Finite Group Databasebeta

← C151×#9714 #50314639

Subgroups — C151×#9714 #50314639

Order 38656.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2857×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C2×#328×C151C214yesmaximal
4#1434×C151C211yesmaximal, characteristic
5C2×C4⋊Q8×C151C411yescharacteristic, complemented
6C2×C22⋊Q8×C151C2212yes—
7C22×C42×C151C2211yescharacteristic
8C2×C4⋊C8×C151—21no—
9C2×C22⋊C8×C151C2212yes—
10#391×C151C412yescomplemented
11#389×C151—21no—
12#389×C151—21no—
13#384×C151C411yescharacteristic, complemented
14#380×C151—21no—
15#380×C151—21no—
16C2×#95×C151—21no—
17C2×#95×C151—21no—
18C2×#95×C151C2212yes—
19#336×C151—21no—
20#328×C151—28no—
21C22×Q8×C151C2×C412yes—
22C23×C4×C151—22no—
23C23×C4×C151D411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C23×C4×C151C2311yescharacteristic
26C22×C8×C151—22no—
27C4⋊Q8×C151—42no—
28C22⋊Q8×C151—24no—
29C22⋊Q8×C151—24no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—22no—
35C2×C4⋊C4×C151C2×C412yes—
36C2×C22⋊C4×C151—22no—
37C2×C42×C151—42no—
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151C2×C411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C2×C42×C151D411yescharacteristic
42C4⋊C8×C151—42no—
43C22⋊C8×C151—24no—
44#95×C151—22no—
45#95×C151—22no—
46#95×C151—22no—
47#95×C151—42no—
48#95×C151—42no—
49#95×C151D414yes—
50C24×C151C2×D411yescharacteristic
51C2×Q8×C151—24no—
52C2×Q8×C151—42no—
53C2×Q8×C151—42no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—24no—
59C22×C4×C151—41no—
60C22×C4×C151—41no—
61C22×C4×C151—41no—
62C22×C4×C151—41no—
63C22×C4×C151—41no—
64C22×C4×C151—42no—
65C22×C4×C151—42no—
66C22×C4×C151—42no—
67C22×C4×C151—42no—
68C22×C4×C151—42no—
69C22×C4×C151—42no—
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22⋊C411yescharacteristic
72C22×C4×C151C22⋊C411yescharacteristic
73C22×C4×C151C22⋊C411yescharacteristic
74C22×C4×C151SD1612yes—
75C22×C4×C151Q1612yes—
76C22×C4×C151C22×C411yescharacteristic
77C22×C4×C151C2×D411yescharacteristic
78C22×C4×C151C2×D412yes—
79C22×C4×C151#4112yes—
80C2×C8×C151—42no—
81C2×C8×C151—42no—
82C2×C8×C151—42no—
83C4⋊C4×C151—24no—
84C4⋊C4×C151—42no—
85C4⋊C4×C151—42no—
86C4⋊C4×C151—42no—
87C4⋊C4×C151—42no—
88C4⋊C4×C151—42no—
89C4⋊C4×C151—42no—
90C22⋊C4×C151—44no—
91C42×C151—22no—
92C42×C151—22no—
93C42×C151—41no—
94C42×C151—41no—
95C23×C151—21no—
96C23×C151—21no—
97C23×C151—21no—
98C23×C151—21no—
99C23×C151C2×C22⋊C411yescharacteristic
100C23×C151#12112yes—
101C23×C151C2×SD1611yescharacteristic
102C23×C151C2×Q1611yescharacteristic
103C23×C151#13712yes—
104Q8×C151—84no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151—44no—
123C2×C4×C151—44no—
124C2×C4×C151—44no—
125C2×C4×C151—42no—
126C2×C4×C151—42no—
127C2×C4×C151—42no—
128C2×C4×C151—42no—
129C2×C4×C151—42no—
130C2×C4×C151—42no—
131C2×C4×C151—44no—
132C2×C4×C151—82no—
133C2×C4×C151—82no—
134C2×C4×C151—82no—
135C2×C4×C151—82no—
136C2×C4×C151#9912yes—
137C2×C4×C151#10312yes—
138C2×C4×C151#10312yes—
139C2×C4×C151C4×D412yes—
140C2×C4×C151#12411yescharacteristic
141C2×C4×C151#12711yescharacteristic
142C8×C151—82no—
143C22×C151—22no—
144C22×C151—22no—
145C22×C151—22no—
146C22×C151—22no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151#39011yescharacteristic
152C22×C151C2×#9911yescharacteristic
153C22×C151#41011yescharacteristic
154C22×C151C2×#10311yescharacteristic
155C22×C151#41911yescharacteristic
156C22×C151#42111yescharacteristic
157C22×C151#42111yescharacteristic
158C22×C151#46112yes—
159C22×C151#46212yes—
160C4×C151—21no—
161C4×C151—22no—
162C4×C151—21no—
163C4×C151—22no—
164C4×C151—22no—
165C4×C151—22no—
166C4×C151—41no—
167C4×C151—84no—
168C4×C151—82no—
169C4×C151—82no—
170C2×C151—22no—
171C2×C151—22no—
172C2×C151#151111yescharacteristic
173C2×C151#151511yescharacteristic
174C2×C151#151811yescharacteristic
175C2×C151#152011yescharacteristic
176C2×C151#196311yescharacteristic
177C2×C151#196411yescharacteristic
178C2×C151#198111yescharacteristic
179#9714C15111yesmaximal, characteristic, direct product factor, Sylow
180C151#971411yescharacteristic, direct product factor, Sylow
181#2857C2×C15111yescharacteristic
182#1797C2×C15111yescharacteristic
183C2×#328C2×C15114yes—
184#1434C2×C15111yescharacteristic
185C2×C4⋊Q8C4×C15111yescharacteristic, complemented
186C2×C22⋊Q8C22×C15112yes—
187C22×C42C22×C15111yescharacteristic
188C2×C4⋊C8—21no—
189C2×C22⋊C8C22×C15112yes—
190#391C4×C15112yescomplemented
191#389—21no—
192#389—21no—
193#384C4×C15111yescharacteristic, complemented
194#380—21no—
195#380—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95C22×C15112yes—
199#336—21no—
200#328—28no—
201C22×Q8C2×C4×C15112yes—
202C23×C4—22no—
203C23×C4D4×C15111yescharacteristic
204C23×C4D4×C15111yescharacteristic
205C23×C4C23×C15111yescharacteristic
206C22×C8—22no—
207C4⋊Q8—42no—
208C22⋊Q8—24no—
209C22⋊Q8—24no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4C2×C4×C15112yes—
216C2×C22⋊C4—22no—
217C2×C42—42no—
218C2×C42C2×C4×C15111yescharacteristic
219C2×C42C2×C4×C15111yescharacteristic
220C2×C42D4×C15111yescharacteristic
221C2×C42D4×C15111yescharacteristic
222C4⋊C8—42no—
223C22⋊C8—24no—
224#95—22no—
225#95—22no—
226#95—22no—
227#95—42no—
228#95—42no—
229#95D4×C15114yes—
230C24C2×D4×C15111yescharacteristic
231C2×Q8—24no—
232C2×Q8—42no—
233C2×Q8—42no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4C22⋊C4×C15111yescharacteristic
251C22×C4C22⋊C4×C15111yescharacteristic
252C22×C4C22⋊C4×C15111yescharacteristic
253C22×C4C22⋊C4×C15111yescharacteristic
254C22×C4SD16×C15112yes—
255C22×C4Q16×C15112yes—
256C22×C4C22×C4×C15111yescharacteristic
257C22×C4C2×D4×C15111yescharacteristic
258C22×C4C2×D4×C15112yes—
259C22×C4#41×C15112yes—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—44no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C22⋊C4×C15111yescharacteristic
280C23#121×C15112yes—
281C23C2×SD16×C15111yescharacteristic
282C23C2×Q16×C15111yescharacteristic
283C23#137×C15112yes—
284Q8—84no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4#99×C15112yes—
317C2×C4#103×C15112yes—
318C2×C4#103×C15112yes—
319C2×C4C4×D4×C15112yes—
320C2×C4#124×C15111yescharacteristic
321C2×C4#127×C15111yescharacteristic
322C8—82no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22#390×C15111yescharacteristic
332C22C2×#99×C15111yescharacteristic
333C22#410×C15111yescharacteristic
334C22C2×#103×C15111yescharacteristic
335C22#419×C15111yescharacteristic
336C22#421×C15111yescharacteristic
337C22#421×C15111yescharacteristic
338C22#461×C15112yes—
339C22#462×C15112yes—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—84no—
348C4—82no—
349C4—82no—
350C2—22no—
351C2—22no—
352C2#1511×C15111yescharacteristic
353C2#1515×C15111yescharacteristic
354C2#1518×C15111yescharacteristic
355C2#1520×C15111yescharacteristic
356C2#1963×C15111yescharacteristic
357C2#1964×C15111yescharacteristic
358C2#1981×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C2×D4
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
5. C2×C4⋊Q8×C151C4semidirect
10. #391×C151C4semidirect
13. #384×C151C4semidirect
179. #9714C151direct (N × H)
180. C151#9714direct (N × H)
185. C2×C4⋊Q8C4×C151semidirect
190. #391C4×C151semidirect
193. #384C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2857×C1512
#1797×C1512
C2×#328×C1512
#1434×C1512
#9714151