Finite Group Databasebeta

← C151×#10054 #50314979

Subgroups — C151×#10054 #50314979

Order 38656.

838 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic, complemented
3#2541×C151C211yesmaximal, characteristic
4#1987×C151C211yesmaximal, characteristic, complemented
5C2×#331×C151C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—22no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×#127×C151—21no—
11C2×#127×C151C2211yescharacteristic
12C2×#121×C151—22no—
13C2×C4×D4×C151C2211yescharacteristic
14#492×C151—22no—
15#492×C151—22no—
16#476×C151—22no—
17#476×C151—22no—
18C2×#106×C151—21no—
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C2×#102×C151—21no—
22C2×C4×C8×C151C2211yescharacteristic
23#392×C151—22no—
24#390×C151—21no—
25C4×C4⋊C4×C151C2211yescharacteristic
26#340×C151—22no—
27#331×C151—22no—
28D4⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×D4×C151—24no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151D411yescharacteristic
34C22×D4×C151D412yes—
35C23×C4×C151—21no—
36C2×SD16×C151—28no—
37C2×SD16×C151—48no—
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×C151D412yescomplemented
45#127×C151—21no—
46#127×C151—21no—
47#127×C151—21no—
48#127×C151—21no—
49#127×C151—42no—
50#127×C151—42no—
51#121×C151—44no—
52#121×C151—44no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C4×D4×C151—21no—
56C4×D4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151D411yescharacteristic
60C2×C4⋊C4×C151D412yes—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—21no—
63C2×C42×C151—21no—
64C2×C42×C151C2311yescharacteristic
65#106×C151—24no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68C4⋊C8×C151—21no—
69C4⋊C8×C151D412yescomplemented
70#102×C151—24no—
71C4×C8×C151—21no—
72C4×C8×C151D412yescomplemented
73#95×C151—21no—
74C24×C151—21no—
75C24×C151—22no—
76C2×Q8×C151—22no—
77C2×Q8×C151—44no—
78C2×Q8×C151—41no—
79C2×D4×C151—21no—
80C2×D4×C151—22no—
81C2×D4×C151—21no—
82C2×D4×C151—22no—
83C2×D4×C151—21no—
84C2×D4×C151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—44no—
87C2×D4×C151—48no—
88C2×D4×C151—48no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—42no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—42no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—84no—
100C2×D4×C151SD1612yescomplemented
101C22×C4×C151—22no—
102C22×C4×C151—21no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151—42no—
107C22×C4×C151—42no—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D411yescharacteristic
111SD16×C151—416no—
112C2×C8×C151—24no—
113C2×C8×C151—22no—
114C2×C8×C151—22no—
115C2×C8×C151—41no—
116C2×C8×C151—41no—
117C2×C8×C151—41no—
118C2×C8×C151—42no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151SD1614yescomplemented
127C22⋊C4×C151—48no—
128C22⋊C4×C151—41no—
129C22⋊C4×C151—41no—
130C42×C151—41no—
131C42×C151—41no—
132C42×C151C2×D411yescharacteristic
133C42×C151C2×D411yescharacteristic
134C42×C151C2×D411yescharacteristic
135C42×C151#4111yescharacteristic
136C23×C151—22no—
137C23×C151—41no—
138C23×C151—42no—
139C23×C151—41no—
140C23×C151—42no—
141C23×C151—42no—
142C23×C151—44no—
143C23×C151—42no—
144C23×C151—42no—
145C23×C151—44no—
146C23×C151#12011yescharacteristic
147Q8×C151—44no—
148Q8×C151—82no—
149D4×C151—22no—
150D4×C151—22no—
151D4×C151—44no—
152D4×C151—41no—
153D4×C151—41no—
154D4×C151—82no—
155D4×C151—816no—
156D4×C151—81no—
157D4×C151—81no—
158D4×C151—82no—
159D4×C151—81no—
160D4×C151—81no—
161D4×C151—81no—
162D4×C151—81no—
163C2×C4×C151—22no—
164C2×C4×C151—24no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—82no—
171C2×C4×C151—82no—
172C2×C4×C151—81no—
173C2×C4×C151—81no—
174C2×C4×C151#12011yescharacteristic
175C2×C4×C151#12011yescharacteristic
176C2×C4×C151#12111yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151#12111yescharacteristic
179C2×C4×C151#12711yescharacteristic
180C2×C4×C151C2×SD1611yescharacteristic
181C2×C4×C151C2×SD1612yes—
182C2×C4×C151#13511yescharacteristic
183C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C151AGL(1,ℤ/8)12yes—
185C2×C4×C151#13711yescharacteristic
186C8×C151—24no—
187C8×C151—42no—
188C8×C151—81no—
189C22×C151—44no—
190C22×C151—42no—
191C22×C151—82no—
192C22×C151—81no—
193C22×C151—81no—
194C22×C151—84no—
195C22×C151—84no—
196C22×C151—82no—
197C22×C151—82no—
198C22×C151—82no—
199C22×C151#39211yescharacteristic
200C22×C151#45011yescharacteristic
201C22×C151#45012yes—
202C22×C151#45211yescharacteristic
203C22×C151#45312yes—
204C4×C151—21no—
205C4×C151—21no—
206C4×C151—44no—
207C4×C151—82no—
208C4×C151—81no—
209C4×C151#44811yescharacteristic
210C4×C151#44911yescharacteristic
211C4×C151#46012yes—
212C4×C151#46511yescharacteristic
213C4×C151#46811yescharacteristic
214C4×C151#49211yescharacteristic
215C4×C151#49611yescharacteristic
216C2×C151—82no—
217C2×C151—162no—
218C2×C151#162912yes—
219C2×C151#163112yes—
220C2×C151#200011yescharacteristic
221C2×C151#200211yescharacteristic
222C2×C151#201411yescharacteristic
223#10054C15111yesmaximal, characteristic, direct product factor, Sylow
224C151#1005411yescharacteristic, direct product factor, Sylow
225C2×#492C2×C15111yescharacteristic, complemented
226C2×#476C2×C15111yescharacteristic, complemented
227#2541C2×C15111yescharacteristic
228#1987C2×C15111yescharacteristic, complemented
229C2×#331C2×C15111yescharacteristic, complemented
230C2×D4⋊C8C2×C15111yescharacteristic, complemented
231#1279C2×C15111yescharacteristic, complemented
232C22×SD16—22no—
233C2×C4⋊Q8C22×C15111yescharacteristic
234C2×#127—21no—
235C2×#127C22×C15111yescharacteristic
236C2×#121—22no—
237C2×C4×D4C22×C15111yescharacteristic
238#492—22no—
239#492—22no—
240#476—22no—
241#476—22no—
242C2×#106—21no—
243C2×C4⋊C8C22×C15111yescharacteristic
244C2×C4⋊C8C22×C15111yescharacteristic
245C2×#102—21no—
246C2×C4×C8C22×C15111yescharacteristic
247#392—22no—
248#390—21no—
249C4×C4⋊C4C22×C15111yescharacteristic
250#340—22no—
251#331—22no—
252D4⋊C8—22no—
253C22×Q8—21no—
254C22×D4—24no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4D4×C15111yescharacteristic
258C22×D4D4×C15112yes—
259C23×C4—21no—
260C2×SD16—28no—
261C2×SD16—48no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8D4×C15112yescomplemented
269#127—21no—
270#127—21no—
271#127—21no—
272#127—21no—
273#127—42no—
274#127—42no—
275#121—44no—
276#121—44no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4D4×C15111yescharacteristic
284C2×C4⋊C4D4×C15112yes—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—21no—
287C2×C42—21no—
288C2×C42C23×C15111yescharacteristic
289#106—24no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8D4×C15112yescomplemented
294#102—24no—
295C4×C8—21no—
296C4×C8D4×C15112yescomplemented
297#95—21no—
298C24—21no—
299C24—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—44no—
311C2×D4—48no—
312C2×D4—48no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—42no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—42no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—84no—
324C2×D4SD16×C15112yescomplemented
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4C2×D4×C15111yescharacteristic
333C22×C4C2×D4×C15111yescharacteristic
334C22×C4C2×D4×C15111yescharacteristic
335SD16—416no—
336C2×C8—24no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—42no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4SD16×C15114yescomplemented
351C22⋊C4—48no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—41no—
355C42—41no—
356C42C2×D4×C15111yescharacteristic
357C42C2×D4×C15111yescharacteristic
358C42C2×D4×C15111yescharacteristic
359C42#41×C15111yescharacteristic
360C23—22no—
361C23—41no—
362C23—42no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—44no—
370C23#120×C15111yescharacteristic
371Q8—44no—
372Q8—82no—
373D4—22no—
374D4—22no—
375D4—44no—
376D4—41no—
377D4—41no—
378D4—82no—
379D4—816no—
380D4—81no—
381D4—81no—
382D4—82no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4#120×C15111yescharacteristic
399C2×C4#120×C15111yescharacteristic
400C2×C4#121×C15111yescharacteristic
401C2×C4#121×C15111yescharacteristic
402C2×C4#121×C15111yescharacteristic
403C2×C4#127×C15111yescharacteristic
404C2×C4C2×SD16×C15111yescharacteristic
405C2×C4C2×SD16×C15112yes—
406C2×C4#135×C15111yescharacteristic
407C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
408C2×C4AGL(1,ℤ/8)×C15112yes—
409C2×C4#137×C15111yescharacteristic
410C8—24no—
411C8—42no—
412C8—81no—
413C22—44no—
414C22—42no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—84no—
419C22—84no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22#392×C15111yescharacteristic
424C22#450×C15111yescharacteristic
425C22#450×C15112yes—
426C22#452×C15111yescharacteristic
427C22#453×C15112yes—
428C4—21no—
429C4—21no—
430C4—44no—
431C4—82no—
432C4—81no—
433C4#448×C15111yescharacteristic
434C4#449×C15111yescharacteristic
435C4#460×C15112yes—
436C4#465×C15111yescharacteristic
437C4#468×C15111yescharacteristic
438C4#492×C15111yescharacteristic
439C4#496×C15111yescharacteristic
440C2—82no—
441C2—162no—
442C2#1629×C15112yes—
443C2#1631×C15112yes—
444C2#2000×C15111yescharacteristic
445C2#2002×C15111yescharacteristic
446C2#2014×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#2541×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×#492×C151C2semidirect
2. C2×#476×C151C2semidirect
4. #1987×C151C2semidirect
5. C2×#331×C151C2semidirect
6. C2×D4⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
44. C4⋊Q8×C151D4semidirect
69. C4⋊C8×C151D4semidirect
72. C4×C8×C151D4semidirect
100. C2×D4×C151SD16semidirect
126. C4⋊C4×C151SD16semidirect
223. #10054C151direct (N × H)
224. C151#10054direct (N × H)
225. C2×#492C2×C151semidirect
226. C2×#476C2×C151semidirect
228. #1987C2×C151semidirect
229. C2×#331C2×C151semidirect
230. C2×D4⋊C8C2×C151semidirect
231. #1279C2×C151semidirect
268. C4⋊Q8D4×C151semidirect
293. C4⋊C8D4×C151semidirect
296. C4×C8D4×C151semidirect
324. C2×D4SD16×C151semidirect
350. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1512
C2×#476×C1512
#2541×C1512
#1987×C1512
C2×#331×C1512
C2×D4⋊C8×C1512
#1279×C1512
#10054151