Finite Group Databasebeta

← C151×#9249 #50314174

Subgroups — C151×#9249 #50314174

Order 38656.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C151C211yesmaximal, characteristic
2D4×M16×C151C211yesmaximal, characteristic
3#1997×C151C211yesmaximal, characteristic, complemented
4#1549×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic
6#1292×C151C211yesmaximal, characteristic, complemented
7#1283×C151C211yesmaximal, characteristic, complemented
8C22×M16×C151—21no—
9C2×C4⋊Q8×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#476×C151—21no—
12#476×C151—21no—
13#476×C151—21no—
14#476×C151—21no—
15#436×C151—21no—
16#435×C151—22no—
17C8×D4×C151—21no—
18#431×C151C2211yescharacteristic
19C2×#106×C151C412yes—
20#423×C151C2211yescharacteristic
21#423×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#102×C151C412yes—
24#407×C151—21no—
25C4×M16×C151C2211yescharacteristic
26#343×C151—21no—
27#343×C151—21no—
28#332×C151—22no—
29D4⋊C8×C151—21no—
30D4⋊C8×C151—21no—
31C22×Q8×C151—21no—
32C22×D4×C151C2×C411yescharacteristic
33C23×C4×C151—21no—
34C2×M16×C151—22no—
35C2×M16×C151—21no—
36C2×M16×C151—21no—
37C2×M16×C151—42no—
38C2×M16×C151—42no—
39C2×M16×C151D411yescharacteristic
40C2×M16×C151D411yescharacteristic
41C22×C8×C151—22no—
42C22×C8×C151C2×C412yes—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—21no—
45C4⋊Q8×C151—21no—
46C4⋊Q8×C151—21no—
47C4×D4×C151—21no—
48C4×D4×C151—21no—
49C4×D4×C151D411yescharacteristic
50C4×D4×C151D411yescharacteristic
51C4×D4×C151D411yescharacteristic
52C4×D4×C151D411yescharacteristic
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151C2×C412yes—
55C2×C4⋊C4×C151C2×C411yescharacteristic
56C2×C22⋊C4×C151—21no—
57C2×C42×C151C2311yescharacteristic
58#106×C151—22no—
59#106×C151—22no—
60C4⋊C8×C151—21no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151D412yes—
67#102×C151—22no—
68#102×C151—22no—
69C22⋊C8×C151—22no—
70C22⋊C8×C151—22no—
71C22⋊C8×C151—21no—
72#97×C151—21no—
73C4×C8×C151—21no—
74C4×C8×C151—21no—
75C24×C151—21no—
76C2×Q8×C151—41no—
77C2×Q8×C151—41no—
78C2×Q8×C151—82no—
79C2×D4×C151—22no—
80C2×D4×C151—21no—
81C2×D4×C151—41no—
82C2×D4×C151C22⋊C411yescharacteristic
83C2×D4×C151C22⋊C411yescharacteristic
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—22no—
90C22×C4×C151—41no—
91C22×C4×C151—41no—
92C22×C4×C151—41no—
93C22×C4×C151—41no—
94C22×C4×C151C22×C411yescharacteristic
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151#4111yescharacteristic
97M16×C151—21no—
98M16×C151—21no—
99M16×C151—21no—
100M16×C151—44no—
101M16×C151—41no—
102M16×C151—41no—
103M16×C151—41no—
104M16×C151—41no—
105M16×C151SD1612yes—
106C2×C8×C151—21no—
107C2×C8×C151—22no—
108C2×C8×C151—21no—
109C2×C8×C151—22no—
110C2×C8×C151—44no—
111C2×C8×C151—42no—
112C2×C8×C151—41no—
113C2×C8×C151—41no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151C22⋊C411yescharacteristic
120C4⋊C4×C151C22⋊C411yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C22⋊C4×C151—21no—
124C22⋊C4×C151—21no—
125C42×C151C2×D411yescharacteristic
126C42×C151C2×D411yescharacteristic
127C42×C151C2×D411yescharacteristic
128C42×C151#4111yescharacteristic
129C23×C151—21no—
130C23×C151—21no—
131C23×C151—42no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151—81no—
135C23×C151C4×D411yescharacteristic
136Q8×C151—82no—
137Q8×C151—82no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—42no—
142D4×C151#10112yes—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—41no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—42no—
159C2×C4×C151—82no—
160C2×C4×C151C2×C22⋊C411yescharacteristic
161C2×C4×C151C4×D411yescharacteristic
162C2×C4×C151#12011yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12311yescharacteristic
166C2×C4×C151C2×SD1611yescharacteristic
167C2×C4×C151#13511yescharacteristic
168C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C151#13711yescharacteristic
170C8×C151—22no—
171C8×C151—42no—
172C8×C151—42no—
173C8×C151—41no—
174C8×C151—81no—
175C8×C151—81no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—22no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—82no—
185C22×C151—82no—
186C22×C151#38611yescharacteristic
187C22×C151C4×SD1611yescharacteristic
188C22×C151#44011yescharacteristic
189C4×C151—21no—
190C4×C151—21no—
191C4×C151—21no—
192C4×C151—41no—
193C4×C151—41no—
194C4×C151—82no—
195C4×C151C2×#10111yescharacteristic
196C4×C151#41311yescharacteristic
197C4×C151#45011yescharacteristic
198C4×C151#45211yescharacteristic
199C4×C151#46111yescharacteristic
200C4×C151#46311yescharacteristic
201C2×C151—21no—
202C2×C151—21no—
203C2×C151—42no—
204C2×C151—81no—
205C2×C151#187711yescharacteristic
206C2×C151#190111yescharacteristic
207C2×C151#190311yescharacteristic
208#9249C15111yesmaximal, characteristic, direct product factor, Sylow
209C151#924911yescharacteristic, direct product factor, Sylow
210C2×#476C2×C15111yescharacteristic
211D4×M16C2×C15111yescharacteristic
212#1997C2×C15111yescharacteristic, complemented
213#1549C2×C15111yescharacteristic, complemented
214#1486C2×C15111yescharacteristic
215#1292C2×C15111yescharacteristic, complemented
216#1283C2×C15111yescharacteristic, complemented
217C22×M16—21no—
218C2×C4⋊Q8C22×C15111yescharacteristic
219C2×C4×D4C22×C15111yescharacteristic
220#476—21no—
221#476—21no—
222#476—21no—
223#476—21no—
224#436—21no—
225#435—22no—
226C8×D4—21no—
227#431C22×C15111yescharacteristic
228C2×#106C4×C15112yes—
229#423C22×C15111yescharacteristic
230#423C22×C15111yescharacteristic
231C2×C4⋊C8C22×C15111yescharacteristic
232C2×#102C4×C15112yes—
233#407—21no—
234C4×M16C22×C15111yescharacteristic
235#343—21no—
236#343—21no—
237#332—22no—
238D4⋊C8—21no—
239D4⋊C8—21no—
240C22×Q8—21no—
241C22×D4C2×C4×C15111yescharacteristic
242C23×C4—21no—
243C2×M16—22no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—42no—
247C2×M16—42no—
248C2×M16D4×C15111yescharacteristic
249C2×M16D4×C15111yescharacteristic
250C22×C8—22no—
251C22×C8C2×C4×C15112yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4D4×C15111yescharacteristic
259C4×D4D4×C15111yescharacteristic
260C4×D4D4×C15111yescharacteristic
261C4×D4D4×C15111yescharacteristic
262C2×C4⋊C4—21no—
263C2×C4⋊C4C2×C4×C15112yes—
264C2×C4⋊C4C2×C4×C15111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C23×C15111yescharacteristic
267#106—22no—
268#106—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8D4×C15112yes—
276#102—22no—
277#102—22no—
278C22⋊C8—22no—
279C22⋊C8—22no—
280C22⋊C8—21no—
281#97—21no—
282C4×C8—21no—
283C4×C8—21no—
284C24—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4C22⋊C4×C15111yescharacteristic
292C2×D4C22⋊C4×C15111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C22×C4×C15111yescharacteristic
304C22×C4C2×D4×C15111yescharacteristic
305C22×C4#41×C15111yescharacteristic
306M16—21no—
307M16—21no—
308M16—21no—
309M16—44no—
310M16—41no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16SD16×C15112yes—
315C2×C8—21no—
316C2×C8—22no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—44no—
320C2×C8—42no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C22⋊C4×C15111yescharacteristic
329C4⋊C4C22⋊C4×C15111yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C42C2×D4×C15111yescharacteristic
335C42C2×D4×C15111yescharacteristic
336C42C2×D4×C15111yescharacteristic
337C42#41×C15111yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—41no—
342C23—41no—
343C23—81no—
344C23C4×D4×C15111yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4#101×C15112yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4C2×C22⋊C4×C15111yescharacteristic
370C2×C4C4×D4×C15111yescharacteristic
371C2×C4#120×C15111yescharacteristic
372C2×C4#121×C15111yescharacteristic
373C2×C4#121×C15111yescharacteristic
374C2×C4#123×C15111yescharacteristic
375C2×C4C2×SD16×C15111yescharacteristic
376C2×C4#135×C15111yescharacteristic
377C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
378C2×C4#137×C15111yescharacteristic
379C8—22no—
380C8—42no—
381C8—42no—
382C8—41no—
383C8—81no—
384C8—81no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—82no—
394C22—82no—
395C22#386×C15111yescharacteristic
396C22C4×SD16×C15111yescharacteristic
397C22#440×C15111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—82no—
404C4C2×#101×C15111yescharacteristic
405C4#413×C15111yescharacteristic
406C4#450×C15111yescharacteristic
407C4#452×C15111yescharacteristic
408C4#461×C15111yescharacteristic
409C4#463×C15111yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—81no—
414C2#1877×C15111yescharacteristic
415C2#1901×C15111yescharacteristic
416C2#1903×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1997×C151C2semidirect
4. #1549×C151C2semidirect
6. #1292×C151C2semidirect
7. #1283×C151C2semidirect
208. #9249C151direct (N × H)
209. C151#9249direct (N × H)
212. #1997C2×C151semidirect
213. #1549C2×C151semidirect
215. #1292C2×C151semidirect
216. #1283C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1512
D4×M16×C1512
#1997×C1512
#1549×C1512
#1486×C1512
#1292×C1512
#1283×C1512
#9249151