Finite Group Databasebeta

← C2×#2081×C151 #50328575

Subgroups — C2×#2081×C151 #50328575

Order 38656.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C151C211yesmaximal, characteristic, complemented
2C2×#418×C151C211yesmaximal, characteristic
3C2×#418×C151C211yesmaximal, characteristic
4C22×#100×C151C211yesmaximal, characteristic
5#2081×C151C218yesmaximal, direct product factor
6C2×#344×C151C211yesmaximal, characteristic, complemented
7C2×#344×C151C211yesmaximal, characteristic, complemented
8C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
9C23×D4×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16#430×C151—22no—
17#430×C151C2214yescomplemented
18C2×#108×C151—22no—
19#418×C151—22no—
20#418×C151—22no—
21#418×C151C2214yes—
22#418×C151C2214yes—
23C2×#102×C151—22no—
24C2×#102×C151—22no—
25C2×#100×C151—22no—
26C2×#100×C151—22no—
27C2×#100×C151C2214yes—
28#344×C151C2214yescomplemented
29#344×C151C2214yescomplemented
30H(3,ℤ/4)×C151C2214yescomplemented
31C25×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151—21no—
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—21no—
38C22×D4×C151—21no—
39C22×D4×C151—21no—
40C22×D4×C151—21no—
41C22×D4×C151—21no—
42C22×D4×C151—21no—
43C22×D4×C151D412yes—
44C22×D4×C151D412yes—
45C22×D4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C2×M16×C151—21no—
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C2×M16×C151—21no—
66C2×M16×C151D412yes—
67C2×M16×C151C2312yes—
68C2×M16×C151C2312yes—
69C2×M16×C151C2312yes—
70C2×M16×C151C2312yes—
71C22×C8×C151—21no—
72C22×C8×C151—21no—
73C22×C8×C151—21no—
74C22×C8×C151D412yes—
75#117×C151—21no—
76#117×C151—21no—
77#117×C151—21no—
78#117×C151—21no—
79#117×C151—21no—
80#117×C151—21no—
81#117×C151C2312yes—
82#117×C151C2312yes—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151—21no—
89#108×C151—28no—
90#102×C151—28no—
91#102×C151—28no—
92#100×C151—28no—
93C24×C151—22no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—41no—
97C24×C151—41no—
98C24×C151—41no—
99C24×C151—41no—
100C24×C151—84no—
101C24×C151#4111yescharacteristic
102C2×D4×C151—22no—
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151—22no—
106C2×D4×C151—22no—
107C2×D4×C151—22no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—22no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—41no—
118C2×D4×C151—41no—
119C2×D4×C151—41no—
120C2×D4×C151—41no—
121C2×D4×C151—41no—
122C2×D4×C151—41no—
123C2×D4×C151—41no—
124C2×D4×C151—41no—
125C2×D4×C151—41no—
126C2×D4×C151—41no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151C2×D414yes—
130C22×C4×C151—41no—
131C22×C4×C151—41no—
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151#4111yescharacteristic
137C22×C4×C151#4111yescharacteristic
138C22×C4×C151#4111yescharacteristic
139C22×C4×C151#4111yescharacteristic
140C22×C4×C151#4111yescharacteristic
141C22×C4×C151#4111yescharacteristic
142C22×C4×C151#4111yescharacteristic
143C22×C4×C151#4111yescharacteristic
144C22×C4×C151#4111yescharacteristic
145C22×C4×C151C2411yescharacteristic
146M16×C151—22no—
147M16×C151—22no—
148M16×C151—22no—
149M16×C151—22no—
150M16×C151—22no—
151M16×C151—22no—
152M16×C151—22no—
153M16×C151—22no—
154M16×C151—22no—
155M16×C151—22no—
156M16×C151—41no—
157M16×C151—41no—
158M16×C151—41no—
159M16×C151—41no—
160M16×C151—41no—
161M16×C151—41no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—41no—
168C2×C8×C151—41no—
169C2×C8×C151—41no—
170C2×C8×C151—41no—
171C2×C8×C151—41no—
172C2×C8×C151—41no—
173C2×C8×C151C2×D414yes—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—41no—
177C4⋊C4×C151—41no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—41no—
181C22⋊C4×C151—41no—
182C42×C151—22no—
183C42×C151—22no—
184C42×C151—41no—
185C42×C151—41no—
186C23×C151—24no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—84no—
195C23×C151—84no—
196C23×C151—84no—
197C23×C151—84no—
198C23×C151—84no—
199C23×C151—84no—
200C23×C151—84no—
201C23×C151#12311yescharacteristic
202C23×C151#12311yescharacteristic
203C23×C151#12411yescharacteristic
204C23×C151#12411yescharacteristic
205C23×C151#12611yescharacteristic
206C23×C151#12611yescharacteristic
207C23×C151C2×#4111yescharacteristic
208D4×C151—24no—
209D4×C151—24no—
210D4×C151—42no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—82no—
219C2×C4×C151—82no—
220C2×C4×C151#12111yescharacteristic
221C2×C4×C151#12111yescharacteristic
222C2×C4×C151#12111yescharacteristic
223C2×C4×C151#12111yescharacteristic
224C2×C4×C151#12311yescharacteristic
225C2×C4×C151#12311yescharacteristic
226C2×C4×C151#12311yescharacteristic
227C2×C4×C151#12311yescharacteristic
228C2×C4×C151#12311yescharacteristic
229C2×C4×C151#12311yescharacteristic
230C2×C4×C151#12311yescharacteristic
231C2×C4×C151#12311yescharacteristic
232C2×C4×C151#12311yescharacteristic
233C2×C4×C151#12311yescharacteristic
234C2×C4×C151#12411yescharacteristic
235C2×C4×C151#12411yescharacteristic
236C2×C4×C151#12611yescharacteristic
237C2×C4×C151#12611yescharacteristic
238C2×C4×C151#12611yescharacteristic
239C2×C4×C151#12611yescharacteristic
240C2×C4×C151#12611yescharacteristic
241C2×C4×C151#12611yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C8×C151—24no—
249C8×C151—42no—
250C8×C151—42no—
251C8×C151—42no—
252C22×C151—22no—
253C22×C151—22no—
254C22×C151—22no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—44no—
260C22×C151—84no—
261C22×C151—84no—
262C22×C151—84no—
263C22×C151—84no—
264C22×C151—84no—
265C22×C151—84no—
266C22×C151—84no—
267C22×C151#39711yescharacteristic
268C22×C151#39711yescharacteristic
269C22×C151#39711yescharacteristic
270C22×C151#39711yescharacteristic
271C22×C151C2×#12311yescharacteristic
272C22×C151C2×#12411yescharacteristic
273C22×C151C2×#12611yescharacteristic
274C4×C151—82no—
275C4×C151—82no—
276C4×C151#39711yescharacteristic
277C4×C151#39711yescharacteristic
278C4×C151#39711yescharacteristic
279C4×C151#39711yescharacteristic
280C4×C151C2×#12111yescharacteristic
281C4×C151C2×#12311yescharacteristic
282C4×C151C2×#12311yescharacteristic
283C4×C151C2×#12611yescharacteristic
284C2×C151—21no—
285C2×C151—21no—
286C2×C151—21no—
287C2×C151—21no—
288C2×C151—21no—
289C2×C151—21no—
290C2×C151—84no—
291C2×C151#208112yesdirect product factor
292C2×C151C2×#39711yescharacteristic
293C2×#2081C15111yesmaximal, characteristic, direct product factor, Sylow
294C151C2×#208111yescharacteristic, direct product factor, Sylow
295C2×#430C2×C15111yescharacteristic, complemented
296C2×#418C2×C15111yescharacteristic
297C2×#418C2×C15111yescharacteristic
298C22×#100C2×C15111yescharacteristic
299#2081C2×C15118yesdirect product factor
300C2×#344C2×C15111yescharacteristic, complemented
301C2×#344C2×C15111yescharacteristic, complemented
302C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
303C23×D4C22×C15111yescharacteristic
304C22×M16C22×C15111yescharacteristic
305C22×M16C22×C15111yescharacteristic
306C22×M16C22×C15111yescharacteristic
307C22×M16C22×C15111yescharacteristic
308C2×#117C22×C15111yescharacteristic
309C2×#117C22×C15111yescharacteristic
310#430—22no—
311#430C22×C15114yescomplemented
312C2×#108—22no—
313#418—22no—
314#418—22no—
315#418C22×C15114yes—
316#418C22×C15114yes—
317C2×#102—22no—
318C2×#102—22no—
319C2×#100—22no—
320C2×#100—22no—
321C2×#100C22×C15114yes—
322#344C22×C15114yescomplemented
323#344C22×C15114yescomplemented
324H(3,ℤ/4)C22×C15114yescomplemented
325C25—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4D4×C15112yes—
338C22×D4D4×C15112yes—
339C22×D4C23×C15112yes—
340C23×C4C23×C15111yescharacteristic
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16D4×C15112yes—
361C2×M16C23×C15112yes—
362C2×M16C23×C15112yes—
363C2×M16C23×C15112yes—
364C2×M16C23×C15112yes—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8D4×C15112yes—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117C23×C15112yes—
376#117C23×C15112yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383#108—28no—
384#102—28no—
385#102—28no—
386#100—28no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—84no—
395C24#41×C15111yescharacteristic
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4C2×D4×C15114yes—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4#41×C15111yescharacteristic
431C22×C4#41×C15111yescharacteristic
432C22×C4#41×C15111yescharacteristic
433C22×C4#41×C15111yescharacteristic
434C22×C4#41×C15111yescharacteristic
435C22×C4#41×C15111yescharacteristic
436C22×C4#41×C15111yescharacteristic
437C22×C4#41×C15111yescharacteristic
438C22×C4#41×C15111yescharacteristic
439C22×C4C24×C15111yescharacteristic
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—22no—
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—41no—
455M16—41no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8C2×D4×C15114yes—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—22no—
477C42—22no—
478C42—41no—
479C42—41no—
480C23—24no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23—84no—
494C23—84no—
495C23#123×C15111yescharacteristic
496C23#123×C15111yescharacteristic
497C23#124×C15111yescharacteristic
498C23#124×C15111yescharacteristic
499C23#126×C15111yescharacteristic
500C23#126×C15111yescharacteristic
501C23C2×#41×C15111yescharacteristic
502D4—24no—
503D4—24no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4#121×C15111yescharacteristic
515C2×C4#121×C15111yescharacteristic
516C2×C4#121×C15111yescharacteristic
517C2×C4#121×C15111yescharacteristic
518C2×C4#123×C15111yescharacteristic
519C2×C4#123×C15111yescharacteristic
520C2×C4#123×C15111yescharacteristic
521C2×C4#123×C15111yescharacteristic
522C2×C4#123×C15111yescharacteristic
523C2×C4#123×C15111yescharacteristic
524C2×C4#123×C15111yescharacteristic
525C2×C4#123×C15111yescharacteristic
526C2×C4#123×C15111yescharacteristic
527C2×C4#123×C15111yescharacteristic
528C2×C4#124×C15111yescharacteristic
529C2×C4#124×C15111yescharacteristic
530C2×C4#126×C15111yescharacteristic
531C2×C4#126×C15111yescharacteristic
532C2×C4#126×C15111yescharacteristic
533C2×C4#126×C15111yescharacteristic
534C2×C4#126×C15111yescharacteristic
535C2×C4#126×C15111yescharacteristic
536C2×C4C22×D4×C15111yescharacteristic
537C2×C4C22×D4×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C2×C4C2×#41×C15111yescharacteristic
541C2×C4C2×#41×C15111yescharacteristic
542C8—24no—
543C8—42no—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—44no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22#397×C15111yescharacteristic
562C22#397×C15111yescharacteristic
563C22#397×C15111yescharacteristic
564C22#397×C15111yescharacteristic
565C22C2×#123×C15111yescharacteristic
566C22C2×#124×C15111yescharacteristic
567C22C2×#126×C15111yescharacteristic
568C4—82no—
569C4—82no—
570C4#397×C15111yescharacteristic
571C4#397×C15111yescharacteristic
572C4#397×C15111yescharacteristic
573C4#397×C15111yescharacteristic
574C4C2×#121×C15111yescharacteristic
575C4C2×#123×C15111yescharacteristic
576C4C2×#123×C15111yescharacteristic
577C4C2×#126×C15111yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—84no—
585C2#2081×C15112yesdirect product factor
586C2C2×#397×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#397
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C151C2semidirect
5. #2081×C151C2direct (N × H)
6. C2×#344×C151C2semidirect
7. C2×#344×C151C2semidirect
8. C2×H(3,ℤ/4)×C151C2semidirect
17. #430×C151C22semidirect
28. #344×C151C22semidirect
29. #344×C151C22semidirect
30. H(3,ℤ/4)×C151C22semidirect
291. C2×C151#2081direct (N × H)
293. C2×#2081C151direct (N × H)
294. C151C2×#2081direct (N × H)
295. C2×#430C2×C151semidirect
299. #2081C2×C151direct (N × H)
300. C2×#344C2×C151semidirect
301. C2×#344C2×C151semidirect
302. C2×H(3,ℤ/4)C2×C151semidirect
311. #430C22×C151semidirect
322. #344C22×C151semidirect
323. #344C22×C151semidirect
324. H(3,ℤ/4)C22×C151semidirect
585. C2#2081×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#430×C1512
C2×#418×C1512
C22×#100×C1512
#2081×C1512
C2×#344×C1512
C2×H(3,ℤ/4)×C1512
C2×#2081151