Finite Group Databasebeta

← C151×#10051 #50314976

Subgroups — C151×#10051 #50314976

Order 38656.

670 conjugacy classes of subgroups.

The subgroup lattice has 428 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#2546×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×C151—21no—
10C2×C4⋊Q8×C151C2211yescharacteristic
11C2×#127×C151C2211yescharacteristic
12C2×C4×Q8×C151C2211yescharacteristic
13#486×C151—22no—
14#486×C151—22no—
15#460×C151—22no—
16#460×C151—22no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—22no—
20C2×#102×C151—21no—
21C2×#102×C151—22no—
22C2×C4×C8×C151C2211yescharacteristic
23#398×C151—22no—
24#391×C151—21no—
25#389×C151—22no—
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—
44C4⋊Q8×C151—42no—
45C4⋊Q8×C151—42no—
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—24no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D412yes—
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—28no—
69#102×C151—44no—
70C4×C8×C151—21no—
71C4×C8×C151D412yes—
72#95×C151—24no—
73#95×C151—21no—
74C24×C151—41no—
75C2×Q8×C151—21no—
76C2×Q8×C151—21no—
77C2×Q8×C151—21no—
78C2×Q8×C151—21no—
79C2×Q8×C151—21no—
80C2×Q8×C151—41no—
81C2×Q8×C151—41no—
82C2×Q8×C151—41no—
83C2×Q8×C151—41no—
84C2×Q8×C151—41no—
85C2×Q8×C151—41no—
86C2×Q8×C151D812yes—
87C2×D4×C151—22no—
88C2×D4×C151—22no—
89C2×D4×C151—22no—
90C2×D4×C151—44no—
91C2×D4×C151—41no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—42no—
96C2×D4×C151—41no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—42no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—22no—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D411yescharacteristic
106C22×C4×C151C2×D411yescharacteristic
107SD16×C151—48no—
108C2×C8×C151—22no—
109C2×C8×C151—22no—
110C2×C8×C151—42no—
111C2×C8×C151—41no—
112C2×C8×C151—41no—
113C2×C8×C151—41no—
114C2×C8×C151—42no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—21no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—21no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—48no—
121C4⋊C4×C151—41no—
122C4⋊C4×C151—41no—
123C4⋊C4×C151—41no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151SD1614yescomplemented
126C42×C151—41no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151—41no—
130C42×C151C2×D411yescharacteristic
131C42×C151C2×D411yescharacteristic
132C42×C151C2×D411yescharacteristic
133C42×C151#4111yescharacteristic
134C23×C151—42no—
135C23×C151—81no—
136C23×C151—82no—
137C23×C151—81no—
138C23×C151—82no—
139C23×C151#12011yescharacteristic
140Q8×C151—22no—
141Q8×C151—22no—
142Q8×C151—41no—
143Q8×C151—41no—
144Q8×C151—81no—
145Q8×C151—81no—
146Q8×C151—81no—
147Q8×C151—81no—
148D4×C151—44no—
149D4×C151—42no—
150D4×C151—42no—
151D4×C151—44no—
152D4×C151—82no—
153D4×C151—81no—
154D4×C151—81no—
155D4×C151—81no—
156D4×C151—81no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—24no—
160C2×C4×C151—41no—
161C2×C4×C151—42no—
162C2×C4×C151—41no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—41no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151#12011yescharacteristic
170C2×C4×C151#12011yescharacteristic
171C2×C4×C151#12111yescharacteristic
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151#12711yescharacteristic
175C2×C4×C151C2×D811yescharacteristic
176C2×C4×C151C2×SD1612yes—
177C2×C4×C151#13511yescharacteristic
178C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C151#13712yes—
181C8×C151—42no—
182C8×C151—42no—
183C8×C151—81no—
184C22×C151—82no—
185C22×C151—82no—
186C22×C151—82no—
187C22×C151—162no—
188C22×C151—162no—
189C22×C151#39211yescharacteristic
190C22×C151#44711yescharacteristic
191C22×C151#44812yes—
192C22×C151#44911yescharacteristic
193C22×C151#45412yes—
194C4×C151—21no—
195C4×C151—21no—
196C4×C151—44no—
197C4×C151—42no—
198C4×C151—82no—
199C4×C151—81no—
200C4×C151#44711yescharacteristic
201C4×C151#44911yescharacteristic
202C4×C151#46112yes—
203C4×C151#46611yescharacteristic
204C4×C151#46911yescharacteristic
205C4×C151#49211yescharacteristic
206C4×C151#49711yescharacteristic
207C2×C151—162no—
208C2×C151#162612yes—
209C2×C151#162712yes—
210C2×C151#199911yescharacteristic
211C2×C151#200311yescharacteristic
212C2×C151#201311yescharacteristic
213#10051C15111yesmaximal, characteristic, direct product factor, Sylow
214C151#1005111yescharacteristic, direct product factor, Sylow
215C2×#486C2×C15111yescharacteristic
216C2×#460C2×C15111yescharacteristic
217#2546C2×C15111yescharacteristic, complemented
218#1982C2×C15111yescharacteristic
219C2×#332C2×C15111yescharacteristic, complemented
220C2×Q8⋊C8C2×C15111yescharacteristic, complemented
221#1279C2×C15111yescharacteristic, complemented
222C22×SD16—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C22×C15111yescharacteristic
225C2×#127C22×C15111yescharacteristic
226C2×C4×Q8C22×C15111yescharacteristic
227#486—22no—
228#486—22no—
229#460—22no—
230#460—22no—
231C2×C4⋊C8C22×C15111yescharacteristic
232C2×C4⋊C8C22×C15111yescharacteristic
233C2×#102—22no—
234C2×#102—21no—
235C2×#102—22no—
236C2×C4×C8C22×C15111yescharacteristic
237#398—22no—
238#391—21no—
239#389—22no—
240C4×C4⋊C4C22×C15111yescharacteristic
241#332—22no—
242Q8⋊C8—22no—
243C22×Q8—21no—
244C22×Q8D4×C15111yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C2×SD16—24no—
249C2×SD16—42no—
250C2×SD16—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—42no—
259C4⋊Q8—42no—
260#127—21no—
261#127—21no—
262#127—21no—
263#127D4×C15112yes—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4D4×C15111yescharacteristic
272C2×C4⋊C4D4×C15112yes—
273C2×C4⋊C4D4×C15112yes—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42C23×C15111yescharacteristic
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8D4×C15112yes—
281#102—24no—
282#102—28no—
283#102—44no—
284C4×C8—21no—
285C4×C8D4×C15112yes—
286#95—24no—
287#95—21no—
288C24—41no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8D8×C15112yes—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—44no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4C2×D4×C15111yescharacteristic
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4C2×D4×C15111yescharacteristic
321SD16—48no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—42no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—42no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—48no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4SD16×C15114yescomplemented
340C42—41no—
341C42—41no—
342C42—41no—
343C42—41no—
344C42C2×D4×C15111yescharacteristic
345C42C2×D4×C15111yescharacteristic
346C42C2×D4×C15111yescharacteristic
347C42#41×C15111yescharacteristic
348C23—42no—
349C23—81no—
350C23—82no—
351C23—81no—
352C23—82no—
353C23#120×C15111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361Q8—81no—
362D4—44no—
363D4—42no—
364D4—42no—
365D4—44no—
366D4—82no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4#120×C15111yescharacteristic
384C2×C4#120×C15111yescharacteristic
385C2×C4#121×C15111yescharacteristic
386C2×C4#121×C15111yescharacteristic
387C2×C4#121×C15111yescharacteristic
388C2×C4#127×C15111yescharacteristic
389C2×C4C2×D8×C15111yescharacteristic
390C2×C4C2×SD16×C15112yes—
391C2×C4#135×C15111yescharacteristic
392C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
393C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
394C2×C4#137×C15112yes—
395C8—42no—
396C8—42no—
397C8—81no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—162no—
402C22—162no—
403C22#392×C15111yescharacteristic
404C22#447×C15111yescharacteristic
405C22#448×C15112yes—
406C22#449×C15111yescharacteristic
407C22#454×C15112yes—
408C4—21no—
409C4—21no—
410C4—44no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4#447×C15111yescharacteristic
415C4#449×C15111yescharacteristic
416C4#461×C15112yes—
417C4#466×C15111yescharacteristic
418C4#469×C15111yescharacteristic
419C4#492×C15111yescharacteristic
420C4#497×C15111yescharacteristic
421C2—162no—
422C2#1626×C15112yes—
423C2#1627×C15112yes—
424C2#1999×C15111yescharacteristic
425C2#2003×C15111yescharacteristic
426C2#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. #2546×C151C2semidirect
5. C2×#332×C151C2semidirect
6. C2×Q8⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
125. C4⋊C4×C151SD16semidirect
213. #10051C151direct (N × H)
214. C151#10051direct (N × H)
217. #2546C2×C151semidirect
219. C2×#332C2×C151semidirect
220. C2×Q8⋊C8C2×C151semidirect
221. #1279C2×C151semidirect
339. C4⋊C4SD16×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
#2546×C1512
#1982×C1512
C2×#332×C1512
C2×Q8⋊C8×C1512
#1279×C1512
#10051151