Finite Group Databasebeta

← C151×#18907 #50323832

Subgroups — C151×#18907 #50323832

Order 38656.

882 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic
2#3227×C151C211yesmaximal, characteristic
3#3209×C151C211yesmaximal, characteristic, complemented
4C2×#475×C151C211yesmaximal, characteristic, complemented
5#1653×C151C214yesmaximal, complemented
6#1640×C151C214yesmaximal, complemented
7#1540×C151C211yesmaximal, characteristic
8#1481×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10#559×C151C2212yes—
11#557×C151C2212yes—
12#556×C151—21no—
13#556×C151—22no—
14#554×C151—21no—
15#552×C151—22no—
16#539×C151—22no—
17#536×C151—21no—
18#533×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21#529×C151—22no—
22#520×C151—21no—
23C2×C4×Q8×C151C2211yescharacteristic
24#498×C151C2212yes—
25#494×C151—21no—
26#487×C151—21no—
27#486×C151C2212yes—
28#481×C151—22no—
29#476×C151—22no—
30#475×C151—22no—
31#475×C151C2214yes—
32#462×C151C2214yes—
33#451×C151—22no—
34#431×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36C2×#106×C151—21no—
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151—21no—
39#332×C151C2212yes—
40#331×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—21no—
45C22×Q8×C151D411yescharacteristic
46C2×Q16×C151—24no—
47C22×C8×C151—21no—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—22no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151D411yescharacteristic
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151C2312yes—
55C4⋊Q8×C151C2311yescharacteristic
56#127×C151C2311yescharacteristic
57#126×C151—24no—
58#126×C151—24no—
59#125×C151—22no—
60#125×C151—24no—
61#125×C151—21no—
62#124×C151—21no—
63#124×C151—22no—
64#124×C151—22no—
65#123×C151—24no—
66#123×C151—24no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—24no—
70C22⋊Q8×C151—21no—
71C22⋊Q8×C151D412yes—
72#121×C151—21no—
73#121×C151D412yes—
74C4×Q8×C151—22no—
75C4×Q8×C151—21no—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151—22no—
79C4×Q8×C151D412yes—
80C4×Q8×C151C2312yes—
81C4×Q8×C151C2312yes—
82C4×D4×C151—24no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—21no—
86C4×D4×C151D412yes—
87#117×C151—22no—
88#117×C151—24no—
89#117×C151—21no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C42×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#106×C151—24no—
98#106×C151—24no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151C2312yes—
102C4⋊C8×C151C2312yes—
103#103×C151—24no—
104#103×C151—24no—
105#102×C151—24no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—42no—
111#41×C151—42no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—41no—
119C2×Q8×C151—82no—
120C2×Q8×C151C2×D412yes—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—22no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151C2×D412yes—
126C22×C4×C151—21no—
127C22×C4×C151—24no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—41no—
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134Q16×C151—84no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—42no—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151C2×D412yes—
156C4⋊C4×C151C2×D412yes—
157C4⋊C4×C151C2×D412yes—
158C22⋊C4×C151—24no—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—22no—
164C42×C151—24no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—22no—
168C42×C151C2×D411yescharacteristic
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2411yescharacteristic
172C23×C151—22no—
173C23×C151#12011yescharacteristic
174Q8×C151—22no—
175Q8×C151—22no—
176Q8×C151—24no—
177Q8×C151—41no—
178Q8×C151—41no—
179Q8×C151—42no—
180Q8×C151—44no—
181Q8×C151—81no—
182Q8×C151—82no—
183D4×C151—42no—
184D4×C151—44no—
185D4×C151—41no—
186D4×C151—41no—
187D4×C151—42no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—41no—
195C2×C4×C151—42no—
196C2×C4×C151—44no—
197C2×C4×C151—42no—
198C2×C4×C151—81no—
199C2×C4×C151—84no—
200C2×C4×C151—82no—
201C2×C4×C151#12011yescharacteristic
202C2×C4×C151#12011yescharacteristic
203C2×C4×C151#12011yescharacteristic
204C2×C4×C151#13512yes—
205C2×C4×C151#13712yes—
206C2×C4×C151C22×D411yescharacteristic
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C22×D411yescharacteristic
209C8×C151—42no—
210C8×C151—42no—
211C8×C151—42no—
212C22×C151—21no—
213C22×C151—21no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151#45212yes—
218C22×C151C2×#12011yescharacteristic
219C4×C151—21no—
220C4×C151—21no—
221C4×C151—21no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—82no—
228C4×C151#45212yes—
229C4×C151C2×#13511yescharacteristic
230C4×C151C2×#13711yescharacteristic
231C4×C151#57712yes—
232C2×C151—22no—
233C2×C151—82no—
234C2×C151C2×#45211yescharacteristic
235C2×C151#301011yescharacteristic
236C2×C151#302211yescharacteristic
237#18907C15111yesmaximal, characteristic, direct product factor, Sylow
238C151#1890711yescharacteristic, direct product factor, Sylow
239#3507C2×C15111yescharacteristic
240#3227C2×C15111yescharacteristic
241#3209C2×C15111yescharacteristic, complemented
242C2×#475C2×C15111yescharacteristic, complemented
243#1653C2×C15114yescomplemented
244#1640C2×C15114yescomplemented
245#1540C2×C15111yescharacteristic
246#1481C2×C15111yescharacteristic, complemented
247#1479C2×C15111yescharacteristic, complemented
248#559C22×C15112yes—
249#557C22×C15112yes—
250#556—21no—
251#556—22no—
252#554—21no—
253#552—22no—
254#539—22no—
255#536—21no—
256#533C22×C15111yescharacteristic
257#532C22×C15111yescharacteristic
258C2×C4⋊Q8C22×C15111yescharacteristic
259#529—22no—
260#520—21no—
261C2×C4×Q8C22×C15111yescharacteristic
262#498C22×C15112yes—
263#494—21no—
264#487—21no—
265#486C22×C15112yes—
266#481—22no—
267#476—22no—
268#475—22no—
269#475C22×C15114yes—
270#462C22×C15114yes—
271#451—22no—
272#431C22×C15111yescharacteristic
273#431C22×C15111yescharacteristic
274C2×#106—21no—
275C2×C4⋊C8C22×C15111yescharacteristic
276C2×#103—21no—
277#332C22×C15112yes—
278#331C22×C15112yes—
279Q8⋊C8C22×C15114yes—
280Q8⋊C8C22×C15114yes—
281C2×#41—21no—
282C22×Q8—21no—
283C22×Q8D4×C15111yescharacteristic
284C2×Q16—24no—
285C22×C8—21no—
286C4⋊Q8—22no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8D4×C15111yescharacteristic
291C4⋊Q8D4×C15111yescharacteristic
292C4⋊Q8C23×C15112yes—
293C4⋊Q8C23×C15111yescharacteristic
294#127C23×C15111yescharacteristic
295#126—24no—
296#126—24no—
297#125—22no—
298#125—24no—
299#125—21no—
300#124—22no—
301#124—22no—
302#124—21no—
303#123—24no—
304#123—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—21no—
309C22⋊Q8D4×C15112yes—
310#121—21no—
311#121D4×C15112yes—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8D4×C15112yes—
318C4×Q8C23×C15112yes—
319C4×Q8C23×C15112yes—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—21no—
324C4×D4D4×C15112yes—
325#117—22no—
326#117—24no—
327#117—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4D4×C15111yescharacteristic
333C2×C42—21no—
334C2×C42C23×C15111yescharacteristic
335#106—24no—
336#106—24no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C15112yes—
340C4⋊C8C23×C15112yes—
341#103—24no—
342#103—24no—
343#102—24no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C4×C8—21no—
347C4×C8C23×C15112yes—
348#41—42no—
349#41—42no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—41no—
357C2×Q8—82no—
358C2×Q8C2×D4×C15112yes—
359C2×Q8C2×D4×C15112yes—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4C2×D4×C15112yes—
364C22×C4—21no—
365C22×C4—24no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4C2×D4×C15111yescharacteristic
371C22×C4C2×D4×C15111yescharacteristic
372Q16—84no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C2×D4×C15112yes—
394C4⋊C4C2×D4×C15112yes—
395C4⋊C4C2×D4×C15112yes—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C42—24no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42C2×D4×C15111yescharacteristic
407C42C2×D4×C15111yescharacteristic
408C42C2×D4×C15111yescharacteristic
409C42C24×C15111yescharacteristic
410C23—22no—
411C23#120×C15111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—24no—
415Q8—42no—
416Q8—41no—
417Q8—41no—
418Q8—44no—
419Q8—81no—
420Q8—82no—
421D4—42no—
422D4—44no—
423D4—41no—
424D4—41no—
425D4—42no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—84no—
438C2×C4—82no—
439C2×C4#120×C15111yescharacteristic
440C2×C4#120×C15111yescharacteristic
441C2×C4#120×C15111yescharacteristic
442C2×C4#135×C15112yes—
443C2×C4#137×C15112yes—
444C2×C4C22×D4×C15111yescharacteristic
445C2×C4C22×D4×C15111yescharacteristic
446C2×C4C22×D4×C15111yescharacteristic
447C8—42no—
448C8—42no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22#452×C15112yes—
456C22C2×#120×C15111yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—82no—
466C4#452×C15112yes—
467C4C2×#135×C15111yescharacteristic
468C4C2×#137×C15111yescharacteristic
469C4#577×C15112yes—
470C2—22no—
471C2—82no—
472C2C2×#452×C15111yescharacteristic
473C2#3010×C15111yescharacteristic
474C2#3022×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
3. #3209×C151C2semidirect
4. C2×#475×C151C2semidirect
5. #1653×C151C2semidirect
6. #1640×C151C2semidirect
8. #1481×C151C2semidirect
9. #1479×C151C2semidirect
237. #18907C151direct (N × H)
238. C151#18907direct (N × H)
241. #3209C2×C151semidirect
242. C2×#475C2×C151semidirect
243. #1653C2×C151semidirect
244. #1640C2×C151semidirect
246. #1481C2×C151semidirect
247. #1479C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3227×C1512
#3209×C1512
C2×#475×C1512
#1653×C1512
#1640×C1512
#1540×C1512
#1481×C1512
#1479×C1512
#18907151