Finite Group Databasebeta

← C151×#10021 #50314946

Subgroups — C151×#10021 #50314946

Order 38656.

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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#3142×C151C211yesmaximal, characteristic
2#3112×C151C211yesmaximal, characteristic
3#2634×C151C211yesmaximal, characteristic, complemented
4#1534×C151C211yesmaximal, characteristic, complemented
5#1514×C151C211yesmaximal, characteristic
6#1491×C151C211yesmaximal, characteristic, complemented
7#1288×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×#125×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#491×C151—21no—
12#490×C151—21no—
13#488×C151—22no—
14#480×C151—21no—
15#477×C151—21no—
16#460×C151—21no—
17#448×C151—21no—
18#440×C151—22no—
19#432×C151C2211yescharacteristic
20#432×C151C2211yescharacteristic
21#417×C151—21no—
22#417×C151—21no—
23C4×M16×C151C2211yescharacteristic
24#400×C151—21no—
25#400×C151—21no—
26#398×C151—21no—
27#395×C151—21no—
28#387×C151—22no—
29#383×C151C2211yescharacteristic
30#330×C151—22no—
31#327×C151—22no—
32Q8⋊C8×C151—22no—
33C2×#41×C151—21no—
34C22×Q8×C151D411yescharacteristic
35C2×SD16×C151—22no—
36C2×M16×C151—21no—
37C4⋊Q8×C151D411yescharacteristic
38#127×C151D411yescharacteristic
39#125×C151—21no—
40#125×C151—21no—
41#125×C151—21no—
42#125×C151—21no—
43#124×C151—21no—
44#121×C151—21no—
45#121×C151—21no—
46C4×Q8×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×D4×C151—21no—
51C4×D4×C151—21no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C42×C151—21no—
60C2×C42×C151C2311yescharacteristic
61#107×C151—22no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64#103×C151—22no—
65#103×C151—22no—
66#103×C151—22no—
67#102×C151—22no—
68#102×C151—22no—
69#102×C151—22no—
70C22⋊C8×C151—21no—
71C22⋊C8×C151—21no—
72#97×C151—21no—
73#97×C151—21no—
74#97×C151D412yes—
75C4×C8×C151D412yes—
76#95×C151—22no—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151—21no—
80#95×C151—21no—
81#95×C151D412yes—
82#41×C151—44no—
83C2×Q8×C151—21no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—42no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—41no—
91C22×C4×C151—21no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—41no—
97C22×C4×C151C2×D411yescharacteristic
98C22×C4×C151C2×D411yescharacteristic
99C22×C4×C151C2×D411yescharacteristic
100SD16×C151—44no—
101M16×C151—42no—
102C2×C8×C151—22no—
103C2×C8×C151—22no—
104C2×C8×C151—41no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—44no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C22⋊C4×C151—41no—
121C22⋊C4×C151—41no—
122C42×C151—41no—
123C42×C151—41no—
124C42×C151C2×D411yescharacteristic
125C42×C151C2×D411yescharacteristic
126C42×C151C2×D411yescharacteristic
127C42×C151#4111yescharacteristic
128C23×C151—41no—
129C23×C151#12011yescharacteristic
130Q8×C151—22no—
131Q8×C151—22no—
132Q8×C151—41no—
133Q8×C151—41no—
134Q8×C151—42no—
135D4×C151—42no—
136D4×C151—42no—
137D4×C151—81no—
138D4×C151—82no—
139C2×C4×C151—22no—
140C2×C4×C151—22no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—42no—
146C2×C4×C151—42no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—42no—
154C2×C4×C151—42no—
155C2×C4×C151—82no—
156C2×C4×C151#12011yescharacteristic
157C2×C4×C151#12011yescharacteristic
158C2×C4×C151#12111yescharacteristic
159C2×C4×C151#12111yescharacteristic
160C2×C4×C151#12111yescharacteristic
161C2×C4×C151#12711yescharacteristic
162C8×C151—42no—
163C8×C151—42no—
164C8×C151—81no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—81no—
168C22×C151—81no—
169C22×C151—81no—
170C22×C151#39211yescharacteristic
171C22×C151#45412yes—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—21no—
178C4×C151—42no—
179C4×C151—82no—
180C4×C151—81no—
181C4×C151—81no—
182C4×C151—81no—
183C4×C151—81no—
184C2×C151—22no—
185C2×C151—161no—
186C2×C151#200311yescharacteristic
187C2×C151#200911yescharacteristic
188C2×C151#201011yescharacteristic
189#10021C15111yesmaximal, characteristic, direct product factor, Sylow
190C151#1002111yescharacteristic, direct product factor, Sylow
191#3142C2×C15111yescharacteristic
192#3112C2×C15111yescharacteristic
193#2634C2×C15111yescharacteristic, complemented
194#1534C2×C15111yescharacteristic, complemented
195#1514C2×C15111yescharacteristic
196#1491C2×C15111yescharacteristic, complemented
197#1288C2×C15111yescharacteristic, complemented
198#532C22×C15111yescharacteristic
199C2×#125C22×C15111yescharacteristic
200C2×C4×Q8C22×C15111yescharacteristic
201#491—21no—
202#490—21no—
203#488—22no—
204#480—21no—
205#477—21no—
206#460—21no—
207#448—21no—
208#440—22no—
209#432C22×C15111yescharacteristic
210#432C22×C15111yescharacteristic
211#417—21no—
212#417—21no—
213C4×M16C22×C15111yescharacteristic
214#400—21no—
215#400—21no—
216#398—21no—
217#395—21no—
218#387—22no—
219#383C22×C15111yescharacteristic
220#330—22no—
221#327—22no—
222Q8⋊C8—22no—
223C2×#41—21no—
224C22×Q8D4×C15111yescharacteristic
225C2×SD16—22no—
226C2×M16—21no—
227C4⋊Q8D4×C15111yescharacteristic
228#127D4×C15111yescharacteristic
229#125—21no—
230#125—21no—
231#125—21no—
232#125—21no—
233#124—21no—
234#121—21no—
235#121—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C15111yescharacteristic
247C2×C4⋊C4D4×C15111yescharacteristic
248C2×C4⋊C4D4×C15111yescharacteristic
249C2×C42—21no—
250C2×C42C23×C15111yescharacteristic
251#107—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254#103—22no—
255#103—22no—
256#103—22no—
257#102—22no—
258#102—22no—
259#102—22no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262#97—21no—
263#97—21no—
264#97D4×C15112yes—
265C4×C8D4×C15112yes—
266#95—22no—
267#95—22no—
268#95—22no—
269#95—21no—
270#95—21no—
271#95D4×C15112yes—
272#41—44no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—42no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4C2×D4×C15111yescharacteristic
288C22×C4C2×D4×C15111yescharacteristic
289C22×C4C2×D4×C15111yescharacteristic
290SD16—44no—
291M16—42no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—44no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—41no—
313C42—41no—
314C42C2×D4×C15111yescharacteristic
315C42C2×D4×C15111yescharacteristic
316C42C2×D4×C15111yescharacteristic
317C42#41×C15111yescharacteristic
318C23—41no—
319C23#120×C15111yescharacteristic
320Q8—22no—
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—42no—
325D4—42no—
326D4—42no—
327D4—81no—
328D4—82no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4#120×C15111yescharacteristic
347C2×C4#120×C15111yescharacteristic
348C2×C4#121×C15111yescharacteristic
349C2×C4#121×C15111yescharacteristic
350C2×C4#121×C15111yescharacteristic
351C2×C4#127×C15111yescharacteristic
352C8—42no—
353C8—42no—
354C8—81no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#392×C15111yescharacteristic
361C22#454×C15112yes—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—82no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C2—22no—
375C2—161no—
376C2#2003×C15111yescharacteristic
377C2#2009×C15111yescharacteristic
378C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#532×C151C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2634×C151C2semidirect
4. #1534×C151C2semidirect
6. #1491×C151C2semidirect
7. #1288×C151C2semidirect
189. #10021C151direct (N × H)
190. C151#10021direct (N × H)
193. #2634C2×C151semidirect
194. #1534C2×C151semidirect
196. #1491C2×C151semidirect
197. #1288C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3142×C1512
#3112×C1512
#2634×C1512
#1534×C1512
#1514×C1512
#1491×C1512
#1288×C1512
#10021151