Finite Group Databasebeta

← C151×#9049 #50313974

Subgroups — C151×#9049 #50313974

Order 38656.

544 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
1#3100×C151C211yesmaximal, characteristic
2#2932×C151C211yesmaximal, characteristic, complemented
3#1955×C151C211yesmaximal, characteristic, complemented
4#1540×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic, complemented
6#1301×C151C211yesmaximal, characteristic, complemented
7#1281×C151C211yesmaximal, characteristic, complemented
8C2×#131×C151—21no—
9#532×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#480×C151C412yes—
12#474×C151—21no—
13#459×C151—21no—
14#447×C151C412yes—
15C4×D8×C151—22no—
16#435×C151—22no—
17#435×C151—22no—
18#431×C151C2211yescharacteristic
19#431×C151C2211yescharacteristic
20#423×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22#408×C151—21no—
23C2×C22⋊C8×C151—21no—
24C2×C22⋊C8×C151—21no—
25C2×#97×C151C2211yescharacteristic
26#332×C151—21no—
27#331×C151—21no—
28D4⋊C8×C151—22no—
29C2×#41×C151—21no—
30C22×D4×C151C2×C411yescharacteristic
31C23×C4×C151—21no—
32C2×D8×C151—22no—
33#131×C151—42no—
34#131×C151—42no—
35C2×M16×C151—22no—
36C2×M16×C151—21no—
37C22×C8×C151—22no—
38C22×C8×C151—21no—
39C22×C8×C151D411yescharacteristic
40C22×C8×C151D411yescharacteristic
41C4⋊Q8×C151D411yescharacteristic
42#127×C151D411yescharacteristic
43#124×C151—21no—
44#121×C151—21no—
45#121×C151C2×C412yes—
46C4×D4×C151—21no—
47C4×D4×C151—21no—
48C4×D4×C151—21no—
49C4×D4×C151—21no—
50C4×D4×C151—21no—
51C4×D4×C151D412yes—
52C2×C4⋊C4×C151C2×C411yescharacteristic
53C2×C22⋊C4×C151—21no—
54C2×C42×C151C2311yescharacteristic
55#107×C151—22no—
56C4⋊C8×C151—21no—
57C4⋊C8×C151—21no—
58C4⋊C8×C151—21no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151—21no—
61C4⋊C8×C151D412yes—
62#102×C151—22no—
63#102×C151—22no—
64C22⋊C8×C151—24no—
65C22⋊C8×C151—21no—
66C22⋊C8×C151—42no—
67C22⋊C8×C151—42no—
68C22⋊C8×C151C2×C412yes—
69#97×C151—21no—
70#97×C151—21no—
71C4×C8×C151—21no—
72C4×C8×C151—21no—
73C24×C151—21no—
74#41×C151—41no—
75#41×C151—41no—
76#41×C151—41no—
77#41×C151—41no—
78C2×Q8×C151—21no—
79C2×D4×C151—22no—
80C2×D4×C151—21no—
81C2×D4×C151—21no—
82C2×D4×C151—21no—
83C2×D4×C151—21no—
84C2×D4×C151—42no—
85C2×D4×C151C22⋊C412yes—
86C22×C4×C151—22no—
87C22×C4×C151—21no—
88C22×C4×C151—41no—
89C22×C4×C151—41no—
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
97D8×C151—44no—
98M16×C151—44no—
99M16×C151—41no—
100M16×C151—41no—
101C2×C8×C151—21no—
102C2×C8×C151—21no—
103C2×C8×C151—22no—
104C2×C8×C151—21no—
105C2×C8×C151—22no—
106C2×C8×C151—21no—
107C2×C8×C151—21no—
108C2×C8×C151—44no—
109C2×C8×C151—41no—
110C2×C8×C151—41no—
111C2×C8×C151—41no—
112C2×C8×C151—41no—
113C2×C8×C151D812yescomplemented
114C4⋊C4×C151—21no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151—21no—
117C4⋊C4×C151C22⋊C412yes—
118C22⋊C4×C151—22no—
119C22⋊C4×C151—22no—
120C22⋊C4×C151—41no—
121C22⋊C4×C151—41no—
122C42×C151C2×D411yescharacteristic
123C42×C151C2×D411yescharacteristic
124C42×C151C2×D411yescharacteristic
125C42×C151#4111yescharacteristic
126C23×C151—22no—
127C23×C151—22no—
128C23×C151—41no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151—41no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151C4×D411yescharacteristic
135Q8×C151—41no—
136Q8×C151—41no—
137D4×C151—22no—
138D4×C151—22no—
139D4×C151—42no—
140D4×C151—41no—
141D4×C151—41no—
142D4×C151—42no—
143D4×C151—42no—
144D4×C151—41no—
145D4×C151—41no—
146D4×C151—81no—
147C2×C4×C151—22no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—81no—
156C2×C4×C151—81no—
157C2×C4×C151—81no—
158C2×C4×C151—81no—
159C2×C4×C151C2×C22⋊C411yescharacteristic
160C2×C4×C151C4×D411yescharacteristic
161C2×C4×C151#12011yescharacteristic
162C2×C4×C151#12111yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12311yescharacteristic
165C2×C4×C151C2×D811yescharacteristic
166C2×C4×C151#13511yescharacteristic
167C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
169C8×C151—22no—
170C8×C151—42no—
171C8×C151—42no—
172C8×C151—41no—
173C8×C151—81no—
174C8×C151—81no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—42no—
178C22×C151—42no—
179C22×C151—42no—
180C22×C151—42no—
181C22×C151—42no—
182C22×C151—42no—
183C22×C151—81no—
184C22×C151—81no—
185C22×C151—81no—
186C22×C151—81no—
187C22×C151#38611yescharacteristic
188C22×C151C4×D811yescharacteristic
189C22×C151#44211yescharacteristic
190C4×C151—21no—
191C4×C151—21no—
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—42no—
195C4×C151—81no—
196C4×C151#44711yescharacteristic
197C4×C151#44911yescharacteristic
198C4×C151#45911yescharacteristic
199C4×C151#46311yescharacteristic
200C2×C151—21no—
201C2×C151—21no—
202C2×C151—82no—
203C2×C151—82no—
204C2×C151#187911yescharacteristic
205C2×C151#188111yescharacteristic
206C2×C151#189111yescharacteristic
207#9049C15111yesmaximal, characteristic, direct product factor, Sylow
208C151#904911yescharacteristic, direct product factor, Sylow
209#3100C2×C15111yescharacteristic
210#2932C2×C15111yescharacteristic, complemented
211#1955C2×C15111yescharacteristic, complemented
212#1540C2×C15111yescharacteristic, complemented
213#1486C2×C15111yescharacteristic, complemented
214#1301C2×C15111yescharacteristic, complemented
215#1281C2×C15111yescharacteristic, complemented
216C2×#131—21no—
217#532C22×C15111yescharacteristic
218C2×C4×D4C22×C15111yescharacteristic
219#480C4×C15112yes—
220#474—21no—
221#459—21no—
222#447C4×C15112yes—
223C4×D8—22no—
224#435—22no—
225#435—22no—
226#431C22×C15111yescharacteristic
227#431C22×C15111yescharacteristic
228#423C22×C15111yescharacteristic
229C2×C4⋊C8C22×C15111yescharacteristic
230#408—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8—21no—
233C2×#97C22×C15111yescharacteristic
234#332—21no—
235#331—21no—
236D4⋊C8—22no—
237C2×#41—21no—
238C22×D4C2×C4×C15111yescharacteristic
239C23×C4—21no—
240C2×D8—22no—
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C22×C8—22no—
246C22×C8—21no—
247C22×C8D4×C15111yescharacteristic
248C22×C8D4×C15111yescharacteristic
249C4⋊Q8D4×C15111yescharacteristic
250#127D4×C15111yescharacteristic
251#124—21no—
252#121—21no—
253#121C2×C4×C15112yes—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4D4×C15112yes—
260C2×C4⋊C4C2×C4×C15111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C23×C15111yescharacteristic
263#107—22no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C15112yes—
270#102—22no—
271#102—22no—
272C22⋊C8—24no—
273C22⋊C8—21no—
274C22⋊C8—42no—
275C22⋊C8—42no—
276C22⋊C8C2×C4×C15112yes—
277#97—21no—
278#97—21no—
279C4×C8—21no—
280C4×C8—21no—
281C24—21no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C2×D4C22⋊C4×C15112yes—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C22×C4×C15111yescharacteristic
303C22×C4C2×D4×C15111yescharacteristic
304C22×C4#41×C15111yescharacteristic
305D8—44no—
306M16—44no—
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—44no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8D8×C15112yescomplemented
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4C22⋊C4×C15112yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42C2×D4×C15111yescharacteristic
331C42C2×D4×C15111yescharacteristic
332C42C2×D4×C15111yescharacteristic
333C42#41×C15111yescharacteristic
334C23—22no—
335C23—22no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23C4×D4×C15111yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—22no—
346D4—22no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—81no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4C2×C22⋊C4×C15111yescharacteristic
368C2×C4C4×D4×C15111yescharacteristic
369C2×C4#120×C15111yescharacteristic
370C2×C4#121×C15111yescharacteristic
371C2×C4#121×C15111yescharacteristic
372C2×C4#123×C15111yescharacteristic
373C2×C4C2×D8×C15111yescharacteristic
374C2×C4#135×C15111yescharacteristic
375C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
376C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
377C8—22no—
378C8—42no—
379C8—42no—
380C8—41no—
381C8—81no—
382C8—81no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22#386×C15111yescharacteristic
396C22C4×D8×C15111yescharacteristic
397C22#442×C15111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4#447×C15111yescharacteristic
405C4#449×C15111yescharacteristic
406C4#459×C15111yescharacteristic
407C4#463×C15111yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—82no—
412C2#1879×C15111yescharacteristic
413C2#1881×C15111yescharacteristic
414C2#1891×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radical#3100×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2932×C151C2semidirect
3. #1955×C151C2semidirect
4. #1540×C151C2semidirect
5. #1486×C151C2semidirect
6. #1301×C151C2semidirect
7. #1281×C151C2semidirect
113. C2×C8×C151D8semidirect
207. #9049C151direct (N × H)
208. C151#9049direct (N × H)
210. #2932C2×C151semidirect
211. #1955C2×C151semidirect
212. #1540C2×C151semidirect
213. #1486C2×C151semidirect
214. #1301C2×C151semidirect
215. #1281C2×C151semidirect
321. C2×C8D8×C151semidirect

Maximal subgroups

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

subgroupindex
#3100×C1512
#2932×C1512
#1955×C1512
#1540×C1512
#1486×C1512
#1301×C1512
#1281×C1512
#9049151