Finite Group Databasebeta

← C151×#9682 #50314607

Subgroups — C151×#9682 #50314607

Order 38656.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2850×C151C211yesmaximal, characteristic
2#1749×C151C211yesmaximal, characteristic, complemented
3C2×#328×C151C212yesmaximal, complemented
4C2×#327×C151C212yesmaximal
5C4⋊#95×C151C211yesmaximal, characteristic, complemented
6C2×#124×C151C411yescharacteristic, complemented
7C2×C22⋊Q8×C151C2211yescharacteristic
8C2×#121×C151C2211yescharacteristic
9C22×C4⋊C4×C151—21no—
10C22×C42×C151C2211yescharacteristic
11C2×C22⋊C8×C151C2212yes—
12C2×#97×C151—21no—
13#391×C151C411yescharacteristic, complemented
14#390×C151C411yescharacteristic, complemented
15#388×C151—21no—
16#388×C151—21no—
17#386×C151—21no—
18#386×C151—21no—
19#382×C151C411yescharacteristic, complemented
20C2×#95×C151—21no—
21C2×#95×C151C2212yes—
22#336×C151—21no—
23#328×C151—24no—
24#327×C151—24no—
25C22×Q8×C151C2×C411yescharacteristic
26C22×D4×C151—21no—
27C22×D4×C151C2×C411yescharacteristic
28C23×C4×C151—22no—
29C23×C4×C151D411yescharacteristic
30C23×C4×C151D411yescharacteristic
31C23×C4×C151C2311yescharacteristic
32C22×C8×C151—22no—
33#124×C151—42no—
34C22⋊Q8×C151—22no—
35C22⋊Q8×C151—22no—
36#121×C151—22no—
37#121×C151—22no—
38C2×C4⋊C4×C151—24no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151—42no—
41C2×C4⋊C4×C151—42no—
42C2×C4⋊C4×C151C2×C411yescharacteristic
43C2×C4⋊C4×C151C2×C411yescharacteristic
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—21no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—21no—
49C2×C22⋊C4×C151—21no—
50C2×C42×C151—42no—
51C2×C42×C151C2×C411yescharacteristic
52C2×C42×C151C2×C411yescharacteristic
53C2×C42×C151D411yescharacteristic
54C2×C42×C151D411yescharacteristic
55C22⋊C8×C151—22no—
56C22⋊C8×C151D414yes—
57#97×C151—42no—
58#95×C151—21no—
59#95×C151—21no—
60#95×C151—21no—
61#95×C151—21no—
62#95×C151—22no—
63#95×C151—22no—
64#95×C151—42no—
65C24×C151—21no—
66C24×C151C2×D411yescharacteristic
67C2×Q8×C151—22no—
68C2×Q8×C151—41no—
69C2×Q8×C151—41no—
70C2×D4×C151—22no—
71C2×D4×C151—41no—
72C2×D4×C151—41no—
73C2×D4×C151—41no—
74C2×D4×C151—41no—
75C2×D4×C151—41no—
76C2×D4×C151—41no—
77C2×D4×C151—41no—
78C2×D4×C151—41no—
79C22×C4×C151—21no—
80C22×C4×C151—21no—
81C22×C4×C151—22no—
82C22×C4×C151—22no—
83C22×C4×C151—21no—
84C22×C4×C151—21no—
85C22×C4×C151—24no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—41no—
90C22×C4×C151—41no—
91C22×C4×C151—41no—
92C22×C4×C151—41no—
93C22×C4×C151—42no—
94C22×C4×C151—42no—
95C22×C4×C151—42no—
96C22×C4×C151—42no—
97C22×C4×C151—42no—
98C22×C4×C151—42no—
99C22×C4×C151C22⋊C411yescharacteristic
100C22×C4×C151C22⋊C411yescharacteristic
101C22×C4×C151C22⋊C411yescharacteristic
102C22×C4×C151C22⋊C411yescharacteristic
103C22×C4×C151C22×C411yescharacteristic
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D412yes—
106C22×C4×C151#4112yes—
107C2×C8×C151—24no—
108C2×C8×C151—42no—
109C2×C8×C151—42no—
110C4⋊C4×C151—22no—
111C4⋊C4×C151—22no—
112C4⋊C4×C151—48no—
113C4⋊C4×C151—42no—
114C22⋊C4×C151—42no—
115C22⋊C4×C151—42no—
116C22⋊C4×C151—41no—
117C22⋊C4×C151—41no—
118C22⋊C4×C151—42no—
119C22⋊C4×C151—42no—
120C22⋊C4×C151—42no—
121C42×C151—22no—
122C42×C151—22no—
123C42×C151—41no—
124C42×C151—41no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151—21no—
128C23×C151—21no—
129C23×C151—41no—
130C23×C151—41no—
131C23×C151—41no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151—41no—
135C23×C151—41no—
136C23×C151C2×C22⋊C411yescharacteristic
137C23×C151#12411yescharacteristic
138C23×C151#12711yescharacteristic
139C23×C151AGL(1,ℤ/8)11yescharacteristic
140C23×C151AGL(1,ℤ/8)11yescharacteristic
141C23×C151#13711yescharacteristic
142C23×C151#13711yescharacteristic
143Q8×C151—82no—
144D4×C151—82no—
145D4×C151—81no—
146D4×C151—81no—
147D4×C151—81no—
148D4×C151—81no—
149C2×C4×C151—24no—
150C2×C4×C151—24no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—42no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—42no—
169C2×C4×C151—44no—
170C2×C4×C151—44no—
171C2×C4×C151—44no—
172C2×C4×C151—41no—
173C2×C4×C151—41no—
174C2×C4×C151—41no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—82no—
182C2×C4×C151—82no—
183C2×C4×C151—82no—
184C2×C4×C151—82no—
185C2×C4×C151#9912yes—
186C2×C4×C151#10412yes—
187C2×C4×C151C4×D412yes—
188C2×C4×C151#12112yes—
189C8×C151—44no—
190C22×C151—21no—
191C22×C151—21no—
192C22×C151—21no—
193C22×C151—21no—
194C22×C151—21no—
195C22×C151—21no—
196C22×C151—21no—
197C22×C151—21no—
198C22×C151—21no—
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—21no—
202C22×C151—81no—
203C22×C151—81no—
204C22×C151—81no—
205C22×C151—81no—
206C22×C151—81no—
207C22×C151—81no—
208C22×C151—81no—
209C22×C151#39011yescharacteristic
210C22×C151C2×#9911yescharacteristic
211C22×C151#41011yescharacteristic
212C22×C151#41711yescharacteristic
213C22×C151#41711yescharacteristic
214C22×C151C2×#10411yescharacteristic
215C22×C151#42111yescharacteristic
216C22×C151#48911yescharacteristic
217C22×C151#48911yescharacteristic
218C22×C151#49611yescharacteristic
219C22×C151#49711yescharacteristic
220C4×C151—22no—
221C4×C151—22no—
222C4×C151—22no—
223C4×C151—22no—
224C4×C151—41no—
225C4×C151—41no—
226C4×C151—84no—
227C4×C151—81no—
228C4×C151—81no—
229C4×C151—81no—
230C2×C151—21no—
231C2×C151—21no—
232C2×C151—21no—
233C2×C151—21no—
234C2×C151—161no—
235C2×C151#150411yescharacteristic
236C2×C151#150911yescharacteristic
237C2×C151#151211yescharacteristic
238C2×C151#151311yescharacteristic
239C2×C151#195911yescharacteristic
240C2×C151#196411yescharacteristic
241C2×C151#198011yescharacteristic
242#9682C15111yesmaximal, characteristic, direct product factor, Sylow
243C151#968211yescharacteristic, direct product factor, Sylow
244#2850C2×C15111yescharacteristic
245#1749C2×C15111yescharacteristic, complemented
246C2×#328C2×C15112yescomplemented
247C2×#327C2×C15112yes—
248C4⋊#95C2×C15111yescharacteristic, complemented
249C2×#124C4×C15111yescharacteristic, complemented
250C2×C22⋊Q8C22×C15111yescharacteristic
251C2×#121C22×C15111yescharacteristic
252C22×C4⋊C4—21no—
253C22×C42C22×C15111yescharacteristic
254C2×C22⋊C8C22×C15112yes—
255C2×#97—21no—
256#391C4×C15111yescharacteristic, complemented
257#390C4×C15111yescharacteristic, complemented
258#388—21no—
259#388—21no—
260#386—21no—
261#386—21no—
262#382C4×C15111yescharacteristic, complemented
263C2×#95—21no—
264C2×#95C22×C15112yes—
265#336—21no—
266#328—24no—
267#327—24no—
268C22×Q8C2×C4×C15111yescharacteristic
269C22×D4—21no—
270C22×D4C2×C4×C15111yescharacteristic
271C23×C4—22no—
272C23×C4D4×C15111yescharacteristic
273C23×C4D4×C15111yescharacteristic
274C23×C4C23×C15111yescharacteristic
275C22×C8—22no—
276#124—42no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279#121—22no—
280#121—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4C2×C4×C15111yescharacteristic
286C2×C4⋊C4C2×C4×C15111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C42—42no—
294C2×C42C2×C4×C15111yescharacteristic
295C2×C42C2×C4×C15111yescharacteristic
296C2×C42D4×C15111yescharacteristic
297C2×C42D4×C15111yescharacteristic
298C22⋊C8—22no—
299C22⋊C8D4×C15114yes—
300#97—42no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—22no—
306#95—22no—
307#95—42no—
308C24—21no—
309C24C2×D4×C15111yescharacteristic
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—24no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4C22⋊C4×C15111yescharacteristic
343C22×C4C22⋊C4×C15111yescharacteristic
344C22×C4C22⋊C4×C15111yescharacteristic
345C22×C4C22⋊C4×C15111yescharacteristic
346C22×C4C22×C4×C15111yescharacteristic
347C22×C4C2×D4×C15111yescharacteristic
348C22×C4C2×D4×C15112yes—
349C22×C4#41×C15112yes—
350C2×C8—24no—
351C2×C8—42no—
352C2×C8—42no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—48no—
356C4⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C42—22no—
365C42—22no—
366C42—41no—
367C42—41no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C2×C22⋊C4×C15111yescharacteristic
380C23#124×C15111yescharacteristic
381C23#127×C15111yescharacteristic
382C23AGL(1,ℤ/8)×C15111yescharacteristic
383C23AGL(1,ℤ/8)×C15111yescharacteristic
384C23#137×C15111yescharacteristic
385C23#137×C15111yescharacteristic
386Q8—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4#99×C15112yes—
429C2×C4#104×C15112yes—
430C2×C4C4×D4×C15112yes—
431C2×C4#121×C15112yes—
432C8—44no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#390×C15111yescharacteristic
453C22C2×#99×C15111yescharacteristic
454C22#410×C15111yescharacteristic
455C22#417×C15111yescharacteristic
456C22#417×C15111yescharacteristic
457C22C2×#104×C15111yescharacteristic
458C22#421×C15111yescharacteristic
459C22#489×C15111yescharacteristic
460C22#489×C15111yescharacteristic
461C22#496×C15111yescharacteristic
462C22#497×C15111yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—84no—
470C4—81no—
471C4—81no—
472C4—81no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—161no—
478C2#1504×C15111yescharacteristic
479C2#1509×C15111yescharacteristic
480C2#1512×C15111yescharacteristic
481C2#1513×C15111yescharacteristic
482C2#1959×C15111yescharacteristic
483C2#1964×C15111yescharacteristic
484C2#1980×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1749×C151C2semidirect
3. C2×#328×C151C2semidirect
5. C4⋊#95×C151C2semidirect
6. C2×#124×C151C4semidirect
13. #391×C151C4semidirect
14. #390×C151C4semidirect
19. #382×C151C4semidirect
242. #9682C151direct (N × H)
243. C151#9682direct (N × H)
245. #1749C2×C151semidirect
246. C2×#328C2×C151semidirect
248. C4⋊#95C2×C151semidirect
249. C2×#124C4×C151semidirect
256. #391C4×C151semidirect
257. #390C4×C151semidirect
262. #382C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2850×C1512
#1749×C1512
C2×#328×C1512
C2×#327×C1512
C4⋊#95×C1512
#9682151