Finite Group Databasebeta

← C151×#18725 #50323650

Subgroups — C151×#18725 #50323650

Order 38656.

876 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#3550×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3#3209×C151C211yesmaximal, characteristic, complemented
4#3141×C151C211yesmaximal, characteristic
5#1645×C151C214yesmaximal, complemented
6#1640×C151C214yesmaximal, complemented
7#1543×C151C211yesmaximal, characteristic
8#1485×C151C211yesmaximal, characteristic, complemented
9#1485×C151C211yesmaximal, characteristic, complemented
10#563×C151—22no—
11#559×C151C2212yes—
12Q82×C151C2212yes—
13#556×C151—21no—
14#556×C151—21no—
15D4×Q8×C151—21no—
16D4×Q8×C151—21no—
17#542×C151—22no—
18#542×C151—22no—
19#536×C151—22no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#498×C151—21no—
25#494×C151—21no—
26#489×C151—22no—
27#487×C151—21no—
28#487×C151—21no—
29#487×C151C2212yes—
30#486×C151C2212yes—
31#483×C151—22no—
32#475×C151C2214yes—
33#462×C151C2214yes—
34#451×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#417×C151—22no—
38C4×M16×C151C2211yescharacteristic
39#333×C151C2212yes—
40#331×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C2×#41×C151D412yes—
44C22×Q8×C151—22no—
45C22×Q8×C151—21no—
46C2×Q16×C151—24no—
47C2×M16×C151—21no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151—22no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—24no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151D411yescharacteristic
57C4⋊Q8×C151D411yescharacteristic
58C4⋊Q8×C151C2312yes—
59C4⋊Q8×C151C2311yescharacteristic
60#127×C151C2311yescharacteristic
61#126×C151—24no—
62#126×C151—24no—
63#125×C151—21no—
64#125×C151—21no—
65#124×C151—24no—
66#124×C151—22no—
67#124×C151—22no—
68#124×C151D412yes—
69#123×C151—24no—
70#123×C151—24no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151D412yes—
78C22⋊Q8×C151D412yes—
79#121×C151—21no—
80#121×C151—21no—
81C4×Q8×C151—21no—
82C4×Q8×C151—21no—
83C4×Q8×C151—22no—
84C4×Q8×C151—22no—
85C4×Q8×C151C2312yes—
86C4×Q8×C151C2312yes—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91#117×C151—22no—
92#117×C151—21no—
93#117×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#106×C151—24no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—24no—
101#103×C151—24no—
102#103×C151—24no—
103#102×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—44no—
111C2×Q8×C151—24no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—41no—
116C2×Q8×C151—82no—
117C2×Q8×C151—84no—
118C2×Q8×C151C2×D412yes—
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—22no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151C2×D412yes—
125C22×C4×C151—24no—
126C22×C4×C151—22no—
127C22×C4×C151—41no—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131Q16×C151—84no—
132M16×C151—42no—
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C4⋊C4×C151—24no—
137C4⋊C4×C151—24no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151C2×D412yes—
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—24no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—22no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C42×C151—24no—
164C42×C151—22no—
165C42×C151—22no—
166C42×C151C2×D411yescharacteristic
167C42×C151C2×D411yescharacteristic
168C42×C151C2×D411yescharacteristic
169C42×C151C2411yescharacteristic
170C23×C151—22no—
171C23×C151#12011yescharacteristic
172Q8×C151—24no—
173Q8×C151—24no—
174Q8×C151—42no—
175Q8×C151—42no—
176Q8×C151—42no—
177Q8×C151—44no—
178Q8×C151—82no—
179Q8×C151—84no—
180D4×C151—42no—
181D4×C151—42no—
182D4×C151—42no—
183D4×C151—82no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—44no—
193C2×C4×C151—42no—
194C2×C4×C151—84no—
195C2×C4×C151—82no—
196C2×C4×C151#12011yescharacteristic
197C2×C4×C151#12011yescharacteristic
198C2×C4×C151#12011yescharacteristic
199C2×C4×C151C22×D411yescharacteristic
200C2×C4×C151C22×D411yescharacteristic
201C2×C4×C151C22×D411yescharacteristic
202C8×C151—42no—
203C8×C151—42no—
204C8×C151—42no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—21no—
208C22×C151—42no—
209C22×C151—42no—
210C22×C151—42no—
211C22×C151C2×#12011yescharacteristic
212C4×C151—21no—
213C4×C151—21no—
214C4×C151—21no—
215C4×C151—42no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—42no—
219C4×C151—42no—
220C4×C151—82no—
221C4×C151#45512yes—
222C4×C151#57712yes—
223C4×C151#57812yes—
224C2×C151—41no—
225C2×C151—82no—
226C2×C151#301011yescharacteristic
227C2×C151#301111yescharacteristic
228C2×C151C2×#45511yescharacteristic
229#18725C15111yesmaximal, characteristic, direct product factor, Sylow
230C151#1872511yescharacteristic, direct product factor, Sylow
231#3550C2×C15111yescharacteristic
232#3229C2×C15111yescharacteristic, complemented
233#3209C2×C15111yescharacteristic, complemented
234#3141C2×C15111yescharacteristic
235#1645C2×C15114yescomplemented
236#1640C2×C15114yescomplemented
237#1543C2×C15111yescharacteristic
238#1485C2×C15111yescharacteristic, complemented
239#1485C2×C15111yescharacteristic, complemented
240#563—22no—
241#559C22×C15112yes—
242Q82C22×C15112yes—
243#556—21no—
244#556—21no—
245D4×Q8—21no—
246D4×Q8—21no—
247#542—22no—
248#542—22no—
249#536—22no—
250#533C22×C15111yescharacteristic
251#533C22×C15111yescharacteristic
252#532C22×C15111yescharacteristic
253C2×C4⋊Q8C22×C15111yescharacteristic
254#498—21no—
255#494—21no—
256#489—22no—
257#487—21no—
258#487—21no—
259#487C22×C15112yes—
260#486C22×C15112yes—
261#483—22no—
262#475C22×C15114yes—
263#462C22×C15114yes—
264#451—22no—
265#431C22×C15111yescharacteristic
266#431C22×C15111yescharacteristic
267#417—22no—
268C4×M16C22×C15111yescharacteristic
269#333C22×C15112yes—
270#331C22×C15112yes—
271Q8⋊C8C22×C15114yes—
272Q8⋊C8C22×C15114yes—
273C2×#41D4×C15112yes—
274C22×Q8—22no—
275C22×Q8—21no—
276C2×Q16—24no—
277C2×M16—21no—
278C4⋊Q8—24no—
279C4⋊Q8—22no—
280C4⋊Q8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8D4×C15111yescharacteristic
285C4⋊Q8D4×C15111yescharacteristic
286C4⋊Q8D4×C15111yescharacteristic
287C4⋊Q8D4×C15111yescharacteristic
288C4⋊Q8C23×C15112yes—
289C4⋊Q8C23×C15111yescharacteristic
290#127C23×C15111yescharacteristic
291#126—24no—
292#126—24no—
293#125—21no—
294#125—21no—
295#124—24no—
296#124—22no—
297#124—22no—
298#124D4×C15112yes—
299#123—24no—
300#123—24no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8—24no—
304C22⋊Q8—24no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8D4×C15112yes—
308C22⋊Q8D4×C15112yes—
309#121—21no—
310#121—21no—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8C23×C15112yes—
316C4×Q8C23×C15112yes—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—21no—
320C4×D4—21no—
321#117—22no—
322#117—21no—
323#117—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42C23×C15111yescharacteristic
327#106—24no—
328C4⋊C8C23×C15112yes—
329C4⋊C8C23×C15112yes—
330#103—24no—
331#103—24no—
332#103—24no—
333#102—24no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336#97—21no—
337C4×C8—21no—
338C4×C8—21no—
339C4×C8C23×C15112yes—
340#41—44no—
341C2×Q8—24no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—41no—
346C2×Q8—82no—
347C2×Q8—84no—
348C2×Q8C2×D4×C15112yes—
349C2×Q8C2×D4×C15112yes—
350C2×Q8C2×D4×C15112yes—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C2×D4×C15112yes—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—41no—
358C22×C4C2×D4×C15111yescharacteristic
359C22×C4C2×D4×C15111yescharacteristic
360C22×C4C2×D4×C15111yescharacteristic
361Q16—84no—
362M16—42no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C15112yes—
385C4⋊C4C2×D4×C15112yes—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C42—24no—
394C42—22no—
395C42—22no—
396C42C2×D4×C15111yescharacteristic
397C42C2×D4×C15111yescharacteristic
398C42C2×D4×C15111yescharacteristic
399C42C24×C15111yescharacteristic
400C23—22no—
401C23#120×C15111yescharacteristic
402Q8—24no—
403Q8—24no—
404Q8—42no—
405Q8—42no—
406Q8—42no—
407Q8—44no—
408Q8—82no—
409Q8—84no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—82no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—84no—
425C2×C4—82no—
426C2×C4#120×C15111yescharacteristic
427C2×C4#120×C15111yescharacteristic
428C2×C4#120×C15111yescharacteristic
429C2×C4C22×D4×C15111yescharacteristic
430C2×C4C22×D4×C15111yescharacteristic
431C2×C4C22×D4×C15111yescharacteristic
432C8—42no—
433C8—42no—
434C8—42no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22C2×#120×C15111yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4#455×C15112yes—
452C4#577×C15112yes—
453C4#578×C15112yes—
454C2—41no—
455C2—82no—
456C2#3010×C15111yescharacteristic
457C2#3011×C15111yescharacteristic
458C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3229×C151C2semidirect
3. #3209×C151C2semidirect
5. #1645×C151C2semidirect
6. #1640×C151C2semidirect
8. #1485×C151C2semidirect
9. #1485×C151C2semidirect
229. #18725C151direct (N × H)
230. C151#18725direct (N × H)
232. #3229C2×C151semidirect
233. #3209C2×C151semidirect
235. #1645C2×C151semidirect
236. #1640C2×C151semidirect
238. #1485C2×C151semidirect
239. #1485C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3550×C1512
#3229×C1512
#3209×C1512
#3141×C1512
#1645×C1512
#1640×C1512
#1543×C1512
#1485×C1512
#18725151