Finite Group Databasebeta

← C151×#9818 #50314743

Subgroups — C151×#9818 #50314743

Order 38656.

536 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C151C211yesmaximal, characteristic
2#1810×C151C211yesmaximal, characteristic, complemented
3#1752×C151C211yesmaximal, characteristic, complemented
4#1507×C151C212yesmaximal, complemented
5#1471×C151C212yesmaximal, complemented
6C22×D8×C151C411yescharacteristic, complemented
7C23×C8×C151C2211yescharacteristic
8C2×#121×C151C2212yes—
9#466×C151—21no—
10#466×C151—21no—
11#466×C151—21no—
12#466×C151—21no—
13C2×#108×C151—21no—
14C2×#107×C151C411yescharacteristic, complemented
15C2×#102×C151C412yescomplemented
16#407×C151C2212yes—
17C2×C22⋊C8×C151C2211yescharacteristic
18C2×#97×C151—21no—
19C4×C22⋊C4×C151C2211yescharacteristic
20#341×C151—21no—
21#336×C151—21no—
22#327×C151—24no—
23#323×C151—24no—
24C22×D4×C151—22no—
25C22×D4×C151C2×C412yes—
26C23×C4×C151C2311yescharacteristic
27C2×D8×C151—21no—
28C2×D8×C151—21no—
29C2×D8×C151—42no—
30C2×M16×C151—22no—
31C22×C8×C151—21no—
32C22×C8×C151—42no—
33C22×C8×C151C2×C411yescharacteristic
34C22×C8×C151C2×C411yescharacteristic
35C22×C8×C151D411yescharacteristic
36C22×C8×C151D411yescharacteristic
37C22×C8×C151D411yescharacteristic
38C22×C8×C151D411yescharacteristic
39#121×C151—22no—
40#121×C151—22no—
41#121×C151—22no—
42#121×C151—22no—
43C2×C4⋊C4×C151C2×C412yes—
44C2×C22⋊C4×C151—22no—
45C2×C22⋊C4×C151—21no—
46C2×C42×C151—21no—
47#108×C151—42no—
48#107×C151—21no—
49#107×C151—21no—
50#102×C151—22no—
51#102×C151—22no—
52C22⋊C8×C151—21no—
53C22⋊C8×C151—22no—
54C22⋊C8×C151—22no—
55C22⋊C8×C151D412yes—
56#97×C151—42no—
57#95×C151D412yes—
58C24×C151—22no—
59C24×C151#4111yescharacteristic
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—42no—
63C2×D4×C151—42no—
64C2×D4×C151—42no—
65C2×D4×C151—42no—
66C2×D4×C151—84no—
67C22×C4×C151—22no—
68C22×C4×C151—22no—
69C22×C4×C151—41no—
70C22×C4×C151—41no—
71C22×C4×C151C22×C411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76C22×C4×C151#4111yescharacteristic
77D8×C151—42no—
78D8×C151—42no—
79M16×C151—42no—
80M16×C151—42no—
81C2×C8×C151—22no—
82C2×C8×C151—22no—
83C2×C8×C151—22no—
84C2×C8×C151—22no—
85C2×C8×C151—41no—
86C2×C8×C151—41no—
87C2×C8×C151—41no—
88C2×C8×C151—41no—
89C2×C8×C151—41no—
90C2×C8×C151—42no—
91C2×C8×C151C22⋊C411yescharacteristic
92C2×C8×C151C22⋊C411yescharacteristic
93C2×C8×C151C22⋊C411yescharacteristic
94C2×C8×C151C22⋊C411yescharacteristic
95C4⋊C4×C151—22no—
96C4⋊C4×C151—22no—
97C22⋊C4×C151—42no—
98C22⋊C4×C151—42no—
99C22⋊C4×C151—42no—
100C42×C151—41no—
101C42×C151—41no—
102C23×C151—22no—
103C23×C151—22no—
104C23×C151—41no—
105C23×C151—42no—
106C23×C151—44no—
107C23×C151—82no—
108C23×C151—82no—
109C23×C151C4×D411yescharacteristic
110C23×C151#12111yescharacteristic
111C23×C151#12411yescharacteristic
112D4×C151—42no—
113D4×C151—42no—
114D4×C151—82no—
115D4×C151—84no—
116D4×C151—84no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—42no—
127C2×C4×C151—42no—
128C2×C4×C151—42no—
129C2×C4×C151—42no—
130C2×C4×C151—82no—
131C2×C4×C151C2×C22⋊C411yescharacteristic
132C2×C4×C151C4×D411yescharacteristic
133C2×C4×C151#12111yescharacteristic
134C2×C4×C151#12711yescharacteristic
135C8×C151—21no—
136C8×C151—21no—
137C8×C151—21no—
138C8×C151—42no—
139C8×C151—82no—
140C8×C151#9912yes—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—21no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—44no—
149C22×C151—82no—
150C22×C151—82no—
151C22×C151—82no—
152C22×C151—164no—
153C22×C151#39011yescharacteristic
154C22×C151#44412yes—
155C22×C151#47212yes—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—82no—
160C4×C151—82no—
161C4×C151C2×#9911yescharacteristic
162C4×C151#41011yescharacteristic
163C2×C151—22no—
164C2×C151—22no—
165C2×C151—41no—
166C2×C151—162no—
167C2×C151#196411yescharacteristic
168C2×C151#197511yescharacteristic
169C2×C151#197811yescharacteristic
170#9818C15111yesmaximal, characteristic, direct product factor, Sylow
171C151#981811yescharacteristic, direct product factor, Sylow
172C2×#466C2×C15111yescharacteristic
173#1810C2×C15111yescharacteristic, complemented
174#1752C2×C15111yescharacteristic, complemented
175#1507C2×C15112yescomplemented
176#1471C2×C15112yescomplemented
177C22×D8C4×C15111yescharacteristic, complemented
178C23×C8C22×C15111yescharacteristic
179C2×#121C22×C15112yes—
180#466—21no—
181#466—21no—
182#466—21no—
183#466—21no—
184C2×#108—21no—
185C2×#107C4×C15111yescharacteristic, complemented
186C2×#102C4×C15112yescomplemented
187#407C22×C15112yes—
188C2×C22⋊C8C22×C15111yescharacteristic
189C2×#97—21no—
190C4×C22⋊C4C22×C15111yescharacteristic
191#341—21no—
192#336—21no—
193#327—24no—
194#323—24no—
195C22×D4—22no—
196C22×D4C2×C4×C15112yes—
197C23×C4C23×C15111yescharacteristic
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—42no—
201C2×M16—22no—
202C22×C8—21no—
203C22×C8—42no—
204C22×C8C2×C4×C15111yescharacteristic
205C22×C8C2×C4×C15111yescharacteristic
206C22×C8D4×C15111yescharacteristic
207C22×C8D4×C15111yescharacteristic
208C22×C8D4×C15111yescharacteristic
209C22×C8D4×C15111yescharacteristic
210#121—22no—
211#121—22no—
212#121—22no—
213#121—22no—
214C2×C4⋊C4C2×C4×C15112yes—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—22no—
217C2×C42—21no—
218#108—42no—
219#107—21no—
220#107—21no—
221#102—22no—
222#102—22no—
223C22⋊C8—21no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8D4×C15112yes—
227#97—42no—
228#95D4×C15112yes—
229C24—22no—
230C24#41×C15111yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—84no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C22×C4×C15111yescharacteristic
243C22×C4C2×D4×C15111yescharacteristic
244C22×C4C2×D4×C15111yescharacteristic
245C22×C4C2×D4×C15111yescharacteristic
246C22×C4C2×D4×C15111yescharacteristic
247C22×C4#41×C15111yescharacteristic
248D8—42no—
249D8—42no—
250M16—42no—
251M16—42no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8C22⋊C4×C15111yescharacteristic
263C2×C8C22⋊C4×C15111yescharacteristic
264C2×C8C22⋊C4×C15111yescharacteristic
265C2×C8C22⋊C4×C15111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—22no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—41no—
272C42—41no—
273C23—22no—
274C23—22no—
275C23—41no—
276C23—42no—
277C23—44no—
278C23—82no—
279C23—82no—
280C23C4×D4×C15111yescharacteristic
281C23#121×C15111yescharacteristic
282C23#124×C15111yescharacteristic
283D4—42no—
284D4—42no—
285D4—82no—
286D4—84no—
287D4—84no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4C2×C22⋊C4×C15111yescharacteristic
303C2×C4C4×D4×C15111yescharacteristic
304C2×C4#121×C15111yescharacteristic
305C2×C4#127×C15111yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8—42no—
310C8—82no—
311C8#99×C15112yes—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—44no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—164no—
324C22#390×C15111yescharacteristic
325C22#444×C15112yes—
326C22#472×C15112yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—82no—
331C4—82no—
332C4C2×#99×C15111yescharacteristic
333C4#410×C15111yescharacteristic
334C2—22no—
335C2—22no—
336C2—41no—
337C2—162no—
338C2#1964×C15111yescharacteristic
339C2#1975×C15111yescharacteristic
340C2#1978×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#390
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC2×#466×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1810×C151C2semidirect
3. #1752×C151C2semidirect
4. #1507×C151C2semidirect
5. #1471×C151C2semidirect
6. C22×D8×C151C4semidirect
14. C2×#107×C151C4semidirect
15. C2×#102×C151C4semidirect
170. #9818C151direct (N × H)
171. C151#9818direct (N × H)
173. #1810C2×C151semidirect
174. #1752C2×C151semidirect
175. #1507C2×C151semidirect
176. #1471C2×C151semidirect
177. C22×D8C4×C151semidirect
185. C2×#107C4×C151semidirect
186. C2×#102C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1512
#1810×C1512
#1752×C1512
#1507×C1512
#1471×C1512
#9818151