Finite Group Databasebeta

← C151×#18541 #50323466

Subgroups — C151×#18541 #50323466

Order 38656.

886 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic
2#3165×C151C211yesmaximal, characteristic
3#3113×C151C211yesmaximal, characteristic
4#3113×C151C211yesmaximal, characteristic
5#1653×C151C214yesmaximal, complemented
6#1648×C151C214yesmaximal, complemented
7#1556×C151C211yesmaximal, characteristic
8#1491×C151C211yesmaximal, characteristic
9#1491×C151C211yesmaximal, characteristic
10#557×C151—22no—
11#557×C151—22no—
12#557×C151—22no—
13#557×C151C2214yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151—21no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#125×C151—22no—
18C2×#125×C151—21no—
19C2×C4×Q8×C151—21no—
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23#501×C151—22no—
24#500×C151C2212yes—
25#498×C151C2212yes—
26#483×C151—21no—
27#483×C151—21no—
28#475×C151C2212yes—
29#475×C151C2212yes—
30#462×C151C2212yes—
31#462×C151C2212yes—
32#451×C151—21no—
33#451×C151—21no—
34#441×C151—22no—
35#441×C151—22no—
36#432×C151C2211yescharacteristic
37#432×C151C2211yescharacteristic
38#428×C151—22no—
39C4×M16×C151C2211yescharacteristic
40#332×C151C2214yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C22×Q8×C151—21no—
44C22×Q8×C151D411yescharacteristic
45C22×Q8×C151D411yescharacteristic
46C2×Q16×C151—22no—
47C2×Q16×C151—22no—
48C2×M16×C151—21no—
49C4⋊Q8×C151—24no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—24no—
53C4⋊Q8×C151D412yes—
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2311yescharacteristic
56C4⋊Q8×C151C2312yes—
57#125×C151—28no—
58#125×C151—24no—
59#125×C151—28no—
60#125×C151—24no—
61#125×C151—21no—
62C22⋊Q8×C151—21no—
63C22⋊Q8×C151—21no—
64C4×Q8×C151—24no—
65C4×Q8×C151—24no—
66C4×Q8×C151—24no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×Q8×C151—21no—
73C4×Q8×C151—24no—
74C4×Q8×C151D412yes—
75C4×Q8×C151D412yes—
76C4×Q8×C151C2312yes—
77C4×Q8×C151C2312yes—
78#117×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151D412yes—
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C42×C151—22no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—24no—
93#106×C151—24no—
94#106×C151—22no—
95#106×C151—22no—
96C4⋊C8×C151C2312yes—
97C4⋊C8×C151C2312yes—
98#103×C151—22no—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102C22⋊C8×C151—21no—
103C22⋊C8×C151—21no—
104#97×C151—21no—
105#97×C151—21no—
106#97×C151—21no—
107C4×C8×C151C2312yes—
108C2×Q8×C151—24no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—42no—
116C2×Q8×C151—44no—
117C2×Q8×C151C2×D412yes—
118C2×Q8×C151C2×D412yes—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127Q16×C151—44no—
128Q16×C151—44no—
129M16×C151—24no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C4⋊C4×C151—28no—
134C4⋊C4×C151—28no—
135C4⋊C4×C151—28no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151C2×D412yes—
152C4⋊C4×C151C2×D412yes—
153C4⋊C4×C151C2×D414yes—
154C22⋊C4×C151—41no—
155C42×C151—28no—
156C42×C151—22no—
157C42×C151—22no—
158C42×C151—22no—
159C42×C151—22no—
160C42×C151—41no—
161C42×C151C2×D411yescharacteristic
162C42×C151C2×D411yescharacteristic
163C42×C151C2×D411yescharacteristic
164C42×C151C2411yescharacteristic
165C23×C151#12011yescharacteristic
166Q8×C151—24no—
167Q8×C151—22no—
168Q8×C151—22no—
169Q8×C151—22no—
170Q8×C151—42no—
171Q8×C151—44no—
172Q8×C151—44no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151#13714yes—
176C2×C4×C151—24no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—24no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—42no—
186C2×C4×C151—44no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151#12011yescharacteristic
192C2×C4×C151#12011yescharacteristic
193C2×C4×C151#12011yescharacteristic
194C2×C4×C151C22×D411yescharacteristic
195C2×C4×C151C22×D411yescharacteristic
196C2×C4×C151C22×D411yescharacteristic
197C8×C151—24no—
198C8×C151—42no—
199C8×C151—42no—
200C22×C151—21no—
201C22×C151—21no—
202C22×C151#45612yes—
203C22×C151C2×#12011yescharacteristic
204C4×C151—24no—
205C4×C151—21no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—42no—
210C4×C151—44no—
211C4×C151—42no—
212C4×C151—42no—
213C4×C151—81no—
214C4×C151—81no—
215C4×C151C2×#13712yes—
216C4×C151#57512yes—
217C2×C151—22no—
218C2×C151#300411yescharacteristic
219C2×C151#300511yescharacteristic
220C2×C151C2×#45611yescharacteristic
221#18541C15111yesmaximal, characteristic, direct product factor, Sylow
222C151#1854111yescharacteristic, direct product factor, Sylow
223C2×#557C2×C15111yescharacteristic
224#3165C2×C15111yescharacteristic
225#3113C2×C15111yescharacteristic
226#3113C2×C15111yescharacteristic
227#1653C2×C15114yescomplemented
228#1648C2×C15114yescomplemented
229#1556C2×C15111yescharacteristic
230#1491C2×C15111yescharacteristic
231#1491C2×C15111yescharacteristic
232#557—22no—
233#557—22no—
234#557—22no—
235#557C22×C15114yes—
236#533C22×C15111yescharacteristic
237C2×C4⋊Q8—21no—
238C2×C4⋊Q8C22×C15111yescharacteristic
239C2×#125—22no—
240C2×#125—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C22×C15111yescharacteristic
244C2×C4×Q8C22×C15111yescharacteristic
245#501—22no—
246#500C22×C15112yes—
247#498C22×C15112yes—
248#483—21no—
249#483—21no—
250#475C22×C15112yes—
251#475C22×C15112yes—
252#462C22×C15112yes—
253#462C22×C15112yes—
254#451—21no—
255#451—21no—
256#441—22no—
257#441—22no—
258#432C22×C15111yescharacteristic
259#432C22×C15111yescharacteristic
260#428—22no—
261C4×M16C22×C15111yescharacteristic
262#332C22×C15114yes—
263Q8⋊C8C22×C15114yes—
264Q8⋊C8C22×C15114yes—
265C22×Q8—21no—
266C22×Q8D4×C15111yescharacteristic
267C22×Q8D4×C15111yescharacteristic
268C2×Q16—22no—
269C2×Q16—22no—
270C2×M16—21no—
271C4⋊Q8—24no—
272C4⋊Q8—24no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8D4×C15112yes—
276C4⋊Q8C23×C15111yescharacteristic
277C4⋊Q8C23×C15111yescharacteristic
278C4⋊Q8C23×C15112yes—
279#125—28no—
280#125—24no—
281#125—28no—
282#125—24no—
283#125—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C4×Q8—24no—
287C4×Q8—24no—
288C4×Q8—24no—
289C4×Q8—24no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8D4×C15112yes—
297C4×Q8D4×C15112yes—
298C4×Q8C23×C15112yes—
299C4×Q8C23×C15112yes—
300#117—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4D4×C15111yescharacteristic
308C2×C4⋊C4D4×C15111yescharacteristic
309C2×C4⋊C4D4×C15112yes—
310C2×C42—22no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42C23×C15111yescharacteristic
314#107—24no—
315#106—24no—
316#106—22no—
317#106—22no—
318C4⋊C8C23×C15112yes—
319C4⋊C8C23×C15112yes—
320#103—22no—
321#103—22no—
322#103—22no—
323#103—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—21no—
327#97—21no—
328#97—21no—
329C4×C8C23×C15112yes—
330C2×Q8—24no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C2×Q8—44no—
339C2×Q8C2×D4×C15112yes—
340C2×Q8C2×D4×C15112yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4C2×D4×C15111yescharacteristic
347C22×C4C2×D4×C15111yescharacteristic
348C22×C4C2×D4×C15111yescharacteristic
349Q16—44no—
350Q16—44no—
351M16—24no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C4⋊C4—28no—
356C4⋊C4—28no—
357C4⋊C4—28no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4C2×D4×C15112yes—
374C4⋊C4C2×D4×C15112yes—
375C4⋊C4C2×D4×C15114yes—
376C22⋊C4—41no—
377C42—28no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—22no—
382C42—41no—
383C42C2×D4×C15111yescharacteristic
384C42C2×D4×C15111yescharacteristic
385C42C2×D4×C15111yescharacteristic
386C42C24×C15111yescharacteristic
387C23#120×C15111yescharacteristic
388Q8—24no—
389Q8—22no—
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—44no—
394Q8—44no—
395Q8—42no—
396Q8—42no—
397Q8#137×C15114yes—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4#120×C15111yescharacteristic
414C2×C4#120×C15111yescharacteristic
415C2×C4#120×C15111yescharacteristic
416C2×C4C22×D4×C15111yescharacteristic
417C2×C4C22×D4×C15111yescharacteristic
418C2×C4C22×D4×C15111yescharacteristic
419C8—24no—
420C8—42no—
421C8—42no—
422C22—21no—
423C22—21no—
424C22#456×C15112yes—
425C22C2×#120×C15111yescharacteristic
426C4—24no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—44no—
433C4—42no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4C2×#137×C15112yes—
438C4#575×C15112yes—
439C2—22no—
440C2#3004×C15111yescharacteristic
441C2#3005×C15111yescharacteristic
442C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC23×C151#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #1653×C151C2semidirect
6. #1648×C151C2semidirect
221. #18541C151direct (N × H)
222. C151#18541direct (N × H)
227. #1653C2×C151semidirect
228. #1648C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
#3165×C1512
#3113×C1512
#1653×C1512
#1648×C1512
#1556×C1512
#1491×C1512
#18541151