Finite Group Databasebeta

← C151×#9096 #50314021

Subgroups — C151×#9096 #50314021

Order 38656.

514 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C151C211yesmaximal, characteristic
2C4×#137×C151C211yesmaximal, characteristic
3#1477×C151C211yesmaximal, characteristic
4C2×Q8⋊C8×C151C211yesmaximal, characteristic, complemented
5#1461×C151C211yesmaximal, characteristic, complemented
6#1283×C151C211yesmaximal, characteristic, complemented
7#1278×C151C211yesmaximal, characteristic, complemented
8C2×#137×C151C411yescharacteristic
9C4×#41×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11C8×Q8×C151—21no—
12#441×C151—21no—
13#440×C151—21no—
14C4×Q16×C151—21no—
15C4×SD16×C151—21no—
16C8×D4×C151—21no—
17C8×D4×C151—22no—
18#431×C151—21no—
19#431×C151C2211yescharacteristic
20#431×C151C2211yescharacteristic
21#428×C151C411yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23#419×C151C411yescharacteristic
24#417×C151C411yescharacteristic
25C4×M16×C151C2211yescharacteristic
26C2×C4×C8×C151—21no—
27C2×C4×C8×C151C2211yescharacteristic
28Q8⋊C8×C151—21no—
29Q8⋊C8×C151—21no—
30Q8⋊C8×C151—21no—
31D4⋊C8×C151—21no—
32#324×C151—22no—
33C2×#41×C151C2×C411yescharacteristic
34C22×Q8×C151C2×C411yescharacteristic
35#137×C151—22no—
36#137×C151C814yescomplemented
37C2×Q16×C151—21no—
38C2×SD16×C151—21no—
39C2×M16×C151C2×C411yescharacteristic
40C2×M16×C151C2×C411yescharacteristic
41C22×C8×C151—22no—
42C22×C8×C151—21no—
43C22×C8×C151—21no—
44C4×Q8×C151—21no—
45C4×Q8×C151—21no—
46C4×Q8×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151D411yescharacteristic
49C4×Q8×C151D411yescharacteristic
50C4×D4×C151—21no—
51C4×D4×C151—21no—
52C4×D4×C151D411yescharacteristic
53C4×D4×C151D411yescharacteristic
54#117×C151—21no—
55#117×C151C2×C411yescharacteristic
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151C2×C411yescharacteristic
58C2×C42×C151—21no—
59C2×C42×C151—21no—
60C2×C42×C151C2311yescharacteristic
61#107×C151—21no—
62#106×C151—21no—
63C4⋊C8×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68#103×C151—21no—
69#103×C151—21no—
70#103×C151—21no—
71#102×C151—21no—
72C22⋊C8×C151—22no—
73C22⋊C8×C151—21no—
74C22⋊C8×C151D412yes—
75#97×C151—21no—
76C4×C8×C151—22no—
77C4×C8×C151—21no—
78C4×C8×C151—21no—
79C4×C8×C151—21no—
80C4×C8×C151—21no—
81C4×C8×C151D411yescharacteristic
82C4×C8×C151D411yescharacteristic
83#41×C151—21no—
84#41×C151—21no—
85#41×C151C2×C812yes—
86#41×C151M1612yes—
87C2×Q8×C151—21no—
88C2×Q8×C151—21no—
89C2×Q8×C151—21no—
90C2×Q8×C151—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151C22⋊C411yescharacteristic
93C2×Q8×C151C2×C812yescomplemented
94C2×D4×C151—21no—
95C2×D4×C151C22⋊C411yescharacteristic
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151C22×C411yescharacteristic
102C22×C4×C151C2×D411yescharacteristic
103C22×C4×C151#4111yescharacteristic
104Q16×C151—24no—
105SD16×C151—24no—
106M16×C151—21no—
107M16×C151—21no—
108M16×C151—21no—
109M16×C151C2×C812yescomplemented
110C2×C8×C151—21no—
111C2×C8×C151—21no—
112C2×C8×C151—21no—
113C2×C8×C151—22no—
114C2×C8×C151—21no—
115C2×C8×C151—42no—
116C2×C8×C151—44no—
117C2×C8×C151—41no—
118C2×C8×C151—41no—
119C2×C8×C151—81no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—21no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151C22⋊C411yescharacteristic
127C4⋊C4×C151C22⋊C411yescharacteristic
128C22⋊C4×C151—21no—
129C22⋊C4×C151—21no—
130C22⋊C4×C151—21no—
131C42×C151—21no—
132C42×C151—21no—
133C42×C151—21no—
134C42×C151—41no—
135C42×C151—41no—
136C42×C151C2×D411yescharacteristic
137C42×C151C2×D411yescharacteristic
138C42×C151C2×D411yescharacteristic
139C42×C151#4111yescharacteristic
140C23×C151—21no—
141C23×C151C4×D411yescharacteristic
142Q8×C151—21no—
143Q8×C151—22no—
144Q8×C151—22no—
145Q8×C151—41no—
146Q8×C151—41no—
147Q8×C151C22⋊C812yes—
148D4×C151—22no—
149D4×C151—22no—
150D4×C151—21no—
151D4×C151C22⋊C812yes—
152C2×C4×C151—21no—
153C2×C4×C151—22no—
154C2×C4×C151—22no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—22no—
160C2×C4×C151—41no—
161C2×C4×C151—42no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151—41no—
167C2×C4×C151—81no—
168C2×C4×C151C2×C22⋊C411yescharacteristic
169C2×C4×C151C4×D411yescharacteristic
170C2×C4×C151#12011yescharacteristic
171C2×C4×C151#12111yescharacteristic
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12311yescharacteristic
174C2×C4×C151C22×C811yescharacteristic
175C2×C4×C151C2×M1611yescharacteristic
176C2×C4×C151#13111yescharacteristic
177C2×C4×C151#13111yescharacteristic
178C8×C151—22no—
179C8×C151—22no—
180C8×C151—42no—
181C8×C151—41no—
182C8×C151—41no—
183C8×C151—81no—
184C8×C151—81no—
185C22×C151—21no—
186C22×C151—21no—
187C22×C151—22no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151#38611yescharacteristic
191C22×C151C8×D411yescharacteristic
192C22×C151#43511yescharacteristic
193C4×C151—22no—
194C4×C151—21no—
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—42no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151—81no—
201C4×C151C2×C22⋊C811yescharacteristic
202C4×C151#40811yescharacteristic
203C4×C151C8×D411yescharacteristic
204C4×C151#43511yescharacteristic
205C4×C151#47111yescharacteristic
206C4×C151#47311yescharacteristic
207C2×C151—21no—
208C2×C151—21no—
209C2×C151—42no—
210C2×C151#186911yescharacteristic
211C2×C151#190611yescharacteristic
212C2×C151#190811yescharacteristic
213#9096C15111yesmaximal, characteristic, direct product factor, Sylow
214C151#909611yescharacteristic, direct product factor, Sylow
215C8×#41C2×C15111yescharacteristic
216C4×#137C2×C15111yescharacteristic
217#1477C2×C15111yescharacteristic
218C2×Q8⋊C8C2×C15111yescharacteristic, complemented
219#1461C2×C15111yescharacteristic, complemented
220#1283C2×C15111yescharacteristic, complemented
221#1278C2×C15111yescharacteristic, complemented
222C2×#137C4×C15111yescharacteristic
223C4×#41C22×C15111yescharacteristic
224C2×C4×Q8C22×C15111yescharacteristic
225C8×Q8—21no—
226#441—21no—
227#440—21no—
228C4×Q16—21no—
229C4×SD16—21no—
230C8×D4—21no—
231C8×D4—22no—
232#431—21no—
233#431C22×C15111yescharacteristic
234#431C22×C15111yescharacteristic
235#428C4×C15111yescharacteristic
236C2×C4⋊C8C22×C15111yescharacteristic
237#419C4×C15111yescharacteristic
238#417C4×C15111yescharacteristic
239C4×M16C22×C15111yescharacteristic
240C2×C4×C8—21no—
241C2×C4×C8C22×C15111yescharacteristic
242Q8⋊C8—21no—
243Q8⋊C8—21no—
244Q8⋊C8—21no—
245D4⋊C8—21no—
246#324—22no—
247C2×#41C2×C4×C15111yescharacteristic
248C22×Q8C2×C4×C15111yescharacteristic
249#137—22no—
250#137C8×C15114yescomplemented
251C2×Q16—21no—
252C2×SD16—21no—
253C2×M16C2×C4×C15111yescharacteristic
254C2×M16C2×C4×C15111yescharacteristic
255C22×C8—22no—
256C22×C8—21no—
257C22×C8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8D4×C15111yescharacteristic
263C4×Q8D4×C15111yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C15111yescharacteristic
267C4×D4D4×C15111yescharacteristic
268#117—21no—
269#117C2×C4×C15111yescharacteristic
270C2×C4⋊C4—21no—
271C2×C4⋊C4C2×C4×C15111yescharacteristic
272C2×C42—21no—
273C2×C42—21no—
274C2×C42C23×C15111yescharacteristic
275#107—21no—
276#106—21no—
277C4⋊C8—22no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282#103—21no—
283#103—21no—
284#103—21no—
285#102—21no—
286C22⋊C8—22no—
287C22⋊C8—21no—
288C22⋊C8D4×C15112yes—
289#97—21no—
290C4×C8—22no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8D4×C15111yescharacteristic
296C4×C8D4×C15111yescharacteristic
297#41—21no—
298#41—21no—
299#41C2×C8×C15112yes—
300#41M16×C15112yes—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8C22⋊C4×C15111yescharacteristic
307C2×Q8C2×C8×C15112yescomplemented
308C2×D4—21no—
309C2×D4C22⋊C4×C15111yescharacteristic
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4C22×C4×C15111yescharacteristic
316C22×C4C2×D4×C15111yescharacteristic
317C22×C4#41×C15111yescharacteristic
318Q16—24no—
319SD16—24no—
320M16—21no—
321M16—21no—
322M16—21no—
323M16C2×C8×C15112yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—42no—
330C2×C8—44no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—81no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4C22⋊C4×C15111yescharacteristic
341C4⋊C4C22⋊C4×C15111yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—41no—
349C42—41no—
350C42C2×D4×C15111yescharacteristic
351C42C2×D4×C15111yescharacteristic
352C42C2×D4×C15111yescharacteristic
353C42#41×C15111yescharacteristic
354C23—21no—
355C23C4×D4×C15111yescharacteristic
356Q8—21no—
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8C22⋊C8×C15112yes—
362D4—22no—
363D4—22no—
364D4—21no—
365D4C22⋊C8×C15112yes—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4C2×C22⋊C4×C15111yescharacteristic
383C2×C4C4×D4×C15111yescharacteristic
384C2×C4#120×C15111yescharacteristic
385C2×C4#121×C15111yescharacteristic
386C2×C4#121×C15111yescharacteristic
387C2×C4#123×C15111yescharacteristic
388C2×C4C22×C8×C15111yescharacteristic
389C2×C4C2×M16×C15111yescharacteristic
390C2×C4#131×C15111yescharacteristic
391C2×C4#131×C15111yescharacteristic
392C8—22no—
393C8—22no—
394C8—42no—
395C8—41no—
396C8—41no—
397C8—81no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22#386×C15111yescharacteristic
405C22C8×D4×C15111yescharacteristic
406C22#435×C15111yescharacteristic
407C4—22no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4C2×C22⋊C8×C15111yescharacteristic
416C4#408×C15111yescharacteristic
417C4C8×D4×C15111yescharacteristic
418C4#435×C15111yescharacteristic
419C4#471×C15111yescharacteristic
420C4#473×C15111yescharacteristic
421C2—21no—
422C2—21no—
423C2—42no—
424C2#1869×C15111yescharacteristic
425C2#1906×C15111yescharacteristic
426C2#1908×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutatorC2×C4C22×C8×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radicalC2×#41×C151C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊C8×C151C2semidirect
5. #1461×C151C2semidirect
6. #1283×C151C2semidirect
7. #1278×C151C2semidirect
36. #137×C151C8semidirect
93. C2×Q8×C151C2×C8semidirect
109. M16×C151C2×C8semidirect
213. #9096C151direct (N × H)
214. C151#9096direct (N × H)
218. C2×Q8⋊C8C2×C151semidirect
219. #1461C2×C151semidirect
220. #1283C2×C151semidirect
221. #1278C2×C151semidirect
250. #137C8×C151semidirect
307. C2×Q8C2×C8×C151semidirect
323. M16C2×C8×C151semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C1512
C4×#137×C1512
#1477×C1512
C2×Q8⋊C8×C1512
#1461×C1512
#1283×C1512
#1278×C1512
#9096151