Finite Group Databasebeta

← C151×#10044 #50314969

Subgroups — C151×#10044 #50314969

Order 38656.

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

normal subgroups only

This group has 466 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#3235×C151C211yesmaximal, characteristic
2#3113×C151C211yesmaximal, characteristic, complemented
3#3103×C151C211yesmaximal, characteristic
4#1536×C151C211yesmaximal, characteristic
5#1497×C151C211yesmaximal, characteristic, complemented
6#1467×C151C211yesmaximal, characteristic, complemented
7#1287×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9#532×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#501×C151—21no—
12#490×C151—21no—
13#483×C151—21no—
14#482×C151—22no—
15#481×C151—21no—
16#476×C151—21no—
17#475×C151—21no—
18#475×C151—21no—
19#474×C151—21no—
20#462×C151—21no—
21#460×C151—21no—
22#451×C151—21no—
23#448×C151—21no—
24#441×C151—22no—
25C4×SD16×C151—22no—
26#432×C151C2211yescharacteristic
27#432×C151C2211yescharacteristic
28#432×C151C2211yescharacteristic
29#431×C151C2211yescharacteristic
30#329×C151—22no—
31Q8⋊C8×C151—22no—
32#324×C151—22no—
33C2×#41×C151—21no—
34C22×Q8×C151D411yescharacteristic
35C2×Q16×C151—22no—
36C2×SD16×C151—22no—
37C4⋊Q8×C151D411yescharacteristic
38C4⋊Q8×C151D411yescharacteristic
39C4⋊Q8×C151D411yescharacteristic
40#127×C151D411yescharacteristic
41#125×C151—21no—
42#124×C151—21no—
43C22⋊Q8×C151—21no—
44C22⋊Q8×C151—21no—
45#121×C151—21no—
46#121×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×Q8×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55#117×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C42×C151—21no—
59C2×C42×C151C2311yescharacteristic
60#107×C151—22no—
61#106×C151—22no—
62#106×C151—22no—
63#106×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68#103×C151—22no—
69#103×C151—22no—
70#103×C151—22no—
71#102×C151—22no—
72#102×C151—22no—
73#102×C151—22no—
74C22⋊C8×C151—21no—
75C22⋊C8×C151—21no—
76C22⋊C8×C151—21no—
77C22⋊C8×C151D412yes—
78#97×C151—21no—
79#97×C151—21no—
80#97×C151D412yes—
81C4×C8×C151D412yes—
82#41×C151—82no—
83C2×Q8×C151—21no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—21no—
87C2×Q8×C151—21no—
88C2×Q8×C151—42no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—41no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—41no—
96C22×C4×C151C2×D411yescharacteristic
97C22×C4×C151C2×D411yescharacteristic
98C22×C4×C151#4111yescharacteristic
99Q16×C151—44no—
100SD16×C151—44no—
101C2×C8×C151—22no—
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—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C22⋊C4×C151—41no—
118C22⋊C4×C151—41no—
119C22⋊C4×C151—41no—
120C42×C151—41no—
121C42×C151—41no—
122C42×C151—41no—
123C42×C151C2×D411yescharacteristic
124C42×C151C2×D411yescharacteristic
125C42×C151C2×D411yescharacteristic
126C42×C151C2×D411yescharacteristic
127C23×C151—41no—
128C23×C151#12111yescharacteristic
129Q8×C151—22no—
130Q8×C151—22no—
131Q8×C151—41no—
132Q8×C151—41no—
133Q8×C151—42no—
134Q8×C151—42no—
135Q8×C151—81no—
136D4×C151—42no—
137D4×C151—42no—
138D4×C151—81no—
139D4×C151—82no—
140C2×C4×C151—22no—
141C2×C4×C151—22no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
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—82no—
151C2×C4×C151—81no—
152C2×C4×C151#12011yescharacteristic
153C2×C4×C151#12011yescharacteristic
154C2×C4×C151#12011yescharacteristic
155C2×C4×C151#12111yescharacteristic
156C2×C4×C151#12111yescharacteristic
157C2×C4×C151#12711yescharacteristic
158C8×C151—42no—
159C8×C151—42no—
160C8×C151—42no—
161C8×C151—81no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—81no—
166C22×C151—81no—
167C22×C151—81no—
168C22×C151#39211yescharacteristic
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—42no—
175C4×C151—81no—
176C4×C151—81no—
177C4×C151—81no—
178C4×C151—81no—
179C4×C151#47112yes—
180C2×C151—41no—
181C2×C151—161no—
182C2×C151#200911yescharacteristic
183C2×C151#201011yescharacteristic
184C2×C151#201911yescharacteristic
185#10044C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#1004411yescharacteristic, direct product factor, Sylow
187#3235C2×C15111yescharacteristic
188#3113C2×C15111yescharacteristic, complemented
189#3103C2×C15111yescharacteristic
190#1536C2×C15111yescharacteristic
191#1497C2×C15111yescharacteristic, complemented
192#1467C2×C15111yescharacteristic, complemented
193#1287C2×C15111yescharacteristic, complemented
194#533C22×C15111yescharacteristic
195#532C22×C15111yescharacteristic
196C2×C4×Q8C22×C15111yescharacteristic
197#501—21no—
198#490—21no—
199#483—21no—
200#482—22no—
201#481—21no—
202#476—21no—
203#475—21no—
204#475—21no—
205#474—21no—
206#462—21no—
207#460—21no—
208#451—21no—
209#448—21no—
210#441—22no—
211C4×SD16—22no—
212#432C22×C15111yescharacteristic
213#432C22×C15111yescharacteristic
214#432C22×C15111yescharacteristic
215#431C22×C15111yescharacteristic
216#329—22no—
217Q8⋊C8—22no—
218#324—22no—
219C2×#41—21no—
220C22×Q8D4×C15111yescharacteristic
221C2×Q16—22no—
222C2×SD16—22no—
223C4⋊Q8D4×C15111yescharacteristic
224C4⋊Q8D4×C15111yescharacteristic
225C4⋊Q8D4×C15111yescharacteristic
226#127D4×C15111yescharacteristic
227#125—21no—
228#124—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—21no—
240C4×D4—21no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C15111yescharacteristic
244C2×C42—21no—
245C2×C42C23×C15111yescharacteristic
246#107—22no—
247#106—22no—
248#106—22no—
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
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—
262C22⋊C8—21no—
263C22⋊C8D4×C15112yes—
264#97—21no—
265#97—21no—
266#97D4×C15112yes—
267C4×C8D4×C15112yes—
268#41—82no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4C2×D4×C15111yescharacteristic
283C22×C4C2×D4×C15111yescharacteristic
284C22×C4#41×C15111yescharacteristic
285Q16—44no—
286SD16—44no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—41no—
308C42—41no—
309C42C2×D4×C15111yescharacteristic
310C42C2×D4×C15111yescharacteristic
311C42C2×D4×C15111yescharacteristic
312C42C2×D4×C15111yescharacteristic
313C23—41no—
314C23#121×C15111yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—41no—
318Q8—41no—
319Q8—42no—
320Q8—42no—
321Q8—81no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—82no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4#120×C15111yescharacteristic
339C2×C4#120×C15111yescharacteristic
340C2×C4#120×C15111yescharacteristic
341C2×C4#121×C15111yescharacteristic
342C2×C4#121×C15111yescharacteristic
343C2×C4#127×C15111yescharacteristic
344C8—42no—
345C8—42no—
346C8—42no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22#392×C15111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4#471×C15112yes—
366C2—41no—
367C2—161no—
368C2#2009×C15111yescharacteristic
369C2#2010×C15111yescharacteristic
370C2#2019×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
2. #3113×C151C2semidirect
5. #1497×C151C2semidirect
6. #1467×C151C2semidirect
7. #1287×C151C2semidirect
185. #10044C151direct (N × H)
186. C151#10044direct (N × H)
188. #3113C2×C151semidirect
191. #1497C2×C151semidirect
192. #1467C2×C151semidirect
193. #1287C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3235×C1512
#3113×C1512
#3103×C1512
#1536×C1512
#1497×C1512
#1467×C1512
#1287×C1512
#10044151