Finite Group Databasebeta

← C151×#18205 #50323130

Subgroups — C151×#18205 #50323130

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2C2×#484×C151C212yesmaximal, complemented
3#2487×C151C211yesmaximal, characteristic
4#1617×C151C214yesmaximal, complemented
5#1614×C151C214yesmaximal, complemented
6#1520×C151C212yesmaximal, complemented
7#1459×C151C211yesmaximal, characteristic
8#554×C151—24no—
9#554×C151—22no—
10D4×Q8×C151—22no—
11#544×C151C2212yes—
12#543×C151—21no—
13#543×C151C2212yes—
14#533×C151—21no—
15C2×C22⋊Q8×C151—21no—
16C2×C22⋊Q8×C151C2212yes—
17#518×C151—21no—
18C2×C4×D4×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic
20#484×C151—24no—
21#484×C151C2218yes—
22C2×#107×C151—22no—
23C2×#103×C151—22no—
24C2×C22⋊C8×C151C2212yes—
25#400×C151C2212yes—
26#399×C151C2212yes—
27#389×C151—21no—
28#386×C151—21no—
29#385×C151—21no—
30#380×C151—21no—
31#380×C151C2211yescharacteristic
32#328×C151C2218yes—
33#324×C151C2212yes—
34#323×C151C2212yes—
35C22×Q8×C151—21no—
36C22×Q8×C151D412yes—
37C22×D4×C151D411yescharacteristic
38C23×C4×C151—21no—
39C23×C4×C151D411yescharacteristic
40C23×C4×C151C2311yescharacteristic
41C22×C8×C151—22no—
42C4⋊Q8×C151—21no—
43C4⋊Q8×C151—21no—
44C4⋊Q8×C151—24no—
45#125×C151—22no—
46#125×C151—24no—
47C22⋊Q8×C151—22no—
48C22⋊Q8×C151—22no—
49C22⋊Q8×C151—24no—
50C22⋊Q8×C151—24no—
51C22⋊Q8×C151—22no—
52C22⋊Q8×C151—22no—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—22no—
55C22⋊Q8×C151—24no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151D414yes—
58C22⋊Q8×C151C2314yes—
59C4×Q8×C151—22no—
60C4×Q8×C151—22no—
61C4×D4×C151—24no—
62C4×D4×C151—24no—
63C4×D4×C151—22no—
64C4×D4×C151—22no—
65#117×C151—22no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151D412yes—
75C2×C4⋊C4×C151C2312yes—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151D411yescharacteristic
82C2×C22⋊C4×C151C2311yescharacteristic
83C2×C42×C151D411yescharacteristic
84#107×C151—28no—
85#103×C151—28no—
86C22⋊C8×C151—22no—
87C22⋊C8×C151C2314yes—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151C2312yes—
91C24×C151C2×D411yescharacteristic
92C24×C151C2×D411yescharacteristic
93C2×Q8×C151—22no—
94C2×Q8×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151—44no—
97C2×Q8×C151—82no—
98C2×Q8×C151C2×D414yes—
99C2×D4×C151—22no—
100C2×D4×C151—22no—
101C2×D4×C151Q1614yes—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151—42no—
113C22×C4×C151—82no—
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D412yes—
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2411yescharacteristic
121C2×C8×C151—24no—
122C2×C8×C151—44no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—24no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—24no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—24no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—24no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151—41no—
136C4⋊C4×C151—41no—
137C4⋊C4×C151—82no—
138C4⋊C4×C151C2×D414yes—
139C22⋊C4×C151—24no—
140C22⋊C4×C151—24no—
141C22⋊C4×C151—22no—
142C22⋊C4×C151—24no—
143C22⋊C4×C151—22no—
144C22⋊C4×C151—42no—
145C22⋊C4×C151—82no—
146C42×C151—24no—
147C42×C151—21no—
148C42×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151—41no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—41no—
155C23×C151#12012yes—
156C23×C151C2×Q1612yes—
157C23×C151C2×Q1612yes—
158C23×C151#13712yes—
159C23×C151C22×D411yescharacteristic
160Q8×C151—44no—
161Q8×C151—44no—
162Q8×C151—82no—
163Q8×C151—82no—
164D4×C151—28no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—24no—
168C2×C4×C151—22no—
169C2×C4×C151—24no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—24no—
173C2×C4×C151—42no—
174C2×C4×C151—41no—
175C2×C4×C151—42no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—42no—
179C2×C4×C151—42no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—81no—
185C2×C4×C151—82no—
186C2×C4×C151—82no—
187C2×C4×C151—82no—
188C2×C4×C151—82no—
189C2×C4×C151—84no—
190C2×C4×C151#12011yescharacteristic
191C2×C4×C151#12011yescharacteristic
192C2×C4×C151C2×Q1612yes—
193C2×C4×C151C22×D412yes—
194C8×C151—44no—
195C22×C151—21no—
196C22×C151—22no—
197C22×C151—21no—
198C22×C151—22no—
199C22×C151—22no—
200C22×C151—42no—
201C22×C151—42no—
202C22×C151—42no—
203C22×C151—41no—
204C22×C151—41no—
205C22×C151—81no—
206C22×C151#45114yes—
207C22×C151C2×#12011yescharacteristic
208C22×C151C22×Q1611yescharacteristic
209C22×C151C2×#13711yescharacteristic
210C4×C151—22no—
211C4×C151—22no—
212C4×C151—21no—
213C4×C151—41no—
214C4×C151—44no—
215C4×C151—41no—
216C4×C151—44no—
217C4×C151—82no—
218C4×C151—82no—
219C4×C151#45812yes—
220C2×C151—21no—
221C2×C151—21no—
222C2×C151—24no—
223C2×C151—42no—
224C2×C151C2×#45111yescharacteristic
225C2×C151#302111yescharacteristic
226C2×C151C2×#45811yescharacteristic
227#18205C15111yesmaximal, characteristic, direct product factor, Sylow
228C151#1820511yescharacteristic, direct product factor, Sylow
229#3501C2×C15111yescharacteristic
230C2×#484C2×C15112yescomplemented
231#2487C2×C15111yescharacteristic
232#1617C2×C15114yescomplemented
233#1614C2×C15114yescomplemented
234#1520C2×C15112yescomplemented
235#1459C2×C15111yescharacteristic
236#554—24no—
237#554—22no—
238D4×Q8—22no—
239#544C22×C15112yes—
240#543—21no—
241#543C22×C15112yes—
242#533—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C22×C15112yes—
245#518—21no—
246C2×C4×D4C22×C15111yescharacteristic
247C22×C4⋊C4C22×C15111yescharacteristic
248#484—24no—
249#484C22×C15118yes—
250C2×#107—22no—
251C2×#103—22no—
252C2×C22⋊C8C22×C15112yes—
253#400C22×C15112yes—
254#399C22×C15112yes—
255#389—21no—
256#386—21no—
257#385—21no—
258#380—21no—
259#380C22×C15111yescharacteristic
260#328C22×C15118yes—
261#324C22×C15112yes—
262#323C22×C15112yes—
263C22×Q8—21no—
264C22×Q8D4×C15112yes—
265C22×D4D4×C15111yescharacteristic
266C23×C4—21no—
267C23×C4D4×C15111yescharacteristic
268C23×C4C23×C15111yescharacteristic
269C22×C8—22no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—24no—
273#125—22no—
274#125—24no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—24no—
278C22⋊Q8—24no—
279C22⋊Q8—24no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—24no—
285C22⋊Q8D4×C15114yes—
286C22⋊Q8C23×C15114yes—
287C4×Q8—22no—
288C4×Q8—22no—
289C4×D4—24no—
290C4×D4—24no—
291C4×D4—22no—
292C4×D4—22no—
293#117—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4D4×C15112yes—
303C2×C4⋊C4C23×C15112yes—
304C2×C4⋊C4C23×C15111yescharacteristic
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4D4×C15111yescharacteristic
310C2×C22⋊C4C23×C15111yescharacteristic
311C2×C42D4×C15111yescharacteristic
312#107—28no—
313#103—28no—
314C22⋊C8—22no—
315C22⋊C8C23×C15114yes—
316#95—22no—
317#95—22no—
318#95C23×C15112yes—
319C24C2×D4×C15111yescharacteristic
320C24C2×D4×C15111yescharacteristic
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—44no—
325C2×Q8—82no—
326C2×Q8C2×D4×C15114yes—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4Q16×C15114yes—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—82no—
342C22×C4C2×D4×C15111yescharacteristic
343C22×C4C2×D4×C15112yes—
344C22×C4C2×D4×C15111yescharacteristic
345C22×C4C2×D4×C15111yescharacteristic
346C22×C4C2×D4×C15111yescharacteristic
347C22×C4C2×D4×C15112yes—
348C22×C4C24×C15111yescharacteristic
349C2×C8—24no—
350C2×C8—44no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—22no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—42no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—82no—
366C4⋊C4C2×D4×C15114yes—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—22no—
370C22⋊C4—24no—
371C22⋊C4—22no—
372C22⋊C4—42no—
373C22⋊C4—82no—
374C42—24no—
375C42—21no—
376C42—21no—
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#120×C15112yes—
384C23C2×Q16×C15112yes—
385C23C2×Q16×C15112yes—
386C23#137×C15112yes—
387C23C22×D4×C15111yescharacteristic
388Q8—44no—
389Q8—44no—
390Q8—82no—
391Q8—82no—
392D4—28no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—81no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—84no—
418C2×C4#120×C15111yescharacteristic
419C2×C4#120×C15111yescharacteristic
420C2×C4C2×Q16×C15112yes—
421C2×C4C22×D4×C15112yes—
422C8—44no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22#451×C15114yes—
435C22C2×#120×C15111yescharacteristic
436C22C22×Q16×C15111yescharacteristic
437C22C2×#137×C15111yescharacteristic
438C4—22no—
439C4—22no—
440C4—21no—
441C4—41no—
442C4—44no—
443C4—41no—
444C4—44no—
445C4—82no—
446C4—82no—
447C4#458×C15112yes—
448C2—21no—
449C2—21no—
450C2—24no—
451C2—42no—
452C2C2×#451×C15111yescharacteristic
453C2#3021×C15111yescharacteristic
454C2C2×#458×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#484×C151C2semidirect
4. #1617×C151C2semidirect
5. #1614×C151C2semidirect
6. #1520×C151C2semidirect
227. #18205C151direct (N × H)
228. C151#18205direct (N × H)
230. C2×#484C2×C151semidirect
232. #1617C2×C151semidirect
233. #1614C2×C151semidirect
234. #1520C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
C2×#484×C1512
#2487×C1512
#1617×C1512
#1614×C1512
#1520×C1512
#1459×C1512
#18205151