Finite Group Databasebeta

← C151×#9998 #50314923

Subgroups — C151×#9998 #50314923

Order 38656.

602 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3103×C151C211yesmaximal, characteristic, complemented
2#3036×C151C211yesmaximal, characteristic
3#2580×C151C211yesmaximal, characteristic, complemented
4#1517×C151C211yesmaximal, characteristic, complemented
5#1487×C151C211yesmaximal, characteristic, complemented
6#1478×C151C211yesmaximal, characteristic, complemented
7#1286×C151C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C151—21no—
9#532×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11C2×C4×D4×C151C2211yescharacteristic
12#481×C151—21no—
13#475×C151—21no—
14#463×C151—22no—
15#461×C151—21no—
16#460×C151—21no—
17#459×C151—21no—
18#448×C151—21no—
19C4×SD16×C151—22no—
20#431×C151C2211yescharacteristic
21#431×C151C2211yescharacteristic
22#423×C151C2211yescharacteristic
23#417×C151—21no—
24#399×C151—21no—
25#393×C151—21no—
26#390×C151—21no—
27#389×C151—21no—
28#385×C151—22no—
29#382×C151C2211yescharacteristic
30#327×C151—22no—
31Q8⋊C8×C151—22no—
32D4⋊C8×C151—22no—
33C2×#41×C151—21no—
34C22×Q8×C151D411yescharacteristic
35C22×D4×C151D411yescharacteristic
36C23×C4×C151—21no—
37AGL(1,ℤ/8)×C151—42no—
38AGL(1,ℤ/8)×C151—42no—
39C2×SD16×C151—22no—
40C2×SD16×C151—22no—
41C2×D8×C151—22no—
42C2×M16×C151—21no—
43C4⋊Q8×C151D411yescharacteristic
44#127×C151D411yescharacteristic
45#124×C151—21no—
46#121×C151—21no—
47#121×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C4×D4×C151—21no—
56C4×D4×C151—21no—
57C4×D4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151D411yescharacteristic
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C22⋊C4×C151—22no—
64C2×C22⋊C4×C151—21no—
65C2×C22⋊C4×C151—22no—
66C2×C42×C151—21no—
67C2×C42×C151C2311yescharacteristic
68#106×C151—22no—
69C4⋊C8×C151—21no—
70C4⋊C8×C151—21no—
71C4⋊C8×C151—21no—
72C4⋊C8×C151D412yes—
73#103×C151—22no—
74#103×C151—22no—
75#102×C151—22no—
76#102×C151—22no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C4×C8×C151—21no—
80C4×C8×C151D412yes—
81#95×C151—22no—
82#95×C151—21no—
83#95×C151D412yes—
84C24×C151—21no—
85#41×C151—41no—
86#41×C151—41no—
87#41×C151—41no—
88#41×C151—41no—
89C2×Q8×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151—42no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—41no—
102C2×D4×C151SD1612yescomplemented
103C22×C4×C151—21no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—41no—
108C22×C4×C151—41no—
109C22×C4×C151—41no—
110C22×C4×C151—82no—
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114SD16×C151—44no—
115SD16×C151—44no—
116D8×C151—44no—
117M16×C151—41no—
118M16×C151—41no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—41no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—41no—
129C4⋊C4×C151—41no—
130C4⋊C4×C151—41no—
131C4⋊C4×C151—41no—
132C4⋊C4×C151—82no—
133C22⋊C4×C151—44no—
134C22⋊C4×C151—41no—
135C22⋊C4×C151—41no—
136C22⋊C4×C151—41no—
137C22⋊C4×C151—41no—
138C22⋊C4×C151—82no—
139C42×C151—41no—
140C42×C151—41no—
141C42×C151C2×D411yescharacteristic
142C42×C151C2×D411yescharacteristic
143C42×C151C2×D411yescharacteristic
144C42×C151#4111yescharacteristic
145C23×C151—22no—
146C23×C151—42no—
147C23×C151—42no—
148C23×C151—41no—
149C23×C151—41no—
150C23×C151—41no—
151C23×C151#12011yescharacteristic
152Q8×C151—22no—
153Q8×C151—22no—
154Q8×C151—41no—
155Q8×C151—41no—
156Q8×C151—41no—
157Q8×C151—41no—
158D4×C151—22no—
159D4×C151—22no—
160D4×C151—42no—
161D4×C151—41no—
162D4×C151—41no—
163D4×C151—41no—
164D4×C151—41no—
165D4×C151—81no—
166D4×C151—81no—
167D4×C151—81no—
168C2×C4×C151—22no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—42no—
174C2×C4×C151—41no—
175C2×C4×C151—42no—
176C2×C4×C151—41no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—82no—
183C2×C4×C151—82no—
184C2×C4×C151—81no—
185C2×C4×C151—81no—
186C2×C4×C151#12011yescharacteristic
187C2×C4×C151#12011yescharacteristic
188C2×C4×C151#12111yescharacteristic
189C2×C4×C151#12111yescharacteristic
190C2×C4×C151#12111yescharacteristic
191C2×C4×C151#12711yescharacteristic
192C2×C4×C151C2×SD1611yescharacteristic
193C2×C4×C151#13511yescharacteristic
194C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C151#13711yescharacteristic
196C8×C151—42no—
197C8×C151—42no—
198C8×C151—81no—
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—44no—
202C22×C151—42no—
203C22×C151—82no—
204C22×C151—81no—
205C22×C151—81no—
206C22×C151—81no—
207C22×C151—81no—
208C22×C151—81no—
209C22×C151#39211yescharacteristic
210C22×C151#44811yescharacteristic
211C22×C151#44911yescharacteristic
212C4×C151—21no—
213C4×C151—21no—
214C4×C151—21no—
215C4×C151—21no—
216C4×C151—42no—
217C4×C151—82no—
218C4×C151—81no—
219C4×C151—81no—
220C4×C151—81no—
221C4×C151#45011yescharacteristic
222C4×C151#45211yescharacteristic
223C4×C151#46511yescharacteristic
224C4×C151#46811yescharacteristic
225C2×C151—21no—
226C2×C151—21no—
227C2×C151—82no—
228C2×C151—161no—
229C2×C151#200011yescharacteristic
230C2×C151#200811yescharacteristic
231C2×C151#201011yescharacteristic
232#9998C15111yesmaximal, characteristic, direct product factor, Sylow
233C151#999811yescharacteristic, direct product factor, Sylow
234#3103C2×C15111yescharacteristic, complemented
235#3036C2×C15111yescharacteristic
236#2580C2×C15111yescharacteristic, complemented
237#1517C2×C15111yescharacteristic, complemented
238#1487C2×C15111yescharacteristic, complemented
239#1478C2×C15111yescharacteristic, complemented
240#1286C2×C15111yescharacteristic, complemented
241C2×AGL(1,ℤ/8)—21no—
242#532C22×C15111yescharacteristic
243C2×C4×Q8C22×C15111yescharacteristic
244C2×C4×D4C22×C15111yescharacteristic
245#481—21no—
246#475—21no—
247#463—22no—
248#461—21no—
249#460—21no—
250#459—21no—
251#448—21no—
252C4×SD16—22no—
253#431C22×C15111yescharacteristic
254#431C22×C15111yescharacteristic
255#423C22×C15111yescharacteristic
256#417—21no—
257#399—21no—
258#393—21no—
259#390—21no—
260#389—21no—
261#385—22no—
262#382C22×C15111yescharacteristic
263#327—22no—
264Q8⋊C8—22no—
265D4⋊C8—22no—
266C2×#41—21no—
267C22×Q8D4×C15111yescharacteristic
268C22×D4D4×C15111yescharacteristic
269C23×C4—21no—
270AGL(1,ℤ/8)—42no—
271AGL(1,ℤ/8)—42no—
272C2×SD16—22no—
273C2×SD16—22no—
274C2×D8—22no—
275C2×M16—21no—
276C4⋊Q8D4×C15111yescharacteristic
277#127D4×C15111yescharacteristic
278#124—21no—
279#121—21no—
280#121—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4D4×C15111yescharacteristic
295C2×C4⋊C4D4×C15111yescharacteristic
296C2×C22⋊C4—22no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C42—21no—
300C2×C42C23×C15111yescharacteristic
301#106—22no—
302C4⋊C8—21no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8D4×C15112yes—
306#103—22no—
307#103—22no—
308#102—22no—
309#102—22no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C4×C8—21no—
313C4×C8D4×C15112yes—
314#95—22no—
315#95—21no—
316#95D4×C15112yes—
317C24—21no—
318#41—41no—
319#41—41no—
320#41—41no—
321#41—41no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—42no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—41no—
335C2×D4SD16×C15112yescomplemented
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—82no—
344C22×C4C2×D4×C15111yescharacteristic
345C22×C4C2×D4×C15111yescharacteristic
346C22×C4C2×D4×C15111yescharacteristic
347SD16—44no—
348SD16—44no—
349D8—44no—
350M16—41no—
351M16—41no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—41no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—82no—
366C22⋊C4—44no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—82no—
372C42—41no—
373C42—41no—
374C42C2×D4×C15111yescharacteristic
375C42C2×D4×C15111yescharacteristic
376C42C2×D4×C15111yescharacteristic
377C42#41×C15111yescharacteristic
378C23—22no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23#120×C15111yescharacteristic
385Q8—22no—
386Q8—22no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—22no—
392D4—22no—
393D4—42no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—81no—
399D4—81no—
400D4—81no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4#120×C15111yescharacteristic
420C2×C4#120×C15111yescharacteristic
421C2×C4#121×C15111yescharacteristic
422C2×C4#121×C15111yescharacteristic
423C2×C4#121×C15111yescharacteristic
424C2×C4#127×C15111yescharacteristic
425C2×C4C2×SD16×C15111yescharacteristic
426C2×C4#135×C15111yescharacteristic
427C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
428C2×C4#137×C15111yescharacteristic
429C8—42no—
430C8—42no—
431C8—81no—
432C22—21no—
433C22—21no—
434C22—44no—
435C22—42no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22#392×C15111yescharacteristic
443C22#448×C15111yescharacteristic
444C22#449×C15111yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4#450×C15111yescharacteristic
455C4#452×C15111yescharacteristic
456C4#465×C15111yescharacteristic
457C4#468×C15111yescharacteristic
458C2—21no—
459C2—21no—
460C2—82no—
461C2—161no—
462C2#2000×C15111yescharacteristic
463C2#2008×C15111yescharacteristic
464C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#3036×C151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3103×C151C2semidirect
3. #2580×C151C2semidirect
4. #1517×C151C2semidirect
5. #1487×C151C2semidirect
6. #1478×C151C2semidirect
7. #1286×C151C2semidirect
102. C2×D4×C151SD16semidirect
232. #9998C151direct (N × H)
233. C151#9998direct (N × H)
234. #3103C2×C151semidirect
236. #2580C2×C151semidirect
237. #1517C2×C151semidirect
238. #1487C2×C151semidirect
239. #1478C2×C151semidirect
240. #1286C2×C151semidirect
335. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3103×C1512
#3036×C1512
#2580×C1512
#1517×C1512
#1487×C1512
#1478×C1512
#1286×C1512
#9998151