Finite Group Databasebeta

← C151×#11222 #50316147

Subgroups — C151×#11222 #50316147

Order 38656.

1190 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2315×C151C211yesmaximal, characteristic
2C2×#385×C151C211yesmaximal, characteristic
3C2×#342×C151C212yesmaximal
4C2×#342×C151C211yesmaximal, characteristic
5C22⋊#95×C151C212yesmaximal
6C24×C4×C151C2211yescharacteristic
7C22×C4⋊C4×C151—21no—
8C22×C22⋊C4×C151C2212yes—
9C22×C22⋊C4×C151C2212yes—
10C22×C22⋊C4×C151C2211yescharacteristic
11C22×C22⋊C4×C151C2211yescharacteristic
12#385×C151—24no—
13#385×C151—22no—
14#385×C151C414yescomplemented
15#380×C151—21no—
16#380×C151—21no—
17C2×#95×C151—21no—
18C2×#95×C151—24no—
19#342×C151—22no—
20#342×C151—24no—
21C25×C151C2311yescharacteristic
22C23×C4×C151—22no—
23C23×C4×C151—21no—
24C23×C4×C151—21no—
25C23×C4×C151—22no—
26C23×C4×C151—21no—
27C23×C4×C151—22no—
28C23×C4×C151—44no—
29C23×C4×C151C2×C412yes—
30C23×C4×C151D414yes—
31C23×C4×C151D411yescharacteristic
32C23×C4×C151D411yescharacteristic
33C2×C4⋊C4×C151—24no—
34C2×C4⋊C4×C151—22no—
35C2×C4⋊C4×C151—22no—
36C2×C4⋊C4×C151—44no—
37C2×C22⋊C4×C151—22no—
38C2×C22⋊C4×C151—21no—
39C2×C22⋊C4×C151—22no—
40C2×C22⋊C4×C151—22no—
41C2×C22⋊C4×C151—22no—
42C2×C22⋊C4×C151—22no—
43C2×C22⋊C4×C151—22no—
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—22no—
47C2×C22⋊C4×C151—22no—
48C2×C22⋊C4×C151—22no—
49C2×C22⋊C4×C151—22no—
50C2×C22⋊C4×C151—22no—
51C2×C22⋊C4×C151—22no—
52C2×C22⋊C4×C151—22no—
53C2×C22⋊C4×C151C2×C412yes—
54C2×C22⋊C4×C151C2×C412yes—
55C2×C22⋊C4×C151D412yes—
56C2×C22⋊C4×C151D412yes—
57C2×C22⋊C4×C151Q814yes—
58C2×C22⋊C4×C151Q812yes—
59#95×C151—22no—
60#95×C151—22no—
61#95×C151—24no—
62#95×C151—48no—
63C24×C151—42no—
64C24×C151—42no—
65C24×C151C22×C411yescharacteristic
66C24×C151C2×D411yescharacteristic
67C24×C151C2×D412yes—
68C24×C151C2×D411yescharacteristic
69C24×C151C2×D411yescharacteristic
70C24×C151C2×Q811yescharacteristic
71C24×C151C2×Q812yes—
72C24×C151#4111yescharacteristic
73C24×C151#4111yescharacteristic
74C24×C151#4112yes—
75C24×C151#4112yes—
76C22×C4×C151—28no—
77C22×C4×C151—24no—
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—24no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—24no—
88C22×C4×C151—24no—
89C22×C4×C151—24no—
90C22×C4×C151—24no—
91C22×C4×C151—44no—
92C22×C4×C151—44no—
93C22×C4×C151—48no—
94C22×C4×C151—42no—
95C22×C4×C151—42no—
96C22×C4×C151—44no—
97C22×C4×C151—42no—
98C22×C4×C151—41no—
99C22×C4×C151—42no—
100C22×C4×C151—41no—
101C22×C4×C151—44no—
102C22×C4×C151—42no—
103C22×C4×C151—42no—
104C22×C4×C151—44no—
105C22×C4×C151—44no—
106C22×C4×C151—44no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151C22⋊C412yes—
110C22×C4×C151C22⋊C412yes—
111C4⋊C4×C151—48no—
112C4⋊C4×C151—82no—
113C4⋊C4×C151—82no—
114C22⋊C4×C151—22no—
115C22⋊C4×C151—24no—
116C22⋊C4×C151—22no—
117C22⋊C4×C151—24no—
118C22⋊C4×C151—22no—
119C22⋊C4×C151—24no—
120C22⋊C4×C151—24no—
121C22⋊C4×C151—42no—
122C22⋊C4×C151—42no—
123C22⋊C4×C151—42no—
124C22⋊C4×C151—42no—
125C22⋊C4×C151—42no—
126C22⋊C4×C151—42no—
127C22⋊C4×C151C4⋊C414yescomplemented
128C23×C151—22no—
129C23×C151—24no—
130C23×C151—22no—
131C23×C151—24no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151—41no—
135C23×C151—42no—
136C23×C151—41no—
137C23×C151—42no—
138C23×C151—44no—
139C23×C151—42no—
140C23×C151—42no—
141C23×C151—42no—
142C23×C151—44no—
143C23×C151—42no—
144C23×C151C2×C22⋊C411yescharacteristic
145C23×C151C2×C4⋊C411yescharacteristic
146C23×C151#11711yescharacteristic
147C23×C151C4×D412yes—
148C23×C151C4×Q812yes—
149C23×C151#12011yescharacteristic
150C23×C151#12111yescharacteristic
151C23×C151#12112yes—
152C23×C151#12112yes—
153C23×C151#12111yescharacteristic
154C23×C151C22⋊Q811yescharacteristic
155C23×C151C22⋊Q812yes—
156C23×C151C22⋊Q811yescharacteristic
157C23×C151C22⋊Q812yes—
158C23×C151C22⋊Q812yes—
159C23×C151#12311yescharacteristic
160C23×C151#12312yes—
161C23×C151#12411yescharacteristic
162C23×C151#12512yes—
163C23×C151#12512yes—
164C23×C151#12612yes—
165C23×C151C4⋊Q812yes—
166C23×C151C4⋊Q811yescharacteristic
167C2×C4×C151—24no—
168C2×C4×C151—28no—
169C2×C4×C151—24no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—42no—
173C2×C4×C151—44no—
174C2×C4×C151—42no—
175C2×C4×C151—44no—
176C2×C4×C151—42no—
177C2×C4×C151—44no—
178C2×C4×C151—48no—
179C2×C4×C151—44no—
180C2×C4×C151—42no—
181C2×C4×C151—42no—
182C2×C4×C151—44no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—48no—
187C2×C4×C151—48no—
188C2×C4×C151—44no—
189C2×C4×C151—44no—
190C2×C4×C151—44no—
191C2×C4×C151—44no—
192C2×C4×C151—81no—
193C2×C4×C151—81no—
194C2×C4×C151—82no—
195C2×C4×C151—82no—
196C2×C4×C151—84no—
197C2×C4×C151—84no—
198C22×C151—22no—
199C22×C151—24no—
200C22×C151—24no—
201C22×C151—22no—
202C22×C151—21no—
203C22×C151—22no—
204C22×C151—22no—
205C22×C151—21no—
206C22×C151—21no—
207C22×C151—22no—
208C22×C151—21no—
209C22×C151—22no—
210C22×C151—22no—
211C22×C151—24no—
212C22×C151—24no—
213C22×C151—22no—
214C22×C151—41no—
215C22×C151—41no—
216C22×C151—42no—
217C22×C151—41no—
218C22×C151—41no—
219C22×C151—42no—
220C22×C151—42no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—42no—
224C22×C151#38011yescharacteristic
225C22×C151#38611yescharacteristic
226C22×C151#38712yes—
227C22×C151#38912yes—
228C22×C151#39111yescharacteristic
229C22×C151#39411yescharacteristic
230C22×C151#39511yescharacteristic
231C22×C151#39612yes—
232C22×C151#39811yescharacteristic
233C22×C151#39812yes—
234C22×C151#40011yescharacteristic
235C22×C151B(4,𝔽2)12yes—
236C22×C151#45812yes—
237C4×C151—44no—
238C4×C151—44no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—84no—
242C4×C151—84no—
243C2×C151—21no—
244C2×C151—22no—
245C2×C151—22no—
246C2×C151—22no—
247C2×C151—21no—
248C2×C151—22no—
249C2×C151—21no—
250C2×C151—21no—
251C2×C151#144111yescharacteristic
252C2×C151#188911yescharacteristic
253C2×C151#189011yescharacteristic
254C2×C151#204412yes—
255C2×C151#206212yes—
256#11222C15111yesmaximal, characteristic, direct product factor, Sylow
257C151#1122211yescharacteristic, direct product factor, Sylow
258#2315C2×C15111yescharacteristic
259C2×#385C2×C15111yescharacteristic
260C2×#342C2×C15112yes—
261C2×#342C2×C15111yescharacteristic
262C22⋊#95C2×C15112yes—
263C24×C4C22×C15111yescharacteristic
264C22×C4⋊C4—21no—
265C22×C22⋊C4C22×C15112yes—
266C22×C22⋊C4C22×C15112yes—
267C22×C22⋊C4C22×C15111yescharacteristic
268C22×C22⋊C4C22×C15111yescharacteristic
269#385—24no—
270#385—22no—
271#385C4×C15114yescomplemented
272#380—21no—
273#380—21no—
274C2×#95—21no—
275C2×#95—24no—
276#342—22no—
277#342—24no—
278C25C23×C15111yescharacteristic
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—21no—
285C23×C4—44no—
286C23×C4C2×C4×C15112yes—
287C23×C4D4×C15114yes—
288C23×C4D4×C15111yescharacteristic
289C23×C4D4×C15111yescharacteristic
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—44no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4C2×C4×C15112yes—
311C2×C22⋊C4C2×C4×C15112yes—
312C2×C22⋊C4D4×C15112yes—
313C2×C22⋊C4D4×C15112yes—
314C2×C22⋊C4Q8×C15114yes—
315C2×C22⋊C4Q8×C15112yes—
316#95—22no—
317#95—22no—
318#95—24no—
319#95—48no—
320C24—42no—
321C24—42no—
322C24C22×C4×C15111yescharacteristic
323C24C2×D4×C15111yescharacteristic
324C24C2×D4×C15112yes—
325C24C2×D4×C15111yescharacteristic
326C24C2×D4×C15111yescharacteristic
327C24C2×Q8×C15111yescharacteristic
328C24C2×Q8×C15112yes—
329C24#41×C15111yescharacteristic
330C24#41×C15111yescharacteristic
331C24#41×C15112yes—
332C24#41×C15112yes—
333C22×C4—28no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—48no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—41no—
358C22×C4—44no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4—44no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C22⋊C4×C15112yes—
367C22×C4C22⋊C4×C15112yes—
368C4⋊C4—48no—
369C4⋊C4—82no—
370C4⋊C4—82no—
371C22⋊C4—22no—
372C22⋊C4—24no—
373C22⋊C4—22no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4C4⋊C4×C15114yescomplemented
385C23—22no—
386C23—24no—
387C23—22no—
388C23—24no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—44no—
394C23—42no—
395C23—42no—
396C23—44no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23C2×C22⋊C4×C15111yescharacteristic
402C23C2×C4⋊C4×C15111yescharacteristic
403C23#117×C15111yescharacteristic
404C23C4×D4×C15112yes—
405C23C4×Q8×C15112yes—
406C23#120×C15111yescharacteristic
407C23#121×C15111yescharacteristic
408C23#121×C15112yes—
409C23#121×C15112yes—
410C23#121×C15111yescharacteristic
411C23C22⋊Q8×C15111yescharacteristic
412C23C22⋊Q8×C15112yes—
413C23C22⋊Q8×C15111yescharacteristic
414C23C22⋊Q8×C15112yes—
415C23C22⋊Q8×C15112yes—
416C23#123×C15111yescharacteristic
417C23#123×C15112yes—
418C23#124×C15111yescharacteristic
419C23#125×C15112yes—
420C23#125×C15112yes—
421C23#126×C15112yes—
422C23C4⋊Q8×C15112yes—
423C23C4⋊Q8×C15111yescharacteristic
424C2×C4—24no—
425C2×C4—28no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—48no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—48no—
444C2×C4—48no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—84no—
454C2×C4—84no—
455C22—21no—
456C22—22no—
457C22—22no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—22no—
463C22—22no—
464C22—24no—
465C22—24no—
466C22—22no—
467C22—22no—
468C22—24no—
469C22—24no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22#380×C15111yescharacteristic
482C22#386×C15111yescharacteristic
483C22#387×C15112yes—
484C22#389×C15112yes—
485C22#391×C15111yescharacteristic
486C22#394×C15111yescharacteristic
487C22#395×C15111yescharacteristic
488C22#396×C15112yes—
489C22#398×C15111yescharacteristic
490C22#398×C15112yes—
491C22#400×C15111yescharacteristic
492C22B(4,𝔽2)×C15112yes—
493C22#458×C15112yes—
494C4—44no—
495C4—44no—
496C4—42no—
497C4—42no—
498C4—84no—
499C4—84no—
500C2—21no—
501C2—22no—
502C2—22no—
503C2—22no—
504C2—21no—
505C2—22no—
506C2—21no—
507C2—21no—
508C2#1441×C15111yescharacteristic
509C2#1889×C15111yescharacteristic
510C2#1890×C15111yescharacteristic
511C2#2044×C15112yes—
512C2#2062×C15112yes—
subgroupG/H
center, socleC23×C151#120
commutatorC24C22×C4×C151
Frattini, cosocleC25C23×C151
prime radicalC25×C151C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
14. #385×C151C4semidirect
127. C22⋊C4×C151C4⋊C4semidirect
256. #11222C151direct (N × H)
257. C151#11222direct (N × H)
271. #385C4×C151semidirect
384. C22⋊C4C4⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2315×C1512
C2×#385×C1512
C2×#342×C1512
C22⋊#95×C1512
#11222151