Finite Group Databasebeta

← C151×#13318 #50318243

Subgroups — C151×#13318 #50318243

Order 38656.

532 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3414×C151C211yesmaximal, characteristic, complemented
2#3067×C151C211yesmaximal, characteristic, complemented
3#3060×C151C211yesmaximal, characteristic, complemented
4C2×#360×C151C211yesmaximal, characteristic, complemented
5#2143×C151C211yesmaximal, characteristic, complemented
6#2117×C151C211yesmaximal, characteristic, complemented
7#1383×C151C211yesmaximal, characteristic, complemented
8#575×C151—21no—
9C2×#135×C151C2211yescharacteristic
10C2×#135×C151C2211yescharacteristic
11C2×#131×C151C2211yescharacteristic
12#537×C151—21no—
13#510×C151—21no—
14#510×C151—21no—
15#509×C151—21no—
16#509×C151—21no—
17#508×C151—22no—
18C2×M32×C151C2211yescharacteristic
19C2×M32×C151C2211yescharacteristic
20#473×C151—21no—
21#472×C151—21no—
22#471×C151—22no—
23#470×C151—21no—
24#469×C151—21no—
25#465×C151—22no—
26C2×#108×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28#417×C151—21no—
29#413×C151—21no—
30#360×C151—22no—
31#359×C151—22no—
32#350×C151—22no—
33C2×#41×C151—21no—
34C2×#41×C151—21no—
35C2×#41×C151D411yescharacteristic
36#137×C151—22no—
37#137×C151—41no—
38AGL(1,ℤ/8)×C151—22no—
39AGL(1,ℤ/8)×C151—41no—
40#135×C151—21no—
41#135×C151—21no—
42#135×C151—21no—
43#135×C151—21no—
44#135×C151—21no—
45#135×C151—21no—
46#135×C151—21no—
47#135×C151—21no—
48#135×C151—42no—
49C2×Q16×C151D411yescharacteristic
50C2×Q16×C151D411yescharacteristic, complemented
51C2×SD16×C151—21no—
52C2×SD16×C151—21no—
53C2×D8×C151D411yescharacteristic
54C2×D8×C151D411yescharacteristic, complemented
55#131×C151—21no—
56#131×C151—21no—
57#131×C151—21no—
58#131×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151D411yescharacteristic
62C22×C8×C151—21no—
63C22×C8×C151C2311yescharacteristic
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—41no—
66#121×C151—22no—
67#121×C151—42no—
68#121×C151—41no—
69C2×C4⋊C4×C151—21no—
70Q32×C151—22no—
71SD32×C151—22no—
72SD32×C151—22no—
73D16×C151—22no—
74M32×C151—21no—
75M32×C151—21no—
76M32×C151—21no—
77M32×C151—21no—
78C2×C16×C151—21no—
79C2×C16×C151D412yescomplemented
80#108×C151—21no—
81#108×C151D412yescomplemented
82#106×C151—21no—
83#106×C151D412yes—
84#103×C151—22no—
85#102×C151—22no—
86#101×C151—22no—
87#100×C151—22no—
88#41×C151—21no—
89#41×C151—21no—
90#41×C151—21no—
91#41×C151—21no—
92#41×C151—41no—
93#41×C151—41no—
94#41×C151—41no—
95#41×C151—41no—
96#41×C151—41no—
97#41×C151—41no—
98#41×C151—41no—
99#41×C151—41no—
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151D811yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—42no—
109C2×D4×C151D811yescharacteristic
110C22×C4×C151—21no—
111C22×C4×C151—41no—
112C22×C4×C151—41no—
113C22×C4×C151—41no—
114C22×C4×C151C2×D411yescharacteristic
115Q16×C151—21no—
116Q16×C151—21no—
117Q16×C151—21no—
118Q16×C151—21no—
119Q16×C151—42no—
120SD16×C151—42no—
121SD16×C151—42no—
122SD16×C151—41no—
123SD16×C151—41no—
124SD16×C151—41no—
125SD16×C151—41no—
126D8×C151—21no—
127D8×C151—21no—
128D8×C151—21no—
129D8×C151—21no—
130D8×C151—42no—
131M16×C151—21no—
132M16×C151—22no—
133M16×C151—21no—
134M16×C151—41no—
135M16×C151—41no—
136M16×C151—41no—
137C2×C8×C151—21no—
138C2×C8×C151—41no—
139C2×C8×C151—41no—
140C2×C8×C151—41no—
141C2×C8×C151C2×D411yescharacteristic
142C2×C8×C151C2×D411yescharacteristic
143C2×C8×C151C2×D411yescharacteristic
144C2×C8×C151C2×D411yescharacteristic
145C2×C8×C151C2×D411yescharacteristic
146C2×C8×C151#4111yescharacteristic
147C4⋊C4×C151—22no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151—41no—
150C22⋊C4×C151—42no—
151C22⋊C4×C151—42no—
152C16×C151—22no—
153C16×C151—41no—
154C23×C151—21no—
155C23×C151—41no—
156C23×C151—41no—
157C23×C151AGL(1,ℤ/8)11yescharacteristic
158Q8×C151—21no—
159Q8×C151—21no—
160Q8×C151—41no—
161Q8×C151—41no—
162Q8×C151—41no—
163Q8×C151—41no—
164D4×C151—21no—
165D4×C151—21no—
166D4×C151—41no—
167D4×C151—41no—
168D4×C151—41no—
169D4×C151—41no—
170D4×C151—41no—
171D4×C151—41no—
172D4×C151—81no—
173D4×C151—81no—
174D4×C151—81no—
175D4×C151—81no—
176D4×C151—162no—
177C2×C4×C151—21no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—41no—
183C2×C4×C151—81no—
184C2×C4×C151—81no—
185C2×C4×C151—81no—
186C2×C4×C151—81no—
187C2×C4×C151—161no—
188C2×C4×C151#12011yescharacteristic
189C2×C4×C151#12011yescharacteristic
190C2×C4×C151#12111yescharacteristic
191C2×C4×C151C2×D811yescharacteristic
192C2×C4×C151#13511yescharacteristic
193C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
194C8×C151—41no—
195C8×C151—42no—
196C8×C151#12011yescharacteristic
197C8×C151#12111yescharacteristic
198C8×C151#12111yescharacteristic
199C8×C151#12711yescharacteristic
200C22×C151—41no—
201C22×C151—42no—
202C22×C151—41no—
203C22×C151—81no—
204C22×C151—81no—
205C22×C151—81no—
206C22×C151—81no—
207C22×C151—161no—
208C22×C151#44711yescharacteristic
209C22×C151#44911yescharacteristic
210C22×C151#46911yescharacteristic
211C4×C151—41no—
212C4×C151—82no—
213C4×C151—81no—
214C4×C151—81no—
215C4×C151#39211yescharacteristic
216C4×C151#44711yescharacteristic
217C4×C151#44911yescharacteristic
218C4×C151#46611yescharacteristic
219C2×C151—21no—
220C2×C151—21no—
221C2×C151—21no—
222C2×C151—81no—
223C2×C151—161no—
224C2×C151—161no—
225C2×C151#199911yescharacteristic
226#13318C15111yesmaximal, characteristic, direct product factor, Sylow
227C151#1331811yescharacteristic, direct product factor, Sylow
228#3414C2×C15111yescharacteristic, complemented
229#3067C2×C15111yescharacteristic, complemented
230#3060C2×C15111yescharacteristic, complemented
231C2×#360C2×C15111yescharacteristic, complemented
232#2143C2×C15111yescharacteristic, complemented
233#2117C2×C15111yescharacteristic, complemented
234#1383C2×C15111yescharacteristic, complemented
235#575—21no—
236C2×#135C22×C15111yescharacteristic
237C2×#135C22×C15111yescharacteristic
238C2×#131C22×C15111yescharacteristic
239#537—21no—
240#510—21no—
241#510—21no—
242#509—21no—
243#509—21no—
244#508—22no—
245C2×M32C22×C15111yescharacteristic
246C2×M32C22×C15111yescharacteristic
247#473—21no—
248#472—21no—
249#471—22no—
250#470—21no—
251#469—21no—
252#465—22no—
253C2×#108C22×C15111yescharacteristic
254C2×#106C22×C15111yescharacteristic
255#417—21no—
256#413—21no—
257#360—22no—
258#359—22no—
259#350—22no—
260C2×#41—21no—
261C2×#41—21no—
262C2×#41D4×C15111yescharacteristic
263#137—22no—
264#137—41no—
265AGL(1,ℤ/8)—22no—
266AGL(1,ℤ/8)—41no—
267#135—21no—
268#135—21no—
269#135—21no—
270#135—21no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—42no—
276C2×Q16D4×C15111yescharacteristic
277C2×Q16D4×C15111yescharacteristic, complemented
278C2×SD16—21no—
279C2×SD16—21no—
280C2×D8D4×C15111yescharacteristic
281C2×D8D4×C15111yescharacteristic, complemented
282#131—21no—
283#131—21no—
284#131—21no—
285#131—21no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16D4×C15111yescharacteristic
289C22×C8—21no—
290C22×C8C23×C15111yescharacteristic
291C22⋊Q8—22no—
292C22⋊Q8—41no—
293#121—22no—
294#121—42no—
295#121—41no—
296C2×C4⋊C4—21no—
297Q32—22no—
298SD32—22no—
299SD32—22no—
300D16—22no—
301M32—21no—
302M32—21no—
303M32—21no—
304M32—21no—
305C2×C16—21no—
306C2×C16D4×C15112yescomplemented
307#108—21no—
308#108D4×C15112yescomplemented
309#106—21no—
310#106D4×C15112yes—
311#103—22no—
312#102—22no—
313#101—22no—
314#100—22no—
315#41—21no—
316#41—21no—
317#41—21no—
318#41—21no—
319#41—41no—
320#41—41no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—41no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8D8×C15111yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4D8×C15111yescharacteristic
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4C2×D4×C15111yescharacteristic
342Q16—21no—
343Q16—21no—
344Q16—21no—
345Q16—21no—
346Q16—42no—
347SD16—42no—
348SD16—42no—
349SD16—41no—
350SD16—41no—
351SD16—41no—
352SD16—41no—
353D8—21no—
354D8—21no—
355D8—21no—
356D8—21no—
357D8—42no—
358M16—21no—
359M16—22no—
360M16—21no—
361M16—41no—
362M16—41no—
363M16—41no—
364C2×C8—21no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8C2×D4×C15111yescharacteristic
369C2×C8C2×D4×C15111yescharacteristic
370C2×C8C2×D4×C15111yescharacteristic
371C2×C8C2×D4×C15111yescharacteristic
372C2×C8C2×D4×C15111yescharacteristic
373C2×C8#41×C15111yescharacteristic
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C16—22no—
380C16—41no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23AGL(1,ℤ/8)×C15111yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—162no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—161no—
415C2×C4#120×C15111yescharacteristic
416C2×C4#120×C15111yescharacteristic
417C2×C4#121×C15111yescharacteristic
418C2×C4C2×D8×C15111yescharacteristic
419C2×C4#135×C15111yescharacteristic
420C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
421C8—41no—
422C8—42no—
423C8#120×C15111yescharacteristic
424C8#121×C15111yescharacteristic
425C8#121×C15111yescharacteristic
426C8#127×C15111yescharacteristic
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—161no—
435C22#447×C15111yescharacteristic
436C22#449×C15111yescharacteristic
437C22#469×C15111yescharacteristic
438C4—41no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4#392×C15111yescharacteristic
443C4#447×C15111yescharacteristic
444C4#449×C15111yescharacteristic
445C4#466×C15111yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—81no—
450C2—161no—
451C2—161no—
452C2#1999×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1999
commutator, Frattini, cosocleC22×C8C23×C151
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3414×C151C2semidirect
2. #3067×C151C2semidirect
3. #3060×C151C2semidirect
4. C2×#360×C151C2semidirect
5. #2143×C151C2semidirect
6. #2117×C151C2semidirect
7. #1383×C151C2semidirect
50. C2×Q16×C151D4semidirect
54. C2×D8×C151D4semidirect
79. C2×C16×C151D4semidirect
81. #108×C151D4semidirect
226. #13318C151direct (N × H)
227. C151#13318direct (N × H)
228. #3414C2×C151semidirect
229. #3067C2×C151semidirect
230. #3060C2×C151semidirect
231. C2×#360C2×C151semidirect
232. #2143C2×C151semidirect
233. #2117C2×C151semidirect
234. #1383C2×C151semidirect
277. C2×Q16D4×C151semidirect
281. C2×D8D4×C151semidirect
306. C2×C16D4×C151semidirect
308. #108D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3414×C1512
#3067×C1512
#3060×C1512
C2×#360×C1512
#2143×C1512
#2117×C1512
#1383×C1512
#13318151