Finite Group Databasebeta

← C151×#9156 #50314081

Subgroups — C151×#9156 #50314081

Order 38656.

692 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C151C211yesmaximal, characteristic
2C2×#382×C151C211yesmaximal, characteristic, complemented
3#1817×C151C211yesmaximal, characteristic, complemented
4C2×#327×C151C212yesmaximal
5#1294×C151C212yesmaximal, complemented
6C2×#123×C151—21no—
7C2×#121×C151C2211yescharacteristic
8C22×C4⋊C4×C151—21no—
9C22×C42×C151C2211yescharacteristic
10C2×C22⋊C8×C151C2212yes—
11#390×C151C412yescomplemented
12#389×C151C412yescomplemented
13#388×C151—22no—
14#386×C151—21no—
15#382×C151—24no—
16#380×C151C2211yescharacteristic
17C2×#95×C151—21no—
18C2×#95×C151C2212yes—
19#336×C151—22no—
20#327×C151—24no—
21C22×D4×C151—21no—
22C22×D4×C151C2×C411yescharacteristic
23C23×C4×C151—22no—
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C23×C4×C151C2311yescharacteristic
27C22×C8×C151—22no—
28#123×C151—42no—
29#123×C151—42no—
30#121×C151—22no—
31#121×C151—22no—
32C2×C4⋊C4×C151—24no—
33C2×C4⋊C4×C151—22no—
34C2×C4⋊C4×C151—42no—
35C2×C4⋊C4×C151—42no—
36C2×C4⋊C4×C151C2×C411yescharacteristic
37C2×C4⋊C4×C151C2×C412yes—
38C2×C22⋊C4×C151—22no—
39C2×C22⋊C4×C151—22no—
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—21no—
42C2×C42×C151—22no—
43C2×C42×C151—22no—
44C2×C42×C151C2×C412yes—
45C2×C42×C151D412yes—
46C22⋊C8×C151—22no—
47C22⋊C8×C151—22no—
48#95×C151—24no—
49#95×C151—22no—
50#95×C151—22no—
51#95×C151—21no—
52#95×C151D414yes—
53C24×C151—21no—
54C24×C151C2×D411yescharacteristic
55C2×D4×C151—22no—
56C2×D4×C151—42no—
57C2×D4×C151—41no—
58C2×D4×C151—41no—
59C2×D4×C151—41no—
60C2×D4×C151—41no—
61C2×D4×C151—41no—
62C2×D4×C151—41no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—22no—
70C22×C4×C151—21no—
71C22×C4×C151—24no—
72C22×C4×C151—42no—
73C22×C4×C151—42no—
74C22×C4×C151—44no—
75C22×C4×C151—44no—
76C22×C4×C151—42no—
77C22×C4×C151—42no—
78C22×C4×C151C22⋊C412yes—
79C22×C4×C151C22⋊C412yes—
80C22×C4×C151D812yes—
81C22×C4×C151SD1612yes—
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151C2×D412yes—
85C22×C4×C151#4112yes—
86C2×C8×C151—44no—
87C2×C8×C151—42no—
88C4⋊C4×C151—22no—
89C4⋊C4×C151—42no—
90C4⋊C4×C151—48no—
91C4⋊C4×C151—44no—
92C22⋊C4×C151—44no—
93C22⋊C4×C151—41no—
94C22⋊C4×C151—41no—
95C22⋊C4×C151—44no—
96C22⋊C4×C151—42no—
97C42×C151—24no—
98C42×C151—24no—
99C23×C151—22no—
100C23×C151—22no—
101C23×C151—41no—
102C23×C151—42no—
103C23×C151—41no—
104C23×C151—41no—
105C23×C151—42no—
106C23×C151C2×C22⋊C411yescharacteristic
107C23×C151#12011yescharacteristic
108C23×C151#12311yescharacteristic
109C23×C151C2×D811yescharacteristic
110C23×C151C2×SD1611yescharacteristic
111C23×C151AGL(1,ℤ/8)11yescharacteristic
112C23×C151#13711yescharacteristic
113D4×C151—82no—
114D4×C151—81no—
115D4×C151—81no—
116D4×C151—81no—
117D4×C151—81no—
118C2×C4×C151—22no—
119C2×C4×C151—22no—
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—22no—
123C2×C4×C151—22no—
124C2×C4×C151—22no—
125C2×C4×C151—22no—
126C2×C4×C151—22no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—42no—
130C2×C4×C151—42no—
131C2×C4×C151—42no—
132C2×C4×C151—42no—
133C2×C4×C151—44no—
134C2×C4×C151—44no—
135C2×C4×C151—41no—
136C2×C4×C151—42no—
137C2×C4×C151—42no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—42no—
141C2×C4×C151—44no—
142C2×C4×C151—84no—
143C2×C4×C151—84no—
144C2×C4×C151#10214yes—
145C2×C4×C151C4×D412yes—
146C2×C4×C151#12112yes—
147C8×C151—82no—
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—22no—
153C22×C151—22no—
154C22×C151—22no—
155C22×C151—22no—
156C22×C151—81no—
157C22×C151—81no—
158C22×C151—81no—
159C22×C151—82no—
160C22×C151—82no—
161C22×C151#38611yescharacteristic
162C22×C151#41012yes—
163C22×C151C2×#10211yescharacteristic
164C22×C151#41711yescharacteristic
165C22×C151#42112yes—
166C22×C151#44711yescharacteristic
167C22×C151#44811yescharacteristic
168C22×C151#48011yescharacteristic
169C22×C151#48111yescharacteristic
170C4×C151—24no—
171C4×C151—22no—
172C4×C151—22no—
173C4×C151—42no—
174C4×C151—84no—
175C4×C151—81no—
176C4×C151—82no—
177C2×C151—21no—
178C2×C151—21no—
179C2×C151—21no—
180C2×C151—21no—
181C2×C151—161no—
182C2×C151#151212yes—
183C2×C151#151712yes—
184C2×C151#187411yescharacteristic
185C2×C151#189711yescharacteristic
186C2×C151#189911yescharacteristic
187#9156C15111yesmaximal, characteristic, direct product factor, Sylow
188C151#915611yescharacteristic, direct product factor, Sylow
189#2854C2×C15111yescharacteristic
190C2×#382C2×C15111yescharacteristic, complemented
191#1817C2×C15111yescharacteristic, complemented
192C2×#327C2×C15112yes—
193#1294C2×C15112yescomplemented
194C2×#123—21no—
195C2×#121C22×C15111yescharacteristic
196C22×C4⋊C4—21no—
197C22×C42C22×C15111yescharacteristic
198C2×C22⋊C8C22×C15112yes—
199#390C4×C15112yescomplemented
200#389C4×C15112yescomplemented
201#388—22no—
202#386—21no—
203#382—24no—
204#380C22×C15111yescharacteristic
205C2×#95—21no—
206C2×#95C22×C15112yes—
207#336—22no—
208#327—24no—
209C22×D4—21no—
210C22×D4C2×C4×C15111yescharacteristic
211C23×C4—22no—
212C23×C4D4×C15111yescharacteristic
213C23×C4D4×C15111yescharacteristic
214C23×C4C23×C15111yescharacteristic
215C22×C8—22no—
216#123—42no—
217#123—42no—
218#121—22no—
219#121—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4C2×C4×C15111yescharacteristic
225C2×C4⋊C4C2×C4×C15112yes—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42C2×C4×C15112yes—
233C2×C42D4×C15112yes—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—24no—
237#95—22no—
238#95—22no—
239#95—21no—
240#95D4×C15114yes—
241C24—21no—
242C24C2×D4×C15111yescharacteristic
243C2×D4—22no—
244C2×D4—42no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C15112yes—
267C22×C4C22⋊C4×C15112yes—
268C22×C4D8×C15112yes—
269C22×C4SD16×C15112yes—
270C22×C4C22×C4×C15111yescharacteristic
271C22×C4C2×D4×C15111yescharacteristic
272C22×C4C2×D4×C15112yes—
273C22×C4#41×C15112yes—
274C2×C8—44no—
275C2×C8—42no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C42—24no—
286C42—24no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—42no—
291C23—41no—
292C23—41no—
293C23—42no—
294C23C2×C22⋊C4×C15111yescharacteristic
295C23#120×C15111yescharacteristic
296C23#123×C15111yescharacteristic
297C23C2×D8×C15111yescharacteristic
298C23C2×SD16×C15111yescharacteristic
299C23AGL(1,ℤ/8)×C15111yescharacteristic
300C23#137×C15111yescharacteristic
301D4—82no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—84no—
331C2×C4—84no—
332C2×C4#102×C15114yes—
333C2×C4C4×D4×C15112yes—
334C2×C4#121×C15112yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—82no—
348C22—82no—
349C22#386×C15111yescharacteristic
350C22#410×C15112yes—
351C22C2×#102×C15111yescharacteristic
352C22#417×C15111yescharacteristic
353C22#421×C15112yes—
354C22#447×C15111yescharacteristic
355C22#448×C15111yescharacteristic
356C22#480×C15111yescharacteristic
357C22#481×C15111yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—81no—
364C4—82no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—161no—
370C2#1512×C15112yes—
371C2#1517×C15112yes—
372C2#1874×C15111yescharacteristic
373C2#1897×C15111yescharacteristic
374C2#1899×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC2×#121×C151C22
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
2. C2×#382×C151C2semidirect
3. #1817×C151C2semidirect
5. #1294×C151C2semidirect
11. #390×C151C4semidirect
12. #389×C151C4semidirect
187. #9156C151direct (N × H)
188. C151#9156direct (N × H)
190. C2×#382C2×C151semidirect
191. #1817C2×C151semidirect
193. #1294C2×C151semidirect
199. #390C4×C151semidirect
200. #389C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2854×C1512
C2×#382×C1512
#1817×C1512
C2×#327×C1512
#1294×C1512
#9156151