Finite Group Databasebeta

← C151×#18683 #50323608

Subgroups — C151×#18683 #50323608

Order 38656.

1058 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543×C151C211yesmaximal, characteristic
2#3238×C151C212yesmaximal, complemented
3C2×#492×C151C211yesmaximal, characteristic, complemented
4#1631×C151C214yesmaximal, complemented
5#1630×C151C212yesmaximal, complemented
6#1629×C151C212yesmaximal, complemented
7#1555×C151C211yesmaximal, characteristic, complemented
8#1494×C151C212yesmaximal, complemented
9C22×SD16×C151—22no—
10#560×C151—22no—
11#559×C151C2211yescharacteristic
12#550×C151C2212yes—
13#546×C151—22no—
14D42×C151—22no—
15D42×C151C2211yescharacteristic
16#540×C151—22no—
17#535×C151—22no—
18#534×C151—22no—
19C2×C4⋊Q8×C151C2211yescharacteristic, complemented
20C2×#127×C151C2211yescharacteristic
21#529×C151C2212yes—
22#501×C151—22no—
23#492×C151—22no—
24#492×C151C2212yes—
25#492×C151C2212yescomplemented
26#489×C151—22no—
27#483×C151—22no—
28#480×C151—22no—
29#477×C151C2214yescomplemented
30#476×C151C2214yescomplemented
31#432×C151C2212yescomplemented
32C2×C4×C8×C151C2211yescharacteristic, complemented
33#331×C151C2212yes—
34#331×C151C2212yescomplemented
35Q8⋊C8×C151C2214yescomplemented
36D4⋊C8×C151C2214yescomplemented
37C2×#41×C151—22no—
38C22×Q8×C151—21no—
39C22×D4×C151—22no—
40C22×D4×C151—22no—
41C22×D4×C151—22no—
42C22×D4×C151D412yes—
43C2×SD16×C151—24no—
44C2×SD16×C151—24no—
45C2×SD16×C151—48no—
46C22×C8×C151—21no—
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151C2312yes—
50#127×C151—22no—
51#127×C151—22no—
52#127×C151D412yes—
53#127×C151C2311yescharacteristic
54#127×C151C2311yescharacteristic
55#126×C151—22no—
56#125×C151D412yes—
57#124×C151—22no—
58#124×C151D412yes—
59#123×C151—22no—
60#123×C151—24no—
61#123×C151—22no—
62#123×C151—22no—
63C22⋊Q8×C151D412yes—
64#121×C151—24no—
65#121×C151—24no—
66#121×C151—24no—
67#121×C151—24no—
68#121×C151—22no—
69#121×C151—22no—
70#121×C151D412yes—
71#120×C151—22no—
72#120×C151—24no—
73#120×C151—24no—
74#120×C151—22no—
75C4×Q8×C151C2312yes—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78C4×D4×C151—22no—
79C4×D4×C151C2312yes—
80#117×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C42×C151C2311yescharacteristic
84#107×C151—24no—
85#106×C151—24no—
86C4⋊C8×C151C2314yes—
87#103×C151—24no—
88#102×C151—24no—
89C22⋊C8×C151—22no—
90#97×C151—22no—
91C4×C8×C151—21no—
92C4×C8×C151C2312yes—
93C24×C151—22no—
94C24×C151—22no—
95#41×C151—84no—
96C2×Q8×C151—22no—
97C2×Q8×C151—44no—
98C2×Q8×C151—41no—
99C2×Q8×C151C2×D412yes—
100C2×D4×C151—22no—
101C2×D4×C151—24no—
102C2×D4×C151—24no—
103C2×D4×C151—24no—
104C2×D4×C151—22no—
105C2×D4×C151—24no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—44no—
109C2×D4×C151—84no—
110C2×D4×C151—84no—
111C2×D4×C151—84no—
112C2×D4×C151C2×D412yes—
113C2×D4×C151C2×D412yes—
114C2×D4×C151C2×D412yes—
115C22×C4×C151—24no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—41no—
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2×D411yescharacteristic
121SD16×C151—48no—
122SD16×C151—48no—
123C2×C8×C151—24no—
124C2×C8×C151—22no—
125C2×C8×C151—24no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—42no—
132C4⋊C4×C151C2×D412yes—
133C4⋊C4×C151C2×D412yes—
134C22⋊C4×C151—22no—
135C22⋊C4×C151—22no—
136C22⋊C4×C151—24no—
137C22⋊C4×C151—24no—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—22no—
141C22⋊C4×C151—22no—
142C22⋊C4×C151—22no—
143C42×C151—22no—
144C42×C151C2×D411yescharacteristic
145C42×C151C2×D412yes—
146C42×C151C2411yescharacteristic
147C23×C151—22no—
148C23×C151—22no—
149C23×C151—22no—
150C23×C151—44no—
151C23×C151—84no—
152C23×C151—84no—
153C23×C151—82no—
154C23×C151#12011yescharacteristic
155Q8×C151—24no—
156Q8×C151—44no—
157Q8×C151—82no—
158D4×C151—24no—
159D4×C151—42no—
160D4×C151—42no—
161D4×C151—44no—
162D4×C151—44no—
163D4×C151—44no—
164D4×C151—82no—
165D4×C151—84no—
166D4×C151—84no—
167D4×C151—84no—
168D4×C151—84no—
169C2×C4×C151—22no—
170C2×C4×C151—24no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—44no—
175C2×C4×C151—42no—
176C2×C4×C151—84no—
177C2×C4×C151—82no—
178C2×C4×C151—82no—
179C2×C4×C151#12011yescharacteristic
180C2×C4×C151#12012yes—
181C2×C4×C151C22×D411yescharacteristic
182C2×C4×C151C22×D412yes—
183C8×C151—24no—
184C8×C151—44no—
185C22×C151—22no—
186C22×C151—42no—
187C22×C151—44no—
188C22×C151—42no—
189C22×C151—44no—
190C22×C151—42no—
191C22×C151—42no—
192C22×C151—42no—
193C22×C151—164no—
194C22×C151—164no—
195C22×C151#45312yes—
196C22×C151C2×#12011yescharacteristic
197C4×C151—22no—
198C4×C151—21no—
199C4×C151—21no—
200C4×C151—42no—
201C4×C151—42no—
202C4×C151—42no—
203C4×C151—82no—
204C4×C151#57714yes—
205C2×C151—22no—
206C2×C151—82no—
207C2×C151—82no—
208C2×C151—82no—
209C2×C151#300912yes—
210C2×C151C2×#45311yescharacteristic
211#18683C15111yesmaximal, characteristic, direct product factor, Sylow
212C151#1868311yescharacteristic, direct product factor, Sylow
213#3543C2×C15111yescharacteristic
214#3238C2×C15112yescomplemented
215C2×#492C2×C15111yescharacteristic, complemented
216#1631C2×C15114yescomplemented
217#1630C2×C15112yescomplemented
218#1629C2×C15112yescomplemented
219#1555C2×C15111yescharacteristic, complemented
220#1494C2×C15112yescomplemented
221C22×SD16—22no—
222#560—22no—
223#559C22×C15111yescharacteristic
224#550C22×C15112yes—
225#546—22no—
226D42—22no—
227D42C22×C15111yescharacteristic
228#540—22no—
229#535—22no—
230#534—22no—
231C2×C4⋊Q8C22×C15111yescharacteristic, complemented
232C2×#127C22×C15111yescharacteristic
233#529C22×C15112yes—
234#501—22no—
235#492—22no—
236#492C22×C15112yes—
237#492C22×C15112yescomplemented
238#489—22no—
239#483—22no—
240#480—22no—
241#477C22×C15114yescomplemented
242#476C22×C15114yescomplemented
243#432C22×C15112yescomplemented
244C2×C4×C8C22×C15111yescharacteristic, complemented
245#331C22×C15112yes—
246#331C22×C15112yescomplemented
247Q8⋊C8C22×C15114yescomplemented
248D4⋊C8C22×C15114yescomplemented
249C2×#41—22no—
250C22×Q8—21no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4D4×C15112yes—
255C2×SD16—24no—
256C2×SD16—24no—
257C2×SD16—48no—
258C22×C8—21no—
259C4⋊Q8—22no—
260C4⋊Q8—21no—
261C4⋊Q8C23×C15112yes—
262#127—22no—
263#127—22no—
264#127D4×C15112yes—
265#127C23×C15111yescharacteristic
266#127C23×C15111yescharacteristic
267#126—22no—
268#125D4×C15112yes—
269#124—22no—
270#124D4×C15112yes—
271#123—22no—
272#123—24no—
273#123—22no—
274#123—22no—
275C22⋊Q8D4×C15112yes—
276#121—24no—
277#121—24no—
278#121—24no—
279#121—24no—
280#121—22no—
281#121—22no—
282#121D4×C15112yes—
283#120—22no—
284#120—24no—
285#120—24no—
286#120—22no—
287C4×Q8C23×C15112yes—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4C23×C15112yes—
292#117—22no—
293C2×C4⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C42C23×C15111yescharacteristic
296#107—24no—
297#106—24no—
298C4⋊C8C23×C15114yes—
299#103—24no—
300#102—24no—
301C22⋊C8—22no—
302#97—22no—
303C4×C8—21no—
304C4×C8C23×C15112yes—
305C24—22no—
306C24—22no—
307#41—84no—
308C2×Q8—22no—
309C2×Q8—44no—
310C2×Q8—41no—
311C2×Q8C2×D4×C15112yes—
312C2×D4—22no—
313C2×D4—24no—
314C2×D4—24no—
315C2×D4—24no—
316C2×D4—22no—
317C2×D4—24no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—44no—
321C2×D4—84no—
322C2×D4—84no—
323C2×D4—84no—
324C2×D4C2×D4×C15112yes—
325C2×D4C2×D4×C15112yes—
326C2×D4C2×D4×C15112yes—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4C2×D4×C15112yes—
332C22×C4C2×D4×C15111yescharacteristic
333SD16—48no—
334SD16—48no—
335C2×C8—24no—
336C2×C8—22no—
337C2×C8—24no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—42no—
344C4⋊C4C2×D4×C15112yes—
345C4⋊C4C2×D4×C15112yes—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C42—22no—
356C42C2×D4×C15111yescharacteristic
357C42C2×D4×C15112yes—
358C42C24×C15111yescharacteristic
359C23—22no—
360C23—22no—
361C23—22no—
362C23—44no—
363C23—84no—
364C23—84no—
365C23—82no—
366C23#120×C15111yescharacteristic
367Q8—24no—
368Q8—44no—
369Q8—82no—
370D4—24no—
371D4—42no—
372D4—42no—
373D4—44no—
374D4—44no—
375D4—44no—
376D4—82no—
377D4—84no—
378D4—84no—
379D4—84no—
380D4—84no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—44no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—84no—
390C2×C4—82no—
391C2×C4#120×C15112yes—
392C2×C4#120×C15111yescharacteristic
393C2×C4C22×D4×C15111yescharacteristic
394C2×C4C22×D4×C15112yes—
395C8—24no—
396C8—44no—
397C22—22no—
398C22—42no—
399C22—44no—
400C22—42no—
401C22—44no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—164no—
406C22—164no—
407C22#453×C15112yes—
408C22C2×#120×C15111yescharacteristic
409C4—22no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4#577×C15114yes—
417C2—22no—
418C2—82no—
419C2—82no—
420C2—82no—
421C2#3009×C15112yes—
422C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3543×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3238×C151C2semidirect
3. C2×#492×C151C2semidirect
4. #1631×C151C2semidirect
5. #1630×C151C2semidirect
6. #1629×C151C2semidirect
7. #1555×C151C2semidirect
8. #1494×C151C2semidirect
19. C2×C4⋊Q8×C151C22semidirect
25. #492×C151C22semidirect
29. #477×C151C22semidirect
30. #476×C151C22semidirect
31. #432×C151C22semidirect
32. C2×C4×C8×C151C22semidirect
34. #331×C151C22semidirect
35. Q8⋊C8×C151C22semidirect
36. D4⋊C8×C151C22semidirect
211. #18683C151direct (N × H)
212. C151#18683direct (N × H)
214. #3238C2×C151semidirect
215. C2×#492C2×C151semidirect
216. #1631C2×C151semidirect
217. #1630C2×C151semidirect
218. #1629C2×C151semidirect
219. #1555C2×C151semidirect
220. #1494C2×C151semidirect
231. C2×C4⋊Q8C22×C151semidirect
237. #492C22×C151semidirect
241. #477C22×C151semidirect
242. #476C22×C151semidirect
243. #432C22×C151semidirect
244. C2×C4×C8C22×C151semidirect
246. #331C22×C151semidirect
247. Q8⋊C8C22×C151semidirect
248. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3543×C1512
#3238×C1512
C2×#492×C1512
#1631×C1512
#1630×C1512
#1629×C1512
#1555×C1512
#1494×C1512
#18683151