Finite Group Databasebeta

← C151×#13317 #50318242

Subgroups — C151×#13317 #50318242

Order 38656.

552 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
1C2×#510×C151C211yesmaximal, characteristic, complemented
2#3054×C151C211yesmaximal, characteristic
3C2×#470×C151C211yesmaximal, characteristic, complemented
4C2×#360×C151C211yesmaximal, characteristic, complemented
5#2141×C151C211yesmaximal, characteristic, complemented
6C2×#349×C151C211yesmaximal, characteristic, complemented
7#1386×C151C211yesmaximal, characteristic, complemented
8C2×#135×C151C2211yescharacteristic
9C22×Q16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11#525×C151—21no—
12C2×C22⋊Q8×C151—21no—
13#510×C151—22no—
14#510×C151—22no—
15C2×Q32×C151—21no—
16C2×SD32×C151—21no—
17C2×M32×C151C2211yescharacteristic
18C2×M32×C151C2211yescharacteristic
19#470×C151—21no—
20#470×C151—22no—
21#470×C151—22no—
22#469×C151—21no—
23#468×C151—22no—
24#427×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26#416×C151—21no—
27C2×#103×C151—21no—
28#360×C151—22no—
29#358×C151—22no—
30#349×C151—22no—
31C2×#41×C151—21no—
32C22×Q8×C151—21no—
33C23×C4×C151D411yescharacteristic
34#135×C151—21no—
35#135×C151—21no—
36#135×C151—21no—
37#135×C151—21no—
38C2×Q16×C151—21no—
39C2×Q16×C151—21no—
40C2×Q16×C151—21no—
41C2×Q16×C151—21no—
42C2×Q16×C151—21no—
43C2×Q16×C151D411yescharacteristic
44C2×Q16×C151D412yescomplemented
45C2×SD16×C151—21no—
46C2×D8×C151D411yescharacteristic
47C2×M16×C151—21no—
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C22×C8×C151D411yescharacteristic
54C22×C8×C151C2311yescharacteristic
55#123×C151—41no—
56C22⋊Q8×C151—22no—
57C22⋊Q8×C151—24no—
58C22⋊Q8×C151—42no—
59#121×C151—22no—
60#120×C151—41no—
61C4×D4×C151—42no—
62#117×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—41no—
65C2×C22⋊C4×C151—41no—
66Q32×C151—24no—
67SD32×C151—24no—
68M32×C151—21no—
69M32×C151—21no—
70M32×C151—21no—
71M32×C151D412yescomplemented
72C2×C16×C151—21no—
73C2×C16×C151—21no—
74#107×C151D412yes—
75#106×C151—21no—
76#106×C151—21no—
77#106×C151D412yescomplemented
78#103×C151—24no—
79#103×C151—22no—
80#102×C151—22no—
81C24×C151D811yescharacteristic
82#41×C151—41no—
83#41×C151—41no—
84#41×C151—41no—
85#41×C151—41no—
86C2×Q8×C151—21no—
87C2×Q8×C151—22no—
88C2×Q8×C151—41no—
89C2×Q8×C151—41no—
90C2×Q8×C151—41no—
91C2×Q8×C151—41no—
92C2×Q8×C151—41no—
93C2×D4×C151—21no—
94C2×D4×C151—42no—
95C2×D4×C151—41no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151D811yescharacteristic
106C22×C4×C151C2×D411yescharacteristic
107Q16×C151—22no—
108Q16×C151—21no—
109Q16×C151—22no—
110Q16×C151—21no—
111Q16×C151—41no—
112Q16×C151—41no—
113SD16×C151—41no—
114SD16×C151—41no—
115D8×C151—21no—
116D8×C151—21no—
117M16×C151—41no—
118M16×C151—41no—
119M16×C151—41no—
120M16×C151—41no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—21no—
124C2×C8×C151C2×D411yescharacteristic
125C2×C8×C151C2×D411yescharacteristic
126C2×C8×C151C2×D411yescharacteristic
127C2×C8×C151C2×D411yescharacteristic
128C2×C8×C151C2×D411yescharacteristic
129C2×C8×C151#4111yescharacteristic
130C4⋊C4×C151—22no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—44no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—41no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—44no—
137C22⋊C4×C151—42no—
138C22⋊C4×C151—41no—
139C42×C151—41no—
140C16×C151—22no—
141C16×C151—41no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—42no—
146C23×C151—41no—
147C23×C151C2×D811yescharacteristic
148Q8×C151—42no—
149Q8×C151—41no—
150Q8×C151—42no—
151Q8×C151—41no—
152Q8×C151—81no—
153Q8×C151—81no—
154D4×C151—41no—
155D4×C151—41no—
156D4×C151—84no—
157D4×C151—81no—
158D4×C151—81no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—82no—
171C2×C4×C151—81no—
172C2×C4×C151—81no—
173C2×C4×C151—81no—
174C2×C4×C151—81no—
175C2×C4×C151#12011yescharacteristic
176C2×C4×C151#12011yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151#13511yescharacteristic
179C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
181C8×C151—41no—
182C8×C151#12011yescharacteristic
183C8×C151#12111yescharacteristic
184C8×C151#12111yescharacteristic
185C8×C151#12711yescharacteristic
186C22×C151—22no—
187C22×C151—42no—
188C22×C151—42no—
189C22×C151—41no—
190C22×C151—81no—
191C22×C151—82no—
192C22×C151—81no—
193C22×C151#44711yescharacteristic
194C22×C151#44711yescharacteristic
195C22×C151#46611yescharacteristic
196C4×C151—41no—
197C4×C151—82no—
198C4×C151—82no—
199C4×C151—81no—
200C4×C151—82no—
201C4×C151#39211yescharacteristic
202C4×C151#44911yescharacteristic
203C4×C151#44911yescharacteristic
204C4×C151#46911yescharacteristic
205C2×C151—21no—
206C2×C151—21no—
207C2×C151—81no—
208C2×C151—161no—
209C2×C151#199911yescharacteristic
210C2×C151#219112yes—
211#13317C15111yesmaximal, characteristic, direct product factor, Sylow
212C151#1331711yescharacteristic, direct product factor, Sylow
213C2×#510C2×C15111yescharacteristic, complemented
214#3054C2×C15111yescharacteristic
215C2×#470C2×C15111yescharacteristic, complemented
216C2×#360C2×C15111yescharacteristic, complemented
217#2141C2×C15111yescharacteristic, complemented
218C2×#349C2×C15111yescharacteristic, complemented
219#1386C2×C15111yescharacteristic, complemented
220C2×#135C22×C15111yescharacteristic
221C22×Q16C22×C15111yescharacteristic
222C22×M16C22×C15111yescharacteristic
223#525—21no—
224C2×C22⋊Q8—21no—
225#510—22no—
226#510—22no—
227C2×Q32—21no—
228C2×SD32—21no—
229C2×M32C22×C15111yescharacteristic
230C2×M32C22×C15111yescharacteristic
231#470—21no—
232#470—22no—
233#470—22no—
234#469—21no—
235#468—22no—
236#427C22×C15111yescharacteristic
237C2×#106C22×C15111yescharacteristic
238#416—21no—
239C2×#103—21no—
240#360—22no—
241#358—22no—
242#349—22no—
243C2×#41—21no—
244C22×Q8—21no—
245C23×C4D4×C15111yescharacteristic
246#135—21no—
247#135—21no—
248#135—21no—
249#135—21no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—21no—
255C2×Q16D4×C15111yescharacteristic
256C2×Q16D4×C15112yescomplemented
257C2×SD16—21no—
258C2×D8D4×C15111yescharacteristic
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C22×C8D4×C15111yescharacteristic
266C22×C8C23×C15111yescharacteristic
267#123—41no—
268C22⋊Q8—24no—
269C22⋊Q8—22no—
270C22⋊Q8—42no—
271#121—22no—
272#120—41no—
273C4×D4—42no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—41no—
277C2×C22⋊C4—41no—
278Q32—24no—
279SD32—24no—
280M32—21no—
281M32—21no—
282M32—21no—
283M32D4×C15112yescomplemented
284C2×C16—21no—
285C2×C16—21no—
286#107D4×C15112yes—
287#106—21no—
288#106—21no—
289#106D4×C15112yescomplemented
290#103—24no—
291#103—22no—
292#102—22no—
293C24D8×C15111yescharacteristic
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×D4—21no—
306C2×D4—42no—
307C2×D4—41no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4D8×C15111yescharacteristic
318C22×C4C2×D4×C15111yescharacteristic
319Q16—22no—
320Q16—21no—
321Q16—22no—
322Q16—21no—
323Q16—41no—
324Q16—41no—
325SD16—41no—
326SD16—41no—
327D8—21no—
328D8—21no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—41no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8C2×D4×C15111yescharacteristic
337C2×C8C2×D4×C15111yescharacteristic
338C2×C8C2×D4×C15111yescharacteristic
339C2×C8C2×D4×C15111yescharacteristic
340C2×C8C2×D4×C15111yescharacteristic
341C2×C8#41×C15111yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—44no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C22⋊C4—42no—
348C22⋊C4—44no—
349C22⋊C4—42no—
350C22⋊C4—41no—
351C42—41no—
352C16—22no—
353C16—41no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—42no—
358C23—41no—
359C23C2×D8×C15111yescharacteristic
360Q8—41no—
361Q8—42no—
362Q8—42no—
363Q8—41no—
364Q8—81no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—84no—
369D4—81no—
370D4—81no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4#120×C15111yescharacteristic
388C2×C4#120×C15111yescharacteristic
389C2×C4#121×C15111yescharacteristic
390C2×C4#135×C15111yescharacteristic
391C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
392C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
393C8—41no—
394C8#120×C15111yescharacteristic
395C8#121×C15111yescharacteristic
396C8#121×C15111yescharacteristic
397C8#127×C15111yescharacteristic
398C22—22no—
399C22—42no—
400C22—42no—
401C22—41no—
402C22—81no—
403C22—82no—
404C22—81no—
405C22#447×C15111yescharacteristic
406C22#447×C15111yescharacteristic
407C22#466×C15111yescharacteristic
408C4—41no—
409C4—82no—
410C4—82no—
411C4—81no—
412C4—82no—
413C4#392×C15111yescharacteristic
414C4#449×C15111yescharacteristic
415C4#449×C15111yescharacteristic
416C4#469×C15111yescharacteristic
417C2—21no—
418C2—21no—
419C2—81no—
420C2—161no—
421C2#1999×C15111yescharacteristic
422C2#2191×C15112yes—
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC22×C8C23×C151
prime radical#3054×C151C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#510×C151C2semidirect
3. C2×#470×C151C2semidirect
4. C2×#360×C151C2semidirect
5. #2141×C151C2semidirect
6. C2×#349×C151C2semidirect
7. #1386×C151C2semidirect
44. C2×Q16×C151D4semidirect
71. M32×C151D4semidirect
77. #106×C151D4semidirect
211. #13317C151direct (N × H)
212. C151#13317direct (N × H)
213. C2×#510C2×C151semidirect
215. C2×#470C2×C151semidirect
216. C2×#360C2×C151semidirect
217. #2141C2×C151semidirect
218. C2×#349C2×C151semidirect
219. #1386C2×C151semidirect
256. C2×Q16D4×C151semidirect
283. M32D4×C151semidirect
289. #106D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1512
#3054×C1512
C2×#470×C1512
C2×#360×C1512
#2141×C1512
C2×#349×C1512
#1386×C1512
#13317151