Finite Group Databasebeta

← C151×#11217 #50316142

Subgroups — C151×#11217 #50316142

Order 38656.

778 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C151C211yesmaximal, characteristic
2#2317×C151C211yesmaximal, characteristic
3C2×#343×C151C211yesmaximal, characteristic
4#1736×C151C211yesmaximal, characteristic
5C2×#339×C151C211yesmaximal, characteristic
6C2×#339×C151C211yesmaximal, characteristic
7C4⋊#95×C151C211yesmaximal, characteristic
8C22×M16×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C2×#117×C151C2211yescharacteristic
11C2×#117×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C42×C151C2211yescharacteristic
15#428×C151—22no—
16#428×C151C414yescomplemented
17C2×#107×C151—21no—
18C2×#106×C151—21no—
19#389×C151—21no—
20#389×C151—21no—
21#385×C151—22no—
22#384×C151—21no—
23#382×C151—21no—
24C2×#95×C151—22no—
25#343×C151—22no—
26#340×C151—21no—
27#340×C151—21no—
28#339×C151—22no—
29#339×C151—22no—
30C23×C4×C151—21no—
31C23×C4×C151—21no—
32C23×C4×C151D412yes—
33C23×C4×C151C2311yescharacteristic
34C2×M16×C151—21no—
35C2×M16×C151—21no—
36C2×M16×C151—21no—
37C2×M16×C151—21no—
38C2×M16×C151—21no—
39C2×M16×C151—21no—
40C2×M16×C151—21no—
41C2×M16×C151—21no—
42C2×M16×C151C2×C412yes—
43C2×M16×C151D412yes—
44C2×M16×C151Q812yes—
45C2×M16×C151Q812yes—
46C22×C8×C151—21no—
47C22×C8×C151—21no—
48#117×C151—21no—
49#117×C151—21no—
50#117×C151—21no—
51#117×C151—21no—
52#117×C151—21no—
53#117×C151—21no—
54#117×C151C2×C412yes—
55#117×C151D412yes—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151C2×C412yes—
70C2×C4⋊C4×C151D411yescharacteristic
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C4⋊C4×C151D411yescharacteristic
73C2×C4⋊C4×C151D411yescharacteristic
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C42×C151—21no—
77C2×C42×C151—21no—
78C2×C42×C151—21no—
79C2×C42×C151—21no—
80C2×C42×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151—21no—
83C2×C42×C151Q812yes—
84#107×C151—24no—
85#106×C151—24no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—44no—
89C24×C151C2×D411yescharacteristic
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—22no—
98C22×C4×C151—21no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—41no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—41no—
105C22×C4×C151—42no—
106C22×C4×C151—42no—
107C22×C4×C151—42no—
108C22×C4×C151—42no—
109C22×C4×C151—41no—
110C22×C4×C151—41no—
111C22×C4×C151C22×C411yescharacteristic
112C22×C4×C151C2×D411yescharacteristic
113C22×C4×C151C2×D411yescharacteristic
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D411yescharacteristic
116C22×C4×C151C2×Q811yescharacteristic
117C22×C4×C151C2×Q811yescharacteristic
118C22×C4×C151C2×Q811yescharacteristic
119C22×C4×C151#4111yescharacteristic
120C22×C4×C151#4111yescharacteristic
121C22×C4×C151#4111yescharacteristic
122C22×C4×C151#4111yescharacteristic
123C22×C4×C151#4111yescharacteristic
124C22×C4×C151#4111yescharacteristic
125M16×C151—22no—
126M16×C151—22no—
127M16×C151—22no—
128M16×C151—22no—
129M16×C151—22no—
130M16×C151—41no—
131M16×C151—41no—
132M16×C151C4⋊C414yescomplemented
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—41no—
138C2×C8×C151—41no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—41no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—82no—
154C4⋊C4×C151—82no—
155C4⋊C4×C151C22⋊C412yes—
156C4⋊C4×C151C22⋊C412yes—
157C22⋊C4×C151—22no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—41no—
160C22⋊C4×C151—41no—
161C42×C151—22no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151—22no—
165C42×C151—41no—
166C42×C151—41no—
167C42×C151—41no—
168C42×C151—41no—
169C23×C151—21no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151—21no—
173C23×C151C4×D411yescharacteristic
174C23×C151#12011yescharacteristic
175C23×C151#12111yescharacteristic
176C23×C151#12111yescharacteristic
177C23×C151C22⋊Q811yescharacteristic
178C23×C151#12311yescharacteristic
179C23×C151C4⋊Q811yescharacteristic
180C2×C4×C151—24no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—44no—
194C2×C4×C151—44no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—42no—
199C2×C4×C151—41no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—82no—
206C2×C4×C151—81no—
207C2×C4×C151—81no—
208C2×C4×C151—82no—
209C2×C4×C151C2×C22⋊C411yescharacteristic
210C2×C4×C151C2×C4⋊C411yescharacteristic
211C2×C4×C151#11711yescharacteristic
212C2×C4×C151C4×D411yescharacteristic
213C2×C4×C151C4×Q811yescharacteristic
214C2×C4×C151C4×Q811yescharacteristic
215C2×C4×C151#12111yescharacteristic
216C2×C4×C151#12111yescharacteristic
217C2×C4×C151#12111yescharacteristic
218C2×C4×C151#12111yescharacteristic
219C2×C4×C151C22⋊Q811yescharacteristic
220C2×C4×C151C22⋊Q811yescharacteristic
221C2×C4×C151C22⋊Q811yescharacteristic
222C2×C4×C151C22⋊Q811yescharacteristic
223C2×C4×C151C22⋊Q811yescharacteristic
224C2×C4×C151C22⋊Q811yescharacteristic
225C2×C4×C151C22⋊Q811yescharacteristic
226C2×C4×C151#12311yescharacteristic
227C2×C4×C151#12311yescharacteristic
228C2×C4×C151#12411yescharacteristic
229C2×C4×C151#12511yescharacteristic
230C2×C4×C151#12511yescharacteristic
231C2×C4×C151#12511yescharacteristic
232C2×C4×C151#12511yescharacteristic
233C2×C4×C151#12611yescharacteristic
234C2×C4×C151#12611yescharacteristic
235C2×C4×C151C4⋊Q811yescharacteristic
236C2×C4×C151C4⋊Q811yescharacteristic
237C8×C151—24no—
238C8×C151—42no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—21no—
247C22×C151—21no—
248C22×C151—21no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151#38611yescharacteristic
252C22×C151#38711yescharacteristic
253C22×C151#38911yescharacteristic
254C22×C151#39411yescharacteristic
255C22×C151#39511yescharacteristic
256C22×C151#39611yescharacteristic
257C22×C151#39811yescharacteristic
258C22×C151#45311yescharacteristic
259C22×C151#45411yescharacteristic
260C22×C151#45511yescharacteristic
261C22×C151#45611yescharacteristic
262C4×C151—44no—
263C4×C151—42no—
264C4×C151—42no—
265C4×C151—82no—
266C4×C151—81no—
267C4×C151—82no—
268C4×C151—81no—
269C4×C151#38011yescharacteristic
270C4×C151#38711yescharacteristic
271C4×C151#38911yescharacteristic
272C4×C151#39111yescharacteristic
273C4×C151#39611yescharacteristic
274C4×C151#39811yescharacteristic
275C4×C151#39811yescharacteristic
276C4×C151#40011yescharacteristic
277C2×C151—21no—
278C2×C151—21no—
279C2×C151—21no—
280C2×C151—21no—
281C2×C151#144111yescharacteristic
282C2×C151#188211yescharacteristic
283C2×C151#188311yescharacteristic
284C2×C151#203711yescharacteristic
285C2×C151#203811yescharacteristic
286C2×C151#206011yescharacteristic
287C2×C151#206111yescharacteristic
288#11217C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1121711yescharacteristic, direct product factor, Sylow
290C2×#428C2×C15111yescharacteristic
291#2317C2×C15111yescharacteristic
292C2×#343C2×C15111yescharacteristic
293#1736C2×C15111yescharacteristic
294C2×#339C2×C15111yescharacteristic
295C2×#339C2×C15111yescharacteristic
296C4⋊#95C2×C15111yescharacteristic
297C22×M16C22×C15111yescharacteristic
298C22×M16C22×C15111yescharacteristic
299C2×#117C22×C15111yescharacteristic
300C2×#117C22×C15111yescharacteristic
301C22×C4⋊C4C22×C15111yescharacteristic
302C22×C4⋊C4C22×C15111yescharacteristic
303C22×C42C22×C15111yescharacteristic
304#428—22no—
305#428C4×C15114yescomplemented
306C2×#107—21no—
307C2×#106—21no—
308#389—21no—
309#389—21no—
310#385—22no—
311#384—21no—
312#382—21no—
313C2×#95—22no—
314#343—22no—
315#340—21no—
316#340—21no—
317#339—22no—
318#339—22no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4D4×C15112yes—
322C23×C4C23×C15111yescharacteristic
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16C2×C4×C15112yes—
332C2×M16D4×C15112yes—
333C2×M16Q8×C15112yes—
334C2×M16Q8×C15112yes—
335C22×C8—21no—
336C22×C8—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117C2×C4×C15112yes—
344#117D4×C15112yes—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4C2×C4×C15112yes—
359C2×C4⋊C4D4×C15111yescharacteristic
360C2×C4⋊C4D4×C15111yescharacteristic
361C2×C4⋊C4D4×C15111yescharacteristic
362C2×C4⋊C4D4×C15111yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42Q8×C15112yes—
373#107—24no—
374#106—24no—
375#95—22no—
376#95—22no—
377#95—44no—
378C24C2×D4×C15111yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4C22×C4×C15111yescharacteristic
401C22×C4C2×D4×C15111yescharacteristic
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×Q8×C15111yescharacteristic
406C22×C4C2×Q8×C15111yescharacteristic
407C22×C4C2×Q8×C15111yescharacteristic
408C22×C4#41×C15111yescharacteristic
409C22×C4#41×C15111yescharacteristic
410C22×C4#41×C15111yescharacteristic
411C22×C4#41×C15111yescharacteristic
412C22×C4#41×C15111yescharacteristic
413C22×C4#41×C15111yescharacteristic
414M16—22no—
415M16—22no—
416M16—22no—
417M16—22no—
418M16—22no—
419M16—41no—
420M16—41no—
421M16C4⋊C4×C15114yescomplemented
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—41no—
427C2×C8—41no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—82no—
443C4⋊C4—82no—
444C4⋊C4C22⋊C4×C15112yes—
445C4⋊C4C22⋊C4×C15112yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C42—22no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—41no—
455C42—41no—
456C42—41no—
457C42—41no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23C4×D4×C15111yescharacteristic
463C23#120×C15111yescharacteristic
464C23#121×C15111yescharacteristic
465C23#121×C15111yescharacteristic
466C23C22⋊Q8×C15111yescharacteristic
467C23#123×C15111yescharacteristic
468C23C4⋊Q8×C15111yescharacteristic
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—82no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4C2×C22⋊C4×C15111yescharacteristic
499C2×C4C2×C4⋊C4×C15111yescharacteristic
500C2×C4#117×C15111yescharacteristic
501C2×C4C4×D4×C15111yescharacteristic
502C2×C4C4×Q8×C15111yescharacteristic
503C2×C4C4×Q8×C15111yescharacteristic
504C2×C4#121×C15111yescharacteristic
505C2×C4#121×C15111yescharacteristic
506C2×C4#121×C15111yescharacteristic
507C2×C4#121×C15111yescharacteristic
508C2×C4C22⋊Q8×C15111yescharacteristic
509C2×C4C22⋊Q8×C15111yescharacteristic
510C2×C4C22⋊Q8×C15111yescharacteristic
511C2×C4C22⋊Q8×C15111yescharacteristic
512C2×C4C22⋊Q8×C15111yescharacteristic
513C2×C4C22⋊Q8×C15111yescharacteristic
514C2×C4C22⋊Q8×C15111yescharacteristic
515C2×C4#123×C15111yescharacteristic
516C2×C4#123×C15111yescharacteristic
517C2×C4#124×C15111yescharacteristic
518C2×C4#125×C15111yescharacteristic
519C2×C4#125×C15111yescharacteristic
520C2×C4#125×C15111yescharacteristic
521C2×C4#125×C15111yescharacteristic
522C2×C4#126×C15111yescharacteristic
523C2×C4#126×C15111yescharacteristic
524C2×C4C4⋊Q8×C15111yescharacteristic
525C2×C4C4⋊Q8×C15111yescharacteristic
526C8—24no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22#386×C15111yescharacteristic
541C22#387×C15111yescharacteristic
542C22#389×C15111yescharacteristic
543C22#394×C15111yescharacteristic
544C22#395×C15111yescharacteristic
545C22#396×C15111yescharacteristic
546C22#398×C15111yescharacteristic
547C22#453×C15111yescharacteristic
548C22#454×C15111yescharacteristic
549C22#455×C15111yescharacteristic
550C22#456×C15111yescharacteristic
551C4—44no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—82no—
556C4—81no—
557C4—81no—
558C4#380×C15111yescharacteristic
559C4#387×C15111yescharacteristic
560C4#389×C15111yescharacteristic
561C4#391×C15111yescharacteristic
562C4#396×C15111yescharacteristic
563C4#398×C15111yescharacteristic
564C4#398×C15111yescharacteristic
565C4#400×C15111yescharacteristic
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2#1441×C15111yescharacteristic
571C2#1882×C15111yescharacteristic
572C2#1883×C15111yescharacteristic
573C2#2037×C15111yescharacteristic
574C2#2038×C15111yescharacteristic
575C2#2060×C15111yescharacteristic
576C2#2061×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
16. #428×C151C4semidirect
132. M16×C151C4⋊C4semidirect
288. #11217C151direct (N × H)
289. C151#11217direct (N × H)
305. #428C4×C151semidirect
421. M16C4⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1512
#2317×C1512
C2×#343×C1512
#1736×C1512
C2×#339×C1512
C4⋊#95×C1512
#11217151