Finite Group Databasebeta

← C151×#10049 #50314974

Subgroups — C151×#10049 #50314974

Order 38656.

714 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C151C211yesmaximal, characteristic
2C2×#460×C151C211yesmaximal, characteristic
3#2567×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic
5C2×#333×C151C211yesmaximal, characteristic, complemented
6C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—22no—
9C22×SD16×C151—21no—
10C2×C4⋊Q8×C151C2211yescharacteristic
11C2×#127×C151C2211yescharacteristic
12C2×C4×Q8×C151C2211yescharacteristic
13#492×C151—22no—
14#492×C151—22no—
15#460×C151—22no—
16#460×C151—22no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—21no—
20C2×#102×C151—22no—
21C2×C4×C8×C151C2211yescharacteristic
22#395×C151—22no—
23#391×C151—21no—
24#389×C151—22no—
25#384×C151—21no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#333×C151—22no—
28Q8⋊C8×C151—22no—
29C22×Q8×C151D411yescharacteristic
30C22×Q8×C151D412yes—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C2×SD16×C151—24no—
35C2×SD16×C151—28no—
36C2×SD16×C151—42no—
37C2×SD16×C151—48no—
38C2×SD16×C151—42no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C22×C8×C151—21no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—21no—
45C4⋊Q8×C151—21no—
46#127×C151—21no—
47#127×C151—21no—
48#127×C151—21no—
49#127×C151D412yes—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×Q8×C151—21no—
53C4×Q8×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C4⋊C4×C151D412yes—
60C2×C42×C151—21no—
61C2×C42×C151—21no—
62C2×C42×C151C2311yescharacteristic
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151D412yes—
67#102×C151—24no—
68#102×C151—44no—
69C4×C8×C151—21no—
70C4×C8×C151D412yes—
71#95×C151—24no—
72#95×C151—21no—
73C24×C151—41no—
74C2×Q8×C151—21no—
75C2×Q8×C151—21no—
76C2×Q8×C151—22no—
77C2×Q8×C151—21no—
78C2×Q8×C151—22no—
79C2×Q8×C151—21no—
80C2×Q8×C151—21no—
81C2×Q8×C151—44no—
82C2×Q8×C151SD1612yescomplemented
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—42no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—42no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151C2×D411yescharacteristic
103SD16×C151—416no—
104SD16×C151—48no—
105C2×C8×C151—24no—
106C2×C8×C151—22no—
107C2×C8×C151—22no—
108C2×C8×C151—41no—
109C2×C8×C151—41no—
110C2×C8×C151—41no—
111C2×C8×C151—42no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—84no—
122C4⋊C4×C151SD1614yescomplemented
123C42×C151—41no—
124C42×C151—41no—
125C42×C151—41no—
126C42×C151—41no—
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151C2×D411yescharacteristic
130C42×C151#4111yescharacteristic
131C23×C151—42no—
132C23×C151—81no—
133C23×C151—82no—
134C23×C151—81no—
135C23×C151—82no—
136C23×C151#12011yescharacteristic
137Q8×C151—22no—
138Q8×C151—22no—
139Q8×C151—44no—
140Q8×C151—41no—
141Q8×C151—41no—
142Q8×C151—82no—
143D4×C151—44no—
144D4×C151—42no—
145D4×C151—42no—
146D4×C151—44no—
147D4×C151—82no—
148D4×C151—81no—
149D4×C151—81no—
150D4×C151—81no—
151D4×C151—81no—
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—24no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—42no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—41no—
161C2×C4×C151—44no—
162C2×C4×C151—42no—
163C2×C4×C151#12011yescharacteristic
164C2×C4×C151#12011yescharacteristic
165C2×C4×C151#12111yescharacteristic
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12111yescharacteristic
168C2×C4×C151#12711yescharacteristic
169C2×C4×C151C2×SD1611yescharacteristic
170C2×C4×C151C2×SD1612yes—
171C2×C4×C151#13511yescharacteristic
172C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C151#13711yescharacteristic
174C2×C4×C151#13712yes—
175C8×C151—24no—
176C8×C151—42no—
177C8×C151—81no—
178C22×C151—82no—
179C22×C151—82no—
180C22×C151—82no—
181C22×C151—162no—
182C22×C151—162no—
183C22×C151#39211yescharacteristic
184C22×C151#44812yes—
185C22×C151#44811yescharacteristic
186C22×C151#44911yescharacteristic
187C22×C151#45312yes—
188C4×C151—21no—
189C4×C151—21no—
190C4×C151—44no—
191C4×C151—42no—
192C4×C151—81no—
193C4×C151—82no—
194C4×C151#45011yescharacteristic
195C4×C151#45211yescharacteristic
196C4×C151#46112yes—
197C4×C151#46511yescharacteristic
198C4×C151#46811yescharacteristic
199C4×C151#49211yescharacteristic
200C4×C151#49711yescharacteristic
201C2×C151—162no—
202C2×C151#162212yes—
203C2×C151#162312yes—
204C2×C151#200011yescharacteristic
205C2×C151#200211yescharacteristic
206C2×C151#201311yescharacteristic
207#10049C15111yesmaximal, characteristic, direct product factor, Sylow
208C151#1004911yescharacteristic, direct product factor, Sylow
209C2×#492C2×C15111yescharacteristic
210C2×#460C2×C15111yescharacteristic
211#2567C2×C15111yescharacteristic, complemented
212#1982C2×C15111yescharacteristic
213C2×#333C2×C15111yescharacteristic, complemented
214C2×Q8⋊C8C2×C15111yescharacteristic, complemented
215#1279C2×C15111yescharacteristic, complemented
216C22×SD16—22no—
217C22×SD16—21no—
218C2×C4⋊Q8C22×C15111yescharacteristic
219C2×#127C22×C15111yescharacteristic
220C2×C4×Q8C22×C15111yescharacteristic
221#492—22no—
222#492—22no—
223#460—22no—
224#460—22no—
225C2×C4⋊C8C22×C15111yescharacteristic
226C2×C4⋊C8C22×C15111yescharacteristic
227C2×#102—21no—
228C2×#102—22no—
229C2×C4×C8C22×C15111yescharacteristic
230#395—22no—
231#391—21no—
232#389—22no—
233#384—21no—
234C4×C4⋊C4C22×C15111yescharacteristic
235#333—22no—
236Q8⋊C8—22no—
237C22×Q8D4×C15111yescharacteristic
238C22×Q8D4×C15112yes—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4—21no—
242C2×SD16—24no—
243C2×SD16—28no—
244C2×SD16—48no—
245C2×SD16—42no—
246C2×SD16—42no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254#127—21no—
255#127—21no—
256#127—21no—
257#127D4×C15112yes—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4D4×C15111yescharacteristic
267C2×C4⋊C4D4×C15112yes—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42C23×C15111yescharacteristic
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8D4×C15112yes—
275#102—24no—
276#102—44no—
277C4×C8—21no—
278C4×C8D4×C15112yes—
279#95—24no—
280#95—21no—
281C24—41no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—22no—
285C2×Q8—21no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—44no—
290C2×Q8SD16×C15112yescomplemented
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—44no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4C2×D4×C15111yescharacteristic
309C22×C4C2×D4×C15111yescharacteristic
310C22×C4C2×D4×C15111yescharacteristic
311SD16—416no—
312SD16—48no—
313C2×C8—24no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—42no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—84no—
330C4⋊C4SD16×C15114yescomplemented
331C42—41no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42C2×D4×C15111yescharacteristic
336C42C2×D4×C15111yescharacteristic
337C42C2×D4×C15111yescharacteristic
338C42#41×C15111yescharacteristic
339C23—42no—
340C23—81no—
341C23—82no—
342C23—81no—
343C23—82no—
344C23#120×C15111yescharacteristic
345Q8—22no—
346Q8—22no—
347Q8—44no—
348Q8—41no—
349Q8—41no—
350Q8—82no—
351D4—44no—
352D4—42no—
353D4—42no—
354D4—44no—
355D4—82no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4#120×C15111yescharacteristic
372C2×C4#120×C15111yescharacteristic
373C2×C4#121×C15111yescharacteristic
374C2×C4#121×C15111yescharacteristic
375C2×C4#121×C15111yescharacteristic
376C2×C4#127×C15111yescharacteristic
377C2×C4C2×SD16×C15111yescharacteristic
378C2×C4C2×SD16×C15112yes—
379C2×C4#135×C15111yescharacteristic
380C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
381C2×C4#137×C15111yescharacteristic
382C2×C4#137×C15112yes—
383C8—24no—
384C8—42no—
385C8—81no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22#392×C15111yescharacteristic
392C22#448×C15112yes—
393C22#448×C15111yescharacteristic
394C22#449×C15111yescharacteristic
395C22#453×C15112yes—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—42no—
400C4—82no—
401C4—81no—
402C4#450×C15111yescharacteristic
403C4#452×C15111yescharacteristic
404C4#461×C15112yes—
405C4#465×C15111yescharacteristic
406C4#468×C15111yescharacteristic
407C4#492×C15111yescharacteristic
408C4#497×C15111yescharacteristic
409C2—162no—
410C2#1622×C15112yes—
411C2#1623×C15112yes—
412C2#2000×C15111yescharacteristic
413C2#2002×C15111yescharacteristic
414C2#2013×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. #2567×C151C2semidirect
5. C2×#333×C151C2semidirect
6. C2×Q8⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
82. C2×Q8×C151SD16semidirect
122. C4⋊C4×C151SD16semidirect
207. #10049C151direct (N × H)
208. C151#10049direct (N × H)
211. #2567C2×C151semidirect
213. C2×#333C2×C151semidirect
214. C2×Q8⋊C8C2×C151semidirect
215. #1279C2×C151semidirect
290. C2×Q8SD16×C151semidirect
330. 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×#460×C1512
#2567×C1512
#1982×C1512
C2×#333×C1512
C2×Q8⋊C8×C1512
#1279×C1512
#10049151