Finite Group Databasebeta

← C151×#13338 #50318263

Subgroups — C151×#13338 #50318263

Order 38656.

566 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C151C211yesmaximal, characteristic, complemented
2C22×SD32×C151C211yesmaximal, characteristic, complemented
3#3155×C151C211yesmaximal, characteristic
4C2×#361×C151C211yesmaximal, characteristic, complemented
5C2×#359×C151C211yesmaximal, characteristic, complemented
6#1979×C151C211yesmaximal, characteristic, complemented
7#1379×C151C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C151—21no—
9C2×#135×C151C2211yescharacteristic
10C22×Q16×C151C2211yescharacteristic
11C22×D8×C151C2211yescharacteristic
12#535×C151—21no—
13#510×C151—22no—
14#510×C151—22no—
15C2×Q32×C151—21no—
16C2×SD32×C151—22no—
17C2×SD32×C151—22no—
18C2×SD32×C151—21no—
19C2×SD32×C151—22no—
20C2×M32×C151C2211yescharacteristic
21C22×C16×C151C2211yescharacteristic
22#496×C151—22no—
23#495×C151—21no—
24#493×C151—21no—
25C2×#108×C151C2211yescharacteristic
26#419×C151—21no—
27C2×#101×C151—21no—
28#405×C151C2211yescharacteristic
29#361×C151—22no—
30#359×C151—22no—
31C2×#41×C151—21no—
32C22×Q8×C151—21no—
33C22×D4×C151—21no—
34AGL(1,ℤ/8)×C151—42no—
35AGL(1,ℤ/8)×C151—42no—
36#135×C151—21no—
37#135×C151—21no—
38#135×C151—21no—
39#135×C151—21no—
40C2×Q16×C151—21no—
41C2×Q16×C151—21no—
42C2×Q16×C151—21no—
43C2×Q16×C151—21no—
44C2×Q16×C151—21no—
45C2×Q16×C151D411yescharacteristic
46C2×Q16×C151D412yescomplemented
47C2×SD16×C151—22no—
48C2×SD16×C151—21no—
49C2×D8×C151—22no—
50C2×D8×C151—21no—
51C2×D8×C151—21no—
52C2×D8×C151—21no—
53C2×D8×C151—21no—
54C2×D8×C151—21no—
55C2×D8×C151D411yescharacteristic
56C2×D8×C151D412yes—
57C2×M16×C151—21no—
58C2×M16×C151D411yescharacteristic
59C22×C8×C151C2311yescharacteristic
60#127×C151—22no—
61#124×C151—22no—
62#121×C151—42no—
63#120×C151—42no—
64#117×C151D411yescharacteristic
65Q32×C151—24no—
66SD32×C151—28no—
67SD32×C151—24no—
68M32×C151—21no—
69M32×C151D412yescomplemented
70C2×C16×C151—21no—
71C2×C16×C151—21no—
72C2×C16×C151—21no—
73C2×C16×C151D412yescomplemented
74#108×C151—21no—
75#108×C151—21no—
76#103×C151—42no—
77#101×C151—42no—
78#97×C151—21no—
79C4×C8×C151—21no—
80C24×C151—41no—
81#41×C151—41no—
82#41×C151—41no—
83#41×C151—41no—
84#41×C151—41no—
85C2×Q8×C151—21no—
86C2×Q8×C151—22no—
87C2×Q8×C151—41no—
88C2×Q8×C151—41no—
89C2×Q8×C151—41no—
90C2×Q8×C151—41no—
91C2×Q8×C151—41no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—44no—
95C2×D4×C151—41no—
96C2×D4×C151—41no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—41no—
100C2×D4×C151—41no—
101C22×C4×C151—41no—
102C22×C4×C151—41no—
103C22×C4×C151C2×D411yescharacteristic
104Q16×C151—22no—
105Q16×C151—22no—
106Q16×C151—21no—
107Q16×C151—21no—
108Q16×C151—41no—
109Q16×C151—41no—
110SD16×C151—44no—
111SD16×C151—41no—
112SD16×C151—41no—
113D8×C151—22no—
114D8×C151—21no—
115D8×C151—22no—
116D8×C151—21no—
117D8×C151—44no—
118D8×C151—41no—
119D8×C151—41no—
120M16×C151—21no—
121M16×C151—41no—
122M16×C151—41no—
123M16×C151D812yes—
124C2×C8×C151—21no—
125C2×C8×C151—41no—
126C2×C8×C151C2×D411yescharacteristic
127C2×C8×C151C2×D411yescharacteristic
128C2×C8×C151C2×D411yescharacteristic
129C2×C8×C151C2×D411yescharacteristic
130C2×C8×C151C2×D411yescharacteristic
131C2×C8×C151#4111yescharacteristic
132C4⋊C4×C151D812yes—
133C22⋊C4×C151—21no—
134C22⋊C4×C151—44no—
135C42×C151—21no—
136C16×C151—22no—
137C16×C151—22no—
138C23×C151—42no—
139C23×C151—41no—
140C23×C151—81no—
141C23×C151—81no—
142C23×C151—162no—
143C23×C151AGL(1,ℤ/8)11yescharacteristic
144Q8×C151—42no—
145Q8×C151—41no—
146Q8×C151—41no—
147Q8×C151—42no—
148Q8×C151—81no—
149Q8×C151—81no—
150D4×C151—41no—
151D4×C151—42no—
152D4×C151—41no—
153D4×C151—42no—
154D4×C151—81no—
155D4×C151—81no—
156D4×C151—81no—
157D4×C151—81no—
158D4×C151—164no—
159C2×C4×C151—22no—
160C2×C4×C151—41no—
161C2×C4×C151—42no—
162C2×C4×C151—81no—
163C2×C4×C151—81no—
164C2×C4×C151—81no—
165C2×C4×C151—81no—
166C2×C4×C151#12011yescharacteristic
167C2×C4×C151#12111yescharacteristic
168C2×C4×C151#12711yescharacteristic
169C2×C4×C151C2×D811yescharacteristic
170C2×C4×C151C2×D811yescharacteristic
171C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
172C8×C151—22no—
173C8×C151—81no—
174C8×C151#12011yescharacteristic
175C8×C151#12011yescharacteristic
176C8×C151#12111yescharacteristic
177C8×C151#12111yescharacteristic
178C22×C151—22no—
179C22×C151—82no—
180C22×C151—84no—
181C22×C151—81no—
182C22×C151—82no—
183C22×C151—162no—
184C22×C151—162no—
185C22×C151#44711yescharacteristic
186C22×C151#45911yescharacteristic
187C22×C151#49611yescharacteristic
188C4×C151—42no—
189C4×C151—81no—
190C4×C151—82no—
191C4×C151#39211yescharacteristic
192C4×C151#44711yescharacteristic
193C4×C151#45911yescharacteristic
194C4×C151#49311yescharacteristic
195C2×C151—21no—
196C2×C151—21no—
197C2×C151—161no—
198C2×C151—162no—
199C2×C151#201111yescharacteristic
200C2×C151#219412yes—
201#13338C15111yesmaximal, characteristic, direct product factor, Sylow
202C151#1333811yescharacteristic, direct product factor, Sylow
203C2×#510C2×C15111yescharacteristic, complemented
204C22×SD32C2×C15111yescharacteristic, complemented
205#3155C2×C15111yescharacteristic
206C2×#361C2×C15111yescharacteristic, complemented
207C2×#359C2×C15111yescharacteristic, complemented
208#1979C2×C15111yescharacteristic, complemented
209#1379C2×C15111yescharacteristic, complemented
210C2×AGL(1,ℤ/8)—21no—
211C2×#135C22×C15111yescharacteristic
212C22×Q16C22×C15111yescharacteristic
213C22×D8C22×C15111yescharacteristic
214#535—21no—
215#510—22no—
216#510—22no—
217C2×Q32—21no—
218C2×SD32—22no—
219C2×SD32—22no—
220C2×SD32—21no—
221C2×SD32—22no—
222C2×M32C22×C15111yescharacteristic
223C22×C16C22×C15111yescharacteristic
224#496—22no—
225#495—21no—
226#493—21no—
227C2×#108C22×C15111yescharacteristic
228#419—21no—
229C2×#101—21no—
230#405C22×C15111yescharacteristic
231#361—22no—
232#359—22no—
233C2×#41—21no—
234C22×Q8—21no—
235C22×D4—21no—
236AGL(1,ℤ/8)—42no—
237AGL(1,ℤ/8)—42no—
238#135—21no—
239#135—21no—
240#135—21no—
241#135—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16D4×C15111yescharacteristic
248C2×Q16D4×C15112yescomplemented
249C2×SD16—22no—
250C2×SD16—21no—
251C2×D8—22no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8D4×C15112yes—
258C2×D8D4×C15111yescharacteristic
259C2×M16—21no—
260C2×M16D4×C15111yescharacteristic
261C22×C8C23×C15111yescharacteristic
262#127—22no—
263#124—22no—
264#121—42no—
265#120—42no—
266#117D4×C15111yescharacteristic
267Q32—24no—
268SD32—28no—
269SD32—24no—
270M32—21no—
271M32D4×C15112yescomplemented
272C2×C16—21no—
273C2×C16—21no—
274C2×C16—21no—
275C2×C16D4×C15112yescomplemented
276#108—21no—
277#108—21no—
278#103—42no—
279#101—42no—
280#97—21no—
281C4×C8—21no—
282C24—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—44no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C2×D4×C15111yescharacteristic
306Q16—22no—
307Q16—22no—
308Q16—21no—
309Q16—21no—
310Q16—41no—
311Q16—41no—
312SD16—44no—
313SD16—41no—
314SD16—41no—
315D8—22no—
316D8—21no—
317D8—22no—
318D8—21no—
319D8—44no—
320D8—41no—
321D8—41no—
322M16—21no—
323M16—41no—
324M16—41no—
325M16D8×C15112yes—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8C2×D4×C15111yescharacteristic
329C2×C8C2×D4×C15111yescharacteristic
330C2×C8C2×D4×C15111yescharacteristic
331C2×C8C2×D4×C15111yescharacteristic
332C2×C8C2×D4×C15111yescharacteristic
333C2×C8#41×C15111yescharacteristic
334C4⋊C4D8×C15112yes—
335C22⋊C4—21no—
336C22⋊C4—44no—
337C42—21no—
338C16—22no—
339C16—22no—
340C23—42no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—162no—
345C23AGL(1,ℤ/8)×C15111yescharacteristic
346Q8—41no—
347Q8—42no—
348Q8—41no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—42no—
353D4—41no—
354D4—41no—
355D4—42no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—164no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4#120×C15111yescharacteristic
369C2×C4#121×C15111yescharacteristic
370C2×C4#127×C15111yescharacteristic
371C2×C4C2×D8×C15111yescharacteristic
372C2×C4C2×D8×C15111yescharacteristic
373C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
374C8—22no—
375C8—81no—
376C8#120×C15111yescharacteristic
377C8#120×C15111yescharacteristic
378C8#121×C15111yescharacteristic
379C8#121×C15111yescharacteristic
380C22—22no—
381C22—82no—
382C22—84no—
383C22—81no—
384C22—82no—
385C22—162no—
386C22—162no—
387C22#447×C15111yescharacteristic
388C22#459×C15111yescharacteristic
389C22#496×C15111yescharacteristic
390C4—42no—
391C4—81no—
392C4—82no—
393C4#392×C15111yescharacteristic
394C4#447×C15111yescharacteristic
395C4#459×C15111yescharacteristic
396C4#493×C15111yescharacteristic
397C2—21no—
398C2—21no—
399C2—162no—
400C2—161no—
401C2#2011×C15111yescharacteristic
402C2#2194×C15112yes—
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC22×C8C23×C151
prime radical#3155×C151C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#510×C151C2semidirect
2. C22×SD32×C151C2semidirect
4. C2×#361×C151C2semidirect
5. C2×#359×C151C2semidirect
6. #1979×C151C2semidirect
7. #1379×C151C2semidirect
46. C2×Q16×C151D4semidirect
69. M32×C151D4semidirect
73. C2×C16×C151D4semidirect
201. #13338C151direct (N × H)
202. C151#13338direct (N × H)
203. C2×#510C2×C151semidirect
204. C22×SD32C2×C151semidirect
206. C2×#361C2×C151semidirect
207. C2×#359C2×C151semidirect
208. #1979C2×C151semidirect
209. #1379C2×C151semidirect
248. C2×Q16D4×C151semidirect
271. M32D4×C151semidirect
275. C2×C16D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1512
C22×SD32×C1512
#3155×C1512
C2×#361×C1512
C2×#359×C1512
#1979×C1512
#1379×C1512
#13338151