Finite Group Databasebeta

← C151×#10048 #50314973

Subgroups — C151×#10048 #50314973

Order 38656.

746 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C151C211yesmaximal, characteristic, complemented
2C2×#459×C151C211yesmaximal, characteristic
3#2563×C151C211yesmaximal, characteristic, complemented
4#1982×C151C211yesmaximal, characteristic, complemented
5C2×#333×C151C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C151C211yesmaximal, characteristic, complemented
7#1279×C151C211yesmaximal, characteristic, complemented
8C22×SD16×C151—22no—
9C22×D8×C151—21no—
10C2×C4⋊Q8×C151C2211yescharacteristic
11C2×#127×C151C2211yescharacteristic
12C2×C4×D4×C151C2211yescharacteristic
13#492×C151—22no—
14#492×C151—22no—
15#459×C151—22no—
16#459×C151—22no—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—21no—
20C2×#102×C151—22no—
21C2×C4×C8×C151C2211yescharacteristic
22#393×C151—22no—
23#390×C151—21no—
24#382×C151—21no—
25#380×C151—22no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#333×C151—22no—
28D4⋊C8×C151—22no—
29C22×Q8×C151D412yes—
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151D411yescharacteristic
34C23×C4×C151—21no—
35C2×SD16×C151—28no—
36C2×SD16×C151—48no—
37C2×D8×C151—24no—
38C2×D8×C151—42no—
39C2×D8×C151—42no—
40C22×C8×C151—21no—
41C22×C8×C151—21no—
42C22×C8×C151—21no—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—21no—
45C4⋊Q8×C151—21no—
46C4⋊Q8×C151—21no—
47#127×C151—21no—
48#127×C151—21no—
49#127×C151—21no—
50#127×C151D412yes—
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151D412yes—
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—24no—
61C2×C42×C151—21no—
62C2×C42×C151C2311yescharacteristic
63C4⋊C8×C151—21no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151D412yes—
67#102×C151—24no—
68#102×C151—44no—
69C4×C8×C151—21no—
70C4×C8×C151D412yes—
71#95×C151—24no—
72#95×C151—21no—
73C24×C151—21no—
74C24×C151—41no—
75C2×Q8×C151—22no—
76C2×Q8×C151—22no—
77C2×Q8×C151—44no—
78C2×D4×C151—21no—
79C2×D4×C151—22no—
80C2×D4×C151—22no—
81C2×D4×C151—21no—
82C2×D4×C151—22no—
83C2×D4×C151—21no—
84C2×D4×C151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—44no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—42no—
93C2×D4×C151—42no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151SD1612yescomplemented
97C22×C4×C151—21no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—41no—
101C22×C4×C151—41no—
102C22×C4×C151—42no—
103C22×C4×C151—42no—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D411yescharacteristic
106C22×C4×C151C2×D411yescharacteristic
107SD16×C151—416no—
108D8×C151—48no—
109C2×C8×C151—24no—
110C2×C8×C151—22no—
111C2×C8×C151—22no—
112C2×C8×C151—41no—
113C2×C8×C151—41no—
114C2×C8×C151—41no—
115C2×C8×C151—42no—
116C4⋊C4×C151—21no—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—41no—
121C4⋊C4×C151—41no—
122C4⋊C4×C151—41no—
123C4⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C22⋊C4×C151—41no—
126C22⋊C4×C151—84no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151C2×D411yescharacteristic
130C42×C151C2×D411yescharacteristic
131C42×C151C2×D411yescharacteristic
132C42×C151#4111yescharacteristic
133C23×C151—22no—
134C23×C151—41no—
135C23×C151—42no—
136C23×C151—41no—
137C23×C151—42no—
138C23×C151—42no—
139C23×C151—81no—
140C23×C151—81no—
141C23×C151—82no—
142C23×C151—82no—
143C23×C151#12011yescharacteristic
144Q8×C151—44no—
145Q8×C151—82no—
146D4×C151—22no—
147D4×C151—22no—
148D4×C151—44no—
149D4×C151—42no—
150D4×C151—41no—
151D4×C151—42no—
152D4×C151—44no—
153D4×C151—41no—
154D4×C151—82no—
155D4×C151—81no—
156D4×C151—81no—
157D4×C151—81no—
158D4×C151—81no—
159C2×C4×C151—22no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—44no—
166C2×C4×C151—42no—
167C2×C4×C151—82no—
168C2×C4×C151—81no—
169C2×C4×C151—81no—
170C2×C4×C151#12011yescharacteristic
171C2×C4×C151#12011yescharacteristic
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151#12111yescharacteristic
175C2×C4×C151#12711yescharacteristic
176C2×C4×C151C2×SD1611yescharacteristic
177C2×C4×C151#13511yescharacteristic
178C2×C4×C151#13512yes—
179C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C151AGL(1,ℤ/8)12yes—
181C2×C4×C151#13711yescharacteristic
182C8×C151—24no—
183C8×C151—42no—
184C8×C151—81no—
185C22×C151—44no—
186C22×C151—42no—
187C22×C151—82no—
188C22×C151—81no—
189C22×C151—81no—
190C22×C151—82no—
191C22×C151—82no—
192C22×C151—82no—
193C22×C151—162no—
194C22×C151—162no—
195C22×C151#39211yescharacteristic
196C22×C151#44811yescharacteristic
197C22×C151#44912yes—
198C22×C151#44911yescharacteristic
199C22×C151#45312yes—
200C4×C151—21no—
201C4×C151—21no—
202C4×C151—82no—
203C4×C151—82no—
204C4×C151—81no—
205C4×C151#45011yescharacteristic
206C4×C151#45211yescharacteristic
207C4×C151#46312yes—
208C4×C151#46511yescharacteristic
209C4×C151#46811yescharacteristic
210C4×C151#49511yescharacteristic
211C4×C151#49611yescharacteristic
212C2×C151—82no—
213C2×C151—162no—
214C2×C151#162212yes—
215C2×C151#162412yes—
216C2×C151#200011yescharacteristic
217C2×C151#200211yescharacteristic
218C2×C151#201211yescharacteristic
219#10048C15111yesmaximal, characteristic, direct product factor, Sylow
220C151#1004811yescharacteristic, direct product factor, Sylow
221C2×#492C2×C15111yescharacteristic, complemented
222C2×#459C2×C15111yescharacteristic
223#2563C2×C15111yescharacteristic, complemented
224#1982C2×C15111yescharacteristic, complemented
225C2×#333C2×C15111yescharacteristic, complemented
226C2×D4⋊C8C2×C15111yescharacteristic, complemented
227#1279C2×C15111yescharacteristic, complemented
228C22×SD16—22no—
229C22×D8—21no—
230C2×C4⋊Q8C22×C15111yescharacteristic
231C2×#127C22×C15111yescharacteristic
232C2×C4×D4C22×C15111yescharacteristic
233#492—22no—
234#492—22no—
235#459—22no—
236#459—22no—
237C2×C4⋊C8C22×C15111yescharacteristic
238C2×C4⋊C8C22×C15111yescharacteristic
239C2×#102—21no—
240C2×#102—22no—
241C2×C4×C8C22×C15111yescharacteristic
242#393—22no—
243#390—21no—
244#382—21no—
245#380—22no—
246C4×C4⋊C4C22×C15111yescharacteristic
247#333—22no—
248D4⋊C8—22no—
249C22×Q8D4×C15112yes—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4D4×C15111yescharacteristic
254C23×C4—21no—
255C2×SD16—28no—
256C2×SD16—48no—
257C2×D8—24no—
258C2×D8—42no—
259C2×D8—42no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267#127—21no—
268#127—21no—
269#127—21no—
270#127D4×C15112yes—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C15111yescharacteristic
278C2×C4⋊C4D4×C15112yes—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—24no—
281C2×C42—21no—
282C2×C42C23×C15111yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8D4×C15112yes—
287#102—24no—
288#102—44no—
289C4×C8—21no—
290C4×C8D4×C15112yes—
291#95—24no—
292#95—21no—
293C24—21no—
294C24—41no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—44no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—21no—
302C2×D4—22no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4SD16×C15112yescomplemented
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4C2×D4×C15111yescharacteristic
325C22×C4C2×D4×C15111yescharacteristic
326C22×C4C2×D4×C15111yescharacteristic
327SD16—416no—
328D8—48no—
329C2×C8—24no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—42no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—84no—
347C42—41no—
348C42—41no—
349C42C2×D4×C15111yescharacteristic
350C42C2×D4×C15111yescharacteristic
351C42C2×D4×C15111yescharacteristic
352C42#41×C15111yescharacteristic
353C23—22no—
354C23—41no—
355C23—42no—
356C23—41no—
357C23—42no—
358C23—42no—
359C23—81no—
360C23—81no—
361C23—82no—
362C23—82no—
363C23#120×C15111yescharacteristic
364Q8—44no—
365Q8—82no—
366D4—22no—
367D4—22no—
368D4—44no—
369D4—42no—
370D4—41no—
371D4—42no—
372D4—44no—
373D4—41no—
374D4—82no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4#120×C15111yescharacteristic
391C2×C4#120×C15111yescharacteristic
392C2×C4#121×C15111yescharacteristic
393C2×C4#121×C15111yescharacteristic
394C2×C4#121×C15111yescharacteristic
395C2×C4#127×C15111yescharacteristic
396C2×C4C2×SD16×C15111yescharacteristic
397C2×C4#135×C15111yescharacteristic
398C2×C4#135×C15112yes—
399C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
400C2×C4AGL(1,ℤ/8)×C15112yes—
401C2×C4#137×C15111yescharacteristic
402C8—24no—
403C8—42no—
404C8—81no—
405C22—44no—
406C22—42no—
407C22—82no—
408C22—81no—
409C22—81no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22#392×C15111yescharacteristic
416C22#448×C15111yescharacteristic
417C22#449×C15112yes—
418C22#449×C15111yescharacteristic
419C22#453×C15112yes—
420C4—21no—
421C4—21no—
422C4—82no—
423C4—82no—
424C4—81no—
425C4#450×C15111yescharacteristic
426C4#452×C15111yescharacteristic
427C4#463×C15112yes—
428C4#465×C15111yescharacteristic
429C4#468×C15111yescharacteristic
430C4#495×C15111yescharacteristic
431C4#496×C15111yescharacteristic
432C2—82no—
433C2—162no—
434C2#1622×C15112yes—
435C2#1624×C15112yes—
436C2#2000×C15111yescharacteristic
437C2#2002×C15111yescharacteristic
438C2#2012×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#459×C151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#492×C151C2semidirect
3. #2563×C151C2semidirect
4. #1982×C151C2semidirect
5. C2×#333×C151C2semidirect
6. C2×D4⋊C8×C151C2semidirect
7. #1279×C151C2semidirect
96. C2×D4×C151SD16semidirect
219. #10048C151direct (N × H)
220. C151#10048direct (N × H)
221. C2×#492C2×C151semidirect
223. #2563C2×C151semidirect
224. #1982C2×C151semidirect
225. C2×#333C2×C151semidirect
226. C2×D4⋊C8C2×C151semidirect
227. #1279C2×C151semidirect
316. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C1512
C2×#459×C1512
#2563×C1512
#1982×C1512
C2×#333×C1512
C2×D4⋊C8×C1512
#1279×C1512
#10048151