Finite Group Databasebeta

← C151×#20890 #50325815

Subgroups — C151×#20890 #50325815

Order 38656.

1458 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3428×C151C211yesmaximal, characteristic
2C2×#410×C151C211yesmaximal, characteristic
3#2317×C151C212yesmaximal, complemented
4#2311×C151C211yesmaximal, characteristic
5#1867×C151C218yesmaximal, complemented
6#1740×C151C212yesmaximal, complemented
7C22×#41×C151C2211yescharacteristic
8#520×C151—22no—
9#520×C151—22no—
10#519×C151—21no—
11#518×C151—21no—
12#518×C151C2214yes—
13C4×#41×C151—24no—
14C2×#117×C151—22no—
15C2×#117×C151C2211yescharacteristic
16C2×#117×C151C2212yes—
17C2×#117×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19#410×C151C418yescomplemented
20C2×#99×C151C2214yes—
21#391×C151—21no—
22#390×C151—21no—
23#389×C151—24no—
24#386×C151C2214yes—
25#385×C151C2218yes—
26#384×C151—22no—
27#382×C151—22no—
28#380×C151—22no—
29#342×C151C2218yes—
30C2×#41×C151—22no—
31C2×#41×C151—22no—
32C2×#41×C151—24no—
33C2×#41×C151C2×C414yes—
34C2×#41×C151Q814yes—
35C22×Q8×C151D411yescharacteristic
36C22×D4×C151D411yescharacteristic
37C22×D4×C151C2312yes—
38C23×C4×C151D412yes—
39C23×C4×C151C2312yes—
40C23×C4×C151C2311yescharacteristic
41C4×Q8×C151—24no—
42C4×Q8×C151—24no—
43C4×D4×C151—24no—
44C4×D4×C151—24no—
45C4×D4×C151—28no—
46C4×D4×C151—28no—
47#117×C151—24no—
48#117×C151—24no—
49#117×C151—22no—
50#117×C151—24no—
51#117×C151—22no—
52#117×C151—22no—
53#117×C151—22no—
54#117×C151—24no—
55#117×C151—24no—
56#117×C151C2×C418yescomplemented
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—28no—
66C2×C4⋊C4×C151D412yes—
67C2×C4⋊C4×C151D412yes—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151C2312yes—
71C2×C22⋊C4×C151C2314yes—
72C2×C22⋊C4×C151C2314yes—
73C2×C42×C151—24no—
74C2×C42×C151—22no—
75C2×C42×C151—21no—
76C2×C42×C151D414yes—
77#99×C151C2×C4116yescomplemented
78#95×C151—24no—
79#95×C151—28no—
80C24×C151C2×D412yes—
81C24×C151C2411yescharacteristic
82#41×C151—28no—
83#41×C151—28no—
84#41×C151—28no—
85#41×C151—28no—
86C2×Q8×C151—22no—
87C2×Q8×C151—22no—
88C2×Q8×C151C4⋊C414yescomplemented
89C2×D4×C151—24no—
90C2×D4×C151—24no—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151C4⋊C414yescomplemented
94C2×D4×C151C22×C414yes—
95C2×D4×C151C2×Q814yes—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—24no—
99C22×C4×C151—24no—
100C22×C4×C151—24no—
101C22×C4×C151—24no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—24no—
105C22×C4×C151—82no—
106C22×C4×C151C4⋊C418yescomplemented
107C22×C4×C151C22×C412yes—
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D414yes—
110C22×C4×C151C2×D414yes—
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D412yes—
115C22×C4×C151C2×Q812yes—
116C22×C4×C151#4114yes—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—28no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—42no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151—41no—
127C4⋊C4×C151—42no—
128C4⋊C4×C151—88no—
129C22⋊C4×C151—28no—
130C22⋊C4×C151—24no—
131C22⋊C4×C151—24no—
132C22⋊C4×C151—24no—
133C22⋊C4×C151—24no—
134C22⋊C4×C151—84no—
135C22⋊C4×C151C22×C418yes—
136C42×C151—28no—
137C42×C151—28no—
138C42×C151—24no—
139C42×C151—24no—
140C42×C151—42no—
141C23×C151—22no—
142C23×C151—22no—
143C23×C151—41no—
144C23×C151—41no—
145C23×C151—42no—
146C23×C151—42no—
147C23×C151C2×C4⋊C414yes—
148C23×C151C23×C411yescharacteristic
149C23×C151C22×D411yescharacteristic
150C23×C151C22×D412yes—
151C23×C151C22×Q811yescharacteristic
152C23×C151C2×#4112yes—
153Q8×C151—28no—
154D4×C151—28no—
155D4×C151—28no—
156D4×C151—28no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—28no—
160C2×C4×C151—28no—
161C2×C4×C151—28no—
162C2×C4×C151—24no—
163C2×C4×C151—24no—
164C2×C4×C151—44no—
165C2×C4×C151—44no—
166C2×C4×C151—44no—
167C2×C4×C151—44no—
168C2×C4×C151—42no—
169C2×C4×C151—44no—
170C2×C4×C151—48no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—42no—
174C2×C4×C151—84no—
175C2×C4×C151—84no—
176C2×C4×C151C2×C4⋊C414yes—
177C2×C4×C151C2×C4⋊C412yes—
178C2×C4×C151C2×C4⋊C412yes—
179C2×C4×C151C4×D414yes—
180C2×C4×C151C4×D414yes—
181C2×C4×C151#12012yes—
182C2×C4×C151#12011yescharacteristic
183C2×C4×C151#12011yescharacteristic
184C2×C4×C151C22⋊Q814yes—
185C2×C4×C151C22⋊Q814yes—
186C2×C4×C151#12312yes—
187C2×C4×C151#12312yes—
188C22×C151—22no—
189C22×C151—21no—
190C22×C151—22no—
191C22×C151—21no—
192C22×C151—24no—
193C22×C151—41no—
194C22×C151—41no—
195C22×C151—42no—
196C22×C151—44no—
197C22×C151—42no—
198C22×C151—42no—
199C22×C151—82no—
200C22×C151C22×C4⋊C411yescharacteristic
201C22×C151C2×C4×D412yes—
202C22×C151C2×#12011yescharacteristic
203C22×C151C2×C22⋊Q812yes—
204C22×C151C2×#12311yescharacteristic
205C4×C151—24no—
206C4×C151—48no—
207C4×C151—44no—
208C4×C151—44no—
209C4×C151—82no—
210C4×C151—82no—
211C4×C151#38512yes—
212C4×C151#38512yes—
213C4×C151#38514yes—
214C2×C151—22no—
215C2×C151—21no—
216C2×C151—21no—
217C2×C151—22no—
218C2×C151—44no—
219C2×C151C2×#38511yescharacteristic
220C2×C151#302711yescharacteristic
221C2×C151#302811yescharacteristic
222#20890C15111yesmaximal, characteristic, direct product factor, Sylow
223C151#2089011yescharacteristic, direct product factor, Sylow
224#3428C2×C15111yescharacteristic
225C2×#410C2×C15111yescharacteristic
226#2317C2×C15112yescomplemented
227#2311C2×C15111yescharacteristic
228#1867C2×C15118yescomplemented
229#1740C2×C15112yescomplemented
230C22×#41C22×C15111yescharacteristic
231#520—22no—
232#520—22no—
233#519—21no—
234#518—21no—
235#518C22×C15114yes—
236C4×#41—24no—
237C2×#117—22no—
238C2×#117C22×C15111yescharacteristic
239C2×#117C22×C15112yes—
240C2×#117C22×C15112yes—
241C22×C4⋊C4C22×C15111yescharacteristic
242#410C4×C15118yescomplemented
243C2×#99C22×C15114yes—
244#391—21no—
245#390—21no—
246#389—24no—
247#386C22×C15114yes—
248#385C22×C15118yes—
249#384—22no—
250#382—22no—
251#380—22no—
252#342C22×C15118yes—
253C2×#41—24no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41C2×C4×C15114yes—
257C2×#41Q8×C15114yes—
258C22×Q8D4×C15111yescharacteristic
259C22×D4D4×C15111yescharacteristic
260C22×D4C23×C15112yes—
261C23×C4D4×C15112yes—
262C23×C4C23×C15112yes—
263C23×C4C23×C15111yescharacteristic
264C4×Q8—24no—
265C4×Q8—24no—
266C4×D4—24no—
267C4×D4—24no—
268C4×D4—28no—
269C4×D4—28no—
270#117—24no—
271#117—24no—
272#117—24no—
273#117—22no—
274#117—24no—
275#117—22no—
276#117—22no—
277#117—22no—
278#117—24no—
279#117C2×C4×C15118yescomplemented
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4D4×C15112yes—
290C2×C4⋊C4D4×C15112yes—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4C23×C15112yes—
294C2×C22⋊C4C23×C15114yes—
295C2×C22⋊C4C23×C15114yes—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42D4×C15114yes—
300#99C2×C4×C151116yescomplemented
301#95—24no—
302#95—28no—
303C24C2×D4×C15112yes—
304C24C24×C15111yescharacteristic
305#41—28no—
306#41—28no—
307#41—28no—
308#41—28no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8C4⋊C4×C15114yescomplemented
312C2×D4—24no—
313C2×D4—24no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4C4⋊C4×C15114yescomplemented
317C2×D4C22×C4×C15114yes—
318C2×D4C2×Q8×C15114yes—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—24no—
328C22×C4—82no—
329C22×C4C4⋊C4×C15118yescomplemented
330C22×C4C22×C4×C15112yes—
331C22×C4C2×D4×C15112yes—
332C22×C4C2×D4×C15114yes—
333C22×C4C2×D4×C15114yes—
334C22×C4C2×D4×C15111yescharacteristic
335C22×C4C2×D4×C15111yescharacteristic
336C22×C4C2×D4×C15112yes—
337C22×C4C2×D4×C15112yes—
338C22×C4C2×Q8×C15112yes—
339C22×C4#41×C15114yes—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—28no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—41no—
350C4⋊C4—42no—
351C4⋊C4—88no—
352C22⋊C4—28no—
353C22⋊C4—24no—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—84no—
358C22⋊C4C22×C4×C15118yes—
359C42—28no—
360C42—28no—
361C42—24no—
362C42—24no—
363C42—42no—
364C23—22no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23C2×C4⋊C4×C15114yes—
371C23C23×C4×C15111yescharacteristic
372C23C22×D4×C15111yescharacteristic
373C23C22×D4×C15112yes—
374C23C22×Q8×C15111yescharacteristic
375C23C2×#41×C15112yes—
376Q8—28no—
377D4—28no—
378D4—28no—
379D4—28no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—28no—
384C2×C4—28no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—44no—
393C2×C4—48no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—84no—
398C2×C4—84no—
399C2×C4C2×C4⋊C4×C15114yes—
400C2×C4C2×C4⋊C4×C15112yes—
401C2×C4C2×C4⋊C4×C15112yes—
402C2×C4C4×D4×C15114yes—
403C2×C4C4×D4×C15114yes—
404C2×C4#120×C15111yescharacteristic
405C2×C4#120×C15112yes—
406C2×C4#120×C15111yescharacteristic
407C2×C4C22⋊Q8×C15114yes—
408C2×C4C22⋊Q8×C15114yes—
409C2×C4#123×C15112yes—
410C2×C4#123×C15112yes—
411C22—22no—
412C22—21no—
413C22—22no—
414C22—21no—
415C22—24no—
416C22—41no—
417C22—41no—
418C22—42no—
419C22—44no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22C22×C4⋊C4×C15111yescharacteristic
424C22C2×C4×D4×C15112yes—
425C22C2×#120×C15111yescharacteristic
426C22C2×C22⋊Q8×C15112yes—
427C22C2×#123×C15111yescharacteristic
428C4—24no—
429C4—48no—
430C4—44no—
431C4—44no—
432C4—82no—
433C4—82no—
434C4#385×C15112yes—
435C4#385×C15112yes—
436C4#385×C15114yes—
437C2—22no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—44no—
442C2C2×#385×C15111yescharacteristic
443C2#3027×C15111yescharacteristic
444C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2317×C151C2semidirect
5. #1867×C151C2semidirect
6. #1740×C151C2semidirect
19. #410×C151C4semidirect
56. #117×C151C2×C4semidirect
77. #99×C151C2×C4semidirect
88. C2×Q8×C151C4⋊C4semidirect
93. C2×D4×C151C4⋊C4semidirect
106. C22×C4×C151C4⋊C4semidirect
222. #20890C151direct (N × H)
223. C151#20890direct (N × H)
226. #2317C2×C151semidirect
228. #1867C2×C151semidirect
229. #1740C2×C151semidirect
242. #410C4×C151semidirect
279. #117C2×C4×C151semidirect
300. #99C2×C4×C151semidirect
311. C2×Q8C4⋊C4×C151semidirect
316. C2×D4C4⋊C4×C151semidirect
329. C22×C4C4⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3428×C1512
C2×#410×C1512
#2317×C1512
#2311×C1512
#1867×C1512
#1740×C1512
#20890151