Finite Group Databasebeta

← C151×#24076 #50329001

Subgroups — C151×#24076 #50329001

Order 38656.

1174 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3492×C151C211yesmaximal, characteristic
2#3092×C151C212yesmaximal, complemented
3C2×#384×C151C211yesmaximal, characteristic, complemented
4#2060×C151C212yesmaximal, complemented
5#2039×C151C212yesmaximal, complemented
6#1896×C151C212yesmaximal, complemented
7#1859×C151C214yesmaximal, complemented
8#1821×C151C211yesmaximal, characteristic, complemented
9#554×C151—22no—
10#553×C151—22no—
11#552×C151—22no—
12#547×C151—22no—
13#544×C151C2211yescharacteristic
14#539×C151—22no—
15#537×C151C2211yescharacteristic
16#525×C151—22no—
17#525×C151C2212yes—
18#520×C151C2212yes—
19C22×C4⋊C4×C151—22no—
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C42×C151C2211yescharacteristic
23#484×C151—22no—
24#483×C151—22no—
25#481×C151—22no—
26#480×C151—22no—
27#428×C151C2214yes—
28C2×#104×C151C2214yes—
29#417×C151C2214yes—
30#407×C151C2212yes—
31#384×C151—22no—
32#384×C151C2212yes—
33#384×C151C2212yes—
34#343×C151C2212yes—
35#343×C151C2212yes—
36#339×C151C2214yes—
37C2×#41×C151—22no—
38C2×#41×C151C2312yes—
39C23×C4×C151—21no—
40C23×C4×C151—21no—
41C23×C4×C151D412yes—
42C23×C4×C151C2311yescharacteristic
43C2×M16×C151C2314yes—
44C4⋊Q8×C151—22no—
45#126×C151—24no—
46#125×C151—24no—
47#125×C151—22no—
48#123×C151—24no—
49#123×C151—24no—
50#123×C151—22no—
51C22⋊Q8×C151—22no—
52C22⋊Q8×C151—24no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—22no—
55C22⋊Q8×C151D412yes—
56C22⋊Q8×C151D412yes—
57#121×C151—22no—
58#121×C151—22no—
59#121×C151—22no—
60#121×C151D412yes—
61#121×C151D412yes—
62#120×C151—22no—
63C4×Q8×C151—22no—
64C4×D4×C151—24no—
65C4×D4×C151—22no—
66C4×D4×C151—24no—
67C4×D4×C151—22no—
68C4×D4×C151—22no—
69#117×C151—22no—
70#117×C151—22no—
71#117×C151C2312yes—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—24no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151—48no—
81C2×C4⋊C4×C151D412yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C42×C151—21no—
86C2×C42×C151—24no—
87C2×C42×C151C2312yes—
88#107×C151—24no—
89#106×C151—24no—
90#104×C151—28no—
91#103×C151—24no—
92#102×C151—24no—
93C22⋊C8×C151—22no—
94C22⋊C8×C151—22no—
95C24×C151C2×D411yescharacteristic
96#41×C151—24no—
97#41×C151—24no—
98#41×C151—84no—
99C2×Q8×C151—22no—
100C2×Q8×C151C2×D412yes—
101C2×D4×C151—22no—
102C2×D4×C151—22no—
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151C2×D412yes—
106C22×C4×C151—24no—
107C22×C4×C151—24no—
108C22×C4×C151—24no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—24no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—44no—
118C22×C4×C151—44no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D412yes—
123C22×C4×C151C2×D412yes—
124C22×C4×C151C2×D412yes—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2411yescharacteristic
127M16×C151—24no—
128M16×C151—24no—
129C2×C8×C151—24no—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—24no—
134C4⋊C4×C151—24no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—48no—
141C4⋊C4×C151—48no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151C2×D412yes—
144C4⋊C4×C151C2×D412yes—
145C22⋊C4×C151—24no—
146C22⋊C4×C151—24no—
147C22⋊C4×C151—22no—
148C22⋊C4×C151—22no—
149C22⋊C4×C151—22no—
150C22⋊C4×C151—22no—
151C22⋊C4×C151—22no—
152C42×C151—24no—
153C42×C151—24no—
154C42×C151—22no—
155C42×C151—22no—
156C42×C151#4114yescomplemented
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151#12011yescharacteristic
163C23×C151#12011yescharacteristic
164C23×C151C22×D411yescharacteristic
165Q8×C151—24no—
166Q8×C151—82no—
167D4×C151—24no—
168D4×C151—42no—
169D4×C151—42no—
170D4×C151—44no—
171D4×C151—44no—
172D4×C151—82no—
173C2×C4×C151—24no—
174C2×C4×C151—216no—
175C2×C4×C151—24no—
176C2×C4×C151—21no—
177C2×C4×C151—24no—
178C2×C4×C151—21no—
179C2×C4×C151—24no—
180C2×C4×C151—24no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—44no—
187C2×C4×C151—44no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—44no—
191C2×C4×C151—42no—
192C2×C4×C151—82no—
193C2×C4×C151—84no—
194C2×C4×C151—82no—
195C2×C4×C151—82no—
196C2×C4×C151#12012yes—
197C2×C4×C151C22×D412yes—
198C2×C4×C151C2×#4112yes—
199C2×C4×C1512−1+412yes—
200C8×C151—44no—
201C22×C151—24no—
202C22×C151—24no—
203C22×C151—21no—
204C22×C151—21no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—21no—
208C22×C151—21no—
209C22×C151—42no—
210C22×C151—42no—
211C22×C151—42no—
212C22×C151#45312yes—
213C22×C151#45612yes—
214C22×C151C2×#12011yescharacteristic
215C22×C151#52511yescharacteristic
216C22×C151#53611yescharacteristic
217C4×C151—28no—
218C4×C151—22no—
219C4×C151—42no—
220C4×C151—42no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—82no—
225C4×C151#54714yes—
226C2×C151—21no—
227C2×C151—21no—
228C2×C151—22no—
229C2×C151—22no—
230C2×C151—82no—
231C2×C151#240611yescharacteristic
232C2×C151C2×#45311yescharacteristic
233C2×C151C2×#45611yescharacteristic
234#24076C15111yesmaximal, characteristic, direct product factor, Sylow
235C151#2407611yescharacteristic, direct product factor, Sylow
236#3492C2×C15111yescharacteristic
237#3092C2×C15112yescomplemented
238C2×#384C2×C15111yescharacteristic, complemented
239#2060C2×C15112yescomplemented
240#2039C2×C15112yescomplemented
241#1896C2×C15112yescomplemented
242#1859C2×C15114yescomplemented
243#1821C2×C15111yescharacteristic, complemented
244#554—22no—
245#553—22no—
246#552—22no—
247#547—22no—
248#544C22×C15111yescharacteristic
249#539—22no—
250#537C22×C15111yescharacteristic
251#525—22no—
252#525C22×C15112yes—
253#520C22×C15112yes—
254C22×C4⋊C4—22no—
255C22×C4⋊C4C22×C15111yescharacteristic
256C22×C4⋊C4C22×C15111yescharacteristic
257C22×C42C22×C15111yescharacteristic
258#484—22no—
259#483—22no—
260#481—22no—
261#480—22no—
262#428C22×C15114yes—
263C2×#104C22×C15114yes—
264#417C22×C15114yes—
265#407C22×C15112yes—
266#384—22no—
267#384C22×C15112yes—
268#384C22×C15112yes—
269#343C22×C15112yes—
270#343C22×C15112yes—
271#339C22×C15114yes—
272C2×#41—22no—
273C2×#41C23×C15112yes—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4D4×C15112yes—
277C23×C4C23×C15111yescharacteristic
278C2×M16C23×C15114yes—
279C4⋊Q8—22no—
280#126—24no—
281#125—24no—
282#125—22no—
283#123—24no—
284#123—24no—
285#123—22no—
286C22⋊Q8—22no—
287C22⋊Q8—24no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8D4×C15112yes—
291C22⋊Q8D4×C15112yes—
292#121—22no—
293#121—22no—
294#121—22no—
295#121D4×C15112yes—
296#121D4×C15112yes—
297#120—22no—
298C4×Q8—22no—
299C4×D4—24no—
300C4×D4—22no—
301C4×D4—24no—
302C4×D4—22no—
303C4×D4—22no—
304#117—22no—
305#117—22no—
306#117C23×C15112yes—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—48no—
316C2×C4⋊C4D4×C15112yes—
317C2×C4⋊C4C23×C15112yes—
318C2×C4⋊C4C23×C15111yescharacteristic
319C2×C4⋊C4C23×C15111yescharacteristic
320C2×C42—21no—
321C2×C42—24no—
322C2×C42C23×C15112yes—
323#107—24no—
324#106—24no—
325#104—28no—
326#103—24no—
327#102—24no—
328C22⋊C8—22no—
329C22⋊C8—22no—
330C24C2×D4×C15111yescharacteristic
331#41—24no—
332#41—24no—
333#41—84no—
334C2×Q8—22no—
335C2×Q8C2×D4×C15112yes—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4C2×D4×C15112yes—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C15111yescharacteristic
357C22×C4C2×D4×C15112yes—
358C22×C4C2×D4×C15112yes—
359C22×C4C2×D4×C15112yes—
360C22×C4C2×D4×C15112yes—
361C22×C4C24×C15111yescharacteristic
362M16—24no—
363M16—24no—
364C2×C8—24no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—24no—
375C4⋊C4—48no—
376C4⋊C4—48no—
377C4⋊C4—42no—
378C4⋊C4C2×D4×C15112yes—
379C4⋊C4C2×D4×C15112yes—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—24no—
388C42—24no—
389C42—22no—
390C42—22no—
391C42#41×C15114yescomplemented
392C23—22no—
393C23—22no—
394C23—21no—
395C23—21no—
396C23—22no—
397C23#120×C15111yescharacteristic
398C23#120×C15111yescharacteristic
399C23C22×D4×C15111yescharacteristic
400Q8—24no—
401Q8—82no—
402D4—24no—
403D4—44no—
404D4—44no—
405D4—42no—
406D4—42no—
407D4—82no—
408C2×C4—24no—
409C2×C4—216no—
410C2×C4—24no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—82no—
428C2×C4—84no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4#120×C15112yes—
432C2×C4C22×D4×C15112yes—
433C2×C4C2×#41×C15112yes—
434C2×C42−1+4×C15112yes—
435C8—44no—
436C22—24no—
437C22—24no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22#453×C15112yes—
448C22#456×C15112yes—
449C22C2×#120×C15111yescharacteristic
450C22#525×C15111yescharacteristic
451C22#536×C15111yescharacteristic
452C4—28no—
453C4—22no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—82no—
460C4#547×C15114yes—
461C2—21no—
462C2—22no—
463C2—22no—
464C2—21no—
465C2—82no—
466C2#2406×C15111yescharacteristic
467C2C2×#453×C15111yescharacteristic
468C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3492×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3092×C151C2semidirect
3. C2×#384×C151C2semidirect
4. #2060×C151C2semidirect
5. #2039×C151C2semidirect
6. #1896×C151C2semidirect
7. #1859×C151C2semidirect
8. #1821×C151C2semidirect
156. C42×C151#41semidirect
234. #24076C151direct (N × H)
235. C151#24076direct (N × H)
237. #3092C2×C151semidirect
238. C2×#384C2×C151semidirect
239. #2060C2×C151semidirect
240. #2039C2×C151semidirect
241. #1896C2×C151semidirect
242. #1859C2×C151semidirect
243. #1821C2×C151semidirect
391. C42#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3492×C1512
#3092×C1512
C2×#384×C1512
#2060×C1512
#2039×C1512
#1896×C1512
#1859×C1512
#1821×C1512
#24076151