Finite Group Databasebeta

← C151×#11697 #50316622

Subgroups — C151×#11697 #50316622

Order 38656.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2392×C151C211yesmaximal, characteristic
2#1742×C151C211yesmaximal, characteristic, complemented
3#1458×C151C211yesmaximal, characteristic, complemented
4#1346×C151C212yesmaximal, complemented
5#1345×C151C212yesmaximal, complemented
6C22×M16×C151—21no—
7C2×C4×D4×C151—21no—
8C2×C4×D4×C151C411yescharacteristic
9C2×#117×C151C2211yescharacteristic
10#431×C151—21no—
11#398×C151C2211yescharacteristic
12#397×C151C411yescharacteristic
13#396×C151—21no—
14#394×C151—21no—
15#394×C151C2211yescharacteristic
16#392×C151C411yescharacteristic
17C4×C4⋊C4×C151C411yescharacteristic
18C4×C22⋊C4×C151—21no—
19#343×C151—21no—
20#343×C151C2212yes—
21#324×C151C2212yes—
22#323×C151—21no—
23C22×D4×C151—21no—
24C22×D4×C151C2×C411yescharacteristic
25C23×C4×C151—21no—
26C23×C4×C151D411yescharacteristic
27C2×M16×C151—24no—
28C2×M16×C151—22no—
29C2×M16×C151—41no—
30C2×M16×C151—42no—
31C22×C8×C151—41no—
32C4×D4×C151—41no—
33C4×D4×C151—41no—
34C4×D4×C151—42no—
35C4×D4×C151—42no—
36#117×C151—41no—
37#117×C151—41no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151C2×C411yescharacteristic
41C2×C4⋊C4×C151D411yescharacteristic
42C2×C4⋊C4×C151C2311yescharacteristic
43C2×C22⋊C4×C151—21no—
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—21no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151C2×C411yescharacteristic
49C2×C22⋊C4×C151D411yescharacteristic
50C2×C42×C151—21no—
51C2×C42×C151C2×C411yescharacteristic
52C2×C42×C151D411yescharacteristic
53C4⋊C8×C151—41no—
54C22⋊C8×C151—22no—
55C4×C8×C151—41no—
56#95×C151—21no—
57#95×C151—21no—
58#95×C151C2×C411yescharacteristic
59#95×C151C2×C411yescharacteristic
60C24×C151—21no—
61C24×C151C22⋊C411yescharacteristic
62C2×D4×C151—41no—
63C2×D4×C151—42no—
64C2×D4×C151—42no—
65C2×D4×C151—42no—
66C2×D4×C151—42no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—22no—
70C22×C4×C151—21no—
71C22×C4×C151—21no—
72C22×C4×C151—21no—
73C22×C4×C151—41no—
74C22×C4×C151—41no—
75C22×C4×C151—42no—
76C22×C4×C151—42no—
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22⋊C411yescharacteristic
79C22×C4×C151C22⋊C411yescharacteristic
80C22×C4×C151D812yes—
81C22×C4×C151SD1612yes—
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151C2×D411yescharacteristic
85M16×C151—24no—
86M16×C151—44no—
87M16×C151—42no—
88C2×C8×C151—42no—
89C2×C8×C151—44no—
90C2×C8×C151—42no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—42no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C22⋊C4×C151—41no—
98C22⋊C4×C151—41no—
99C22⋊C4×C151—42no—
100C22⋊C4×C151—42no—
101C22⋊C4×C151—42no—
102C22⋊C4×C151—42no—
103C22⋊C4×C151—41no—
104C22⋊C4×C151—41no—
105C42×C151—21no—
106C42×C151—21no—
107C42×C151—21no—
108C42×C151—21no—
109C42×C151—42no—
110C23×C151—21no—
111C23×C151—21no—
112C23×C151—22no—
113C23×C151—41no—
114C23×C151—41no—
115C23×C151—41no—
116C23×C151—41no—
117C23×C151—41no—
118C23×C151—41no—
119C23×C151—41no—
120C23×C151—41no—
121C23×C151#10212yes—
122C23×C151C2×C22⋊C411yescharacteristic
123D4×C151—42no—
124D4×C151—48no—
125D4×C151—42no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151—22no—
132C2×C4×C151—22no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
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—82no—
150C2×C4×C151—82no—
151C2×C4×C151#9911yescharacteristic
152C2×C4×C151#9911yescharacteristic
153C2×C4×C151#10212yes—
154C2×C4×C151#10412yes—
155C2×C4×C151C2×D811yescharacteristic
156C2×C4×C151C2×SD1611yescharacteristic
157C8×C151—44no—
158C8×C151—82no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—22no—
162C22×C151—42no—
163C22×C151—42no—
164C22×C151—42no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—42no—
168C22×C151—81no—
169C22×C151—81no—
170C22×C151—81no—
171C22×C151—81no—
172C22×C151—81no—
173C22×C151C2×#9911yescharacteristic
174C22×C151C2×#10211yescharacteristic
175C22×C151C2×#10411yescharacteristic
176C4×C151—21no—
177C4×C151—21no—
178C4×C151—42no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—81no—
184C4×C151—81no—
185C4×C151#32712yes—
186C4×C151#32712yes—
187C2×C151—21no—
188C2×C151—21no—
189C2×C151—42no—
190C2×C151—82no—
191C2×C151C2×#32711yescharacteristic
192C2×C151#212011yescharacteristic
193C2×C151#213211yescharacteristic
194#11697C15111yesmaximal, characteristic, direct product factor, Sylow
195C151#1169711yescharacteristic, direct product factor, Sylow
196#2392C2×C15111yescharacteristic
197#1742C2×C15111yescharacteristic, complemented
198#1458C2×C15111yescharacteristic, complemented
199#1346C2×C15112yescomplemented
200#1345C2×C15112yescomplemented
201C22×M16—21no—
202C2×C4×D4—21no—
203C2×C4×D4C4×C15111yescharacteristic
204C2×#117C22×C15111yescharacteristic
205#431—21no—
206#398C22×C15111yescharacteristic
207#397C4×C15111yescharacteristic
208#396—21no—
209#394—21no—
210#394C22×C15111yescharacteristic
211#392C4×C15111yescharacteristic
212C4×C4⋊C4C4×C15111yescharacteristic
213C4×C22⋊C4—21no—
214#343—21no—
215#343C22×C15112yes—
216#324C22×C15112yes—
217#323—21no—
218C22×D4—21no—
219C22×D4C2×C4×C15111yescharacteristic
220C23×C4—21no—
221C23×C4D4×C15111yescharacteristic
222C2×M16—24no—
223C2×M16—22no—
224C2×M16—41no—
225C2×M16—42no—
226C22×C8—41no—
227C4×D4—41no—
228C4×D4—41no—
229C4×D4—42no—
230C4×D4—42no—
231#117—41no—
232#117—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×C4×C15111yescharacteristic
236C2×C4⋊C4D4×C15111yescharacteristic
237C2×C4⋊C4C23×C15111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4C2×C4×C15111yescharacteristic
244C2×C22⋊C4D4×C15111yescharacteristic
245C2×C42—21no—
246C2×C42C2×C4×C15111yescharacteristic
247C2×C42D4×C15111yescharacteristic
248C4⋊C8—41no—
249C22⋊C8—22no—
250C4×C8—41no—
251#95—21no—
252#95—21no—
253#95C2×C4×C15111yescharacteristic
254#95C2×C4×C15111yescharacteristic
255C24—21no—
256C24C22⋊C4×C15111yescharacteristic
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C22⋊C4×C15111yescharacteristic
273C22×C4C22⋊C4×C15111yescharacteristic
274C22×C4C22⋊C4×C15111yescharacteristic
275C22×C4D8×C15112yes—
276C22×C4SD16×C15112yes—
277C22×C4C22×C4×C15111yescharacteristic
278C22×C4C2×D4×C15111yescharacteristic
279C22×C4C2×D4×C15111yescharacteristic
280M16—24no—
281M16—44no—
282M16—42no—
283C2×C8—42no—
284C2×C8—44no—
285C2×C8—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—42no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#102×C15112yes—
317C23C2×C22⋊C4×C15111yescharacteristic
318D4—42no—
319D4—48no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4#99×C15111yescharacteristic
347C2×C4#99×C15111yescharacteristic
348C2×C4#102×C15112yes—
349C2×C4#104×C15112yes—
350C2×C4C2×D8×C15111yescharacteristic
351C2×C4C2×SD16×C15111yescharacteristic
352C8—44no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×#99×C15111yescharacteristic
369C22C2×#102×C15111yescharacteristic
370C22C2×#104×C15111yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4#327×C15112yes—
381C4#327×C15112yes—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—82no—
386C2C2×#327×C15111yescharacteristic
387C2#2120×C15111yescharacteristic
388C2#2132×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
socleC22×C151C2×#99
prime radical#392×C151C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C22×C4×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1742×C151C2semidirect
3. #1458×C151C2semidirect
4. #1346×C151C2semidirect
5. #1345×C151C2semidirect
194. #11697C151direct (N × H)
195. C151#11697direct (N × H)
197. #1742C2×C151semidirect
198. #1458C2×C151semidirect
199. #1346C2×C151semidirect
200. #1345C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2392×C1512
#1742×C1512
#1458×C1512
#1346×C1512
#1345×C1512
#11697151