Finite Group Databasebeta

← C151×#10053 #50314978

Subgroups — C151×#10053 #50314978

Order 38656.

634 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C151C211yesmaximal, characteristic
2C2×#460×C151C211yesmaximal, characteristic
3#2568×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic
5C2×#332×C151C211yesmaximal, characteristic, complemented
6C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×#127×C151C2211yescharacteristic
11C2×C4×Q8×C151C2211yescharacteristic
12#486×C151—22no—
13#486×C151—22no—
14#460×C151—22no—
15#460×C151—22no—
16C2×C4⋊C8×C151C2211yescharacteristic
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×#102×C151—22no—
19C2×#102×C151—21no—
20C2×#102×C151—22no—
21C2×C4×C8×C151C2211yescharacteristic
22#400×C151—22no—
23#391×C151—21no—
24#391×C151—22no—
25#382×C151—21no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#332×C151—22no—
28Q8⋊C8×C151—22no—
29C22×Q8×C151—21no—
30C22×Q8×C151D411yescharacteristic
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C2×SD16×C151—24no—
35C2×SD16×C151—42no—
36C2×SD16×C151—42no—
37C22×C8×C151—21no—
38C22×C8×C151—21no—
39C22×C8×C151—21no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151—21no—
44#127×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#127×C151D412yes—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151D412yes—
55C2×C4⋊C4×C151D411yescharacteristic
56C2×C4⋊C4×C151D412yes—
57C2×C42×C151—21no—
58C2×C42×C151—21no—
59C2×C42×C151C2311yescharacteristic
60C4⋊C8×C151—21no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151D412yes—
64#102×C151—24no—
65#102×C151—28no—
66#102×C151—44no—
67C4×C8×C151—21no—
68C4×C8×C151D412yes—
69#95×C151—24no—
70#95×C151—24no—
71#95×C151—21no—
72C24×C151—41no—
73C2×Q8×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—21no—
76C2×Q8×C151—21no—
77C2×Q8×C151—21no—
78C2×Q8×C151—41no—
79C2×Q8×C151—41no—
80C2×Q8×C151—42no—
81C2×Q8×C151—42no—
82C2×Q8×C151SD1612yes—
83C2×D4×C151—22no—
84C2×D4×C151—22no—
85C2×D4×C151—22no—
86C2×D4×C151—44no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—42no—
93C2×D4×C151—42no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151C2×D411yescharacteristic
103SD16×C151—48no—
104C2×C8×C151—22no—
105C2×C8×C151—22no—
106C2×C8×C151—42no—
107C2×C8×C151—41no—
108C2×C8×C151—41no—
109C2×C8×C151—41no—
110C2×C8×C151—42no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—22no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C42×C151—41no—
122C42×C151—41no—
123C42×C151—41no—
124C42×C151—41no—
125C42×C151C2×D411yescharacteristic
126C42×C151C2×D411yescharacteristic
127C42×C151C2×D411yescharacteristic
128C42×C151#4111yescharacteristic
129C23×C151—42no—
130C23×C151—81no—
131C23×C151—81no—
132C23×C151—82no—
133C23×C151—82no—
134C23×C151#12011yescharacteristic
135Q8×C151—22no—
136Q8×C151—22no—
137Q8×C151—41no—
138Q8×C151—41no—
139Q8×C151—82no—
140Q8×C151—81no—
141Q8×C151—81no—
142D4×C151—44no—
143D4×C151—42no—
144D4×C151—42no—
145D4×C151—44no—
146D4×C151—82no—
147D4×C151—81no—
148D4×C151—81no—
149D4×C151—81no—
150D4×C151—81no—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—44no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—42no—
162C2×C4×C151#12011yescharacteristic
163C2×C4×C151#12011yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12111yescharacteristic
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12711yescharacteristic
168C2×C4×C151C2×SD1611yescharacteristic
169C2×C4×C151#13511yescharacteristic
170C2×C4×C151#13512yes—
171C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C151AGL(1,ℤ/8)12yes—
173C2×C4×C151#13711yescharacteristic
174C8×C151—42no—
175C8×C151—42no—
176C8×C151—81no—
177C22×C151—82no—
178C22×C151—82no—
179C22×C151—82no—
180C22×C151—162no—
181C22×C151—162no—
182C22×C151#39211yescharacteristic
183C22×C151#44811yescharacteristic
184C22×C151#44912yes—
185C22×C151#44911yescharacteristic
186C22×C151#45412yes—
187C4×C151—21no—
188C4×C151—21no—
189C4×C151—42no—
190C4×C151—82no—
191C4×C151—81no—
192C4×C151—82no—
193C4×C151#45011yescharacteristic
194C4×C151#45211yescharacteristic
195C4×C151#46312yes—
196C4×C151#46511yescharacteristic
197C4×C151#46811yescharacteristic
198C4×C151#49511yescharacteristic
199C4×C151#49611yescharacteristic
200C2×C151—162no—
201C2×C151#162612yes—
202C2×C151#162812yes—
203C2×C151#200011yescharacteristic
204C2×C151#200311yescharacteristic
205C2×C151#201211yescharacteristic
206#10053C15111yesmaximal, characteristic, direct product factor, Sylow
207C151#1005311yescharacteristic, direct product factor, Sylow
208C2×#486C2×C15111yescharacteristic
209C2×#460C2×C15111yescharacteristic
210#2568C2×C15111yescharacteristic, complemented
211#1982C2×C15111yescharacteristic
212C2×#332C2×C15111yescharacteristic, complemented
213C2×Q8⋊C8C2×C15111yescharacteristic, complemented
214#1279C2×C15111yescharacteristic, complemented
215C22×SD16—21no—
216C2×C4⋊Q8C22×C15111yescharacteristic
217C2×#127C22×C15111yescharacteristic
218C2×C4×Q8C22×C15111yescharacteristic
219#486—22no—
220#486—22no—
221#460—22no—
222#460—22no—
223C2×C4⋊C8C22×C15111yescharacteristic
224C2×C4⋊C8C22×C15111yescharacteristic
225C2×#102—22no—
226C2×#102—21no—
227C2×#102—22no—
228C2×C4×C8C22×C15111yescharacteristic
229#400—22no—
230#391—21no—
231#391—22no—
232#382—21no—
233C4×C4⋊C4C22×C15111yescharacteristic
234#332—22no—
235Q8⋊C8—22no—
236C22×Q8—21no—
237C22×Q8D4×C15111yescharacteristic
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C2×SD16—24no—
242C2×SD16—42no—
243C2×SD16—42no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251#127—21no—
252#127—21no—
253#127—21no—
254#127D4×C15112yes—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C15111yescharacteristic
262C2×C4⋊C4D4×C15112yes—
263C2×C4⋊C4D4×C15112yes—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C23×C15111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C15112yes—
271#102—24no—
272#102—28no—
273#102—44no—
274C4×C8—21no—
275C4×C8D4×C15112yes—
276#95—24no—
277#95—24no—
278#95—21no—
279C24—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8SD16×C15112yes—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—44no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4C2×D4×C15111yescharacteristic
308C22×C4C2×D4×C15111yescharacteristic
309C22×C4C2×D4×C15111yescharacteristic
310SD16—48no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—42no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42C2×D4×C15111yescharacteristic
333C42C2×D4×C15111yescharacteristic
334C42C2×D4×C15111yescharacteristic
335C42#41×C15111yescharacteristic
336C23—42no—
337C23—81no—
338C23—81no—
339C23—82no—
340C23—82no—
341C23#120×C15111yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346Q8—82no—
347Q8—81no—
348Q8—81no—
349D4—44no—
350D4—42no—
351D4—42no—
352D4—44no—
353D4—82no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4#120×C15111yescharacteristic
370C2×C4#120×C15111yescharacteristic
371C2×C4#121×C15111yescharacteristic
372C2×C4#121×C15111yescharacteristic
373C2×C4#121×C15111yescharacteristic
374C2×C4#127×C15111yescharacteristic
375C2×C4C2×SD16×C15111yescharacteristic
376C2×C4#135×C15111yescharacteristic
377C2×C4#135×C15112yes—
378C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
379C2×C4AGL(1,ℤ/8)×C15112yes—
380C2×C4#137×C15111yescharacteristic
381C8—42no—
382C8—42no—
383C8—81no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22#392×C15111yescharacteristic
390C22#448×C15111yescharacteristic
391C22#449×C15112yes—
392C22#449×C15111yescharacteristic
393C22#454×C15112yes—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—82no—
398C4—81no—
399C4—82no—
400C4#450×C15111yescharacteristic
401C4#452×C15111yescharacteristic
402C4#463×C15112yes—
403C4#465×C15111yescharacteristic
404C4#468×C15111yescharacteristic
405C4#495×C15111yescharacteristic
406C4#496×C15111yescharacteristic
407C2—162no—
408C2#1626×C15112yes—
409C2#1628×C15112yes—
410C2#2000×C15111yescharacteristic
411C2#2003×C15111yescharacteristic
412C2#2012×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
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
3. #2568×C151C2semidirect
5. C2×#332×C151C2semidirect
6. C2×Q8⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
206. #10053C151direct (N × H)
207. C151#10053direct (N × H)
210. #2568C2×C151semidirect
212. C2×#332C2×C151semidirect
213. C2×Q8⋊C8C2×C151semidirect
214. #1279C2×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×#460×C1512
#2568×C1512
#1982×C1512
C2×#332×C1512
C2×Q8⋊C8×C1512
#1279×C1512
#10053151