Finite Group Databasebeta

← C151×#23670 #50328595

Subgroups — C151×#23670 #50328595

Order 38656.

950 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C151C211yesmaximal, characteristic
2C2×#423×C151C211yesmaximal, characteristic
3#2296×C151C211yesmaximal, characteristic
4C2×#389×C151C211yesmaximal, characteristic
5#2088×C151C212yesmaximal, complemented
6#2088×C151C212yesmaximal, complemented
7#2087×C151C212yesmaximal, complemented
8#2086×C151C212yesmaximal, complemented
9#1736×C151C211yesmaximal, characteristic
10#1736×C151C211yesmaximal, characteristic
11#1736×C151C211yesmaximal, characteristic
12C22×M16×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16C22×C4⋊C4×C151—21no—
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C42×C151C2211yescharacteristic
20#428×C151—24no—
21C2×#107×C151C2212yes—
22C2×#106×C151C2212yes—
23#423×C151—24no—
24C2×C4⋊C8×C151C2212yes—
25C2×C4⋊C8×C151C2212yes—
26#389×C151—21no—
27#389×C151—21no—
28#389×C151C2211yescharacteristic
29#389×C151C2212yes—
30#389×C151C2211yescharacteristic
31#389×C151C2212yes—
32#389×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#385×C151—21no—
35#385×C151—21no—
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151—21no—
38C2×#95×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C23×C4×C151—21no—
46C23×C4×C151—21no—
47C23×C4×C151D411yescharacteristic
48C23×C4×C151D411yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C2×M16×C151—22no—
51C2×M16×C151—22no—
52C2×M16×C151—22no—
53C2×M16×C151—22no—
54C2×M16×C151—22no—
55C2×M16×C151D414yes—
56C22×C8×C151C2312yes—
57C22×C8×C151C2312yes—
58#117×C151—22no—
59#117×C151—22no—
60#117×C151—22no—
61#117×C151Q814yes—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—44no—
74C2×C4⋊C4×C151Q814yes—
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2312yes—
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2312yes—
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—21no—
83C2×C42×C151—21no—
84C2×C42×C151—22no—
85C2×C42×C151—22no—
86C2×C42×C151—21no—
87C2×C42×C151D411yescharacteristic
88C2×C42×C151D411yescharacteristic
89C2×C42×C151C2311yescharacteristic
90C2×C42×C151C2311yescharacteristic
91#107×C151—24no—
92#106×C151—24no—
93C4⋊C8×C151—24no—
94C4⋊C8×C151—24no—
95#95×C151—22no—
96#95×C151—22no—
97#95×C151—21no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101C24×C151C2×D411yescharacteristic
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—24no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—41no—
114C22×C4×C151—41no—
115C22×C4×C151—42no—
116C22×C4×C151—42no—
117C22×C4×C151—42no—
118C22×C4×C151—42no—
119C22×C4×C151—42no—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×Q812yes—
127C22×C4×C151C2×Q812yes—
128C22×C4×C151#4112yes—
129C22×C4×C151#4112yes—
130C22×C4×C151#4112yes—
131C22×C4×C151C2411yescharacteristic
132M16×C151—28no—
133M16×C151—44no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151C2×D414yes—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151—44no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151—42no—
155C4⋊C4×C151—44no—
156C4⋊C4×C151—42no—
157C4⋊C4×C151C2×Q814yes—
158C4⋊C4×C151C2×Q812yes—
159C4⋊C4×C151C2×Q812yes—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—42no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151—24no—
165C42×C151—21no—
166C42×C151—21no—
167C42×C151—21no—
168C42×C151—21no—
169C42×C151—42no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151—21no—
173C23×C151—21no—
174C23×C151#12112yes—
175C23×C151C22⋊Q812yes—
176C23×C151C22⋊Q812yes—
177C23×C151C22×D411yescharacteristic
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—44no—
192C2×C4×C151—44no—
193C2×C4×C151—48no—
194C2×C4×C151—42no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—84no—
210C2×C4×C151#12112yes—
211C2×C4×C151C22⋊Q812yes—
212C2×C4×C151C22⋊Q812yes—
213C2×C4×C151#12314yes—
214C2×C4×C151#12514yes—
215C2×C4×C151#12514yes—
216C2×C4×C151C4⋊Q814yes—
217C2×C4×C151AGL(1,ℤ/8)12yes—
218C2×C4×C151#13712yes—
219C2×C4×C151C22×D411yescharacteristic
220C2×C4×C151C22×Q811yescharacteristic
221C2×C4×C151C22×Q811yescharacteristic
222C2×C4×C151C2×#4111yescharacteristic
223C2×C4×C151C2×#4111yescharacteristic
224C2×C4×C151C2×#4111yescharacteristic
225C8×C151—24no—
226C8×C151—42no—
227C22×C151—22no—
228C22×C151—22no—
229C22×C151—22no—
230C22×C151—22no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151#39814yes—
234C22×C151C2×#12111yescharacteristic
235C22×C151C2×C22⋊Q811yescharacteristic
236C22×C151C2×C22⋊Q811yescharacteristic
237C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
238C22×C151C2×#13711yescharacteristic
239C22×C151#57511yescharacteristic
240C22×C151#57511yescharacteristic
241C4×C151—22no—
242C4×C151—22no—
243C4×C151—44no—
244C4×C151—42no—
245C4×C151—42no—
246C4×C151—41no—
247C4×C151—41no—
248C4×C151—81no—
249C4×C151—82no—
250C4×C151—81no—
251C4×C151#39814yes—
252C4×C151C2×#12311yescharacteristic
253C4×C151C2×#12511yescharacteristic
254C4×C151C2×#12511yescharacteristic
255C4×C151C2×C4⋊Q811yescharacteristic
256C2×C151—24no—
257C2×C151C2×#39811yescharacteristic
258C2×C151#305511yescharacteristic
259C2×C151#305611yescharacteristic
260C2×C151#307711yescharacteristic
261C2×C151#307811yescharacteristic
262C2×C151#307911yescharacteristic
263C2×C151#308011yescharacteristic
264#23670C15111yesmaximal, characteristic, direct product factor, Sylow
265C151#2367011yescharacteristic, direct product factor, Sylow
266C2×#428C2×C15111yescharacteristic
267C2×#423C2×C15111yescharacteristic
268#2296C2×C15111yescharacteristic
269C2×#389C2×C15111yescharacteristic
270#2088C2×C15112yescomplemented
271#2088C2×C15112yescomplemented
272#2087C2×C15112yescomplemented
273#2086C2×C15112yescomplemented
274#1736C2×C15111yescharacteristic
275#1736C2×C15111yescharacteristic
276#1736C2×C15111yescharacteristic
277C22×M16C22×C15111yescharacteristic
278C22×M16C22×C15111yescharacteristic
279C2×#117C22×C15111yescharacteristic
280C2×#117C22×C15111yescharacteristic
281C22×C4⋊C4—21no—
282C22×C4⋊C4C22×C15111yescharacteristic
283C22×C4⋊C4C22×C15111yescharacteristic
284C22×C42C22×C15111yescharacteristic
285#428—24no—
286C2×#107C22×C15112yes—
287C2×#106C22×C15112yes—
288#423—24no—
289C2×C4⋊C8C22×C15112yes—
290C2×C4⋊C8C22×C15112yes—
291#389—21no—
292#389—21no—
293#389C22×C15111yescharacteristic
294#389C22×C15112yes—
295#389C22×C15111yescharacteristic
296#389C22×C15112yes—
297#389C22×C15111yescharacteristic
298#389C22×C15111yescharacteristic
299#385—21no—
300#385—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C2×#95—21no—
304#340C22×C15112yes—
305#340C22×C15112yes—
306#340C22×C15112yes—
307#340C22×C15112yes—
308#340C22×C15112yes—
309#340C22×C15112yes—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4D4×C15111yescharacteristic
313C23×C4D4×C15111yescharacteristic
314C23×C4C23×C15111yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16D4×C15114yes—
321C22×C8C23×C15112yes—
322C22×C8C23×C15112yes—
323#117—22no—
324#117—22no—
325#117—22no—
326#117Q8×C15114yes—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4Q8×C15114yes—
340C2×C4⋊C4C23×C15112yes—
341C2×C4⋊C4C23×C15111yescharacteristic
342C2×C4⋊C4C23×C15111yescharacteristic
343C2×C4⋊C4C23×C15112yes—
344C2×C4⋊C4C23×C15111yescharacteristic
345C2×C4⋊C4C23×C15111yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42—22no—
349C2×C42—21no—
350C2×C42—22no—
351C2×C42—21no—
352C2×C42D4×C15111yescharacteristic
353C2×C42D4×C15111yescharacteristic
354C2×C42C23×C15111yescharacteristic
355C2×C42C23×C15111yescharacteristic
356#107—24no—
357#106—24no—
358C4⋊C8—24no—
359C4⋊C8—24no—
360#95—22no—
361#95—22no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366C24C2×D4×C15111yescharacteristic
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15111yescharacteristic
390C22×C4C2×D4×C15112yes—
391C22×C4C2×Q8×C15112yes—
392C22×C4C2×Q8×C15112yes—
393C22×C4#41×C15112yes—
394C22×C4#41×C15112yes—
395C22×C4#41×C15112yes—
396C22×C4C24×C15111yescharacteristic
397M16—28no—
398M16—44no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8C2×D4×C15114yes—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—44no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—44no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4C2×Q8×C15114yes—
423C4⋊C4C2×Q8×C15112yes—
424C4⋊C4C2×Q8×C15112yes—
425C22⋊C4—24no—
426C22⋊C4—42no—
427C42—22no—
428C42—22no—
429C42—24no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42—21no—
434C42—42no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23#121×C15112yes—
440C23C22⋊Q8×C15112yes—
441C23C22⋊Q8×C15112yes—
442C23C22×D4×C15111yescharacteristic
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4#121×C15112yes—
476C2×C4C22⋊Q8×C15112yes—
477C2×C4C22⋊Q8×C15112yes—
478C2×C4#123×C15114yes—
479C2×C4#125×C15114yes—
480C2×C4#125×C15114yes—
481C2×C4C4⋊Q8×C15114yes—
482C2×C4AGL(1,ℤ/8)×C15112yes—
483C2×C4#137×C15112yes—
484C2×C4C22×D4×C15111yescharacteristic
485C2×C4C22×Q8×C15111yescharacteristic
486C2×C4C22×Q8×C15111yescharacteristic
487C2×C4C2×#41×C15111yescharacteristic
488C2×C4C2×#41×C15111yescharacteristic
489C2×C4C2×#41×C15111yescharacteristic
490C8—24no—
491C8—42no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22#398×C15114yes—
499C22C2×#121×C15111yescharacteristic
500C22C2×C22⋊Q8×C15111yescharacteristic
501C22C2×C22⋊Q8×C15111yescharacteristic
502C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
503C22C2×#137×C15111yescharacteristic
504C22#575×C15111yescharacteristic
505C22#575×C15111yescharacteristic
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—44no—
511C4—42no—
512C4—42no—
513C4—82no—
514C4—81no—
515C4—81no—
516C4#398×C15114yes—
517C4C2×#123×C15111yescharacteristic
518C4C2×#125×C15111yescharacteristic
519C4C2×#125×C15111yescharacteristic
520C4C2×C4⋊Q8×C15111yescharacteristic
521C2—24no—
522C2C2×#398×C15111yescharacteristic
523C2#3055×C15111yescharacteristic
524C2#3056×C15111yescharacteristic
525C2#3077×C15111yescharacteristic
526C2#3078×C15111yescharacteristic
527C2#3079×C15111yescharacteristic
528C2#3080×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2088×C151C2semidirect
6. #2088×C151C2semidirect
7. #2087×C151C2semidirect
8. #2086×C151C2semidirect
264. #23670C151direct (N × H)
265. C151#23670direct (N × H)
270. #2088C2×C151semidirect
271. #2088C2×C151semidirect
272. #2087C2×C151semidirect
273. #2086C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1512
C2×#423×C1512
#2296×C1512
C2×#389×C1512
#2088×C1512
#2087×C1512
#2086×C1512
#1736×C1512
#23670151