Finite Group Databasebeta

← C151×#23988 #50328913

Subgroups — C151×#23988 #50328913

Order 38656.

1466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3491×C151C211yesmaximal, characteristic, complemented
2#2613×C151C212yesmaximal, complemented
3#2309×C151C211yesmaximal, characteristic, complemented
4#2029×C151C212yesmaximal, complemented
5#2021×C151C212yesmaximal, complemented
6#1899×C151C212yesmaximal, complemented
7#1889×C151C214yesmaximal, complemented
8#1820×C151C211yesmaximal, characteristic, complemented
9C23×D4×C151C2211yescharacteristic
10#552×C151—24no—
11#551×C151—24no—
12#543×C151C2211yescharacteristic
13#539×C151—22no—
14#534×C151C2211yescharacteristic
15#529×C151—22no—
16C2×#123×C151C2212yes—
17C2×#120×C151C2214yes—
18#518×C151C2212yes—
19C2×#117×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C2×#99×C151C2214yes—
22#394×C151—24no—
23#392×C151—24no—
24#390×C151—22no—
25#390×C151—22no—
26#381×C151C2212yes—
27#379×C151C2214yes—
28#379×C151C2212yes—
29#379×C151C2212yes—
30#342×C151C2212yes—
31#342×C151C2212yes—
32#342×C151C2214yes—
33C25×C151C2312yes—
34C22×D4×C151—21no—
35C22×D4×C151—21no—
36C22×D4×C151—24no—
37C22×D4×C151—24no—
38C22×D4×C151—24no—
39C22×D4×C151—42no—
40C22×D4×C151C2312yes—
41C23×C4×C151C2311yescharacteristic
42#126×C151—24no—
43#126×C151—24no—
44#125×C151—22no—
45#125×C151—24no—
46#124×C151—22no—
47#123×C151—24no—
48#123×C151—22no—
49#123×C151—22no—
50#123×C151—24no—
51#123×C151—22no—
52C22⋊Q8×C151—24no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—24no—
55#121×C151—22no—
56#120×C151—22no—
57#120×C151—28no—
58#120×C151—44no—
59C4×Q8×C151—22no—
60C4×D4×C151—22no—
61C4×D4×C151—24no—
62C4×D4×C151—24no—
63#117×C151—24no—
64#117×C151—24no—
65#117×C151—22no—
66#117×C151—42no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151D412yescomplemented
69C2×C4⋊C4×C151D414yescomplemented
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—28no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151D414yescomplemented
76C2×C22⋊C4×C151C2314yes—
77C2×C22⋊C4×C151C2312yes—
78C2×C22⋊C4×C151C2311yescharacteristic
79C2×C22⋊C4×C151C2311yescharacteristic
80C2×C22⋊C4×C151C2312yes—
81C2×C42×C151—21no—
82C2×C42×C151D412yescomplemented
83#99×C151—44no—
84#95×C151—24no—
85C24×C151—22no—
86C24×C151—24no—
87C24×C151—22no—
88C24×C151—24no—
89C24×C151—84no—
90C24×C151C2×D412yes—
91C24×C151#4114yes—
92C24×C151C2411yescharacteristic
93C2×Q8×C151—22no—
94C2×D4×C151—24no—
95C2×D4×C151—24no—
96C2×D4×C151—22no—
97C2×D4×C151—22no—
98C2×D4×C151—24no—
99C2×D4×C151—24no—
100C2×D4×C151—22no—
101C2×D4×C151—416no—
102C2×D4×C151—42no—
103C2×D4×C151—42no—
104C2×D4×C151—48no—
105C2×D4×C151—42no—
106C2×D4×C151—42no—
107C2×D4×C151—88no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—24no—
111C22×C4×C151—24no—
112C22×C4×C151—22no—
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D414yes—
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D412yes—
118C22×C4×C151C2×D412yes—
119C22×C4×C151C2×D414yes—
120C4⋊C4×C151—24no—
121C4⋊C4×C151—24no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—24no—
125C4⋊C4×C151—24no—
126C4⋊C4×C151—24no—
127C4⋊C4×C151—42no—
128C22⋊C4×C151—24no—
129C22⋊C4×C151—24no—
130C22⋊C4×C151—22no—
131C22⋊C4×C151—22no—
132C22⋊C4×C151—22no—
133C22⋊C4×C151—22no—
134C22⋊C4×C151—24no—
135C22⋊C4×C151—24no—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—24no—
138C22⋊C4×C151—24no—
139C22⋊C4×C151—48no—
140C22⋊C4×C151—84no—
141C22⋊C4×C151—84no—
142C22⋊C4×C151—88no—
143C42×C151—24no—
144C42×C151—22no—
145C42×C151—22no—
146C42×C151—42no—
147C23×C151—22no—
148C23×C151—24no—
149C23×C151—28no—
150C23×C151—24no—
151C23×C151—42no—
152C23×C151—44no—
153C23×C151—44no—
154C23×C151—48no—
155C23×C151—48no—
156C23×C151—44no—
157C23×C151—42no—
158C23×C151—42no—
159C23×C151—44no—
160C23×C151—84no—
161C23×C151—84no—
162C23×C151—88no—
163C23×C151C22×D411yescharacteristic
164C23×C151C22×D412yes—
165C23×C151C2×#4112yes—
166C23×C151H(5,𝔽2)12yes—
167Q8×C151—82no—
168D4×C151—48no—
169D4×C151—48no—
170D4×C151—42no—
171D4×C151—42no—
172D4×C151—44no—
173D4×C151—82no—
174D4×C151—816no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—28no—
180C2×C4×C151—22no—
181C2×C4×C151—24no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—24no—
185C2×C4×C151—42no—
186C2×C4×C151—44no—
187C2×C4×C151—42no—
188C2×C4×C151—44no—
189C2×C4×C151—48no—
190C2×C4×C151—42no—
191C2×C4×C151—44no—
192C2×C4×C151—84no—
193C2×C4×C151#12012yes—
194C2×C4×C151#12012yes—
195C22×C151—22no—
196C22×C151—24no—
197C22×C151—42no—
198C22×C151—42no—
199C22×C151—48no—
200C22×C151—48no—
201C22×C151—44no—
202C22×C151—44no—
203C22×C151—44no—
204C22×C151—42no—
205C22×C151—44no—
206C22×C151—84no—
207C22×C151—84no—
208C22×C151—88no—
209C22×C151—84no—
210C22×C151C2×#12011yescharacteristic
211C22×C151#52511yescharacteristic
212C22×C151#53511yescharacteristic
213C22×C151#54614yes—
214C4×C151—22no—
215C4×C151—22no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—44no—
219C4×C151—42no—
220C4×C151—82no—
221C4×C151—84no—
222C2×C151—21no—
223C2×C151—24no—
224C2×C151—21no—
225C2×C151—84no—
226C2×C151—82no—
227C2×C151#240411yescharacteristic
228C2×C151#302712yes—
229#23988C15111yesmaximal, characteristic, direct product factor, Sylow
230C151#2398811yescharacteristic, direct product factor, Sylow
231#3491C2×C15111yescharacteristic, complemented
232#2613C2×C15112yescomplemented
233#2309C2×C15111yescharacteristic, complemented
234#2029C2×C15112yescomplemented
235#2021C2×C15112yescomplemented
236#1899C2×C15112yescomplemented
237#1889C2×C15114yescomplemented
238#1820C2×C15111yescharacteristic, complemented
239C23×D4C22×C15111yescharacteristic
240#552—24no—
241#551—24no—
242#543C22×C15111yescharacteristic
243#539—22no—
244#534C22×C15111yescharacteristic
245#529—22no—
246C2×#123C22×C15112yes—
247C2×#120C22×C15114yes—
248#518C22×C15112yes—
249C2×#117C22×C15111yescharacteristic
250C2×#117C22×C15111yescharacteristic
251C2×#99C22×C15114yes—
252#394—24no—
253#392—24no—
254#390—22no—
255#390—22no—
256#381C22×C15112yes—
257#379C22×C15112yes—
258#379C22×C15112yes—
259#379C22×C15114yes—
260#342C22×C15112yes—
261#342C22×C15112yes—
262#342C22×C15114yes—
263C25C23×C15112yes—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—24no—
269C22×D4—42no—
270C22×D4C23×C15112yes—
271C23×C4C23×C15111yescharacteristic
272#126—24no—
273#126—24no—
274#125—22no—
275#125—24no—
276#124—22no—
277#123—24no—
278#123—22no—
279#123—22no—
280#123—24no—
281#123—22no—
282C22⋊Q8—24no—
283C22⋊Q8—22no—
284C22⋊Q8—24no—
285#121—22no—
286#120—22no—
287#120—28no—
288#120—44no—
289C4×Q8—22no—
290C4×D4—22no—
291C4×D4—24no—
292C4×D4—24no—
293#117—24no—
294#117—24no—
295#117—22no—
296#117—42no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C15112yescomplemented
299C2×C4⋊C4D4×C15114yescomplemented
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4D4×C15114yescomplemented
306C2×C22⋊C4C23×C15112yes—
307C2×C22⋊C4C23×C15114yes—
308C2×C22⋊C4C23×C15111yescharacteristic
309C2×C22⋊C4C23×C15111yescharacteristic
310C2×C22⋊C4C23×C15112yes—
311C2×C42—21no—
312C2×C42D4×C15112yescomplemented
313#99—44no—
314#95—24no—
315C24—22no—
316C24—24no—
317C24—22no—
318C24—24no—
319C24—84no—
320C24C2×D4×C15112yes—
321C24#41×C15114yes—
322C24C24×C15111yescharacteristic
323C2×Q8—22no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—22no—
331C2×D4—416no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—48no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—88no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4C2×D4×C15112yes—
344C22×C4C2×D4×C15114yes—
345C22×C4C2×D4×C15111yescharacteristic
346C22×C4C2×D4×C15111yescharacteristic
347C22×C4C2×D4×C15112yes—
348C22×C4C2×D4×C15112yes—
349C22×C4C2×D4×C15114yes—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—42no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—48no—
370C22⋊C4—84no—
371C22⋊C4—84no—
372C22⋊C4—88no—
373C42—24no—
374C42—22no—
375C42—22no—
376C42—42no—
377C23—22no—
378C23—24no—
379C23—28no—
380C23—24no—
381C23—42no—
382C23—44no—
383C23—44no—
384C23—48no—
385C23—48no—
386C23—44no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—84no—
391C23—84no—
392C23—88no—
393C23C22×D4×C15111yescharacteristic
394C23C22×D4×C15112yes—
395C23C2×#41×C15112yes—
396C23H(5,𝔽2)×C15112yes—
397Q8—82no—
398D4—48no—
399D4—48no—
400D4—42no—
401D4—42no—
402D4—44no—
403D4—82no—
404D4—816no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—28no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—84no—
423C2×C4#120×C15112yes—
424C2×C4#120×C15112yes—
425C22—22no—
426C22—24no—
427C22—42no—
428C22—42no—
429C22—48no—
430C22—48no—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—42no—
435C22—44no—
436C22—84no—
437C22—84no—
438C22—88no—
439C22—84no—
440C22C2×#120×C15111yescharacteristic
441C22#525×C15111yescharacteristic
442C22#535×C15111yescharacteristic
443C22#546×C15114yes—
444C4—22no—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—44no—
449C4—42no—
450C4—84no—
451C4—82no—
452C2—21no—
453C2—24no—
454C2—21no—
455C2—84no—
456C2—82no—
457C2#2404×C15111yescharacteristic
458C2#3027×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3491×C151C2semidirect
2. #2613×C151C2semidirect
3. #2309×C151C2semidirect
4. #2029×C151C2semidirect
5. #2021×C151C2semidirect
6. #1899×C151C2semidirect
7. #1889×C151C2semidirect
8. #1820×C151C2semidirect
68. C2×C4⋊C4×C151D4semidirect
69. C2×C4⋊C4×C151D4semidirect
75. C2×C22⋊C4×C151D4semidirect
82. C2×C42×C151D4semidirect
229. #23988C151direct (N × H)
230. C151#23988direct (N × H)
231. #3491C2×C151semidirect
232. #2613C2×C151semidirect
233. #2309C2×C151semidirect
234. #2029C2×C151semidirect
235. #2021C2×C151semidirect
236. #1899C2×C151semidirect
237. #1889C2×C151semidirect
238. #1820C2×C151semidirect
298. C2×C4⋊C4D4×C151semidirect
299. C2×C4⋊C4D4×C151semidirect
305. C2×C22⋊C4D4×C151semidirect
312. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3491×C1512
#2613×C1512
#2309×C1512
#2029×C1512
#2021×C1512
#1899×C1512
#1889×C1512
#1820×C1512
#23988151