Finite Group Databasebeta

← C151×#18213 #50323138

Subgroups — C151×#18213 #50323138

Order 38656.

974 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#3104×C151C212yesmaximal, complemented
3#2580×C151C211yesmaximal, characteristic
4#1614×C151C214yesmaximal, complemented
5#1602×C151C214yesmaximal, complemented
6#1518×C151C212yesmaximal, complemented
7#1460×C151C211yesmaximal, characteristic
8#554×C151—22no—
9#554×C151—24no—
10D4×Q8×C151—22no—
11#544×C151—21no—
12#543×C151C2214yes—
13#533×C151C2212yes—
14C2×C22⋊Q8×C151—22no—
15#518×C151—21no—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#484×C151C2214yes—
19#477×C151—22no—
20#462×C151—22no—
21#451×C151C2214yes—
22C4×Q16×C151—24no—
23#431×C151C2212yes—
24#399×C151C2212yes—
25#393×C151C2212yes—
26#390×C151—21no—
27#389×C151—21no—
28#385×C151—22no—
29#382×C151C2211yescharacteristic
30#328×C151C2218yes—
31#323×C151C2214yes—
32C22×Q8×C151—22no—
33C22×Q8×C151C2311yescharacteristic
34C22×D4×C151D411yescharacteristic
35C23×C4×C151D412yes—
36C2×Q16×C151—24no—
37C4⋊Q8×C151—24no—
38C4⋊Q8×C151D412yes—
39C4⋊Q8×C151D412yes—
40#125×C151—24no—
41#125×C151—22no—
42C22⋊Q8×C151—24no—
43C22⋊Q8×C151—24no—
44C22⋊Q8×C151—22no—
45C22⋊Q8×C151—24no—
46C22⋊Q8×C151—28no—
47C22⋊Q8×C151—28no—
48C22⋊Q8×C151C2314yes—
49C4×Q8×C151—22no—
50C4×Q8×C151—22no—
51C4×Q8×C151—22no—
52C4×Q8×C151D414yes—
53C4×D4×C151—24no—
54C4×D4×C151—24no—
55C4×D4×C151—22no—
56C4×D4×C151—22no—
57#117×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151D411yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151C2312yes—
69C2×C42×C151—21no—
70C2×C42×C151C2311yescharacteristic
71#107×C151—24no—
72C4⋊C8×C151—22no—
73#103×C151—24no—
74#103×C151—24no—
75C22⋊C8×C151C2314yes—
76C4×C8×C151—22no—
77#95×C151—21no—
78#95×C151—22no—
79#95×C151C2312yes—
80C24×C151C2×D412yes—
81C2×Q8×C151—24no—
82C2×Q8×C151—22no—
83C2×Q8×C151—22no—
84C2×Q8×C151—42no—
85C2×Q8×C151—84no—
86C2×Q8×C151C2×D414yes—
87C2×D4×C151—22no—
88C2×D4×C151—22no—
89C2×D4×C151Q1614yescomplemented
90C22×C4×C151—21no—
91C22×C4×C151—24no—
92C22×C4×C151—24no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—82no—
98C22×C4×C151C2×D412yes—
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2411yescharacteristic
102Q16×C151—48no—
103C2×C8×C151—24no—
104C4⋊C4×C151—24no—
105C4⋊C4×C151—28no—
106C4⋊C4×C151—22no—
107C4⋊C4×C151—24no—
108C4⋊C4×C151—22no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—24no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—42no—
116C4⋊C4×C151—82no—
117C4⋊C4×C151C2×D414yes—
118C22⋊C4×C151—28no—
119C22⋊C4×C151—24no—
120C22⋊C4×C151—24no—
121C22⋊C4×C151—44no—
122C22⋊C4×C151—82no—
123C42×C151—24no—
124C42×C151—42no—
125C42×C151C2×D412yes—
126C42×C151C2×D412yes—
127C23×C151—22no—
128C23×C151—22no—
129C23×C151—42no—
130C23×C151—42no—
131C23×C151C2×Q1614yes—
132C23×C151C22×D411yescharacteristic
133Q8×C151—24no—
134Q8×C151—44no—
135Q8×C151—42no—
136Q8×C151—44no—
137Q8×C151—84no—
138D4×C151—28no—
139C2×C4×C151—22no—
140C2×C4×C151—24no—
141C2×C4×C151—22no—
142C2×C4×C151—24no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—44no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151—41no—
151C2×C4×C151—42no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—42no—
155C2×C4×C151—82no—
156C2×C4×C151—84no—
157C2×C4×C151—84no—
158C2×C4×C151#12011yescharacteristic
159C2×C4×C151#12011yescharacteristic
160C2×C4×C151#12012yes—
161C2×C4×C151C2×Q1612yes—
162C2×C4×C151#13712yes—
163C2×C4×C151C22×D412yes—
164C8×C151—44no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—24no—
168C22×C151—44no—
169C22×C151—42no—
170C22×C151—42no—
171C22×C151—82no—
172C22×C151C2×#12011yescharacteristic
173C22×C151C22×Q1611yescharacteristic
174C22×C151C2×#13711yescharacteristic
175C4×C151—21no—
176C4×C151—21no—
177C4×C151—22no—
178C4×C151—42no—
179C4×C151—44no—
180C4×C151—42no—
181C4×C151—44no—
182C4×C151—82no—
183C4×C151—81no—
184C4×C151#45114yes—
185C2×C151—21no—
186C2×C151—21no—
187C2×C151—44no—
188C2×C151C2×#45111yescharacteristic
189C2×C151#301911yescharacteristic
190C2×C151#302511yescharacteristic
191#18213C15111yesmaximal, characteristic, direct product factor, Sylow
192C151#1821311yescharacteristic, direct product factor, Sylow
193#3501C2×C15111yescharacteristic
194#3104C2×C15112yescomplemented
195#2580C2×C15111yescharacteristic
196#1614C2×C15114yescomplemented
197#1602C2×C15114yescomplemented
198#1518C2×C15112yescomplemented
199#1460C2×C15111yescharacteristic
200#554—22no—
201#554—24no—
202D4×Q8—22no—
203#544—21no—
204#543C22×C15114yes—
205#533C22×C15112yes—
206C2×C22⋊Q8—22no—
207#518—21no—
208C2×C4×Q8C22×C15111yescharacteristic
209C2×C4×D4C22×C15111yescharacteristic
210#484C22×C15114yes—
211#477—22no—
212#462—22no—
213#451C22×C15114yes—
214C4×Q16—24no—
215#431C22×C15112yes—
216#399C22×C15112yes—
217#393C22×C15112yes—
218#390—21no—
219#389—21no—
220#385—22no—
221#382C22×C15111yescharacteristic
222#328C22×C15118yes—
223#323C22×C15114yes—
224C22×Q8—22no—
225C22×Q8C23×C15111yescharacteristic
226C22×D4D4×C15111yescharacteristic
227C23×C4D4×C15112yes—
228C2×Q16—24no—
229C4⋊Q8—24no—
230C4⋊Q8D4×C15112yes—
231C4⋊Q8D4×C15112yes—
232#125—24no—
233#125—22no—
234C22⋊Q8—24no—
235C22⋊Q8—24no—
236C22⋊Q8—28no—
237C22⋊Q8—22no—
238C22⋊Q8—24no—
239C22⋊Q8—28no—
240C22⋊Q8C23×C15114yes—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8D4×C15114yes—
245C4×D4—24no—
246C4×D4—24no—
247C4×D4—22no—
248C4×D4—22no—
249#117—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4D4×C15111yescharacteristic
256C2×C4⋊C4C23×C15111yescharacteristic
257C2×C22⋊C4—24no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4C23×C15112yes—
261C2×C42—21no—
262C2×C42C23×C15111yescharacteristic
263#107—24no—
264C4⋊C8—22no—
265#103—24no—
266#103—24no—
267C22⋊C8C23×C15114yes—
268C4×C8—22no—
269#95—21no—
270#95—22no—
271#95C23×C15112yes—
272C24C2×D4×C15112yes—
273C2×Q8—24no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—42no—
277C2×Q8—84no—
278C2×Q8C2×D4×C15114yes—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4Q16×C15114yescomplemented
282C22×C4—21no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—82no—
290C22×C4C2×D4×C15112yes—
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×D4×C15111yescharacteristic
293C22×C4C24×C15111yescharacteristic
294Q16—48no—
295C2×C8—24no—
296C4⋊C4—24no—
297C4⋊C4—28no—
298C4⋊C4—22no—
299C4⋊C4—24no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—82no—
309C4⋊C4C2×D4×C15114yes—
310C22⋊C4—28no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—44no—
314C22⋊C4—82no—
315C42—24no—
316C42—42no—
317C42C2×D4×C15112yes—
318C42C2×D4×C15112yes—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×Q16×C15114yes—
324C23C22×D4×C15111yescharacteristic
325Q8—24no—
326Q8—44no—
327Q8—42no—
328Q8—44no—
329Q8—84no—
330D4—28no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—84no—
349C2×C4—84no—
350C2×C4#120×C15111yescharacteristic
351C2×C4#120×C15111yescharacteristic
352C2×C4#120×C15112yes—
353C2×C4C2×Q16×C15112yes—
354C2×C4#137×C15112yes—
355C2×C4C22×D4×C15112yes—
356C8—44no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×#120×C15111yescharacteristic
365C22C22×Q16×C15111yescharacteristic
366C22C2×#137×C15111yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—44no—
372C4—42no—
373C4—44no—
374C4—82no—
375C4—81no—
376C4#451×C15114yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×#451×C15111yescharacteristic
381C2#3019×C15111yescharacteristic
382C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
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
2. #3104×C151C2semidirect
4. #1614×C151C2semidirect
5. #1602×C151C2semidirect
6. #1518×C151C2semidirect
89. C2×D4×C151Q16semidirect
191. #18213C151direct (N × H)
192. C151#18213direct (N × H)
194. #3104C2×C151semidirect
196. #1614C2×C151semidirect
197. #1602C2×C151semidirect
198. #1518C2×C151semidirect
281. C2×D4Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3104×C1512
#2580×C1512
#1614×C1512
#1602×C1512
#1518×C1512
#1460×C1512
#18213151