Finite Group Databasebeta

← C151×#13574 #50318499

Subgroups — C151×#13574 #50318499

Order 38656.

486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3018×C151C211yesmaximal, characteristic
2#2132×C151C211yesmaximal, characteristic, complemented
3#1560×C151C211yesmaximal, characteristic, complemented
4#1405×C151C214yesmaximal, complemented
5#585×C151C411yescharacteristic
6#575×C151—21no—
7#532×C151C2211yescharacteristic
8#456×C151C2212yes—
9#455×C151—21no—
10#454×C151C412yes—
11#453×C151—21no—
12#423×C151—21no—
13C2×#104×C151—21no—
14#413×C151—21no—
15#413×C151C411yescharacteristic
16#356×C151C2212yescomplemented
17#355×C151—21no—
18#333×C151C2212yescomplemented
19#331×C151—21no—
202−1+4×C151—41no—
212−1+4×C151C2×C412yes—
22H(5,𝔽2)×C151—21no—
23H(5,𝔽2)×C151—41no—
24H(5,𝔽2)×C151—41no—
25C2×#41×C151—21no—
26C2×#41×C151—42no—
27C2×#41×C151—41no—
28C2×#41×C151C2×C411yescharacteristic
29C2×#41×C151D411yescharacteristic
30#137×C151—22no—
31#137×C151—41no—
32AGL(1,ℤ/8)×C151—22no—
33AGL(1,ℤ/8)×C151—41no—
34#135×C151—42no—
35C2×M16×C151—21no—
36C2×M16×C151—41no—
37C2×M16×C151—41no—
38C4⋊Q8×C151C2311yescharacteristic
39#127×C151D411yescharacteristic
40#124×C151C2×C411yescharacteristic
41#124×C151D411yescharacteristic
42#121×C151—41no—
43C4×D4×C151—41no—
44C2×C42×C151D411yescharacteristic
45C4⋊C8×C151—22no—
46C4⋊C8×C151—41no—
47#104×C151—22no—
48#104×C151—22no—
49#101×C151—22no—
50#101×C151C2×C412yes—
51#100×C151—21no—
52#100×C151—41no—
53#41×C151—22no—
54#41×C151—22no—
55#41×C151—41no—
56#41×C151—42no—
57#41×C151—41no—
58#41×C151—41no—
59#41×C151—41no—
60#41×C151—41no—
61#41×C151—42no—
62#41×C151—42no—
63#41×C151—44no—
64#41×C151—42no—
65#41×C151—41no—
66#41×C151—42no—
67C2×Q8×C151—21no—
68C2×Q8×C151—42no—
69C2×Q8×C151—41no—
70C2×Q8×C151C22×C411yescharacteristic
71C2×Q8×C151C2×D411yescharacteristic
72C2×D4×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—21no—
75C2×D4×C151—41no—
76C2×D4×C151—42no—
77C2×D4×C151—42no—
78C2×D4×C151—44no—
79C2×D4×C151—41no—
80C2×D4×C151—41no—
81C2×D4×C151C22⋊C411yescharacteristic
82C2×D4×C151C22⋊C411yescharacteristic
83C22×C4×C151—21no—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—41no—
87C22×C4×C151—42no—
88C22×C4×C151C22⋊C411yescharacteristic
89Q16×C151—42no—
90SD16×C151—42no—
91SD16×C151—42no—
92D8×C151—42no—
93M16×C151—22no—
94M16×C151—41no—
95M16×C151—42no—
96M16×C151—82no—
97M16×C151—81no—
98C2×C8×C151—41no—
99C2×C8×C151—42no—
100C2×C8×C151—81no—
101C4⋊C4×C151—41no—
102C22⋊C4×C151—41no—
103C22⋊C4×C151—41no—
104C42×C151—21no—
105C42×C151C22⋊C411yescharacteristic
106C42×C151C2×D411yescharacteristic
107C23×C151—21no—
108C23×C151—21no—
109C23×C151—41no—
110C23×C151—42no—
111C23×C151#9911yescharacteristic
112Q8×C151—22no—
113Q8×C151—41no—
114Q8×C151—41no—
115Q8×C151—42no—
116Q8×C151—41no—
117D4×C151—22no—
118D4×C151—41no—
119D4×C151—41no—
120D4×C151—42no—
121D4×C151—42no—
122D4×C151—42no—
123D4×C151—44no—
124D4×C151—42no—
125D4×C151—41no—
126D4×C151—81no—
127D4×C151—81no—
128D4×C151—81no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—42no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—44no—
140C2×C4×C151—42no—
141C2×C4×C151—41no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151#9911yescharacteristic
147C2×C4×C151C2×C22⋊C411yescharacteristic
148C8×C151—42no—
149C8×C151—82no—
150C8×C151—82no—
151C22×C151—21no—
152C22×C151—41no—
153C22×C151—42no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—81no—
157C22×C151—81no—
158C22×C151—161no—
159C22×C151—162no—
160C22×C151C2×#9911yescharacteristic
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151—42no—
168C4×C151AΣL(1,𝔽16)11yescharacteristic
169C4×C151AΣL(1,𝔽16)11yescharacteristic
170C2×C151—21no—
171C2×C151—41no—
172C2×C151—81no—
173C2×C151—81no—
174C2×C151—82no—
175C2×C151C2×AΣL(1,𝔽16)11yescharacteristic
176#13574C15111yesmaximal, characteristic, direct product factor, Sylow
177C151#1357411yescharacteristic, direct product factor, Sylow
178#3018C2×C15111yescharacteristic
179#2132C2×C15111yescharacteristic, complemented
180#1560C2×C15111yescharacteristic, complemented
181#1405C2×C15114yescomplemented
182#585C4×C15111yescharacteristic
183#575—21no—
184#532C22×C15111yescharacteristic
185#456C22×C15112yes—
186#455—21no—
187#454C4×C15112yes—
188#453—21no—
189#423—21no—
190C2×#104—21no—
191#413—21no—
192#413C4×C15111yescharacteristic
193#356C22×C15112yescomplemented
194#355—21no—
195#333C22×C15112yescomplemented
196#331—21no—
1972−1+4—41no—
1982−1+4C2×C4×C15112yes—
199H(5,𝔽2)—21no—
200H(5,𝔽2)—41no—
201H(5,𝔽2)—41no—
202C2×#41—21no—
203C2×#41—41no—
204C2×#41—42no—
205C2×#41C2×C4×C15111yescharacteristic
206C2×#41D4×C15111yescharacteristic
207#137—22no—
208#137—41no—
209AGL(1,ℤ/8)—22no—
210AGL(1,ℤ/8)—41no—
211#135—42no—
212C2×M16—21no—
213C2×M16—41no—
214C2×M16—41no—
215C4⋊Q8C23×C15111yescharacteristic
216#127D4×C15111yescharacteristic
217#124C2×C4×C15111yescharacteristic
218#124D4×C15111yescharacteristic
219#121—41no—
220C4×D4—41no—
221C2×C42D4×C15111yescharacteristic
222C4⋊C8—22no—
223C4⋊C8—41no—
224#104—22no—
225#104—22no—
226#101—22no—
227#101C2×C4×C15112yes—
228#100—21no—
229#100—41no—
230#41—22no—
231#41—22no—
232#41—41no—
233#41—42no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—42no—
239#41—42no—
240#41—44no—
241#41—42no—
242#41—41no—
243#41—42no—
244C2×Q8—21no—
245C2×Q8—42no—
246C2×Q8—41no—
247C2×Q8C22×C4×C15111yescharacteristic
248C2×Q8C2×D4×C15111yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—44no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4C22⋊C4×C15111yescharacteristic
259C2×D4C22⋊C4×C15111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4C22⋊C4×C15111yescharacteristic
266Q16—42no—
267SD16—42no—
268SD16—42no—
269D8—42no—
270M16—22no—
271M16—41no—
272M16—42no—
273M16—82no—
274M16—81no—
275C2×C8—41no—
276C2×C8—42no—
277C2×C8—81no—
278C4⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42—21no—
282C42C22⋊C4×C15111yescharacteristic
283C42C2×D4×C15111yescharacteristic
284C23—21no—
285C23—21no—
286C23—41no—
287C23—42no—
288C23#99×C15111yescharacteristic
289Q8—22no—
290Q8—41no—
291Q8—41no—
292Q8—42no—
293Q8—41no—
294D4—22no—
295D4—41no—
296D4—41no—
297D4—42no—
298D4—42no—
299D4—42no—
300D4—44no—
301D4—42no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4#99×C15111yescharacteristic
324C2×C4C2×C22⋊C4×C15111yescharacteristic
325C8—42no—
326C8—82no—
327C8—82no—
328C22—21no—
329C22—41no—
330C22—42no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—161no—
336C22—162no—
337C22C2×#99×C15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—42no—
345C4AΣL(1,𝔽16)×C15111yescharacteristic
346C4AΣL(1,𝔽16)×C15111yescharacteristic
347C2—21no—
348C2—41no—
349C2—81no—
350C2—81no—
351C2—82no—
352C2C2×AΣL(1,𝔽16)×C15111yescharacteristic
subgroupG/H
center, socleC2×C151C2×AΣL(1,𝔽16)
commutatorC2×Q8C22×C4×C151
Frattini, cosocleC4⋊Q8C23×C151
prime radical#3018×C151C2
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C22×C4×C151 ◁ #532×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2132×C151C2semidirect
3. #1560×C151C2semidirect
4. #1405×C151C2semidirect
16. #356×C151C22semidirect
18. #333×C151C22semidirect
176. #13574C151direct (N × H)
177. C151#13574direct (N × H)
179. #2132C2×C151semidirect
180. #1560C2×C151semidirect
181. #1405C2×C151semidirect
193. #356C22×C151semidirect
195. #333C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3018×C1512
#2132×C1512
#1560×C1512
#1405×C1512
#13574151