Finite Group Databasebeta

← C151×#10476 #50315401

Subgroups — C151×#10476 #50315401

Order 38656.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic
2#1990×C151C211yesmaximal, characteristic, complemented
3#1954×C151C211yesmaximal, characteristic
4#1802×C151C211yesmaximal, characteristic
5C2×#335×C151C211yesmaximal, characteristic, complemented
6C2×#332×C151C211yesmaximal, characteristic, complemented
7#1296×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#461×C151—22no—
12#461×C151—22no—
13C2×C4⋊C8×C151C2211yescharacteristic
14C2×C4⋊C8×C151C2211yescharacteristic
15C2×C4⋊C8×C151C2211yescharacteristic
16C2×#103×C151—21no—
17C2×#102×C151—21no—
18C2×C22⋊C8×C151—21no—
19C2×C22⋊C8×C151—21no—
20C2×C4×C8×C151C2211yescharacteristic
21#384×C151C2211yescharacteristic
22#340×C151—21no—
23#340×C151—21no—
24#340×C151—21no—
25#335×C151—22no—
26#332×C151—22no—
27C22×Q8×C151—21no—
28C22×D4×C151D411yescharacteristic
29C23×C4×C151—21no—
30C2×SD16×C151—24no—
31C2×SD16×C151—42no—
32C2×SD16×C151—42no—
33C22×C8×C151—21no—
34C22×C8×C151—21no—
35C22×C8×C151—21no—
36C22×C8×C151D411yescharacteristic
37C22×C8×C151D411yescharacteristic
38C4⋊Q8×C151—21no—
39C4⋊Q8×C151—21no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151D412yes—
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151—21no—
45C4×D4×C151—21no—
46C2×C4⋊C4×C151—21no—
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×C22⋊C4×C151—21no—
53C2×C42×C151C2311yescharacteristic
54C4⋊C8×C151—21no—
55C4⋊C8×C151—21no—
56C4⋊C8×C151—21no—
57C4⋊C8×C151—21no—
58C4⋊C8×C151—21no—
59C4⋊C8×C151D412yes—
60#103×C151—24no—
61#102×C151—42no—
62C22⋊C8×C151—42no—
63C22⋊C8×C151—42no—
64C4×C8×C151—21no—
65C4×C8×C151—21no—
66C24×C151—21no—
67C2×Q8×C151—22no—
68C2×Q8×C151—41no—
69C2×Q8×C151—41no—
70C2×Q8×C151—41no—
71C2×Q8×C151—41no—
72C2×Q8×C151—41no—
73C2×D4×C151—21no—
74C2×D4×C151—21no—
75C2×D4×C151—21no—
76C2×D4×C151—21no—
77C2×D4×C151—21no—
78C2×D4×C151D812yes—
79C22×C4×C151—21no—
80C22×C4×C151—41no—
81C22×C4×C151—41no—
82C22×C4×C151—41no—
83C22×C4×C151—41no—
84C22×C4×C151—41no—
85C22×C4×C151—41no—
86C22×C4×C151—41no—
87C22×C4×C151—41no—
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90C22×C4×C151#4111yescharacteristic
91SD16×C151—48no—
92C2×C8×C151—21no—
93C2×C8×C151—21no—
94C2×C8×C151—22no—
95C2×C8×C151—21no—
96C2×C8×C151—21no—
97C2×C8×C151—21no—
98C2×C8×C151—41no—
99C2×C8×C151—41no—
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×C151SD1612yescomplemented
107C4⋊C4×C151—21no—
108C4⋊C4×C151—22no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—41no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—81no—
118C22⋊C4×C151—41no—
119C22⋊C4×C151—41no—
120C42×C151C2×D411yescharacteristic
121C42×C151C2×D411yescharacteristic
122C42×C151#4111yescharacteristic
123C42×C151#4111yescharacteristic
124C23×C151—22no—
125C23×C151—41no—
126C23×C151—41no—
127C23×C151—41no—
128C23×C151—41no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151#12111yescharacteristic
132Q8×C151—42no—
133Q8×C151—42no—
134Q8×C151—81no—
135Q8×C151—81no—
136D4×C151—22no—
137D4×C151—22no—
138D4×C151—41no—
139D4×C151—41no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—81no—
147C2×C4×C151—81no—
148C2×C4×C151—81no—
149C2×C4×C151—81no—
150C2×C4×C151—81no—
151C2×C4×C151—81no—
152C2×C4×C151—81no—
153C2×C4×C151—81no—
154C2×C4×C151—81no—
155C2×C4×C151#12011yescharacteristic
156C2×C4×C151#12111yescharacteristic
157C2×C4×C151#12111yescharacteristic
158C2×C4×C151#12311yescharacteristic
159C2×C4×C151#12311yescharacteristic
160C2×C4×C151#12411yescharacteristic
161C2×C4×C151C2×D811yescharacteristic
162C2×C4×C151C2×SD1611yescharacteristic
163C2×C4×C151#13511yescharacteristic
164C2×C4×C151#13511yescharacteristic
165C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C151#13711yescharacteristic
168C2×C4×C151#13711yescharacteristic
169C8×C151—22no—
170C8×C151—42no—
171C8×C151—41no—
172C8×C151—81no—
173C8×C151—81no—
174C22×C151—42no—
175C22×C151—42no—
176C22×C151—42no—
177C22×C151—81no—
178C22×C151—81no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151#39411yescharacteristic
182C22×C151#46111yescharacteristic
183C22×C151#46311yescharacteristic
184C22×C151#46611yescharacteristic
185C22×C151#46811yescharacteristic
186C22×C151#47111yescharacteristic
187C22×C151#47311yescharacteristic
188C4×C151—21no—
189C4×C151—21no—
190C4×C151—81no—
191C4×C151—82no—
192C4×C151—161no—
193C4×C151#44711yescharacteristic
194C4×C151#45211yescharacteristic
195C4×C151#46011yescharacteristic
196C4×C151#46411yescharacteristic
197C4×C151#46511yescharacteristic
198C4×C151#46811yescharacteristic
199C4×C151#48011yescharacteristic
200C4×C151#48211yescharacteristic
201C2×C151—82no—
202C2×C151#167311yescharacteristic
203C2×C151#168111yescharacteristic
204C2×C151#169111yescharacteristic
205C2×C151#169911yescharacteristic
206C2×C151#203311yescharacteristic
207C2×C151#205211yescharacteristic
208C2×C151#205511yescharacteristic
209#10476C15111yesmaximal, characteristic, direct product factor, Sylow
210C151#1047611yescharacteristic, direct product factor, Sylow
211C2×#461C2×C15111yescharacteristic
212#1990C2×C15111yescharacteristic, complemented
213#1954C2×C15111yescharacteristic
214#1802C2×C15111yescharacteristic
215C2×#335C2×C15111yescharacteristic, complemented
216C2×#332C2×C15111yescharacteristic, complemented
217#1296C2×C15111yescharacteristic, complemented
218C22×SD16—21no—
219C2×C4⋊Q8C22×C15111yescharacteristic
220C2×C4×D4C22×C15111yescharacteristic
221#461—22no—
222#461—22no—
223C2×C4⋊C8C22×C15111yescharacteristic
224C2×C4⋊C8C22×C15111yescharacteristic
225C2×C4⋊C8C22×C15111yescharacteristic
226C2×#103—21no—
227C2×#102—21no—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230C2×C4×C8C22×C15111yescharacteristic
231#384C22×C15111yescharacteristic
232#340—21no—
233#340—21no—
234#340—21no—
235#335—22no—
236#332—22no—
237C22×Q8—21no—
238C22×D4D4×C15111yescharacteristic
239C23×C4—21no—
240C2×SD16—24no—
241C2×SD16—42no—
242C2×SD16—42no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8D4×C15111yescharacteristic
247C22×C8D4×C15111yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D4×C15112yes—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C15111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C15111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C15112yes—
270#103—24no—
271#102—42no—
272C22⋊C8—42no—
273C22⋊C8—42no—
274C4×C8—21no—
275C4×C8—21no—
276C24—21no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4D8×C15112yes—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C15111yescharacteristic
299C22×C4C2×D4×C15111yescharacteristic
300C22×C4#41×C15111yescharacteristic
301SD16—48no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8SD16×C15112yescomplemented
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—81no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42C2×D4×C15111yescharacteristic
331C42C2×D4×C15111yescharacteristic
332C42#41×C15111yescharacteristic
333C42#41×C15111yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23#121×C15111yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—22no—
347D4—22no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4#120×C15111yescharacteristic
366C2×C4#121×C15111yescharacteristic
367C2×C4#121×C15111yescharacteristic
368C2×C4#123×C15111yescharacteristic
369C2×C4#123×C15111yescharacteristic
370C2×C4#124×C15111yescharacteristic
371C2×C4C2×D8×C15111yescharacteristic
372C2×C4C2×SD16×C15111yescharacteristic
373C2×C4#135×C15111yescharacteristic
374C2×C4#135×C15111yescharacteristic
375C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
376C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
377C2×C4#137×C15111yescharacteristic
378C2×C4#137×C15111yescharacteristic
379C8—22no—
380C8—42no—
381C8—41no—
382C8—81no—
383C8—81no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#394×C15111yescharacteristic
392C22#461×C15111yescharacteristic
393C22#463×C15111yescharacteristic
394C22#466×C15111yescharacteristic
395C22#468×C15111yescharacteristic
396C22#471×C15111yescharacteristic
397C22#473×C15111yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—81no—
402C4—161no—
403C4#447×C15111yescharacteristic
404C4#452×C15111yescharacteristic
405C4#460×C15111yescharacteristic
406C4#464×C15111yescharacteristic
407C4#465×C15111yescharacteristic
408C4#468×C15111yescharacteristic
409C4#480×C15111yescharacteristic
410C4#482×C15111yescharacteristic
411C2—82no—
412C2#1673×C15111yescharacteristic
413C2#1681×C15111yescharacteristic
414C2#1691×C15111yescharacteristic
415C2#1699×C15111yescharacteristic
416C2#2033×C15111yescharacteristic
417C2#2052×C15111yescharacteristic
418C2#2055×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#121
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
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
2. #1990×C151C2semidirect
5. C2×#335×C151C2semidirect
6. C2×#332×C151C2semidirect
7. #1296×C151C2semidirect
106. C2×C8×C151SD16semidirect
209. #10476C151direct (N × H)
210. C151#10476direct (N × H)
212. #1990C2×C151semidirect
215. C2×#335C2×C151semidirect
216. C2×#332C2×C151semidirect
217. #1296C2×C151semidirect
316. C2×C8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
#1990×C1512
#1954×C1512
#1802×C1512
C2×#335×C1512
C2×#332×C1512
#1296×C1512
#10476151