Finite Group Databasebeta

← C151×#18369 #50323294

Subgroups — C151×#18369 #50323294

Order 38656.

904 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#3502×C151C211yesmaximal, characteristic, complemented
2#3215×C151C212yesmaximal
3#2632×C151C211yesmaximal, characteristic
4#1605×C151C214yesmaximal, complemented
5#1599×C151C214yesmaximal
6#1515×C151C212yesmaximal, complemented
7#1467×C151C211yesmaximal, characteristic, complemented
8Q82×C151—22no—
9#557×C151—22no—
10#557×C151—24no—
11#544×C151—21no—
12#544×C151C2214yes—
13#533×C151—22no—
14#533×C151C2212yes—
15C2×#124×C151C2211yescharacteristic
16#519×C151—21no—
17C2×C4×Q8×C151C2211yescharacteristic
18#497×C151—22no—
19#489×C151—22no—
20#464×C151—24no—
21#451×C151C2214yes—
22#450×C151C2214yes—
23#432×C151C2212yes—
24#399×C151—21no—
25#395×C151C2212yes—
26#394×C151C2212yes—
27#393×C151—21no—
28#388×C151—22no—
29#383×C151C2211yescharacteristic
30#328×C151C2218yes—
31#324×C151C2214yes—
32C22×Q8×C151D411yescharacteristic
33C22×Q8×C151C2311yescharacteristic
34C22×D4×C151C2311yescharacteristic
35C2×Q16×C151—24no—
36C2×SD16×C151—24no—
37C4⋊Q8×C151—22no—
38C4⋊Q8×C151—22no—
39C4⋊Q8×C151—24no—
40C4⋊Q8×C151—28no—
41C4⋊Q8×C151D412yes—
42C4⋊Q8×C151D412yes—
43#125×C151—24no—
44#125×C151—24no—
45#125×C151—28no—
46#125×C151—22no—
47#124×C151—22no—
48#124×C151—22no—
49C22⋊Q8×C151—22no—
50C22⋊Q8×C151—24no—
51C22⋊Q8×C151C2314yes—
52C4×Q8×C151—24no—
53C4×Q8×C151—24no—
54C4×Q8×C151—24no—
55C4×Q8×C151—24no—
56C4×Q8×C151—22no—
57C4×Q8×C151—22no—
58C4×Q8×C151—22no—
59C4×Q8×C151D414yes—
60#117×C151—24no—
61#117×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151D411yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151—22no—
69C2×C42×C151D412yes—
70C2×C42×C151C2311yescharacteristic
71C4⋊C8×C151—22no—
72#103×C151—24no—
73#102×C151—24no—
74C22⋊C8×C151C2314yes—
75#97×C151—22no—
76#95×C151—21no—
77#95×C151—21no—
78#95×C151—22no—
79#95×C151C2312yes—
80C24×C151—21no—
81C2×Q8×C151—24no—
82C2×Q8×C151—22no—
83C2×Q8×C151—22no—
84C2×Q8×C151—24no—
85C2×Q8×C151—22no—
86C2×Q8×C151—81no—
87C2×Q8×C151C2×D414yes—
88C2×D4×C151—22no—
89C2×D4×C151—81no—
90C22×C4×C151—22no—
91C22×C4×C151—21no—
92C22×C4×C151C2×D411yescharacteristic
93C22×C4×C151C2×D412yes—
94C22×C4×C151C2×D412yes—
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151C2411yescharacteristic
97Q16×C151—84no—
98SD16×C151—84no—
99C2×C8×C151—24no—
100C4⋊C4×C151—24no—
101C4⋊C4×C151—24no—
102C4⋊C4×C151—24no—
103C4⋊C4×C151—28no—
104C4⋊C4×C151—22no—
105C4⋊C4×C151—22no—
106C4⋊C4×C151—22no—
107C4⋊C4×C151—22no—
108C4⋊C4×C151—24no—
109C4⋊C4×C151—24no—
110C4⋊C4×C151—24no—
111C4⋊C4×C151—82no—
112C4⋊C4×C151C2×D414yes—
113C22⋊C4×C151—24no—
114C22⋊C4×C151—41no—
115C22⋊C4×C151—42no—
116C22⋊C4×C151—41no—
117C22⋊C4×C151—44no—
118C22⋊C4×C151—82no—
119C42×C151—28no—
120C42×C151—22no—
121C42×C151—22no—
122C42×C151—24no—
123C42×C151C2×D412yes—
124C42×C151C2×D412yes—
125C23×C151—42no—
126C23×C151—42no—
127C23×C151—41no—
128C23×C151—42no—
129C23×C151C22×D411yescharacteristic
130Q8×C151—28no—
131Q8×C151—44no—
132Q8×C151—44no—
133Q8×C151—44no—
134Q8×C151—84no—
135D4×C151—44no—
136C2×C4×C151—22no—
137C2×C4×C151—22no—
138C2×C4×C151—22no—
139C2×C4×C151—24no—
140C2×C4×C151—22no—
141C2×C4×C151—24no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—42no—
145C2×C4×C151—42no—
146C2×C4×C151—42no—
147C2×C4×C151—42no—
148C2×C4×C151—41no—
149C2×C4×C151—42no—
150C2×C4×C151#12011yescharacteristic
151C2×C4×C151#12012yes—
152C2×C4×C151#12011yescharacteristic
153C2×C4×C151#13714yes—
154C2×C4×C151C22×D412yes—
155C8×C151—44no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—84no—
159C22×C151—81no—
160C22×C151—81no—
161C22×C151—81no—
162C22×C151C2×#12011yescharacteristic
163C22×C151C2×#13712yes—
164C4×C151—22no—
165C4×C151—24no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—22no—
169C4×C151—44no—
170C4×C151—42no—
171C4×C151—44no—
172C4×C151—82no—
173C4×C151—81no—
174C2×C151—22no—
175C2×C151—161no—
176C2×C151#300411yescharacteristic
177C2×C151#302011yescharacteristic
178C2×C151#302711yescharacteristic
179#18369C15111yesmaximal, characteristic, direct product factor, Sylow
180C151#1836911yescharacteristic, direct product factor, Sylow
181#3502C2×C15111yescharacteristic, complemented
182#3215C2×C15112yes—
183#2632C2×C15111yescharacteristic
184#1605C2×C15114yescomplemented
185#1599C2×C15114yes—
186#1515C2×C15112yescomplemented
187#1467C2×C15111yescharacteristic, complemented
188Q82—22no—
189#557—22no—
190#557—24no—
191#544—21no—
192#544C22×C15114yes—
193#533—22no—
194#533C22×C15112yes—
195C2×#124C22×C15111yescharacteristic
196#519—21no—
197C2×C4×Q8C22×C15111yescharacteristic
198#497—22no—
199#489—22no—
200#464—24no—
201#451C22×C15114yes—
202#450C22×C15114yes—
203#432C22×C15112yes—
204#399—21no—
205#395C22×C15112yes—
206#394C22×C15112yes—
207#393—21no—
208#388—22no—
209#383C22×C15111yescharacteristic
210#328C22×C15118yes—
211#324C22×C15114yes—
212C22×Q8D4×C15111yescharacteristic
213C22×Q8C23×C15111yescharacteristic
214C22×D4C23×C15111yescharacteristic
215C2×Q16—24no—
216C2×SD16—24no—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C4⋊Q8—24no—
220C4⋊Q8—28no—
221C4⋊Q8D4×C15112yes—
222C4⋊Q8D4×C15112yes—
223#125—24no—
224#125—24no—
225#125—28no—
226#125—22no—
227#124—22no—
228#124—22no—
229C22⋊Q8—22no—
230C22⋊Q8—24no—
231C22⋊Q8C23×C15114yes—
232C4×Q8—24no—
233C4×Q8—24no—
234C4×Q8—24no—
235C4×Q8—24no—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8D4×C15114yes—
240#117—24no—
241#117—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4D4×C15111yescharacteristic
244C2×C4⋊C4C23×C15112yes—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C42D4×C15112yes—
250C2×C42C23×C15111yescharacteristic
251C4⋊C8—22no—
252#103—24no—
253#102—24no—
254C22⋊C8C23×C15114yes—
255#97—22no—
256#95—21no—
257#95—21no—
258#95—22no—
259#95C23×C15112yes—
260C24—21no—
261C2×Q8—24no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—22no—
266C2×Q8—81no—
267C2×Q8C2×D4×C15114yes—
268C2×D4—22no—
269C2×D4—81no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4C2×D4×C15111yescharacteristic
273C22×C4C2×D4×C15112yes—
274C22×C4C2×D4×C15112yes—
275C22×C4C2×D4×C15111yescharacteristic
276C22×C4C24×C15111yescharacteristic
277Q16—84no—
278SD16—84no—
279C2×C8—24no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—24no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C4⋊C4—82no—
292C4⋊C4C2×D4×C15114yes—
293C22⋊C4—24no—
294C22⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—44no—
298C22⋊C4—82no—
299C42—28no—
300C42—22no—
301C42—22no—
302C42—24no—
303C42C2×D4×C15112yes—
304C42C2×D4×C15112yes—
305C23—42no—
306C23—42no—
307C23—41no—
308C23—42no—
309C23C22×D4×C15111yescharacteristic
310Q8—28no—
311Q8—44no—
312Q8—44no—
313Q8—44no—
314Q8—84no—
315D4—44no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4#120×C15111yescharacteristic
331C2×C4#120×C15112yes—
332C2×C4#120×C15111yescharacteristic
333C2×C4#137×C15114yes—
334C2×C4C22×D4×C15112yes—
335C8—44no—
336C22—21no—
337C22—21no—
338C22—84no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22C2×#120×C15111yescharacteristic
343C22C2×#137×C15112yes—
344C4—22no—
345C4—24no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—44no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C2—22no—
355C2—161no—
356C2#3004×C15111yescharacteristic
357C2#3020×C15111yescharacteristic
358C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3502×C151C2semidirect
4. #1605×C151C2semidirect
6. #1515×C151C2semidirect
7. #1467×C151C2semidirect
179. #18369C151direct (N × H)
180. C151#18369direct (N × H)
181. #3502C2×C151semidirect
184. #1605C2×C151semidirect
186. #1515C2×C151semidirect
187. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3502×C1512
#3215×C1512
#2632×C1512
#1605×C1512
#1599×C1512
#1515×C1512
#1467×C1512
#18369151