Finite Group Databasebeta

← C151×#8988 #50313913

Subgroups — C151×#8988 #50313913

Order 38656.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic
2#2354×C151C211yesmaximal, characteristic
3#1990×C151C211yesmaximal, characteristic, complemented
4#1988×C151C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C151C211yesmaximal, characteristic
6#1296×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11C2×#117×C151—21no—
12#461×C151—22no—
13#461×C151C414yescomplemented
14C2×C4⋊C8×C151C2211yescharacteristic
15C2×C4⋊C8×C151C2211yescharacteristic
16C2×#103×C151—21no—
17C2×C4×C8×C151C2211yescharacteristic
18#390×C151—21no—
19#388×C151—22no—
20#384×C151C2211yescharacteristic
21#380×C151—21no—
22C4×C4⋊C4×C151—21no—
23C4×C4⋊C4×C151C2211yescharacteristic
24#340×C151—21no—
25#340×C151—21no—
26#340×C151—22no—
27D4⋊C8×C151—22no—
28C22×Q8×C151—21no—
29C22×D4×C151D411yescharacteristic
30C23×C4×C151—21no—
31C2×SD16×C151—24no—
32C2×SD16×C151—42no—
33C2×SD16×C151—42no—
34C22×C8×C151—21no—
35C22×C8×C151—21no—
36C22×C8×C151—21no—
37C4⋊Q8×C151—21no—
38C4⋊Q8×C151—21no—
39C4⋊Q8×C151—21no—
40C4⋊Q8×C151C2×C412yes—
41C4×D4×C151—21no—
42C4×D4×C151—21no—
43C4×D4×C151C2×C412yes—
44C4×D4×C151D412yes—
45#117×C151—42no—
46#117×C151—42no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151—21no—
51C2×C4⋊C4×C151D411yescharacteristic
52C2×C4⋊C4×C151D411yescharacteristic
53C2×C4⋊C4×C151D411yescharacteristic
54C2×C4⋊C4×C151D412yes—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—22no—
57C2×C22⋊C4×C151—22no—
58C2×C42×C151—22no—
59C2×C42×C151—21no—
60C2×C42×C151C2311yescharacteristic
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151C2×C412yes—
65#103×C151—24no—
66C4×C8×C151—21no—
67C4×C8×C151—21no—
68#95×C151—22no—
69#95×C151—21no—
70C24×C151—21no—
71C2×Q8×C151—22no—
72C2×Q8×C151—41no—
73C2×Q8×C151—41no—
74C2×Q8×C151—41no—
75C2×Q8×C151—41no—
76C2×Q8×C151—41no—
77C2×D4×C151—21no—
78C2×D4×C151—21no—
79C2×D4×C151—21no—
80C2×D4×C151—21no—
81C2×D4×C151—21no—
82C2×D4×C151C22⋊C412yes—
83C22×C4×C151—21no—
84C22×C4×C151—21no—
85C22×C4×C151—22no—
86C22×C4×C151—22no—
87C22×C4×C151—21no—
88C22×C4×C151—22no—
89C22×C4×C151—41no—
90C22×C4×C151—41no—
91C22×C4×C151—41no—
92C22×C4×C151—41no—
93C22×C4×C151—41no—
94C22×C4×C151C2×D411yescharacteristic
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151C2×D411yescharacteristic
97SD16×C151—48no—
98C2×C8×C151—22no—
99C2×C8×C151—22no—
100C2×C8×C151—41no—
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151—41no—
105C2×C8×C151—41no—
106C2×C8×C151—41no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—42no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151C22⋊C412yes—
121C4⋊C4×C151SD1612yescomplemented
122C22⋊C4×C151—22no—
123C22⋊C4×C151—22no—
124C22⋊C4×C151—44no—
125C22⋊C4×C151—82no—
126C42×C151—44no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151C22×C411yescharacteristic
130C42×C151C2×D411yescharacteristic
131C42×C151#4111yescharacteristic
132C42×C151#4111yescharacteristic
133C23×C151—22no—
134C23×C151—41no—
135C23×C151—41no—
136C23×C151—41no—
137C23×C151—41no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151#12011yescharacteristic
141Q8×C151—42no—
142Q8×C151—42no—
143Q8×C151—81no—
144Q8×C151—81no—
145D4×C151—22no—
146D4×C151—22no—
147D4×C151—41no—
148D4×C151—41no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—42no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—42no—
162C2×C4×C151—41no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—42no—
168C2×C4×C151—81no—
169C2×C4×C151—81no—
170C2×C4×C151C2×C22⋊C411yescharacteristic
171C2×C4×C151C4×D411yescharacteristic
172C2×C4×C151C4×D411yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151#12111yescharacteristic
175C2×C4×C151#12311yescharacteristic
176C2×C4×C151C2×SD1611yescharacteristic
177C2×C4×C151#13511yescharacteristic
178C2×C4×C151#13511yescharacteristic
179C2×C4×C151#13511yescharacteristic
180C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C151#13711yescharacteristic
184C8×C151—42no—
185C8×C151—42no—
186C8×C151—81no—
187C22×C151—42no—
188C22×C151—42no—
189C22×C151—42no—
190C22×C151—81no—
191C22×C151—81no—
192C22×C151—81no—
193C22×C151—81no—
194C22×C151#38611yescharacteristic
195C22×C151#44911yescharacteristic
196C22×C151#44911yescharacteristic
197C22×C151#45011yescharacteristic
198C22×C151#45211yescharacteristic
199C22×C151#45511yescharacteristic
200C22×C151#45611yescharacteristic
201C4×C151—21no—
202C4×C151—21no—
203C4×C151—42no—
204C4×C151—42no—
205C4×C151—82no—
206C4×C151—82no—
207C4×C151—81no—
208C4×C151#41611yescharacteristic
209C4×C151#41811yescharacteristic
210C4×C151C4×SD1611yescharacteristic
211C4×C151#44011yescharacteristic
212C4×C151#46111yescharacteristic
213C4×C151#46311yescharacteristic
214C4×C151#48211yescharacteristic
215C4×C151#48211yescharacteristic
216C2×C151—82no—
217C2×C151#164211yescharacteristic
218C2×C151#164611yescharacteristic
219C2×C151#165011yescharacteristic
220C2×C151#165411yescharacteristic
221C2×C151#187511yescharacteristic
222C2×C151#187711yescharacteristic
223C2×C151#188211yescharacteristic
224#8988C15111yesmaximal, characteristic, direct product factor, Sylow
225C151#898811yescharacteristic, direct product factor, Sylow
226C2×#461C2×C15111yescharacteristic
227#2354C2×C15111yescharacteristic
228#1990C2×C15111yescharacteristic, complemented
229#1988C2×C15111yescharacteristic, complemented
230C2×D4⋊C8C2×C15111yescharacteristic
231#1296C2×C15111yescharacteristic, complemented
232#1279C2×C15111yescharacteristic, complemented
233C22×SD16—21no—
234C2×C4⋊Q8C22×C15111yescharacteristic
235C2×C4×D4C22×C15111yescharacteristic
236C2×#117—21no—
237#461—22no—
238#461C4×C15114yescomplemented
239C2×C4⋊C8C22×C15111yescharacteristic
240C2×C4⋊C8C22×C15111yescharacteristic
241C2×#103—21no—
242C2×C4×C8C22×C15111yescharacteristic
243#390—21no—
244#388—22no—
245#384C22×C15111yescharacteristic
246#380—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C22×C15111yescharacteristic
249#340—21no—
250#340—21no—
251#340—22no—
252D4⋊C8—22no—
253C22×Q8—21no—
254C22×D4D4×C15111yescharacteristic
255C23×C4—21no—
256C2×SD16—24no—
257C2×SD16—42no—
258C2×SD16—42no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8C2×C4×C15112yes—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×C4×C15112yes—
269C4×D4D4×C15112yes—
270#117—42no—
271#117—42no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C15111yescharacteristic
277C2×C4⋊C4D4×C15111yescharacteristic
278C2×C4⋊C4D4×C15111yescharacteristic
279C2×C4⋊C4D4×C15112yes—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C42—22no—
284C2×C42—21no—
285C2×C42C23×C15111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8C2×C4×C15112yes—
290#103—24no—
291C4×C8—21no—
292C4×C8—21no—
293#95—22no—
294#95—21no—
295C24—21no—
296C2×Q8—22no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4C22⋊C4×C15112yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4C2×D4×C15111yescharacteristic
321C22×C4C2×D4×C15111yescharacteristic
322SD16—48no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—42no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C22⋊C4×C15112yes—
346C4⋊C4SD16×C15112yescomplemented
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—44no—
350C22⋊C4—82no—
351C42—44no—
352C42—41no—
353C42—41no—
354C42C22×C4×C15111yescharacteristic
355C42C2×D4×C15111yescharacteristic
356C42#41×C15111yescharacteristic
357C42#41×C15111yescharacteristic
358C23—22no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23#120×C15111yescharacteristic
366Q8—42no—
367Q8—42no—
368Q8—81no—
369Q8—81no—
370D4—22no—
371D4—22no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C2×C22⋊C4×C15111yescharacteristic
396C2×C4C4×D4×C15111yescharacteristic
397C2×C4C4×D4×C15111yescharacteristic
398C2×C4#121×C15111yescharacteristic
399C2×C4#121×C15111yescharacteristic
400C2×C4#123×C15111yescharacteristic
401C2×C4C2×SD16×C15111yescharacteristic
402C2×C4#135×C15111yescharacteristic
403C2×C4#135×C15111yescharacteristic
404C2×C4#135×C15111yescharacteristic
405C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
406C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
407C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
408C2×C4#137×C15111yescharacteristic
409C8—42no—
410C8—42no—
411C8—81no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22#386×C15111yescharacteristic
420C22#449×C15111yescharacteristic
421C22#449×C15111yescharacteristic
422C22#450×C15111yescharacteristic
423C22#452×C15111yescharacteristic
424C22#455×C15111yescharacteristic
425C22#456×C15111yescharacteristic
426C4—21no—
427C4—21no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4—82no—
432C4—81no—
433C4#416×C15111yescharacteristic
434C4#418×C15111yescharacteristic
435C4C4×SD16×C15111yescharacteristic
436C4#440×C15111yescharacteristic
437C4#461×C15111yescharacteristic
438C4#463×C15111yescharacteristic
439C4#482×C15111yescharacteristic
440C4#482×C15111yescharacteristic
441C2—82no—
442C2#1642×C15111yescharacteristic
443C2#1646×C15111yescharacteristic
444C2#1650×C15111yescharacteristic
445C2#1654×C15111yescharacteristic
446C2#1875×C15111yescharacteristic
447C2#1877×C15111yescharacteristic
448C2#1882×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1990×C151C2semidirect
4. #1988×C151C2semidirect
6. #1296×C151C2semidirect
7. #1279×C151C2semidirect
13. #461×C151C4semidirect
121. C4⋊C4×C151SD16semidirect
224. #8988C151direct (N × H)
225. C151#8988direct (N × H)
228. #1990C2×C151semidirect
229. #1988C2×C151semidirect
231. #1296C2×C151semidirect
232. #1279C2×C151semidirect
238. #461C4×C151semidirect
346. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
#2354×C1512
#1990×C1512
#1988×C1512
C2×D4⋊C8×C1512
#1296×C1512
#1279×C1512
#8988151