Finite Group Databasebeta

← C151×#10052 #50314977

Subgroups — C151×#10052 #50314977

Order 38656.

738 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic
3#2542×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic, complemented
5C2×#332×C151C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×D8×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×#127×C151C2211yescharacteristic
11C2×C22⋊Q8×C151—22no—
12C2×C4×D4×C151C2211yescharacteristic
13#486×C151—22no—
14#486×C151—22no—
15#459×C151—22no—
16#459×C151—22no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—22no—
20C2×#102×C151—21no—
21C2×#102×C151—22no—
22C2×C4×C8×C151C2211yescharacteristic
23#399×C151—22no—
24#390×C151—21no—
25#384×C151—21no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#332×C151—22no—
28D4⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151D411yescharacteristic
34C23×C4×C151—21no—
35C2×D8×C151—24no—
36C2×D8×C151—42no—
37C2×D8×C151—42no—
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#127×C151—21no—
48#127×C151D412yes—
49C22⋊Q8×C151—44no—
50C22⋊Q8×C151—44no—
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D412yes—
59C2×C4⋊C4×C151D412yes—
60C2×C22⋊C4×C151—24no—
61C2×C22⋊C4×C151—21no—
62C2×C42×C151—21no—
63C2×C42×C151C2311yescharacteristic
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151D412yes—
68#102×C151—24no—
69#102×C151—28no—
70#102×C151—44no—
71C4×C8×C151—21no—
72C4×C8×C151D412yes—
73#95×C151—21no—
74C24×C151—21no—
75C24×C151—41no—
76C2×Q8×C151—41no—
77C2×Q8×C151—41no—
78C2×Q8×C151—42no—
79C2×Q8×C151—42no—
80C2×D4×C151—21no—
81C2×D4×C151—22no—
82C2×D4×C151—22no—
83C2×D4×C151—21no—
84C2×D4×C151—22no—
85C2×D4×C151—21no—
86C2×D4×C151—21no—
87C2×D4×C151—21no—
88C2×D4×C151—44no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—42no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—42no—
97C2×D4×C151—41no—
98C2×D4×C151SD1612yes—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—42no—
105C22×C4×C151—42no—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D411yescharacteristic
109D8×C151—48no—
110C2×C8×C151—22no—
111C2×C8×C151—22no—
112C2×C8×C151—42no—
113C2×C8×C151—41no—
114C2×C8×C151—41no—
115C2×C8×C151—41no—
116C2×C8×C151—42no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—21no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—48no—
123C4⋊C4×C151—41no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151D814yescomplemented
126C22⋊C4×C151—48no—
127C22⋊C4×C151—41no—
128C22⋊C4×C151—41no—
129C42×C151—41no—
130C42×C151—41no—
131C42×C151C2×D411yescharacteristic
132C42×C151C2×D411yescharacteristic
133C42×C151C2×D411yescharacteristic
134C42×C151#4111yescharacteristic
135C23×C151—22no—
136C23×C151—41no—
137C23×C151—42no—
138C23×C151—41no—
139C23×C151—42no—
140C23×C151—42no—
141C23×C151—82no—
142C23×C151—81no—
143C23×C151—81no—
144C23×C151—82no—
145C23×C151#12011yescharacteristic
146Q8×C151—82no—
147Q8×C151—81no—
148Q8×C151—81no—
149D4×C151—22no—
150D4×C151—22no—
151D4×C151—44no—
152D4×C151—42no—
153D4×C151—41no—
154D4×C151—42no—
155D4×C151—44no—
156D4×C151—41no—
157D4×C151—82no—
158D4×C151—81no—
159D4×C151—81no—
160D4×C151—81no—
161D4×C151—81no—
162C2×C4×C151—22no—
163C2×C4×C151—24no—
164C2×C4×C151—42no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151—41no—
168C2×C4×C151—44no—
169C2×C4×C151—42no—
170C2×C4×C151—82no—
171C2×C4×C151—81no—
172C2×C4×C151—81no—
173C2×C4×C151#12011yescharacteristic
174C2×C4×C151#12011yescharacteristic
175C2×C4×C151#12111yescharacteristic
176C2×C4×C151#12111yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151#12711yescharacteristic
179C2×C4×C151C2×D812yes—
180C2×C4×C151C2×SD1611yescharacteristic
181C2×C4×C151#13511yescharacteristic
182C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C151AGL(1,ℤ/8)12yes—
184C2×C4×C151#13711yescharacteristic
185C8×C151—42no—
186C8×C151—42no—
187C8×C151—81no—
188C22×C151—44no—
189C22×C151—42no—
190C22×C151—82no—
191C22×C151—81no—
192C22×C151—81no—
193C22×C151—82no—
194C22×C151—82no—
195C22×C151—82no—
196C22×C151—162no—
197C22×C151—162no—
198C22×C151#39211yescharacteristic
199C22×C151#44712yes—
200C22×C151#44811yescharacteristic
201C22×C151#44911yescharacteristic
202C22×C151#45412yes—
203C4×C151—21no—
204C4×C151—21no—
205C4×C151—44no—
206C4×C151—81no—
207C4×C151—82no—
208C4×C151#45011yescharacteristic
209C4×C151#45211yescharacteristic
210C4×C151#45912yes—
211C4×C151#46511yescharacteristic
212C4×C151#46811yescharacteristic
213C4×C151#49311yescharacteristic
214C4×C151#49611yescharacteristic
215C2×C151—82no—
216C2×C151—162no—
217C2×C151#162512yes—
218C2×C151#162712yes—
219C2×C151#200011yescharacteristic
220C2×C151#200311yescharacteristic
221C2×C151#201111yescharacteristic
222#10052C15111yesmaximal, characteristic, direct product factor, Sylow
223C151#1005211yescharacteristic, direct product factor, Sylow
224C2×#486C2×C15111yescharacteristic, complemented
225C2×#459C2×C15111yescharacteristic
226#2542C2×C15111yescharacteristic, complemented
227#1982C2×C15111yescharacteristic, complemented
228C2×#332C2×C15111yescharacteristic, complemented
229C2×D4⋊C8C2×C15111yescharacteristic, complemented
230#1279C2×C15111yescharacteristic, complemented
231C22×D8—21no—
232C2×C4⋊Q8C22×C15111yescharacteristic
233C2×#127C22×C15111yescharacteristic
234C2×C22⋊Q8—22no—
235C2×C4×D4C22×C15111yescharacteristic
236#486—22no—
237#486—22no—
238#459—22no—
239#459—22no—
240C2×C4⋊C8C22×C15111yescharacteristic
241C2×C4⋊C8C22×C15111yescharacteristic
242C2×#102—22no—
243C2×#102—21no—
244C2×#102—22no—
245C2×C4×C8C22×C15111yescharacteristic
246#399—22no—
247#390—21no—
248#384—21no—
249C4×C4⋊C4C22×C15111yescharacteristic
250#332—22no—
251D4⋊C8—22no—
252C22×Q8—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C15111yescharacteristic
257C23×C4—21no—
258C2×D8—24no—
259C2×D8—42no—
260C2×D8—42no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268#127—21no—
269#127—21no—
270#127—21no—
271#127D4×C15112yes—
272C22⋊Q8—44no—
273C22⋊Q8—44no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4D4×C15111yescharacteristic
281C2×C4⋊C4D4×C15112yes—
282C2×C4⋊C4D4×C15112yes—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—21no—
285C2×C42—21no—
286C2×C42C23×C15111yescharacteristic
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C15112yes—
291#102—24no—
292#102—28no—
293#102—44no—
294C4×C8—21no—
295C4×C8D4×C15112yes—
296#95—21no—
297C24—21no—
298C24—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—42no—
302C2×Q8—42no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—44no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4SD16×C15112yes—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4C2×D4×C15111yescharacteristic
330C22×C4C2×D4×C15111yescharacteristic
331C22×C4C2×D4×C15111yescharacteristic
332D8—48no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—42no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—42no—
340C4⋊C4—22no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—48no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4D8×C15114yescomplemented
349C22⋊C4—48no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—41no—
353C42—41no—
354C42C2×D4×C15111yescharacteristic
355C42C2×D4×C15111yescharacteristic
356C42C2×D4×C15111yescharacteristic
357C42#41×C15111yescharacteristic
358C23—22no—
359C23—41no—
360C23—42no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—82no—
365C23—81no—
366C23—81no—
367C23—82no—
368C23#120×C15111yescharacteristic
369Q8—82no—
370Q8—81no—
371Q8—81no—
372D4—22no—
373D4—22no—
374D4—44no—
375D4—42no—
376D4—41no—
377D4—42no—
378D4—44no—
379D4—41no—
380D4—82no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4#120×C15111yescharacteristic
397C2×C4#120×C15111yescharacteristic
398C2×C4#121×C15111yescharacteristic
399C2×C4#121×C15111yescharacteristic
400C2×C4#121×C15111yescharacteristic
401C2×C4#127×C15111yescharacteristic
402C2×C4C2×D8×C15112yes—
403C2×C4C2×SD16×C15111yescharacteristic
404C2×C4#135×C15111yescharacteristic
405C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
406C2×C4AGL(1,ℤ/8)×C15112yes—
407C2×C4#137×C15111yescharacteristic
408C8—42no—
409C8—42no—
410C8—81no—
411C22—44no—
412C22—42no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—162no—
420C22—162no—
421C22#392×C15111yescharacteristic
422C22#447×C15112yes—
423C22#448×C15111yescharacteristic
424C22#449×C15111yescharacteristic
425C22#454×C15112yes—
426C4—21no—
427C4—21no—
428C4—44no—
429C4—81no—
430C4—82no—
431C4#450×C15111yescharacteristic
432C4#452×C15111yescharacteristic
433C4#459×C15112yes—
434C4#465×C15111yescharacteristic
435C4#468×C15111yescharacteristic
436C4#493×C15111yescharacteristic
437C4#496×C15111yescharacteristic
438C2—82no—
439C2—162no—
440C2#1625×C15112yes—
441C2#1627×C15112yes—
442C2#2000×C15111yescharacteristic
443C2#2003×C15111yescharacteristic
444C2#2011×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#459×C151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#486×C151C2semidirect
3. #2542×C151C2semidirect
4. #1982×C151C2semidirect
5. C2×#332×C151C2semidirect
6. C2×D4⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
125. C4⋊C4×C151D8semidirect
222. #10052C151direct (N × H)
223. C151#10052direct (N × H)
224. C2×#486C2×C151semidirect
226. #2542C2×C151semidirect
227. #1982C2×C151semidirect
228. C2×#332C2×C151semidirect
229. C2×D4⋊C8C2×C151semidirect
230. #1279C2×C151semidirect
348. C4⋊C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#486×C1512
C2×#459×C1512
#2542×C1512
#1982×C1512
C2×#332×C1512
C2×D4⋊C8×C1512
#1279×C1512
#10052151