Finite Group Databasebeta

← C151×#18761 #50323686

Subgroups — C151×#18761 #50323686

Order 38656.

878 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic
3#3104×C151C211yesmaximal, characteristic
4#3078×C151C211yesmaximal, characteristic
5#1653×C151C214yesmaximal, complemented
6#1636×C151C214yesmaximal, complemented
7#1546×C151C211yesmaximal, characteristic
8#1487×C151C211yesmaximal, characteristic
9#1479×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#498×C151C2212yes—
24#487×C151C2212yes—
25#484×C151—21no—
26#483×C151—22no—
27#479×C151—22no—
28#477×C151C2212yes—
29#477×C151C2212yes—
30#475×C151—22no—
31#475×C151C2212yes—
32#462×C151C2212yes—
33#451×C151—21no—
34C4×Q16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#419×C151—21no—
40#332×C151C2214yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C22×Q8×C151—21no—
44C22×Q8×C151D411yescharacteristic
45C22×Q8×C151D411yescharacteristic
46C2×Q16×C151—22no—
47C2×M16×C151—21no—
48C4⋊Q8×C151—24no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—24no—
52C4⋊Q8×C151D412yes—
53C4⋊Q8×C151C2311yescharacteristic
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2312yes—
56#125×C151—28no—
57#125×C151—24no—
58#125×C151—28no—
59#125×C151—24no—
60#125×C151—21no—
61C22⋊Q8×C151—21no—
62C22⋊Q8×C151—21no—
63C4×Q8×C151—24no—
64C4×Q8×C151—24no—
65C4×Q8×C151—24no—
66C4×Q8×C151—21no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×Q8×C151—24no—
73C4×Q8×C151D412yes—
74C4×Q8×C151D412yes—
75C4×Q8×C151C2312yes—
76C4×Q8×C151C2312yes—
77#117×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D412yes—
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C42×C151—22no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151C2311yescharacteristic
91#107×C151—22no—
92#107×C151—22no—
93#106×C151—22no—
94#106×C151—24no—
95C4⋊C8×C151—21no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151C2312yes—
98C4⋊C8×C151C2312yes—
99#103×C151—22no—
100#103×C151—24no—
101#103×C151—22no—
102#103×C151—22no—
103#103×C151—22no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106C4×C8×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—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—42no—
118C2×Q8×C151—42no—
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151C2×D412yes—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—22no—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129Q16×C151—44no—
130M16×C151—42no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C4⋊C4×C151—28no—
135C4⋊C4×C151—28no—
136C4⋊C4×C151—28no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151C2×D414yes—
153C4⋊C4×C151C2×D412yes—
154C4⋊C4×C151C2×D412yes—
155C22⋊C4×C151—41no—
156C42×C151—28no—
157C42×C151—22no—
158C42×C151—22no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—41no—
162C42×C151C2×D411yescharacteristic
163C42×C151C2×D411yescharacteristic
164C42×C151C2×D411yescharacteristic
165C42×C151C2411yescharacteristic
166C23×C151#12011yescharacteristic
167Q8×C151—24no—
168Q8×C151—22no—
169Q8×C151—22no—
170Q8×C151—22no—
171Q8×C151—42no—
172Q8×C151—42no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—44no—
176Q8×C151—42no—
177Q8×C151#13714yes—
178C2×C4×C151—24no—
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—41no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—44no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151#12011yescharacteristic
193C2×C4×C151#12011yescharacteristic
194C2×C4×C151#12011yescharacteristic
195C2×C4×C151#13512yes—
196C2×C4×C151#13712yes—
197C2×C4×C151C22×D411yescharacteristic
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C22×D411yescharacteristic
200C8×C151—42no—
201C8×C151—42no—
202C8×C151—42no—
203C22×C151—21no—
204C22×C151—21no—
205C22×C151#45212yes—
206C22×C151C2×#12011yescharacteristic
207C4×C151—24no—
208C4×C151—21no—
209C4×C151—21no—
210C4×C151—21no—
211C4×C151—42no—
212C4×C151—44no—
213C4×C151—42no—
214C4×C151—42no—
215C4×C151—81no—
216C4×C151—81no—
217C4×C151#45212yes—
218C4×C151C2×#13511yescharacteristic
219C4×C151C2×#13711yescharacteristic
220C4×C151C2×#13712yes—
221C2×C151—22no—
222C2×C151C2×#45211yescharacteristic
223C2×C151#300411yescharacteristic
224C2×C151#302011yescharacteristic
225#18761C15111yesmaximal, characteristic, direct product factor, Sylow
226C151#1876111yescharacteristic, direct product factor, Sylow
227C2×#557C2×C15111yescharacteristic
228#3229C2×C15111yescharacteristic
229#3104C2×C15111yescharacteristic
230#3078C2×C15111yescharacteristic
231#1653C2×C15114yescomplemented
232#1636C2×C15114yescomplemented
233#1546C2×C15111yescharacteristic
234#1487C2×C15111yescharacteristic
235#1479C2×C15111yescharacteristic
236#557—22no—
237#557—22no—
238#557—22no—
239#557C22×C15114yes—
240#533C22×C15111yescharacteristic
241C2×C4⋊Q8—21no—
242C2×C4⋊Q8C22×C15111yescharacteristic
243C2×#125—22no—
244C2×#125—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8C22×C15111yescharacteristic
248C2×C4×Q8C22×C15111yescharacteristic
249#498C22×C15112yes—
250#487C22×C15112yes—
251#484—21no—
252#483—22no—
253#479—22no—
254#477C22×C15112yes—
255#477C22×C15112yes—
256#475—22no—
257#475C22×C15112yes—
258#462C22×C15112yes—
259#451—21no—
260C4×Q16—22no—
261#431C22×C15111yescharacteristic
262#431C22×C15111yescharacteristic
263#428—21no—
264#423C22×C15111yescharacteristic
265#419—21no—
266#332C22×C15114yes—
267Q8⋊C8C22×C15114yes—
268Q8⋊C8C22×C15114yes—
269C22×Q8—21no—
270C22×Q8D4×C15111yescharacteristic
271C22×Q8D4×C15111yescharacteristic
272C2×Q16—22no—
273C2×M16—21no—
274C4⋊Q8—24no—
275C4⋊Q8—24no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8D4×C15112yes—
279C4⋊Q8C23×C15111yescharacteristic
280C4⋊Q8C23×C15111yescharacteristic
281C4⋊Q8C23×C15112yes—
282#125—28no—
283#125—24no—
284#125—28no—
285#125—24no—
286#125—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C4×Q8—24no—
290C4×Q8—24no—
291C4×Q8—24no—
292C4×Q8—24no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8D4×C15112yes—
300C4×Q8D4×C15112yes—
301C4×Q8C23×C15112yes—
302C4×Q8C23×C15112yes—
303#117—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4×C15111yescharacteristic
311C2×C4⋊C4D4×C15111yescharacteristic
312C2×C4⋊C4D4×C15112yes—
313C2×C42—22no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42C23×C15111yescharacteristic
317#107—22no—
318#107—22no—
319#106—22no—
320#106—24no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8C23×C15112yes—
324C4⋊C8C23×C15112yes—
325#103—22no—
326#103—22no—
327#103—22no—
328#103—22no—
329#103—24no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C4×C8—21no—
333C4×C8C23×C15112yes—
334C2×Q8—24no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8C2×D4×C15112yes—
346C2×Q8C2×D4×C15112yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4C2×D4×C15111yescharacteristic
353C22×C4C2×D4×C15111yescharacteristic
354C22×C4C2×D4×C15111yescharacteristic
355Q16—44no—
356M16—42no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C4⋊C4—28no—
361C4⋊C4—28no—
362C4⋊C4—28no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4C2×D4×C15114yes—
379C4⋊C4C2×D4×C15112yes—
380C4⋊C4C2×D4×C15112yes—
381C22⋊C4—41no—
382C42—28no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—22no—
387C42—41no—
388C42C2×D4×C15111yescharacteristic
389C42C2×D4×C15111yescharacteristic
390C42C2×D4×C15111yescharacteristic
391C42C24×C15111yescharacteristic
392C23#120×C15111yescharacteristic
393Q8—24no—
394Q8—22no—
395Q8—22no—
396Q8—22no—
397Q8—42no—
398Q8—42no—
399Q8—44no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403Q8#137×C15114yes—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4#120×C15111yescharacteristic
419C2×C4#120×C15111yescharacteristic
420C2×C4#120×C15111yescharacteristic
421C2×C4#135×C15112yes—
422C2×C4#137×C15112yes—
423C2×C4C22×D4×C15111yescharacteristic
424C2×C4C22×D4×C15111yescharacteristic
425C2×C4C22×D4×C15111yescharacteristic
426C8—42no—
427C8—42no—
428C8—42no—
429C22—21no—
430C22—21no—
431C22#452×C15112yes—
432C22C2×#120×C15111yescharacteristic
433C4—24no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—44no—
439C4—42no—
440C4—42no—
441C4—81no—
442C4—81no—
443C4#452×C15112yes—
444C4C2×#135×C15111yescharacteristic
445C4C2×#137×C15111yescharacteristic
446C4C2×#137×C15112yes—
447C2—22no—
448C2C2×#452×C15111yescharacteristic
449C2#3004×C15111yescharacteristic
450C2#3020×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. #1636×C151C2semidirect
225. #18761C151direct (N × H)
226. C151#18761direct (N × H)
231. #1653C2×C151semidirect
232. #1636C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
#3229×C1512
#3104×C1512
#3078×C1512
#1653×C1512
#1636×C1512
#1546×C1512
#1487×C1512
#1479×C1512
#18761151