151#10012yes—
162C2×C4×C151#10412yes—
163C2×C4×C151#10412yes—
164C2×C4×C151C4×D412yes—
165C2×C4×C151#12011yescharacteristic
166C2×C4×C151#12112yes—
167C2×C4×C151#12311yescharacteristic
168C8×C151—28no—
169C8×C151—44no—
170C22×C151—22no—
171C22×C151—22no—
172C22×C151—22no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—81no—
178C22×C151—81no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151—81no—
182C22×C151—81no—
183C22×C151—81no—
184C22×C151#38611yescharacteristic
185C22×C151C2×#10011yescharacteristic
186C22×C151#41311yescharacteristic
187C22×C151C2×#10411yescharacteristic
188C22×C151C2×#10411yescharacteristic
189C22×C151C2×#10411yescharacteristic
190C22×C151#42111yescharacteristic
191C4×C151—22no—
192C4×C151—22no—
193C4×C151—21no—
194C4×C151—22no—
195C4×C151—21no—
196C4×C151—22no—
197C4×C151—22no—
198C4×C151—81no—
199C4×C151—81no—
200C4×C151—81no—
201C2×C151—42no—
202C2×C151—161no—
203C2×C151#152411yescharacteristic
204C2×C151#152511yescharacteristic
205C2×C151#152711yescharacteristic
206C2×C151#152911yescharacteristic
207C2×C151#187111yescharacteristic
208C2×C151#189611yescharacteristic
209C2×C151#190011yescharacteristic
210#9120C15111yesmaximal, characteristic, direct product factor, Sylow
211C151#912011yescharacteristic, direct product factor, Sylow
212C2×C4×M16C2×C15111yescharacteristic, complemented
213#2850C2×C15111yescharacteristic
214#1749C2×C15111yescharacteristic, complemented
215C2×#329C2×C15112yescomplemented
216#1295C2×C15112yescomplemented
217C22×M16—21no—
218C2×#124C22×C15111yescharacteristic
219C2×C22⋊Q8C4×C15111yescharacteristic
220C2×#121C4×C15111yescharacteristic
221C22×C42C22×C15111yescharacteristic
222C2×C22⋊C8—21no—
223C4×M16—24no—
224C2×#97C22×C15112yes—
225C2×#97C22×C15112yes—
226C2×C4×C8—21no—
227#391C4×C15111yescharacteristic
228#390C4×C15111yescharacteristic
229#388—21no—
230#388—21no—
231#386—21no—
232#386—21no—
233#382C22×C15111yescharacteristic
234#336—21no—
235#329—24no—
236C22×Q8C2×C4×C15111yescharacteristic
237C22×D4—21no—
238C22×D4C2×C4×C15111yescharacteristic
239C23×C4C2×C4×C15111yescharacteristic
240C23×C4D4×C15111yescharacteristic
241C23×C4D4×C15111yescharacteristic
242C2×M16—24no—
243C2×M16—24no—
244C2×M16—24no—
245C22×C8—22no—
246C22×C8—22no—
247#124—22no—
248#124—22no—
249C22⋊Q8—42no—
250#121—42no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C15111yescharacteristic
253C2×C4⋊C4C2×C4×C15111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42—22no—
261C2×C42—22no—
262C2×C42C2×C4×C15111yescharacteristic
263C2×C42D4×C15111yescharacteristic
264C2×C42D4×C15111yescharacteristic
265C2×C42C23×C15111yescharacteristic
266C22⋊C8—24no—
267#97—22no—
268#97—22no—
269#97—22no—
270#97D4×C15114yescomplemented
271C4×C8—24no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276C24—21no—
277C24C22⋊C4×C15111yescharacteristic
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C22⋊C4×C15111yescharacteristic
301C22×C4C22⋊C4×C15111yescharacteristic
302C22×C4C22⋊C4×C15111yescharacteristic
303C22×C4C22×C4×C15111yescharacteristic
304C22×C4C2×D4×C15111yescharacteristic
305C22×C4C2×D4×C15111yescharacteristic
306M16—216no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8—24no—
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C42—22no—
324C42—21no—
325C42—22no—
326C42—21no—
327C42C2×D4×C15112yes—
328C42#41×C15112yes—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#104×C15112yes—
343C23C2×C22⋊C4×C15111yescharacteristic
344Q8—82no—
345D4—82no—
346D4—84no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4#100×C15112yes—
373C2×C4#104×C15112yes—
374C2×C4#104×C15112yes—
375C2×C4C4×D4×C15112yes—
376C2×C4#120×C15111yescharacteristic
377C2×C4#121×C15112yes—
378C2×C4#123×C15111yescharacteristic
379C8—28no—
380C8—44no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22#386×C15111yescharacteristic
396C22C2×#100×C15111yescharacteristic
397C22#413×C15111yescharacteristic
398C22C2×#104×C15111yescharacteristic
399C22C2×#104×C15111yescharacteristic
400C22C2×#104×C15111yescharacteristic
401C22#421×C15111yescharacteristic
402C4—22no—
403C4—22no—
404C4—21no—
405C4—22no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—81no—
410C4—81no—
411C4—81no—
412C2—42no—
413C2—161no—
414C2#1524×C15111yescharacteristic
415C2#1525×C15111yescharacteristic
416C2#1527×C15111yescharacteristic
417C2#1529×C15111yescharacteristic
418C2#1871×C15111yescharacteristic
419C2#1896×C15111yescharacteristic
420C2#1900×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#121×C151C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×M16×C151C2semidirect
3. #1749×C151C2semidirect
4. C2×#329×C151C2semidirect
5. #1295×C151C2semidirect
59. #97×C151D4semidirect
210. #9120C151direct (N × H)
211. C151#9120direct (N × H)
212. C2×C4×M16C2×C151semidirect
214. #1749C2×C151semidirect
215. C2×#329C2×C151semidirect
216. #1295C2×C151semidirect
270. #97D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×M16×C1512
#2850×C1512
#1749×C1512
C2×#329×C1512
#1295×C1512
#9120151