Finite Group Databasebeta

← C151×#18769 #50323694

Subgroups — C151×#18769 #50323694

Order 38656.

922 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
1C2×Q82×C151C211yesmaximal, characteristic
2#3209×C151C211yesmaximal, characteristic
3#3104×C151C211yesmaximal, characteristic
4#3078×C151C211yesmaximal, characteristic
5#1645×C151C214yesmaximal, complemented
6#1633×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic
8#1487×C151C211yesmaximal, characteristic
9#1479×C151C211yesmaximal, characteristic
10Q82×C151—22no—
11Q82×C151—22no—
12Q82×C151—22no—
13Q82×C151C2214yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151—22no—
16C2×C4⋊Q8×C151—21no—
17C2×C4⋊Q8×C151—21no—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C4×Q8×C151—21no—
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23#494×C151C2212yes—
24#487×C151C2212yes—
25#484×C151—21no—
26#479×C151—22no—
27#477×C151C2212yes—
28#477×C151C2212yes—
29#475×C151C2212yes—
30#462×C151—22no—
31#462×C151C2212yes—
32#451×C151—21no—
33#451×C151—22no—
34C4×Q16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#419×C151—21no—
40#333×C151C2214yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C22×Q8×C151—22no—
44C22×Q8×C151D411yescharacteristic
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151D412yes—
47C2×Q16×C151—22no—
48C2×Q16×C151—24no—
49C2×M16×C151—21no—
50C4⋊Q8×C151—24no—
51C4⋊Q8×C151—24no—
52C4⋊Q8×C151—28no—
53C4⋊Q8×C151—24no—
54C4⋊Q8×C151—24no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—28no—
58C4⋊Q8×C151D412yes—
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2312yes—
62#125×C151—21no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151—21no—
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×C151—24no—
75C4×Q8×C151D412yes—
76C4×Q8×C151D412yes—
77C4×Q8×C151C2312yes—
78C4×Q8×C151C2312yes—
79#117×C151—21no—
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×C151—21no—
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—22no—
93#107×C151—22no—
94#106×C151—22no—
95C4⋊C8×C151—21no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151C2312yes—
98C4⋊C8×C151C2312yes—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102#103×C151—22no—
103#103×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106C4×C8×C151—21no—
107C4×C8×C151C2312yes—
108C2×Q8×C151—24no—
109C2×Q8×C151—28no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—82no—
117C2×Q8×C151—84no—
118C2×Q8×C151Q1614yescomplemented
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151C2×D412yes—
121C2×Q8×C151C2×D414yes—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130Q16×C151—44no—
131Q16×C151—84no—
132M16×C151—42no—
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C4⋊C4×C151—28no—
137C4⋊C4×C151—28no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151C2×D412yes—
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—41no—
157C42×C151—28no—
158C42×C151—22no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—41no—
163C42×C151C2×D411yescharacteristic
164C42×C151C2×D411yescharacteristic
165C42×C151C2×D411yescharacteristic
166C42×C151C2411yescharacteristic
167C23×C151#12011yescharacteristic
168Q8×C151—24no—
169Q8×C151—22no—
170Q8×C151—22no—
171Q8×C151—24no—
172Q8×C151—44no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—82no—
176Q8×C151—88no—
177Q8×C151C2×Q1614yes—
178Q8×C151#13714yes—
179C2×C4×C151—24no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—24no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—41no—
188C2×C4×C151—44no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151#12011yescharacteristic
194C2×C4×C151#12011yescharacteristic
195C2×C4×C151#12011yescharacteristic
196C2×C4×C151C2×Q1612yes—
197C2×C4×C151#13712yes—
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C22×D411yescharacteristic
200C2×C4×C151C22×D411yescharacteristic
201C8×C151—42no—
202C8×C151—42no—
203C8×C151—42no—
204C22×C151—21no—
205C22×C151—21no—
206C22×C151#45112yes—
207C22×C151C2×#12011yescharacteristic
208C4×C151—24no—
209C4×C151—24no—
210C4×C151—21no—
211C4×C151—21no—
212C4×C151—21no—
213C4×C151—44no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—81no—
217C4×C151—81no—
218C4×C151#45112yes—
219C4×C151C22×Q1611yescharacteristic
220C4×C151C2×#13711yescharacteristic
221C4×C151C2×#13712yes—
222C2×C151—22no—
223C2×C151C2×#45111yescharacteristic
224C2×C151#300411yescharacteristic
225C2×C151#301911yescharacteristic
226#18769C15111yesmaximal, characteristic, direct product factor, Sylow
227C151#1876911yescharacteristic, direct product factor, Sylow
228C2×Q82C2×C15111yescharacteristic
229#3209C2×C15111yescharacteristic
230#3104C2×C15111yescharacteristic
231#3078C2×C15111yescharacteristic
232#1645C2×C15114yescomplemented
233#1633C2×C15114yescomplemented
234#1548C2×C15111yescharacteristic
235#1487C2×C15111yescharacteristic
236#1479C2×C15111yescharacteristic
237Q82—22no—
238Q82—22no—
239Q82—22no—
240Q82C22×C15114yes—
241#533C22×C15111yescharacteristic
242C2×C4⋊Q8—22no—
243C2×C4⋊Q8—21no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8C22×C15111yescharacteristic
246C2×C4×Q8—21no—
247C2×C4×Q8—21no—
248C2×C4×Q8C22×C15111yescharacteristic
249C2×C4×Q8C22×C15111yescharacteristic
250#494C22×C15112yes—
251#487C22×C15112yes—
252#484—21no—
253#479—22no—
254#477C22×C15112yes—
255#477C22×C15112yes—
256#475C22×C15112yes—
257#462—22no—
258#462C22×C15112yes—
259#451—21no—
260#451—22no—
261C4×Q16—22no—
262#431C22×C15111yescharacteristic
263#431C22×C15111yescharacteristic
264#428—21no—
265#423C22×C15111yescharacteristic
266#419—21no—
267#333C22×C15114yes—
268Q8⋊C8C22×C15114yes—
269Q8⋊C8C22×C15114yes—
270C22×Q8—22no—
271C22×Q8D4×C15111yescharacteristic
272C22×Q8D4×C15111yescharacteristic
273C22×Q8D4×C15112yes—
274C2×Q16—22no—
275C2×Q16—24no—
276C2×M16—21no—
277C4⋊Q8—28no—
278C4⋊Q8—24no—
279C4⋊Q8—24no—
280C4⋊Q8—28no—
281C4⋊Q8—24no—
282C4⋊Q8—24no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8D4×C15112yes—
286C4⋊Q8C23×C15111yescharacteristic
287C4⋊Q8C23×C15111yescharacteristic
288C4⋊Q8C23×C15112yes—
289#125—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×Q8—24no—
293C4×Q8—24no—
294C4×Q8—24no—
295C4×Q8—24no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8D4×C15112yes—
303C4×Q8D4×C15112yes—
304C4×Q8C23×C15112yes—
305C4×Q8C23×C15112yes—
306#117—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4D4×C15111yescharacteristic
314C2×C4⋊C4D4×C15111yescharacteristic
315C2×C42—22no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42C23×C15111yescharacteristic
319#107—22no—
320#107—22no—
321#106—22no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8C23×C15112yes—
325C4⋊C8C23×C15112yes—
326#103—22no—
327#103—22no—
328#103—22no—
329#103—24no—
330#103—22no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C4×C8—21no—
334C4×C8C23×C15112yes—
335C2×Q8—24no—
336C2×Q8—28no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—82no—
344C2×Q8—84no—
345C2×Q8Q16×C15114yescomplemented
346C2×Q8C2×D4×C15112yes—
347C2×Q8C2×D4×C15112yes—
348C2×Q8C2×D4×C15114yes—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4C2×D4×C15111yescharacteristic
355C22×C4C2×D4×C15111yescharacteristic
356C22×C4C2×D4×C15111yescharacteristic
357Q16—44no—
358Q16—84no—
359M16—42no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C4⋊C4—28no—
364C4⋊C4—28no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C15112yes—
382C4⋊C4C2×D4×C15112yes—
383C22⋊C4—41no—
384C42—28no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42—41no—
390C42C2×D4×C15111yescharacteristic
391C42C2×D4×C15111yescharacteristic
392C42C2×D4×C15111yescharacteristic
393C42C24×C15111yescharacteristic
394C23#120×C15111yescharacteristic
395Q8—24no—
396Q8—24no—
397Q8—22no—
398Q8—22no—
399Q8—44no—
400Q8—42no—
401Q8—42no—
402Q8—82no—
403Q8—88no—
404Q8C2×Q16×C15114yes—
405Q8#137×C15114yes—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4#120×C15111yescharacteristic
421C2×C4#120×C15111yescharacteristic
422C2×C4#120×C15111yescharacteristic
423C2×C4C2×Q16×C15112yes—
424C2×C4#137×C15112yes—
425C2×C4C22×D4×C15111yescharacteristic
426C2×C4C22×D4×C15111yescharacteristic
427C2×C4C22×D4×C15111yescharacteristic
428C8—42no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22#451×C15112yes—
434C22C2×#120×C15111yescharacteristic
435C4—24no—
436C4—24no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—44no—
441C4—42no—
442C4—42no—
443C4—81no—
444C4—81no—
445C4#451×C15112yes—
446C4C22×Q16×C15111yescharacteristic
447C4C2×#137×C15111yescharacteristic
448C4C2×#137×C15112yes—
449C2—22no—
450C2C2×#451×C15111yescharacteristic
451C2#3004×C15111yescharacteristic
452C2#3019×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. #1645×C151C2semidirect
6. #1633×C151C2semidirect
118. C2×Q8×C151Q16semidirect
226. #18769C151direct (N × H)
227. C151#18769direct (N × H)
232. #1645C2×C151semidirect
233. #1633C2×C151semidirect
345. C2×Q8Q16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1512
#3209×C1512
#3104×C1512
#3078×C1512
#1645×C1512
#1633×C1512
#1548×C1512
#1487×C1512
#1479×C1512
#18769151